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Computer control of an anaerobic reactor utilizing a nonlinear self-tuning regulator

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Computer control of an anaerobic reactor utilizing a nonlinear self-tuning regulator
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Chou, Chu-Yang, 1956-
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English
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xii, 148 leaves : ill. ; 28 cm.

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Anaerobic digestion ( jstor )
Estimators ( jstor )
Flow velocity ( jstor )
Kinetics ( jstor )
Mathematical independent variables ( jstor )
Methane ( jstor )
Methane production ( jstor )
Parametric models ( jstor )
Raw materials ( jstor )
Subroutines ( jstor )
Agricultural Engineering thesis Ph. D
Anaerobic bacteria -- Automation ( lcsh )
Biogas ( lcsh )
Dissertations, Academic -- Agricultural Engineering -- UF
Methane ( lcsh )
Organic waste -- Metabolism ( lcsh )
Self-tuning controllers ( lcsh )
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bibliography ( marcgt )
non-fiction ( marcgt )

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Thesis:
Thesis (Ph. D.)--University of Florida, 1989.
Bibliography:
Includes bibliographical references (leaves 139-147).
General Note:
Typescript.
General Note:
Vita.
Statement of Responsibility:
by Chu-Yang Chou.

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University of Florida
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Copyright [name of dissertation author]. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
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COMPUTER CONTROL OF AN ANAEROBIC REACTOR UTILIZING
A NONLINEAR SELF-TUNING REGULATOR










By

CHU-YANG CHOU



























A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 1989




COMPUTER CONTROL OF AN ANAEROBIC REACTOR UTILIZING
A NONLINEAR SELF-TUNING REGULATOR
By
CHU-YANG CHOU
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1989


I want to know how God created this world.
I want to know his thoughts.
The rest are details.
Albert Einstein


ACKNOWLEDGEMENTS
The author wishes to express his sincere gratitude to
Dr. Roger A. Nordstedt, his major advisor, for his guidance,
encouragement, and support throughout the course of this
research and for his patience in reviewing the manuscript.
Appreciation is also extended to Dr. Spyros A. Svoronos, Dr.
Roy C. Harrell, Dr. Fedro S. Zazueta, Dr. Ben L. Koopman,
and Dr. David P. Chynoweth for their valuable advice and
assistance while serving as his supervisory committee.
The author is grateful to all the members of the
Agricultural Engineering Department for their assistance.
Special thanks go to Veronica Campbell for her enthusiasm
and helpfulness, and to Dr. Ten Hong Chen for his valuable
advice.
The author would like to thank his family for their
support during this study, and especially thanks his wife,
Pei-Huey, for her understanding, patience, and endless
support, which made this work successful.
iii


TABLE OF CONTENTS
Page
ACKNOWLEDGEMENTS
LIST OF TABLES V
LIST OF FIGURES viii
ABSTRACT xi
CHAPTERS
1 INTRODUCTION 1
2 LITERATURE REVIEW 3
Anaerobic Process 3
General Background 3
Process Microbiology 3
Digester Operation 6
Process Stability 9
Kinetics and Modeling 12
General Kinetic Model 12
Anaerobic Digestion Modeling 16
Computer-Controlled Anaerobic Digestion
Process 21
3 CONTROL SYSTEM DEVELOPMENT 25
Process 25
Reactor Setup 25
Feedstock Preparation 28
Operation 30
Analytical Methods 32
Controller 36
Model Development 36
Definition of variables and
parameters 37
Mass balance 40
Control Algorithm 42
Nonlinear self-tuning regulator
(NSTR) 43
Parameter estimator 46
Optimizer 52
Hardware 59
Computer 59
IV


Page
Data Acquisition Workstation 61
Final Control Elements 63
4 RESULTS AND DISCUSSION 64
Overall Performance 64
Mass Balance 68
COD-TOC-VS Correlation 70
Steady State Operation 74
Verification of the Parameter Estimator ... 79
Comparison between the Observed and the
Predicted Results 79
Different Numbers of Runs for the
Parameter Estimator 81
Dynamic Control Using NSTR 85
Designated MPR Operation 99
Maximum MPR operation 99
Adaptability of Changing Operations ... 100
Gas Production Pattern 103
5 SUMMARY AND CONCLUSIONS 106
6 RECOMMENDATIONS FOR FURTHER STUDY 109
APPENDICES
A NOMENCLATURE Ill
B PROGRAM LISTING 113
Parameter Estimator 113
Optimizer 129
Control Program 137
REFERENCES 139
BIOGRAPHICAL SKETCH 148
V


LIST OF TABLES
Table Page
3-1 Stock solutions for preparation of
feedstock 29
3-2 Procedure for preparing feedstock 29
3-3 Characteristics of the inoculum and
feedstock 30
3-4 Operating procedures for the anaerobic
digestion using cellulose as feedstock 31
3-5. Sampling frequency and measured variables for
the anaerobic digestion using cellulose as
feedstock 3 3
3-6 Definition of variables used in the control
system 39
3-7 Definition of parameters used in the
control system 39
3-8 Parameter values for the anaerobic
digestion process 48
3-9 Range of search for parameter values 49
4-1 Mass balance of the anaerobic reactor using
cellulose as feedstock 71
4-2 Performance data of steady state
operation 75
4-3 Parameter values found by using the
parameter estimator and the experimental data
from S2 and S3 8 0
4-4 Comparison of average performance between the
experimental data and the simulation results
found with the parameter estimator 84
4-5 Parametric values and RSS found by using the
different numbers of runs for the parameter
estimator 86
vi


Page
Table
4-6 Comparison of average simulated performance
between different numbers of runs of the
parameter estimator 87
4-7 Controlled outputs for operating at
different target times with a set point of
0.4 L CH4/L-day 90
4-8 Performance data of dynamic control
operation 95
vii


LIST OF FIGURES
Figure Page
2-1 Flow diagram of the microbial
transformations in the anaerobic digestion
process (modified from Zeikus, 1980) 5
3-1 Schematic diagram of a typical control
system 2 6
3-2 Reactor setup for the control system 27
3-3 Standard curve for TOC concentration
determination 35
3-4 Schematic diagram of the CSTR anaerobic
digestion system 38
3-5 Flow diagram of the control algorithmNSTR
for operating at a designated methane
production rate, where MPRp is the predicted
methane production rate 44
3-6 Flow diagram of the control algorithmNSTR
for operating at the maximum methane
production rate, where MPRp is the predicted
methane production rate 45
3-7 Flow chart of the parameter estimator 53
3-8 Flow chart of the optimizer 58
3-9 Schematic diagram of the integrated control
system 60
3-10 Flow chart of the control program 62
4-1 Operational characteristics and performance of
the anaerobic reactor using cellulose as
feedstock (HRT, organic loading rates, methane
content and gas production rate) 65
4-2 Performance of the anaerobic reactor using
cellulose as feedstock (solids, COD, volatile
acids and pH) 66
viii


Figure Page
4-3 Performance of the anaerobic reactor using
cellulose as feedstock (organic removal
efficiency and gas yield) 67
4-4 Schematic COD mass flow in a small time
period 69
4-5 Relationship between COD and TOC 72
4-6 Relationship between VS and TOC 73
4-7 Operational performance during steady state
operation (HRT, loading rate, methane content
and gas production rate) 76
4-8 Operational performance during steady state
operation (solids, COD, TOC, volatile acids
and pH) 77
4-9 Operational performance during steady state
operation (removal efficiency and gas
yield) 78
4-10 Comparison of COD, COD removal efficiency and
volatile acids between the experimental data
and the simulated data found with the
parameter estimator 82
4-11 Comparison of methane content, gas and
methane production rate between the
experimental data and the simulated data
found with the parameter estimator 83
4-12 Comparison of simulated results for
different numbers of runs of the parameter
estimator (COD, VA and RCOD) 88
4-13 Comparison of simulated results for
different numbers of runs of the parameter
estimator (GPR, MPR and PCH4) 89
4-14 Manipulated and controlled variables for
operating at 60 hours target time with a
designated methane production rate of
0.4 L CH4/L-day 91
4-15 Manipulated and controlled variables for
operating at 36 hours target time with a
designated methane production rate of
0.4 L CH4/L-day 92
ix


Figure Page
4-16 Manipulated and controlled variables for
operating at 24 hours target time with a
designated methane production rate of
0.4 L CH4/L-day 93
4-17 Manipulated and controlled variables for
operating at 12 hours target time with a
designated methane production rate of
0.4 L CH4/L-day 94
4-18 Operational performance of dynamic control
operation (HRT, flow rate, loading rate,
methane content and gas production rate) ... 96
4-19 Operational performance of dynamic control
operation (solids, COD, TOC, volatile acids
and pH) 97
4-20 Operational performance of dynamic control
operation (removal efficiency and gas
yield) 98
4-21 Daily performance of MPR and flow rate for
the maximum MPR operation (D2) 101
4-22 Transient behavior for changing
operational objectives from D2 to D3 102
4-23 Distribution curve of gas production for
the sampling period of day 427 427.5 .... 104
4-24 Distribution curve of gas production for
the sampling period of day 440 440.5 .... 105
x


Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
COMPUTER CONTROL OF AN ANAEROBIC REACTOR UTILIZING
A NONLINEAR SELF-TUNING REGULATOR
By
Chu-Yang Chou
May 1989
Chairman: Roger A. Nordstedt
Major Department: Agricultural Engineering
A computerized system was developed to control an
anaerobic continuously stirred tank reactor utilizing
cellulose as the feedstock for different operational
objectives: designated methane production rate (MPR) and the
maximum methane production rate under a constraint of
minimal chemical oxygen demand (COD) removal efficiency.
The control algorithm, a nonlinear self-tuning
regulator (NSTR), was developed to direct the control
action. The NSTR was the combination of an adaptive
parameter estimator and an optimizer. The parameter
estimator used a complex searching technique to find the
best-fitted parameters based on historical data which was
updated at each sampling time. With the parameters found in
the parameter estimator, the optimizer used an interval-
xi


reducing algorithm to locate the flow rate which would
produce the optimum methane production rate in order to
achieve the defined objective.
To verify the proposed control algorithm, a bench-scale
reactor was set up and equipped with hardware including
computer, data acquisition and control system, and final
control elements. The parameter estimator and optimizer
were coded in FORTRAN and executed in a Sun model 3/260
minicomputer. Based on the information obtained from the
optimizer, control signals were generated by executing the
control software in a Zenith model 248 microcomputer and
transferred to a plug-in power relay control board through a
Keithley 570 data acquisition and control workstation.
In one of the designated MPR operations, the average
controlled output was 0.4 L CH4/L-day, which was the same as
the desired set point. The results for another set point
operation showed that the average MPR was 0.209 L CH4/L-day,
which was only slightly higher than the desired 0.2 L CH4/L-
day. For the maximum MPR operation, the results showed the
reactor performed at an average MPR of 0.492 L CH4/L-day and
remained stable. The COD removal efficiency in all three
tests was higher than the minimal limit of 85%.
xii


CHAPTER 1
INTRODUCTION
Anaerobic digestion is a biological process for
conversion of organic matter and biomass to methane and
carbon dioxide in the absence of oxygen. It has been
recommended and implemented for waste treatment and energy
production for several years. This process involves complex
microbial interactions and is easily harmed by many factors.
Therefore, a close control of one or more of the process
variables is necessary for efficient operation.
Operation and control of conventional anaerobic
digesters are based on empirical data collected with the
reactor performing at steady state. These data are not
suitable for the development of control systems that handle
dynamic situations, such as varying feedstocks, changing
environmental conditions, or even modifying operational
objectives. Additionally, dynamic control requires real
time data of variables important to the description of the
anaerobic digestion process. Some of the variables are
difficult or too costly to measure. However, a computer can
be used to estimate the unmeasurable variables through the
dynamic simulation of the process. In addition, it can
conduct data acquisition and control for the process.
1


2
As computer technology develops and the cost becomes
lower, interest in computer-controlled systems is
increasing. Applications of computer control in industries
such as chemical engineering and food engineering have grown
tremendously in recent years. However, applications in
using computer control in anaerobic digestion processes are
very limited, and they have not involved dynamic control.
Therefore, development of a computer-controlled dynamic
system has significant meaning at this stage.
The objectives of this research are as follows:
1. to derive a dynamic model to characterize anaerobic
reactor performance based on microbial processes,
2. to develop control algorithms for operating the anaerobic
reactor at a designated methane production rate and at
the maximum methane production rate, and
3. to verify the proposed control algorithms in a bench-
scale computer-controlled system.


CHAPTER 2
LITERATURE REVIEW
Anaerobic Process
General Background
Methane formation from organic materials has been known
since the eighteenth century (Pine, 1971). However, the
application of this process was not reported as a method to
treat municipal wastewater until 1881 (McCarty, 1982).
Besides its ability to reduce organic pollution, this
process also produces a useful by-product, a combustible
gas, methane. As a result, interest in this technology has
grown considerably since the energy crisis occurred in the
1970s. This process can be applied to many types of organic
material, including animal manures, crop residues, food
processing wastes, human waste, and municipal sludge, for
both energy production and waste treatment.
Process Microbiology
Anaerobic digestion is a microbial process which
stabilizes organic matter in the absence of oxygen and
produces gases, such as methane and carbon dioxide, and a
small amount of sludge.
3


4
In early studies, the anaerobic process was described
as a two-stage process (McCarty, 1964a, 1964b). In the
first stage, complex organics were hydrolyzed and fermented
to simple organic materials by a group of facultative and
anaerobic acid-forming bacteria. Most of the end products
in this stage were organic fatty acids. In the second
stage, a group of complex methane-forming anaerobic bacteria
converted the products from the acid-forming stage into the
gaseous end products, methane and carbon dioxide.
Bryant et al. (1967) reported that a nonmethanogenic
species produced acetate and hydrogen from ethanol, and the
methanogenic bacteria only degraded methanol and acetate.
Therefore, another group of bacteria named H2-producing
acetogenic bacteria was added to explain this process
(Bryant, 1979). This group degraded the fatty acids
produced from the first stage to acetate, C02, and H2.
Recently, another group called homoacetogenic bacteria was
found to synthesize acetate using C02, H2, and formate
(Zeikus, 1980). However, in the gastrointestinal tract of
animals, acetogenic bacteria were probably not important
because of the short retention times, and only the
fermentative bacteria and the H2-utilizing methanogenic
bacteria were involved in the partial methane fermentation
(Hashimoto et al., 1981; Mclnerney and Bryant, 1981). Flow
diagram of the microbial transformations in the anaerobic
digestion process is shown in Figure 2-1 (modified from
Zeikus, 1980) .


5
Figure 2-1. Flow diagram of the microbial transformations
in the anaerobic digestion process (modified
from Zeikus, 1980).


6
Digester Operation
Since the anaerobic process involves complex biological
reactions, some key factors which should be considered for
successfully operating an anaerobic digester include
temperature, retention time (both hydraulic and solids),
mixing, and process configuration (Hashimoto et al., 1981;
Chynoweth et al., 1984; Loehr, 1984; Parkin and Owen, 1986).
Temperature. Temperature is an important environmental
factor in the anaerobic digestion process since it affects
the activity of the microorganisms. Methane production has
been found at temperatures ranging from 0 to 60 C (Kotz et
al., 1969; Svensson, 1984). However, practical applications
are usually performed under mesophilic (20 to 40 C) or
thermophilic (50 to 60 C) conditions. Within each range,
the maximum methane production occurred at a specific
temperature (Farquhar and Rovers, 1973). In general, higher
temperature will promote faster reaction rates and thus
permit operating at higher loading rates without reduction
in conversion efficiency. The optimum temperature is 30 -
37 C for mesophilic anaerobic digestion (Loehr, 1984) and
55 60 C for thermophilic condition (Zinder et al., 1984).
Although thermophilic anaerobic digestion has a higher
methane production rate at a lower hydraulic retention time
(Shelef et al., 1980; Hill et al., 1985; Liao and Lo, 1985;
Lo et al., 1985), thermophilic conditions are not widely
used because of the high requirement for external energy to
maintain the desired temperature for the system. Also, the


7
process is not as stable as under mesophilic conditions
(Chynoweth et al., 1984).
Retention time. Retention time is a factor which
affects bacterial growth and the system cost. It can be
classified as hydraulic retention time (HRT) and solids
retention time (SRT). HRT is defined as the time required
to replace the fluid volume of the culture, i.e., the
reactor volume (V) divided by the flow rate (Q). When flow
rate is constant, a low HRT means a small reactor volume.
Thus, a low HRT can reduce the reactor volume as well as the
construction cost of the reactor. Although a lower HRT is
preferable, the washout of the slow-growing microorganisms
may cause reactor failure. Therefore, a minimum HRT without
sacrificing the process stability should be considered in
designing a reactor. SRT is an index that can reflect the
detention of microorganisms and fixed solids in the reactor.
Fundamentally, SRT is defined as the weight of solids in the
system divided by the weight of solids leaving the system
per unit time (Loehr, 1984). If SRT is less than the
required time for microbial reproduction, microorganisms
will be removed from the system faster than they can be
reproduced, and methane formation will cease. The minimum
SRT for anaerobic digestion was estimated in the range of 2
- 6 days (Loehr, 1984). Many researchers reported that a
longer SRT will increase the stabilization of organic matter
and enhance the stability of the process (McCarty, 1964b;
Pfeffer, 1968; Andrews, 1969). Therefore, increasing the


8
SRT/HRT ratio is desirable when designing a reactor (Speece,
1983) .
Mixing. Mixing is used to (1) maintain an intimate
contact between the microorganisms and their substrates, (2)
efficiently utilize the digester volume, (3) disperse
organics and inhibitory substances within a digester, (4)
prevent stratification and temperature gradients, and (5)
minimize scum layer formation (Stafford, 1982; Parkin and
Owen, 1986; U.S. Environmental Protection Agency, 1987). In
an inefficiently mixed reactor, zones of different pH's and
different temperatures will occur and reduce the efficiency
of the reactor. One of the disadvantages of complete mixing
is that some substrates will leave the reactor unmetabolized
(Kotz et al., 1969). The quantity lost depends on the
hydraulic retention time and the conversion efficiency of
that substrate. Fannin et al. (1982) showed that an unmixed
digester had a higher methane production rate than a
continuously stirred tank reactor (CSTR) using sea kelp as
substrate. Mixing should be considered to be dependent on
the type of anaerobic process and the type of substrate
being treated.
Process configuration. Several types of anaerobic
processes have been used for treating food processing
wastes, animal manures, wastewaters, and many other wastes.
In general, they can be classified into two categories:
single-stage and two-stage processes. In a single-stage
process, microbial stabilization and liquid-solid separation


9
occur in the same reactor. Plug flow reactors and CSTR are
examples of this type of process. Some modifications, such
as baffles for the plug flow system and mechanical mixing
for the CSTR, were added to increase the treatment
efficiency (McCarty, 1982).
Since it was realized that anaerobic digestion was a
two-stage process (acid forming and methane forming), phase
separation was thought to be a method to optimize each stage
and improve the efficiency of the whole system (Smith et
al., 1977; Cohen et al., 1979; Ghosh et al. 1982; Mata-
Alvarez, 1987). Many studies have shown that two-phase
anaerobic digestion can operate at a higher organic loading
rate and have a comparable or higher conversion than those
in single-stage CSTR digestion (Colleran et al., 1983; Yang
and Chou, 1986; Sarasevat and Khanna, 1986; Ghosh, 1986;
Stephenson and Lester, 1986; Howerton and Young, 1987).
Though many novel and promising designs have been developed,
the selection of an anaerobic process depends upon the
substrate and the objectives of the system.
Process Stability
Anaerobic digestion processes can be harmed by any
factor that changes the environmental conditions or causes
the accumulation of toxic substances. Examples include
organic shock loading, abrupt change of temperature, and
exposure to oxygen or antibiotics. Some key variables which
can reflect the stability of the anaerobic digestion process


10
should be monitored, controlled, and corrected when any
adverse condition occurs. These variables include gas
production and composition, conversion of organic matter,
pH, alkalinity, and volatile acids (Chynoweth et al., 1984;
Parkin and Owen, 1986).
Gas production and composition. The gaseous products
of anaerobic digestion are methane, carbon dioxide, and some
trace gases such as hydrogen and hydrogen sulfide. Although
gas production is a direct index for the conversion of
organic matter, the destruction of organic matter may
contribute to the formation of gases other than methane.
Therefore, methane production is a more sensitive indicator
for overall digester performance. Typically, the
destruction of 1 gram of COD, regardless of substrate
source, will produce 0.35 std liter of methane (McCarty,
1964a). When methane content decreases and carbon dioxide
increases, it indicates digester instability or inhibition
of the methane bacteria.
Conversion of organic matter. To determine the
efficiency of the digestion, measurements of organic matter
are required. The commonly used measurements of organic
matter include volatile solids (VS) and chemical oxygen
demand (COD). Other measurements such as 5-day biochemical
oxygen demand (BOD5) and total organic carbon (TOC) are also
used as a measure of organic content. Because the BOD5 test
requires a long time to get the result, it is not suitable
for reactor control. Although TOC is a more rapid


11
measurement, the cost of the instrumentation is high when
compared with VS and COD. If the organic matter in the
influent and effluent are measured, the removal efficiency
can be determined. When the reactor is in steady state, the
removal efficiency of organic matter will be stable. In
addition, measurements of the influent and effluent organic
levels are necessary for calculation of the system mass
balance.
Alkalinity, volatile acids, and pH. Alkalinity,
volatile acids (VA), and pH are interdependent and very
important in control of a reactor (McCarty, 1964c; Kroeker
et al., 1979; Asinari Di San Marzano et al., 1981; Stafford,
1982; Parkin and Owen, 1986). The optimum pH for anaerobic
digestion is between 6.6 and 7.6 (McCarty, 1964c). When pH
deviates significantly from this range, it indicates the
imbalance or failure of the digester. Alkalinity is the
buffering capacity of the digester. Under stable
conditions, bicarbonate alkalinity is approximately equal to
total alkalinity. When volatile acids begin to increase,
bicarbonate alkalinity is neutralized, and volatile acid
alkalinity results. As the bicarbonate alkalinity is
depleted by the accumulation of the volatile acids, the pH
decreases and the condition of the digester will become
toxic to methane bacteria. If the bicarbonate alkalinity is
in the range of about 2500 5000 mg/L, even a large
increase in volatile acids can be handled (McCarty, 1964c).
Volatile acids such as acetic, propionic and butyric acids


12
are formed by acid-forming bacteria. The most important
volatile acid in methane fermentation is acetic acid, which
contributes 72% of methane formation (McCarty, 1964b). In a
healthy reactor, the formation of volatile acids and the
utilization by the methane-forming bacteria is balanced.
Any factor that stimulates the production of acids or
inhibits the methane-forming bacteria will cause the
accumulation of the volatile acids, and thus decrease the pH
and alkalinity.
Kinetics and Modeling
Kinetics and modeling are essential for process design,
performance prediction, operation, and control. With the
help of the digital computer, hypotheses of the biological
process can be tested more economically and faster than
before. Additionally, the feedback of the calculated
results can help scientists to prove or modify their
understanding of the experimental data, and another
experiment can be planned and initiated. The components in
the loop of experimentation, observation, hypothesis, and
modeling are interdependent and can be beneficial to each
other.
General Kinetic Model
Aiba et al. (1973) described kinetics as the rates of
cell synthesis and/or fermentation product formation and the


13
effect of environment on these rates. The kinetic equations
of bacterial growth were introduced by Monod (1942). Later,
researchers developed some modifications of "Monod kinetics"
(Lawrence and McCarty, 1969; Contois, 1959; Andrews, 1968).
Monod kinetics. In 1942, Monod proposed a relationship
between the limiting substrate concentration and the
microbial growth rate. Since then, it has been used as the
basis for most of the anaerobic digestion models. With the
same form as the rate equation for a one-substrate enzyme-
catalyzed reaction (Lehninger, 1982), the Monod equation
states that
s
Ks + S
(2-1)
where
/i = specific growth rate, time1
= maximum specific growth rate, time'1
S = substrate concentration, mass/volume
Ks = saturation constant, S at n = M/2.
Substrate utilization rate and decay coefficient. The
Monod equation for the substrate utilization rate is
dF k*M*S
dt Ks + S
(2-2)
where dF/dt = substrate utilization rate,
mass/volume-time
M = microorganism concentration, mass/volume
k = maximum specific rate of substrate
utilization, time1.
Including a decay rate (Lawrence and McCarty, 1969), the net
growth rate can be expressed as


14
dM dF
= a*( ) b-M (2-3)
dt dt
where dM/dt = microorganism net growth rate,
mass/volume-time
a = growth yield coefficient, dimensionles^
b = microorganism decay coefficient, time .
Decrease in cell mass may be caused by the energy required
for cell maintenance, death and predation of the cells.
Therefore, the decay coefficient b in the above expression
is a lumped factor (Metcalf & Eddy, 1979).
Combining the above two equations, a relationship
between specific growth rate and specific substrate
utilization rate was obtained:
dM/dt a*k*S
b (2-4)
M Ks + S
The quantity (dM/dt)/M is the specific growth rate n, which
is equal to the mean hydraulic retention time under steady
state condition for a completely mixed reactor. And a*k is
equal to the maximum specific growth rate nm.
Contois kinetics. Contois (1959) presented a model
which related the bacteria specific growth rate to the
microorganism concentration and the limiting substrate
concentration:
* S
M =
BX + S
(2-5)


15
where X = microorganism concentration, mass/volume
B = dimensionless kinetic parameter.
In his report, Contois pointed out that the saturation
constant Ks in the Monod equation is a function of
microorganism concentration.
Substrate inhibition kinetics. In order to present the
inhibitory effect of a high concentration of substrate,
Andrews (1968) proposed a substrate inhibition model:
/x = (2-6)
1 + Ks/S + S/K-
where Kt- = inhibition coefficient, mass/volume.
According to Andrews, his model was able to predict process
failure due to organic and hydraulic overloading.
First-order kinetics. After being unsuccessful in
fitting his experimental data with the Monod equation,
Pfeffer (1974) adopted the first-order rate expression:
dS
= -KS (2-7)
dt
where K = rate constant, time"1 (not the same as Ks or k) .
Using an estimated maximum gas yield (0.547 liter gas/g VS
added), Pfeffer calculated the substrate concentration and
deduced rate constants.
Other forms of kinetic models. Some other expressions
of growth kinetics have also been developed, such as product


16
inhibition kinetics by Aiba et al. (1968), multi-step Monod
equation by Hill (1982c), Hill et al. (1987) and Braha and
Hafner (1985), and some exponent-included curve fitting
models (Bailey and Ollis, 1986).
Anaerobic Digestion Modeling
Anaerobic digestion models can be classified into two
categories: steady state models and dynamic models. A
steady state model is useful in predicting gas production,
gas composition and effluent characteristics under stable
operating conditions of feedstock, temperature, and loading
rate. However, a steady state model is not suitable for
predicting failure and transient behavior of the process. A
dynamic model can be used to make these predictions. Thus,
a dynamic model can be useful in predicting response
following start-up and shock loading.
Andrews (1968, 1969) showed that a pure Monod equation
is not valid in a reaction in which volatile acids serve as
the substrate and in which they are also inhibitory to the
methane production when they accumulate to a toxic level.
He modified the Monod equation and presented a substrate
inhibition model (eq. 2-6). In this modified Monod model,
Andrews used an inhibition function to relate volatile acids
concentration and specific growth rate for the methane
bacteria. Also, unionized volatile acids were considered as
both the limiting substrate and the inhibiting agent.


17
Using the same inhibition kinetics, Andrews and Graef
(1971) modified their previous model by adding the
interactions between the liguid, gas, and biological phase
of the digester to predict the volatile acids concentration,
alkalinity, pH, gas flow rate, and gas composition. the
same kinetic model was adopted by Bolle et al. (1986) and
Moletta et al. (1986) in their studies on different
substrates.
Hill and Barth (1977) extended Andrews' model to
include the inhibitory effect of unionized ammonia on the
methanogens and developed a simulation model for digestion
of animal wastes. Using the dimensionless form of coupled
time-dependent eguations, Van den Heuvel and Zoetemeyer
(1982) applied substrate inhibition kinetics to a CSTR with
cell recycle to predict the process behaviors in both steady
state and dynamic state and to establish the criteria for
reactor operation.
The above modified Monod kinetic models are accurate in
predicting process failure and optima but have difficulty in
identifying the problem parameters. Contrary to the
complexity of the Monod type of model, the first-order
kinetic model is simple in terms of input parameters (Grady
et al., 1972, Pfeffer, 1974, Oleszkiewicz and Koziarski,
1986). However, this type of model is unable to predict the
optima and process failure (Hill, 1983).
Another type of model was developed by Chen and
Hashimoto (1978, 1980) by modifying the Contois model. They


18
proposed the following equation to relate the influent and
effluent substrate concentration to the specific growth rate
for a completely mixed reactor without solids recycle:
M
Mm*S/Sc
(1-K)-S
K +
(2-8)
where S0 and S are the influent and effluent substrate
concentration (mass/volume) respectively, and K (different
from the K in the first-order kinetics) is a dimensionless
kinetic parameter. In this model, the input parameters
reduce to only and K. Incorporating the relationship
between the destroyed substrate and the theoretical methane
production, this model can be used to predict effluent
substrate concentration, methane production rate and the
optimal retention time for the maximum methane production
rate, and the maximum substrate utilization rate. To obtain
the maximum specific growth rate nm for the above model,
Hashimoto et al. (1981) used a linear relationship between
temperature and jzm:
= 0.013(T) 0.129 (2-9)
where T is the temperature between 20 and 60 C.
Using the above model, the effects of temperature,
influent volatile solids concentration and hydraulic
retention time on the kinetic constant K were evaluated


19
(Hashimoto and Hruska, 1982; Hashimoto and Hruska, 1984).
It was found that K increased exponentially as influent
substrate concentration S0 increased and was described by
K = 0.8 + 0.0016* exp(0.0 6SQ) (2-10)
for cattle manure, and
K = 0.6 + 0.0206*exp(0.51*S0) (2-11)
for swine manure.
Chen and Hashimoto's model has been adopted in many
studies. In anaerobic treatment of landfill leachate, Lema
and Ibaez (1985) found kinetic parameters: = 0.275 d"1, K
= 0.465 and the refractory portion R = 0.1. Mata-Alvarez
and Llabrs (1988) successfully applied the model to down
flow stationary fixed film (DSFF) reactors for swine waste
digestion and found kinetic parameters: |xm = 0.1 d1 and K =
0.9. Hill (1982a) developed design criteria for the maximum
methane production in an animal waste digestion system.
Hill (1982b) further modified the model by subtracting the
death coefficient Kd as 10% of the maximum specific growth
rate (im) from the net specific growth rate n and
established the optimum operational criteria for the
digestion of animal manure.
Although the above modified Contois model has the
advantages of simplified parameter input and can predict


20
failure due to washout of the microorganisms, it is only
applicable to steady state conditions and unable to predict
process failure due to inhibition of the methanogens (Hill,
1983) .
In an attempt to achieve both accuracy and simplicity
for the dynamic process, Hill (1983) developed a "lumped
parameter" method based on Monod kinetics for modeling a
continuous expanding reactor (CER). The uniqueness of this
method is in lumping two or three basic Monod parameters
into one parameter that varies with waste type. In this
method, any type of waste can be categorized by two factors:
biodegradability and acid factor. The biodegradability is
defined as the portion that the volatile solids can be
destroyed at an infinite detention time, and the acid factor
is the fraction of the biodegradable volatile solids that
are in the form of volatile acids. Other than these two
factors, the other parameters used in the model are
constant, regardless of the waste type. In order to better
predict the transient behavior of the process, Hill et al.
(1983) modified the above "lumped parameter" model by
changing the form of the death coefficient Kd from a
constant (0.1 /m) to a Monod-based function.
The models described above are two-microorganism
models, including only acetogens and methanogens. Hill
(1982c) developed a dynamic model with four groups of
microorganisms, including acetic acid metabolism
(hydrogenogenic bacteria) and the reduction of carbon


21
dioxide with hydrogen (homoacetogenic bacteria). In this
model, kinetic constants were developed from computer
iteration and basic stoichiometry.
Though much research has been done, the current
modeling efforts are concentrating on the guantifying of the
unidentified microorganisms. With better understanding of
the microorganisms involved and their reactions in the basic
process, a more sophisticated model can be developed which
will better predict process performance.
Computer-Controlled Anaerobic Digestion Process
Since anaerobic digestion processes are easily harmed
by a change in environmental factors and the accumulation of
toxic substances, close control of this process is necessary
to keep the reactor healthy and to achieve a specific goal
such as maintaining a designated methane production rate. A
digital computer can be implemented to achieve the above
objectives due to its high-speed computation and large
information storage capacity. In addition, the cost of
microcomputers has decreased dramatically in recent years,
and this makes computer control more attractive than ever.
Computer control of the anaerobic digestion process is
a field which combines the expertise of process
biochemistry, control theory, sensor development and
computer technology. General control theory has been well
established and applied in conventional chemical and


22
electrical engineering processes and can be adapted to this
particular process. Though sensors for direct measurements
of cell concentration and activity are not available, this
problem can be solved with the help of mathematical modeling
and monitoring of indirect measurements (Wang, 1984; Shimizu
et al., 1984; Goto, 1986). Following the development of
computer technology, the application of the computer in
process control has progressed from the earlier analog
controller to direct digital control (DDC). Also, functions
of control systems have improved from data acguisition to
data analyzing and decision making.
Computers emerged in control systems for missiles and
aircraft around 1950. Their application in industrial
process control has been increasing exponentially since 1960
(strm and Wittenmark, 1984). Along with this trend,
computer control has been used extensively in conventional
activated sludge plants (Horan et al., 1985; Crowther et
al., 1977; Corder and Lee, 1986; Vasicek, 1982; Arthur,
1982) and aerobic processes (Van Breugel et al., 1986).
Computer control has been applied in only a few
anaerobic digestion process. Guarino (1972) used a
radioactive-type density gauge to measure the percent solids
in sludge in order to meet the desired solids level for
sludge treatment. In addition, C02 was monitored on-line
and pH, volatile acids, and alkalinity were determined in
the laboratory and supplied as the reference indices for
control.


23
Graef and Andrews (1972) reported a control strategy,
scrubbing of carbon dioxide from the biogas with subseguent
recycle of the treated gas, that could provide the
adjustment of digester pH and thus remove the carbonic acid
without adding base. Andrews (1978) also proposed another
control strategy which recycled the sludge from a second
stage digester and used methane production rate as a
feedback signal. Though the control action was not new,
methane production rate as the indicator of the digester
condition was a novel idea. Both the above strategies have
been proven feasible through simulation studies.
Rozzi et al. (1983) developed a method for monitoring
the carbon dioxide content of biogas by measuring the pH of
a sodium bicarbonate solution which the biogas was passed
through. This method had to be calibrated with a standard
N2/C02 gas mixture to arrive at a temperature-independent
condition.
An automatic control system for anaerobic sludge
treatment was developed by Russell et al. (1985). This
system was designed primarily for maintaining steady state
of the process. Variables controlled in this system
included temperature, pH, flow, and tank level. The 1800 m3
anaerobic digester had a 93% removal for soluble COD and
soluble BOD, and produced a total gas flow of 3.8 L/L-day
with 78% of methane.
Whitmore et al. (1986, 1987) demonstrated a control
system which monitored the dissolved hydrogen through a mass


24
spectrometer. The hydrogen signal from the mass
spectrometer in a feedback loop was used to regulate the
hydrogen level by controlled addition of the carbon source
(glucose). The results showed that volumetric methane
production rate of 1.4 L CH4/L-day could be maintained when
hydrogen concentration was controlled at 1 /M for a
mesophilic anaerobic digester.
All systems listed above were for constant set-point
control. They are suitable only for the designated
feedstock at steady state but not proper for dynamic
control. A reliable, efficient anaerobic digestion process
could be expected if an integrated system of dynamic
modeling and computer control can be developed.


CHAPTER 3
CONTROL SYSTEM DEVELOPMENT
The major components in a typical control system
include the process, measuring devices, controller, final
control element and transmission lines for measurements, and
the control signal (Figure 3-1). This chapter will discuss
the development of each component, including hardware and
software.
Process
Reactor Setup
A continuously stirred tank reactor (CSTR) with 10-
liter liquid volume, shown in Figure 3-2, was set up for
this study. The reactor was mixed intermittently for 20
minutes every hour with a Dayton 2Z814 motor (Dayton
Electric Mfg., Co., Chicago, Illinois) at a speed of 33 rpm.
During twice per day feeding, the feedstock was kept in a
glass bottle and was also mixed for the same length of time
as the reactor by using a magnetic stirrer. In order to
eliminate the effect of temperature variations on the
process, the reactor was submerged in an insulated water
bath where the temperature was maintained at 37 1 'C by
25


Set
point
Figure 3-1.
Schematic diagram of a typical control system.
O
&


relay
Figure 3-2. Reactor setup for the control system.


28
using a thermostat-controlled copper tubing immersion
heater.
Influent and effluent flow were controlled by using
Masterflex pumps (Cole-Parmer Instrument Co., Chicago,
Illinois) at a rate of 15 ml/min. To insure that the
influent and effluent were well mixed, the flow pumps were
started 5 minutes after mixing of the reactor liquids and
influent were initiated.
Gas produced from the reactor was passed through a
water-trap bottle to a sampling bulb for gas composition
measurement and through a gas meter for the measurement of
gas volume.
Feedstock Preparation
In order to have better control of the mass flow, a
synthetic substrate, a purified and partially depolymerized
cellulose (Avicel, FMC Corporation, Philadelphia,
Pennsylvania), was chosen as the primary component of the
feedstock. The inoculum used for this experiment was
effluent from an anaerobic digester using sorghum as
feedstock. To start the experiment, 9 liters of the
inoculum was mixed with 1 liter of the feedstock and fed
into the reactor.
Nutrients and vitamins added to the feedstock were
modified from the studies of Owen et al. (1979) and were
prepared as concentrated stock solutions. The prepared
feedstock and stock solutions were stored at 4 C. The


stock solutions and the procedure for preparing feedstock
are listed in Tables 3-1 and 3-2. The characteristics of
the inoculum and the feedstock are presented in Table 3-3.
Table 3-1. Stock solutions for preparation of
feedstock.
Solution
Compound
Concentration (g/L)
Sol-3
(nh4)2hpo4
26.7
Sol-4
CaCl22H20
16.7
nh4ci
26.6
MgCl2 6H20
120.0
KC1
86.7
MnCl2*4H20
1.33
CoCl2* 6H20
2.0
H3BO3
0.38
CuC12*2H20
0.18
Na2Mo04 2H20
0.17
ZnCl2
0.14
NiCl2*6H20
0.15
h2wo4
0.007
Table 3-2. Procedure for preparing feedstock at a
concentration of 30 g cellulose/L*.
Step
Instruction
1. Prepare a 2-liter flask.
2. Add: 2.8 ml of Sol-3
14 ml of Sol-4
6.98 g of NaHC03
3.33 g of yeast extract
3.33 g of casein
30 g of cellulose (Avicel).
3. Add distilled water up to
1 liter.
4. Store at 4 C until use.
* To prepare 22.5 g/L cellulose feedstock, three
portions of 30 g/L cellulose solution was mixed
with one portion of distilled water.


30
Table 3-3. Characteristics of the inoculum and
feedstock.
Characteristics
Inoculum
Feedstock*
pH
7.16
7.75
TS, g/L
20.0
37.2
VS, g/L
12.4
30.8
COD, g/L
13.3
40.3
VA, mg/L as
acetic acid
130
510
* Average value for 16 different lots of feedstock
at a concentration of 30 g/L cellulose. For finding
the characteristics of 22.5 g/L cellulose feedstock,
a conversion factor of 0.75 need be multiplied.
Operation
According to the mode of operation, there were two
phases for this study: the first phase included start-up and
steady state operation; the second phase was the dynamic
state operation for verifying the control algorithm. To
start the reactor, a feedstock with a concentration of 30
g/L cellulose was used. When instability of the reactor was
observed, the feedstock concentration was reduced to 22.5
g/L and kept constant for the rest of the experiment.
During steady state operation in the first phase, three
different flow rates (or 3 different organic loading rates,
since the feedstock concentration was constant) were used.
Performance data collected in this stage were analyzed and
used to initialize the dynamic control operation for the
second phase.


31
Three tests were conducted for the second phase. One
was for the objective of "maximum" methane production rate
(MPR) operation and another two were designed for the
designated MPR operations at set points of 0.4 L CH4/L-D and
0.2 L CH4/L-D. The set point of 0.4 L CH4/L-D was selected
because it was about 80% of the maximum MPR achieved in the
steady state operation. The set point of 0.2 L CH4/L-D was
chosen to test the flexibility of the system, i.e., to
examine whether it would function at both high (0.4) and low
(0.2) set points. The "maximum" MPR was defined as the
maximum MPR which could be achieved under the current
reactor conditions without causing any instability of the
reactor. The operating procedures for each test are
summarized in Table 3-4.
Table 3-4. Operating procedures for the anaerobic
digestion using cellulose as feedstock.
Test no. Operation
First phase: (steady state)
S.,a at a flow rate of 250 ml/day
52 at a flow rate of 375 ml/day
53 at a flow rate of 450 ml/day
Second phase: (dynamic control)
D,b set point MPRsp = 0.4 L CH4/L-day
D2 maximum MPR
D3 set point MPRsp = 0.2 L CH4/L-day
a. "S" indicates the steady state operation.
b. "D" indicates the dynamic control operation.


32
The reactor was fed every 12 hours (twice a day) for
both phases. The sampling frequency was every two or three
days in the first phase and twice a day for the second
phase. Chemical oxygen demand (COD), total organic carbon
(TOC), pH, gas production and gas composition were measured
for each sample. Total solids (TS), volatile solids (VS)
and volatile acids (VA) were monitored the same frequency as
other measurements in the first phase and were changed to
once every three days for the second phase. Because the
determination of COD takes much longer than that of TOC (2-3
hours compared with 15-20 minutes), COD was estimated from
correlations with TOC during dynamic control in the second
phase. The sampling frequencies and variables monitored for
both phases are summarized in Table 3-5.
Analytical Methods
Total solids (TS) and volatile solids (VS) were
analyzed according to the procedures of Standard Methods
(APHA, 1985). Total volatile acids concentrations were
analyzed using the methods of DiLallo and Albertson (1961).
pH was measured with an Orion 701 digital ionalyzer.
Chemical oxygen demand (COD) was determined using Hach
COD vials (Hach Co., Colorado). The titration method was
used at the beginning of the experiment, and the
colorimetric method was used after comparing two lots of
standard solution for both methods. The results showed that
the colorimetric method was more accurate than the titration


33
Table 3-5. Sampling frequency and measured variables for
the anaerobic digestion using cellulose as
feedstock.
Phase 1
Phase 2
Sampling frequency
every 2 or 3 days
every 12 hours
Measured variables3
TS, g/L
Yes
Yesb
VS, g/L
Yes
Yesb
COD, g/L
Yes
Yes
TOC, g/L
Yes
Yes
VA, g/L
Yes
Yesb
PH
Yes
Yes
Gas production, L
Yes
Yes
Gas composition
Yes
Yes
a. Measurements were conducted for each sample except
those indicated.
b. Measured once every 3 days.


34
method. Transmittance against distilled water was read at
620 nm on a Bausch & Lomb spectrophotometer (Spectronic 70).
Standard curve and regression line were calculated by using
the standard solution prepared from potassium hydrogen
phthalate (KHP) for each set of samples.
Total organic carbon (TOC) was measured by using an
Astro 1200 Carbon Analyzer combined with an Astro 5000
Infrared Analyzer (Astro Resources Corp., Texas). The
sample was acidified by using a solution of 5 N Phosphoric
acid (HjP04) to bring the sample pH within a range of 2 to 3
before injecting into the analyzer. Standard curve (Figure
3-3) of TOC concentration versus analog output (millivolt)
was made by using the standard solution prepared from
potassium hydrogen phthalate (as stated in Standard Methods,
APHA, 1985) To assure its reliability, the standard curve
was checked and modified (if necessary) each week. The
first 5 minutes after injection for each new sample was
skipped as the stabilization time and the analog output was
read every 10 seconds for a period of 10 minutes. A Zenith
248 microcomputer and a Keithley 570 workstation were
combined to receive analog outputs (as mV) from the infrared
analyzer and display the TOC concentration (as mg/L) on the
console.
Gas production was measured before each sampling with a
Wet Test Gas Meter (Model 63115, Precision Scientific,
Chicago, Illinois) at a room temperature of 27 C. Gas
composition was determined on a Gow-Mac 550 Gas


TOC cone., mg/L
(Thousands)
Figure 3-3. Standard curve for TOC concentration determination.
U>


36
Chromatograph with a thermal conductivity detector (Gow-Mac
Inst. Co., Madison, New Jersey). A stainless steel column
(2.44 m by 6.35 mm) packed with 50/80 Porapak Q (Supelco,
Bellefonte, Pennsylvania) was used. Helium was used as the
carrier gas at a flow of 60 ml/min. The temperatures of
injection port, column and detector were 90, 70 and 150 C,
respectively. Results were recorded and integrated by using
an Apple II compatible computer which was equipped with a
Chromcard (Anadata, Inc., Glen Ellyn, Illinois) for
chromatography data handling.
Controller
The controller is an element which receives the
information from the measuring devices, makes decisions
based upon the control algorithm, and takes the appropriate
control action to adjust the values of the manipulated
variables. Therefore, the controller in a computer control
system is a combination of hardware and software. This
section will discuss only the software related to the
control algorithm, and the hardware and the control action
(or actuating signal) generating program will be described
in a later section.
Model Development
Because it has well defined characteristics, a
continuous stirred tank reactor (CSTR) was selected for this


37
control system. The mathematical model is a set of state
equations to relate the state variables to the various
independent variables. The principle of conservation states
that:
Accumulation = Input Output + formation consumption
The mathematical model of this anaerobic digestion system
was developed based on the mass balance of the system
components shown in Figure 3-4. Although four groups of
bacteria have been recognized in anaerobic digestion
processes, two-culture Monod growth kinetics were adopted
here because of their simplicity and accuracy for real-time
control. The bioconversion steps from cellulose to biogas
are shown below:
Cellulose
Volatile
. > Volatile acids + CO, + Cells
Acetogens 2
acids
.. .. > CO, + CH, + Cells
Methanogens 2 4
Definition of variables and parameters
The definition of variables (including input, output
and state variables) and parameters used in this study are
listed in Tables 3-6 and 3-7, respectively. A complete
listing of notations is shown in Appendix A.


38
Figure 3-4.
Schematic diagram of the CSTR anaerobic
digestion system.


39
Table 3-6. Definition of variables used in the control
system.
Variable
Definition
S Substrate concentration in reactor, g/L
Va Total volatile acids cone, in reactor, g/L
Xa Acetogen concentration in reactor, g/L
Xm Methanogen concentration in reactor, g/L
SQ Initial substrate concentration in reactor, g/L
Va0 Initial total volatile acids cone, in reactor, g/L
Xa0 Initial acetogen concentration in reactor, g/L
XmQ Initial methanogen concentration in reactor, g/L
Si Influent substrate concentration, g/L
Vai Influent total volatile acids cone., g/L
Xai Influent acetogen concentration, g/L
Xmi Influent methanogen concentration, g/L
Q Flow rate, L/day
Qm Manipulated flow rate, L/day
V Liquid volume of reactor, L
Specific growth rate of Xa, l/day
/x2 Specific growth rate of Xm, l/day
Qch4 Daily methane production, L CH4/day
Qco2 Daily carbon dioxide production, L C02/day
Qgas Daily biogas production, L/day
GPR Volumetric biogas production rate, L/L-day
MPR Volumetric methane production rate, L CH4/L-day
MPRp Predicted methane production rate, L CH^/L-day
MPR Set point of volumetric methane production rate,
L CH4/L-day
Table 3-7. Definition of parameters used in the control
system.
Parameter
Definition
Maximum specific growth rate of Xa, day"1
Mm2 Maximum specific growth rate of Xm, day"1
Ks1 Saturation coeff. for Xa, g/L
Ks2 Saturation coeff. for Xm, g/L
Kd, Decay rate coeff. for Xa, day"1
Kd2 Decay rate coeff. for Xm, day"1
Ya Xa yield coeff., g Xa prod./g S used
Yb Va yield coeff., g Va prod./g S used
Yc Xm yield coeff., g Xm prod/g Va used
Yd CH4 yield coeff. L CH4 prod./g Va used
Ye C02 yield coeff. via acetogen, L C02/g Xa prod.
Yf C02 yield coeff. via methanogen, L C02/g Xm prod.


40
Mass balance
Substrate (S) Substrate used for the mathematical
model can be any indicator, such as volatile solids,
chemical oxygen demand or organic carbon, which is able to
reflect the organic level of the digester.
Change of S = S from the influent S in the effluent
- utilization of S to form acetogen (Xa)
dS /i, *Xa*V
V* ( ) = Q*si Q-S (3-1)
dt Ya
^rs
where /1 =
Ks.,+S
Volatile acids (Va).
Change of Va = Va from the influent Va in the
effluent + formation from S -
utilization for methanogen (Xm) growth
dVa Yb'/i, *Xa*V /Lt2-Xm-V
V ( ) = Q Vai Q Va + -
dt Ya Yc
(3-2)
V*s
where n2 =
Ks2+S
Acetogen (Xa).
Change of Xa = Xa in influent Xa in effluent + Xa
formed from S decay of Xa
dXa
V* ( ) = Q*Xai Q*Xa + Mi*Xa*V Kd.'Xa-V (3-3)
dt


41
Methanoqen (Xm) .
Change of Xm = Xm in influent Xm in effluent + Xm
formed from Va decay of Xm
dXm
V*( ) = Q*Xmi Q Xm + /x2*Xm*V Kd2*Xm*V (3-4)
dt
Gas production. Methane and carbon dioxide production
were calculated based on the cell mass produced, and the gas
production was the sum of methane and carbon dioxide
produced.
V* Yd*jU2*Xm
QCh4 = (3-5)
Yc
C02
= Ye-ji^Xa + Yf*ju2*Xm
(3-6)
GAS
= CH4 + C02
(3-7)
Volumetric methane production rate (MPR) was found by
integrating the methane produced during a certain period and
then divided by the time length of that period.
MPR
t+it
QCH4dt
V-6t
(3-8)
Volumetric gas production rate (GPR) was found in the same
way as methane production rate but including both methane
and carbon dioxide produced.
pt+t
QGASdt
J t
GPR
V* 6t
(3-9)


42
The above model can be used to simulate the dynamic
behavior of the digester and find the desired variables with
the entry of parameter values and initial conditions.
Identification of the required parameters and the model
validation will be discussed in a later section.
Control Algorithm
Selecting the proper measurements and the variable for
control is essential for establishing a control algorithm.
Gas production, gas composition, and total organic carbon
(TOC) were selected as the measured variables for the
control system. Gas production and gas composition were
combined to find the methane production ratethe output (or
controlled) variable. Total organic carbon was chosen
because of its on-line characteristics and being directly
related to the organic matter content. The flow rate (Q)
was selected as the sole manipulated variable because of its
ease of operation and close relationship with the organic
loading and the methane production for a given feedstock.
A variety of algorithms, from the conventional
proportional control to the modern adaptive control, are
available for process control (Stephanopoulos, 1984; Banks,
1986; Balchen and Mumm, 1988; Landau, 1979; Chalam, 1987).
To select an appropriate control algorithm for the system,
both the mathematical model and the objective function need
be considered. The objectives for this study were to
operate the anaerobic reactor (1) at a designated methane


43
production rate (minimize |MPRsp-MPR|) and, (2) at the
maximum methane production rate (maximize MPR) without
causing the failure of the reactor. In order to maintain
reactor stability, a constraint of minimum organic removal
was added to the objective function. Therefore, the control
algorithm for this system had to conduct a set-point control
as well as to predict the state variables for the system.
The model proposed above is a nonlinear model. The
preliminary results showed that this system was unobservable
which meant that the state variables could not be completely
observed from the measurements of the outputs (Kuo, 1987;
Banks, 1986). Since the prediction of the state variables
and the set-point variation were requisite for this control
system, a nonlinear self-tuning regulator was chosen to
achieve the objective function.
Nonlinear self-tuning regulator (NSTR)
The nonlinear self-tuning regulator (NSTR), a type of
adaptive controller (Stephanopoulos, 1984; Chalam, 1987), is
the combination of an adaptive parameter estimator (PE) and
an optimizer (OP). As shown in Figures 3-5 and 3-6, the
database required for running PE and OP is updated with the
measured outputs (including the controlled output MPR) and
the calculated control variable (Qm, for current feeding) at
each sampling time. Using the least-square principle, a
parameter estimator generates a set of parameters to fit the
historical data. The optimizer then revises the simulation


New values of model parameters
Figure 3-5. Flow diagram of the control algorithm NSTR for operating
at a designated methane production rate, where MPR^ is the
predicted methane production rate. p


New values of model parameters
Figure 3-6. Flow diagram of the control algorithm NSTR for operating
at the maximum methane production rate, where MPR^ is the
predicted methane production rate. p


46
model with the above parameters and finds the optimum
manipulated variable (Qm, for next feeding) for the next
sampling time to approach the desired output (MPRsp or
maximum MPRp) .
Parameter estimator
Method. The algorithm used in this study for parameter
estimation is modified from the "Complex" method developed
by Box (1965). The Complex method is a sequential search
technique for solving problems with a nonlinear function of
multiple variables subject to nonlinear inequality
constraints. In other words, it searches for the objective
function in a feasible region defined by the upper and lower
bounds. This method requires no derivatives and should tend
to find the global optimum because the initial set of points
are randomly scattered throughout the feasible region. In
the modified method used in this study, the objective
function was set to minimize total residual sum of squares
of GPR (gas production rate), MPR (methane production rate),
PCH4 (methane content) and COD (chemical oxygen demand).
The values of parameters were adjusted recursively inside
the defined region to approach the objective function. The
residue was found by comparing the simulation results and
the observed data. Therefore, the set of parameters which
satisfied the objective function fitted the curve the best.
To avoid the bias caused by the different scale between each


47
variable, the residue was corrected as the fraction of the
observed data as follows:
Y Yp
corrected residue =
Y
where Y is the observed data and Yp is the predicted data
from simulation.
Range for searching parameters. In order that the
parameters found have physical meaning, the upper and lower
bounds were carefully selected by referring to several
kinetic studies of the anaerobic digestion process. The
parameter values from the referred studies are listed in
Table 3-8, and the bounds of search were initially set by
using or covering the extreme points from these studies.
However, preliminary results showed that error code occurred
for some parameter values during execution of the program.
Therefore, modifications were made for those parameters to
successfully execute the computer program. The final ranges
for searching are listed in Table 3-9. The initial
conditions for Xa and Xm (Xa0 and XmQ), which were unknown,
were added to the estimation process even though they were
not kinetic parameters. The searching bounds for Xa0 and
XmQ were set as 1% 20% and 0.1% 10%, respectively, of
the initial VS concentration of the reactor.


Table 3-8. Parameter values for the anaerobic digestion process
Parameters
Ya
Yb
Yc
Yd
Ye
Yf
ICs1
Ks2
Kd1
Kd2
'ml
'm2
0.10
0.578
0.0315



9.00
2.00
0.40
0.40
0.40
0.40
Hill et al. (1983)
0.3185
1.468
0.03185

0.915
9.317
0.09
0.30
0.025
0.04
0.40
0.40
Hill & Nordstedt (1980)


0.04




0.154
0.019



Lawrence & McCarty (1969)
0.56

0.3125



0.05
0.10
0.0175
0.0175
0.04
0.004
Ruggeri (1986)
0.10
0.05
0.20




9.00
2.00




Hill (1983)






5.83
7.50


0.94
1.25
Noike et al. (1985)
0.77

0.0427
0.351

8.221
1.00

0.432

3.84
0.35
Torre et al. (1986)
0.82
0.83
0.82
0.36


0.26
0.003


1.50
0.138
Moletta et al. (1986)


0.753
13.35
1.482
9.596
8.88
4.20
0.04
0.02
0.325
0.50
Lee & Donaldson (1984)
00


49
Table 3-9. Range of search for parameter values.
Parameter
Lower bound
Upper bound
Ya, g Xa/g
S
0.1
1.0
Yb, g Va/g
S
0.05
2.0
Yc, g Xm/g
Va
0.03
1.0
Yd, L CH4/g
Va
0.3
5.0
Ye, L C02/g
Xa
0.5
2.0
Yf, L C02/g
Xm
2.0
10.0
Ks1, g/L
0.1
10.0
Ks2, g/L
0.15
10.0
Kd1, day
Kd2, day'1
Mmi' day.
daY*
0.01
0.5
0.01
0.05
0.04
5.0
0.004
1.5
Xa0, g/L,
0.1
2.0
Xm0, g/L
0.01
1.0
* Variable included in the estimation procedure
but not covered in Table 3-8.
Algorithm. The parameter searching algorithm proceeded
as follows:
1. A feasible starting point G1 (a set of model parameters
of which the parameter values were within the range
listed in Table 3-9) was chosen, and N additional points
were generated by using the pseudorandom numbers r, ¡ and
the constraints for each individual parameters (MAXIMj
and MINIMj) to make an N+l by N matrix as the initial
guesses for the parameters.
Gi,j = {Gl,j + [MINIMj+rj j* (MAXIMj-MINIMj) ] } + 2 (3-10)
i = 2,N+l and j = 1,N
where G1(J- is the jth parameter (same order as in Table 3-
9) of the ith point (each point is a set of parameters),
N is the number of parameters to be estimated (N is egual


50
to 14 in this study), G. ¡ is the feasible starting point,
' i J
MINIMj and MAXIMj are values of the jth lower and upper
bound as in Table 3-9, respectively, and r. are
uniformly distributed over the interval [0,1]. This
algorithm requires N+l points to estimate N parameters.
2. The objective function, total residual sum of squares
(RSS), was evaluated at each point based on the initial
guesses found above:
RSS = RSSGPR + RSSMPR + RSSCOD + RSSPCH4
where RSSGPR, RSSMPR, RSSCOD and RSSPCH4 are the residual
sum of squares for GPR, MPR, COD and methane content
(PCH4), respectively. Residual sum of squares for each
variable were calculated as the sum of the corrected
residues (as described in the previous section) during
the simulation period. Within the N+l RSS's, the best
guess (minimum RSS) and worst guess (maximum RSS) were
selected and assigned indexes as "ic" and "ir",
respectively.
3. A new set of parameters (new point) was determined and
added to the bottom of the parameter matrix as follows:
N+1
G,
N+2, i
N
(3-11)
a > 1 and i = 1,N
where Gjr was the set of parameters which produces the
maximum RSS and a was the over-reflection factor. Box


51
(1965) recommended a value of a=1.3, and a=l was selected
and used here after some preliminary runs.
4.RSS of the new guess was evaluated and compared with RSS
of the worst guess. The worst guess was replaced if its
RSS was greater than that of the new guess (Gir ,i GN+2,i'
i=l,N). If RSS of the new guess was greater than or
equal to that of the worst guess, each point was moved
one half of the distance to the best guess.
(3-12)
where G- ¡ was the set of parameters which produced the
1 C, J
minimum RSS.
5. All the selected points had to be located in the feasible
region. In case that a parameter for a guess was beyond
this region, the value of the lower or upper bound was
assigned to that particular parameter, depending on which
bound was closer.
6. A stopping rule was set at the time at which the
parameter matrix was reduced to an acceptably small size
e1 (convergence test) or the RSS of the best guess was
less than a predetermined small number e2 (minimum RSS
test). The convergence test was conducted as follows:
2 1/2
< e
(3-13)
where RSSC is the RSS of the centroid and RSS,. is the RSS
of the ith guess. The centroid is determined by:


52
1 N+1
CENTRO, = -- ( Z G,_, G,r>,) ,1 = 1,N (3-14)
where CENTRO,- was the ith parameter of the centroid.
The flow chart of the parameter estimator is shown in
Figure 3-7 and the program is listed in Appendix B.
Optimizer
Method. Fibonacci search method was used to find the
optimum value of the control variable (flow rate, Qm) It
is an interval elimination search method for the unimodal
function (Jacoby et al., 1972; Dixon, 1972; Kuester and
Mize, 1973). The advantages of the Fibonacci method are no
requirement of derivatives, guarantee of a prescribed
accuracy, and simplicity of coding.
Similar to the parameter estimator, the optimizer also
used the simulation results to calculate the values of
objective function. However, the parameter estimator only
simulated the real experimental data, whereas the optimizer
extended its simulation one more step to the next sampling
time which had no real data with which to compare.
Depending upon the purpose, the objective functions were set
to minimize the square residue
Min. (MPRsp MPRp) 2,
or to maximize the controlled output
Max. MPRp.


53
Figure 3-7
Flow chart of the parameter estimator


54
Both functions were subject to the following constraints:
COD_ < COD and
p SP
0 < Qm < QHIGH
where CODp is the predicted COD from the simulation model,
CODsp is the predetermined COD concentration, Qm is the
manipulated flow rate and QHIGH is the upper bound of the
flow rate.
The COD constraint was set to maintain a minimum limit
of 85% organic removal efficiency to avoid failure of the
process. Selection of the original searching region was
critical for the final solution, and it was possible that
there were more than one value that could satisfy the
objective function. However, a conservative range of flow
rate from 0 to 1 L/day (i.e. HRT > 10 days) was selected and
runs with different maximum flows (0.25, 0.5, 0.75 and 1.0
L/day) were made to circumvent these problems. In the case
of multiple solutions, the smallest value was used for safe
operation.
Algorithm. The algorithm for designated MPR operation
proceeded as follows:
1. An original search region R1 was specified with QLOW and
QHIGH as the lower and upper boundaries, respectively,
where
R, = QHIGH QLOW. (3-15)
2. The predetermined desired accuracy a was defined as the
ratio of the final region divided by the original search


55
region. Using the value of a, the largest Fibonacci
number FN was defined as
a <
(3-16)
and F0 = F1 = 1,
Fn = Fn-1 + Fn-2' fr n > 2
where Fn is called a Fibonacci number, and N is equal to
the number of iterations of the search procedure.
3. Find the first two interior points Q, and Q2 (Q1 < Q2) ,
where
Q, = QLOW +
' N-2
R,
(3-17)
Q2 = QHIGH -
N-2
(3-18)
and compute values of the objective function, M(Qt) and
M(Q2), at these two points. M(Q.,) and M(Q2) were
calculated as the square residues for MPR at different
flow rates Q1 and Q2, respectively.
| MPRp MPRsp|2
where MPRp is the predicted MPR and MPRgp is the desired
MPR.
4. Adjust the search region as follows:
If M(Q2) < M(Q.,) the lower region [QLOWjQ^ was
discarded, and the boundary was reset as QLOW = Q1.


56
The new search region was defined as
FN-1 FN-2
R2 = R, = R, R, (3-19)
fn Fn
while the interior points,
Q1 = Q2, and
fn-3
Q2 = QHIGH R2. (3-2 0)
If M(Q2) > M(Q,) the upper region (Q2,QHIGH] was
discarded, and the boundary was reset as QHIGH = Q2.
The new search region was the same as the expression in
Eg. 3-19, and the interior points were defined as
follows:
Q, = QLOW +
Qp = Qi-
N-3
R? >
(3-21)
N-1
5. Continue the above region reducing procedure for N
evaluations using the following general eguations:
Rk =
N-(k-l)
R1 Rk-i
N-k
R
k-1
(3-22)
N-Oc-2)
and the interior points
N-Ck+1>
N-(k-l)
Q, = QLOW +
(3-23)


57
or
FN-(k+1)
Q2 = QHIGH Rk. (3-24)
FN-(k-1)
6. After discarding the proper region in each iteration, the
last two test points would be coincident and located in
the center of the remaining region. To determine which
half of the remaining region the optimum belonged to, one
of the last two points was shifted by a small distance e.
The objective function was then evaluated at this point
and the final region where the optimum was located would
be determined. The location of the optimum point was
assumed to be the midpoint of the final region.
7. Check if the COD concentration for the optimum point was
within the limit of the constraint. If the COD was
beyond the specified limit, the value of the optimum
point was reduced by 0.05 L/day each time until the
resulting COD was within the limit. The objective
function and the predicted MPR were also evaluated for
this "final" optimum point.
Besides the difference in the objective function, the
algorithmic structure of the maximum MPR operation was the
same as the above designated MPR operation. The only
modification reguired was inverting the "<" to ">" in the
"IF" statement of step (4).
The flow chart of the optimizer is shown in Figure 3-8
and the program listing for the optimizer is shown in
Appendix B.


Figure 3-8. Flow chart of the optimizer.


59
Hardware
In order to verify the above proposed control
algorithm, a real-time control system was set up and
different operational objectives were tested. A schematic
diagram of the integrated control system is shown in Figure
3-9. For the designated MPR operation, 0.2 and 0.4 L CH4/L-
day were selected as the set points. The maximum MPR
operation was also tested.
This section will cover the hardware used in the
control system and the required programming to generate the
control action. The hardware consisted of computer, data
acquisition system, analog-digital (A/D and D/A) converters
and the final control elements.
Computer
Computers were used in this system for input of the TOC
(via an A/D converter), estimating model parameters, finding
the optimum value for the control variable and sending
digital signals (turn flow pumps on or off) to take the
control action. In order not to interrupt each other, two
different computers were used. As shown in Figure 3-9, both
parameter estimator and optimizer were coded in FORTRAN and
run in a Sun 3/260 minicomputer where the database was
stored. The reason for choosing the Sun computer was its
rapid speed of calculation. The other computer used in this
system was a Zenith 248 microcomputer which served as a


Kiethley 570 flow pump
workstation
Figure 3-9. Schematic diagram of the integrated control system.
CT*
O


61
supervisor to receive the information from the optimizer and
then generate the proper control action at the right time.
To accomplish the supervisory function, a control program
was developed to calculate the reguired pumping time based
on the optimum flow rate found in the optimizer. The
control program also performed as a timer and sent the
signals to the following power control system. To work as a
timer, this control program had a loop to read the computer
clock for continuously monitoring the process. This control
program was coded in a programing language, SOFT500, which
is unigue to the Keithley 570 system and compatible with the
BASIC programming language. The flow chart for the control
program is shown in Figure 3-10, and the program code is
listed in Appendix B.
Data Acquisition Workstation
The data acguisition system used to receive signals
from the microcomputer was a Keithley 570 workstation
(Keithley Data Acguisition & Control, Cleveland, Ohio) which
contained different slots to achieve functions of analog
I/O, digital I/O and relay control. The communication
between the microcomputer and the workstation was
accomplished by an interface card which was plugged into a
full length slot of the microcomputer. The signal sent to
the workstation was then transmitted to a power control
board (Opto 22, Huntington Beach, California) which
contained plug-in relays to regulate the on/off of the flow


62
Figure 3-10. Flow chart of the control program


63
pumps. There were 16 channels on the power control board,
and the on/off status for each channel was assigned by a 8-
bit binary code from the control program executed in the
Zenith 248 microcomputer.
Final Control Elements
As stated in an earlier section, the final control
elements were Cole-Parmer Masterflex pumps (Cole-Parmer
Instrument Co., Chicago, Illinois) to adjust the influent
and effluent flows. The pumping rate was set at 15 ml/min.
The required pumping time was equal to the ratio of the
optimum flow volume divided by the pumping rate. In the
control program, the resolution of the pumping time was set
to "seconds", and the computer clock was used for the real
time control.


CHAPTER 4
RESULTS AND DISCUSSION
Overall Performance
The operational characteristics and performance of the
experimental reactor, including HRT, organic loading rate,
methane content, gas production rate, methane production
rate, solids, COD, volatile acids, pH, organic removal
efficiency, gas yield and methane yield are presented in
Figures 4-1, 4-2 and 4-3. As shown in the curves of the
methane content and volatile acids, instability was observed
at days 106 and 182. Nevertheless, the reactor was able to
recover and remain healthy after the feedstock concentration
was changed and a longer hydraulic retention time was used.
This data was helpful in setting the constraint for dynamic
control, i.e., a minimum organic removal efficiency was
required to achieve the energy-oriented objective functions
without sacrificing the stability of the reactor. Based on
the experimental data, a constraint of minimum 85% COD
removal efficiency was then selected and added to the
objective functions for the dynamic control experiments.
64


HRT Loading rate Methane content Gas prod, rate
days g/L-day % L/L-day
1.8
1.2
0.6
0.0
70
50 -
30 -
10
0 100 200 300 400 500
Time, days
Figure 4-1. Operational characteristics and performance of the anaerobic
reactor using cellulose as feedstock (HRT, organic loading rates,
methane content and gas production rate).
ui


Solids COD Volatile acids
g/L g/L g/L
x
a
8.0
7.5
7.0
6.5
4.5
3.0
1.5
0.0
0 100 200 300 400 500
Time, days
Figure 4-2.
Performance of the anaerobic reactor using cellulose as feedstock
(solids, COD, volatile acids and pH).
CTi
C\


COD Solids Cellulose COD
removal eff. removal eff. gas yield gas yield
% % L/g added L/g added
0 100 200 300 400 500
Time, days
Figure 4-3
Performance of the anaerobic reactor using cellulose as feedstock
(organic removal efficiency and gas yield).
o\


68
Mass Balance
To test the reliability of the experimental data, mass
balance was conducted by using COD as the index. The COD
mass flow of the reactor system in a small time period from
time t|(.1 to time tk is shown in Figure 4-4. From the
conservation law, mass balance for this time block is
COD,-(k-1) + CODr(k-l) = CODr(k) + CODe(k-l) + CODg(k) (4-1)
where the subscripts "i", "e", "r" and "g" denote the COD
amount in the influent, effluent, reactor and gas,
respectively. The corresponding COD amount in the gas
produced was calculated as follows:
1 mole 273
Gas COD (g) = total gas produced (L) x x
22.4 L 300
16 g CH4 44 g C02
X ( x % CH4 + X % C02) (4-2)
1 mole CH4 1 mole C02
where the ratio 273/300 is the adjustment for the gas volume
since the measurement was conducted at a room temperature of
27 C (= 300 K). Using equation 4-1, the mass balance from
time tQ to tn was deduced as follows:
CODj(O) + CODp(0) = C0Dp(l) + CODe(0) + COD (1)
COD,-(1) + CODr(l) = CODp(2) + CODe(l) + CODg(2)
*
CODj (n-2) + C0Dr(n-2) = CODp(n-l) + CODe(n-2) + COD (n-1)
+ COD,, (n-1) + CODr(n-1) = C0Dr(n) + CODe(n-l) + C0Dg(n)
"z COD,.(t) + CODr(0) = C0Dr(n) + "z CODe(t) + J] C0De(t)
(4-3)


CODg(k)
i
COD¡(k-1)
Change of COD in reactor =
CODr (k-1) COD r(k)
CODe(k-1)
time block: tk_-j to t k
*k* k-1 + A
Figure 4-4. Schematic COD mass flow in a small time period.
ON
VO


70
or could be stated as
Total input COD + Initial COD in reactor = Final COD in
reactor + Total output COD + Total Gas COD
(4-4)
The results listed in Table 4-1 show that the ratios of
input/output are within an range from 1.070 to 1.086 for
each particular testing period and average from 1.045 to
1.066 for the daily mass balance.
COD-TOC-VS Correlation
Generally, for a given substrate, a relationship exits
between the indexes of organic content such as chemical
oxygen demand (COD), volatile solids (VS) and organic carbon
(TOC). In this study, TOC was selected as the monitored
variable during dynamic control operation because it can be
determined much faster than COD and VS. However, since
parameter values were not available for a TOC-based dynamic
model, it was necessary to choose either COD or VS as the
indirect measurement which would be determined by
correlation with the TOC measurements. To determine which
one was more suitable for the secondary measurement, a
comparison was made using the experimental data in phase 1.
The linear regression eguations were found as follows
(Figures 4-5 and 4-6):
COD (mg/L) = 3.15 x TOC (mg/L) + 590, r2 = 0.99
(4-5)
and VS (mg/L) = 2.23 x TOC (mg/L) + 640, r2 = 0.89
(4-6)


Table 4-1. Mass balance of the anaerobic reactor using cellulose as feedstock.
Test
(1)
Total
input
COD
g
(2)
Initial
COD in
reactor
g
(3)
Final
COD in
reactor
g
(4)
Total
output
COD
g
(5)
Total
Gas
COD
g
(6)
(D + (2)
(?)
Average
ratio of
Daily balance
(3) + (4) + (5)
Phase Ia
5360
133
50.4
918
4160
1.07
1.070.03b
Phase 2a:
Di
397
50.4
40.8
57.8
315
1.08
1.060.03
2
116
40.8
34.7
14.4
96.4
1.08
1.050.05
3
58.5
34.7
29.0
5.9
50.9
1.09
1.050.03
a. Refer to Table 3-4 for the description of Phase 1 and Phase 2.
b. Average standard deviation.


(Thousands)
\
o
(Thousands)
TOC cone., mg/L
Figure 4-5. Relationship between COD and TOC.
j
to


(Thousands)
TOC cone., mg/L
Figure 4-6. Relationship between VS and TOC.
GO


74
The result indicated that COD and TOC had a high correlation
with an r square of 0.99, while the correlation between VS
and TOC was lower and had an r square of 0.89. Therefore,
COD was chosen as the state variable to represent the
organic level for monitoring the reactor during dynamic
control operation.
Steady State Operation
During steady state operation of the reactor, data were
collected primarily for use in verifying the parameter
estimator and constructing the initial model for dynamic
control operation. After recovering from a near-failure
state, the reactor was operated at different loading rates
with a constant concentration of feedstock and stayed
healthy for the remainder of the experiment. The loading
rates were applied in an ascending order by gradually
increasing the flow rate so that shock loading of the
reactor would not occur. These tests were described in the
previous chapter as S1# S2 and S3. The operational
performance of these tests are presented in Table 4-2 and in
Figures 4-7, 4-8 and 4-9. These data were helpful in
choosing the set point for the objective function in
dynamic control. As shown in Table 4-2, among the three
steady state experiments, S3 was operated at an average HRT
of 21.6 days with the highest MPR of 0.487 L CH4/L-day and a
methane yield of 0.317 L CH4/g COD added (or 0.369 L CH4/g


75
Table 4-2. Performance data for steady state operation.
Parameters
Test
S1
s2
S3
Q, L/day
0.2 580.006a
0.38310.007
0.46310.013
HRT, days
38.810.9
26.110.5
21.610.6
LRC,
g cellulose/L-day
0.58010.019
0.86210.017
1.04110.029
LRO, g COD/L-day
0.78010.019
1.16010.022
1.40010.039
PH
7.2310.07
7.1710.08
7.1410.04
COD, g/L
3.6010.30
3.1310.37
4.2810.67
TOC, g/L
0.9410.10
0.8710.12
1.1910.23
TS, g/L
7.4610.27
7.5510.39
8.2510.41
VS, g/L
2.8610.25
3.1410.33
3.7610.52
VA, g/L
0.1110.03
0.1110.04
0.2110.12
Methane content,
%
51.911.3
51.811.1
51.611.1
GPR, L gas/L-day
0.48810.053
0.76810.039
0.94410.086
MPR, L CH4/L-day
0.25410.031
0.39810.021
0.48710.044
YGCb, L gas/
g cellulose added
0.76610.087
0.80410.056
0.82710.076
YMCb, L CH4/
g cellulose added
0.39910.051
0.41710.030
0.42610.038
YGOb, L gas/
g COD added
0.57010.065
0.59810.042
0.61510.056
YMOb, L CH4/
g COD added
0.29710.037
0.30910.023
0.31710.028
COD removal eff. ,
%
88.111.0
89.611.2
85.912.2
TS removal eff.,
%
73.211.0
72.911.4
70.411.5
VS removal eff. ,
%
87.611.1
86.411.4
83.712.2
a. average standard deviation.
b. Values reported at standard temperature (0 C).


Methane Gas
HRT Loading rate content prod, rate
days g/L-day % L/L-day
Figure 4-7. Operational performance during steady state operation (HRT, loading
rate, methane content and gas production rate).


Solids COD TOC Volatile acids
g/L g/L g/L mg/L
8.0
7.5
5. 7.0
6.5
6.0
600
400
200
0
2.0
1.5
1.0
0.5
0.0
7
5
3
1
10
8 -
6 -
2 H r i i i i i i i i i i i i i i i i i i i
210 230 250 270 290 310 330 350 370 390 410
Time, days
Figure 4-8. Operational performance during steady state operation (solids, COD,
TOC, volatile acids and pH).
-j


COD Solids Cellulose COD
removal eff. removal eff. gas yield gas yield
% % L/g added L/g added
Figure 4-9. Operational performance during steady state operation (removal
efficiency and gas yield).
00


79
COD destroyed), which was close to the theoretical value of
0.35 L CH4/g COD destroyed reported by McCarty (1964a). In
addition, as stated previously, the reactor had experienced
instability at HRT of 20 days. Based on this information,
the maximum MPR that could be achieved without causing
failure of the reactor should be close to the MPR of S3, and
a set point higher than that may cause instability of the
reactor. Thus, a MPR of 0.4 L CH4/L-day, which was about
80% of the theoretical maximum MPR, was selected as the set
point to be tested. The COD removal efficiency was also
incorporated to regulate the operation of the reactor.
Although the COD removal efficiency was the highest in S2 at
89.6% and lowest in S3 at 85.9%, all three tests were stable
during operation. Therefore, the reactor should have been
capable of maintaining its stability if the removal
efficiency was 85% or higher. This condition was then added
to the objective function as a constraint in dynamic
control.
Verification of the Parameter Estimator
Comparison between the Observed and the Predicted Results
To make sure that the parameter estimator functioned
properly in the dynamic control stage, verification was
conducted by comparing the observed and simulated results.
A set of parameter values, as listed in Table 4-3, was found
using the algorithm and program described in Chapter 3 and


80
Table 4-3. Parameter values found by using the
parameter estimator and the experimental
data from S2 and S3.
Parameters
Values
Ya, g Xa/g S
0.1679
Yb, g Va/g S
0.0703
Yc, g Xm/g Va
0.1815
Yd, L CH4/g Va
2.623
Ye, L C02/g Xa
0.6069
Yf, L C02/g Xm
7.370
Ks1, g/L
2.596
Ks2, g/L
0.7553
Kd1, day1
0.1880
Kd2, day1
0.03500
day'1
0.5361
day1
1.114
Xa0, g/L
1.123
Xm0, g/L
0.8951


81
the experimental data from S2 and S3. With these
parameters, the simulation results were generated and
compared with the experimental data of S2 and S3 in the
first phase (Figures 4-10 and 4-11). The comparisons of the
average performance for different testing periods are listed
in Table 4-4. The results showed that the curve of the
*
simulated data can follow the trend of the experimental
data. This indicated that the reactor performance could be
well predicted by using the parameter estimator.
Different Numbers of Runs for the Parameter Estimator
There was a question as to whether the initial feasible
guess would affect the efficiency of the parameter estimator
in reaching the "real" (or optimum) parameter set. Also, if
the previously found parameter set was used as the initial
guess to start the searching, the newly found parameter set
might fit the data better than the previous one. Therefore,
for a group of given data, more repetitions of the above
procedure would produce more accurate results, i.e., a
smaller residual sum of squares (RSS). However, the
complicated iteration procedures required a large amount of
computer time to execute the program. Seventy-five data
points and 166 days of simulation time took around 3 hours
of CPU time to complete one run. Considering the sampling
period of 12 hours and the time required to execute the
optimizer, three runs was the maximum that could be adopted.
A comparison of the parameters, total residual sum of


COD COD removal eff. VA
g/L % g/L
Time, days
Figure 4-10. Comparison of COD, COD removal efficiency and volatile
acids between the experimental data and the simulated
data found with the parameter estimator.


Gas prod, rate Methane prod, rate Methane content
L/L-day L/L-day %
60
55
50 -3
45
40
s2
s3
\-
observed
predicted
240 260 280 300 320 340
Time, days
360
380
400
420
Figure 4-11. Comparison of methane content, gas and methane production
rate between the experimental data and the simulated data
found with the parameter estimator.
a>
w


Table 4-4. Comparison of average performance between the experimental data
and the simulation results found with the parameter estimator.
GPR
L gas/
L-day
MPR
L CH4/
L-day
Methane
content
%
COD
g/L
COD
removal
eff., %
VA
g/L
s2 (day 242 344):
Observed
0.768
0.398
51.8
3.13
89.6
0.11
Predicted
0.802
0.405
50.5
3.17
89.5
0.11
residual3
0.048
0.019
1.9
0.29
1.0
0.03
S3 (day 345 413):
Observed
0.944
0.487
51.6
4.28
85.9
0.141
Predicted
0.902
0.453
50.2
3.84
87.3
0.15
residual3
0.071
0.047
2.0
0.63
2.1
0.06
a. Residual was calculated as the
average
of daily
absolute
residuals:
|predicted observed|.
b. Volatile acids was not analyzed the same frequency as other parameters in
this period. Data used to compare was from days 345 395.


85
squares and simulated results using different numbers of
runs for the parameter estimator are displayed in Tables 4-5
and 4-6 and in Figures 4-12 and 4-13. Although the tenth
run had the smallest RSS and was the closest to the
experimental data, the difference was insignificant and
could be neglected. Therefore, parameters found in the
third run of the parameter estimator were used for executing
the optimizer.
Dynamic Control Using NSTR
To start a control action, the initial model used a
database which included only the data points in test S3 to
save computer time, and then a new data point was added to
the database every 12 hours.
Since the cellulose is insoluble and degrades slowly
compared with other organic materials such as glucose (Noike
et al., 1985; Lee and Donaldson, 1984), there may have been
a lag in reactor response to the manipulated input. To
examine the proper response time for this system, the
optimizer was initially designed to find an optimal flow
rate with which the reactor MPR would reach the set point
MPR within the next 60 hours. Different target times, 36,
24 and 12 hours, were also tested, and the output data are
presented in Table 4-7 and in Figures 4-14 to 4-17.
The results showed that the outputs for 12 and 60 hours
were within 5% of the set point after the target time. In


86
Table 4-5. Parameter values and RSS found by using
the different numbers of runs for the
parameter estimator.
First
run
Third
run
Tenth
run
Parameters:
Ya, g Xa/g S
0.1683
0.1679
0.1704
Yb, g Va/g S
0.0699
0.0703
0.0695
Yc, g Xm/g Va
0.1840
0.1815
0.1735
Yd, L CH4/g Va
2.622
2.623
2.676
Ye, L C02/g Xa
0.6096
0.6069
0.6193
Yf, L C02/g Xm
7.372
7.370
7.286
Ks1, g/L
2.605
2.596
2.701
Ks2, g/L
0.7494
0.7553
0.7965
Kd1, day1
0.1884
0.1880
0.1891
Kd2, day1
0.03505
0.03500
0.03471
Mmi, day1
0.5385
0.5361
0.5486
Mm2, day1
1.113
1.114
1.110
Xa0, g/L
1.127
1.123
1.100
Xm0, g/L
0.8950
0.8951
0.8839
RSS
2.807
2.753
2.680


Table 4-6. Comparison of average simulated performance between different
numbers of runs of the parameter estimator.
GPR
L gas/
L-day
MPR
L CH4/
L-day
Methane
content
%
COD
g/L
COD
removal
eff., %
VA
g/L
S2
(day 242 344):
First run
0.809
0.401
49.6
3.16
89.6
0.10
Third run
0.807
0.403
49.9
3.17
89.5
0.10
Tenth run
0.802
0.405
50.5
3.17
89.5
0.11
S3
(day 345 413):
First run
0.910
0.449
49.4
3.86
87.2
0.14
Third run
0.907
0.450
49.7
3.88
87.2
0.14
Tenth run
0.902
0.453
50.2
3.84
87.3
0.15
03
vj


Full Text

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I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree of Doctor of Philosophy.
^
Ben L. Koopman ^
Associate Professor of
Environmental Engineering
Sciences
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree of Doctor of Philosophy.
A;
Spyros A. Svoronos
Associate Professor of
Chemical Engineering
This dissertation was submitted to the Graduate Faculty
of the College of Engineering and to the Graduate School and
was accepted as partial fulfillment of the requirements for
the degree of Doctor of Philosophy.
May 1989
Dean, College of Engineering
Dean, Graduate School