Chemical engineering education
C
C. Stewart Slater
,LU ... of Rowan University
C
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S. Random Thoughts: The Ten Worst Teaching Mistakes II. Mistakes 14 (p. 15")
2' Felder, Brent
u An Innovative Method for Integrating a Diversity Workshop in a Chemical Engineering Course (p. 10)
u/ Yokoyama
C
Multiple Comparisons of Observation MeansAre the Means Significantly Different? (p. 17"i
 Fahidy
�< ^TaylorAris Dispersion: An Explicit Example for Understanding Multiscale Analysis Via Volume Averaging (p. 29)
c '', Wood
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., " Using Simulation Module PCLAB for Steady State Disturbance Sensitivity Analysis in Process Control (p. 51)
5 U Ali, Idriss
0) E Process Systems Engineering Education: Learning By Research (p. 58)
C a)
U Abbas. Alhammadi, Romagnoli
.c o Teaching Chemical Engineering Thermodynamics at Three LevelsExperience from theTechnical University
C of Denmark (p. 70)
L . Kontogeorgis, Michelsen, Clement
. c A Process Dynamics and Control Experiment for the Undergraduate Laboratory (p. 23)
E Spencer
.C U
U Combined SteadyState and Dynamic Heat Exchanger Experiment ip. 39)
E_ Luyben,Tuzla. Bader
First Principles Modeling of the Performance of a HydrogenPeroxideDriven ChemECar (p. 65)
Farhadi, Azadi, Zarinpanjeh
V
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Vol. 43, No. 1, Winter 2009
Chemical Engineering Education
Volume 43 Number 1 Winter 2009
> EDUCATOR
2 C. Stewart Slater of Rowan University
Robert P. Hesketh, Helen C. Hollein, and James H. Tracey
> RANDOM THOUGHTS
15 The 10 Worst Teaching Mistakes II. Mistakes 14
Richard M. Felder and Rebecca Brent
> CLASSROOM
10 An Innovative Method for Integrating a Diversity Workshop in a
Chemical Engineering Course
Ayumu Yokoyama
17 Multiple Comparisons of Observation MeansAre the Means
Significantly Different?
T.Z. Fahidy
29 TaylorAris Dispersion: An Explicit Example for Understanding
Multiscale Analysis Via Volume Averaging
Brian D. Wood
51 Using Simulation Module PCLAB for Steady State Disturbance
Sensitivity Analysis in Process Control
Emad Ali and Arimiyawo Idriss
58 Process Systems Engineering Education: Learning By Research
A. Abbas, H.Y. Alhammadi, And J.A. Romagnoli
> CURRICULUM
70 Teaching Chemical Engineering Thermodynamics at Three Levels
Experience from the Technical University of Denmark
Georgios M. Kontogeorgis, Michael L. Michelsen, and Karsten H. Clement
> LABORATORY
23 A Process Dynamics and Control Experiment for the Undergraduate
Laboratory
Jordan L. Spencer
> UNIT OPERATIONS
39 Combined SteadyState and Dynamic Heat Exchanger Experiment
William Luyben, Kemal Tuzla, and Paul Bader
> CLASS AND HOME PROBLEMS
65 First Principles Modeling of the Performance of a HydrogenPeroxide
Driven ChemECar
Maryam Farhadi, Pooya Azadi, and Nima Zarinpanjeh
CHEMICAL ENGINEERING EDUCATION (ISSN 00092479) is published quarterly by the Chemical Engineering
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1
RI educatorr
  s_____________________________________
C. Stewart Slater
Above: Stew in the atrium of Rowan Hall, home of the Chemical Ei
Below: Stew's students compete on his handheld reverse osmosis e
It is always an exciting time seeing chemical engineer
ing students in the classroom working vigorously on
an experiment. Teams of students are at a station that
has a hand pump connected to a cylinder, a tank of blue salt
water, and a second tank with a small amount of clear fluid.
Next to these students there is a professor who is vigorously
encouraging these students to "Pump it up!" He has gotten
of Rowan
University
ROBERT P. HESKETH
(Professor and Chair, Rowan
University),
HELEN C. HOLLEIN
(Professor and Chair Emeritus,
Manhattan College),
JAMES H. TRACEY
gineefing Department. (Founding Dean Emeritus,
experiment. Rowan University)
them so excited that they are competing to see how quickly
they can fill a 1L graduated cylinder with pure water. Then
you remember that C. Stewart Slater (Stew) is teaching re
verse osmosis membrane separations today! Next you hear
Stew commenting, "Now you can physically understand the
applied pressure necessary to overcome the osmotic pressure
of the salt solution."
Stew exhibits this high level of enthusiasm whether teaching
students, faculty at workshops, or board of trustees members
of the university. Based on his accomplishments, Stew has
received many accolades for his teaching, research, and
service activities.
But Stew considers his most significant achievement to be
the job he did as founding chair of the Chemical Engineering
Department at New Jersey's Rowan University, a school that
he's proud to say has provided the opportunity for students
from the part of his home state locals call South Jersey to
receive a firstrate chemical engineering education. Sup
porting that belief: The program he created has been ranked
by U.S. News & World Report as one of the country's best
� Copyright ChE Division ofASEE 2009
Chemical Engineering Education
undergraduate chemical engineering programs for
seven consecutive years (20032009).
GROWING UP AT THE JERSEY SHORE
Stew grew up in Ventnor, N.J., a small resort
town on the South Jersey shore. He was the young
est child in a family of professional educators. His
father was a department head at Atlantic City High
School and his two older sisters are both teachers,
Susan in elementary education and Elizabeth in
high school mathematics. The Jersey shore was a
great laboratory for a young scientist. Digging in
the sand for crabs and observing the dynamics of
tides and beach erosion were nearby introductions
to natural phenomena that fascinated him. Even
today, Stew usually spends his weekends at the
Jersey shore with his sisters and mother who still
live in Ventnor. He comments that although the
region has changed a lot in the last several decades,
it is always comforting to come back to the place
where you grew up.
Stew excelled in elementary and middle school;
he always loved math, science, and history topics.
Stew went to Atlantic City High School, where he
followed a collegeprep track with emphasis on
science and mathematics. He took A.P. chemistry
in his senior year and says that the intense labora
tory experience and project work made the class
fun. His math experience was equally engaging, advancing toA.P. Calculus
in his senior year and winning a school award for excellence in mathemat
ics. His teachers encouraged him to consider an engineering career.
During high school, Stew worked parttime for the various conventions
held in Atlantic City hotels and the convention center. One of these would
have a pivotal impact on his life. In 1971, he worked as a session aide for
the AIChE 70th National Meeting in Atlantic City. At this meeting, Stew
got the chance to hear various talks from the sessions he aided. One session
focused on pilot plants, which really excited Stew because of the concept
of how processes are scaled up.
ON THE BANKS OF THE RARITAN
When Stew made the decision to go to college to study engineering, he
looked at many colleges and attended the open house at Rutgers University
in New Brunswick, N.J.. He was most impressed with the chemical and
biochemical engineering department's equipment demonstrations, and
became convinced that this program was the best choice for him.
Stew excelled at Rutgers, earning straight A's in his first Spring term.
Sadly, his father died of cancer in the summer after his freshman year,
but Stew's strong faith and family helped him through this difficult time.
Stew says he was always encouraged in his career that he was following
in his father's footsteps.
While at Rutgers, Stew joined AIChE as a student member and in his
senior year was elected student chapter treasurer. Stew helped the chap
ter with a fundraising campaign to support student activities such as a
Thanksgiving party with turkeys and cider, and numerous social events.
He especially enjoyed the camaraderie with fellow engineering students.
Before teamwork was as popularized as it is today, Stew was a member
of a study group that he recalls as being key to helping him succeed; the
benefit students gain from working with other team members on various
assignments was something he learned to appreciate firsthand.
Left, Stew playing and learning on the Jersey shore. Right, Stew with sisters Elizabeth and Susan (1 to r).
Vol. 43, No. 1, Winter 2009
Stew with his . r
college friends and
study group at But
gers: (1 to r) Stew,
John Jacquin,
George Swier,
John Nikityn. i .
When Stew graduated in 1979, he interviewed with many
of the companies that visited campus. He was intrigued with
nontraditional aspects of chemical engineering, so a pre
sentation by Procter & Gamble on chemical engineering in
product development excited him. Stew accepted a job offer
in Product Development for their Personal Products Divi
sion, located in Cincinnati, Ohio. He worked in dentifrice
(toothpaste) process development on a gelbased product
to complement the Crest� line. He met senior scientists and
engineers from the Research Division, and soon realized that
a career path in research would require an advanced degree.
He was also told that his presentations were quite good and
that he should consider being a professor since he was able
to explain difficult concepts equally well to technicians and
to nonchemical engineers.
When Stew decided to return to graduate school, he talked
to his former professors at Rutgers, who strongly encouraged
him to come back. At that time, Robert Ahlert had secured a
major grant from the U.S. Environmental Protection Agency
to examine the treatment of hazardous wastes from landfill
leachates. Stew signed on to Ahlert's group at Rutgers and
worked on the use of membrane processes, such as ultrafiltra
tion and reverse osmosis, in the treatment of the leachates from
a New Jersey Superfund site. One of the aspects Stew liked
best was when he got the chance to involve undergraduate
students in his research. This provided a meaningful mentor
ship opportunity for these students as well as giving Stew the
chance to learn how to effectively supervise students. He also
enjoyed his teaching duties when he was asked to fill in for a
faculty member going to a conference or to help undergradu
ates with class projects and grade homework assignments.
IN THE BIG APPLE
While completing his dissertation, Stew pondered his future
plans and decided to enter the academic ranks, once again
honoring his father's influence. He wanted to work for an
institution that valued teaching while allowing him to continue
developing his expertise in membrane processes.
In September 1983, he accepted a tenuretrack position at
Manhattan College. There, Stew immersed himself in the
triad of teaching, scholarship, and service, and rose through
the ranks, reaching full professor in 1992. During his time
at Manhattan, he was very active in developing new labo
ratories for advanced separation processes and biochemical
engineering with financial support from the National Science
Foundation and from industry.
Stew says that he was influenced by numerous faculty
members during his time at Manhattan College, including
Br. Conrad Timothy Burris and Helen (Connie) Hollein. Br.
Burris, who was Stew's first department chair, provided the
support and encouragement necessary for faculty development
and initiated Stew's involvement in ASEE. Connie was hired
the year before Stew and they shared many of the growing
pains of new faculty. They also worked together in the areas
of educational development and bioseparations research. Stew
earned high marks for his teaching, research, and service, and
was recognized by his peers with the ASEE New Engineer
ing Educator Excellence Award, the Dow Outstanding New
Chemical Engineering Education
Faculty Award, and ASEE's
Fluke Corporation Award
for Excellence in Laboratory
Instruction.
Stew continued to expand
his research and teaching in
terest in membrane technol
ogy, developing new courses
at both the senior and mas
ter's level. He analyzed what
was taught in separations
courses and found that new
separations, such as mem
branes, were underserved. As
a result he developed meth
ods to incorporate membrane
processes. He developed new Above, Stew with a student
courseware and experiments member
for membrane processes that
are still used in Manhattan College's undergraduate laborato
ries (as well as in other universities across the country). His
work resulted in many pedagogical publications and in new
approaches that would later earn him the prestigious Chester
Carlson award from ASEE. It also left a positive impact on
the many whose lives he has touched. Stew embraced the
LaSallian tradition of excellence in teaching.
As A Teacher
Br. Christopher Dardis, who served for many years as direc
tor of Manhattan's Center for Teaching & Learning, remem
bers Stew fondly as a faculty member who came to him for
help to improve his teachinghelp he clearly did not need, as
Br. Christopher calls Stew one of the best teachers that he has
ever seen. Br. Christopher cited Stew's demonstrations with
"cutaway" membrane modules as an ingenious and highly
effective teaching method.
Connie Hollein, who served as Chemical Engineering De
partment Chair after Br. Burris retired, recalls Stew's winning
style in the classroom. "He was one of the most organized
faculty members I've known, with stepbystep detailed
notes and the reputation as a tough but fair teacher." But in
balance with that serious side, Connie notes, " His jokes and
funny stories kept the students engaged even at the end of a
long day."
She recalls one story in particular: "When he showed a
cutaway hollow fiber membrane permeator to the students,
he would tell them that last year's class took one of the cut
away permeators and he didn't know where it went. He went
on to claim that at the end of that semester, he got a present
from the class and it was the hollow fiber permeatorwith
the fibers removed and cut up into a hair piece for him! Then,
he takes a cutup bundle of fibers and places it on his head.
The whole class erupts in laughter!"
,] a a
m m.  l P21.
in the Unit Operations lab; below, working with a student on a
rane laboratory experiment he developed.
As a Mentor
Supplementing his natural gifts in the classroom, Stew
was mentored by Br. Burris in how to obtain industrial fund
ing from industry for his research activities. His research
focused on: reverse osmosis for industrial waste minimiza
tion, modeling and simulation, and water recovery and reuse;
ultra/microfiltration for protein separation; and pervaporation
for separation of various organicwater mixtures. He became
well known for his work in organophilic pervaporation, which
provided him an opportunity to attend numerous international
conferences and seminars. These projects were supported
by various companies including Air Products & Chemicals,
ExxonMobil, Pfizer, Joseph E. Seagram & Sons, and United
Technologies. In all of these projects Stew passed along the
gift of mentoring, involving undergraduate and master's stu
dents, many of whom went on to obtain advanced degrees and
Vol. 43, No. 1, Winter 2009
related positions in industry, academia, and government.
Kevin Devine, who has risen to the current job tide Group
Leader at Kraft Foods, Inc., says, "Dr. Slater was a demanding
research advisor but did it in a way that encouraged us to suc
ceed with our pervaporation projects. His mentorship taught
me numerous things from experimental design and effective
time management to presentation techniques, all of which
have helped me advance in my professional career."
Stew is deservedly proud of the successful careers of his
research students and of the fact that four of his pervaporation
research students won Manhattan's campuswide Sigma Xi
medal for research, and three won awards when they presented
research papers at International Pervaporation Conferences.
Another former student, John Paccione currently with the
New York State Department of Health and on the faculty of
State University of New York atAlbanywas an undergraduate
who worked with Stew during his early years. "Stew taught
me how to design, develop, and operate stateoftheart reverse
osmosis systems. This work provided my colleagues and me
with a greater view of opportunities in chemical engineering
and an introduction into the activities of research. One of Stew's
greatest abilities was to inspire students to work to higher levels
of achievement, which in my case included earning a Ph.D. at
Rensselaer Polytechnic Institute. One of the greatest attributes
of an educator is the ability to inspire his students and to provide
visions of the possibilities beyond the classroom."
Marco Castaldi (now on the faculty at Columbia Univer
sity) is another former student. He remembers Stew for his
genuine interest helping Marco during unit operations labo
ratory. Marco comments, "Unlike most professors in charge
of student laboratory courses, Stew took the time to read my
preliminary report and suggest improvements and changes
that enabled me to see the important aspects of the labs. This
directly translated to my abilities to develop excellent labora
tory skills and techniques that have served me well during
my graduate studies and subsequent industrial and academic
career. In the classroom, he showed another side. One in
which he could present complex, new material in a way that
left you feeling confident you could understand and use it in
reallife applications."
As a Peer
Early in his career, Stew became quite active in professional
societies and attended AlChE, ACS, andASEE conferences to
present papers and network with colleagues. One of the pro
fessors that he met at ASEE meetings, Angelo (Angie) Perna
of New Jersey Institute of Technology, encouraged him to get
more involved in that society. Stew began to rise through the
ranks of leadership in ASEE, first in the Division for Experi
mentation and LaboratoryOriented Studies (DELOS) and then
in the Chemical Engineering Division, rising to Division Chair
in each. Stew currently serves as vicechair of the publications
board of Chemical Engineering Education.
Chemical Engineering Education
Facing page, Stew teaches
other teachers at an NSF
workshop.
Left, Stew at the ASEE
2003 Annual Conference
along with Rowan Chemi
cal Engineering faculty
Stephanie Farrell (far
right) and Robert Hesketh
(second from left), who
are flanking ASEE Presi
dent Jerry Jakubowski.
SOUTH JERSEY HOMECOMING
In 1992 Henry and Betty Rowan gave a gift of $100 million
to start a new engineering school at Glassboro State College,
which was renamed Rowan University in their honor. When
the enviable position of founding chair of Chemical Engineer
ing at the university was being created in 1995, Stew was a
finalist for the job. Dean James Tracey recounted that Stew was
very excited about this opportunity since it was a rare chance to
create a new way of teaching engineering. Stew was addition
ally eager to return to his roots in southern New Jersey, where
his family still lived. In pursuing the post, Stew's showman
skills stood out. Jim Tracey comments, "Stew insisted on do
ing a membrane demonstration during his interview that really
impressed me; I had never had a candidate insist on doing a
demonstration before. But, Stew firmly believed in 'handson
education,' and knew that this would be a critical component
of our program." Stew got the job.
He spent his first year at Rowan multitaskingsplitting
time between curriculum development, facilities/lab develop
ment, student recruitment, and faculty recruitment, each of
which had its challenges. Jim Tracey challenged the founding
chairs to create an innovative program that would produce a
21st Century engineer. The resulting curricula was designed
to produce graduates who could communicate effectively,
have knowledge of business/entrepreneurship, work in mul
tidisciplinary teams, and have a handson, mindson approach
to problem solving.
During Stew's initial year at Rowan he spent many hours
working on plans for an innovative engineering building.
Stew, who is well known for his detailed planning, devoted
many hours to ensuring that the engineering labs were suited
for chemical work. The end result is that every room in
Rowan Hall has the capability of being easily converted to a
chemical laboratory. Stew worked tirelessly on making sure
Vol. 43, No. 1, Winter 2009
that the freshair exchange, hoods, point exhausts, and the
like were sufficient to support chemical work. Of course,
water sources and drains were placed in every lab, but Stew
made sure that a pressurized water system was installed in
the building so that no experiment would have a shortage of
water flow in high demand times. Similarly, pressurized air,
vacuum, and steam lines were placed in the building. Again,
to get the steam lines Stew had to work with the architectural
firm to install a special heat exchanger on the fourth floor.
Most notably in this building, Stew had to defend the need for
high bay laboratories that at first got removed from the plans
as a costcutting measure, and then were reinstated only after
his defense of these as absolutely necessary for a handson,
mindson curriculum.
Stew instilled the quote "Tell me and I forget, show me and
I may remember, but involve me and I understand," that he
attributes to Benjamin Franklin, as a fundamental philosophy
for the engineering college. For example, one of the essential
jobs of the first chairs and dean was to recruit a new set of
students to a new program without an engineering building!
This tall task involved many trips and visits to high schools
and college fairs alongside admissions office staff. As Jim
Tracey recalls, Stew's unique slant on this activity was to
bring his trademark handheld reverse osmosis demo to al
low high school students to get involved and run an actual
chemical engineering process. Stew was able to convince
students that Rowan would not be a place where you only sat
in class and took notes; instead Rowan would be the place
where you would become actively engaged in the learning
process. Stew also convinced the University Board of Trustees
that engineering at Rowan would be unique by having them
perform this same experiment.
In working with the other founding chairs, Stew contrib
uted to developing a program in which students are involved
in the learning process from the first day of the program,
7
through multidisciplinary engineering clinics. These clinics
are similar to the medical school approach to teaching (first
used in engineering by Harvey Mudd College) in which
students work in teams on actual engineering problems each
semester. Each section of the engineering clinic sequence
involves students from all four of the engineering disciplines,
and many of the clinic projects are funded by industry and
facultyresearch grants. The Rowan program was one of the
first in the country to have a oneyear freshman experience
with engineering experimentation, multidisciplinary team
work, and communication skills. In the Fall semester, students
start by conducting guided experiments, and then finish the
semester with an openended project.
In 1996 the first engineering clinic was housed in an old
cafeteria, which especially pleased Stew because he had
water and what appeared to be drains. After doing some
plumbing, these freshman students worked with pressure and
flow measurement devices using newly purchased 40gallon
tanks. The students also learned some onthejob training in
trouble shooting: They found that the cafeteria drains had been
plugged from previous use, and they observed that water will
always take the path of least resistance!
In the Spring semester the freshman engineers worked on
a reverse engineering project that focused on the coffee ma
chinea perfect match for a foodgrade cafeteria lab.
By the time the first class graduated in May 2000, eight
faculty had been hired and the labs were full of equipment
and advanced instrumentation for teaching and project work.
Based on his educational innovation and leadership, Stew
was awarded the George Westinghouse Award from ASEE in
1996. Several years later, in 2000, ASEE recognized him with
the Chester Carlson Award for his innovations in developing
laboratory experiments and course materials on membrane
technology. Stew excelled in teaching future educators at
ASEE Summer Schools, EPA workshops, and NATO Ad
vanced Study Institutes. He has conducted six NSFsponsored
workshops on novel process science and engineering, mem
brane technology, and advanced separation processes.
Stew's experience gained from some of his initial faculty
workshops was very useful in inspiring new experiments
for use in the Rowan courses. Stew helped faculty to obtain
funding for these new teaching methods by introducing them
to the NSF funding opportunities in laboratory development
as well as in presenting national workshops. Through his
leadership, faculty started out as coPI's on these grants and
then were mentored by him and became the lead on new
education grants. Stew recalls one of the best things about
Rowan is this willingness of faculty to work collaboratively.
Whether it is team teaching a class or partnering in supervising
a clinic project, the enthusiasm of faculty to work in teams
has provided rewarding learning experiences for both students
and faculty. Stew has worked alongside every member of the
departmentKevin Dahmn, Stephanie Farrell, Zenaida Ge
8
phardt, Robert Hesketh, Brian Lefebvre, James Newell, and
Mariano Savelskion educational and research projects.
As chair, Stew encouraged Rowan's talented young faculty
to develop and publish their educational innovations. Kevin
Dahm points out, "Stew served as an outstanding mentor and
passionate and effective advocate for his faculty. His support
and encouragement led to numerous national awards garnered
by members of the department." Once again, Stew's detailed
planning paid off. He had even listed in advance who would
be nominated for regional and national awards.
Rowan's Junior and Senior engineering clinics are primar
ily sponsored by industry. Getting these sponsors requires
a tremendous amount of energy and skill. Not surprisingly,
Stew was a very effective pitchman in obtaining sponsors; his
tremendous enthusiasm and ideas are very convincing. He was
the lead presenter to nearly all of the sponsors of engineering
clinic projects during his tenure as chair, and faculty who have
presented with him have observed the effectiveness of these
presentations to industry.
Stew acknowledges that industrial clinic projects have been
the most interesting to him, especially those with either food
or pharmaceutical companies. His involvement in most of
these projects has been in his area of interest of membrane
separations, but recently Stew has "gotten green." He has
been involved in EPA projects on the development of edu
cational modules in green engineering for the undergraduate
curriculum. In the last several years he has collaborated with
Mariano Savelski on green engineering research in pharma
ceutical manufacture focusing on organic solvent metrics,
solvent reduction/recovery, and life cycle assessment, funded
by EPA, BristolMyers Squibb, and Pfizer.
Mariano says, \\ l kikng with Stew has been a wonderful
experience for me; he is one of the bestorganized people I
have ever worked with. His attention to detail, his persever
ance, patience, and organizational skills are beyond descrip
tion. In our projects, he helps guide students by giving them
clear objectives for their work. As they present the results of
their work he gives detailed feedback to the students both in
meetings with students as well as on their written work."
Mariano is also impressed with Stew's planning, "He never
misses a deadline! In fact, Stew always has everything ready
days, if not weeks, in advance."
Stew's attention to detail was essential for starting a new
department. He is always prepared for every meeting whether
it is with an individual faculty member or the entire college
of engineering. Based on either his agenda or an agenda he
has been given, Stew carefully considers each point listed
and makes extensive notes on his yellow legal pad. During
the meeting he continues to take notes on important aspects
so that they can be relayed to faculty. Stew's careful pre
planning was very useful for keeping discussions focused
on accomplishing the required tasks on the agenda. One
example of his attention to detail was in planning and
Chemical Engineering Education
"One of Stew's greatest abilities was to inspire students to work to higher levels of
achievement, which in my case included earning a Ph.D. at Rensselaer Polytechnic In
stitute. One of the greatest attributes of an educator is the ability to inspire his students
and to provide visions of the possibilities beyond the classroom."
A former student
preparing an NSFsponsored workshop. In addition to all
that is required in developing new experiments, preparing
lecture and lab sessions, printing handouts, and recruiting
participants and speakers, Stew paid attention to even the
incidental detailspillows, for example. He personally
visited every dorm room that the faculty would be staying
in to make sure that it was suitable; when he discovered bed
pillows were in short supply, it was Stew who went out and
purchased them.
Stew also makes extensive use of this aptitude for planning
in his lectures and presentations. His lecture notes are filled
with comments directing students to conduct activelearning
exercises as well as notes on some of his famous jokes. Class
after class of students have been amused and bemused by
Stew's sometimes corny take on the subject matter.
In a lecture on thermal conductivity for building materials
Stew tossed students a curve by asking them to look up, "What
is the value for steel? For plywood?...For the natural log?"
Stew loves to stretch the truth and turn things around"Did
you know the origin of membrane terminology can be found
in the Bible? Moses was a breach birth so when he was born
they exclaimed 'Reverse Moses' (Reverse Osmosis)."
Brian Lefebvre, who coteaches the separation course with
Stew, remembered the lecture on ion exchange membranes.
Stew first shows the class two similarlooking polymer sheets
and asks which one is the cation and anion exchange mem
brane?After the students give a variety of answers, Stew then
holds one of the sheets close to a student's ear and obliquely
makes a "meow" sound. (He uses this example to illustrate
the importance of doing experiments.)
Stew says that the success of the Rowan chemical engineer
ing department is based on the great faculty that he is blessed
to be working with. He views his role of founding chair to
go beyond the "bricks and mortar" of a startup program.
Jim Newell comments, "Stew built a department that ran
like a family. He mentored a generation of faculty members
with concern, humor, and a genuine commitment to helping
each one of us develop to our fullest potential. Stew always
said that his job was to hire people that could become even
more successful than him and then to help them achieve
that potential." Stephanie Farrell adds, "Stew is thoughtful,
considerate, loyal, and a natural leader. As a friend and col
league he consistently puts others before himself. His work
ethic and dedication to education are well known; during his
time as department chair he was admired for his fairness,
preparedness, and dedication, all while remaining friendly,
pleasant, and easygoing."
In 2004, Stew decided to return to a faculty position to al
low other chemical engineering faculty to gain experience in
leadership positions. Through his career he has amassed an
impressive record for someone who has taught at primarily
undergraduate institutions. He is principal author or coauthor
(with his students and faculty colleagues) of more than 50
journal articles, 75 conference proceedings, 140 conference
presentations, and nine book chapters. He has served as a prin
cipal investigator or coinvestigator on more than $3 million
in projects from industry and government. He is a Fellow of
the American Society for Engineering Education (ASEE) and
has received many awards from professional societies. Over
the years, he has been asked at times to consider industrial and
government positions, but always responds to such queries
that "teaching is in my blood." Stew loves it when a former
student visits years after graduation and he can see the impact
he has had on that person's professional career.
Stew reminds seniors preparing for graduation that they are
the future of chemical engineering and the ambassadors of the
profession. He knows that these graduating seniors may not
remember all the chemical engineering concepts they learned or
all the jokes he has told. More importantly, Stew wants them to
remember two things: to help others, and to use their chemical
engineering knowhow to serve and improve society. 7
Vol. 43, No. 1, Winter 2009
MR! t classroom
  s_____________________________________
AN INNOVATIVE METHOD FOR
INTEGRATING A DIVERSITY WORKSHOP
in a Chemical Engineering Course
AYUMU YOKOYAMA
DuPont Marshall Labs * Philadelphia, PA 19146
A s chemical engineering students graduate and enter
industries or graduate schools, they will most likely
be working in a diverse work environment where
some of their colleagues, managers, and customers have
cultural backgrounds different from their own. Thus, it is
crucial for engineers to be able to work effectively with people
from different backgrounds. In fact, in many multinational
companies, it is becoming essential for employees to have
successful international assignments as a prerequisite for
moving up the corporate ladder.
Given this context in the corporate world, engineering stu
dents should be exposed to diversity in their undergraduate
education. Diversity education usually takes place outside of
core engineering programs, and it can be difficult for engi
neering students to see the relevance of diversity education
to their engineering curriculum. To demonstrate to students
the importance of diversity for engineering professions, we
integrated a short diversity workshop as part of a chemi
cal engineering course for undergraduate seniors (about 40
students) at the University of Michigan, entitled "Problem
Solving, Troubleshooting, and Making the Transition to the
Workplace." ( for
the course syllabus).[1] This course, taught by Professor H.
Scott Fogler, includes other topics such as critical and creative
thinking skills, negotiation skills, teamwork skills, problem
� Copyright ChE Division of ASEE 2009
solving skills, financial planning, technical communications,
and troubleshooting to prepare senior engineering students
for realworld challenges when they make the transition to
the workplace. Thus, we thought that a diversity workshop
would fit in this course where students can learn how to deal
with diversity in the workplace.
The author, who has a background in corporate diversity
training and consulting at DuPont, designed a short diversity
workshop for this course. The diversity workshop is 1.5 hours
long and focuses on awarenessbuilding of different com
munication styles. The workshop includes various exercises
so that students can experience different communication
styles and cultures through participation. Throughout the
workshop, lecturing is minimized to enhance interaction
among students.
Chemical Engineering Education
Ayumu Yokoyama is currently technical
group leader at DuPont Marshall Labora
tory in Philadelphia. He has B.S. and
M.S.E. degrees in chemical engineering
from Waseda University (Japan) and a
Ph.D. in chemical engineering from the
University of Michigan. His previous as
signments at DuPont include corporate
diversity training, coatings formulation,
and product management.
Asian culture is chosen to highlight and contrast with the
U.S. majority culture. We chose Asian culture because it is the
native background of the author, and it is quite different from
the U.S. majority communication style.[21 Since most students
in the class represent the majority culture, this emphasis gives
students more awareness of their own communication styles
by contrast. Also, understanding Asian communication style
is important for engineers in light of increasing business ties
between U.S. and Asian companies.
DIVERSITY WORKSHOP CONTENT
To make engineering students interested in the subject of
crosscultural communication, this workshop uses various ex
ercises and examples that have relevance for students. The fol
lowing sections describe the framework of the workshop.
Icebreaking Exercise.
CrossCultural Communication Simulation
The goal of this icebreaker is to create an interactive class
environment by having students experience crosscultural
communication in pairs. For this, the following simulation 31
is used.
1 First, students are paired (Student A and Student B).
2. Then, in each pair, one student (Student A) is shown
the slide with the communication styles he/she needs to
present:
a. Ask about B's personal matters.
b. Minimize eye contact.
c. Minimize body language (hand movement).
d. Try to keep distance (2.5 feet or more) from Student
B while talking.
3. The other student in the pair (Student B) is then shown
the slide with the different communication styles he/she
needs to present:
a. First, answer Student A's question.
b. While talking, use excessive body language.
c. Keep eye contact with Student A.
d. Stay close to Student A (1.5 feet or less).
e. After answering Student A's question, ask about
Student A's view on the war in Iraq (or any sensitive
political issue).
4. The pairs then start a crosscultural conversation for a
few minutes.
This situation simulates communication between individu
als with different styles in use of eye contact, body language,
and physical proximity. This exercise will give students a
flavor of crosscultural communication and its potential issues.
Although the exercise is done with the same language (Eng
lish), students can see how different communication styles
can negatively impact effectiveness in communication and the
building of trust in relationships needed in the workplace.
The exercise also serves as a good icebreaker since most
students find it enjoyable because of the acting involved.
For example, since Student A in each pair is trying to keep
their distance while Student B is trying to stay close, the
result can be conversation constantly interrupted by physical
movement.
Learning the Difference Between Generalizing and
Stereotyping
One danger in any diversity workshop is reinforcing ste
reotypes. To avoid this and to let students know that in this
workshop, generalization is used instead of stereotyping, two
graphs are shown using a format familiar to chemical engi
neering students (Figure 1), in which generalization is shown
as two normal distribution curves, whereas stereotyping is
shown as two 6functions. Students can easily understand
that generalization allows some exceptions (for example,
although most Americans behave in a certain way different
from Asians, some Americans do behave in anAsian way); on
the other hand, stereotyping does not allow any exceptions,
and thus needs to be avoided.
Common questions raised during this part are "Are all
stereotypes bad? Are there any good stereotypes? How about
'Asians are good in math,' which seems like a positive stereo
type?" From sociology, we learn that stereotypes are always
harmful because they encourage "mythmaking" and curb the
wants and desires of individuals and ultimately negatively af
fect societal attitudes towards groups. 41 For example, for an
AsianAmerican whose strength is art and design, the math
aptitude stereotype raises false expectations by others or by
selfor worse, funnels individuals into narrow categories.
Understanding Common Asian Cultural Mores
Common Asian cultural norms are presented in the forms of
the following exercises. The purpose of these exercises is not
necessarily to make students understand Asian cultural mores
but rather to make them aware that some cultures are quite
different from their own. Thus, cultures other than Asian can
Figure 1. Difference between generalization
and stereotyping.
Vol. 43, No. 1, Winter 2009
be used here if the instructor is familiar with them.
It is also important in these exercises to urge as many stu
dents as possible to share their interpretation, so that students
can see how diverse the interpretations can be depending on
their upbringing.
Exercise 1.
Japanese Poem for Understanding Group Orientation
The goal of this exercise is to make students realize how
differently people react to a similar situation depending on
whether their culture is based on group orientation or indi
vidual orientation (Asians are more grouporiented than the
U.S. majority group). The students are first asked to read the
following Japanese poem entitled "Sunset."[5]
The train was crowded as usual.
A young woman was ,., down, and an old man was
standing in front of her
The young woman stood up and gave her seat to the old man.
The old man got off at the next station.
The young woman sat down again.
Then, another old man was pushed by the crowd and ended
up standing in front of her
She stood up again and gave her seat to the old man.
The old man got off at the next station.
Another old man happened to be standing in front of her.
But, this time, the young woman did not stand up.
The train passed the next station.... and then the next station
with the young woman looking down and ashamed.
I ,.. i. fil i train. I wonder how long she could endure the pain.
These different interpretations along with the different
proverbs and pictures in Figure 2 can be used to talk about
group orientation ("The nail that sticks out gets hammered
down"is a Japanese proverb) vs. individual orientation ("The
squeaky wheel gets the oil," a U.S. saying).
This exercise will give students a real opportunity for
finding various reactions among participants based on their
various upbringings, especially when the class is diverse.
Exercise 2.
Short Vignette from a Japanese Movie for Understanding
"Saving Face" Concept
The goal of this exercise is to teach students the importance
of saving face in other cultures. Saving face means maintain
ing credibility, honor, the demonstration of kindness, or status
in society or on the job. Saving face is practiced in western
cultures as well, but saving face is especially important in
Asian cultures in public situations or in the eyes of others. 6]
The following example illustrates this when "face" relates to
maintaining credibility as a kind person.
A short vignette from a Japanese comedy movie71 is shown
in the class. The vignette was chosen because it is full of ac
tions and is funny and does not need translation. The vignette
shows a crowded train, where a younger man finds a boy
sitting while an elderly man is standing. This younger man
then forcefully removes the boy from his seat and then tells
the elderly man to sit down. But, the elderly man declines to
sit down. Then the younger man becomes very angry with
the elderly man.
The students are then asked
to interpret why she was
ashamed. It is important here
to tell students that there are
no right or wrong answers so
that they feel at ease in giving
their own interpretation.
NonAsian students in the
class typically will say, "The
young woman was ashamed
because she was not us
ing good manners (younger
people should give seating
to elderly),"or "She was
ashamed because she gave in
to her desire to sit down."
In Japan
The nail that sticks out gets
hammered down."
On the other hand, Asian Figure 2. Grouporiente
students will say "The young
woman has been struggling
to balance good manners against the pain of sticking out in the
crowd (Asians tend to have group orientation and avoid being
singled out even when they are doing the right thing)," or "She
did not want to get attention from other passengers."
In US
*6
d vs.
The squeaky wheel gets the oil.
ST
After viewing the
vignette, students are
asked why the younger
man got angry. Non
Asian students in the
class typically say, "The
younger man got angry
because the elderly man
did not thank him," or
"He got angry because
the elderly man did not
sit down."
Asians' interpretation
' is that the younger man
got angry because he
lost face. In Asian cul
ture, face (in this case
individualoriented culture. kindness shown by the
younger man) must be
acknowledged by other
people present in the situation (in the eyes of others). Since
the young man's face (kindness) was not appreciated by the
elderly man in public, he lost his face in front of other people
and got humiliated and angry. In Asian culture, saving face
Chemical Engineering Education
is much more important in public situations than in private
situations. If other people were not present in this situation,
the younger man would not have been angry.
This exercise will teach students the reason why Asians
often prefer to have private and onetoone meetings to avoid
losing face in public before discussing or negotiating impor
tant or sensitive issues in a large group.
Exercise 3.
Saving Face in the Global Workplace
The goal of this exercise is to show students how saving
face (discussed in Exercise 2) adds complexity to the real
workplace. In this example, "face" relates to credibility and
status/rank on the job. The exercise uses a situation involving
Japanese automotive transplant engineers and an engineer
from their company's supplier. In this situation (shown in
Figure 3), both a Japanese process engineer, Ayumu, and a
Japanese materials engineer, Yoko, are at an equally higher
status than an American manufacturing engineer, Joe (Ayumu
and Yoko give directions to Joe).
One day, the Japanese process engineer Ayumu tells the
American manufacturing engineer Joe to use a new material.
Then, this new material's supplier, Akira (also Japanese),
finds out that the Japanese material engineer Yoko is against
the use of the new material (Ayumu and Yoko are both Japa
nese but have poor communication with each other because
Ayumu is located in the United States while Yoko is located
in Japan).
If the supplier's representative Akira had not told Ayumu
that his coworker Yoko might not agree on the use of the
new material, then Ayumu would have had to change his
directions to the American engineer Joeand would have
lost face in the eyes of others (Engineer Yoko and Engineer
Joe). In this case, face refers to the higher status (giving
directions) or credibility. Since
Ayumu holds a higher status or rank
than Joe, he would lose face if his
directions are later changed by oth
ers' decisions.
To prevent this loss of face, supplier
Akira had to tell Japanese engineer
Ayumu that the Japanese engineer
Yoko was against the use of the new
material. This way, Ayumu and Yoko
could negotiate in private without
involving the American engineer
Joe, and Ayumu's direction would
not be denied completely in the eyes
of Yoko and Joe.
This real situation shows the impor
tance of saving face in the workplace
and the complexity in dealing with
different cultures.
Ayun
High Status Engir
Engir
Japal
Exercise 4.
Highcontext vs. LowContext Communication Styles
The goal of this exercise is to teach students that it is criti
cal to know the communication style (high or lowcontext)
for effective communication. Whereas the U.S. majority
communication style is called lowcontext (the meaning of a
statement is in the words spoken), Asian communication style
is called highcontext (meaning is unspoken but interpreted
indirectly from the context, the history of relationship, or
general social rules).J8] The highcontext style is:
* Subtle, often nonverbal cues used to convey meaning
(body language, facial expressions, silence, tilting head).
* Does not say a lot, but expects you to know a lot.
* Described well with the Chinese proverb, "He who
knows does not speak, he who speaks does not know"
(Laotsu, Chinese sage, 6th century B.C.).
To illustrate this difference and the confusion caused by it,
a few examples are given in the workshop in order for stu
dents to think about possible interpretations for highcontext
communicators with lowcontext statements or questions.
For example:
* A lowcontext question "Are you .11,,, " can be
interpreted by a highcontext communicator to be that
the person asking this question may be actually hungry
and 1,, ,v i,, that they should go to eat .. .,, i,, now,
or the person may be ,i, ,. i,,, that they should take a
break from this intense 1, ,. 1i,.r. n
* A lowcontext statement "I'd like that report as soon as
you can get to it" can be interpreted by a highcontext
communicator to be "Drop the current project you're
working on and finish that report today."
* A lowcontext statement"We need to .,,i, ,, our 'v.,/, t
Communication
because of
distance (Japan
nu, Japanese Us)
leer
leering Dept in I
n Direction
Ir
Vol. 43, No. 1, Winter 2009
Yoko, Japanese
Engineer
Materials Research
Dept in US
Low Status
Joe, American Engineer
Manufacturing in US
Akira, Japanese Engineer
Supplier in US
Figure 3. An example of saving face at Japanese plant in the United States.
can be interpreted by a highcontext communicator to
be "We should not spend at all," or even "My position
might be eliminated. "
Through these examples, students can see negative conse
quences of not understanding highcontext communication
style and can understand why it is so important to know which
communication style is in use for other speakers.
Nonverbal Communications
Nonverbal communications are discussed around use of
silence, use of eyecontact and use of gestures, and emotional
expressions. For example, silence is considered negative in the
U.S. majority culture, whereas silence has many positive aspects
inAsian culture, such as showing respect to superiors. One of the
negative consequences of not knowing this difference would be
that people uncomfortable with anAsian person's silence tend to
disclose too much information during negotiation.
Homework Assignment
A homework assignment is given to reinforce the main
points. The students need to find a person who grew up in a
culture different from the majority culture and find out the
following:
1. What are/were some difficulties in ............. . i1,,, with
Americans or with persons from the majority culture?
2. Ask how he/she communicates with elders, teachers, or
supervisors in their native country.
3. Ask if their native communication style is more indirect
than American communication style. Is what they say in
a native culture what they really mean?
4. What can Americans do differently to make the person
who grew up in a different country feel more comfort
able in communication in the United States?
This assignment can make students become aware of the
reality that people with cultures different from the U.S. major
ity culture feel they always have to adjust their communica
tion styles for majority members. It can also lead majority
students to think about better ways of communicating with
those from other cultures.
OUTCOMES
The goal of this workshop is to give students awareness
of different cultures playing out in the real workplace, in a
nonthreatening way. In general, neither defensive reactions
nor guilty feelings were expressed in the class. This probably
results from the use of Asian culture, which is mostly un
known and nonthreatening for a largely EuropeanAmerican
audience. Feedback from students suggests that they were sur
prised to know how different cultures impact communication
and that they did not know that their U.S. mainstream culture
is so different from other cultures such as Asian culture. Also,
we found that students with backgrounds different from the
U.S. majority culture could help the class understand diverse
cultures when they were encouraged to share their experiences
during the class.
CONCLUSIONS
The diversity workshop can be integrated into a chemical
engineering course so that students can see the relevance
of diversity education for engineering professions, where
engineers from various backgrounds need to work together
effectively. By having a diversity workshop as part of a course
for senior undergraduate students, we can show the impor
tance of diversity in the engineering profession and provide
strong motivation to learn diversity for students who will be
joining a diverse workplace shortly.
Generally, universities offer some type of diversity educa
tion as part of the general education requirements for under
graduates. This may be in many possible formscourses
with crosscultural themes, courses that raise awareness about
racism, or courses that promote a global perspective. Often,
these courses are taken in the first two years of study. The
exercises described here provide an extension of this founda
tion of diversity education during the upperlevel portion of
the undergraduate curriculum.
ACKNOWLEDGMENTS
The author appreciates the support of Arthur F. Thurnau,
Vennema Professor H. Scott Fogler at The University of
Michigan in making this workshop part of his chemical
engineering course (CHE 460), and his encouragement and
suggestions in writing this manuscript. The support of Profes
sor Kristine A. Mulhorn at The University of MichiganFlint
is also acknowledged. She provided sociological insight and
a background in cultural competence in the preparation of
this manuscript.
REFERENCES
1. Fogler, H.S., and S.E. LeBlanc, Strategies for Creative Problem Solv
ing, 2nd Ed., Prentice Hall (2007)
2. Pyong Gap Min, Asian Americans: Contemporary Trends and Issues,
2nd Edition, Pine Forge Press (2005)
3. Foster, D., "Communicating Across Cultures: Developing the Critical
Skills for Business Success in the Global Millennium" Keynote Ad
dress at 31 st Detroit Society of Coatings Technology FOCUS Confer
ence, Troy, Michigan, May (2006)
4. Giddens, A., Sociology, 5th Ed., Polity Publishing Co. (2006)
5. Yohino, H., Yuuyake, Japanese Language Textbook for 8th Graders,
MitsumuraTosho Publishing Co., Tokyo (2000).
6. Rosenberg, S., "Face Beyond Intractability," Guy Burgess and Heidi
Burgess, Eds., ConflictResearch Consortium, University of Colorado,
Boulder, Posted: February 2004
7. Yamada, Y., Otoko Was Tsuraiyo, movie, Shochiku Co. LTD (1989)
8. Adler, R.B., and Elmhorst, J.M., Communication at Work: Principles
and Practices for Business and the Professions, 5th Ed., p. 47, The
McGrawHill Companies, Inc. (1996) [
Chemical Engineering Education
Random Thoughts ...
THE 10 WORST TEACHING MISTAKES
II. Mistakes 14
RICHARD M. FIELDER
North Carolina State University
REBECCA BRENT
Education Designs, Inc.
In our last columnm1, we presented the bottom six of our top
10 list of the worst mistakes college teachers commonly
make. Here are the top four, with #4 being particularly
applicable to engineering instructors.
Mistake #4. Give tests that are too long
Engineering professors routinely give exams that are too
long for most of their students. The exams may include
problems that involve a lot of timeconsuming mathematical
analysis and/or calculations, or problems with unfamiliar
twists that may take a long time to figure out, or just too many
problems. The few students who work fast enough to finish
may make careless mistakes but can still do well thanks to
partial credit, while those who never get to some problems
or who can't quickly figure out the tricks get failing grades.
After several such experiences, many students switch to other
curricula, one factor among several that cause engineering
enrollments to decrease by 40% or more in the first two years
of the curriculum. When concerns are raised about the impact
of this attrition on the engineering pipeline, the instructors
argue that the dropouts are all incompetent or lazy and un
qualified to be engineers.
The instructors are wrong. Studies that have attempted to
correlate grades of graduates with subsequent career success
(as measured by promotions, salary increases, and employer
evaluations) have found that the correlations are negligible[21;
students who drop out of engineering have the same academic
profile as those who stay[31; and no one has ever demonstrated
that students who can solve a quantitative problem in 20 min
utes will do any better as engineers than students who need 35
minutes. In fact, students who are careful and methodical but
slow may be better engineers than students who are quick but
careless. Consider which type you would rather have design
ing the bridges you drive across or the planes you fly in.
If you want to evaluate your students' potential to be suc
cessful professionals, test their mastery of the knowledge
and skills you are teaching, not their problemsolving speed.
After you make up a test and think it's perfect, take it and
time yourself, and make sure you give the students at least
three times longer to take it than you needed (since you made
it up, you don't have to stop and think about it)  and if a test
is particularly challenging or involves a lot of derivations or
calculations, the ratio should be four or five to one for the
test to be fair.[41
Mistake #3. Get stuck in a rut
Some instructors teach a course two or three times, feel
satisfied with their lecture notes and PowerPoint slides and
Richard M. Felder is Hoechst Celanese
Professor Emeritus of Chemical Engineering
at North Carolina State University. He is co
author of Elementary Principles of Chemical
Processes (Wiley, 2005) and numerous
articles on chemical process engineering ?
and engineering and science education,
and regularly presents workshops on ef
fective college teaching at campuses and
conferences around the world. Many of his
publications can be seen at
edu/felderpublic>.
Rebecca Brent is an education consultant
4 specializing in faculty development for ef
, ^ fective university teaching, classroom and
computerbased simulations in teacher
education, and K12 staff development in
language arts and classroom management.
She codirects the ASEE National Effective
Teaching Institute and has published articles
on a variety of topics including writing in un
dergraduate courses, cooperative learning,
public school reform, and effective university
teaching.
SCopyright ChE Division ofASEE 2009
Vol. 43, No. 1, Winter 2009
assignments, and don't change a thing for the rest of their
careers except maybe to update a couple of references. Such
courses often become mechanical for the instructors, boring
for the students, and after a while, hopelessly antiquated.
Things are always happening that provide incentives and
opportunities for improving courses. New developments
in course subject areas are presented in research journals;
changes in the global economy call on programs to equip their
graduates with new skills; improved teaching techniques are
described in conference presentations and papers; and new
instructional resources are made available in digital libraries
such as SMETE (), Merlot (
org/merlot/index.htm>), and the MIT Open Courseware site
().
This is not to say that you have to make major revisions in
your course every time you give ityou probably don't have
time to do that, and there's no reason to. Rather, just keep
your eyes open for possible improvements you might make
in the time available to you. Go to some education sessions at
professional conferences; read articles in educational journals
in your discipline; visit one or two of those digital libraries to
see what tutorials, demonstrations, and simulations they've
got for your course; and commit to making one or two changes
in the course whenever you teach it. If you do that, the course
won't get stale, and neither will you.
Mistake #2. Teach without clear learning objectives
The traditional approach to teaching is to design lectures
and assignments that cover topics listed in the syllabus, give
exams on those topics, and move on. The first time most
instructors think seriously about what they want students to
do with the course material is when they write the exams, by
which time it may be too late to provide sufficient practice
in the skills required to solve the exam problems. It is point
lessand arguably unethicalto test students on skills you
haven't really taught.
A key to making courses coherent and tests fair is to write
learning objectives explicit statements of what students
should be able to do if they have learned what the instructor
wants them to learnand to use the objectives as the basis
for designing lessons, assignments, and exams.Ps] The objec
tives should all specify observable actions (e.g., define, explain,
calculate, solve, model, critique, and de\in), avoiding vague
and unobservable terms such as know, learn, understand, and
appreciate. Besides using the objectives to design your instruc
tion, consider sharing them with the students as study guides for
exams. The clearer you are about your expectations (especially
highlevel ones that involve deep analysis and conceptual un
derstanding, critical thinking, and creative thinking), the more
likely the students will be to meet them, and nothing clarifies
expectations like good learning objectives.
Mistake #1. Disrespect students
How much students learn in a course depends to a great
extent on the instructor's attitude. Two different instructors
could teach the same material to the same group of students
using the same methods, give identical exams, and get dra
matically different results. Under one teacher, the students
might get good grades and give high ratings to the course and
instructor; under the other teacher, the grades could be low,
the ratings could be abysmal, and if the course is a gateway to
the curriculum, many of the students might not be there next
semester. The difference between the students' performance
in the two classes could easily stem from the instructors' at
titudes. If Instructor A conveys respect for the students and
a sense that he/she cares about their learning and Instructor
B appears indifferent and/or disrespectful, the differences in
exam grades and ratings should come as no surprise.
Even if you genuinely respect and care about your students,
you can unintentionally give them the opposite sense. Here
are several ways to do it: (1) Make sarcastic remarks in class
about their skills, intelligence, and work ethics; (2) disparage
their questions or their responses to your questions; (3) give
the impression that you are in front of them because it's your
job, not because you like the subject and enjoy teaching it; (4)
frequently come to class unprepared, run overtime, and cancel
classes; (5) don't show up for office hours, or show up but
act annoyed when students come in with questions. If you've
slipped into any of those practices, try to drop them. If you
give students a sense that you don't respect them, the class will
probably be a bad experience for everyone no matter what else
you do, while if you clearly convey respect and caring, it will
cover a multitude of pedagogical sins you might commit.
REFERENCES
1. Felder, R.M., andR. Brent, "The 10 Worst Teaching Mistakes. I. Mis
takes 510," Chem. Engr. Education, 42(4) 201 (2008)
ncsu.edu/felderpublic/Columns/BadIdeasl .pdf>
2. Cohen, PA., "College Grades and Adult Achievement: A Research
Synthesis, "Res. in HigherEd., 20(3), 281 (1984); Samson, G.E., M.E.
Graue, T. Weinstein, and H.J. Walberg, "Academic and Occupational
Performance: A Quantitative Synthesis, "Am. Educ. Res. Journal, 21(2)
311 (1984)
3. Seymour, E., and N.M. Hewitt, Talking about Leaving: Why Under
graduates Leave the Sciences, Boulder, CO: Westview Press (1997)
4. Felder, R.M., "Designing Tests to Maximize Learning, "J. Prof. Issues
in Engr. Education and Practice, 128(1) 1 (2002),
edulfelderpublic/PapersI .. / I ......>
5. R.M . Felder& R. Brent, * *1.i.1.  1. Speaking,"( t..... i . i. ,t
tion, 31(3) 178 (1997),
Objectives.html> 7
All of the Random Thoughts columns are now available on the World Wide Web at
http://www.ncsu.edu/effective_teaching and at http://che.ufl.edu/~cee/
Chemical Engineering Education
LG= classroom )
MULTIPLE COMPARISONS
OF OBSERVATION MEANS
ARE THE MEANS SIGNIFICANTLY DIFFERENT?
T.Z. FAHIDY
University of Waterloo * Waterloo, Ontario, Canada N2L 3G1
Several currently popular methods of ascertaining which
treatment (population) means are different, via random
samples obtained under each treatment, are briefly
described and illustrated by evaluating catalyst performance
in a chemical reactor.
In a routine undergraduate classroom application of one
way ANOVA (analysis of variance), the null hypothesis
Ho : I1 = r2 = .. k (1
is tested against the alternative hypothesis that at least
two population means are different, given sample means
x1 , x2,..., computed from n1, n2...nk random observations.
If H0 is rejected, it is not always apriori obvious which of the
two or more means differ; multiple comparison tests help to
provide the answer. We are especially interested in the "fate"
of Ho when the individual treatment/population variances
2 2 2
0(T, (T2 ,...,( are considered to be equal, because if they
are not equal, wide dispersion in the data is most likely the
primary cause, and further testing may not be required.
Commonly, the rejection of Ho is made at a 95%, or at a
99% level of confidence. In the first case, under H0, the error
probability of falsely rejecting H0 is (at most) 5%, in the second
case, it is 1%. This, socalled Type I error is also known as
the level of significance: a = 0.05 (significant), and a = 0.01
(highly significant), respectively. An H0 maybe rejected at the
significant level, but not necessarily at the highly significant
level. Consequently, failure to reject Ho at a = 0.05 automati
cally implies no rejection at a = 0.01, as well. The P value is
defined as the smallest level of significance (i.e., the smallest
value of a) that would lead to a rejection of H0. The 5% and
1% levels do not have a privileged position, because the real
life significance of the magnitude of the Type I error is left to
the tester's judgment. In the sequel, we shall adhere to the two
traditional levels inasmuch as certain statistical tables include
only critical values pertaining to a = 0.05 and a = 0.01 (F and
T  tables are, however, notable exceptions).
MOTIVATION: A CHEMICAL REACTOR WITH
DIFFERENT CATALYSTS
In the chemical engineering classroom, we could explore,
for instance, the hydrogenation of nitrobenzene[1] in a
tubular reactor, using three different Nibased catalysts.
Under identical experimental conditions, conversion data
shown in Table 1 (page 19) are assumed to be available
for testing H0 : the three mean conversions are the same.
The alternative hypothesis, Ha, is that at least two catalysts
render different mean conversions. If Ha is upheld, the
next question to ask is which catalysts are significantly
different, by testing whether (93  92); (12  P3); (11  92)
differ significantly from zero. This is the goal of multiple
comparison tests, following a standard ANOVA applied to
H0 in Eq. (1).
Three fundamental assumptions are now made: (1) the three
catalysts act independently of one another; (2) the observed
conversions belong to a normal (Gaussian) population, at
least approximately; and (3) the three observation sets are
homogeneous, i.e., the conversionpopulation variances are
not significantly different. Since, as demonstrated in Appendix
1, the third assumption is not rejected, we expect thatANOVA
will be sufficiently robust, even if the conversion data are only
approximately normal.
We shall look at two variations of the theme. The first
one involves equal observation sizes n = n2  n113 = 8. In the
second one we stipulate that four of the observations are
absent, i.e., n = 8; n2  6; n3 = 6. The multiple comparison
tests are not the same, as seen in the sequel.
Details of ANOVA can be found in undergraduate statistics
textbooks, and are omitted here. Table 1 indicates that rejec
tion of Ho in Eq. (1) carries only a 0.2%, and a 0.1% Type I
error, respectively; we can say that Ho is soundly defeated. Our
inferences about the three catalyst populations (i.e., very large
number of observations) are dataspecific, of course. With dif
Thomas Z. Fahidy is distinguished pro
fessor emeritus and adjunct professor of
chemical engineering at the University of
Waterloo (Canada). He received his B.Sc.
and M.Sc. degrees from Queen's (Canada)
and his Ph.D. from Illinois (UrbanaCham
paign). Recipient of several professional
honors including fellowships, he is a Pro
fessional Engineer of Ontario, and author
of the text Principles of Electrochemical
Reactor Analysis (Elsevier, 1985).
SCopyright ChE Division ofASEE 2009
Vol. 43, No. 1, Winter 2009
ferent sets of observation, the numerical values of the F  statistic and our inferences may well be different.
We now proceed to find out how many of the three catalysts can be expected to behave differently from the others via multiple
comparison tests.
MULTIPLE COMPARISONS: EQUALSIZE OBSERVATIONS
a. The Bonferroni methodt24
This method is based on the concept of the simultaneous level of confidence (SLC), which guarantees that each individual
difference in means carries a level of significance a.B as given below:
a B = a (2)
k(k1)
k
The degrees of freedom for error are n1  k.
In our reactor, n1 + n2 + n3  k = 6, hence aB = 0.0083 for a = 0.05, and aB = 0.0017 for a = 0.01. The confidence interval
may be written as
(x x )t OB;k(nl1) 2(MSE) / n <  ) < (x  xj)t OB;k(n1) 2(MSE)/n (3)
for the difference between two arbitrary population means. The degree of freedom of the T  statistic is k(n1). We find in T
 distribution tables, e.g.,EY' the values: t(0.01;21) = 2.518; t(0.005;21) = 2.831; t(0.001;21) = 3.527. By linear extrapolation we
obtain t(0.0083;21) = 2.623 and t(0.0017;21) = 3.406. With MSE = 7.786, the confidence intervals in Table 2 are obtained.
What can we conclude from the results? Since (p3  p) = 0 is included in BCI32, we cannot assert that the two means are signifi
cantly different. BCI12 and BCI 13, however, exclude zeromeaning that g appears to be significantly different from g2 and p3.
This conclusion is supported even at the highly significant level. In other words, the mean performance of Catalyst 1 appears to
be different from (in fact, better than) the performance of the other two catalysts, but the mean performance of Catalyst 2 does
not appear to be significantly different from the performance of Catalyst 3.
b. The Tukey methodt6"71
In this method the statistic Q belongs to the studentized range distribution, where the degrees of freedom are
DF1 = k and DF2 = k(n1). Critical values of Q[a; k, k(n1)] are tabulated at a = 0.05 and a = 0.01,[8101 but the Qtables are
not widely available in the textbook literature. We need linear interpolation based on the tabulated values q[0.05;3,20] = 3.58;
q[0.05;3,24] = 3.53; q[0.01;3,20] = 4.64; q[0.01;3,24] = 4.55, yielding q[0.05;3,21] = 3.57 and q[0.01;3,21] = 4.62. The confi
dence intervals given by the expression
(x xJ )Q  ;k,k(n1) MST/n / 4(x xj) Q a;k,k(n 1) MST/n (4)
are given in Table 2. Agreement with the Bonferroni method is not the same for (g1  3), inasmuch as the null hypothesis of no
difference between them can be rejected only at the significant, but not at the highly significant, level (if the lower bound of the
interval is set to zero, linear interpolation between the two critical values would indicate a P  value of about 0.023.
c. The Scheffi method1'121
In establishing the confidence intervals, the SnedecorFischer F  distribution provides values of the critical statistic, when
two individual means are compared:
(x x )K(a;k,n)< (il  J)<(x x) +(a;k,n)
K(aY;k,n)  2(k1)(MSE)F a;k1,nk /n (5)
and, specifically in our case,
(x x )0.5 (MSE)F ca;2,21 <(l [J<(x ) + 0.5/(MSE)F ca;2,21 (6)
The significant and highly significant critical F  values are f[0.05;2,21 = 3.47, and f [0.01;2,21] = 5.78.
The confidence intervals in Table 2 indicate complete qualitative agreement with the Bonferroni method, and nearly complete
agreement with the Tukey method.
18 Chemical Engineering Education
d. The Duncan method113J41
In this approach, differences in the sample means are compared
to a statistical parameter to ascertain significance; there are no
confidence intervals to deal with. Only equalsize observations
can be considered for the test. We have seen that in our case
x > x3 > x2 , hence we have two single ranges (p = 2) and one
double range (p = 3) of sample mean differences. If any difference
exceeds the numerical value of the Duncan parameter
For the establishment of the confidence intervals, there are
essentially two modifications with respect to the equalsize
observations case. The MSE multiplier for the confidence in
tervals becomes ( 1121n n ... n 1) , and the second degree
of freedom is smaller due to the smaller number of observa
tions. In our case MSE = 5.988, and the MSEmultipliers are
7/24 and 1/3. For the Bonferroni method, the critical T  sta
tistics are t[0.00833;17] = 2.678 (a = 0.05) and t[0.00167;17]
= 3.521 (a = 0.01). In the Scheff6 method, f[0.05;2;17] =
R =r (MSE)/n=0.9865r;p
then that difference is at least significant,
or even highly significant. The quantity
r , called the ,/ ...., , ti,,. . it! studentized
range, depends on a and the degree of
freedom of MSE = 7.786, i.e., DF =
21. Critical tables of r are provided in
various textbooks, e.g.,115 171 for a = 0.05
and a = 0.01. In our case, r2 = 2.950 (a =
0.05) and 4.024 (a = 0.01), and r3 = 3.097
(a = 0.05) and 4.197 (a = 0.01) at DF =
20. The next set of critical values given
for DF = 24 differing but slightly from
the DF = 20 values, interpolation may be
bypassed and we accept R2 = 2.910 and
R3 = 3.055 at a = 0.05, and R2 = 3.970;
R3 = 4.140 at a = 0.01 . The conclusion
drawn from this test is that (g1  3) and
(g1  2) are different from zero even at a
highly significant level, but H0: (P3  g2)
= 0 is acceptable at a significant (and, of
course, at a highly significant) level.
MULTIPLE COMPARISONS:
UNEQUALSIZE OBSERVATIONS
We now proceed to postulate that the last
two conversion measurements with Cata
lysts 2 and 3, i.e., the entries 81 and 83%,
and 80 and 84%, respectively, are unknown.
In this instance, the mean conversions are
K, =84%; 2, =77%; x, =79%, and on
account of the
computed F 
statistic of 15.45,
H0 in Eq. (1) is
rejected very
strongly, with a
Type I error less
than 0.1%. We
are now ready
to investigate
the differences
in conversion
means.
Vol. 43, No. 1, Winter 2009
2,3 (7)
TABLE 1
Exit conversions in a tubular reactor using three different catalysts. The obser
vations are hypothetical under identical experimental conditions.
Catalyst 1 Catalyst 2 Catalyst 3
82 74 79
86 82 79
79 78 77
83 75 78
85 76 82
84 77 79
86 81 80
87 83 84
Means: 84 78.25 79.75
ANOVA (equal  size)
Source SS DF Mean SS F
Treatments 142.34 2 71.17 9.14
Error 163.50 21 7.786
Total 305.84 23
Critical values of the F  statistic: 3.47 (a = 0.05);5.78 (a = 0.01); 9.77 (a = 0.001);
P value: z 0.002
ANOVA (unequal  size)
(Last two entries in column 2 and 3 above are removed)
Source SS DF Mean SS F
Treatments 185.0 2 92.5 15.45
Error 101.80 17 5.988
Total 286.80 19
Critical values of the F  statistic: 3.59 (a = 0.05); 6.11 (a = 0.01);10.66 (a =0.001)
P value: < 0.001
TABLE 2
Lower (LB) and upper (UB) bounds of the confidence intervals for mean conversions with equalsize
observations
B: Bonferroni; T: Tukey; S: Scheffe'
a = 0.05 Ua = 0.01
Difference Bound B T S B T S
P1  2 LB 2.091 2.228 4.401 0.998 1.192 3.646
UB 9.409 9.272 9.599 10.502 10.308 10.354
P1 p 3 LB 0.591 0.728 2.401 0.502 0.308 1.646
UB 7.909 7.772 7.599 9.002 8.808 8.354
3  2 LB 2.159 2.022 0.599 3.252 3.058 1.354
UB 5.159 5.022 4.599 6.252 6.058 5.354
3.59, and f[0.01;2; 17] = 6.11. The corresponding confidence
intervals in Table 2 indicate complete qualitative agreement
among the three methods.
DISCUSSION
What are the relative merits of the three methods? In ac
cordance with pertinent literature, the following statements
can be made. (A) The Bonferroni method is "very effective"
for smallsize comparisons, and if the observationset sizes
are equal, Tukey's method is "optimal" in the sense of yield
ing the shortest confidence interval.E18] (B) If the product of
the two degrees of freedom of the test statistics is large, the
smaller of the Bonferroni and Scheff6 intervals are to be
taken.1191 Tables 1 and 2 are in compliance with (A), except
ing the Tukey interval for (1  ,3) at a = 0.01, but this result
is not surprising in view of the usually higher power of the
Bonferroni method for small k.
One advantage of dealing with confidence intervals with
only positive bounds resides in the rejection of the null hy
pothesis that a difference in the related two population means
is not significant. The shorter the confidence interval, the less
likely that the lower bound will be negative, therefore Ho: (g,
 g ) = 0 will be rejected. This is the desired outcome, since
rejection of a null hypothesis is a statistically stronger result
than failure to reject it.
It follows from what we have already stated at the outset
that we would be hesitant about preferring Catalyst 1 if the
population variances were shown to be unequal (the case
of heteroscedasticity), especially at a very high degree of
confidence. Data transformation techniques, e.g.,[21 for the
removal of heteroscedasticity are known, but they are beyond
the objective of this paper.
Multiple comparison methods can readily be extended to
contrasts, where arbitrary linear combinations of population
means can be treated. A short description is given in Ap
pendix 2.
Finally, we may be interested in comparing our mean con
versions with the mean conversion obtained with, for instance,
a Nifree metal oxide catalyst. This exercise would fall into
the "treatment comparison with control" test category. In so
doing, the hl p tlkh. c ,
Hoe : D tt =l;i = 1,...,k
H I: [10 :[l;i= l,...,k
are tested by the Dunnett parameter22, 231
X  xo
V22(MSE)/ n
where the 0 subscript denotes control. If the absolute value of
d exceeds the critical value d[(a /2);k,DF2] with first degree of
freedom k, and DF2, the second degree of freedom of MSE,
which includes the control observations, then H in Eq. (8) is
rejected at a chosen a. Critical Dunnett parameter values are
tabulated for two sided tests, e.g., in Reference 24.
For our reactor, if we assume a control conversion set of
73,80,76,82,77,75,79,83%, we obtain SSE = 247.88 and MSE
= 247.88/ [4(81)] = 8.8528. The values d1 = 3.949; d2 = 0.084;
d, = 1.0925 are computed from Eq. (9). Since at a = 0.05,
d[0.025;3,24] = 2.51 and d[0.025;3,30] = 2.47, and at a = 0.01,
d[0.005;3,24] = 3.22, and d[0.005;3,30] = 3.15, only the mean
of Catalyst 1 appears to be significantly different from o0.
CLASSROOM EXPERIENCE
Respecting the necessity of numerous other topics that also
have to be covered in the introductory probability and statistics
course taught to second year undergraduate ChE students, this
author could go beyond Duncan's multiplerange method only
to a rather limited extent in dealing with the subject matter.
Class reaction was (not unexpectedly) mixed, depending on
the degree of willingness to accept the statistical way of rea
soning. Students exposed to statistical techniques during their
work terms (the coop structure of engineering programs at
Waterloo alternates inhouse lecture terms and practicebased
work terms) generally showed more appreciation, if not enthu
siasm, than their fellow classmates with different workterm
orientation. The author's quest for a course devoted solely to
the analysis of variance including multiple comparisons is
motivated not only by personal experience arising from the
introductory course, but also by the steadily increasing impor
tance of probabilitybased thinking in all walks of life.
TABLE 3
Lower (LB) and upper (UB) bounds of the confidence intervals for mean conversions with unequal  size observations.
B: Bonferroni; T*: Tukey; S: Scheffe'
ca = 0.05 a = 0.01
Difference Bound B T S B T S
P1  R2 LB 3.461 3.607 3.459 2.346 2.570 2.380
UB 10.539 10.393 10.541 11.654 11.430 11.619
p1  33 LB 1.461 1.607 1.217 0.346 0.570 0.064
UB 8.539 8.393 8.783 9.654 9.430 9.936
p3  p2 LB  1.783  1.627  1.541  2.975  2.736  2.619
UB 5.783 5.627 5.541 6.975 6.736 6.619
'modified for unequalsize observation sets [Devore, J.,L., loc.cit., (2004), p.434.]
Chemical Engineering Education
FINAL REMARKS
Because the statistically informed chemical engineer is
especially valuable to industry, education of our students in
statistical techniques is highly desirable in today's world. Mul
tiple comparisons make up an integral part of this education
in demonstrating the utility of statistical approaches, and the
importance of applying proper judgment to test results.
ACKNOWLEDGMENTS
This paper was prepared using facilities provided by the
Natural Sciences and Engineering Research Council of Cana
da (NSERC) and the University of Waterloo. The unequalsize
data in Table 1 were adopted from Hogg and Ledolter[25,26]
on ANOVA of beam reflection; the material does not contain
multiplecomparison tests.
NOMENCLATURE
B1;B2
BCI
C
c
D
Bartlettparameters in Equations (A.4;A.7)
Bonferroni confidence interval for (,  Rj)
Bartlettparameter in Equation (A.6)
contrast coefficient [Eq. (11)]
)F degree of freedom
d twosided Dunnett's critical parameter [ Eq. (13)], at level
of significance a
F critical parameter of the FischerSnedecor Fdistribution,
at level of significance a
f numerical value of an Fstatistic
G Cochran statistic in Eq. (A.2)
Ha hypothesis alternative to null hypothesis H0
0 Null hypothesis
k number of treatments (observation sets)
.B lower bound of a confidence interval
M Bartlettparameter in Eq. (A.5)
MSE
MS
N
n
n
Q
q
r
p
R
S
SCI
SS
T
mean square of experimental errors
mean sum of squares
total number of observations
number of observations in each equally sized treatment
number of observations in the i  th treatment
Tukey  statistic in Eq. (4)
numerical value of a Q  statistic
least significant studentized range in Duncan's test in Eq.
(5)
least significant range of means in Duncan's test in Eq. (5)
sample variance
Scheff6 confidence interval
sum of squares
Student's T  statistic
t numerical value of a T  statistic
UB upper bound of a confidence interval
x mean value of x observations in the ith treatment
GREEK SYMBOLS
a level of significance (Type I error, i.e. the maximum value
of the probability of rejecting H0 when H0 is true)
aB simultaneous level of significance (Bonferroni method)
g, the (true) population mean of observations due to the i  th
treatment
REFERENCES
1. Smith, J.M., Chemical Engineering Kinetics, 3rd Ed., Example 135,
p.574, McGraw Hill, NY, (1981)
2. Devore, J.L., Probability and Statistics for Engineers and the Sciences,
1st Ed., Section 10.2, p. 357, Brooks/Cole, Monterey (1982)
3. Petruccelli, J.D., B. Nandram, and M. Chen,, Applied Statistics for
Engineers and Scientists, Section 9.1, p.536, Prentice  Hall, Upper
Saddle River, NJ, (1999)
4. Arnold, S.E, Mathematical Statistics, Section 13.4, p.477, Prentice
Hall, Englewood Cliffs, NJ (1990).
5. Lindley, D.V., and W E Scott, New Cambridge Statistical Tables, 2nd
Ed., Table 10, p. 45, Cambridge Univ. Press (1984)
6. Devore, J.L., and R. Peck, StatisticsThe Exploration and Analysis
of Data, 3rd Ed., Section 13.2, p. 527, Duxbury Press, Pacific Grove
CA, (1997)
7. Devore, J.L., Probability and Statistics for Engineering and the Sci
ences, 6th Ed., Section 10.2, p. 422, Brooks/Cole Thomson Learning,
Belmont, CA, (2004)
8. Devore, J.L., and R. Peck, loc. cit., Table VIII, p. 616
9. Devore, J.L., loc. cit. (2004), Table A.10, p. 754.
10. Kokoska, S., and Ch. Nevison, Statistical Tables and Formulae, Table
12, pp. 6465, Springer  Verlag, NY, (1989)
11. Steel, R.G.D., and J.H. Torrie, Principles and Procedures of Statistics
A Biometrical Approach, 2nd Ed., Sections 9.2 and 9.3, pp. 196;201,
McGraw Hill, NY, (1980)
12. Devore, J.L., loc. cit., (1982), p.366
13. Miller, I.R., J.E. Freund, and R. Johnson, Probability and Statistics for
Engineers, 4th Ed., Section 12.4, p. 405, Prentice  Hall, Englewood
Cliffs, NJ, (1990)
14. Walpole, R.E., R.H. Myers, S.L. Myers, and K. Ye, Probability & Sta
tistics for Engineers & Scientists, 7th Ed., Section 13.6, pp. 480481,
Prentice Hall, Upper Saddle River, NJ, (2002)
15. Miller, I.R., et al., loc. cit., Table 12(a), p. 585, Table 12(b), p. 586
16. Walpole, R.E., et al., loc. cit., Table A. 12, pp. 688689
17. Dougherty, E. R., Probability and Statistics for the Engineering, Com
puting and Physical Sciences, Table A.9, pp. 741742, Prentice Hall,
Englewood Cliffs, NJ, (1990)
18. Petruccelli, J.D., et al., loc. cit., p. 538
19. Petruccelli, J.D., et al., loc. cit., p. 602
20. Devore, J.L., Probability and Statistics for Engineering and the Sciences,
3rd Ed., pp. 392  393, Brooks/Cole, Pacific Grove, CA, (1991)
21. Walpole, R.E., et al., loc. cit., Section 3.17, pp. 481483
22. Dunnett, C.W, "A multiple comparisons procedure for comparing sev
eral treatments with control, "J. Am. Stat. Assoc., 50, 1096 (1955)
23. Dunnett, C.W, "New tables for multiple comparisons with a control,"
Biometrics, 3, 482 (1964)
24. Walpole, R.E., et al., loc. cit., Table A. 13, pp. 690691
25. Hogg, R.V., and J. Ledolter, Engineering Statistics, Example 5.12, p.
195, Macmillan, NY; Collier, London (1987)
26. Hogg, R.V., and J. Ledolter, Applied Statistics for Engineers and
Physical Scientists, 2nd Ed., Example 7.1.2, p. 265, Macmillan, NY,
(1992)
27. Walpole, R. E., et al., loc. cit., p.471
28. Beyer, W.H. (ed.), CRC Handbook of Tables for Probability and Sta
tistics, 2nd Ed., Section VI.5, pp. 325327, CRC Press, Boca Raton,
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29. Kokoska, S., et al., loc. cit., Table 16, p.74
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Vol. 43, No. 1, Winter 2009
APPENDIX 1. TESTING THE HYPOTHESIS OF
EQUALPOPULATION VARIANCES
The null hypothesis
S2 2 = =
o0' 1 2 ... k(Tk
(A.1)
is a statement of homoscedasticity, or homogeneity of vari
ances, against the alternative hypothesis Ha: at least two
variances are unequal.
(i) Equalsize observations
The Cochran test27 311 compares the numerical value of the
G  statistic
max S2
G = k (A.2)
TS2
1=1
composed of the sample variances, to critical values of
g(a;k,n) tabulated for a = 0.05 and 0.01; H0 in Eq. (A.1) is
rejected if G > g(a;k,n). In our case g = 11.857/(6.857+11.3
57+5.0714) = 0.4877 being less than gi 1115 3 Ni= 0.6530,[27
321 we fail to reject the assumption of variance homogeneity
among the three sets of conversion.
(ii) Unequalsize observations
Two versions of the Bartlett test for Eq. (A. 1) are given in
the literature. In the earlier version 33,341 of the test a pooled
variance estimate
k 1)2 S2
NS  (A.3)
is used to compute the Bartlett Nkstatistic
is used to compute the Bartlett  statistic
B1 = In(10)
C
where
M=N k)loglo (S) (n 1) loglo (s2)
1=1
(A.4)
belonging to the Bartlett distribution. It has the curious, if not
confusing, distinction that H0 is rejected if B2 has a numerical
value less than the composite critical value
k
Snb (a;n)
b k( ;no ,n1 ,,, n ), = N
(A.8)
For our catalysts, S2 =6.857; S2 =8; S2 =2.8, hence S2 =6;M
= 0.62441; C= 1.0777, and b = 1.334. At a = 0.05, the critical
chi  square value at DF = 2 is 5.991 (found in any statistics
textbook or tables), and we fail to reject Ho in Eq. (A.1). In
the second version, B2 has the numerical value of 0.919 from
Eq. (A.7). The critical value at a = 0.05 is computed3[6,371 as
b3(0.05;8,6,6) = [8(0.7387)+2(6)(0.6483)]/20 = 0.6845 viaEq.
(A.8). Since (careful!) 0.919 is larger than 0.6845, we fail
to reject the null hypothesis of equal population variances(at
a = 0.01, the critical value, [8(0.6282) + 2(6)(0.514 , 2, i =
0.5602 is expectedly lower).
APPENDIX 2. ELEMENTARY CONCEPTS OF
CONTRAST THEORY
Suppose we have tested a larger numbersay, fivecata
lysts in our reactor and have at our disposal five observation
means x ,x,....,x,. We may want to test more involved
null hypotheses, e.g., H0: (g  g)  (g3  g4) = 0; H0: (glp3)
 (2 5) = 0, etc. for some reason. These combinations are
called contrasts. In general, a contrast is c LI+Cz.L+...+Cm.m
where the c coefficients can be positive, negative, or zero.
The confidence intervals are accordingly more complicated
than for the ones shown in the text. For example, if we employ
the Scheff6 method, the expression
C
n
ZCX
c1 1
(a; n, m) 
S(a; n,m)
(A.5)
3(k )1 nlk Nk
(A.6)
The B  statistic is approximately chi  square distributed
with (k  1) degrees of freedom.
In the more recent version,[35s the pooled variance computed
via Eq. (A.3) is used to obtain the B2  statistic defined as
S11\
l/(Nk
S2
P
(a; n,m) V(n1)(MSE)F(ia;n1,(nm))
(A.9)
provides the alevel confidence interval in the case of unequal
size observation sets. If m =2, Eq. (5) is regained.
For the sake of illustration, we assume that four catalysts
with observation set sizes n = 10; n2 = 8; n, = 7; n4 = 9 yield
mean conversions 72; 75;80;82%, respectively, and MSE
=195.3 . We propose to set the null hypothesis that (g4g2)
 (p3 gl) = 0. Here, c = 1; c2 = 1; c3 = 1 and c = 1. Also,
n  m = 34  4 =30. Accordingly, c x1 + c2x2 + C3X3 + C44 =
1, and (c2 n)12 = 0.6921. Since f[0.05;3,30]) = 2.92, Eq.
(A.9) yields LB = 29.627; UB = 27.627, and we fail to reject
the null hypothesis (Pvalue z 0.004). 7
Chemical Engineering Education
In1 1 laboratory
A PROCESS DYNAMICS AND CONTROL
EXPERIMENT
for the Undergraduate Laboratory
JORDAN L. SPENCER
Columbia University * New York, NY 10027
While the variety of experiments contained in typical
chemical engineering laboratory courses continues
to broaden, it remains important to include experi
ments or projects involving process dynamics and control.
And, in fact, modem hardware and software make such ex
periments more and more possible, realistic, and interesting.
The experiment described here employs relatively simple
and inexpensive equipment to demonstrate several important
aspects of process dynamics and control, both modelfree
and modelbased analyses of process dynamics data, and two
related controller tuning methods.
This experiment permits the students to observe the re
sponse of a flow system to impulse injection of a tracer, to
collect large amounts of data quickly, and to process the data
rapidly using Excel and LabVIEW or QuickBASIC programs.
It also permits students to observe, in action and with short
time constants, the operation of a PID feedback control sys
tem. The students see the actuator (a steppermotor driven
valve) move, see dye enter and pass through a glass flow
system, see the transducer (a spectrophotometer) respond
to changes in the measured variable, and see the controller
(a LabVIEW program) respond to changes in the measured
variable and drive the actuator.
From a pedagogical standpoint, the experimentdescribed
in enough detail to be accurately reproducedprovides a
comprehensive treatment of a PID controlled flow system,
including both standard and more advanced topics. It dem
onstrates also modem data acquisition and data processing
techniques, including the use of LabVIEW. It is designed for
use in either a junior or seniorlevel laboratory, but should
be preceded by or taught in parallel with a course in process
dynamics and control.
APPARATUS
The apparatus is shown schematically in Figure 1. To re
move dissolved air, house water is stored in a polyethylene
carboy and supplied to the experiment by a magneticdrive
Vol. 43, No. 1, Winter 2009
Figure 1. Schematic diagram of the apparatus, showing the
three flasks and valving of the flow system, the water feed
system, the dye feed system with steppermotor controlled
valve, and the spectrophotometer with a flow cuvette.
Jordan L. Spencer is an emeritus profes
sor of chemical engineering at Columbia
University. He received his B.S. in 1953 and
his Ph.D. in 1961, both from the University
of Pennsylvania and both in chemical en
gineering. His research and teaching inter
ests involve control and optimal control, and
the development of chemical engineering
teaching experiments, including Weboper
i C able experiments.
SCopyright ChE Division of ASEE 2009
PUMP
centrifugal pump. A rotameter measures the flow rate, which
is controlled by a manual metering valve. The flow system
consists of three Erlenmeyer flasks, each of volume about 290
ml. The flasks are closed by Teflon stoppers sealed by orings,
and are connected by 1/4 inch stainless tubing. A ball valve
with a connection for a syringe allows impulse injection of
dye solution at the entrance to the flow system. Two stainless
ball valves allow three flow patterns, namely: (a) flow through
one flask only, (b) flow through three flasks in series, and
(c) partial flow through the first two flasks in series and full
flow through the last tank. The tubing connecting the first two
tanks is designed to prevent air accumulation in these tanks,
while the last tank is designed to accumulate air, which can
be vented via a valve before a run. This avoids the passage
of air bubbles to the downstream spectrophotometer. A ball
valve connected to a tee at the entrance to the flow system
allows a dye solution (typically 10 ml of methylene blue dye
at a level of 50 mg/L) to be injected using a syringe.
The transient dye concentration in the effluent water from
the flow system is measured by a spectrophotometer (Milton
Roy, Model Spec 20). A test tube with an oringsealed Tef
lon stopper holding inlet and outlet tubes is inserted into the
spectrophotometer and serves as a flow cuvette. The spectro
photometer is set at a wavelength of 640 nm, with the 0 to 1
volt analog output signal connected to a National Instruments
A/D board (PCI6043E).
Methylene blue solution (10 mg/L) held in a 20 L polyethyl
ene carboy is pumped to steppermotor (Arrick Robotics) driven
needle valve. This valve controls the flow of the dye solution to
a mixing tee upstream of the threeflask flow system. The step
permotor is driven by signals from a LabVIEW VI that imple
ments a standard PID (Stephanopoulosm1l) control algorithm,
corresponding to the following discretetime algorithm
Valve position = Base position + Kc[Present error +
(1/T ) Integral of past errors + TD Derivative of error]
Here Kc is the controller gain, T1 is the integral time, TD is
the derivative time, and error is the set point less the measured
variable. The valve position is measured in steppermotor
steps (400 steps = 1 turn). The algorithm departs slightly from
ideality in that the valve motion is limited to 100 positive or
negative steps in a single iteration. When the system is close
to the steady state and changes in valve position are small,
this feature will have no effect.
The PID algorithm is iterated every four seconds, with
a typical run involving 300 iterations, corresponding to 20
minutes. Users can change the set point and the three control
ler parameters at any time during the run, and a full record
of the controller parameters and state variables is written to
a spreadsheet file at the end of the run.
OPERATION
There are three modes of operation.
Impulse Response Mode
Prior to the run the spectrophotometer is zeroed and then
set to 100 percent transmittance when the dye concentra
tion is zero. The ball valves are set to give singletank flow,
threetanksinseries flow, or parallel flow. The rotameter is
used to set the water flow rate to a value between 300 and
1200 ml/min. At time zero about 10 ml of methylene blue
solution (100 mg/L) is injected rapidly through a ball valve
at the entrance to the flow system, and at the same time a
LabVIEW program (VI) is started. The program samples the
spectrophotometer output signal at a selectable rate of roughly
2 samples per second, for a time long enough that the dye
concentration has returned to zero. The program converts the
transmittance signal to concentration, and also calculates the
mean residence time from the concentration vs. time signal.
The data are also written to a spreadsheet file for later plot
ting and processing.
Control Mode
With the flow rate and the flow system configuration set
and the dye solution pump running, the LabVIEW PID
control program is started. The students first set the control
ler parameters (Kc, T1, TD), and then the set point (typically
about 50 percent Spec 20 transmittance, corresponding to 0.6
dimensionless concentration units). The program samples the
transmittance signal every four seconds, converts it to dimen
sionless concentration, implements the PID algorithm, and
plots the concentration, error, and valve position as functions
of time. (Full valve travel is 3200 steps, equivalent to 8 turns,
and the program limits the number of steps to 100 at each
iteration.) At any time during the 20 minute run (300 points
at 4 seconds per point) the students can change the set point
or the controller gains or the flow system configuration. At
the end of the run complete data on controller parameters, dye
concentration, and valve position are written to a spreadsheet
file for later plotting and analysis.
Step Response Mode
With the needle valve opened manually four turns, the
system is allowed to reach steady state, and 400 baseline
concentration points are acquired. Then the valve is manu
ally opened two more turns, and 400 additional points are
acquired. Subtracting the average baseline concentration
from the step transient produces the desired step response,
as shown in Figure 2.
MODELING AND PARAMETER ESTIMATION
The program used to acquire the impulse injection data also
computes the mean residence time, based on the equation
= ftCdt / Cdt (1)
0 0
where T is the mean residence time, C is effluent stream dye
concentration and t is time. If Q is the volumetric flow rate
Chemical Engineering Education
and V is the volume of the flow system, then
V=QT
Here the volume of the system is defined as the volume ac
cessible to dye and enclosed within boundaries outside of
which no dye can diffuse or move.
Since Q is known, the students can compare the calculated
value of V with the known volume, 290 ml for flow through
a single flask, and 870 ml for flow involving all three tanks.
Note that this analysis is not based on the assumption that the
flasks are well mixed, and in fact is not based on a model for
the flow system. But linearity of the system with respect to
dye concentration measurement, and that no dye can penetrate
upstream of the injection point, are assumed.
In contrast, if we have some information about the structure
of the flow system, we can attempt to estimate the value of one
or more parameters of a model of the system. Such a model
is shown in Figure 3. The model consists of three wellmixed
tanks, corresponding to the three flasks in the flow system, and
connected in the same way. The state variables of the model
are the concentrations (x1, x2, and x3) in the tanks, and the
measured variable is the dye concentration (x3) in the last tank.
The undetermined parameters of the model, to be estimated
by finding a leastsquares fit to the data, 41 are b1, the amount
of dye injected, b2, the overall flow rate, and b3, the flow rate
through the lower leg of the flow system.
The state equations of the model, used in the parameter
estimation step, are as follows:
dx /dt =(b2/V,)X, x, (0)= (b,/V,)(b2/b3) (3)
dx2/dt =(b/Vf)(x x),x,(0)=0 (4)
dx/dt = (b2/V)x2  (b/V)x3,
X3 (0) = (b, / V,)(b3 b2)/b3 (5)
Here x1, x2, and x3 are the dye concentrations in the three
flasks, Vf is the volume of each flask, b1 is the amount of dye
injected, b2 is the flow rate through the first two flasks and b3
is the total flow rate through the whole system.
The best (leastsquares) parameter values are determined
by a QuickBASIC program implementing a standard Gauss
Newton nonlinear regression algorithm.[41 The program
also computes the parameter correlation matrix and the
variancecovariance matrix and the confidence limits for the
estimated parameter values. Note that the amount of dye actu
ally injected is not known, while the total flow rate is known
and can be compared to the estimated value. Note also that
parameter b2,, the flow rate through the first two flasks, cannot
be measured directly with the existing apparatus, which illus
trates the power of using modeling and parameter estimation
methods for indirect measurement of quantities that cannot
be directly measured.
Vol. 43, No. 1, Winter 2009
RESULTS
(2) Impulse Response Runs
Figure 4 shows the concentration vs. time data, and also the
best fit based on the model, for an impulse response run in
which all the flow passes through a single flask only. Samples
were taken every 0.40 seconds. The data correspond closely to
the single exponential expected for impulse injection of tracer
into a wellmixed tank. The first few points (not shown or fit
ted) were close to zero, due to the plug flow in the connecting
tubing of the flow system. The concentration curve (solid line)
0 30
025
0 20
015
010
0o 05
0 00
0 05
0 20 40 60 80 100 120 140 160
TIME (s)
Figure 2. Shifted step response for threetank flow con
figuration, valve opened 800 steps from base position.
b3  b2
b3
1 b 2 x3
DYE
INJECTION
Figure 3. Schematic diagram of a model of the flow sys
tem. The parameters to be estimated are b,, the amount
of dye injected, b2, the flow rate through the first two
flasks and b3, the flow rate through the system. The state
variables are dye concentrations x,, x2, and x .
3.00
2.50  BEST FIT
2.00 DATA
1.50 ,
1.00
0.50
0.00
0 10 20 30 40 50 60
SAMPLE INDEX
Figure 4. The experimental concentration vs. time data
for an impulse injection run in which the lower ball valve
was closed, thus allowing the total flow to pass through
only one flask in series. Also shown, as a solid line, is the
best fit based on the model.
based on the model fits the data almost perfectly, and is also
an almost perfect exponential. Parameter b2, representing the
flow rate through the first two flasks, was less than 10% of
the total flow, but not the expected value of zero. Parameter
b , the total flow rate, was 956 ml/min, reasonably close to
0.8
0DATA
0.4
0.2
0 . B E S T F IT
0 50 100 150
SAMPLE INDEX
Figure 5. The experimental concentration vs. time data for
an impulse injection run in which the upper ball valve was
closed, thus allowing the total flow to pass through three
flasks in series. Also shown is the best fit based on the model.
1 20
1 00BEST FIT = SOLID LINE
1 00 DATA= SYMBOLS
080 
060
o 40
020
000
0 50 100 150
SAMPLE INDEX
Figure 6. The experimental concentration vs. time data
for an impulse injection run in which both ball valves
were open, thus allowing some water to flow through three
flasks in series, and the rest to pass through only the last
flask. Also shown is the best fit based on the model.
VALVE POSITION
ERROR X 100" '
0 200 400 600 800 1000 1200
TIME (s)
Figure 7. Error and valve position for PI control run, with
Kc = 5000 and TI = 30. Initially flow was through a single
tank and the error approached zero relatively rapidly. At
time = 400 seconds, the flow configuration was changed
to three tanks in series, the system became unstable, and
limit cycle oscillations resulted.
the measured value of 860 ml/min. These results reflect the
normal uncertainty associated with parameter estimates.
Figure 5 shows the concentration vs. time data for an im
pulse injection run in which all the flow passes through three
flasks in series, and shows also the best fit based on the model.
Note that the fit is quite good, but not perfect. The estimated
flow through the first two flasks is essentially equal to the
total flow rate, in accord with the physical situation. The
estimated system flow rate is reasonably close to the actual
flow rate, as expected.
Figure 6 shows the concentration vs. time data for an im
pulse response run in which the flow passes partly through
three flasks and partly through only one flask (parallel flow).
The initial shape is very close to the single exponential cor
responding to tracer injection into a single wellmixed vessel.
Later dye that has passed through the first two flasks appears
in, and increases, the spectrophotometer signal. The small
delay near time zero corresponds to plug flow in the tubing
that connects the flasks to each other and to the spectropho
tometer. The run duration was 290 seconds, during which
200 data points were acquired and processed. There is no
evidence of random behavior that might arise from turbulent
poorly mixed flow in the flasks, although such behavior does
appear at very low flow rates.
Figure 6 also shows the best fit based on the model. In general
the fit is quite good. The bestfit value of b1, representing the
amount of dye injected, could not be checked since the amount
of dye injected was not known. The value of b2, the flow rate
through the first two flasks, was 378 ml/min. The value of the
overall flow rate, namely b =780 ml/min, was reasonably close
to the measured value of 850 ml/min. The fair, but not perfect,
agreement illustrates for the students realistic aspects of the
power and limitations of modeling and parameter estimation
methods. The students see also how quantities such as the
lower leg flow rate, not directly measurable, can be estimated
by using a model and parameter estimation.
Pl Control Runs
A PI control run was made with gains Kc = 5000, T =
30, and TD = 0 and (initially) flow through a single flask.
As shown in Figure 7, the error exhibited a rapidly damped
oscillation in the first part of the run, corresponding to an
essentially stable system. (Note, however, a lowamplitude,
highfrequency valve oscillation, probably reflecting the
discretetime nature of the PID algorithm.) Following a flow
configuration change to three flasks in series, the system was
no longer stable, began an increasing oscillation, and rapidly
entered a largeamplitude, lowfrequency limit cycle in which
the valve position eventually reached its lower limit. This
behavior shows clearly the potentially destabilizing effect of
adding time lag to a feedback loop.
The fact that the system shows an oscillatory instability as
the gains are increased is consistent with a root locus analy
Chemical Engineering Education
3000
2500
2000
1500
1000
500
0
500
sis,11 based on a transfer function that corresponds to three
wellstirred tanks (not of equal volume) under PI control.
As an example of such a system we choose an openloop
transfer function
G (s)= K(s+0.5)/s(s+l)s+2)s+3) (6)
This transfer function corresponds to the schematic root locus
plot in Figure 8, which shows that the corresponding closed
loop system is stable for small positive gains K, exhibits an
exponentially decaying oscillation as the gain is increased,
and begins an exponentially increasing oscillation as the gain
increases beyond a critical value. This is in qualitative agree
ment with the observed behavior, except that nonlinearities
produce a limit cycle instead of an exponentially increasing
oscillation.
Controller Tuning
While the gain parameters for a system equipped with a
PID controller can be selected by trial and error, there are
welldeveloped methods for calculating values that are in
some sense optimal, or at least satisfactory. Perhaps the best
known methods are those of Ziegler and Nichols.2, 3]
In the openloop ZieglerNichols version, the response of
the system to a step change in the control variable is recorded
and used to calculate values for the gain Kc, the integral time
T, and the derivative time TD. These parameters appear in the
controller transfer function Gc as follows:
G (s)= K, + (1/TI)(1/s)+ TD (7)
A typical step response, corresponding to flow through three
tanks in series, is shown in Figure 2. This response was gen
erated by manually opening the control valve from 5 turns
to 7 turns, and then shifting the concentration origin to zero.
Based on the times corresponding to concentration increases
of 28.3% and 63.2% of the steady state change, namely 28
and 45 seconds, the PID parameters were calculated as Kc =
4771, T, = 38.8, and TD = 9.7.
The PID controller parameters determined by the openloop
ZieglerNichols method were used in a control run, with the
valve position and error as functions of time shown in Figure
9. The error, initially relatively large, rapidly returned to zero,
corresponding to quite good control. After 300 seconds, dye
solution was injected rapidly at the entry to the flow system.
This produced a rapid decrease in the error. The error then
became positive, followed by a rapid decrease to essentially
zero. At about 750 seconds a larger amount of dye was in
jected, with qualitatively similar results. In general this shows
that the ZieglerNichols openloop tuning method is, at least
in this case, quite effective. Very similar results were obtained
using controller parameters determined by the Ziegler Nich
ols closedloop method.
In the closedloop ZieglerNichols procedure, the con
troller involved proportional action only, with T1 = 10,000
Vol. 43, No. 1, Winter 2009
(which effectively removes any integral action) and TD = 0.
As shown in Figure 10, the gain Kc was initially 12,000 and
was later decreased to 9,000, at which point the error still
oscillated. Then Kc was decreased to 6,000, at which value
the oscillation disappeared. The ultimate gain was estimated
at 7,500, and the ultimate period was 110 seconds. Based
on these results the controller parameters were calculated
as Kc = 4500, T1 = 55, and TD = 13.75. We note that there is
reasonable agreement between the openloop and closedloop
Figure 8. Schematic root locus plot for a PI control sys
tem with open loop transfer function G(s) = K(s + 0.5)/s(s
+ 1)(s + 2)(s + 3).
03
02 
0 1
03 
0 2
o04 
0 200 400 600 800 1000 1200
TIME (s)
Figure 9. Error data for a PID control run with gains
Kc = 4771, Ti = 38.8 and TD = 9.7, corresponding to
ZieglerNichols openloop tuning. The flow configuration
was three tanks in series.
0.20
Kc = 12,000
0.10 ~ Kc = 9000
0.0 n A A A A\ ^ Kc = 6000
0.10
0.20
0.30
0.40
0 200 400 600 800 1000 1200
TIME (s)
Figure 10. Oscillatory behavior for the closedloop system
with three tanks in series, for proportional control with
Kc = 12,000, then 9,000, and finally 6,000.
ZieglerNichols procedure results. The openloop procedure,
however, requires only a single stepresponse run, while the
closedloop procedure requires a series of relatively long
oscillatory steadystate runs.
DISCUSSION
The process dynamics and control teaching experiment
described above is based on a relatively simple apparatus.
It illustrates two basic and important aspects of the subject,
namely the acquisition and processing of impulse response
data, and the operation and tuning of a feedback controller.
The impulse response data are analyzed using a nonlinear
regression method to determine three parameters of a model
of the flow system. In the control studies, the students use
both the openloop and closedloop Ziegler Nichols control
ler tuning procedures to estimate the parameters of the PID
controller. Then they observe the behavior of the system under
PID control using these parameter values.
The experiment allows the students to observe closely and
in detail the interactions of the actuator, plant, transducer, and
controller components of a singlevariable feedback control
system. In particular the opening and closing of the control
valve, the resulting changes in dye concentration in each of the
glass flasks, and the response of the concentration measuring
spectrophotometer are clearly visible. And the key internal
variables of the PID controller program, implemented in the
modem LabVIEW language, can also be followed as the sys
tem responds on a convenient time scale of tens of seconds.
This provides an optimal environment for students to develop
a practicalas opposed to purely theoreticalunderstanding
of a realistic feedback control system.
The experiment also embodies several more general and
relatively more sophisticated concepts, including the use of
modem data acquisition software (LabVIEW), and nonlinear
regression methods to estimate the parameters of a model of
the flow system. The students see how a dynamic model of a
flow system can be used in the estimation of several param
eters of a model, and see also that the parameter estimates are
subject to errors because the model rarely represents perfectly
the modeled system.
REFERENCES
1. Stephanopoulos, G., Chemical Process Control, An Introduction to
Theory and Practice, PrenticeHall, New Jersey (1984)
2. Smith, C.A., and A.B. Corripio, Principles and Practice of Automatic
Process Control, 2nd Ed., John Wiley and Sons, New York (1997)
3. Silva, C.M., P.E Lito, PS. Neves, and EA. Da Silva, "PID Controller
Settings Based On Transient Response Experiment," Chem. Eng. Ed.
42(2) (2008)
4. Raol, J.R., G. Girija, andJ. ....I. I4.,. / ... ..... Parameter Estimation
of Dynamic Systems, The Institution of Electrical Engineers, London
(2004) O
Chemical Engineering Education
MR classroom
  s___________________________________________
TAYLORARIS DISPERSION
An Explicit Example for Understanding Multiscale Analysis
via Volume Averaging
BRIAN D. WOOD
Oregon State University * Corvallis, OR 97330
The idea that the representation of a transport process
is dependent upon the lengthscale of observation
is a perspective that has become widely adopted in
chemical engineering education in recent decades; a graphi
cal presentation of a system in which multiscale transport is
important appears as Figure 1. Perhaps the clearest indication
of this evolution in perspective can be found in the recent
publication of the second edition of Transport Phenomena
by Bird, Stewart and Lightfoot. 21 Anew focus in this second
edition, as distinct from the first edition of 1960,3l] is the
multiscale structure of transport phenomena. This perspec
tive appears throughout that text, and in particular is empha
sized by the addition of a "Chapter 0"in which the connections
among the molecular, microscopic, and macroscopic scales are
discussed in the context of transport phenomena. It is becoming
standard practice to refer to the smaller and more fundamental
of the two scales involved as the "microscale" and the larger as
the "macroscale" regardless of the actual dimensions that define
the two scales, and this terminology will be used throughout the
remainder of this discussion.
The concept of upscaling transport phenomena in complex,
multiphase systems has been developed in the chemical
engineering discipline extensively over the last 40 years.
Although in principle this perspective is more fundamental
in the sense that phenomena at different characteristic length
scales are formally connected, the mathematical machinery
required to understand and apply the theory has tended to
keep it somewhat abstracted from applications.
New interest in the connection of transport phenomena
among scales has developed in chemical engineering, how
ever, (as evidenced, for example, by the second edition of
Bird, Stewart, and Lightfoot,i21 discussed above), driven partly
by the need to understand multiscale systems and partly by
evolving advances in experimental methods that allow mea
surements at small scales with unprecedented resolution. In
particular, developments in nano and microtechnology have
made it clear that a thorough understanding of the micro
macro connection in transport phenomena is essential for
understandingand ultimately engineeringsystems that
involve nano and microscale processes.
Vol. 43, No. 1, Winter 2009
Upscaling is possible and appropriate for systems that have
a significant amount of "redundant" information. Although the
concept of redundant information has a concrete definition in
the context of information theory (e.g., Reference 4), from a
pedagogical perspective we can think of redundant informa
tion as information that can be removed without affecting
Macroscale
(Reactor Scale)
Figure 1. An example of a multiscale hierarchical system.
Brian Woodreceived his Ph.D. in environmen
tal engineering at the University of California,
Davis. He is an associate professor in the
School of Chemical, Biological, and Environ
mental Engineering at Oregon State University
in Corvallis, Ore., where he teaches environ
mental engineering and maintains his research
program. His research interests include mass,
momentum, and energy transport; transport in
biological systems; upscaling in multiphase,
multiscale systems; stochastic methods; and
applied mathematics.
SCopyright ChE Division of ASEE 2009
the interpretabilily of the physical system. An example that
I frequently use to communicate the ideas behind upscaling
is that of the ideal gas. Viewed as a classical mechanical
system, a mole of an ideal gas has an enormous number of
degrees of freedom (6.02 X 1023 molecules times 3 position
and 3 momentum coordinates gives something like 5 X 1024
degrees of freedom!).
If, however, our goal is to predict the pressure of an ideal
gas in a fixed volume, then this constitutes a large amount of
redundant information. Essentially, because of the extremely
large numbers involved, the momentum and coordinates of
any particular molecule of gas are not important for determin
ing the pressure of the gas. Rather, the momentum coordinates
can be grouped as a distribution, and we can take a statistical
approach to computing the pressure of the gas. One can, in
fact, show (e.g., as explained by Feymnan, et al.P5]) that the
system of roughly 5 X 1024 equations
of motion (Newton's laws) for the ideal
gas can be "upscaled" via averaging to
the wellknown result PV=knT, where
k is the Boltzmann constant, n is the
number of molecules involved, and T
is the temperature. For this result to be
obtained one also has to make a number
of assumptions about the behavior of
the system, and for the purposes of this
paper I will refer to such assumptions as
"scaling laws." In the case of the ideal \
gas, one must adopt the scaling laws of
(1) a Maxwellian distribution of speeds
applies to the population of molecules,
and (2) the statistics do not depend on
spatial location (i.e., they are spatially
homogenous). Under these conditions,
.1 Spatially Avera
averaging appropriately yields the ideal Equations (Co
gas law, and the original 5 X 1024 degrees (NRM)
of freedom are replaced by a single degree
of freedomthe temperature T (which Upscaled l
is actually a proxy for the mean kinetic Figure 2. A gra
Figure 2. A grape
energy of the gas).
In Figure 2, a graphical
summary of the upscal
ing process is presented.
The essential features of B
upscaling are represented
here as follows. Complete
information for the system Influent A
of interest (e.g., the loca C
tion and momentum of all
molecules in the ideal gas
example) is represented Figure 3. An experimental d1
at the top of the figure, after Taylor." (A) The capilla
which we might think of The sampling window. (D) A t
as having, say, the number th
N degrees of freedom. We are always at liberty to separate
such a system into two components: a mean and a deviation
from the mean. Note that here there are still N degrees of
freedom; given one of these fields, the other can be obtained
by subtracting from the microscale (complete information)
representation. At this juncture, if redundant information can
be identified, it can be eliminated by upscaling (this requires
identifying a scaling law, which is nothing more than a state
ment about the assumed form of the redundant information).
In the example of the ideal gas, we found that the redundant
information was the list of velocity components and loca
tions. All that was really needed from this information (at
least for the purposes of deriving the ideal gas law) was the
two assumptions of velocity statistics that follow a Maxwell
distribution and spatial stationarity. The third row shows the
results of the upscaled model; a reduction in the number of
hical representation of information flow during the process of
upscaling.
EC Flow
D cA
vice used for examining dispersion of a visible dye in a tube,
ry tube. (B) A ground glass plate illuminated from behind. (C)
ube containing dye at known concentrations for comparison to
e experimentally observed values.
Chemical Engineering Education
degrees of freedom has been accomplished by the elimination
of the redundant information.
The purpose of this paper is to provide an example of up
scaling a multiscale system that has particular pedagogical
value. Most students of chemical engineering become famil
iar with the concept of dispersion, and some will even study
the specific example of TaylorAris dispersion in detail. The
methods used to perform upscaling, in contrast, tend to be
presented almost solely in advanced graduatelevel courses,
and even then there are generally few concrete examples in
which students can test the upscaling methods themselves in
a familiar context. The case of TaylorAris dispersion is an
example that is both familiar and one in which a closedform
analytical solution for the effective dispersion coefficient
can be developed without having to resort to the solution of
a complex, multidimensional partial differential equation.
The development also provides an opportunity to review the
concept of moving coordinate systems, which are always
problematic for students. The objective of this paper is to
present a concrete example of upscaling in a manner that is
suitable for undergraduate and graduate students alike, with
a particular emphasis on generating an analysis where the
assumptions and constraints are explicitly identified.
MICROSCALE FORMULATION OF THE PROBLEM
Background
TaylorAris dispersion has been studied for more than 50
years since the seminal works of Taylor[1, 61 and Aris, 71 in the
mid 1950s, and it continues to remain an archetypical example
for development of new dispersion theory. Partly because it
has been studied so extensively using a variety of mathemati
cal approaches, it also represents an example that has been
fraught with misunderstanding, even by established experts in
the field (e.g., see the exchange of Beard8, 9] and Dorfman and
Brenneri101). In principle, the concept of TaylorAris disper
sion is straightforward. Because the fluid velocity profile in a
capillary tube is parabolic (Figure 1), the fluid at the center of
the tube moves faster than that near the tube walls. This causes
an initially uniform pulse of solute to spread longitudinally
due to fluid convection, which forms strong concentration
gradients in the radial direction and allows radial diffusion
to transport solute across convective streamlines; as time
progresses, this tends to create a uniform concentration on
planes perpendicular to flow. The question addressed by Sir
Geoffrey Taylor (and amended later by Rutherford Aris�71)
was essentially this: If one observes the average concentra
tion in a capillary tube (using, for example, light transmission
of a visible tracer) then is it possible, through knowledge of
the microscale transport phenomena, to predict the effective
longitudinal dispersion coefficient that would be observed
for this averaged concentration? The answer to this question
is ultimately yes, and the analyses by Taylor[1, 6] and Aris 71
provide examples of those rare cases where a very satisfying,
Vol. 43, No. 1, Winter 2009
Developments in nano and micro
technology have made it clear that a
thorough understanding of the micromacro
connection in transport phenomena is
essential for understanding and ultimately
engineeringsystems that involve nano
and microscale processes.
compact result is possible. Taylor investigated this problem
both theoretically and experimentally; an illustration of
Taylor's experimental device is given in Figure 3.
Microscale Description
To begin the multiscale analysis, one first poses the mi
croscale mass balance equations describing solute transport
in a capillary tube. It is useful to recognize at this point that
the microscale equations can be, in principle, formally derived
by upscaling the molecular scale transport phenomena. At
the smallest length scale that we attempt to pursue, however,
we must ultimately adopt the laws governing the balance of
mass as axiomatic. That is, we must assume that the govern
ing laws are true (e.g., in the case of a classical molecular
description, that Hamiltonian dynamics are valid11) but are
fundamentally unprovable. This feature is true of all upscaling
efforts they relate information among scales provided that
one first has axiomatically defined the transport phenomena
at a more fundamental scale (i.e., the microscale).
For the case of transport in a capillary tube, we can pose
the following microscale boundaryinitial value problem for
the solute [see Reference 7, Eqs. (3)(6)]. A simplified ver
sion of Taylor's experimental system is presented in Figure
4, and the mathematical description of solute transport at the
microscale is specified as follows.
A =v _ . vc +V 'VcA),in the fluid phase (1)
at
n (. VcA) = 0 on the tube walls (2)
cA (x,t= 0)= (x), initial condition (3)
Here, cA is the concentration of chemical species A, 3 is
the isotropicc) molecular diffusion coefficient, and v is the
fluid velocity vector. Fick's law has been adopted here for
describing the diffusive flux, and this necessarily requires
that the mole fraction of species A, xA, be small enough such
that xA�<<. For the capillary tube, the velocity field is given
by the wellknown expression
r
v(r,x)= 2U 1 (4)
where U is the average velocity (to be defined later), and r
31
and x are the radial and longitudinal coordinates illustrated
in Figure 4.
Moving Coordinates
For the purposes of this analysis, it is convenient to put this
problem in an inertial coordinate system that moves uniformly
in the xdirection with the average velocity, U. In other words,
the relationship between the nonmoving longitudinal coordinate
z, and the moving longitudinal coordinate x(t) is given by
x(t) = zt + Ut (5)
amot of
current imntial movement
location location
Moving coordinate systems frequently confuse students, and
this is not without good reason. The presentation of moving
coordinate systems is frequently conducted by observation
rather than by showing the detailed conversion from one frame
of reference to another. For that reason, it is worth spending
some time on this concept in class. To start, one can explain
that Eq. (5) is the relationship between a point fixed in the
fluid at the initial time (t = 0) and where that point would be
located later if it were to flow with the fluid at the velocity U;
it is, essentially, the equation that describes a streamline for
the mean velocity field. Sometimes it is easier to think about
this in the reverse. In the moving coordinate system (Figure
4), any point x(t) is related to the point that it originally came
from (at the time t = 0), i.e.,
zt=0 x(t)Ut (6)
The velocity in the new frame of reference can be deter
mined with reference to Figure 5. Here, Z(t) represents the
vector following a fluid parcel in the original (fixed) frame of
reference. We can think of this vector as being broken up into
two parts: the vector that traces the distance to the new coordi
nate system, and the vector that gives the displacement relative
to the new coordinate system. In mathematical terms
r
r=a
r= o  
r\
Ut
z= 0 x0
Figure 4. Geometry of the TaylorAris capillary tube.
Figure 5. Relation
ship among coordi
nate systems. r\
Z(t)= X(t) +x(t) (7)
Taking the derivative of both sides of Eq. (7) and rearranging
terms gives the following relationship
dx(t) dZ(t) dx(t)
dt dt dt
or, substituting in the definitions for velocities
v ( x,r,t)= v(z,r,t) U (9)
For the particular case of interest, we are interested in steady
flow. Referring to Eq. (4), we can put the function describing
the velocity in the new frame of reference in the form
v x,r =2U 1 U
=U 1 2r2 (10)
a2
Simplifications
From these general balance equations, we can make some
substantial simplifications by making the following reasonable
assumptions: (1) the capillary tube is cylindrical, (2) the fluid
is incompressible, (3) the fluid pressure on the crosssectional
area of the two ends of the tube is uniform (which leads to
a cylindrically symmetric fluid velocity field), (4) the initial
condition for the solute is cylindrically symmetric so that
Bc /80=0, and (5) there is no diffusive flux discontinuity at
the center of the tube, so that a8cA/r=0 at r=0. Under these
conditions, we can rewrite Eqs. (1)(3) in term of a cylindrical
(but nonmoving) coordinate system (Figure 4) as follows
OcA 2U[1 rcA
Ot =2U1 2 OX
I CI 'I02C
02C.
'\
in the fluid phase
 cA = 0, atr=0 andr=a
A Or
cA (r,x,t=0) = 3r,x), initial condition
As a final step, we need to put these equations in the moving
frame of reference. To do this, we start by noting from Eq. (10)
2U 1  =U I +U (14)
a a2
Substituting this into Eq. (11) and rearranging gives us
OcA OCA
At u
9t Ox
U 2r2 OCA 1 CA 2CA 02CA
a2 O x r O r Or2 Ox2
in the fluid phase (15)
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As a final step, we note that by the definition of the total
derivative we have
dcA cA cA dx
dt Ot Ox dt
which, by Eq (5), gives
dc A CA OCA
dt Ot Ox
dt 9t 9x
Substituting this result into Eq. (15) yields the form of the
transport problem in the moving frame of reference
dCA
dt
Total De atve
(Moving Frame
ofreference)
_U I 2r2 OCA
a 2 x
Convection Term
with Moving Frame
of Reference Velocity
1 CA 02CA 02CA
Ar Or Or2 Ox2
Diffiion Term in
Moving Frame of Reference
Remains Unchanged
in the fluid phase
 'A Or =0, atr= 0 andr= a (19)
A Or
cA (r,x,t = 0)= (r,x), initial condition (20)
Note that this should be a familiar operationthis is exactly
what happens when one transforms a system into material
coordinates in the study of fluid mechanics. The derivative in
this case is a total derivative that is very similar to the mate
rial derivative that is used routinely in fluid mechanics; in our
case, however, the velocity is the average velocity rather than
the velocity of a material body, and therefore only the average
velocity is incorporated into the total derivative.
AVERAGING
Averaging arises naturally in our experimental observa
tions about systems, but we do not as often think about the
relationship to our theoretical representation of the system.
As an example, few would argue that Eqs. (18)(20) represent
a reasonable model for describing solute transport in a capil
lary tube. When we consider what is measurable for such a
system, however, the answer is generally not "the microscale
concentration, cA. "Although with substantial effort it may, in
fact, be possible to measure the microscale concentration di
rectly, generally we would measure some macroscale property
of the system, such as the fluxaveraged concentration coming
out of the capillary in the effluent, or possibly the spatially
averaged concentration resident within the tube at a particular
time and with a particular spatial resolution that depends on
the instrument used. Although we frequently measure averaged
or otherwise "filtered" properties in experimental systems, we
rarely think about them as such. The problem of Taylor disper
sion in a capillary tube is a cogent, specific example where this
micromacro duality is explicitly recognized, and a full analysis
of the interrelationship among scales is possible.
Vol. 43, No. 1, Winter 2009
y =  8/2 y = 0 y = 8/2
I I
  >
Figure 6. Integration domain for the averaging. Note that
the average is still a function of the location, x. A volume
average is well defined for each such location.
Ideally, then, we would like to develop a mass balance
equation where the dependent variable is related to the
quantity that we can actually measure. To this end, we can
consider averaging the microscale mass balance equations
using a weighting function that represents the influence of
our instrument used for observation (e.g., Reference 12).
At first, this may seem like a curious perspective, but upon
reflection one can recognize that this is actually more in line
with our interpretation of laboratory results than is the set of
microscale equations given by Eqs. (18)(20).
Definition of the Average
To begin, we define an appropriate average. In the most
general context, averages can be taken over any kind of
weighting function that represents an instrument response.
In applications of the volume averaging method in particu
lar, however, the weighting function is usually taken to be a
step function that is defined as being one inside an averaging
volume, and zero outside. For our capillary system, the ap
propriate average is defined by
I r=a I y=8/2
(CA = a2 f A , dy 2lrdr (21)
where y is a variable of integration. An illustration of the
integration domain is given in Figure 6.
A little discussion is warranted here. Note that this is dif
ferent from the area average that is conventionally used in the
TaylorAris analysis. In part, this is due to the idea that we
are attempting to generate an upscaled theory for a measur
able property of the system, for example, the light transmit
ted through a small volume of the capillary tube (as a proxy
for a dye tracer concentration) as Taylor did in his original
experiments (Figure 3). The area average is not the measure
able property, rather the average over some small observation
window is (e.g., as illustrated in Figure 3). We can, however,
33
imagine that when the concentration field does not have large gradients, and the thick
ness, 6, of the averaging volume is small we may be able to neglect the changes in the
concentration, cA, over the interval 6. This essentially converts our observation over a
small volumetric window to one that is equivalent to the area average. More formally,
we can do this by expanding the concentration in a Taylor series cA around the point
AOC
x+y x
1 02CA
2y x+
Substituting into the integral given by Eq (21)
<1 1 ra y/2 y= /2d2 y/2 * C2 dr
C x a 2 dyc x + y dy x 2 2dy Ox2 ... 2r dr
0 )=8/2 y= 2 x y= Ox
Note that the second integral in this expansion is identically zero. The third and higher
terms can be neglected under the conditions that the concentration change over the
distance 6 is small compared to the distance L. To see this, we can pose the following
restriction (see Reference 13)
Moving coordinate
systems frequently
confuse students, and
this is not without
good reason .... For
that reason, it is worth
spending some time
on this concept
in class.
y= d/2
f dyca
y/2 A1 2 02C
yf y 2 2
y 8x/
We can then make the following estimates
y=6/2
f dy=o(6)
y=8/2
y 2
y=6/2
f yydy= Oi3) (26)
0 2C
^ =01^ (27)
Combining these yields with the restriction given in Eq (24)
yields the constraint [See Reference (13)]
If the concentration field meets this condition, we expect
the first term in Eg. (23) to provide a good estimate of the
entire expansion. Under these conditions, the conventional
area average concentration can be recovered.
(A = f c (2r)dr (29)
7a 0
The practical result of this is that, for the purposes of the
upscaling effort, the conventionally adopted area average
is an acceptable average to use, and should be equivalent
to the concentrations found by observations of experi
mental systems provided that the constraint given by Eq.
(28) is met.
Upscaling
In the process of upscaling, simplifications are necessar
ily introduced if a useful theory is to be developed. This is
because a useful macroscale representation is only possible if
there is an underlying structure to the physics of the problem
that allows one to reduce the number of degrees of freedom
in the system without eliminating essential information. Ap
proximations that allow a reduction in the number of degrees
of freedom are called scaling laws. In the case of the Taylor
dispersion problem, one scaling law that we are assuming is
that the constraint given by Eq. (28) is valid. In other words,
we require that the concentration field be smooth enough so
that there are no large fluctuations on a length scale of 6; if
this condition is not met, the method may not work.
With the definition of the average identified, we can apply
the averaging operator to both sides of Eq. (18) (essentially,
this is done by multiplying both sides of the equation by 2jr,
and then integrating with respect to r from r = 0 to r = a).
The result is
dc/ u/1 2r2 OC
dt / a2 Ox/
\r O \r / \ cx2/
(30)
Noting that the averaging operator does not depend on x or t,
we can exchange averaging and differentiation with respect
to x and t.
For the second term on the righthand side of Eq. (30), we
can use integration by parts along with the two boundary
conditions to show
Chemical Engineering Education
c2 CA
0r2
ra Or
A1 CA(2r /r. CA(2
a Or 0 cf a rc
=  rCA (2r)dr
7a2 0r r
=_ 1 OCA
r Or
Combining these results gives a macroscale equation o
form
d(cA)
dt
U (cCA)
Ox
2 A 2U1 2 A
A OX2 2 \r
Except for the last term on the righthand side, this expre
is a macroscale balance equation for the average concentrate
(cA) . We can't simplify the last term as it stands becau
the presence of the multiplier r2 inside the averaging o
tor. To proceed further, we have to propose some metho
expressing (r2cA / OX in terms of the average conce
tion (cA ) rather than the microscale concentration, cA.
this, we define a concentration decomposition that relate
average and microscale concentrations as follows
CA(r,x) = (CA A (r, x)
with the average velocity; for this reason no convection term
arises here. Our remaining goal, then, is to determine how we
can obtain an expression of the form
:r
d(cA)
dt
a2 (CA
D A X2
Aef X2
(37)
where DA,eff defines the effective dispersion coefficient. To ac
complish this, we must find a way of 1 i . itth. pi 41b1k in so that
(31) terms involving only the average concentration, (CA ), appear.
f the CLOSURE
To complete the analysis, we need to find some method
of predicting the concentration deviation, c , in terms of
(32) the average concentration, (CA) . At first, this may seem
like a tall order: it is not clear at this point that there is any
reason to expect that we could express CA as some function
ssion involving (CA ). We will see, however, that this is a tractable
nation, task. To start, we need to develop a balance equation for the
se of concentration deviations.
pera
d for The decomposition given by Eq. (33) suggests a relationship
between the concentrations of the form
ntra
Fo do
es the
(33)
CA CA (CA)
and this suggests that a balance equation for CA can be ob
tained by subtracting the balance equation for (cA) from the
balance equation for cA. This is a straightforward operation,
where the quantity CA is called the concentration deviation
(from here on we will drop the explicit reference to the co
ordinates for all concentrations unless explicitly required). Using this in
Eq. (32) gives
d (cA)
dt
_U (cA) + CA) 2U (CA) 2U r2 \CA
Ox A OX2 2 Ox a2 2 x O
Finally, note that the average of r2 can be readily computed as foll
(r2 2  a 2 ( 2r
r a
2r4 r a2
4a2 r0 2
Combining this result with Eq (34) gives the simplelooking express
d(CA) = 2U 2 &CA
dt A x2 a2 x
Eq. (36) is starting to look like the spatially averaged equation that w
seeking. Recall that we put this analysis in a coordinate system that n
To start, one can explain that
Eq. (5) is the relationship
between a point fixed in the
(34) fluid at the initial time (t = 0)
ows and where that point would
be located later if it were
to flow with the fluid at the
(35) velocity U; it is, essentially,
the equation that describes
sion
a streamline for the mean
(36) velocity field. Sometimes it is
easier to think about this in
ve are
noves the reverse.
Vol. 43, No. 1, Winter 2009
and the result is
dcA 92 CA
dt A OX2
dcA _ 2C A
dt A OX2
U(1 2r2 OCA
U  21
a2 Ox
d (cA 20 (CA)
dt A Ox2
S2r2 1 OC
a2 Ox
1 OCA
Ar Or
2U /2 OA
a2 r Ox
1 OCA
Or
A 0 A
Or 2
A
Or2
2U(2 9C,
a 2 ( ArO
a2\ OX
The key ideas of the
TaylorAris analysis provide
a structure for understand
ing upscaling in many other
kinds of multiscale systems.
For the closure problem, we want a balance equation that in
volves only deviations and averages. Using the decomposition
given by Eq. (33) to eliminate the microscale concentration in
Eq. (39) and the boundary condition given by Eq. (2), we find
a complete description of the closure problem that predicts
the deviation concentration CA is given by
27 CA + _ar
A OX2 r Or Or
_2r 2 (CA)
a2 jOx
Source
A = 0, at r = 0 andr = a
A Or
CA (r,x,t =0) = ir,x), initial condition (42)
Note that in the development of this equation we have used the
fact that (cA) /r=0 (i.e., the average concentration depends
only upon x). In principle, this equation can be solved (using,
for example, Fourier transform methods) provided that the initial
conditions known. This would then provide us with an expression
that describes the time evolution of the deviation concentration.
From a practical perspective, it is useful to consider exam
ining the "long time" solution to Eqs. (40)(42), where the
effective dispersion coefficient is essentially a constant. To
begin the analysis of this approximation, suppose that the
source term has a characteristic time scale of T*. This implies
that the dominant time scale for 8 CA /t is also of order T*.
We can make the following estimates
dc Ac 4
A=0 (43)=
dt T
2 0 OrCA
r Or Or)
[ CA
12r2 2 0 UCA
a2 Ox L
2 CA = CA
02 O 2A L2
Note that the estimates in Eqs. (45) and (46) are identical.
We begin simplification by imposing the restriction
dA  r  (48)
dt r Or Or
and using our estimates, this translates into a constraint of
the form
We can think of the term on the lefthand side of this expres
sion as the relaxation time of CA due to diffusion, whereas
the righthand side indicates the timescale for changes in the
source term. This restriction indicates that diffusion must
relax any radial gradients relatively "quickly" compared
with changes in (cA) . Generally, this kind of relationship is
known as a quasisteady condition, and it is used frequently
in engineering analysis.
We can make two additional restrictions to simplify the
problem. Early on, we indicated that we expected radial dif
fusion to be "fast" relative to longitudinal convection. In the
closure problem, we can formalize this by the restriction
2r2 Oc I OCA1
U  A << r (50)
a2 Ox r Or Or
(44) and making orderofmagnitude estimates as we did above,
this yields a P6clet number constraint
Ua a
(45) i <<1 (51)
Chemical Engineering Education
2U 2 OCA
a2 ter
2U 2 OA
a2 O x
L
Note that this same constraint also allows us to drop the
nonlocal term on the righthand side of Eq. (40) since it is
of the same order of magnitude as the convection term that
we just dropped.
Finally, we expect radial diffusion to dominate over lon
gitudinal diffusion
02c
j2 A
A Ox
__A OX2
rTA OCA 1
r Or Or
Again using the estimates above, the associated constraint is
 <<1 (53)
L
When these three constraints are met, we can describe the
closure problem by
[r = UI 2r2 CA) (54)
r Or Or a2 ax
Oc
_' A = 0, atr=0 and r =a (55)
A Or
(CA)= 0 (56)
In Eq. (56), we have replaced the initial condition present
in the original problem with the constraint that the average
of the deviations must be identically zero. This is necessary
because when we adopt the quasisteady form the initial con
dition no longer enters the problem. Without some additional
constraint, however, there is no longer enough information
to solve the problem. The constraint that the average of the
deviations is zero is consistent with the original initial condi
tion, and allows the constants of integration in the solution to
be explicitly identified.
We have made substantial simplifications here, but the
benefits to these simplifications are (1) they were done in
a manner in which explicit constraints were developed that
indicate their domain of validity, and (2) the resulting balance
still captures the essential physics of the problem, but is now
significantly simpler to solve than the original problem. The
solution to this problem is straightforward, and two integra
tions give the result
Ua2 (CA) r2 r r4
A 4 _ Ox a2 2 a (57)
To determine the constant of integration, K, we use the con
straint imposed on the problem [Eq (56)]. Taking the average
of both sides of Eq (57) and using Eq (56) we find
1 Ua2 (CA (5)
K 3 (58)x
3 42 Ox
so that the final solution is
Ua2 O(CA)2 l r4 1
A 4A OX a2 2a4 3
The Macroscale Dispersion Coefficient
Recall that the unclosed macroscale transport equation that
we developed took the form
d(cA)
dt
2 A 2U 2 CA
A Ox2 + 2\r Ox
(59A)
where the second term on the righthand side represented the
influence of mechanical dispersion due to the nonuniform
flow field. Because we have determined the concentration
deviation field by Eq. (59), we are in a position to close the
macroscale equation. To do this, note that we will need the
derivative of the concentration deviation field
OCA Ua2 r2 1 r4 02(CA) (60)
Ox 4 a2 2 a4 3 x2
Substituting this into the macroscale transport equation above
and regrouping terms yields
d(cA)
dt
U2 r2 2 lr 2 4 02 A
A\r 2r 4 6/x (61)
S;\2a 2 4 a4 6 Ox2
Note that this now takes the form of a dispersion equation,
where the term multiplying the derivative on the righthand
side is the dispersion coefficient. It is straightforward to work
out the term in the angled brackets explicitly using the defini
tion of the average given by Eq (29). This result is
r [2 1 r4 1 (62)
2a2 4 4 a4 (62)
Finally, substituting this result into Eq (61) yields the classical
TaylorAris result
dt(CA)
dt
02 (CA)
DA ft O
A,ef X2
where
DA,eff A[ 48 A
As a final step, we can put this equation back into a fixed
frame of reference rather than one that moves with the mean
flow. Doing this essentially adds back the (mean) convection
term that we initially removed, and the final transport equation
takes the form of the convectiondispersion equation. Using
Eq. (17) we can easily convert our final expression back to
the fixed frame of reference, yielding a macroscale convec
tiondispersion equation of the form
Vol. 43, No. 1, Winter 2009
0(cA)
ot
U (cA) +E
Ox
02 (C A)
A, eff
Note that the interpretation of this new equation, unlike the
microscale equation that we started with, is that it describes
the concentration averaged over the cross section of the
tube. The microscale structure (geometry and flowfield) are
represented in this equation, but only indirectly through the
effective dispersion coefficient.
PERSPECTIVE
The essential ideas of the micromacro duality of multiscale
systems can be communicated to undergraduate and graduate
students alike through the example of TaylorAris dispersion.
Because of the simple geometry involved, this problem has
a macroscale transport equation that is intuitively appealing,
and the effective dispersion coefficient can be predicted in a
simple, closed form from an analysis of the microscale flow
and transport processes. The key ideas of the TaylorAris
analysis provide a structure for understanding upscaling in
many other kinds of multiscale systems. These key ideas can
be summarized as follows.
1. Many systems have a complex, multiscale structure that
would be infeasible or impossible to fully resolve at the
smallest scale of interest (the microscale).
2. For such systems, a macroscale description of the phe
nomena of interest is sought that applies at a scale that
is much larger than the microscale. Such a description
seeks to represent the unresolved microscale processes
in the system by a model. In this way, the net effect of the
microscale processes are captured, even if they are not
explicitly resolved.
3. Upscaling is a method of formally averaging the com
plete microscale description of a system in order to devel
op a valid macroscale representation. The goal in upscal
ing efforts is to make a connection between the microscale
and the macroscale that allows one to predict the effective
parameters that are developed for the macroscale trans
port equations. This is accomplished by breaking the
problem into two separate systems of transport equations:
(1) equations describing the transport of the average of
the quantities of interest, and (2) equations describing the
transport of the deviations from this average.
4. If we use the concept of numbers of degrees of freedom
of a system, then upscaling is the process by which the
number of degrees of freedom of the system is reduced
by il ..... ii ,,, redundant information. For upscaling to
be effective, there must be some identifiable structure or
regularity of the deviation quantities in the system that
leads to information that can be considered redundant.
A scaling law is a statement about the structure of the
deviations in the system that allows one to accomplish
this reduction in degrees of freedom. A few examples of
scaling laws include (1) smoothness conditions (such as
in the case of Taylor dispersion), (2) periodic geometric
structure (such as is done in many analyses of porous me
dia systems), and (3) statistically homogenous structure
(as is done in turbulence).
Often, when upscaling concepts are presented to students
who are unfamiliar with them, a "big picture" perspective is
missing. If this can be first communicated, and then followed
by a tractable example like the case of TaylorAris dispersion,
the concepts underlying upscaling become significantly more
tangible and much easier for students to understand.
ACKNOWLEDGMENTS
This material is based upon work supported by the National
Science Foundation under Grant No. 0449452. The author is
grateful for the input and perspectives provided by Professor
(Emeritus) Stephen Whitaker, University of California, Davis.
EJ. ValdesPareda is thanked for his editing assistance.
REFERENCES
1. Taylor, S.G., "Dispersion of Soluble Matter in Solvent Flowing Slowly
Through a Tube," Proc. Roy. Soc. London, 219, 186203 (1953)
2. Bird, R.B., W.E. Stewart, and E.N. Lightfoot, Transport Phenomena,
2nd Ed., Wiley, New York (2002)
3. Bird, R.B., W.E. Stewart, and E.N. Lightfoot, Transport Phenomena,
Wiley, New York (1960)
4. Beckman, P., Probabililty in Communication Theory, Harbrace Series
in Electrical Engineering, Harcourt, Brace, and World, Inc., New York
(1967)
5. Feynman, R.P, R.B. Leighton, and M.L. Sands, The Feynman Lec
tures on Physics, 2nd Ed. Vol. I., AddisonWesley, Redwood City, CA
(1963)
6. Taylor, G.I., "Conditions under which dispersion of a solute in a stream
of solvent can be used to measure molecular diffusion, "Proc. Roy. Soc.
(London, A) 235, 473477 (1954)
7. Aris, R., "On the dispersion of a solute in a fluid flowing through a
tube, "Proc. Roy. Soc. (London, A), 235, 6777 (1956)
8. Beard, D.A., "Taylor dispersion of a solute in a microfluidic channel,"
J. of Applied Physics, 89(8), 4667 (2001)
9. Beard, D.A., Response to "Comment on 'Taylor dispersion of a solute
in a microfluidic channel' " [J. Appl. Phys., 89, 4667 (2001)]; J. Applied
Physics, 90(12), 6555 (2001)
10. Dorfman, K., and H. Brenner, "Comment on 'Taylor dispersion of a
solute in a microfluidic channel' " [J. Appl. Phys., 89, 4667 (2001)];
J. Applied Physics, 90(12), 6553 (2001)
11. McQuarrie, D.A., Statistical Mechanics, Harper Collins, New York
(1976)
12. Baveye, P., and G. Sposito, "The operational significance of the con
tinuum hypothesis in the theory of water movement through soils and
aquifers," Water Resour. Res., 20, 521 (1984)
13. Whitaker, "Levels of simplification: the use of assumptions, restric
tions, and constraints in engineering analysis," Chem. Eng. Ed., 22,
104 (1988) O
Chemical Engineering Education
IMj11 unit operations '
COMBINED STEADYSTATE AND DYNAMIC
HEAT EXCHANGER EXPERIMENT
WILLIAM LUYBEN, KEMAL TUZLA, AND PAUL BADER
Lehigh University * Bethlehem, PA 18015
Dow Chemical Co. provided a pilotscale heattransfer
experiment to the Department of Chemical Engineer
ing at Lehigh University about 20 years ago. This
experiment has been an important fixture in our unit opera
tions laboratory since that time. Only steadystate experiments
and analysis were performed for most of this period. The
equipment has been modified recently to permit experiments
involving dynamic control studies.
The steadystate aspects of the experiment involve taking
flowrate, temperature, and pressure data so that energy bal
ances around each heat exchanger can be calculated. How
rates are measured by orifice plates and differential pressure
transmitters, but are also checked by the old reliable "bucket
and stop watch" method. There are duplicate temperature
measurements at some locations thermocouplee and dial
thermometer) to give the students an understanding of the
inherent discrepancy between different devices. Overall heat
transfer coefficients are calculated, and Wilson plots are made
to determine inside film coefficients at different processwater
flowrates. Experimental results are compared with the predic
tions of applicable correlations in the literature.
The dynamic aspects of the experiment involve dynamic
tests (step and relayfeedback) and closedloop control of two
process temperatures (process outlet temperature from the
heater and process outlet temperature from the cooler) by
manipulation of steam and cooling water flowrates, respec
� Copyright ChE Division of ASEE 2009
Vol. 43, No. 1, Winter 2009
lively. Computer simulations of the system are developed,
both steady state and dynamic, and results are compared with
experimental data.
William Luyben is a professor of chemi
cal engineering at Lehigh University. He
received his B.S. from Penn State and his
Ph.D. from the University of Delaware. He
teaches Unit Operations Laboratory, Pro
cess Control, and Plant Design courses.
His research interests include process
design and control, distillation, and energy
processes.
Kemal Tuzia is a professor of practice
and associate chair in the Department of
S Chemical Engineering at Lehigh University.
He received his B.S. and Ph.D. from the
Technical University of Istanbul. He teaches
Unit Operations Laboratory, Fluid Mechan
ics, and Heat Transfer courses. His research
interests include
heat transfer in
twophase flows
" and thermal en
ergy storage.
Paul Bader is senior electronics technician in
the Department of Chemical Engineering at
Lehigh University. His special interest is the
unit operations experiments. In the present
work he designed and implemented the con
trol loop for the heat exchanger experiment.
PROCESS DESCRIPTION
Figure 1 shows the flowsheet of the process. Figure 2 gives a
picture of the apparatus. Water from a tank (0.71 m ID, 1.2 m
height) is pumped by a 15 hp centrifugal pump to the heater, which
is a twopass tubeinshell heat exchanger with 0.542 m2 inside
heattransfer surface. Table 1 gives details of the heat exchanger
equipment. Material of construction is stainless steel.
Saturated steam at 3.36 bar from a steam header passes through a
pneumatically operated control valve (CV = 25, airtoopen, equal
percentage trim) into the shell side of the heater. Steam pressure in
the shell side of the heater is about 1.8 bars under typical steady
state conditions, which corresponds to a saturation temperature of
117 �C. Condensate leaves the heater as saturated liquid through
a steam trap. It goes to a threeway valve that permits bucketing
the condensate flowrate or discharging into a drain.
The process water then flows into the cooler, which is a 4pass
tubeinshell heat exchanger with 2.957 m2 of heattransfer area.
Cooling water from a supply header at 3.7 bars flows into the shell
side of the cooler. The temperature of the cooling water supply
is generally around 7 �C. After flowing through the cooler, the
cooling water passes through a pneumatically operated control
valve (CV = 9, airtoclose, equalpercentage trim) and goes
to a threeway valve that permits bucketing the coolingwater
flowrate or discharging into a drain. The process water then flows
through a control valve (CV = 12, air toclose, equalpercentage
trim) and back into the feed tank. Temperatures are measured
at numerous locations and are shown on the flowsheet given in
Figure 1. The three control valves are pneumatic, so the electronic
signals (4 to 20 mA) from the computer control system are fed
to three I/P transducers.
WILSON PLOT METHOD
In a tubeinshell heat exchanger, the overall heattransfer coef
ficient U is defined as follows.
   + Rfo
UA UoAo UA hA o
in I 0
D+RR +  (1)
27kL hoA0
where A and A0 represent inside and outside heattransfer surface
areas of a single tube, h and h0 are inside and outside film coef
ficients, Rf and Rf0 are inside and outside fouling resistances,
D and Do are inside and outside diameters of the tubes, k
is the thermal conductivity of the metal tube wall and L is
the tube length. Using the inside surface area of the tubes
as the basis,
U  h +A R +  Rfo
U h i 27kL fo
1
h0 A0
A1
figure z.
WilsonM1 suggested that experiments can be run to find a
relationship between the overall heattransfer coefficient
(U) and the film coefficient inside the tube (h). In these
experiments, the wall resistance, inside and outside foul
ing and outside film coefficient must be held constant, see
also Hewitt, et al.E21
If we call the sum of the second and the third terms on
the right hand side of Eq. (2) constant "A"
1 1
+A (3)
U1 hi
TABLE 1
Heat Exchanger Parameters
Heater Cooler
Number passes 2 4
Heattransfer area (inside) (m2) 0.542 2.957
Number of tubes 108 104
Tube ID (m) 0.00475 0.00775
Wall thickness (m) 0.0008 0.00089
Tube Length (m) 0.337 1.17
Shell ID (m) 0.105 0.206
Chemical Engineering Education
Where, A=A R + + Rf
* i 2TkL fo
1
o A
For fluid flowing inside tubes, h can be expressed as
Nu hD1  CRem Prn (4)
k
where C, m, and n are constants that depend on the fluid and
flow conditions. Thus, h can be expressed as,
hi k .C .pDJ mPrn (5)
Or, if we keep the properties of the fluid constant,
h =1
B
where  C.k fD .Prn (6)
Introducing this into Eq. (3) gives
I 1I
 =B +A (7)
U vm
Experiments can be carried out by keeping the operating param
eters in "A" and "B" constant while varying velocity of the flow
inside the tube. Measurements of overall heattransfer coefficients
then provide the values of the constants "A" and "B" if the pa
rameter m is known. The data presented here were obtained from
experiments that are carried out in the turbulent regime where m
= 0.8. The constant "C" in Eq. (4) can also be calculated.
To keep the operat
ing heattransfer pa
rameters constant on
the shell sides of both
heat exchangers, the
following conditions
are established:
* The temperature
driving force
(Ts Twai) on the
shell side of the
heater is kept con
stant in order to
have similar film
coefficients during
condensation of
the steam.
* Cooling water
flowrate on the
shell side of the
Vol. 43, No. 1, Winter 2009
cooler is kept at its maximum value in order to have a fixed
and a high film coefficient.
With the above conditions, the Wilson plot method can be
applied to the data to extract tubeside film coefficients from
the measured overall heattransfer coefficients over a range
of process water flowrates.
INSTRUMENTATION CALIBRATION AND
DATA RECONCILIATION
There are two different temperature sensors at every lo
cation where temperature is measured (thermocouples and
gauges). There are up to �2 �C differences between sensor
outputs. Therefore all sensors are calibrated based on a refer
ence temperature measurement device.
Flowrates are sensed using orifice plates and pressure
differences and are recorded using a computerbased data
acquisition system. Calibrations are carried out using the
bucket and stopwatch method.
Even with these calibrations, the inaccuracies in the ex
perimental data do not give perfect energy balances, so the
students learn that some engineering judgment is required to
reconcile the data. Temperature data is adjusted so that the
calculated energy balances on both sides of both exchangers
match perfectly.
EXPERIMENTAL DATA AND SAMPLE
CALCULATIONS
Experimental measurements consist of recording of the
following data:
* Process water inlet temperature to heater Tpl,,
* Process water outlet temperature from heaterT
* Process water outlet temperature from coolerT
* Saturation temperature of the condensing steam on the
TABLE 2
Experimental Data
Description of Parameters TP1 TP2 TP3 TP4 TP5 TP6
PW Inlet Temp. to 23.25 36.16 34.00 34.00 34.59 35.67
Heater (�C)
PW Outlet Temp. From 61.79 72.63 68.24 67.68 66.03 64.93
Heater ( C)
PW Outlet Temp. from 22.40 32.51 33.26 34.71 34.71 36.91
Cooler (�C)
Condensate temperature ( C) 118.23 120.55 118.89 121.67 120.55 120.55
CW Inlet Temp. to 6.79 7.8 7.22 6.7 7.22 7.22
Cooler ( C)
CW Outlet Temp. from 21.95 31.67 31.11 33.33 33.33 34.44
Cooler (�C)
PW Flow Rate (kg/s) 0.241 0.667 0.8275 0.953 1.0435 1.099
Steam Flow Rate (kg/s) 0.0207 0.0473 0.0482 0.0491 0.0498 0.0514
CW Flow Rate (kg/s) 1.1 1.1 1.1 1.1 1.1 1.1
shell side of the heater Ts
* Flow rate of the process waterF,,
* Flow rate of the steamFs
* Flow rate of the cooling waterF
Table 2 (previous page) gives raw experimental data for six
runs with varying processwater flowrates.
To illustrate the calculations and data reconciliation, we take
Run TP3 with a process water flowrate of 0.8275 kg/s.
A. Energy Balances
Under steadystate conditions, if there were no heat losses
in the system, the heat gained by the process water in the
heater would equal the heat lost by the process water in the
cooler. Likewise, the heat lost by the steam would be equal
to the heat gained by the process water, and the heat gained
by the cooling water would be equal to the heat lost by the
process water. Therefore, all four of the heattransfer rates
should be equal.
1. Heater:
The heattransfer rate is calculated on the processwater
side of the heater using Eq. (8) from the measurements of the
processwater flowrate and its inlet and outlet temperatures.
Q PWH
QPWH
FPWp TPWH,out  TWH,n) (8)
0.8275 (kg/s) 4.193 (kJ/kgK) (68.24 34.00) (�C)
= 118.8 kW
The heattransfer rate is calculated on the steam side of the
heater using Eq. (9) from the measurements of the condensate
flowrate, the supply pressure of the saturated steam and the
temperature of the saturated liquid condensate. The enthalpy
of the saturated vapor supply steam at 336 kPa is found in the
steam tables (2730 k.I k.' i. as is the enthalpy of the saturated
liquid condensate at 192 kPa and 119 �C (499 k.I kg, i. The heat
transferred from the condensing steam is found using
Qs = Fs (H supply  coH ndte ) (9:
Qs = 0.0482(kg/s) 2,730 (kJ/kg)  499 (kJ / kg)]
= 107.5kW
Note that these two heattransfer rates do not match per
fectly.
2. Cooler:
The heattransfer rate is calculated on the processwater side
of the cooler using Eq. (10) from the measurements of the
processwater flowrate and its inlet and outlet temperatures.
QPWC FWc (TPWC,ln  Twc,out ) (10)
QPwc = 0.8275 (kg/s) 4.194 (kJ/kgK) (68.24 33.26)(�C)
= 121.4 kW
Of course, Tpwcn is equal to TPWH,out.
The heattransfer rate is also calculated on the coolingwater
side of the cooler using Eq. (11) from the measurements of the
coolingwater flowrate and its inlet and outlet temperatures.
Qcw = Fcwc (Tcw,ou.t  Tcw,ln) (11)
Qcw =1.1 (kg/s) 4.193 (kJ/kgK) (31.117.22)(�C)
= 110.2 kW
The four heat duties are not exactly equal, which is an im
portant lesson for the students to learn and will always be the
case using experimental data. The maximum difference of
11.2 kW corresponds to a maximum error of 10%.
It should be noted that some data are more accurate than
others. The process water and cooling water flowrate mea
surements are more reliable than the measurement of steam
flowrate because there is some flashing of the condensate
even when an ice bucket is used to capture the condensate
leaving the steam trap.
Temperature differences between the inlet and outlet con
ditions are used in the heat duty calculations. The larger the
temperature difference, the more reliable the calculations. For
example, during experiment TP3 the process water is cooled
35.0 �C in the cooler, while the cooling water is heated only
23.9 �C.
As a result, among the four heat duties calculated above, the
two process water heat duties are the most reliable and should
be used in any other calculations for the experiment.
B. Calculation of Overall HeatTransfer Coefficients
1. Heater:
Since the steam condenses at a constant temperature, the
temperature driving forces at the ends of the heater are
(ATH2 = T  TPWH,ln =118.9  34.0 = 84.9 K
(ATH = T  TPWot =118.9 68.2 = 50.7 K (12)
) where Ts is the saturation temperature of the steam at the
pressure in the shell of the heater. The logmean temperature
driving force is then (see Figure 3):
TH (TH )I(ATH)2
ATH ln ( H)
66.3 K
The overall heattransfer coefficient is
U QPWH (14)
UH AH ATH
UH= 118.83 (kW) =3,306 W/K m2
H 05421 (m2) 66.3 (K)
There is no multiplepass correction factor because the steam
side temperature is constant.
Chemical Engineering Education
: 68.2 31.1= 37.1 K
=33.37.2=26.1 K
31.3 K
2. Cooler:
Similar calculations are carried out for the cooler. See Figure 3.
c Ac (AT) LMF
121.4 (kW) _
(2.957 m2 )(31.3�K)(0.96)
The 1shell pass/4tube pass correction factor F.orr = 0.96 is obtained from
Fig. 13.18a of Cengel. 3'
C. Velocities and Reynolds Numbers
The inside diameter of the tubes in the heater is 0.00475 m, and there are 54
tubes per pass. The velocity is
A CS,H = 54(7D2 /4) =0.0009569 m2
0.8275 (kg/s)
0.0009569 (m2) 987(kg/m3)
0.877 m/sec
The Reynolds number is
(Re)H DHVHP 0.00475 (m) 0.877(m/s) 987 (kg/mi3)
H 0.000552 (kg/ms)
The inside diameter of the tubes in the cooler is 0.00775 m, and there
tubes per pass. The velocity is
Acs, = 26(7D2 / 4) = 0.00123 m2
0.8275 (kg/s) 0.684 m/
vc = 0.684 m/s
0.00123 (m2) 987 (kg/m3)
The Reynolds number is
(Re), = D
It
0.00775 (m) 0.684(m/s) 987 (kg/m3)
0.000555 (kg/ms)
9,418
Wilson Plot for the Heater
Test Date: 3/19/07
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5
1/v08 (seco m0B)
Figure 4.
WILSON PLOT FOR HEATER
A. Inside Film Coefficients:
Experimental data for a range of process
water flowrates are evaluated in a similar
fashion as described above to calculate the
overall heattransfer coefficients and fluid
velocities inside the tubes of the heater as
well as the cooler. Results for critical param
eters are presented in Table 3.
Since all but one data point have Reynolds
(18) numbers much greater than 2100, these data
points are in the turbulent regime. Therefore,
the constant "m" for the power of Re is
assumed to be 0.8 according to the Dittus
(19) Boelter correlation. For heating the fluid,
again DittusBoelter suggests n=0.4 for the
are 26 power coefficient of the Pr.
With these coefficients in mind, the
Wilson plot for the heater data is shown in
Figure 4. Several observations can be made
from the Wilson plot.
(20)
* The five data points with high Re show
a linear trend. This confirms that
the power of Re is equal to 0.8, as
was assumed when,.. ,. ,, the
(21) Wilson plot.
* The point with the low Re (1865) shows
TABLE 3. Operating Parameters for the Heater
mpw Avg. Temp. Q PW Prandtl Velocity Re U
(kg/s) (�C) (kW)  (m/s)  (W m 2 K1)
0.241 42.5 38.9 4.20 0.252 1860 969
0.667 54.4 102.0 3.36 0.70 6330 2920
0.8275 51.1 118.8 3.56 0.877 7440 3300
0.953 50.8 134.6 3.58 1.009 8530 3570
1.044 50.3 137.6 3.62 1.105 9260 3670
1.099 50.3 134.8 3.62 1.164 9750 3590
Vol. 43, No. 1, Winter 2009
Heater
Cooler
Figure 3.
0.0010
0.0008
0.0006
0.0004
0.0002
0.0000
0.0000
( A T ) = TPWH,out  TCWn m
(AT c) = T  T
\ C^ PWH Cout CW out
(ATc ) LM
a lower overall heat transfer coefficient as expected.
* The regression line for the data points in the turbulent
regime intersects the ordinate at 1/U = 0.000127. Since
the ordinate is where the process water velocity is infinite
(infinitely large heat transfer coefficient inside the tube),
this value is equal to coefficient "A" of Eq. (3a). Assum
ing minimal level of fouling inside and outside of the tube
(R = Ro = 0.00003 m2 K W'), the shell side film coef
ficient is calculated from Eq. (3a) to be 23,000 W m2 K'.
* The slope of the regression line is equal to the coefficient
"B" in Eq. (7), which is used to calculate coefficient "C"
in Eq. (4), as C = 0.020. The final correlation for the
present experimental data is then:
hD
Nu = 1 = 0.020 Reo8 Pr04 (22)
k
Figures 5 and 6 compare experimentally found internal heat
transfer film coefficients to predictions by the DittusBoelter
correlation. Figure 5 shows this comparison in aNu/Prn vs. Re
plot, and Figure 6 compares heattransfer film coefficients. As
indicated in Eq. (22), experimental results are 15% less than
the predictions of the DittusBoelter correlation.
B. Repeatability:
The results of Wilson plot method are quite sensitive to
100
S1000 ^'^^
900     *
* PRESENT DATA
DITTUSBOELTER CORR
16000    
1000 1000C
Re
Figure 5.
^ 4000
1000 
,00
a 2000 10   40 60 0 7 0 0 100 
Figure 6.
the experimental uncertainty. This is illustrated in Figure 7,
which shows two Wilson plots from the same facility but using
data recorded on two different days. The circles are the data
presented in Figure 4. The triangles represent results of the
other experimental set of runs. It is seen that the two data sets
provide two lines with different slopes. The slopes of the two
data sets are 0.000158 and 0.0002, a difference of 25 %. This
difference will of course affect the film coefficients similarly.
This illustrates one of the problems with the Wilson plot
method. The long extrapolation of the data points to zero on
the abscissa makes the value of the intercept on the ordinate
quite sensitive to the accuracy of the data.
DYNAMICS AND CONTROL
The steadystate experiments described above are per
formed by manually positioning the three control valves.
In the control part of the experiment, two experimental
identification techniques are used to find important dynamic
features of the process: step testing and relayfeedback testing.
Transfer functions and frequency response plots are gener
ated from the experimental dynamic data. PI controllers are
designed, and their closedloop performances are evaluated
experimentally and compared with computer simulations of
the dynamic process.
0.0006
AI WF 5.=07 =.= 00200 +'0.C 00096
*4 W 31910
S0.0004
0.0002 = .0001 58 +  .0 01 27
0.0000
0.0 0.5 1.0
1Iv0 8 ( e 8 m0 B8
1.5 2.0
Figure 8.
Chemical Engineering Education
Figure 7.
One of the interesting control features of this experiment
is dependence of the dynamics on the flowrate of the process
water through the system. The higher the flow, the faster the
dynamic responses of both heat exchangers. Controller tuning
then depends on the process water flowrate.
A. Equipment and Control Structure:
Temperature and flowrate measurements are fed into a
computer using A/D converters. LabView software has been
developed that permits PI control with the three control valves
positioned by three D/A converters from the computer. The
steam valve is airtoopen, AO, so it will fail closed. The
cooling water and process water valves are airtoclose, AC,
so they will fail wide open.
The control structure is shown in Figure 8. There are three
control loops.
1. Processwater flowrate is controlled by j I'"l"in, the
processwater control valve.
2. The process temperature leaving the heater, T , is
controlled by 1,,i q ii.i, i, , the steam valve.
3. The process temperature leaving the cooler, TCOLD , is
controlled by 1,,i q *.,,i.ii , the cooling water valve.
A screen shot is given in Figure 9 showing the three control
ler faceplates on the left. Each has a manual/automatic switch
and displays for the setpoint (SP), the process variable (PV)
and the controller output (OP).
B. Flow Control of Process Water:
The standard tuning of a flow controller is Kc = 0.5 and
T = 0.3 minutes. The loop is quite fast since the flow transmit
ter and the valve respond quickly. Therefore a small integral
time can be used. The gain is kept small so that the noise of
the flow transmitter is not amplified.
Figure 9.
The process water valve is AC, so the flow controller should
have "direct" action (an increase in the flow transmitter signal
PV produces an increase in the controller output signal OP
to the valve, which reduces the opening of the valve). The
equation of a PI controller is:
OP=Bias+Kc E+ fEdt
Tl
E =SP PV (23)
A directacting controller should have a negative gain. Step
changes in the setpoint of the flow controller are made to
confirm that the tuning constants used give good flow control
performance.
C. Step Tests:
With both temperature controllers on manual, positive and
negative step changes in the heater exit temperature control
ler output signal to the steam valve are made to identify a
transfer function relating the controller OP signal to process
PV signal (T ho). See Figure 10.
From the dynamic step response, an approximate transfer
function of the form given in Eq. (24) is determined.
PV K eDs
G M)  P (24)
(sM ) s+l
where K is the process steadystate openloop gain, D is the
deadtime and T is the openloop time constant. The process gain
K must be dimensionless, so the change in temperature must be
divided by the temperature transmitter span (100 �C) to convert
the PV signal to percent of scale. The OP signal is in percent of
scale. The experimental data in Figure 10 show a deadtime of 0.2
minutes, a time constant of 1.1 minutes and a gain of 0.7.
The ultimate gain K. and ultimate frequency o. are calcu
lated from the transfer function using the relationships at the
66
 620_
I I
0 1 2 3 4 5 6 7
!o
50 
450 1 2 3 4 5 6 7
0 1 2 3 4 5 6 7
Time (min)
Figure 10.
Vol. 43, No. 1, Winter 2009
sC HOT m Gh
SP T41M %Ci*
S75 S.
U a 5I ?
o o: ao.0
2, i, ,.
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26.
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31 I
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03L31.40 O0 PM
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Figure 12.
Chemical Engineering Education
TCHOT I nbim 
SP PT THot %Out:
100  100'
W go 2s"
0 0* 0 
SP TCoald %outpt
lsSf UfiC im LOEDI
Figure 11.
OP
X]
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v.
ultimate frequency (o..
argGM(imo )=D0o arctan(o To)=Tr radians.
Kp
GM )I K To)
1 +W0)
The step test results predict an ultimate frequency of 8.4
radians/minute and an ultimate gain of 13.
D. RelayFeedback Test
The relayfeedback test is a very simple, fast, and practical
method for determining accurate information for tuning of feed
back controllers. It is widely used in industry and is also included
in commercial dynamic simulators to facilitate controller tuning.
The test gives values for the ultimate gain and period.
A highgain relay is inserted in the feedback loop that
switches the controller output signal a specified "h" percent
above or below the steadystate OP value as the PV signal
crosses the SP setpoint signal. The SP signal is adjusted so that
the signal to the control valve varies between the + h limits in
symmetrical pulses (approximately the same time at the low
limit as at the high limit). Figure 11 gives a screen shot of the
monitor when the relayfeedback test is running.
The amplitude "a" of PV temperature sinusoidal signal Thot
and the period P are read from a strip chart. The amplitude
a must be in % of scale, using a temperature transmitter span
of 100 �C. Note that h is also in percent of scale.
The ultimate gain and ultimate frequency from the experi
I 5a t SpMcsaB JLMTDF Dan U Meth I k
c "oponen 0=t s OD vF
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SB OA.. .o .
G OTASC
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4 streams Selectedocaicuanonmethod
fiEATER E ho eseic value
I setl S OPowerla,, xpres ilon
TF o pnry Excha geomeehy
e e n Uvs er subSroutne n
Figure 13A.
Vol. 43, No. 1, Winters S ns LMTD Pr Drop 2009ehods
Streams Setd ,cl on nlhod
HEATER 0 Phae specic values
o 5ihsi 0 Por la ,on
 HTFS+ Options 0 Ercharger geonelr
( HTFS+ Bowe, 0 Fir coefficients
'g eomIetry 0 Use, subroutine
n HolHcL..s
s old Hcaves Sa119 factor
Figure 13B.
Vol. 43, No. 1, Winter 2009
mental curves are calculated and compared with the values
obtained from the transfer function.
K =4h
Ku a7
Figure 11 shows a plot of typical data. The value of a is 0.6 %
with a 5% h, and the period is 0.7 minutes. The calculated ulti
mate gain is 10 and the ultimate period is 0.7 minutes, giving an
ultimate frequency of 9 radians/minute. These results are fairly
close to those determined from the step test data and are more
reliable because of the closedloop nature of the relayfeedback
test, which keeps the process in the linear region.
E. Closedloop Control
The TyreusLuyben tuning constants are calculated, and
their performance for disturbances in setpoints and process
water flowrate are observed.
TyreusLuyben:
K K 10
3.2 3.2
T,1 = 2.2P = 2.2(0.7)=
1.5 minutes
Figure 12 shows the closedloop step response of the THOT
temperature controller for a change in setpoint using TL tun
ing. The setpoint is changed from 67 �C to 68 �C (a 1% of
scale change). The OP signal jumps immediately from 33.3%
to 36.4% from the proportional action (Kc = 3.1). There is a
slight overshoot of the setpoint, and it takes about 3 minutes
for the loop to settle out.
The closedloop response of the system for load disturbances
is also explored by making changes in the flowrate of the
process water. Process nonlinearity is studied by seeing how
the dynamics of the process change at different process water
circulation rates. Time constants decrease as process water
flowrates increase.
COMPUTER SIMULATIONS
Our students use process simulation tools extensively in
their design course to develop process flowsheets and study
dynamic plantwide control. Applying these tools for the heat
exchanger experiment provides an important exercise in com
paring model predictions with real experimental data.
A. SteadyState Flowsheet Simulation:
A steadystate simulation of the twoheat exchanger and
feed tank system is developed in Aspen Plus. Equipment sizes,
operating conditions, and experimental heattransfer parameters
are used to match experimental steadystate conditions.
The HeatX unit is used in the Shortcut and Design modes.
The inlet conditions of the steam and the process water are
specified in the heater. In addition, the hot condensate stream
leaving the heater is specified to have a vapor fraction of zero,
as shown in Figure 13A. Figure 13B shows that the overall
heattransfer coefficient U is specified to be the experimen
47
tal value (3.3 kW m 2 K 1). The program then calculates the
required area, which is almost exactly the real heattransfer
area of the heater.
The specification for the cooler, besides the inlet condi
tions of the cooling water and the process water, is the exit
temperature of the process water, as shown in Figure 14.
The simulation is pressure driven, so pressures throughout
the process must be specified. The pump discharge pressure
is set at 5 atm in the simulation, and 1 atm pressure drops of
the process water through each heat exchanger are assumed.
The steam supply pressure is 3.3 atm with 1.5 atm in the
shell side of the heater. The cooling water supply pressure is
5 atm, and the pressure drop through the cooler is assumed
to be 1 atm. Since Aspen Plus does not permit the use of
anything other than directacting control valve with linear
trim, the steadystate positions of all control valves is set at
50% open in the simulation. Figure 15 gives the steadystate
w Q r Poper tEs Cal e cat n � Fo a'ws
* Ha"' TrITSC'
] MettarVAe1 orC B r
Figure 14.
S6OA,. i 'l ..l .. ... ' l l'
ruatm 500 400 0 0 . 30 150 500 403
,e. F TOOO 0000 o000 1000 0 O000 00
SoleFlow knoi% 1O rS1 0 16041 1156 11506 225w 228
SAiOB kg  2974355 2974,414 2974414 207288 207288 408000 46O&M
re oe Vn 50023 52087 50.008 1957.387 3.16 67,082 6.088
r Eh# py MM8tu' 44633 44186 44638 2596 3.044 61407 60955
4.Fiow kgAh
WATER 2971114 2971173 2971173 207288 207288 4068000 4068000
N2 3242 3242 3242
l4deFkW knalw
WATER 164922 164925 164.925 11.506 11.50 2258 22583
SN2 o116 o16 0.116
Figure 15.
Figure 16.
stream information. The Aspen Plus process flow diagram is
shown in Figure 16.
Note that a small nitrogen stream is fed into the feed tank
and a vapor stream is removed. This is a simulation gimmick
to account for the tank being open to the atmosphere.
B. Dynamics Simulation:
Before dynamics can be simulated, the volumes and
weight of metal in the various units must be specified. These
are calculated from the dimensions of the tubes and shell.
Figure 17 shows how these are specified in the simulation
by selecting the Dynamic item in the heater block. The file
is pressure checked and exported into Aspen Dynamics as a
pressuredriven simulation.
Figure 18 shows the initial process flow diagram generated
in Aspen Dynamics. Controllers are installed by opening
Libraries, Dynamic, and ControlModels in the Exploring
Simulation mode on the left side of the screen. A controller is
inserted on the flowsheet by clicking on PIDIncr and dragging
and dropping. Deadtimes are inserted in the same way.
The controllers are connected to the appropriate streams and
valves by opening Stream Types, dragging a ControlSignal
to the flowsheet and connecting its two ends to the appropri
ate spots. Figure 19 shows the TChot controller. It measures
the temperature of the process water leaving the heater. The
signal goes through a firstorder lag and a deadtime before
becoming the PV signal of the TChot temperature controller.
The controller output positions the steam valve.
Figure 20 shows the controller faceplate. The third button
from the right is clicked to open the window shown below the
faceplate. The controller action is set to be Reverse since an
increase in temperature should lower the OP signal. The dead
time in this loop is set at 0.1 minutes, and the lag time constant
is set at 0.4 minutes. These values give an ultimate gain and
frequency that match fairly closely the experimental values.
One of the unique features of the heater is the requirement
that the condensate leaving must be saturated liquid (a vapor
fraction of zero). In Aspen Dynamics, this condition is not the
default. Instead the
pressure is fixed. Of
course, this is not what
really happens. To in
vcw crease flow of steam
CWOUT 8
to the heater, the steam
OOLER "valve opens and the
pressure on the steam
side of the heater must
increase to provide a
higher temperature dif
ferential driving force.
Therefore, some modi
fications must be made
to simulate reality.
Chemical Engineering Education
0 Block: HETE METtX Dyai  Dat Browse
EO Input
9j Spec Groups
Ports
a Stream Results
I HEATER
� Setup
( Options
0 Hetran/Aerotrar
(I Hetran/Aerotrar
SGeometry
Hot Hcurves
A Cold Hcurves
S User Subroutine
m 0Bl Dynamic
S Block Options
A /Heat Exchangei ty /EEpe er tHeatTiansfei
Modeltype: D.C:ynrr..:
/TASC
iBrow
Hot and cold sides volume specification
Hot side
Inlet: 0001  c r, 0 1 001
0001 cur. 0 001 cum
0 ~ ~ ~ ~ ~ ~ ~~I Blc ETRIet)DnmcDt rwe
0 naw.
v MI b MET
0 Eo inp"t
S spec Groups
S Ports
S team Results
8 aj HEATER
is Setup
S Options
* HetruaAerotran/TAS(
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SGeometry
j HotHcurves
� Cold Hcurves
i user S9brouies
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19 M ock Options
�' 4 �<< All
v>> 0� 6 a N%
4Heat Exchange type /Equipment Heat Trane
Options
F[ ModeI eq,.mern hea capacy DC Model hea trandae with env.onent
E
Equipment heat capacity c/gcmn v
Hot e irt Hot ke oute C ide inle Cold
Equixnt mass 4 kg 4 kg 4 kg 4
<. ,>
A Top: Figure 17.
4 Left: Figure 18.
O Bottom left: Figure 19.
V Bottom right: Figure 20.
Vol. 43, No. 1, Winter 2009
Cotd side
cum
.,. < 4 ,, << . l
� > 0 a .*.
6Dynsim.:
 M I MET
"Tune"
PV= 340,
ieO I . WQ pfa s
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Test iingtw
Relay areoudeis 5F i Xouta d ge
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Ubnate2iJiid [ i ]__
S_ _tet' '** d
. ..... . ...... .. , . ., ..
* M
C A
, n _ _ ,_ _ _ _ _ _, _ _ _ _ , _ _, _ _ _ _ , _ _, _ _ _ _ ,_ _ _ _ _ _, _ _
.:; c  ;  ;  ;  ; {    I   ;; ;
S 0.0 001 0.02 0.03 0.04 005 0.06 0.07
Time Hours
I *ReadytolbesI
Experiment (Kc=3 1/taui=1 5) versus Simulation (Kc=3 3/taui=1 3)
Time (min)
These are achieved by using FlowsheetEquations. The heater block is
specified to have a hot stream leaving with a vapor fraction of zero.
Blocks("Heater ").Hotside.pflash2(1).vfr=0;
In addition, the pressure of the condensate stream "COND" is
changed from "fixed" to "free."
C. Dynamic Results:
Step changes are made by putting the controller on manual and
changing the OP signal. Relayfeedback tests are run by clicking the
Tune button on the controller faceplate (see Figure 21). The Closed
loop ATV test is selected. The simulation is run until a steady
state is obtained with the controller on automatic. Then the Start
test button is clicked, and the process is allowed to run through
several cycles, as shown in the strip chart in Figure 21. Clicking
the Finish test button generated the ultimate gain and period: K.
 10.2 and P = 0.60 minutes for the TChot controller.
U
Opening the Tuning parameters page tab, selecting
the type of controller and the tuning rule and clicking
the Calculate button produce the controller tuning con
stants. These settings are inserted into the controller by
clicking the Update controller button.
Figure 22 gives a direct comparison between the ex
perimental and simulation responses for a step change
in setpoint of 1 K. The dynamics of the heater are fairly
well predicted by the Aspen Dynamics simulation.
CONCLUSION
This paper has described an experiment that com
bines steadystate heat transfer analysis and dynamic
controllability. The heat transfer analysis includes data
reconciliation of redundant and conflicting temperature
measurements by checking energy balances on both
sides of the two heat exchangers. The Wilson plot
method is used to calculate tube side film coefficients
from the measured overall heat transfer coefficients.
Experimental dynamic data is obtained from step and
relayfeedback tests. Both steadystate conditions and
control performance are compared with the predictions
of a commercial process simulator.
REFERENCES
1. Wilson, E.E., "A basis for rational design of heat transfer ap
paratus," Trans. Am. Mech. Engrs., 37, 47 (1915)
2. Hewitt, G.E, Shires, G.L. and Polezhaev, Y.V., International
Encyclopedia of Heat & Mass Transfer, CRC Press, New York
(1997)
3. Cengel, Y.A., Heat Transfer, McGraw Hill, New York, (2003) 1
Chemical Engineering Education
> Right: Figure 21.
V Below: Figure 22.
snuaton  /    .  
 S ulation / 
... Experiment
0 1 2 3 4 5
MR classroom
  s___________________________________________
USING SIMULATION MODULE PCLAB
for Steady State Disturbance Sensitivity Analysis
in Process Control
EMAD ALI AND ARIMIYAWO IDRISS
King Saud University * Riyadh 11421, Saudi Arabia
Classical methods of teaching process control have
been practiced in the classroom over the past several
decades. These methods tend to focus on rigorous
solution of differential and/or transfer function equations.
The result is that students get caught up in mathematical algo
rithms rather than conceptualizing what happens in practice.
It became evident to academics and practitioners that the
way process control is taught to chemical engineers needs
updating. It is believed that the strict classical teaching ap
proach needs to be replaced by more practical and concrete
approach.El] To give students insights into the process control
courses they take, laboratory courses and simulation tutori
als were introduced in most chemical engineering curricula
as supplements. This, it was believed, would give students
insight and experience into the actual practice of chemical
engineering. This issue was raised and discussed by many
academic researchers and instructors and by practicing
engineers.1 8]
The introduction of simulation software has given students
an outlet to follow their imagination. Simulation packages
have caught up in all branches of engineering. This is because
simulators have now acted as mergers between theory and
practice that give students better understanding of processes
before they venture into industry. The visualization of the
process helps the student to form solid concepts on various
aspects of chemical engineering. [9 10]
Process simulation technology has evolved dramatically
over the past 10 years. Many packages are available that allow
intuitive visualization with a userfriendly graphical interface
that allows rapid control design using clickanddrag opera
tions. Rivera, et al.,11l1 uses modules incorporated directly in
process control computers. Young, et al.,[11 presented work
shops based on realtime simulation of industrial processes.
Henson and Z li.aig' i have integrated simulation experiments
based on HYSYS into the undergraduate process control
courses. Cooper, et al.,[9,10] introduced a training simulator
called Control Station. Other software packages for control
education include PICLES,[121 and ACS131; however, these
packages do not, in general, adequately handle large practical
scale problems.[141 Doyle, et al.,i151 have developed a process
control module (PCM) simulator based on a MATLAB/
SIMULINK environment that contains case studies illustrat
ing various process control concepts. Despite the benefits of
simulationbased experiments, one main criticism remains
the lack of physical process that can be felt by students. It is
argued, however, that training simulators can provide students
with a broad range of experiences at low cost and in a safe
environment. Moreover, students can achieve these experi
ences conveniently at their own desks.[9]
� Copyright ChE Division of ASEE 2009
Vol. 43, No. 1, Winter 2009
Emad Ali is a faculty member of the
Chemical Engineering Department at
King Saud University. He received his
Ph.D. from the University of Maryland,
College Park, in 1996. For the past 12
years he has been teaching process
control to undergraduate and graduate
students. His main research interest is in
the area of process modeling, identifica
tion, and control.
Arimiyawo Ibn Idriss is a research sci
entist with the Department of Chemical
Engineering in King Saud University.
Having graduated from King Fahd Uni
versity of Petroleum and Minerals with a
Masters in chemical engineering in 1989,
Mr. Idriss has taught the Process Control
Laboratory course for the past 10 years.
His current research interest is in plant
energy analysis and catalysis.
Process Control Laboratory (PCLAB) was developed in the
chemical engineering department at King Saud University
as an educational tool. General introduction of the tool is
given elsewhere.J161 The primary objective of this work is to
unveil one of PCLAB's specific featuresthe steady state
disturbance sensitivity analysis (SSDSA). 171 We focus on
SSDSA because it is a distinguishing contribution of PCLAB
and because its approach is found to be effective in designing
the control structure of multiloops control problems.[18, 19]
Specifically, SSDSA will be carried out on a forcedcirculation
evaporator process, which is one of PCLAB's case studies.
The purpose is to explore the disturbance effects on the output
and controlled parameters and to conclude from the analysis
which manipulated variable could be used to mitigate the
effect of the disturbances.
PCLAB
PCLAB is interactive simulation software for process con
trol analysis and training. It was developed using MATLAB
tools and functions including SIMULINK (a graphical simu
lation toolbox). MATLAB was chosen as the programming
platform because it became a standard among academic and
industrial users alike for use both in research and education.[141
Moreover, one can easily customize or add to existing modules
of MATLAB. The flexibility of this platform allows for migra
tion to many PC and workstation hardware platforms.[141 The
PCLAB software is designed in a userfriendly, menudriven
framework such that the process engineer can easily navigate
through the various parts of the program, carry out simulation
experiments, visualize the results, and draw conclusions on
the effects of different parameters and control configurations.
This is achieved by using the mainmenu shown in Figure
1 which provides a Graphical User Interface (developed in
the MATLAB graphics language). The software will run on
any platform supported by MATLAB (WIN 95, WIN NT,
UNIX). The software consists of several modules that com
prise different case studies based on fundamental process
models of industrial unit operations. The case studies of the
current version of PCLAB shown in Figure 1 include process
models adopted from the literature such as Forced Circulation
Evaporator,P201 Fluid catalytic Cracking Unit,[211 Double Effect
Evaporator,"22l and Two CSTRs in Series.[231 The case studies
also include process models that are developed and validated
by our research group such Polyethylene Reactor,E181 Ethylene
Dimerization Reactor,[191 and Multistage Flash Desalination
Plant.[241 The selected modules in addition to the convenient
visualization feature of the software provide the student
with realworld handson experience. PCLAB is available
for public use. Interested readers can download the program
from the following Web site:
Ali/Pages/PCLab.aspx.>
The main menu of the program, as shown in Figure 1, allows
the user to choose from different case studies. When a case
study is chosen from the main menu, the software will trigger
a submenu that contains the available exercises that can be
carried out on the chosen case study. The submenu, shown
in Figure 2, allows the user to select a specific tutorial from
a variety of exercises, such as steady state analysis, process
dynamic analysis, process identification, control structure
selection and controller tuning for SISO systems, and multiple
SISO loop tuning.
In this paper, we will discuss the SSDSA exercise applied
on the forcedcirculation evaporator case study to explore the
versatility of the current version of PCLAB software. Applica
tion procedure of SSDSA on other case studies is similar.
FORCEDCIRCULATION EVAPORATOR
The forcedcirculation evaporator is a common processing
unit in sugar mills, alumina production, and paper manu
facture. This process is used to concentrate dilute liquor by
evaporating its solvent (usually water), as shown in Figure
3.[20] A feed stream with solute of concentration C1 (mass
percentage) is mixed with high volumetric recycle flow rate
and fed to a vertical evaporator (heat exchanger). The solution
will pass through the tube. A saturated steam is used to heat
the mixture by condensing on the outer surface of the tubes.
The liquor, which passes up inside the tube, boils and then
passes to a separator vessel. In the separator, the liquid and
vapor are separated at constant temperature and pressure. The
liquid is recycled with some being drawn off as product with
solute concentration of C2. The vapor is usually condensed
with water and used as the coolant.
A description of the process parameters and their values are
given elsewhere. 211 For this process we deal with three inputs:
the coolant flow rate, F200; the steam pressure, P100; and
the steam flow rate, F100. Four disturbances are considered:
the feed flow, Fl; feed temperature, TI; feed concentration,
Cl; and the coolant temperature, T200. The process has four
outputs: liquid level, L2; output concentration, C2; Column
pressure, P2; and outlet flow rate, F2.
PROCESS ANALYSIS
In this section, we discuss how steady state disturbance
analysis can be implemented on PCLAB. This procedure is
very useful for designing the appropriate control structure. I81
When controlling a plant or a process with many inputs and
outputs, it is usually difficult to optimally pair variables into a
multi single loops structure. SSDSA is a tool that can help in
this regard, although it cannot be implemented on real plant.
Instead, simulation of the process can be used to perform
the task. Figure 2 illustrates that one can simply click on the
steady state disturbance analysis. As a result a new window
will pop up. The new window is an SSDSA interface module
for the evaporator case study as shown in Figure 4.
Figure 4 shows that the process has three inputs and four
Chemical Engineering Education
possible disturbances, as discussed earlier. The procedure
will focus on investigating the static effect of any disturbance
or any combination of disturbances on the process outputs
in open loop mode. This means that the inputs will remain
fixed during the test. This is known as the open loop test. It
reveals which process output is affected the most and which
one is affected in nonlinear fashion. The test can also be run
in closed loop mode. In this case, an output should be selected
SQuit Clear WorkSpace
Process Control Modules
Department of Chemical Engineering
King Saud University
Forced circulation evaporator
Polyethylene Reactor
Fluid Catalytic Cracking Unit
Ethylene Dimerization
Double Effect Evaporator
Two CSTR in Series
Multistage Flash Desalination
Help Menu
Figure 1. Main menu showing the main case studies.
Figure 2. Sub Menu for Evaporator Case Study showing
available control exercises.
as the controlled variable and a corresponding input should
be selected to be the manipulated variable. The test will then
examine the effectiveness of the chosen input to maintain the
controlled variable at its nominal value in steady state when
the process is under the influence of a range of disturbance
values.
To start the procedure, simply click on the green button or
the start button on Figure 4. By doing so, the SSDSA menu
F
FF4 Cooling
water
Separator c l Ear
Ploo FlT
F1 C1 T F2 2T2
Figure 3. Flow sheet of Forced circulation Evaporator
Process.
E1.4PORT4 OR PRO(E %
.j (NStpldy lPte Disbdatrb E nrL.lyray
Theouir.uL L.' Lt. P" F2
F200, (kg/min)
F10,(kg/min)
F1T Disturbance
C1, (%)
T200, (C)
Ready 100%   iodel
Figure 4. Steady State Disturbance Module
for Evaporator Process.
Vol. 43, No. 1, Winter 2009
Quit Clear Work Space
Evaporator Process Menu
Chemical Engineering Department
King Saud University
Evaporator
Singleloop Control  Evaporator
Feed Forward Control  Evaporator
Multiloop Control  Evaporator
Steady State Disturbance Analysis  Evaporator
Process Identification  Evaporator
Return to Mainmenu
Steady State Disturbance Analysis Parameters
Evaporator Process
1. Select Disturbance 1 I 'ir'i ..... .i i T. . F II(
' ,.. ,,. " ,: t..:,r ,   
P Feed Temperatua, C 
r Feed Coce o ,, . , . , ,  ,
SCoolant inlot Tem r o C . : 1 . ' "
5. Select Controlled O.put
(only if closed loop mode  .. F, I ,
is selected) _
F Lquid Lec e4
F Product ocNcation
r V ..l P....su
F Product FW talte 6. Final Step
When ready click the 'Run' button Run I
t,ng
King Saud Unversity, Chemical Engineering Department
Figure 5. SSDSA menu for the evaporator process.
illustrated in Figure 5 pops up:
The menu in Figure 5 allows the user to enter the key pa
rameters that controls the SSDSA analysis. Basically six steps
are required to carry out the SSDSA analysis procedure, as
discussed in the following two sections.
Open loop mode
First the user should select one of the four possible distur
bances by marking the appropriate checkbox shown on Figure
5, for instance, the feed temperature. (Note that the other case
studies of PCLAB will have a different list of disturbance
variables according to the relevant process.) Next, mark the
open loop checkbox. The third step controls the test range.
For example, if the nominal value for the feed temperature is
To = 40 C and using step size of 0.1 and number of steps of
10, then the disturbance value will have the following range
during the test:
Te T +(10/2) *o0.1 ,T (10/2) *o0.1T Eq.(1)
Increasing the number of steps at the same step size will in
crease the temperature range to be covered. The above values
for the step size and number of steps cover a �50 % range,
which is good enough from practice point of view. Decreas
ing the step size will help in producing smoother response
curves but it will decrease the overall range. Therefore, if one
decreases the step size for better resolution, one should also
increase the number of steps to maintain the same operating
range. It should be noted, however, that smaller step size
requires a higher computational load.
In the open loop mode, steps 4 and 5 are bypassed. (If by
mistake the user marks one of the boxes in step 4 or 5, an error
message will be displayed in the warning box.) Next, press the
run button and look at the results, shown in Figure 6.
Figure 6 illustrates how the four main process outputs
respond at steady state to changes in the feed temperature
from 20 to 60 C. The graphs shows the response of the liq
uid level at the top followed by concentration response, then
pressure response and finally the flow response to changes
in feed temperature. It is obvious that the liquid level in the
separator unit is not affected by this type of disturbance. Thus
in the open loop mode, the user can gain information about
the directional, magnitude, and nonlinearity effect of a distur
bance. For example, as a directional effect, both C2 and P2 will
increase when the feed temperature increases, while the outlet
flow rate F2 will decrease. One can also observe that the solute
concentration (C2) received the highest (magnitude) impact.
Moreover, all outputs are altered linearly with the temperature
variation. Thus, the user can learn how the process operation
and product quality may be significantly influenced when the
feed temperature is changing freely.
Closed loop mode
In this test mode, the student should unmark the open loop
checkbox and mark the closedloop checkbox instead. Further
more, there is a need to specify a controlled variable. Let us
choose, for example, the output concentration, C2. In addition,
the user should select one of the manipulated variables listed
in StepBox 4 as the candidate. Let the candidatemanipulated
variable be the coolant flow rate. See Figure 7 for example.
The user then has the choice to either change the upper and
lower permissible values for the candidatemanipulated vari
able or leave them at their default values. Note that the default
values for the upper and lower limit can be restored at any
time by simply clicking the "reset limit" button. It should be
noted that in this simulation mode no typical control system
is involved. The control objective, i.e., the output deviation
from its set point, is formulated as an algebraic constraint.
These constraints along with the model algebraic equations
are solved at steady state using the manipulated variables as
the design parameters.
After the user finishes marking the required checkboxes
in the SSDSA menu, he can simply click the run button in
StepBox 6. The result for the above specification is shown
in Figure 8.
By inspecting the output response in Figure 8a, one ob
serves that the controlled variable C2 is well maintained at the
nominal value. Not visible here, but on the computer screen,
a red color is used for the controlled variable to distinguish
it from the other uncontrolled outputs. Because the evapora
tor pressure is not controlled, it increases as expected with
disturbance but this time with a larger magnitude. On the
other hand, the feedback control caused the output flow rate
to change slightly with disturbance.
More important is the response of the manipulated variable.
In the righthand plot, Figure 8b, red lines would be seen,
showing the upper and lower limits for the coolant flow rate,
which is set at 400 and 100, respectively. A white line rep
resents the response of the coolant flow rate to disturbances,
Chemical Engineering Education
Figure 6. SSDSA results for open loop test showing the
effect of feed temperature.
Steady State Disturbance Analysis Parameters
Evaporator Process
1. Select Disturbance 2. Select Operation mode 3. Test Range
Select only one tem stp size
r FeedFlowrate, kg/min OpenLoop osedLoop step 0
F F~eed Tpe ue C o
4. Select manipulated varaibles & their limits
F Feed onceationt only if closed loop mode is selected) R mit It
F Coolant let Tenperature. C MV name upper Imit lower limit
F SteCoant F Rat 0 10o
5. Select Controlled Ottput
(only if closed loop mode F Steam Flow late [ rT15i
is selected)
r Liquid Level I I
W Produce Concetation
r Veel Pve F [t_
r ProduciFlowrate 6. Final Step
When ready click the 'Run' button Run
Warning
r
S King Saud Universty, Chemical Engineenng Department
Figure 7. SSDA menu for closed loop case option,
U : [3
Vol. 43, No. 1, Winter 2009
allowing the user to maintain C2 at nominal value. For large
disturbances, i.e., when the feed temperature exceeds 55 �C,
the coolant flow should be reduced slightly below the lower
limit in order to reject the effect of the disturbance. At feed
temperature below 30 �C, however, the coolant flow rate must
be increased multifold, especially below 25 �C, to maintain
the required operation. Low feed temperature requires higher
steam pressure to provide enough heat of vaporization, which
in turn increases the process temperature. As a result a large
amount of coolant flow is needed to absorb the extra heat and
to cool down the vapor. The high demand on coolant flow
may not be physically possible, however. Therefore, one can
conclude that the coolant flow rate is not a good manipulated
variable for negative disturbance in the feed temperature.
The user can also carry out a multivariable S SDSA. For ex
ample, one can add another controlled variable to the control
structure, such as the column pressure. For this case, the user
should consider a suitable manipulated variable, such as the
steam flow rate. Rerunning the SSDSA as before, we obtain
the results shown in Figures 9 and 10 (next page). Figure 9
shows clearly that the controlled variable and consequently the
remaining outputs are well maintained at their targets. (Note
that, onscreen, the controlled variables are distinguished by
the red color.) On the other hand, Figure 10 shows how the
selected manipulated variables change to counteract the ef
fect of the disturbance and ultimately regulate the output at
their set points. Notably, the first manipulated variable (e.g.,
coolant flow rate) has not changed, while the second manipu
lated variable (e.g., steam flow) decreased slightly as the feed
temperature increased. One can accept this control structure
because for a range of �50% changes in the disturbance, the
product concentration and column pressure are well regulated
with minimum change in the manipulated variable. Moreover,
this is achieved without violating the physical bound of the
manipulated variables.
Although Yi and Luyben[171 have used SSDSA for determin
ing basic control structure, its outcome can help in building
4 Figure 8. Output
responses to distur
bance in feed tem
perature when the
coolant flow rate is
used as manipulated
variable.
an appropriate inputoutput pairing. In fact, the user can test
various scenarios by examining other candidatemanipu
lated variable and by repeating the procedure for the other
controlled variables. At the end, the user can build up a sat
isfactory control structure for the process, i.e., can select the
appropriate inputoutput pairing configuration.
Similar studies can be carried out on the remaining dis
turbances and find their effects on the controlled parameter.
Furthermore the case study that was used here can be replaced
by another case study and similar SSDSA analysis can be
carried out.
CONCLUSION
In this paper, the process control laboratory PCLAB is
introduced. PCLAB is based on MATLAB platform and de
signed in a userfriendly environment by using a convenient
graphical interface. The current version of PCLAB thus far
includes seven modules (case studies) that reproduce basic
chemical processes. PCLAB has a number of control design
problems (exercises) that can be applied to each of the seven
case studies. One of the PCLAB exercises is the steady state
disturbance analysis. The exercise is illustrated through a
tutorial using the evaporator case study. The examples il
lustrate how the SSDSA can be carried out in either open
loop or closed loop mode without tedious programming. The
analysis helps in illustrating which disturbance has a detri
mental impact on the process. Furthermore, different control
structure configurations can be screened off line to determine
the most appropriate inputoutput pairing. In addition to this
exercise, there are other control projects that can be studied to
enhance student learning. These exercises can help students
to practice and visualize the theoretical concepts taught in
the classrooms.
REFERENCES
1. Young, B., D. Mahoney, and W Svrcek, "RealTime Computer Simula
tion Workshops for the Process Control Education of Undergraduate
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2. Henson, A.H., and Y. Zhang, "Integration of Commercial Dynamic
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3. Bequette, B.W., K.D. Schott, V. Prasad, V. Natarajan, and R.R. Rao
"Case Study Projects in an Undergraduate Process Control Course,"
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.,, in ,,'., I, .'1 .i ,,7 Control Education Studio, "in Proceedings of the
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5. Brisk, M., and R.B. Newell, "Current Issues and Future Directions
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7. Ramaker, B.L., H.K. Lau, and E. Hernandez, "Control Technology
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York, AIChE Symposium Series No. 316, 93, 17 (1997)
8. Downs, J.J. ,and J.E. Doss, "Present Status & Future needsA View
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Figure 9. SSDSA result for multivariable case,
output response.
File Edit View Insert Tools Desktop Window Help
I. , . �l[ . I .,i m, " ,  1F r 1` T 1 i, �
Figure 10. SSDSA result for multivariable case,
the input response.
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Control IV, Arkun, Y., and WH. Ray, (Eds.), AIChE., New York
(1991)
9. Cooper, D.J., and D. Dougherty, "Enhancing Process Control Education
with the Control Station Training Simulator," Computer Applications
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10. Cooper, D.J., D. Dougherty, and R. Rice, "Building Multivariable
Process Control Intuition Using Control Station," Chem. Eng. Ed.,
37,100 (2003)
11. Rivera, D., K. Jun, V. Sater, and M. Shetty, "Teaching Process Dy
namics and Control Using an IndustrialScale RealTime Computing
Environment," Comput. Appl. Eng. Ed., 4(3), 191 (1996)
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12. Cooper, D.J., "Picles: A simulator for teaching the realworld of process
control," Chem. Eng. Educ., 27, 176 (1993)
13. Koppel, L.B., and Sullivan, G.R., "Use of IBM's Advanced Control
System in Undergraduate Process Control Education," Chem. Eng.
Ed., 20, 70 (1986)
14. Doyle III, EJ., and E Kayihan, "Experiences Using MATLAB/Simu
link for Dynamic 'Realtime' Process Simulation in an Undergraduate
Process Control Course, "American Society for Engineering Education
Conference, Session 3613 (1998)
15. Doyle III, EJ., E. Gatzke, and R. Parker., Process Control Modules, A
Software Laboratory for Control Design, PrenticeHall, NJ (2000)
16. Ali, E., and A. Idriss, "An Overview of Simulation Module, PCLAB,
For Undergraduate Chemical Engineers in Process Control, "accepted
by Computer Applications in Eng. Ed (2008)
17. Yi, C., and W. Luyben, "Evaluation of PlantWide Control Structures
by Steady State Disturbance Sensitivity Analysis," Ind. Eng. Chem.
Res., 34, 2393 (1995)
18. Ali, E., K. AlHumaizi, and A. Ajbar, "Multivariable Control of a
Simulated Industrial GasPhase Polyethylene Reactor," Ind. Eng.
Chem. Res., 42, 2349 (2003)
19. Ali, E., and K. Alhumaizi, "Temperature Control of Ethylene to Bueten
1 Dimerization Reactor, "Ind. Eng. Chem. Res., 39, 1320 (2000)
20. Newell, R.B., and PL. Lee, Applied Process Control A Case Study,
Prentice Hall, Sydney (1989)
21. McFarlane, R.C., R.C. Reineman, J. Bartee, and C. Georgakis, "Dy
namic Simulator for a Model IV Fluid Catalytic Cracking Unit," Comp
Chem. Eng., 17, 275 (1993)
22. Daoutidis, P, and A. Kumar,  Ii.i,, l .11 i. .. and Output Feed
back Control of Nonlinear Multivariable Processes, "AIChE, 40, 647
(1994)
23. Cao, Y., and D. Biss, "An Extension of Singular Value Analysis for
Assessing Manipulated Variable Constraints, " J. Process Control, 6,
34(1996)
24. Ali, E., A. Ajbar, and K. Alhumaizi, "Robust Control of Industrial
Multi Stage Flash Desalination Processes," Desalination, 114, 289
(1997) 1
Vol. 43, No. 1, Winter 2009
MR! t classroom
  s_____________________________________
PROCESS SYSTEMS ENGINEERING
EDUCATION: LEARNING BY RESEARCH
A. ABBAS Ali Abbas received both his B.E. (chem)
University of Sydney * Australia and Ph.D. in chemical engineering from the
University of Sydney, Australia. He is currently
H.Y. ALHAMMADI a senior lecturer at the University of Sydney
S* and director of the Laboratory for Multiscale
University of Bahrain * Bahrain Systems. He held previous appointments as
J.A. ROMAGNOLI assistant professor of chemical engineering
at Nanyang Technological University and Uni
Louisiana State University * Baton Rouge, LA versity of New South Wales Asia, Singapore.
He has strong interests in teaching and learn
C chemical Engineering (ChE) education is a challeng ing research as well as research in modelling
ing task and is quite demanding for both teacher and and control of particulate processes. His
student. The teacher has to effectively convey subject engineering research is in the area of Process Systems Engineering.
student. The teacher has to effectively convey subject
matter while the student must continuously develop knowl Hasan Alhammadiis an assistant professor
edge and skill. In today's world, universities are becoming in the Department of Chemical Engineering,
University of Bahrain. He holds a Ph.D. in
more and more competitive grounds for the elite educators chemical engineering from the University of
serving students who are demanding concise higher educa Sydney (Australia) and an M.Sc. in process
S2Iintegration from UMIST (UK). His recent
tion.[1 2] In this setting, the teacher must respond to this de publications and research interests are in
mand by providing a suitable and effective environment for the areas of process systems engineering
learning. The broad question raised in this paper is "What (process integration and control and optimi
constitutes such an environment?" In trying to answer this, nation) and engineering education.
we must recognize that the learning process is a complex in
teraction between the teacher, the student, the subject matter, Jose Romagnoli received his Bachelor's
(chemical engineering) at Universidad Nacio
and the learning environment. We further recognize that the nal del Sur, Argentina, and Ph.D. (chemical
teacher and the student carry with them inherent education engineering) at the University of Minnesota.
He currently holds the Gordon A. and Mary
attributes that also affect the learning process regardless of Cain Endowed Chair at the Department of
the subject matter and the environment.[3, 4] In dealing with Chemical Engineering at Louisiana State
the question raised, we have come to realize the significance university. He is also the M. Gautreaux/Ethyl
the question raised, we have come to realize the significance Chair Professor at the same university and
of the concepts of "facilitating" knowledge, projectbased director of the Process Systems Engineering
learning, and generic attributes, to which we will first direct Laboratory. He was awarded the Centenary
Medal of Australia by the Prime Minister of
some attention before we discuss the question at hand in the Australia for contributions to the field of Chemical Engineering (2003).
context of Process Systems Engineering (PSE) education.
� Copyright ChE Division of ASEE 2009
58 Chemical Engineering Education
TO FACILITATE
Firstly, the notion of facilitator replacing teacher is wel
comed as a key ideological change in the mind of the educator.
Many academics recognize that learning is the responsibil
ity of the students as much as it is the responsibility of the
teacher, if not more.[51 In many institutions we are starting to
see the term teacher or lecturer being slowly phased out and
replaced by the term facilitator. This is simply because these
institutions see the teacher's role as that of a facilitator and a
mentor rather than as someone who solely teaches. This is one
aspect required for the creation of an effective environment
for learning. Being among those who advocate this shift, we
will use the word facilitator throughout the rest of this article
to refer to the academic teacher.
In the past, teaching could be represented by Figure 1(a),
which is a passive mode of instruction as practiced in the tra
ditional lecture room. Bombarding students with knowledge
during a lecture period does not achieve much learning nor
does it contribute adequately to graduate attribute develop
ment. Enhancing the learning experience calls for active
participation by the students in the subject matter. This is
illustrated in Figure 1 (b) by the activelearning model, where
teacherstudent interaction is promoted. A more advanced
learning model is illustrated in Figure 1(c)the interactive
model, in which studentteacher contact is extended to allow
for studenttostudent interaction on the subject matter. Many
educationalists advocate for this type of learning model, real
izing that students tend to learn more from their peers and
less from the teacher.
PROJECTBASED LEARNING
Secondly, effective learning is inevitably related to the
subject matter and to the degree the student enjoys the sub
ject content. Making the learning of the content a matter of
interest to the student becomes vital. One way of doing this
is to provide students with reallife examples.[6] The learn
ing activity is always made more interesting and appealing
when one can relate what is being taught to something from
previous knowledge or experience, or to a problem relevant
to real life. Problems and projects become important tools
to the facilitator who is able to focus the student's mind on
the ideas and concepts of the subject matter. Problem and
projectbased learning are great environments that allow
the embodiment of learned matter and thus promote deep
learning as opposed to surface learning.7 8] Thus, the con
(a) (b) (c)
Figure 1. Learning models: (a) passive, (b) active,
(c) interactive. (T) teacher, (S) student.
Vol. 43, No. 1, Winter 2009
text the subject matter is delivered in is what has impact on
student learning. For instance, if one of the course's learning
outcomes is to understand model predictive control (MPC),
we could have students read about the control technique and
then instruct them on how to tune the controller parameters.
As an alternative, we could challenge them to implement
MPC algorithm on a reallife dynamic process. Or we could
extend the learning to explore other dimensions influenced
by the control problem such as how the control solution to be
offered by the students impacts process operation, efficiency,
economics, or even the environment. It is argued here that
we should facilitate learning as exemplified in the third case,
where the subject matter (MPC control strategy) is better
and more completely comprehended by the students. This is
because the students' level of interest is elevated because they
relate to the problem and consequently delve into it beyond
its theoretical boundaries. The learning environment benefits
greatly from students' perceptions of the subject matter. The
context in which the problem is posed to students plays a key
part in achieving learning outcomes.[9]
GENERIC ATTRIBUTES
Thirdly, the facilitator also has to consider students' non
technical development, viz. generic attributes. In this way, the
facilitator is not only concerned with developing and extend
ing students' engineering knowledge and technical knowhow,
but also with imparting a set of generic attributes necessary for
postgraduation professional life. Three overarching attributes
have been identifieda scholarly attitude to knowledge and
understanding, global citizenship, and lifelong learning.[101
These are in turn represented by more specific attributes con
textualized differently in different disciplinary domains.
Students in the ChE undergraduate program are being
trained to become engineers with a certain set of skills and
knowledge, and so the course being delivered has certain aims
and learning outcomes.[11] Some of these outcomes directly
relate to learning the subject matter, while others relate to
student development. In this regard, the development of
graduate generic attributes is now well recognized as an es
sential learning outcome and many progressive universities
advocate developing them by imposing them in their academic
policies. The generic attributes set by a higher education in
stitution are a reflection of vision toward the development of
graduates. Generic attributes are usually treated differently
to subject matter and are typically found in university policy
documents. They are less commonly found within the course
outline documentwhich is usually stuffed with tides of con
tent matter and in the cases where they are found, they are
referred to by simple statements that students rarely relate to.
A key approach is to explicitly include the generic attributes
within the course so as to recognize from both the facilitator's
and students' ends that these attributes are partandparcel
of the learning in the course. Students will appreciate that
59
these attributes, when gained, will qualify them to progress
forward in their profession. So, what generic attributes do
you target and how do you manage their facilitation? We
identify four attributes that students should develop through
the PSE class:
1. Research and inquiry: Students will be able to cre
ate new knowledge and understanding . .h , /, the
process of research and inquiry.
2. Critical .h1di , Students should have certain
.h,,i ,,,, skills and exercise critical judgement. This
involves rigorous and independent .i,,,i ,, that has
logical and objective bases.
3. Communication: Students recognize and value com
munication as a tool for ,1 ,. 1.1,1,,, and,. ,*,, new
understanding, u.,t1,.i. i,,, with others, and further
ing their own learning.
4. Professionalism: Students hold personal values and
beliefs consistent with their role as responsible mem
bers of their engineering team.
The facilitation of these attributes in the course can be
achieved through use of key teaching tools. This is also very
much related to, and should be aligned with, assessment.
Table 1 lists assessment items as well as what attributes
these items target. Focusing on generic attributes stimulates
student learning because students perceive this as personal
development preparing them for the workforce. (This is our
conjecture and is yet to be proven.) Beyond being a natural
complement to learning, the development of generic attributes
has direct positive influence on comprehending the subject
matter. In the following sections, we discuss how we have
integrated the three abovementioned factors (i.e., facilita
tion, projectbased learning, and generic attributes) into the
teaching and learning of the PSE course. We first describe
the PSE course.
THE PSE COURSE
This course is offered to finalyear students as an elective
in the ChE degree program for the duration of one semester
(13 weeks). The main objective is to make students familiar
with strategies used by Process Systems Engineers in a team
environment. The course involves students in many aspects
of PSE and in a number of phases of process development,
TABLE 1
The Generic Attributes and Their Corresponding
Teaching Tools
Attribute Assessment Item
Research and inquiry Literature search and review
Critical thinking Problem analysis
Communication Report writing, panel discussion and
presentation
Professionalism Peer evaluation and feedback
including process conceptualization, fundamentals of pro
cess development, process integration, process modelling,
simulation, synthesis and design, optimization, control, and
operation.J121
This course, like the finalyear design project, may be
considered to be a capstone course in ChE, although the
PSE course integrates in a more concentrated way the vari
ous concepts and principles from the earlier PSE stream of
courses (ChE computation, process modelling, process con
trol, advanced process control). The course is designed as a
projectbased course and is dominated by activities aimed at
achieving a practical solution outcome.
The students encounter problems typical of those faced by
a practicing chemical engineer. These problems are carefully
selected from postgraduate research projects and are presented
to the students at the beginning of the semester in the format
of a manager assigning a project to a group of engineers. In
this format the problem is illdefined in the sense that insuf
ficient data and information are provided. Having the problem
very much openended makes the scenario like that of a real
work environment. Problems given do not have a solution to
begin with while any solution is the result of students' efforts
and output. Groups of three or four students are formed by
instructors to distribute intellectual strengths evenly. Groups
work together to achieve project milestones, which form the
assessment items to be graded.
The first milestone, a preliminary report based on a thor
ough literature review, is due at three weeks, after which the
students present a detailed problem definition and project
solution plan. A progress report due at the end of week 8 is the
second assessment task. It requires students to report back on
their advancement toward their solution, and whether changes
are needed in their initial plan. A final report submission at
the end of the course (week 13) is immediately followed by
a final presentation and discussion. Throughout the course
there is continuous review and feedback. Students are asked
to provide confidential feedback on their contributions as well
as their peers' within each group via the report submissions
and across groups via the presentation. This peer review is
used as guidance in the process of grading the students.
The coordination and facilitation of the course is illustrated
in Figure 2. Regular meetings with the project advisors
(postgraduate students) are scheduled on a weekly basis and
it is the responsibility of the students to arrange these. The
course tutors who are postgraduate students hold meetings
with the course coordinator as needed. In Figure 2, the typical
management hierarchy found in an engineering company is
put beside the PSE course organization chart to illustrate the
similarity to a reallife workforce environment.
The course emphasizes the concepts and tools used in
process engineering. Moreover, students are introduced to a
number of new topics in the field of PSE, including
Chemical Engineering Education
* Introduction to process systems engineering
* Costbenefits analysis
* Process  i..t. /,H , (steady state and dynamics)
* Process optimization (theory and applications)
* Advanced process control concepts
* Data management and process data reconciliation
* Process .,,11 ,,1 .. techniques
* Computer aided process engineering (CAPE) students
are introduced to typical commercial packages used by
process engineers
THE COURSE PROJECTS
In this section we report back on three projects previously
given to students in the course and describe them in some
detail.
Project 1. Model predictive control of a propylene
glycol reactor
Model predictive control (MPC) was implemented on a
dynamic HYSYS (Aspentech, USA) model of a propylene
reactor. The controller was designed and built in Excel. The
temperature of the reactor is controlled by manipulation of the
heat input to the reactor. An MPC graphical interface shown
in Figure 3 was developed in Excel and was connected to
HYSYS allowing realtime data transfer. The control of tem
perature by the MPC is compared to that of a conventional PID
controller to determine its control performance. The students
comprehended the advantages of MPC over PID control.
Project 2. Data Reconciliation in a VCM Plant
This project involved the application of data reconciliation
to a Vinyl Chloride Monomer (VCM) plant. In this study, mass
flow rate data from a fully measured and a partially measured
plant were reconciled. The VCM plant studied was modelled
in HYSYS. In developing a solution to the data reconciliation
problem, a number of software packages were used and a data
reconciliation interface developed (Figure 4, next page). The
linking of these packages and development of the interface
were also resolved. A solution for the detection of gross error
in sensor measurements was undertaken and a sample result is
shown in Figure 5 (p. 63). In the conclusion of the submitted
final report, this group of students stated:
"...the model is capable of,L i,. , ,. faulty sensors by the
use of a global error test. More importantly, the partially
measured case study has shown that a reduction in the
number of sensors from 35 to 24 is possible without any loss
in accuracy. This, of course, results in a significant drop
in the cost of the sensors if this model is used in an actual
VCM plant."
Figure 2 (left). PSE
Course organization
chart.
Figure 3 (below).
Model predictive
control of a propylene
glycol reactor. Left
side: Main graphical
interface. Right side:
propylene glycol
reactor HYSYS flow
sheet with control and
monitoring facilities.
Model Predictive Control . ..
Vol. 43, No. 1, Winter 2009
Management
Facilitator
(Course coordinator)
Postgraduate student Postgraduate student Postgraduate student Project supervisor
(Tutor) (Tutor) (Tutor)
Group Group Group
(Students) (Students) (Students) Engineering group
L
ExecInt Sp: L E ecint Sp L
User Interface
Controller
PID MPC
NumberoF Cent1ol I
Number of Mniplad vaakltes i
Number of Dstubance vanables
MPC
SMin Col Var No
Step Change
HYSYS Manual
Step Change Step Change
Implement MPC
PFD 1
I Default Colou Scheme 3
I H M PR N M .0 A P
Process Systems Engineering  Group 2
Data Reconciliation in a VCM Plant
Global Gross Error Detection
Reco Data  Gross Eor
FuyMeasuredl PFD Detetion
Cae
Reconciled Ua
PartiallyMeas ed Results
Case
R . .a Spit r * 
XI. 0h *Jhi ,t. h.1 on
Degrees of Freedom
(equals No MB equations)
Chi squared value
If h> chi value = GROSS ERROR
No Gross Error Detected: System OK.
Execute iSot ctuk
Iflc d l sA _
= 7 .2mS Me d Partiali IMsured
HoreiEs C e c
Figure 4. Data Reconciliation in a VCM Plant. Top left: Main graphical interface. Top right: Gross error
detection interface. Bottom: VCM plant linked flowsheet.
Project 3. Pinch Target Analyzer
In this project, the students developed a good understanding
of heat integration concepts and techniques and made use of
this knowledge to develop an interactive Excel spreadsheet
program that performs pinch analysis (Figure 6). The "Pinch
Target Analyzer," as this group of students named it, is a heat
integration software tool that integrates data extracted from a
process with the available utilities for optimum energy utili
zation and minimum utilities usage. It uses thermodynamic
pinch analysis as the basis for designing a heat exchanger
network where it employs three main concepts: the problem
table, the grand composite curve, and the pinch point. This
program takes the required data (streams and utilities informa
tion) either manually (by the user) or automatically (directly
from HYSYS flowsheet) to decide on the minimum amount
of utilities usage. It plots the grand composite curve and
the problem table, which shows the enthalpy of the process
streams as a function of temperature.
LEARNING AND OTHER OUTCOMES
The projects presented in the previous section are there for
illustrative purposes to provide the reader with a feel for the
kind of activities undertaken by students in this course. From
the result one could judge that in reaching the deliverables
presented here by the students, they would have had to become
competent in the necessary knowledge, knowhow, and soft
skills. It didn't take the students long to discover that what
they had embarked on in this course is not what was previ
ously experienced in the first years of their degree program.
Their solution to their project problems was a unique one and
was fashioned by their creativity. The main outcomes of this
course can be summarized as follow:
1. Positive interdependence and teamwork: Students
grasp the idea of team success when their individual
success depends on group's success. The groups are
instructed to involve all members and determine
the best way to use each member's talents. Students
Chemical Engineering Education
1.7263
19
10.9581
5~k to Coroe
L
L4>4j4rd '  "  n
learned how to get along with others, how to manage
their time, and how to integrate knowledge,1131 areas in
which they enhance their leadership and interpersonal
skills. Students are highly encouraged to be active in
the groups and continuous feedback is given to each
student.
2. Effective communication: Students worked...,. i, .
talked and listened to each other, and respected each
other. Good communication among group members
was enforced and students used other communica
tion tools such as emails and instant messaging. This
improved their level of .. ........... ii.,,, ideas via report
, ,,11, and oral presentation. 141
3. Ownership of learning and research: Students took
charge of their own learning, leading each other
toward a common goal. The realization that the learn
ing was their responsibility had a great impact on the
students, who found themselves in a new homework
scenario where they had to research to learn about
and solve a given problem, rather than relying on the
instructor to provide the relevant knowledge.",5 This
also raised their level of interest as it drew upon their
resourcefulness and creativity.
4. Individual accountability and personal responsibility:
Group members shared the work of the project and
individual accountability was evaluated based on the
corresponding sections of the submitted reports and
presentation. Students had enough flexibility to work
alone as well as.. .,, ti,, in the team.
5. Engineers not students: Students are treated as
professional engineers in an engineering consultancy
environment where they are responsible for discov
ering solutions for openended problems. Students
appreciated the complexities of reallife problems that
lack necessary data for solution.
6. Research at undergraduate level: Teaching strategies
such as peer teaching, collaborative learning, and
individualized learning increase student involvement
and comprehensionespecially so in a researchbased
learning environment.1`61 Moreover, students gain
research skills as they are asked to update their knowl
edge and techniques using journals and other sources
rather than being dependent on the textbooks.
STUDENT FEEDBACK, DISCUSSION, AND
FUTURE DIRECTIONS
Students in this course worked much harder than they
expected, learning how to do literature review and how to
complete a substantial writing project. Later, many students
expressed gratitude toward the course tutors since their ex
perience in the course made it much easier for them to do
and write their finalyear theses and complete the finalyear
design project and in one instance, find a job. Feedback was
collected at the end of the course during interview sessions
with all groups present. Other than administrative issues raised
by the students, positive feedback was prevalent. Students
indicated that this method of learning was new to them but
they found it useful in developing their skills. Students ap
preciated the research environment and the contact with the
postgraduate researchers. Many suggested that this type of
course administration should be delivered earlier in the degree
program. Some students suggested that more assistance be
given in the beginning of the course with learning certain tools
such as the simulation and modelling packages.
Some benefits of conducting the PSE course in this way
include learning by research. Research being conducted
by the academic and/or the postgraduate student would be
used as learning material at the undergraduate level. The
undergraduate student in turn learns by researching the topic
presented to him/her. The efforts of the undergraduate students
are harnessed and their research project output supports the
efforts of the postgraduate student in the first instance and the
facilitating academic in the second. This winwin situation
represents, in our opinion, a necessity in the teaching and
100000
90000
80000 so
70000
S60000 * Measured
50000
50000 * Reconciled
c 40000
o 30000 *
". 20000 , * *
10000 ,
0 *ee  
0 10 20 30 40
Stream Number
Figure 5. Case with two gross errors at streams 9 and 27.
Grand Composite Curve
250
200
0 150
0 
0 10 20 30 40 50
Heat Load (kW)
Figure 6. Pinch technology and energy conservation. Left: Main graphical interface. Right: Grand composite curve.
Vol. 43, No. 1, Winter 2009
Pinch Target Analyser
MANUALLY GRAND ,PROBLEM
T RUN COMPOSITE TABLE RESET
DATA I
Hot Cold Min. Mi. Hot Pinch Cold Pinch Pi.ch
AT stKmi l,,i, iW Oosl ltW , (C Tpmn. r ((�
5 2 4 0 10 2100 2
Hot streams Cold Streams
Stream N.mber Is C It Q(kW mCptk, C) Stream Nmber Ts (CC TtC OikW mCp kW0
1 174 162 20 167 1 56 82 15 058
2 215 198 22 1.29 2 24 38 13 0.93
learning of higher education; all stakeholders in the teach
ing and learning process are rewarded for their efforts. The
student benefits in gaining new knowledge and attributes,
the postgraduate student's efforts in guiding the students
provide him or her with help with the research, while the
whole exercise is profitable for the facilitating academic and
the research area. Effectively, in shifting toward this "learning
by research" model of teaching, we are optimizing the time
and resources available. Another benefit is the exposure of
the students to the research environment, which may entice
some to undertake postgraduate studies.
In this model of university teaching and learning, the owner
ship of learning is transferred directly to the student. To further
enhance this, at the beginning of the course the students could
be required to develop and sign a learning contract. The con
tract details the student's individual learning outcomes and
methods for achieving them.171 This kind of "ownership of
learning" requires students to plan their learning and develop
a path toward their desired outcomes, ultimately leading to
responsible deep learning that is individualised.
Intergroup interaction could be enhanced to provide more
stimulus and convey the interdisciplinary nature of reallife
engineering problems. For instance, the data reconciliation
project could have been integrated with the MPC project.
The purpose of data reconciliation is to eliminate random
errors from plant data so that accurate decisions and control
of a process can be made. By linking the two projects, the
importance of data reconciliation in an industrial control can
be further elucidated. The reconciled data would also help
the control group in the development and operation of their
control system. Integrating projects in this way poses several
challenges and should be considered after several iterations
of conducting the PSE course. A key challenge is to achieve
the desired learning outcomes when integrating projects. To
do this, the facilitator should refine the projects so they are
set at the appropriate skill level for the students, while ensur
ing the link between projects does not negatively affect the
progress of individual groups. For instance, the facilitator
should provide sample data to work with while one group is
waiting for data from another group.
CONCLUSIONS
A projectbased group learning approach in the PSE elec
tive course was presented, with emphasis on both technical
knowledge development and generic attributes. Students
found this learning environment stimulating, especially be
cause the assigned projects were derived from higherlevel,
real research problems and were challenging due to their
openended nature. The course organization was presented,
incorporating the academic supervisor and the postgraduate
students, further enriching the learning environment for the
PSE class. Three typical projects were described and corre
sponding student outputs were presented. These along with
students' feedback demonstrate a deep level of learning and
show the potential of this approach in PSE education.
REFERENCES
1. Varma, A., "Future directions in ChE education: A new path to glory,"
Chem. Eng. Educ., 37(4), 284 (2003)
2. Wankat, P., and F. Oreovicz, Teaching Engineering, McGrawHill
College (1992)
3. Burleson, W., "Developing creativity, motivational and selfactualiza
tion with learning systems," Int. J. HumComput. St., 63(45), 436
(2005)
4. Gillett, J., "Chemical Engineering education in the next century," Chem.
Eng. Technol., 24(6), 561 (2001)
5. Wankat, P., The Effective, Efficient Professor, Boston, Allyn & Bacon,
(2002)
6. Felder, R., and R. Brent, "Learning by Doing," Chem. Eng. Educ.,
37(4), 282 (2003)
7. Adams, R., J. Turns, and C. Atman, "Educating Effective Engineering
Designers: The Role of Reflective Practice, "Design Stud., 24(3), 275
(2003)
8. Felder, R., and R. Brent, "Cooperative Learning in Technical Courses:
Procedures, Pitfalls, and Payoffs," ERIC #ED377038,(1994)
9. Prince, M., "Does Active Learning Work?A Review of the Research,"
J. Eng. Educ., 93(3), 223 (2004)
10. Barrie, S., "Using conceptions of graduate attributes for researchled
systematic curriculum reform," 11th Improving Student Learning
Symposium, 1st  3rd September, Hinckley, UK (2003)
11. Scott, J., Tutoring in Engineering: A Survival Guide, Centre for Teach
ing and Learning, University of Sydney (1997).
12. Perkins, J., "Education in Process Systems Engineering: Past, Present,
and Future," Comput. Chem. Eng., 26(2), 283 (2002)
13. Oakley, B., R. Felder, R. Brent, and I. Elhajj, "Turning Student Groups
Into Effective Teams, "J. Student Centered Learn., 2(1), 9 (2004)
14. Whitehouse, T., B. Choy, J.A. Romagnoli, and G.W Barton, "Global
Chemical Engineering Education: Paradigms for Online Technology,"
Hydrocarb. Process., 80(4), 100B1001 (2001)
15. Favre, E., L. MarchalHeusler, M. Kind, "Chemical Product Engineer
ing: Research and Educational Challenges," Chem. Eng. Res. Des.,
80(1), 65 (2002)
16. Lucky, R., "Engineering Education and Industrial Research and Devel
opmentThe promise and Reality, "IEEE Communication Magazine,
Dec., 1622 (1990)
17. Anderson, G., D. Boud, and J. Sampson, Learning Contracts: A Practi
cal Guide, Routledge, London (1996) 1
Chemical Engineering Education
MR! t class and home problems
The object of this column is to enhance our readers' collections of interesting and novel prob
lems in chemical engineering. Problems of the type that can be used to motivate the student by
presenting a particular principle in class, or in a new light, or that can be assigned as a novel home
problem, are requested, as well as those that are more traditional in nature and that elucidate dif
ficult concepts. Manuscripts should not exceed 14 doublespaced pages and should be accompanied
by the originals of any figures or photographs. Please submit them to Professor James 0. Wilkes
(email: wilkes@umich.edu), Chemical Engineering Department, University of Michigan, Ann
Arbor, MI 481092136.
First Principles Modeling of the Performance of
A HYDROGENPEROXIDEDRIVEN
CHEMECAR
MARYAM FARHADI
University of Tarbiat Modares * Tehran, Iran
POOYA AZADI
University of Toronto * Toronto, Ontario, Canada
NIMA ZARINPANJEH
University of Tehran * Tehran, Iran
In this study, basic principles of thermodynamic, heat, and
momentum transfer,E1 3] are used along with the conserva
tions laws of mass and energy to simulate the transient
conditions of a reactiondriven car or socalled "ChemE
Car." ChemECar competitions are held in countries around
the world to improve teamwork skills of university students
in addition to providing them with a practical situation for
applying their theoretical knowledge. ChemECar is a shoe
boxsize car that should be able to carry a specific load within
a given range (i.e., 0 to 500 g) up to a precise distance within
a given range (i.e., 15 to 30 m).41] Typically, these ranges are
given to competitors a few months in advance, but the specific
values of load and distance will be announced on the compe
tition day. The closest car to the destination line will be the
winner. Teams are free to use any chemical reaction to drive
the car but they are not allowed to employ any mechanical
brake to stop the car at the desirable point. Therefore, the car
should be supplied with an accurate amount of fuel to stop
as closely as possible to the final destination line. The most
popular ChemECar engines are based on the production of a
pressurized gas by decomposition of a substance or by a reac
tion of an acid or base with a neutral salt. Also, combustion of
hydrocarbons and fuel cells are considered as other alternative
methods. Several trial runs should be performed prior to the
competition to identify the behavior of the constructed car.
Simulation of the system has some great advantages both in
the design stage and for decision making on the competition
day. In the design phase, the model can be used to obtain the
Maryam Farhad
1983. She receive
from Mahdavi hi
led economics a
Currently, she is
program between
Sweden and Tar
wIran. Her current
f uof mathematical
of insurance pre.
Pooya Azadi
was born in Teh
ran, Iran. He got a mathematical diploma
from Iranian High Intelligence Organization
in 2001. He received his bachelor's in Chem
ical Engineering from University of Tehran
in 2005 and his master's degree form Uni
versity of Toronto in 2007. Currently, he is
a Ph.D. student at the University of Toronto,
working on supercritical water gasification
of biomass under the supervision of Prof.
Ramin Farnood.
i was born in Babol, Iran, in
ed a mathematical diploma
lh school in 2001. She stud
!t the University of Isfahan.
a master's student at a joint
n the University of Lulea in
biat Modares University in
focus is on the development
models for the optimization
miums.
Nima Zarinpanjeh was born in Tehran,
Iran. He received a mathematical diploma
from Iranian High Intelligence Organization
in 2001. He joined the Department of Geo
informatics and surveying at the University
of Tehran and obtained his bachelor's and
master's degrees. Currently, he is a Ph.D.
student at the University of Tehran, working
on the applications of image analysis to
disaster management.
� Copyright ChE Division of ASEE 2009
Vol. 43, No. 1, Winter 2009
Figure 1.
Schematic of
the proposed
car: fuel tank
(A), reaction
chamber (B),
external load
vessel (C),
exit nozzle
(D), con
necting hose
(E), and fuel
valve (F).
L J
Figure 2. Absolute pressure vs. time for different initial
fuel weights.
maximum expected pressure, thus, the machine's vessel can
be constructed with a proper thickness. More importantly,
sensitivity analyses of the different potential engines and
vessel sizes would help determine a system that has the least
sensitivity to the fuel's weight. After setting up the machine,
the number of trial runs needed to identify the performance of
the system could be reduced through simulation, which saves
both experimental costs and time. Moreover, tuning the simu
lation parameters to the announced requirements right before
the competition helps to find out the corresponding amount of
the fuel. For example, the required traveling distance, load,
surface friction, and ambient temperature would be used as
the inputs of the simulation to obtain the weight of fuel that
should be loaded into the fuel tank.
PROPOSED CAR DESCRIPTION
The performance of a car based on the production of pres
surized oxygen from decomposition of hydrogen peroxide
will be discussed.
2H202 Ki 2H20 +02 (1)
E
F
D
<0
10 .
F= Ft +F +FF = m2 v2  mog+FF = moa
m2 = oxA2v2
The magnitude of the drag force, caused by the motion of the
car, can be calculated using Eq. (6).
F = A A p d (6)
Chemical Engineering Education
The proposed car consists of a fuel tank, a reaction chamber,
and an external load vessel (Figure 1). To maintain a uniform
pressure within the system, vessels are connected together by
means of a highpressure hose. The bottom vessel is equipped
with a nozzle at one end to let the oxygen exit the system at
a high speed. At the beginning of each run, fuel (hydrogen
peroxide 30%) is loaded into the fuel tank while the bottom
tank contains a little amount of dissolved catalyst (KI). The
reaction starts by opening the valve located between two ves
sels. Decomposition of hydrogen peroxide in the presence of
KI solution is an instantaneous exothermic reaction. [5] Due
to the short time of each run (~1 min), the heat dissipation to
the surroundings is assumed negligible.
The physical and chemical properties of H2O2 are obtained
from Reference 5, while Perry's Handbook of Chemical En
.. i,,. ,. 11 i.' was used for all other physical data.
MATHEMATICAL MODEL
To calculate the traveling distance of the car with given
specifications, differential displacements of the car should
be integrated over the range t = [0, co].
x = .Vdt (2)
0
Also, by definition, the time derivative of the instantaneous
velocity equals to the instantaneous acceleration.
a dv1 (3)
idt
There are three distinguishable steps in the movement of the
car throughout each run.
* First, when the pressure is inadequate to create enough
thrust force to overcome the static friction, the car re
mains stationary.
* Second, the pressure inside the chamber is high enough
to cause a positive resultant force while the fuel is still
being consumed.
* Third, from the maximum pressure time to the final
traveling it ,, i, In this step, due to friction, the car's
acceleration gradually becomes , ,.m . which finally
causes the car to stop.
0 20 40 60
Time (s)
80 100 120
Having a maximum velocity of about Im/s and a projected
area of about 20cm2, the maximum amount of the drag force
is calculated using Eq. (7):
1.293x1x0.02x0.30.004N (7)
Fd 0.004N (7)
Comparison of this value with typical values for the friction
force (~0.1 N), makes it apparent that the drag force is two
orders of magnitude smaller than the frictional forces, and
thereby can be neglected.
By substituting Eq. (5) into Eq. (4), it can be seen that
the car's acceleration is a function of oxygen velocity and
density. The density of oxygen is simply calculated from the
following equation.
n MW
S ox x (8)
To obtain the number of oxygen moles in the system, a com
ponent mass balance is used.
2
Pf3 = pfgL
2
m i=p f3A1 =pA,2gL
A dL
3dt
pf A1,2L
The variation of the depth of fuel in the fuel tank can be
obtained by integrating Eq. (16).
fL = A, F2g t (17)
2A3 (17)
L _ m(18)
Pf A3
By substituting the intermediate variables into Eq. (13), the
following expression that describes the variation of pressure
in the system is obtained.
dnox mi A2v2Pox
dt 2MWf MWx
(9) dP 42 P
( dt = + 2 3 2 5 6  t 2 8 9 2 10t
dt a +a ta t
The velocity of oxygen at the exit nozzle is calculated from
Bernoulli's equation.
2 4RT(PP) (10)
2 MW P(10)
Wox
Eq. (10) is used to eliminate v2 from Eqs. (4) and (9). Con
sidering the very fast rate of decomposition of hydrogen
peroxide in presence of KI catalyst, the reaction is assumed
to be instantaneous. Therefore, the temperature of the system
increases due to the heat of reaction.
mi AH
MWf
fimC dT
h c pc dt
Here, Cp is the weight average specific heat of the car's com
ponents and fh is the weight fraction of the car that is heated
due to the heat of reaction. Taking derivatives of both sides
of the ideal gas law equation with respect to time, it can be
shown that the variation of the inside pressure is due to the
simultaneous change in the total number of oxygen molecules
and temperature.
PV= noxRT (12)
dP RT dn noR dT
_  ox  (13)
dt V dt V dt
Equal pressures in the reaction chamber and the fuel tank cause
hydrogen peroxide to flow from the top tank to the reaction
chamber under gravity. One can calculate the flow rate using
Bernoulli's principle and a mass balance on the fuel tank.
Vol. 43, No. 1, Winter 2009
a11Pt 12
5 +a6t  t2 12
13t 14t2 15 16 17t2
P P P
Here, a to a are positive constants that depend on A , A2,
A3' Cp , AH, L0, MW,, MW ox, f, h, and To. The RungeKutta
method has been used to solve the differential equations.
RESULTS AND DISCUSSION
The pressure variation inside the system is independent of
the car's weight, traveled distance, and friction factor between
the wheels and the ground. Therefore, it is possible to analyze
the transient pressure of the system regardless of its weight,
position and friction factor (Figure 2).
Simulation results indicate that the maximum pressure
occurs around the moment when the fuel is completely con
sumed, and after this moment the pressure inside the chamber
starts to decline; this is because no more oxygen is generated
while the existing oxygen gradually exits the reaction chamber
from the exit nozzle.
After illustrating the variation of pressure with time, the
movement of a car with a given weight and friction can be
calculated using Eqs. (2) and (3). Expectedly, a great fraction
of fuel is consumed just to overcome the initial static friction
and to launch the car. After the initial movement, the travel
ing distance of the car is a strong function of the remaining
fuel. Also, simulation demonstrates that the fuel is completely
consumed before the car stops. In other words, after passing
a specific time, the driving force (produced oxygen) is inad
67
0 20 40 60 80
Time (s)
Figure 3. Distance vs. time for different initial fuel
weights, weight of car =750g, p=0.01, To=300 K.
0 20 40 60 80
Time (s)
Figure 4. Distance vs. time for different initial fuel
weights, weight of car =1 kg car, p=0.01, To=300 K.
0 20 40 60 80 100
Time (s)
Figure 5. Distance vs. time for different initial fuel
weights, weight of car = 1.25 kg, p=0.01, To=300 K.
Al Area of fuel supply pipe
A2 Area of the exit nozzle
A3 Area of the fuel tank
a. Acceleration of car
A Cross section area of the car
C Average specific heat of car
F Net force
Cd Drag coefficient
Fd Drag force
fh Mass fraction of car that is
heated by the reaction
Ft Thrust force
F Friction force
g Gravity
AH Heat of reaction
L Depth of fuel
L0 Initial depth of fuel
mi Fuel mass flow rate
m2
m
mf
MWf
MWx
nox
P
p
Oxygen mass flow rate
Overall mass of car
Initial mass of fuel
Molecular weight of fuel
Molecular weight of oxygen
Number of oxygen moles
Pressure inside the car
Atmospheric pressure
m2
m2
m2
m/s2
m2
J/ kg. K
N
N
N
N
m/s2
J/mol
m
m
kg/s
kg/s
kg
kg
kg/mol
kg/mol
mol
Pa
Pa
Chemical Engineering Education
equate to overcome the resistance force (dynamic friction
force), which slows down the speed and finally causes the
car to stop. (See Figures 35.)
To have a more clear picture of the car's performance over
the possible ranges of weight, fuel and distance, the contours
of isodistance lines are created using the contour generator in
MATLAB (Figures 6 and 7). These figures, or similar figures
that are generated and calibrated before the competition, can
help determine the appropriate amount of fuel to meet the
competition requirements.
SUMMARY
The performance of a hydrogenperoxidedriven Chem
ECar was studied using basic engineering principles. The
simulation showed that the car stops a few seconds after
the occurrence of the maximum pressure inside the system.
Also, a noticeable fraction of fuel is consumed to overcome
the static friction and, after the very first movement, a little
amount of fuel can keep the car moving. In other words, the
ultimate traveled distance of the car is very sensitive to the
weight of the remaining fuel right after the initial movement.
Finally, contours of isodistance lines are presented for a
given friction coefficient and ambient temperature. One can
use the same technique to obtain the corresponding contours
for different initial conditions. Results are useful for both
design purpose and decision making on the day of ChemE
Car competition.
NOMENCLATURE
Rate of heat generation
Time
Temperature
Initial temperature
Total volume of the fuel tank
and reaction chamber
Velocity of the car
Velocity of oxygen
Velocity of fuel
Traveled distance
Friction coefficient
Density of fuel
Density of oxygen
Density of air
REFERENCES
m/s
m/s
m/s
m
kg/m3
kg/m3
kg/m3
1. Welty, J., C.E. Wicks, R.E. Wilson, and G.L. Rorrer, Fundamentals
of Momentum, Heat, and Mass Transfer, 4th Ed., John Wiley & Sons
(2001)
2. Holman, J.P, Heat Transfer, 8th Ed., McGrawHill (1997)
3. Basmadjian, D., and R. Farnood, Art of Modeling in Science and En
gineering With Mathematica, 2nd Ed., Chapman & Hall/CRC (2007)
4.
Rules_2007.pdf>
5.
6. Perry, R.H., and D.W. Green, Perry's Handbook of Chemical Engineer
ing, 7th Ed., McGrawHill (1997) [
200 . .. .. ..... . ... ..
Weight of car (kg)
140 .. . . ... .  .    .   
20 m:
30m 25m m:
80
10 ...     m .
60                 
15m
40     
0.75 080 0.85 0.90 0.95 1.00 1.05 1 10 1.15 1.20 1.25
Weight of car (kg)
Figure 6. Contours of
isodistance lines, p=0.01,
To=300 K.
Figure 7. Contours of iso
distance lines, p=0.005,
To=300 K.
Vol. 43, No. 1, Winter 2009
Ln=1 curriculum
TEACHING CHEMICAL ENGINEERING
THERMODYNAMICS AT THREE LEVELS
Experience from the Technical University of Denmark
GEORGIOS M. KONTOGEORGIS, MICHAEL L. MICHELSEN, AND KARSTEN H. CLEMENT
Technical University of Denmark * Lyngby, Denmark
According to the socalled "Bologna model," many
technical universities in Europe have divided their
degree programs into separate 3year Bachelor's
and 2year Master's programs (followed by an optional
Ph.D. study). Following the Bologna model, the Technical
University of Denmark (DTU) has recently transformed its
5year engineering program into a 3year Bachelor (B.Sc.)
and a 2year Master's (M.Sc.) program. Master's graduates
that are interested and have achieved a good grade average
are then in principle qualified for a 3year Ph.D. In addition to
the above, DTU has a 3.5year industrial Bachelor's program
("diplom" or B.Eng.), which directly qualifies its graduates
for an industrial career. In all of these programs there are
studies in applied chemistry and chemical engineering. Four
different courses on chemical engineering thermodynamics
are provided at the four levels mentioned above, thus satisfy
ing the different needs of these programs. This manuscript
discusses the different roles, context, teaching objectives, and
educational methods used in the various courses. Examples
are provided for all courses, with emphasis on the different
types of exercises used. Finally, the suitability of thermody
namics textbooks for these courses is also discussed.
WHY 4 COURSES IN THERMODYNAMICS?
An evident question is why so many different courses
are needed in "applied chemical engineering (technical)
thermodynamics." The necessity for the four courses in
thermodynamics will hopefully become apparent from the
brief description of their characteristics, illustrated in Tables
13, and the description of their similarities and differences
� Copyright ChE Division of ASEE 2009
provided hereafter. In the discussion below, we follow the
notation used in Table 1 for the courses, i.e., A for the B.Eng.,
B for the B.Sc., C for the M.Sc., and D for the Ph.D course.
An important "common" characteristic of the four courses
is that they all focus on aspects of thermodynamics that are
of interest to chemical engineers. This characteristic dif
ferentiates them from more fundamental physical chemistry
Georgios Kontogeorgis is a professor in the
Department of Chemical and Biochemical En
gineering at DTU, Denmark. He is a graduate
of the Technical University of Athens (Greece)
and has a Ph.D. from DTU. His teaching and
research interests are thermodynamics, colloid
and surface chemistry, and chemical product
design. He is the
study coordinator of
the M.Sc. program
"Advanced and Ap
plied Chemistry."
Michael L. Michelsen is a professor in the
Department of Chemical and Biochemical
Engineering, DTU. His main interests are math
ematical models and numerical model solution,
in particular the calculation of phase equilib
rium. He is the coauthor of the books Solution
of Differential Equation Models by Polynomial
Approximation and Thermodynamic Models;
Fundamentals and Computational Aspects.
Karsten Clement is a professorin the Depart
ment of Chemical and Biochemical Engineer
ing at DTU, Denmark. He graduated from DTU
in 1976 and obtained his Ph.D. (in control
engineering) from DTUin 1980. He is director
of Study Programme, B.Eng. (Chemical and
Biochemical Engineering Programme) and
teaches thermodynamics, process control,
and unit operations.
Chemical Engineering Education
TABLE 1
Four Degree Programs and Four Courses in Thermodynamics at DTU
Degree Program Course Name Suggested Semester
A. B.Eng. (industrial B.Sc.) Chemical Engineering Thermodynamics 3
B. B.Sc. Chemical Engineering Thermodynamics 46
C. M.Sc. Phase Equilibrium for Separation Processes > 7
D. Ph.D. Thermodynamic Models: Fundamentals and Computational Aspects 
TABLE 2
Comparison of Important Characteristics of the Four
Thermodynamic Courses
Course/Program Basic Objectives Teaching Methods Evaluation
A. B.Eng. Estimation of physicalchemical properties for Lectures Oral exam + projects
pure compounds and mixtures for use in chemical Excel spreadsheets
processes
B. B.Sc. Application of physical chemistry to solution of Short lectures Three projects on well
practical, industrial problems Excel spreadsheets using defined problems
predeveloped modules that the
students use and combine to simu
late larger units and processes
C. M.Sc. Presentation of thermodynamic models and Lectures One project at the end
theories for a wide range of fluid mixtures ranging Classroom exercises of the course based on
from hydrocarbons and chemicals (and at both Available software with various research articles
low and high pressures) to associating fluids, models
polymers, and electrolytes
D. Ph.D. Fundamentals of thermodynamics, and how to Lectures Final project requiring
program and debug fast and efficient computer Writing own programs writing own Fortran code
codes for thermodynamic models and for a variety
of advanced computational methods
TABLE 3
The Course Context of the Four Courses
Course Course Context (in general lines)
B.Eng. Equations of state for estimating properties (pure fluids and mixtures) including residual, partial molar, and excess properties.
VLE, LLE and SLE calculations with activity coefficient models. Refrigeration and liquefaction processes. Phase diagrams for
VLE/LLE/SVE as used for distillation and extraction processes. Colligative properties for binary mixtures.
B.Sc. Same as for B. Eng., except for the colligative properties. Added are: compression processes, discussion of the assumption behind the
choice of models, derivation of expressions for fugacity, enthalpy and entropy from a given EoS, and parameterization of cubic EoS
M. Sc. Intermolecular forces. Cubic Equations of state with classical and advanced (EoS/GE) mixing rules. Randommixing and local composi
tion activity coefficient models. Corresponding States, group contributions and regular solutions. Association theories (CPA, SAFT).
Phase diagrams and models for electrolytes and polymersemphasis on freevolume concepts. Environmental thermodynamics.
Ph.D. Fundamentals (state functions, equilibrium and stability, reference states, electrolytes, derivatives of thermodynamic functions, check
ing models for consistency). Models (equations of state, activity coefficient models, DebyeHuckel, ion exchange, adsorption equilib
ria). Computational methods (PTflash: successive substitution, RachfordRice, higher order methods. Multiphase flash. General state
function based specifications. Dew and bubblepoints, stability analysis, and the calculation of critical point. Chemical equilibrium
calculation)
In terms of use of textbooks, only course D employs a specific textbook.[1l Courses AC are based on the authors' own teaching notes, but some
recommended teaching is proposed.[2 3] In Table 4, various recent thermodynamic textbooks are discussed, from the point of use of the programs of
DTU. Despite the many positive features of all of these textbooks, we feel that none is suitable for all the purposes. For example, several of these
textbooks do not contain chapters on polymer or electrolyte thermodynamics, environmental applications of thermodynamics, or the newest develop
ments in equations of statee.g., association models (SAFT, etc) and the EoS/GE mixing rules. These remarks by no means constitute criticisms of
these excellent textbooks, rather an observation in relation to the needs of the courses taught at DTU. We do recommend several of these textbooks as
supplementary reading material.
Vol. 43, No. 1, Winter 2009
courses. Moreover, all of them put emphasis on "applied
ways of learning," but there are important differences both
in the teaching methods employed and the level of difficulty,
as will be explained later.
The audience of the three courses and also their interests
and expectations from a course in thermodynamics are dif
ferent. Only the B.Eng. (A) course is mandatory, while all
the other courses (Bachelor, B; M.Sc., C; and, of course, the
Ph.D. course, D) are elective. B.Eng. students, in particular,
expect a brief "tothepoint" course that they can use almost
immediately in relation to other courses in their (chemical
engineering) degree, and naturally later in their future em
ployment, e.g., in the oil and gas and chemical industries.
Since this course is mandatory and also at an early stage
(third semester), it must remain relatively simple and appeal
ing to broader audiences (including students with interest in
biotechnology), while providing all the aspects of technical
thermodynamics expected from a mandatory course. The
students should also understand the role of thermodynamics
in central disciplines of chemical engineering, especially
separation processes and process design. B.Eng. students may
not take more advanced courses in thermodynamics, so the A
course should provide them with all the necessary background
to build on when required.
The B.Sc. course is taken by students in the Chemistry/
Chemical Engineering B.Sc. program (called "Chemistry and
Technology" at DTU) and although elective, it is typically
chosen by students in their fourth to sixth semester. It is also
a basic course, but because the B.Sc. educationunlike the
B.Eng. is not an independent education but rather a prepara
tion for the more advanced M.Sc. studies, several of the B.Sc.
students may wish to take a somewhat more advanced course
than the B.Eng. All the B.Sc. students will have taken, prior to
attending course B, one or two courses in physical chemistry,
and moreover they may, at a later point, choose to take course
C (during their M.Sc. studies). Based on the rather loose
structure of B.Sc. studies at DTU, the students who choose
the B.Sc. course B may not have a "complete idea" of the role
of thermodynamics in chemical engineering and will typically
only take courses on process design and separations later in
their M.Sc. studies. Most of the B.Sc. students taking course
B will have interests in chemistry/chemical engineering but
not so much in biotechnology, as the latter would take another
bachelorprogram line.
The M.Sc. course C has as a prerequisite one of the above
courses (A or B), and builds from those. The audience of this
course, however, is much broader, with not only students from
chemistry and chemical engineering but also students from
petroleum engineering, polymers, and environmental engi
neering (but, in general, not from Biotechnology). Thus, the
thermodynamic models/methods and types of mixtures that
should be covered and students' expectations from course C
are much broader.
Finally, the Ph.D. course builds also on courses A or B. A
Ctype course is not a prerequisite for the Ph.D. course but it
may be useful. The Ph.D. course emphasizes computational
aspects of thermodynamic models and phase equilibria cal
culations, and the students are then able to understand and
write computer programs for phase equilibrium calculations
including all sensitive aspects of stability and flash calcula
TABLE 4
Discussion of Thermodynamic Textbooks
Textbook Recommended Characteristics
for the course
Elliott and LiraE21 B, C (partially) Excellent new textbook. Includes exercises and also some advanced topics (association models).
Nice discussion of local composition models and links between some models. Workedout
examples, software available.
Prausnitz, et al.[4] C Classical textbooknow in its 3rd edition. References to numerous models including the new
est approaches. Includes chapters on polymers, electrolytes, EoS/GE mixing rules. Somewhat
confusing presentation of far too many models and missing unified presentation of the different
approaches.
TassiosE51 A,B,C (partially) Older textbook. Clear presentation of classical topics in thermodynamics including certain ad
vanced topics (intermolecular forces, development of cubic EoS, statistical mechanics).
VidalE61 A,B,C (partially) New textbook with emphasis on oil applications, e.g., characterization, solids (wax, hydrates) are
included. Chapters on EoS/GE mixing rules and polymers.
IsraelaschiviliE71 Supplement to C Excellent discussion of intermolecular (Part 1) and interparticle/interfacial forces in Colloids
(Part 2)
Smith, etal.[31 A,B,C (partially) Classic in the field, now in its 8th edition. Includes chapters on intermolecular forces and certain
advanced topics, e.g., on solidgas equilibria.
Sandler181 A,B,C (partially) Interesting textbook with workedout examples and certain advanced topics such as EoS/GE mix
ing rules. Somewhat confusing nomenclature.
Kontogeorgis and C (supplement) Chapters on several advanced topics (EoS/GE mixing rules, associating models, polymers, elec
GaniE91 trolytes, etc.). Not written in textbook form for students and expensive for use in universities.
'2 Chemical Engineering Education
TABLE 5
Course Layout of "Chemical Engineering Thermodynamics for Industrial Bachelor's"
(Course "A")
No. of 4hour Topics Type of Exercises
modules
2 Pure components, Excel exercises:
Residual properties. Van der Waals EOS PR/SRK EOS
Process applications (using preprogrammed macros)
2 Partial properties. Classroom pocket calculator
Activity
3 Phase diagrams, Classroom pocket calculator
VLE/LLE/SLE
2 VLE models:
Ideal mixtures Excel exercises:
Activity models Dew and bubblepoint calculations,
(Wilson, NRTL) flash calculations (using prepro
grammed Wilson/NRTL macros)
1 LLE calculations: NRTL
1 Colligative properties Excel exercises: Freezing curve
2  Project work (mainly Excel)
partial and excess properties, colliga
tive properties). The rest of the course
is traditional chemical engineering
thermodynamics with more emphasis
on the application aspects and less on
theory. The thermodynamic content
of this course is therefore somewhat
smaller than that of other "traditional"
thermodynamics courses, e.g., Course
"B" for B.Sc. students.
The general objective of this course
could be summarized as follows: Siz
ing and optimization of process units
(distillation, extraction, compression,
cooling, etc.) requires thorough knowl
edge of the thermodynamic properties
of the chemical species (pure/mixture)
present. Physical chemistry provides
the theoretical framework, which
tions in complex situations.
As could be anticipated from the above presentation, the
degree of difficulty (and also student initiative) rises from
level A (B.Eng.) to D (Ph.D.), with courses A and B being
rather close in both level and expectations (although under the
assumptions discussed above). The students work on small
projects in courses A and B and employ preprogrammed
modules in Excel, typically with the thermodynamic models
they should be using specified from the start. The students
actively combine elements such as activity coefficients and
vapor pressures to arrive to the final results.
In course C, software is used that contains numerous ther
modynamic models and tasks (see more detailed description
later), and student selection of appropriate models for specific
applications and evaluation of results is expected, along with
an indepth understanding of the derivation and theoretical
background of the models. Finally, at the final level (course
D), students write their own codes, having been given basic
thermodynamic codes (including derivatives) to start.
Following the general comparative description of the
context and needs of the four courses presented in Tables 1
through 4, we will now present their most important character
istics with some special emphasis on the educational methods
and the software and other tools employed.
ChE THERMODYNAMICS FOR INDUSTRIAL
BACHELOR'S (COURSE "A")
This is a new course that was taught for the first time in the
Fall of 2006. The course is compulsory for the B.Eng. degree
and is given jointly by the Department of Chemistry and the
Department of Chemical Engineering. Onethird of the course
is devoted to physical chemistry (phase diagrams, activity,
makes the calculation of these proper
ties possible with approximate models,
even with limited availability of experimental data. The
goal of this course is to enable the participants to estimate
thermodynamic properties of pure species and mixtures for
application in sizing and optimization of process units.
A more detailed description of the content of the course is
shown in Table 3, while the course layout and distribution of
the various topics in the 13 4hour modules devoted (at DTU)
for a 5 ECTS point course is shown in Table 5.
The students are evaluated based on reports they write in
small groups (three to four students) on three topics
(i) Ammonia cooling circuit: Sizing of an ammonia com
pressor cooling circuit for cooling fermentor broth to
10 �C.
(ii) Binary mixtures VaporLiquid: Calculation of partial
and excess molar volumes based on experimental data
Calculation of phase diagrams (Pxy) given experimen
tal data assuming either ideal behavior or an activity
coefficient model (Wilson equation).
(iii) Freezing point depression, LLE extraction: Calcula
tion of freezing curves for a binary mixture (pure solid
phase only). Calculation of the compositions of the two
liquid phases for ternary mixtures.
Several of these problems are similar to those used in
Course "B" and are described in the next section. Both dur
ing the course and in the abovementioned project, Excel is
used extensively (see also next section). Excel is a versatile
tool that the students most likely will use in their professional
careers, and more than 90% of engineers frequently use Excel
for solving engineering problems, actually many more than
those using commercial process simulators,o101 according to
a recent investigation of CACHE.
Vol. 43, No. 1, Winter 2009
PROBLEM SOLVING IN ChE THERMODYNAMICS
(COURSES "A" AND "B")
The general conceptuse of Excel in thermodynamics
Classical textbook problems in chemical engineering ther
modynamics of the type:
"Carbon dioxide is compressed adiabatically from 300K,
1 Bar, to an outlet pressure of 4 Bar. Calculate the outlet
temperature, assuming isentropic compression and ideal
gas behaviour with a constant heat capacity . .. "
solved with pen and paper and a pocket calculator, tend to bore
students. One may, of course, make the problem more realistic
by incorporating a temperaturedependent heat capacity. In it
self, this does not really make the problem more fun to solve.
Much more interesting possibilities arise with the use of
computers and easytouse tools such as spreadsheets. The
above problem, for example, is easily solved with the spread
sheet PREOS.XLS from the textbook of Elliott and Lira,I2
where an appropriate EoS (equation of state, in this case
PengRobinson) allows us to solve the problem rigorously,
without simplifying assumptions.
In our basic thermodynamic courses, the students solve
three major problems, as also shown in the previous section
for the B.Eng. course. In the case of the B.Sc. course, two of
the projects are described below.
Problem related to "pure components"
The first project has carbon dioxide as its topic. Data are re
trieved from NIST, and the students use Excel to derive Clau
siusClapeyron (by plotting InP vs. 1 /T) parameters and next
Antoine parameters (by nonlinear regression, using Excel's
solver) for the vapor pressure of CO2. Next they investigate,
by comparing to the data for NIST, at what temperature and
pressure ranges the gas phase can be calculated as ideal, and
for a number of isotherms the data are also compared with
those found using the van der Waals (vdW) equation.
Experimental vapor pressures are then compared with those
calculated from the PengRobinson equation by means of
PREOS.XLS. The students are then required to modify the
spreadsheet such that SRK is used instead and to compare the
results with what this EoS gives (which is virtually identical
to that of PR). Finally, they have to modify the spreadsheet
to use vdW, which essentially is shown to be useless for the
vapor pressure calculation.
For the final part of the first project, the students have
to optimize a sequence of compressors with intercooling.
Carbon dioxide has to be compressed from 1 Bar, 300 K,
to 80 Bar in two, three, or four stages, with cooling to 300
K after each compressor. The objective is to determine the
intermediate pressures such that the total work is minimized.
PREOS.XLS can, of course, easily be used to calculate a
single stage compression by
1. C, . i, ii,,,, S and H at inlet conditions.
2. Solving for the outlet temperature where outlet entropy
matches inlet entropy.
3. Ca. ,i, ,,,, the enthalpy at outlet conditions.
4. C. ni.,,,,, the isentropic work as the enthalpy difference.
5. C,a. ,i, ,,i the real work as the isentropic work divided
by the efficiency.
For a twostage cascade it is possible to guess the intermedi
ate pressure, calculate the work for each of the two steps, and
by trial and error adjust the intermediate pressure to arrive
at the minimum work. This process is tedious, however, and
difficult to extend to additional stages.
We, therefore, supply students with an Excel module,
written in Visual Basic, that has the same functionality as
PREOS.XLS but can be called as an ordinary Excel function
anywhere in the spreadsheet (all spreadsheets used in the
course are available from the authors upon request). Actually,
two routines are used:
1. An initialization routine,
=Cub_Ini(Mod,Tcr,Pcr,Omega,Cpcoef),
where Mod is a code for the model (PR or SRK), Tcr, Per
,and Omega are critical temperature and pressure, and acentric
factor for the compound, and Cpcoef are coefficients giving
TABLE 6
Course Layout of "Phase Equilibria for Separation Processes" (M.Sc. course, C)
No. of 4hour Topics Specifics
modules
2 Phase diagramsBasic relationships
Intermolecular forces
4 Classical models Cubic equations of state with vdWIf and EoS/GE mixing rules. Randommix
ing and local composition activity coefficient models incl. group contributions.
1 Environmental thermodynamics Octanolwater partitioning. Distribution of chemicals in environmental ecosystems.
3 Electrolyte thermodynamics Standard states. Nernst equation, osmotic coefficients, and activity coefficient
models.
1.5 Polymers Phase diagrams. Basic approaches (solubility parameters, FloryHuggins) and
freevolume models. Equations of state.
1.5 Association models SAFT and CPAapplications to petroleum, chemical, and polymer industries.
Chemical Engineering Education
the ideal gas Cp as a temperature polynomial.
2. A calculation routine, =Cub prop(T,P,X), where T and
P are the actual temperature and pressure, and X is a text
string specifying the property to calculate, e.g., "HL" for
liquid enthalpy.
It is now possible to formulate the calculation of the com
pression cascade as a constrained optimization that can be
solved in a single step by the solver in Excel. For a threestage
compression, we have
* 5 Decision variables: The 3 outlet temperatures and the 2
intermediate pressures.
* One objective function: The total work, i.e., the isentropic
work, corrected by the compressor efficiencies.
* 3 Constraints: The condition of outlet entropy for the
isentropic compression being equal to the inlet entropy.
There is no problem in determining the solution as long as
suitable initial estimates are available. And here, the "classical"
approach with the ideal gas, constant heat capacity assumption
becomes useful, with its analytic solution to the problem.
What we gain by this approach is the following:
1. We are able to solve quite realistic problems without
using tools where the students just have to "fill in the
numbers."
2. The aid inform of the Excel module is transparent. The
students can see the same .1/,, , done in PREOS.XLS and
the module just represents a different and more useful,
o1 il,.., , I, less flashy, packaging.
3. The creative element ff ....... i.,,, the conditions and
i,,, up the equations to be solved is still left to the
students.
Problem related to mixtures
The final course problem has mixtures and equilibrium cal
culations as subject. For this problem, a new Excel module is
provided, with the following capabilities for multicomponent
mixtures:
1. Activity coefficient models. We provide the following:
* Wilson
* UNIQUAC
* NRTL
2. Equations of State for mixtures. We provide the following:
* SoaveRedlichKwong
* PengRobinson
3. A RachfordRice equation solver.
The property routines include an initialization part in which
the model parameters (i.e., interaction energies and size
parameters for the activity coefficient models, critical proper
ties, and interaction coefficients for the equations of state) are
specified, and a calculation routine that given composition and
temperature returns a vector of activity coefficients (for the
Vol. 43, No. 1, Winter 2009
activity models), or given composition, temperature, pressure
and liquid state returns a vector of fugacity coefficients for the
equations of state. Finally the RachfordRice function returns,
given a composition vector and a Kfactor vector, the vapor
composition.
These tools are used for solving the following problems:
C.ii. ni,i,,, nonideal Pxy and Txydiagrams.
C. ii. ni,,,, an ideal solution PTflash.
C.i. i,/i.,,, PTflash using an EOS for the model de
scription.
Regressing energy parameters from experimental Pxy
or Txydata for a binary mixture.
C.  ..i . 1,,1, a ternary type I diagram using an activity
coefficient model with specified parameters.
The nonideal flash is solved by successive substitution, as
follows:
Initial estimates for the Kfactors are calculated.
The RachfordRice equation is solved.
New compositions are calculated.
New properties (activity or fugacity coefficients) are
calculated that yield new Kfactors.
If calculated Kfactors agree with assumed, terminate;
Otherwise repeat from second step.
This requires that we set Excel to permit iteration. Initially
students are instructed to set the maximum iteration count to 1
to see how rapidly convergence occurs. The backsubstitution
of the calculated Kfactors to the assumed is accomplished by
means of a flag that selects the assumed Kfactors either from
the calculated or from the initial estimates. This enables an
easy restart when things go wrong. For calculating the ternary
diagram, the students start by specifying a feed containing
equimolar amounts of the two immiscible components. The
nonideal flash is used to calculate the corresponding equilib
rium compositions, which yields one tieline. Then, a small
amount of the miscible component is added to the feed, and
a new flash is converged. This process is continued until the
entire diagram is calculated. In the process it becomes neces
sary to adjust the proportions of the immiscible components
to not exit prematurely, too far from the plait point.
The setup gives the students a very good feel for the difficul
ties in doing calculations in the vicinity of the plait point. Even
when the iteration count is increased to 1,000, the calculation
often has to be repeated several times to converge, and the
feed specification frequently is in the singlephase region,
resulting in convergence to the trivial solution of phases of
equal composition.
THE COURSE "PHASE EQUILIBRIA FOR
SEPARATION PROCESSES" (M.Sc. COURSE, C)
Table 6 presents the course outline of the MSc course.
We have found it particularly useful to employ varying
forms of teaching methods in almost every one of the course's
13 4hour blocks including short lectures (via PowerPoint
presentations with notes available in advance to the stu
dents), classroom exercises, and computer exercises. The
course material is currently being enhanced and prepared in
the form of a textbook."131 Different types of exercises have
been employed in this course as well. These include simple
derivations or pocketcalculator calculations, e.g., illustra
tions with activity coefficient models, polymer solutions,
or derivations of EoS/GE mixing rules and association
schemes for novel association models, up to the somewhat
more advanced applications e.g., those where equation
of state calculations are involved that are performed us
ing an inhouse software package (SPECS). This software
resembles the thermodynamic part of a process simulator
in the sense that students can choose among a large variety
of thermodynamic models, databases ("ordinary" systems,
polymers, oil, electrolytes), and tasks (VLE, LLE) includ
ing, if necessary, different models for different phases and
different mixing rules for the equations of state. Several
uptodate thermodynamic models are included (CPA, PC
SAFT, EntropicFV for polymers, etc.).
The course is currently being taught in the present format
for its sixth consecutive year, and based on student evalu
ations and other considerations, some enhancements have
been made, including:
1. The "introductory" part, i.e., the classical models
including localcomposition models and cubic EoS,
includes several exercises aimed at .it,, 1, 1,11, simi
larities and differences among the various models but
also ti, and weaknesses of the models, both from
the theoretical and the application points of view. Al
:,. h., 1, course C has courses A or B (or similar ones)
as prerequisites, we have found that this structure also
facilitates the understanding of complex concepts for
students having different backgrounds, e.g., those from
petroleum, polymer, or environmental engineering.
2. A topic addressed in the introductory lecture is the
"needs of thermodynamic data and models," mostly
from an industrial point of view. This is accomplished
via references to selected articles written by colleagues
from industry and in particular we have found the ar
ticles of Zeck"n1 and Dohrn and Pfohl2"I to be particu
larly useful in this context, as example of one older and
one more recent account of thermodynamic needs in the
chemical industry.
3. Early in the course, a lecture is devoted to intermolecu
lar forces and their application in understanding phase
diagrams, as well as developing and understanding
thermodynamic models. We constantly refer to the use
of intermolecular forces in all subsequent lectures,
including during the software and other exercises, e.g.,
when i,. i ,, models, ., i t, ,, phase diagrams.
A multiple choice is used in this lecture to illustrate
several aspects and "play around" with the various
implications of intermolecular forces.
4. A lecture on "environmental thermodynamics" is includ
ed after the activity coefficient models, so that students
encounter relatively early in the course a somewhat
"different" but, .. It,,, application of thermodynamics.
5. The evaluation used in this course is a short project
(individual or in small groups) provided during the
last lecture, but based on the students' own choice of
area of interest, e.g., oil & gas, polymers, electrolytes,
environment, association theories (students are asked
a week before to complete a relevant questionnaire). To
ensure a satisfactory evaluation of the whole course, the
evaluation will also include, besides the final project,
exercises on selected sessions from the whole course.
6. The course project is based on one or more (recent)
articles in the field of interest to the students (but
chosen by the teachers) and the final report will
include several components, e.g., summary of the
articles, derivations, and calculations including us
ing the software of the course. Critical discussion of
models and results is typically included. The list of
articles is continuously updated and students, in some
cases, may provide i,, , i..11 for articles them
selves, but even in this case, the choice and formula
tion of questions will be made by the instructors.
7. We have found it necessary to provide "overview"
tables and summaries of the lectures outlining the most
important messages (available upon request from the
authors). Tables of "recommended models for specific
types of applications (phase equilibrium calculations
and separation processes) " have been also provided.
One example is given in Table 7, while additional
tables have also been provided outlining 11 ,ui,
and weaknesses of the models mentioned in Table 7.
Of course such tables are not complete (they do not
contain all available models) and they are necessarily
somewhat biased or limited to the models covered in
this course, but they provide a general picture of the
different models or approaches needed/typically used
for different applications.
THE PH.D. COURSE
The objective of this course is that students become able
to write robust and efficient computer programs for solving
phaseequilibrium problems. An essential part of the course
therefore is to implement the theory in algorithms of increas
ing complexity. Programming is done in Fortran.
We provide the students with precompiled modules for routine
tasks such as solving sets of linear equations, and, in addition,
with routines for calculating thermodynamic properties from a
cubic equation of state. These routines contain a small compo
nent database of predominantly hydrocarbons. The students,
given temperature, pressure, and molar amounts of the mixture
species, are able to calculate volume and fugacity coefficients,
Chemical Engineering Education
and, in addition, the derivatives of these properties, with respect
to temperature, pressure, and the molar composition.
The major part of the first week is used to build up a solver
for the PTflash. The students start by writing and testing
a simple routine for solving the RachfordRice equation
(calculation of vapor fraction, given Kfactors and mixture
overall composition). This routine is then used to implement
a solution routine that uses successive substitution. In the
next step, acceleration by the dominant eigenvalue method
is implemented and tested, and finally, stability analysis is
incorporated. The students who can find time for this conclude
by implementing secondorder methods.
The second week is used on more complex tasks. The first
is to write a bubble and dewpoint routine, based on a partial
Newton's method (where composition derivatives are neglect
ed). This is followed by a phase envelope calculation where
a full Newton method has to be implemented, and where the
routines developed by the students are required to be able to
pass the critical point of the mixture. The next problem is the
multiphase flash, where the first step is the implementation of
a general multiphase RachfordRice solver, and the follow
ing steps are successive substitution, accelerated successive
substitution, and stability analysis.
The final problem during the formal part of the course (first
two weeks) is to write an efficient solver for a mixture of
dimerizing and crossdimerizing components described by
the ideal gas law. Essentially, this is the type of solver that is
required in SAFTtype association models.
The participants are graded based on a report they write
afterwards relating to an individual problem they solve (in
teams of two). One example is given below:
"Correlation of VLE frequently requires the calculation
of the equilibrium curve for binary mixtures at fixed tem
perature (Pxycurves) or at fixed pressure (Txycurves).
Write a program for automatic calculation of such
equilibrium curves. The program should be capable of
TABLE 7
Types of Phase Equilibria and Choice of Thermodynamic Models for Specific Applications
Application (e.g. Systems Phase Equilibria Types Models (tools)
separation process)
Distillation/Absorp hydrocarbons gases, nonpolars VLE, GLE cubic EoS (vdWIf)
tion
polars incl. gas/polars VLE, GLE high pressures cubic EoS (EoS/GE rules e.g. MHV2, PSRK
LCVM)
low pressure VLE & LLE act. coef. models (van Laar, Wilson, NRTL,
UNIQUAC, UNIFAC, RST)
polars, associating multicomponent (V)LLE UNIQUAC, CPA, PCSAFT
Azetropic and Ex Polar, associating,... VLE and LLE UNIQUAC, CPA, PCSAFT
tractive Distillation
Extraction polars, associating water LLE UNIQUAC, CPA, PCSAFT
Polymers solutions, blends gas/polymers, VLE (act.coefs.), GLE, solubility parameters, FH, UNIFACFV,
etc. LLE, SLE, etc. EntropicFV, cubic EoS (vdWlf & EoS/GE),
PCSAFT, various complex EoS e.g. Sanchez
Lacombe
Environmental ther water, air, complex pollutants/ Kow, infinite dilution act. UNIFACwater, Kowcorrelations, advanced
modynamics chemicals, biota coefs., VLE/LLE, SLE models
Many others solids, electrolytes, pharma SLE, LLE, SSLLE, SGE all the above and more...
ceuticals,
(adsorption, SCFE, biomolecules, surfactants,
crystallization, com colloids,...
plex products,...)
Abbreviations
act.coef. = activity coefficient PCSAFT = Perturbed Chain Statistical Associating Fluid Theory
EoS = equation of state PSRK = predictive SoaveRedlichKwong EoS
CPA = Cubic Plus Association RST = regular solution theory
FH = FloryHuggins SCFE = Supercritical Fluid Extraction
FV = FreeVolume SGE = solidgas equilibria
GLE gas liquid equilibria SLE = solidliquid equilibria
Kow =octanolwater (partition coefficient) SLE solidliquid equilibria
LCVM = lineac combination Vidal and Michelsen mixing rules vdWf = van der Waals one fluid mixing rules
LLE = liquidliquid equilibria VLE = vaporliquid equilibria
MHV2 = modified HuronVidal mixing rule UNIFAC = Uniquac Functional activity coefficient
NRTL = Nonrandom twoliquid activity coefficient model UNIQUAC = Universal quasichemical activity coefficient
Vol. 43, No. 1, Winter 2009 7
c.i. iiJ.1 i.,, the equilibrium curve for mixtures in which
one of the pure components is supercritical."
CONCLUDING REMARKS
Four different courses in Chemical Engineering Thermo
dynamics have been presented, fulfilling different needs and
offered at different degree levels: Engineering Bachelor,
B.Sc., M.Sc., and Ph.D. The context and learning objectives
of the courses have been comparatively presented with special
emphasis on the different teaching methods employed, e.g.,
use of software at various levels and degrees of complexity.
We consider it a problem that there is a lack of suitable text
books that present chemical engineering thermodynamics in
an applied, thermodynamic framework. Despite this difficulty,
however, the verypositive evaluations of all the courses and
other indicators (e.g., increasing number of students) point out
that the changes implemented in teaching chemical engineer
ing thermodynamics at DTU have led to improved courses
and enhanced both understanding and interest of students in
chemical engineering thermodynamics.
REFERENCES
1. Michelsen, M.L., and J.M. Mollerup, Thermodynamic Models: Fun
damentals & Computational Aspects, TieLine Publications (2004)
2. Elliott, J.R., and C.T. Lira, Introductory Chemical Engineering Ther
modynamics, Prentice Hall Int. (1999)
3. Smith, J.M., H.C. van Ness, and M.M. Abbott, Introduction to Chemical
Engineering Thermodynamics, 7th Ed., McGrawHill Int. (2005)
4. Prausnitz, J.M., R.N. Lichtenthaler, and E.G. deAzevedo, Molecular
Thermodynamics of FluidPhase Equilibria, 3rd Ed., Prentice Hall Int.
(1999)
5. Tassios, D.P, Applied Chemical Engineering Thermodynamics,
Springer Verlag (1993)
6. Vidal, J., Thermodynamics. Applications in Chemical Engineering and
the Petroleum Industry, Technip, IFP publications (1997)
7. Israelachvili, J.N., Intermolecular and Surface Forces with Applica
tions to Colloidal and Biological Surfaces (1985)
8. Sandler, S.I., Chemical and Engineering Thermodynamics, 3rd Ed.,
John Wiley & Sons (1999)
9. Kontogeorgis, G.M., and R. Gani, Eds., ComputerAided Property
Estimation for Process and Product Design, Elsevier (2004)
10. Mathias, PM., "Applied Thermodynamics in Chemical Technology:
Current Practice and Future Challenges, "Fluid Phase Equilibria, 228,
49 (2005)
11. Zeck, S., "Thermodynamics in Process Development in the Chemical
IndustryImportance, Benefits, Current State and Future Develop
ment," Fluid Phase Equilibria, 70, 125 (1991)
12. Dohrn, R., and 0. Pfohl, "Thermophysical PropertiesIndustrial
Directions, "Fluid Phase Equilibria, 194197, 15(2002)
13. Kontogeorgis, G.M., and G.Folas, Thermodynamic Models for In
dustrial Applications. From classical and advanced mixing rules to
association theories, in press, Wiley (expected publication date: Fall
2009) 1
Chemical Engineering Education
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