SIMULATION OF AN INTEGRATED SYSTEM
FOR THE PRODUCTION OF METHANE AND
SINGLE CELL PROTEIN FROM BIOMASS
MICHAEL VERNON THOMAS
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
U OE F LIBRARIES
To my wife, Laurie, without whose love
and encouragement this would never have
The author is deeply indebted to Dr. Roger A.
Nordstedt, his major professor, for his encouragement,
guidance, and patience throughout the course of this work,
and especially for his editorial reviews of the manuscript.
The author is also grateful to Dr. Arthur A. Teixeira,
Dr. Wayne Mishoe, Dr. Ben L. Koopman and Dr. Walter S.
Otwell for their time and valuable suggestions while serving
on the committee.
Thanks are also due to Mr. Charles Jacks of the IFAS
statistical consulting unit for his valuable assistance.
The author wishes to express particular gratitude to
Mr. David W. Beer, AIA, of Amelia Island, Florida, for the
use of his high-speed micro-computer based CAD system. This
permitted simulations to be run in less than 20% of the time
required on slower systems. Thanks are also due to my wife,
Laurie, for drawings done on the above CAD system.
Finally, the author would like to thank Munipalli
Sambamurthi, Thomas Cleveland, David McLendon, and all of
the staff and management of Jacksonville Suburban Utilities
Corporation and General Waterworks Corporation for their
encouragement and support in this endeavor.
Principle funding for this research was provided by the
Tennessee Valley Authority. Additional funds were provided
by the University of Florida and the GRI/IFAS Methane from
TABLE OF CONTENTS
ACKNOWLEDGMENTS . . .
Abstract . . .
INTRODUCTION . .
LITERATURE REVIEW . .
Unit Processes . .
Anaerobic Digestion .
Anaerobic microbiology .
Substrates for anaerobic digestion .
Anaerobic reactor configurations .
Continuous stirred tank reactor
Fixed bed reactor .
Continuously expanding reactor
Algae Production . .
Water Hyacinth Production .
Integrated Systems . .
Mathematical Modeling . .
Kinetics of Anaerobic Digestion .
General kinetics . .
CSTR modeling . .
FBR modeling .
CER modeling . .
Algal Growth Kinetics .
Water Hyacinth Modeling .
Systems Modeling . .
METHODOLOGY . . .
Model Development .. .
General . . .
System Flow and Volatile Solids Mass Balances
Product Mass and Energy Balances .
Costs, Revenues, and Economic Analysis .
Anaerobic Digester Models . .
General process model .
Continuous stirred tank reactor model
Fixed bed reactor model .
Continuously expanding reactor model .
Algal Growth Model . .
Water Hyacinth Growth Model .
Model Validation . .
Continuous Stirred Tank Reactor Model .
Fixed Bed Reactor Model .
Continuously Expanding Reactor Model
Algal Growth Model . .
Water Hyacinth Model .
RESULTS AND DISCUSSION . .
CONCLUSIONS . . .
RECOMMENDATIONS FOR FURTHER RESEARCH .
BIBLIOGRAPHY . . .
APPENDIX A SYSTEM FLOW VARIABLES .
APPENDIX B SYSTEM INPUT VARIABLES. .
APPENDIX C PROGRAM FLOW CHART. .
BIOGRAPHICAL SKETCH . .
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
SIMULATION OF AN INTEGRATED SYSTEM FOR THE
PRODUCTION OF METHANE AND SINGLE CELL
PROTEIN FROM BIOMASS
MICHAEL VERNON THOMAS
Chairman: Roger A. Nordstedt
Major Department: Agricultural Engineering
A numerical model was developed to simulate the
operation of an integrated system for the production of
methane and single-cell algal protein from a variety of
biomass energy crops or waste streams. Economic analysis
was performed at the end of each simulation. The model was
capable of assisting in the determination of design para-
meters by providing relative economic information for
Three configurations of anaerobic reactors were
simulated. These included fixed-bed reactors, conventional
stirred tank reactors, and continuously expanding reactors.
A generic anaerobic digestion process model, using lumped
substrate parameters, was developed for use by type-specific
reactor models. The generic anaerobic digestion model
provided a tool for the testing of conversion efficiencies
and kinetic parameters for a wide range of substrate types
and reactor designs.
Dynamic growth models were used to model the growth of
algae and Eichornia crassipes as a function of daily
incident radiation and temperature. The growth of Eichornia
crassipes was modeled for the production of biomass as a
substrate for digestion.
Computer simulations with the system model indicated
that tropical or subtropical locations offered the most
promise for a viable system. The availability of large
quantities of digestible waste and low land prices were
found to be desirable in order to take advantage of the
economies of scale. Other simulations indicated that
poultry and swine manure produced larger biogas yields than
The model was created in a modular fashion to allow for
testing of a wide variety of unit operations. Coding was
performed in the Pascal language for use on personal com-
The use of various agricultural wastes to produce
energy and to feed livestock is not new. The anaerobic
digestion of animal wastes to produce methane for domestic
consumption has been practiced for over a hundred years
(Meynell, 1978). However, due to the low cost of elec-
tricity and petroleum based fuels anaerobic digestion has
not been widely accepted in the developed world as an energy
source. With the growing awareness of our dwindling natural
resources the potential use of biological methanogenic
conversion processes is attracting increasing attention.
The economics of anaerobic production of methane in the
developed world depend heavily on four main factors: the
cost and availability of substrate; capital and operating
costs of the plant itself; the costs associated with
disposal of the waste stream; and revenues generated by the
sale of products.
One of the methods to improve these economics is to
combine related operations into an integrated system wherein
a regenerative feedback is developed to maximize revenues
while minimizing the associated costs. An operation of this
type studied at the University of Florida involved three
unit operations located on a single site (Figure 1).
Swine waste and chopped water hyacinths were digested
under anaerobic conditions to produce methane. Three types
of digesters were used, a continuous stirred tank reactor
(CSTR), a fixed-bed reactor (FBR), and a continuously
expanding reactor (CER). Nutrient rich supernatant from the
digesters was used to grow algae. The algae were harvested
as a source of single cell protein for inclusion in animal
feed formulations. Water leaving the algae unit flowed
through shallow ponds filled with water hyacinths.
This research was an attempt to model an integrated
system for methane and algal biomass production. The model
was designed to be of a generic nature and was not specif-
ically designed to represent the University of Florida
The objectives of this research were
1. To model an integrated system for use in the
determination of proper design parameters.
2. To provide a research tool to assist in choosing
values of conversion efficiencies and kinetic
parameters for simulation of a variety of anaero-
bic digester configurations and substrates.
3. To simulate system performance as affected by
feedstock characteristics, climate, harvest
cycles, biogas usage, and flow management.
Anaerobic digestion is a microbial process which has
been widely used throughout the world for over a century to
provide biogas for cooking and as a method of waste dis-
posal. However, due to the continued availability of
inexpensive petroleum based energy resources, biogas has not
been used extensively in this country as an alternative
energy source. Only in the last forty years has the
microbiology of the process been studied. Much of the work
has come since the oil embargo of the 1970's when the Organ-
ization of Petroleum Exporting Countries (OPEC) spurred the
search for additional domestic energy sources.
The anaerobic process is particularly well suited for
energy production. It is one of the most important parts of
the carbon cycle since it results in the degradation of
complex organic matter to relatively pure gaseous carbon
dioxide (CO2) and methane (CH4) with a relatively small
yield of bacterial mass (McCarty, 1964a,b). Thus, a large
amount of organic matter is destroyed while about 90% of the
- -1 d=
substrate energy is retained in the methane (Mah et
al.,1976; Thauer, 1979; and Bryant, 1979).
The traditional view of the process classifies the
organisms that carry out this process into two categories,
the acetogenic bacteria and the methanogenic bacteria, as
shown in Figure 2 (Barker, 1956; McCarty, 1964a). In this
approach, the complex organic matter consisting of various
proteins, carbohydrates and fat are broken down into simple
short chain fatty acids and alcohols by the acetogenic, or
acid-forming bacteria. These short chain fatty acids are
metabolized by the methanogens into carbon dioxide and
With the discovery in 1967 that Methanobacillus
omelianskii (Barker, 1956; Wolfe et al., 1966) was in fact a
symbiotic association of two bacteria (Bryant et al., 1967),
it became clear that the methane pathway was much more
complex than first believed. M. omelianskii was originally
thought to metabolize ethanol and CO2 to acetate and CH4.
However, it was later determined that one of the two
organisms metabolized ethanol and water to acetate and H2,
while the other organism utilized the H2 to reduce the C02
to CH4. Other studies have shown that methanogens are
unable to use alcohols other than methanol or to catabolize
organic acids other than acetate and format (Bryant,
1976,1979; McInerney et al., 1979). These discoveries,
along with subsequent work by Mah et al. (1977) and
COMPLEX ORGANIC MATTER
I. ACID FORMING ORGANISMS
Figure 2. The two-population model of anaerobic digestion.
Thauer et al.(1977), led to the three stage model shown in
Figure 3 (Bryant, 1979). In this model fermentative acid-
formers produce short chain saturated fatty acids and al-
cohols. The H2-producing acetogenic bacteria produce H2 and
acetate from the above end products, and the methanogenic
bacteria produce CH4 from acetate, CO2, and H2.
The critical importance of H2 in the linking of this
model cannot be overstated. Thauer et al. (1977) showed
that the reactions which take place in the catabolism of
propionate and butyrate to yield acetate and H2 have a net
positive change in Gibbs free energy. Only when these
reactions are coupled to the strongly negative change -in
free energy associated with the reduction of HC03" can the
Wolfe and Higgins (1979), Zeikus (1979) and Hashimoto
et al.(1980) described a fourth type of bacteria, the
homoacetogens. This group uses H2 to reduce CO2 to acetate
and is represented by such organisms as Acetobacterium and
The existence of an anaerobic fungus in the rumen of
cattle and sheep was described by Bauchop (1979,1981).
Fermentation of cellulose by this fungus, with subsequent
methanogenesis by methanogenic bacteria in co-culture, has
also been described (Bauchop and Mountfort, 1981; Mountfort
et al., 1982). The four-population model (Figure 4) of
anaerobic digestion represents our current understanding of
o S o *
Jc o ^.(
II. HYDROGEN PRODUCING-
I. HYDROLYTIC BACTERIA
IV. METHANOGENIC BACTERIA
Figure 4. The four-population model of anaerobic digestion
presented by Hashimoto et al. (1980). Reprinted by .
the anaerobic digestion process. The role of the anaerobic
fungus is not well understood and no information was found
in the literature on the subject of anaerobic fungal
activity in digesters. As more information becomes avail-
able about the biochemistry of methane formation, par-
ticularly about the electron transfer reactions and role of
molecular hydrogen in acetate catabolism, more pathways and
populations will be defined.
Substrates for anaerobic digestion
Almost any nontoxic, biodegradable substance is a
potential candidate for anaerobic digestion. The most
readily digestible materials are obviously those soluble
compounds which are intermediate products in the metabolic
pathway. For example, the volatile fatty acids (VFA) may be
used directly by H2-producing acetogenic bacteria or
methanogens. Simple sugars and amino acids that result from
the action of the hydrolytic and proteolytic enzymes
secreted by the acetogenic bacteria are quickly metabolized.
The complex lipids, soluble carbohydrates and proteins are
somewhat less readily degradable. These materials can be
readily attacked and metabolized by enzymatic action. It
has been shown that this group is responsible for most of
the biogas production from a number of materials (Habig,
1985). Physical factors such as particle size and the
amount of surface area exposed to enzymatic activity may
have a significant role in the rate of digestion.
Neutral and acid fiber materials such as cellulose,
hemicellulose, and lignocellulose are much less readily
digestible. Although cellulose and hemicellulose have been
shown to be digestible (Khan, 1980; Laube and Martin, 1981;
Singh et al., 1982; Nordstedt and Thomas, 1985a; Partos et
al., 1982), the hydrolysis of this structural biomass is
frequently the rate limiting step in the digestive process
(Doyle et al., 1983; Chynoweth, 1987).
Lignin is not significantly degraded under most
anaerobic conditions (Crawford, 1981; Singh et al., 1982;
Nordstedt and Thomas, 1985b). Much of the emphasis on
pretreatment of lignocellulosic biomass is an attempt to
free the cellulose from lignin compounds and to make it
available for digestion.
Historically human or animal manure, sometimes with the
addition of crop residues, has been the substrate most
frequently used. In the industrialized world the digestion
of municipal sewage sludge has been a common practice. To a
lesser extent, the digestion of animal manures has also been
Generally, the biodegradability (kg volatile solids
(VS) destroyed/kg VS added) of manure from beef cattle is
higher than that of dairy cattle due to the characteristics
of the feed ration. The amount of bedding and other
extraneous material collected with the manure is also a
factor and is influenced by the method of collection (Hill,
1983a; Loehr, 1984; and Chandler, 1980).
The biodegradability of manure from beef cattle in
confinement was reported by Hill (1983a) to be about 0.65,
whereas the factor for cattle on dirt feedlots was only
0.56. Hill also reported a biodegradability factor of 0.36
for dairy waste. Loehr (1984) reported ten values of
biodegradability for dairy waste ranging from 0.37 to 0.62.
In an exhaustive study of substrate biodegradibility,
Chandler (1980) reported a linear relationship between
lignin content and biodegradability. The following rela-
tionship was established between biodegradability and lignin
B = -0.028X + 0.83,
where B is the biodegradable fraction, and X is the percent
lignin of total volatile solids (sulfuric acid method).
Dairy manure is likely to contain a larger amount of
bedding material and a higher lignin content than that from
beef cattle. Loehr (1984) reported the lignin content of
dairy manure to average 14.4 percent of dry matter, whereas
the lignin content of beef manure was reported to be only
8.3 percent of dry matter. Jain et al. (1981) reported
values of 9.9% and 12.7% lignin, respectively, as a per-
centage of dry matter following their analysis of sheep and
cattle waste. Using the relationship developed by Chandler
(1980), B = 0.43 for dairy cattle, and B = 0.60 for beef
cattle. These agree with the values reported by Hill
(1983a) and Loehr (1984).
Poultry manure is substantially more biodegradable than
cattle manure. Values as high as 0.87 (kg VS destroyed / kg
VS added) have been reported for manure from layers, with
somewhat lower values of 0.70 0.76 reported for broiler
manure (Hill, 1983a; Loehr, 1984).
Swine waste is among the most suitable of all manures
for anaerobic digestion. Biodegradability of swine waste
was reported by Hill (1983a) to be 0.90. Swine waste also
yields a higher percentage of methane in the biogas than
most other manures (Loehr, 1984).
Methane productivity (m3/kg VS added) was reported by
Hill (1984a) as 0.32 for swine manure, 0.36 for poultry, and
to vary between 0.13 0.24 for cattle waste.
In the last three decades a large number of other waste
streams have been investigated. Many of these, particularly
those in the food industry, are being successfully treated
by anaerobic digestion. In many cases the methane is of
secondary importance to the environmental effect, but it may
provide a significant economic benefit.
Lovan and Foree (1972) reported on the treatment of
brewery wastes, and Szendrey (1983) described a 13,000 m3
anaerobic treatment system designed to produce methane from
rum distillery wastes. The digestion of cheese whey, pear
peeling wastes, and bean blanching wastes was described by
van den Berg et al. (1981). Stevens and van den Berg (1981)
reported the use of tomato peeling wastes for digestion.
Russell et al. (1985) announced an anaerobic sludge blanket
reactor system for use in the treatment of potato processing
wastes. Treatment of shellfish processing wastewater
(Hudson et al., 1978), ethanol stillage wastes (Hills and
Roberts, 1984), and tannery wastes (Cenni et al., 1982) have
also been reported.
Since the OPEC oil embargo of the 1970's, attention has
been focused on anaerobic digestion as a method of sup-
plementing natural gas production from conventional sources.
Although the use of manures and waste streams to produce
methane may be of economic benefit to the farms or plants
involved, the amount of biogas produced is rarely sufficient
to justify off-site distribution and sale. In order to
produce sufficient quantities of methane to supplement our
commercial natural gas supplies it will be necessary to
produce substrates on a large scale. This realization has
led to an interest in the production of biomass crops which
may be readily digested to methane in large quantities and
on a continuous basis.
One of the potential crops that has been investigated
at length in subtropical areas is the water hyacinth
(Eichornia crassipes). Habig and Ryther (1984) investigated
the methane yields from a number of substrates. They found
that water hyacinth produced 0.15 m3/kg of volatile solids
added and concluded that water hyacinths were a viable sub-
strate for methane production. Much of the work with
digestion of hyacinths has been done with hyacinths grown in
the treatment of domestic sewage (Biljetina et al., 1987;
Joglekar and Sonar, 1987). Blends of hyacinth and municipal
sewage sludge are a more promising substrate for commercial
methane production, a 2:1 blend yielding as high as 0.29 m3
methane/kg VS added (Biljetina et al., 1985). Other
potential substrates under investigation include napier
grass (Pennisetum purpureum) and sorghum (Sorghum bicolor)
(Chynoweth et al., 1984).
Anaerobic reactor configurations
Continuous stirred tank reactor. The classical design
for continuous processing of wastes by anaerobic digestion
is the continuous stirred tank reactor (CSTR) (McCarty,
1964a). It is basically a tank with inlet and outlet, and a
motorized impeller for mixing. The mixing must be suffi-
cient to prevent stratification and settling of the solids.
It is assumed that the mixing is complete and that the
solids residence time is equal to the hydraulic residence
time, or RT = liquid volume/daily flow. Although this is
the most popular design in current use, .it suffers from
The most obvious disadvantage is that it requires
substantial mixing power (Hill, 1983b). In addition to the
higher construction costs refecting the mechanical com-
plexity required, the operating costs may also be signif-
icantly higher than for non-mixed reactors. Another disad-
vantage stems from the slow growth rate of the anaerobic
organisms which define the process. The specific growth
rate of many of the organisms involved is measured in days,
instead of hours or minutes as is the case with most aerobic
organisms. Thus, retention times for CSTR's are usually on
the order of 10-30 days (McCarty, 1964a). Operation of
CSTR's at less than 8-10 days retention time usually results
in failure because the slower growing organisms wash out.
The large capital investment required for a tank volume 15-
30 times the daily flow makes the anaerobic CSTR economi-
cally infeasible in many situations. In an effort to
minimize this size problem many CSTR's are operated at
thermophilic temperatures of 50-55 C. The heating require-
ments are such that a large part of the methane produced be
used for heating, although it can be minimized by heat
recovery from the effluent (Hill 1983b) and use of waste
engine heat from a generator. Thermophilic digesters also
tend to be less stable than mesophilic digesters (Hill,
1983b; Hashimoto, 1983). In colder climates mesophilic
digesters may require substantial external heating.
Fixed bed reactor. The fixed bed reactor (FBR), or
anaerobic filter is designed to overcome some of the
shortcomings of the CSTR when treating dilute waste streams.
A porous packing material is used to provide a surface upon
which bacterial growth can become attached. Since much of
the bacterial mass is retained in the biofilm, bacterial
washout is minimized. A large variety of packing materials
and substrates have been utilized.
The first major investigation of fixed bed reactors was
reported by Young and McCarty (1967). The columns were
filled with smooth quartzite stones, 2.5 to 3.8 cm diameter,
and were operated in an upflow mode. Four distinct ad-
vantages were listed for FBR's over conventional waste
1. FBR's are well suited to dilute wastes.
2. Biological solids are retained in the biofilm,
allowing short hydraulic retention times.
3. High bacterial concentrations permit operation
at nominal temperatures.
4. Very low volumes of sludge are produced.
Studies conducted on pharmaceutical waste by Jennett
and Dennis (1975) used hand-graded smooth quartz stones 2.5
to 3.8 cm in diameter. Retention times varied between 12
and 48 hours with COD removal efficiencies of greater than
93% for all trials. Average methane concentration exceeded
Newell et al. (1979) reported on a 7.57 m3 swine manure
digester using 3.8 cm limestone chips as a support media.
Gas quality exceeded 80% methane and COD removal averaged
Hudson et al. (1978) compared 2.5 to 3.8 cm. stone
packing to whole oyster shells packing media for the treat-
ment of shellfish processing wastewaters. The oyster shells
were expected to provide buffering capacity in addition to
providing a rough surface for biological attachment.
Specific surface areas were approximately 130 m2/m3 for the
stone and approximately 650 to 980 m2/m3 meter for the
oyster shells. Gas production from the oyster shell digester
was nearly double that of the digester with stone packing
and the percent methane averaged over 85% as compared to
only 73% with the stone packing.
Wilkie, Faherty, and Colleran (1983) examined the
effects of media type upon performance of upflow anaerobic
filters. Media which were examined included fired clay
fragments, coral, mussel shells, and plastic rings. Maximum
conversion of COD to methane was attained in 20 days for the
clay fragments, and in 39, 40, and 50 days for the coral,
plastic, and mussel shell filter media, respectively. Feed
material consisted of swine manure slurry loaded at a rate
of 5 kg COD/m3 of liquid reactor volume per day at a
hydraulic retention time of six days.
Person (1980, 1983) used polypropylene plastic media in
his experiments with swine waste. The experiments were
designed to compare the effectiveness of using media vs. no
media, upflow vs. downflow, and to examine loading rates.
Soluble COD removal was in excess of 90% and methane content
was over 80% in those filters which contained media. Person
(1980) concluded that filters with media are more effective
than those without. It was also concluded that filters can
operate with a hydraulic retention time as low as 9 hours at
temperatures above 23.5 C and that most COD removal takes
place in the lower 25% of the upflow filters.
Brumm (1980) examined the use of corncobs as a filter
media in a series of experiments which compared filters
packed with corncobs to those packed with plastic rings. The
filters were loaded daily with dilute swine waste. The
plastic media outperformed the corncobs in removal of
influent volatile solids but lagged behind in the production
of gas. This was determined to be due to the degradation of
the corncob media. Methane content was also slightly lower
for the corncobs, 74.3% vs. 78.3% for the plastic media.
Nordstedt and Thomas (1985b) conducted experiments
using 13 bench-scale anaerobic filters packed with a variety
of wood and plastic media. The wood media performed as well
or better than the plastic media and showed no significant
degradation after 1 year. Reactors were fed supernatant
from settled swine waste. Methane content averaged
80% 84%. Hydraulic retention times varied from 35 days at
startup to a low of 2 days after 1 year of operation.
Continuously expanding reactor. The continuously
expanding reactor (CER) represents another type of reactor.
Unlike the CSTR and the FBR the CER does not operate in a
continuous flow mode, but rather in a semi-batch mode. The
substrate may be loaded into the reactor on a regular or
irregular basis. However, the volume of the reactor is
allowed to expand as it is loaded. It is only emptied on an
infrequent basis, usually when it is convenient to apply the
effluent to the land as a nutrient source. A "seed", or
inoculum, consisting of 10% to 30% of the total digester
volume is left behind after emptying to start the next cycle
(Hill et al. 1981).
CER's tend to be more stable under conditions of very
high loading than continuous processes and may provide a
higher specific methane productivity (Hill et al. 1985).
Most of the known work with CER's has involved the digestion
of cattle manure (Hill et al. 1981) or swine manure (Hill et
The only method of solar energy conversion currently
practiced on a large scale is photosynthesis. Unfortunate-
ly, the theoretical maximum efficiency for this process is
only about 5 or 6% (Hall, 1976). Microalgae, whose
efficiency may be as high as 4% (Oswald, 1969), approach
this theoretical limit to photosynthetic efficiency. The
conversion efficiency rarely exceeds 1% in typical agricul-
tural production. Even then the overall conversion effi-
ciency is frequently negative as the caloric value of
fertilizer and fossil fuels used exceed the value of the
product (Benemann et al., 1976).
Algae have long been used in the treatment of organic
wastes. In the conventional high rate pond the population
is made up of about a 1:3 ratio of aerobic bacteria and
algae (Oron et al., 1979; Hill and Lincoln, 1981). The
aerobic bacteria stabilize the incoming waste and release
C02 into the water. Algae utilize the CO2 and sunlight to
produce algal biomass through photosynthesis. Nitrogen
composes about 10% of the dry weight of algal cells. When
the cells are harvested and removed from the wastewater, up
to 90% nitrogen removal may be obtained (Lincoln et al.,
1977). Although total phosphates compose only 1-2% of the
algal biomass, chemical flocculation of the algae for
harvest usually results in excellent phosphate removal
(Lincoln et al., 1980).
Because algae average about 50% protein considerable
effort has been made to use algal protein as a supplement in
human food and animal feeds (Yang, et al., 1981; Harrison,
1986; Lincoln and Earle, 1987). If problems of cell wall
digestibility can be overcome the feed value of the algae
will far exceed the fuel value (Oswald, 1969; Lincoln et
al., 1986). Algae are also known for a high lipid content.
Algae may be economically used in some circumstances as a
source of neutral lipids for commercial purposes (Dubinsky
et al., 1978).
Species control must be achieved in an algal system in
order to maintain a uniform product with consistent nutri-
tional qualities. Flocculation and harvesting considera-
tions also dictate that some type of species control be
practiced. Benemann et al. (1976) showed that a degree of
species control could be achieved with selective recycling.
Lincoln and Earle (1987) reported that rotifers may be
controlled by adjusting the pH and ammonium ion levels.
The high ash content associated with iron or aluminum
flocculating agents may be overcome by the use of organic
polymers and autoflotation (Koopman and Lincoln, 1983) or
biological flocculation with gravity sedimentation (Koopman
et al., 1987).
Water Hyacinth Production
Water hyacinths (Eichornia crassipes) are one of the
most prolific aquatic plants found in tropical and sub-
tropical regions of the world. They are usually regarded
only as a weed, the state of Florida alone spending several
million dollars per year for control (Bagnall, 1980). Given
adequate space and nutrients, a small mat of plants will
double in area every 6 to 18 days. The mass is roughly
proportional to the area. Wet densities are frequently in
the range of 20 to 40 kg/m2.
The water hyacinth has many characteristics that may
make it an economically useful plant. It has a balanced
nutrient content (Chynoweth et al., 1984) and is readily
digestible to methane. It exhibits a daily growth rate of
20 to 40 g/m2-d of dry biomass. Hyacinths may assimilate 10
kg N/ha-d or more, thus facilitating nitrogen removal from
effluent streams. Nitrogen removal rates of 1726 to 7629 kg
N/ha-yr were reported by Reddy et al. (1985). Several
wastewater treatment processes in the United States current-
ly use hyacinths (Stewart et al., 1987). Joglekar and Sonar
(1987) determined that hyacinths could be used to treat up
to 1250 m3/ha-d of municipal wastewater while yielding 290
kg/ha-d of dry biomass.
DeBusk and Reddy (1987) determined that maintenance of
high densities (1000 g/m2 dw) maximized biomass yields.
However, it has been shown that luxury uptake of nutrients
is most pronounced when the plants are growing slowly (Reddy
et al., 1985).
Because the dense stands of water hyacinths are free
floating they are easily harvested (Bagnall, 1980). They
can be chopped and fed into a digester as a slurry or they
may be pressed to separate the solids from the juice.
Chynoweth et al. (1984) were successful in digesting the
juice fraction separately from the solids. The juice was
found to contain up to 25% of the biogasification potential
of the entire plant.
An important consideration when examining energy
production systems is to compare the cost and forms of
energy produced with that of the energy consumed. The
fundamental objective of developing biomass as an energy
source is to capture solar energy in the form of plant
tissue and to convert it to a higher quality form of energy
(Jenkins and Knutson, 1984). To be truly useful, as opposed
to economically advantageous only in the short term, the
system must require less high quality energy than it
produces. This requires that the system be studied using
the concept of embodied energy in fossil fuel equivalents as
the true measure of feasibility (Odum and Odum, 1976).
However, since there is no demand for a system which is
economically infeasible, the economic aspect should be
The successful integration of energy production proces-
ses into an agricultural or waste treatment system requires
detailed information on how the various components will
interact with all of the other components in the system.
Material and energy flows must be evaluated, and logistical,
managerial, and environmental constraints must be identified
Hayes et al. (1987) reported the operation of an
integrated system for the treatment of municipal waste by
water hyacinths. Methane production from digestion of
hyacinths and sludge was a major goal of the project. It
was determined that methane could be produced from such an
operation at a cost of less than $2.00 /GJ in large cities.
Walker et al. (1984) analyzed operations at a large
dairy farm in New York. It was determined that a combina-
tion of practices could reduce fossil fuel energy demands by
60%. Both energy conservation and fuel substitution were
utilized. The utilization of the methane which was produced
from wastes was a significant factor. The use of methane to
fuel a cogeneration system was determined to be the best use
of the gas.
Yang and Nagano (1985) investigated a system using an
algal biomass raceway to provide additional treatment for
anaerobically digested swine waste. The focus of the study
was on the treatment aspects of the system and not on the
production of algal protein.
Chen (1984) discussed sweet potato production from a
systems point of view. The focus of this work was to
determine optimal times and methods for planting.
Hill (1984b) optimized methane fermentation at swine
production facilities. The parameter used for optimization
was the unit energy production cost. It was determined that
the maximum economic return differed substantially from the
point of maximum methane production. Heavier loading and
shorter retention times were more favorable from an economic
Kinetics of Anaerobic Digestion
As the use of anaerobic digestion has increased in the
last few decades so has the interest in the mathematical
modeling of both digestion systems and the digestion
process. Modeling of such systems may yield many benefits.
In the process of designing a system, it is usually much
faster and less expensive to model a system and simulate its
operation on a digital computer than it is to actually build
a series of pilot scale digesters and operate them over a
long period. It also contributes to an understanding of the
processes involved. Modeling forces the investigator to
quantify the relationships between the component processes.
It highlights the inconsistencies and tends to bring out the
weaknesses in theoretical knowledge. In this manner,
modeling tends to focus the direction of future experimental
Lawrence and McCarty (1969) recognized the need for a
knowledge of the process kinetics of anaerobic digestion and
proposed the following model using the bacterial growth
kinetics proposed by Monod (1949).
= a bM
dt Kg + S
M = Concentration of microorganisms, mass/volume,
dM/dt = net growth rate of microorganisms,
dS/dt = rate of substrate assimilation,
a = growth yield coefficient,
b = microorganism decay coefficient,
S = substrate concentration, mass/volume,
k = maximum rate of substrate utilization per unit weight of
Kg = half velocity coefficient for substrate utilization.
Combining these equations yields:
M Kg + S
The quantity (dM/dt)/M may be designated the net specific
growth rate, mu. However, most later work defines mu as the
specific growth rate and leaves the decay function to be
examined separately. The maximum specific growth rate, mu,
is frequently used to represent a-k, yielding the more
familiar form of the Monod equation:
Kg + S
The solutions to the above equations may be found for
steady state conditions by setting the derivatives to zero
and solving algebraically. However, transient behavior,
which must be examined in order to model maximum system
performance and digester failure, must be solved by numeri-
Contois (1959) proposed the following modification to
the Monod equation:
BP + S
where B is a constant growth parameter, and P is the bac-
Monod defined Kg, the half velocity coefficient for
nutrient utilization, as a constant for a given nutrient and
bacterial population. Contois determined that Kg appeared
to vary with population density. No microbiological basis
has been postulated for this relationship. Contois postu-
lated that the appearance of bacterial density in this
relationship may be due to an inhibitory buildup of end
products. This theory was born out by the work of Grady et
al. (1972), which showed that end product excretion varied
with both the density and growth rate of the population.
They proposed that until these relationships were better
understood, especially in mixed cultures, the generation of
statistical regression equations from operating data of
similar reactors provided the most reliable model for design
purposes. However, such equations are of little use in
dynamic modeling of a system.
McCarty (1971) presented a series of possible stoichio-
metric reactions for methanogenesis in order to more
accurately determine methane production. Reactions for both
the catabolism of carbohydrate to methane, CO2, and water
and for the anabolic synthesis of bacterial cell mass were
Andrews and Graef (1971) presented a dynamic model of
anaerobic digestion using Monod kinetics. This model
included the inhibitory effect of unionized fatty acids.
This has been shown to be an important factor in predicting
digester failure due to factors other than bacterial
washout. The model also included a pH and alkalinity
balance. This was necessary to determine the fraction of
unionized fatty acids as well as to determine CO2 gas
transfer equilibria. The inhibitory effect of the fatty
acid concentration was included in the microorganism
specific growth rate by modifying the Monod equation as
1 + -- + -
where Kg is the saturation constant, Ki is the inhibition
constant, and S is the substrate concentration. The
substrate concentration when the specific growth rate is at
the maximum is then Sm = (Ks*Ki)0.5.
Hill and Barth (1977) provided a substantial expansion
upon the work of Andrews and Graef. The maintenance of a
nitrogen balance and the addition of an ammonia inhibition
term to the methanogenic growth rate equation were of
particular importance. The carbonate mass balance and pH
calculations were also expanded.
The inhibitory effect of ammonia was included in the
specific growth rate of methanogens by modifying the Andrews
and Graef equation as follows:
Ks S NH3
1+- + -+ -
S Ki KiN
Where KiN is the inhibition constant for ammonia and NH3 is
the unionized ammonia concentration.
Hill and Nordstedt (1980) applied the work of Andrews
and Graef (1971) and of Hill and Barth (1977) to anaerobic
lagoons and anaerobic digesters. Yield coefficients and
mass transfer coefficients were determined for a number of
There are several compromises to be made in selecting
which type of model to use. Simple first order models such
as those proposed by Grady et al. (1972) and Srivastava et
al. (1987) are capable of predicting steady state operation
and require relatively few inputs. However, they are unable
to predict process failure. Monod based dynamic models may
very accurately predict process behavior, but, they require
a very large number of kinetic parameters which are fre-
quently unavailable and can only be estimated by computer
iteration (Hill, 1983a).
A third type of model was developed in an attempt to
bridge this gap (Hashimoto et al., 1980). This model was
adapted from the kinetics of Contois for a completely mixed
continuous flow system (Chen and Hashimoto, 1978; Hashimoto
et al., 1980). The model predicts the volumetric methane
production rate according to the following equation:
Bo So K
Y, = [1 ]
e e mu + K
Y, = Steady state volumetric methane productivity L/L day
Bo = ultimate methane yield, L/gm VS added
So = influent VS concentration, gm/L
e = retention time, days
mu = maximum specific growth rate, day-1
K = kinetic parameter, dimensionless.
The above equation states that for a given loading rate
(So/e) the volume of methane produced per day per liter of
digester depends on the biodegradability (Bo) of the
material and the kinetic parameters mu and K. The above
equation is based upon the following (Chen and Hashimoto,
mu = mu [
( 1 K ) S
It should be noted again that this model was derived
for steady state conditions. Under dynamic conditions it
may be seen that mu approaches mu as S approaches So,
regardless of the value of K. Therefore, this model will
not predict process failure due to inhibition, although it
is able to predict washout of the microbial population.
The Contois model of Chen and Hashimoto is adequate for
many types of engineering analysis. It accurately reflects
the methane productivity for steady state operation. Design
and optimization of anaerobic digesters was extensively
investigated by Hill (1982a, 1982b) using this model.
Biodegradability (Bo) and K were both affected by the waste
type, and K also varied with the VS loading rate. It was
determined that maximum volumetric methane productivity
occurred under substantially different conditions than did
the maximum daily production of methane.
Hill (1983a) recognized the value of having only a few
parameters, as in the Chen and Hashimoto model, while
retaining the advantages of non steady state kinetics. Hill
used Monod kinetics in his "lumped parameter" model to
obtain accurate dynamic characteristics. However, in order
to simplify the model as much as possible many of the
typical parameters were "lumped" into only two parameters
which varied with the type of waste being treated. These
parameters are the biodegradabilityy factor" (BO), and the
"acid factor" (ACFACT). To avoid confusion, it should be
noted that the biodegradability factor (BO) is the fraction
of VS which is biodegradable, whereas the biodegradability
(Bo) used by Hashimoto is the ultimate methane yield.
The assumption that all waste types can be reduced to
homogeneous organic mixtures of biodegradable volatile
solids (BVS) or volatile fatty acids (VFA) was fundamental
to the derivation of this model. The amount of BVS and VFA
was dependent upon the BO and ACFACT of the waste type.
These parameters have been determined for a number of waste
types (Hill, 1983a).
The model consisted of only six differential equations.
Four of these were mass balances and two were microbial
growth rate equations. Eight kinetic constants were
required for these six equations, along with two yield
coefficients. However, it should be noted that these were
true constants and did not vary with waste type.
Additional studies were conducted into the kinetics of
microbial death (Hill et al., 1983; Hill, 1985). Continuous-
ly expanding reactors (CER's) were used in these studies in
order to avoid interference from microbial washout. Most
previous models fixed the specific death rate, Kd, at one
tenth of the maximum specific growth rate. It was deter-
mined that this did not provide for adequate removal of
viable microorganisms when there was no term for washout, as
in a CER. A new death rate coeffcient was selected. It was
assumed that the maximum death rate was not likely to exceed
the maximum growth rate except under toxic conditions.
Therefore, the following equations were proposed:
fd = mu
1 + Kid / VFA
where Kid is the half velocity death constant for VFA.
A substantially more complex version of this model was
presented by Hill (1982c). In this model the newly defined
hydrogen-producing acetogenic bacteria and the homoaceto-
genic bacteria were included for the first time. For
mathematical reasons, it was also necessary to simulate two
groups of methanogens, one using H2-CO2 as a substrate and
the other using acetate. Five growth equations and twelve
mass balances were required. The model was validated with
previously published data.
Dwyer (1984) modified Hill's five population model by
adjusting the stoichiometric relationships of the acetogenic
reaction. This resulted in the release of additional
hydrogen and led to more accurate predictions of gas
quality. In addition, some of the kinetic parameters for
the growth models of various populations were changed from
the values used by Hill to yield a better fit to the
Additional work has been done on modeling the
transitory periods during digester start up and failure.
Hill and Bolte (1987) reported significant changes in
modeling of the hydrogenogenic population. Inhibition of
this population was determined to be dependant on both
ammonia and total VFA concentrations. Separate inhibition
constants were derived for each substance. The uptake of
propionate and butyrate was also modified. The proportional
uptake concept was replaced by a competitive substrate
concept. These changes made the five population model much
more accurate in predicting propionic-acetic acid ratios,
which was considered crucial to predicting digester failure
(Hill et al., 1987).
Most of the kinetic equations developed above were
designed to describe a continuous flow homogeneous reactor,
or chemostat. This condition is most nearly approached by
the CSTR. Transient variations in the bacterial population
for such a reactor may be described as follows (Chen and
dt = ( mu )X
dS so -S Amu*X
dt h Y
X = bacterial concentration,
Y = bacterial yield coefficient.
e, = biologically active solids residence time.
Sh = hydraulic residence time.
By definition, es = eh in an ideal CSTR where homogeneity
The fixed bed reactor, or anaerobic filter, presents a
more complicated system than the CSTR. Because much of the
biological activity in a FBR is associated with the biofilm,
the residence time of the biological solids is much longer
than the hydraulic residence time. Early attempts at
modeling of fixed film systems were made by Kornegay and
Andrews (1967) and by Mueller and Mancini (1975).
Bolte et al. (1984) presented a complex model of an
upflow anaerobic filter which portrayed the process dynamics
associated with the biofilm. However, this model is very
cumbersome to use because of the complex transport phenomena
Another model for the FBR was proposed by Bolte and
Hill (1985). This model was derived from the work of
Hashimoto et al. (1980).
Bo So K
Y, = [1 A
h eh mu -eh + K
In an attached growth reactor such as a fixed bed reactor,
es >> eh, so the equation reduces to :
Bo So K
Yv = [1 ]
eh 8h mu + K
The model predicted steady state methane production within
ten percent of the data values used for validation.
However, it is only applicable to steady state conditions.
In an attempt to make the lumped parameter model of
Hill (1983a) applicable to attached growth reactors, Bolte
(1985) proposed the use of the "bacterial retention coeffi-
cient", or BRC. The BRC is a function of the type of
reactor, recycle rate, surface to volume ratio, and media
type. The BRC represents the amount of active biomass which
is retained in the reactor by modifying the washout term in
the bacterial mass balance equation such that,
S= [mu Kd (1-BRC) eh ] X
Bolte did not validate his model and no additional work in
the literature was found which made use of the BRC to
characterize retained biomass effects.
Another technique used in the modeling of nonhomo-
geneous reactors is the simulation of plug flow conditions
by the use of several homogeneous reactors placed in series
with one another. In theory this would require an infinite
number of compartments of zero width. Two to ten compart-
ments are commonly used in practical simulations (Bolte,
The continuously expanding reactor (CER), or semi-batch
reactor, presents another challenge. Because the volume is
continuously changing, one must work with the total biomass
Young (1979) modeled a CER using beef cattle waste as a
substrate. He used the kinetics which were developed by
Hill and Barth (1977) and modified them to use extensive
rather than intensive variables. The model performed
reasonably well, although predictions of digester failure
tended to be protracted and to take place at lower than
Hill et al. (1983) used a CER model to develop the new
death kinetics reported earlier. This model used the lumped
parameter model of Hill (1983a) with modified mass balances
and extensive variables.
Alaal Growth Kinetics
Most of the literature on the growth kinetics of algae
deals with pure culture work in the laboratory. Very little
information is available on mixed culture algal growth in
the natural environment.
Enebo (1969) proposed the first order growth equation
dN/dt = k-N, where N is ammonia nitrogen and k is a function
of species, temperature, substrate concentration, pH,
illumination, etc. More recent work by Williams and Fisher
(1985) on NH4 uptake, by Gotham and Rhee (1981) on phosphate
uptake, by Terry et al. (1985) on N:P ratios and by Turpin
(1986) on C:P ratios are limited in their applicability to
mixed systems where species composition is not constant.
A study on light limitation of growth rate by
Schlesinger and Shuter (1981) provided a more general view.
Their results on the effects of light limitation on the
relative amounts of chlorophyll A and RNA were applicable to
a wide range of species. Further research into the effects
of light on protein synthesis could lead to more mechanistic
models of algal growth. When developed, these models may be
applicable to a wider range of species than currently
Hill and Lincoln (1981) assumed that microalgal
kinetics were similar to bacterial kinetics and proposed the
use of a modified Monod equation to represent algal growth
in a mixed pond. Orthophosphate, ammonia nitrogen, carbon
dioxide and incident solar radiation were treated as
substrates which could be limiting. The specific growth
rate for algae was determined to be:
mualg = mualg (mulim) (1.05)T-25
where mulim was equal to the musub of the most severely
limiting substrate as determined by the equation:
musub Kssub+ [Sub]
where "sub" is one of the aforementioned substrates. The
temperature dependency function was an Arrhenius relation-
ship based on 25 degrees C for each log cycle change in
The model was calibrated using experimental data from
the algal pond at the University of Florida Swine Research
Unit in Gainesville, Florida. It was determined that the
ratio of algal biomass to bacterial biomass was about 3:1.
It was also determined that algae growing on the anaerobic
swine lagoon effluent were not nutrient limited and that
light was the only limiting factor.
Bolte et al. (1986) found the model of Hill and Lincoln
(1981) to be most accurate model available.
Water Hyacinth Modeling
Very little modeling of hyacinth growth has been
reported in the literature. The most comprehensive work to
date has been the model presented by Lorber et al. (1984).
They proposed a basic physiological equation to describe
hyacinth growth as follows:
dt = (Pg Rm) E ] D
W = dry weight, mass/area,
Pg = gross photosynthesis, mass/area,
R, = maintenance respiration, mass/area,
E = conversion efficiency
D = detrital production, mass/area.
It was assumed that the hyacinths were in a vegetative
stage, and phenological stages were not included.
Gross photosynthesis is primarily a function of inci-
dent solar radiation and temperature. Nitrogen and phos-
phate may become limiting factors. Density may be a
limiting factor if the plant population becomes so dense
that shading occurs. The model was extensively validated
with data from several sites in Florida.
Curry et al. (1987) attempted to add nutrient uptake to
the work of Lorber et al. (1984). However, the model
frequently underestimated the nitrogen uptake by 30% or
more. Stewart et al. (1987) presented another model of
nutrient uptake for water hyacinths. Their model used a
Monod relationship for nitrogen and phosphorus uptake. The
model was validated with data from five wastewater treatment
systems. In general, the model was considered adequate for
operational purposes. Nevertheless, additional information
is needed to fully characterize nutrient uptake by water
Modeling may be described as compositional analysis
(Smerage, 1982). There are two levels of systems modeling.
The conceptual model is a qualitative statement of the
components of a system, a generic description of those
components, and a description of their interconecting
relationships. Mathematical models form the second level
and are comprised of mathematical statements which describe
the system components and their interrelationships.
Behaviorial analysis is the determination and inter-
pretation of the behavioral properties of a system by
analysis of a mathematical model. This may be carried out
by direct mathematical analysis for very simple models.
However, computer simulation is required for the analysis of
most real systems.
Simulations of agricultural and biological systems
generally fall into one of two broad, and sometimes over-
lapping, categories. Management oriented models generally
involve the study of existing systems, the comparison of
alternatives, or the design of new systems. Research
oriented models are distinguished by objectives related to
understanding the mechanism of behavior of a system.
Research models are unique in that they may be most
valuable in their failure to predict the system behavior
accurately, thereby disproving the hypothesis and pointing
the direction for further research (France and Thornley,
1984). This statement is supported by Jones et al. (1987,
p.16) in the statement, "a model cannot be validated, it can
only be invalidated".
Jones et al. (1987, p.18) quotes Dent and Blackie
(1979) in their excellent discussion on validation. In
part, they proposed that a model is adequate if
a. the model is not different from the real
existing system to a degree that will detract
from the value of the model for the purposes
for which it was designed.
b. That if the model is accepted as being
adequate then the decisions made with its
assistance will not be measureably less
correct than those made without the benefit
of the model.
Kloss (1982) reported on the use of a farm system model
to determine the optimal layout for a biogas plant. Several
options were investigated, and a number of general recom-
mendations were presented.
A swine waste digestion system was modeled by Durand et
al. (1987). The purpose of the model was to optimize the
system for net energy production. Several recommendations
were made based upon the model, including the use of
psycrophilic digestion to reduce digester heat loss and the
use of fuel cells for energy production in place of an
Walker (1984) presented a detailed description of the
modeling process with special application to the modeling of
a dairy farm. A particularly valuable point was brought out
in the distinction between process integration and system
integration in traditional energy analysis. Walker empha-
sized that focusing on a single process or group of proces-
ses may be counterproductive in shifting dependence from one
material, such as fuel oil, to another, such as scarce and
energy intensive alloys. It was emphasized that all com-
ponents of the system, including management, must be
examined with a view toward the system as a global entity.
A schematic diagram of the system is shown in Figure 5.
Development of the system model is presented in six sec-
tions. First, the overall mass balances for hydraulic flow
and volatile solids will be presented. Second, mass
balances for the system products, algae, hyacinths, and
biogas, will be presented. A discussion of the thermal
energy balance will also be included in this section.
Third, the costs and revenues associated with the system and
their economic impact will be examined. The fourth, fifth,
and sixth sections will describe in detail the simulation
modeling of the bioconversion processes involved in the
anaerobic digesters, the algal growth unit, and the aquatic
plant unit, respectively.
System Flow and Volatile Solids Mass Balances
A diagram showing the hydraulic and volatile solids
(VS) flows in the system is presented in Figure 6. The
system hydraulic flow and VS content are defined by input
data. Refer to Appendix A for nomenclature assigned to the
The first process to be modeled was the initial separa-
tion of the liquid and solid components of the influent
stream and their distribution to the various reactors or to
the system dump, or sink. The system dump represents a
municipal sewer or other outfall which can accept theoreti-
cally unlimited hydraulic and VS flows with an economic
penalty based upon both the hydraulic load and the VS load
accepted. The mass balance for the initial flow distribu-
tion is as follows:
fl + f21 + f3 + fdl fin = 0
S1 + S21 + S3 + Sdl Sin = 0
where fin and Sin are externally specified and:
Sin = fin *in (kg)
fl = fin f%l (m3/d)
f2 = fin f%2 (m3/d)
f3 = fin f%3 (m3/d)
fdl = fin -l f21 f3 (m3/d)
1= Sin VS%1 (kg/m3)
S21 = Sin VS%2
S21 = S21 (kg/m3)
=3 Si VS%3 (kg/m3)
Sdl = Sin s1 fl S21 s3 f3 (kg)
f2 = f21 + f2h (m3/d)
s2 = S21 + S2h (kg/m3)
where f%n is the fraction of flow distributed to a unit and
VS%n is the fraction of VS distributed to a unit.
Flow from the reactors may be distributed to one of
three locations. These are the algal production unit, the
hyacinth growth unit, and the system dump. The fraction of
flow sent to each is externally determined. The mass
balance for this distribution is as follows:
fl + f3 fhr fa fd2 = 0
S1 + S3 Shr Sa Sd2 = 0
fa= fl fal + f3 fa3 (3/d)
fhr = fl % + f3 fh3 (m3/d)
fd2 = l + f3 fa fhr (m3/d)
sa fl = f%al siout + f3 fa3 S3out (kg/m3
shr fl fhl silout + f3 h3 S3out (kg/m3
5hr = (kg/mn3)
Sd2 = fl slout + f3 s3out fa a fhr' shr (kg)
The effluent from the algal production unit may be
directed to the hyacinth pond or to the system dump. The
fraction of effluent sent to the hyacinths is determined by
input data. The mass balance for the distribution of
effluent from the algal pond and for the hyacinth influent
is given below.
fha = faout ha (m3/d)
fd3 = out fha (m3/d)
fh = fhr + fha (m3/d)
sh = (fhr shr + fha sha) / th (kg/m3)
Effluent from the hyacinth growth unit is discharged
from the system.
Product Mass and Energyv Balances
Algae are harvested from the growth ponds at a speci-
fied frequency or when a predetermined density has been
reached. The amount of algae harvested is calculated on a
dry weight basis according to the formula:
algal harvest = [algal density before harvest (g/m3) -
algal density remaining] pond volume.
The harvest is reported in tonnes (metric) dry weight. The
algal mass balance for the system is:
Algae @ t=0O + net algae produced algae harvested -
algae @ t=end = 0.
Similarly, the harvesting of hyacinths occurs at either
a specified frequecy or at a predetermined plant density.
The harvest is calculated as:
hyacinth harvest = [density before harvest (g/m2) -
density remaining] pond area.
The harvest is reported in tonnes dry weight. The mass
balance for the hyacinth system is as follows:
hyacinths @ t=0 + net hyacinth production hyacinths
sold hyacinths fed to the CER hyacinths @ t=end = 0
The biogas produced by the three reactors may be used
to power an electrical generator or fire a boiler. It may
also be stored for future use or, if the storage capacity,
defined by input data, is insufficient, it may be flared off
for safe disposal. Methane was assumed to have a heating
value of 39.1 MJ/m3.
Methane production from the digesters was summed as
M1 + M2 + M3 + Ms = Mt
G1 + G2 + G3 + Gg = Gt
Mt 100 = Qt
where Gn = biogas produced by reactor n, Mn = the methane
produced from reactor n, t = total, s = stored, and Qn is
the percent methane content of the biogas. The mass balance
biogas produced biogas consumed biogas stored = 0.
When adequate biogas was available, the generator was
assumed to produce its rated capacity for a 24 hour period.
If insufficient biogas energy was available to run at full
capacity then only the amount available was converted to
electrical kilowatt-hours. Low grade heat in the form of
hot water was available from the generator cooling system.
The hot water could have been used for digester heating or
other in-plant uses.
Biogas in excess of that needed for electrical power
generation was used to fire a boiler. If sufficient energy
was available the boiler produced steam at its rated capaci-
ty. Otherwise it converted the biogas that remained after
electrical generation into steam. Boiler steam could be
used to heat the digesters, used in-plant or sold for off-
Any biogas remaining after both the generator and the
boiler have operated at their full rated capacity was stored
for future use. If insufficient storage capacity was avail-
able, the remaining gas was flared.
A thermal energy balance of the heated digesters was
performed to determine the heat losses. These losses must
be made up by heat from either co-generated hot water or
from the boiler generated steam. If both of these sources
were insufficient to maintain reactor temperatures, then
heat energy was purchased from an outside source.
Two sources were taken into account during calculation
of the reactor heat losses. These were the conductive
losses through the walls of the reactor vessel and the
convective losses due to warm effluent being replaced by
cooler influent. In the first instance the losses were
calculated using the vessel surface area and an effective
"R" value for the reactor walls. If reactor temperature was
greater than the ambient temperature as defined by input
data the heat losses were calculated by :
Area (T -T
SArea (Treactor ambient)
where Q is in units of Joules/sec.
The second source of heat loss is convective and was
calculated by the equation:
Q = mass flowrate C (Treactor- Tinfluent)
where C is the specific heat of the substrate.
The influent temperature was assumed to be ambient.
However, the system may be defined through the input data to
include a heat exchanger. This reduces the temperature
differential by an amount equal to the heat exchanger
Costs. Revenues, and Economic Analysis
The costs associated with the system were of two types,
capital costs associated with initial construction of the
system, and operating costs.
Capital costs, other than land, were calculated in
terms of 1976 dollars in order to properly account for
inflation. These costs include digester construction, algal
growth unit and aquatic plant unit construction, and a
pumping station. Engineering, contingency and administra-
tive costs were also included. These costs were adjusted to
current values by use of the Engineering News Record (ENR)
Construction Cost Index, the current value of which is input
data. The cost of land was derived from input data in
Operating costs, including depreciation and interest
costs, were calculated in current dollars. Unit costs for
labor, electrical power, flocculating agents, and other
operating expenses are input data.
Most of the equations used to estimate the capital
costs were derived from information presented by Vernick and
Walker (1981). Exceptions were the aquatic plant unit, the
cost of which was derived from McMahon and Pereira (1984),
and the algal unit. The methods used to estimate the
capital cost of the major components are described below.
Vernick and Walker (1981) presented cost data in the
form of graphs of construction cost (in 1976 dollars) vs.
plant size for various waste treatment unit operations.
Data points were taken from these curves and regressions
performed to obtain the cost equations presented herein.
Capital costs associated with the construction of the
anaerobic reactors were estimated by adapting information on
the cost of anaerobic municipal sludge digesters. The
Cost = $6906 Volume 0.494
approximated (r2 = 0.97) the data of Vernick and Walker
The cost of the algal production unit was calculated
from the information presented by Johnson, et al. (1988) for
algal raceways. When adjusted to 1976 dollars, the con-
struction cost was approximately $89,400 per hectare. This
fits well with the $80,000 $100,000 per hectare reported
by Dubinsky et al. (1978).
The growth ponds for the aquatic plant unit were
estimated to cost $2.24 /m3. This figure was based solely
on the earthmoving, compaction, and embankment required to
form the ponds.
The cost for construction of a pumping station was
estimated using the equation:
Cost = $486.5 design flow (m3/d) 0.58,
which matched the data of Vernick and Walker (r2 = 0.96) and
closely approximates the author's experience with sewage
lift stations and water treatment plants.
Non-component capital costs, such as laboratory
instrumentation, materials handling equipment, small build-
ings, and other miscellaneous capital expenditures were
estimated to be 30% of the major component capital cost
(Vernick and Walker, 1981).
Administrative costs were assumed to be 10% of the
total material capital cost. Engineering and contingency
costs were each defined as 15% of the material and adminis-
trative capital costs.
The base capital cost of the system was defined as the
sum of the major component capital costs, non-component
capital costs, and administrative, engineering, and contin-
gency costs. This value was adjusted for inflation using
the ENR construction cost index by the following formula:
adj. capital cost = base cost new index
The cost of the land was added to the adjusted capital cost,
resulting in the total capital cost of the system.
Depreciation was calculated on a straight line basis
from the adjusted base cost. Simple interest was calculated
on the total capital cost of the system.
Operating costs for the system were calculated in terms
of current dollars. Calculation of the daily cost of
operation was performed at the end of each day's simulation.
These daily costs were summed over the simulation period to
reflect a total operating cost for the simulated period.
The operating costs included the power cost of pumping
between various units, mixing the CSTR and algal unit, and
harvesting and processing hyacinths. Other costs included
the purchase of energy to heat the digesters, chemicals to
flocculate the algae during harvest, and charges associated
with disposal of the effluent to the system dump, including
surcharges for VS loading. The cost of labor, including
both a fixed amount of labor to operate the system and a
variable amount dependent upon harvest size and frequency,
was also calculated.
The power required for pumping was estimated to be 1.33
MJ/m3 at 10m of head (Vernick and Walker, 1981). Reactor
mixing requirements were assumed to be 14.9 J/m3-sec. The
daily power requirement for algal mixing, aeration, and
harvest was defined as input data on a per unit volume
basis. Power needed to harvest the water hyacinths varied
directly with the quantity harvested and inversely with the
average diameter of the chopped particles (Bagnall, personal
The fixed labor cost for operating the system was based
on the need for 3 full-time employees for plants up to 3785
m3/d of design flow plus 1 additional employee for each
additional 3785 m3/d (1 mgd) of design flow. Variable labor
costs were based on the number of tonnes of algae or
hyacinths harvested and also on a fixed number of manhours
per harvest for algae.
Revenues were calculated in terms of current dollars.
As with the operating costs, revenues were calculated at the
end of each day's simulation and summed to provide a total
revenue for the period of the simulation. Revenues were
assigned for the sale of algal and hyacinth biomass,
electrical power and for steam from the boiler. Additional
revenues were credited for the use of hot water from the co-
generation system and for the removal of volatile solids,
which would otherwise incur a cost. When these credits were
not to be considered in generating the economic summary, the
respective values were set to zero in the input data.
A summary of the economic performance of the system was
prepared at the end of each simulation. Net operating
revenue was defined as total operating revenue plus total
operating credits less total operating costs. Net revenue
was defined as net operating revenue less interest and
depreciation costs. The rate of return was calculated by
the following equation:
Rate of Return = Net Revenue 100
Tax implications were not considered in the economic
analysis. Due to the complexity of the subject it was
determined that tax implications were outside the scope of
Anaerobic Digester Models
General process model
The anaerobic digestion process model was a generic
model designed to represent a wide variety of reactor
configurations. It was based on the "lumped parameter"
method of Hill (1983a) and Hill et al.(1983). Hill (1983)
used Monod kinetics for dynamic simulation. However, he
simplified the characterization of wastes into only two
factors, the biodegradability factor (BO) and the acid
Bolte (1985) adapted Hill's method to attached film
reactors by incorporation of a bacterial retention coeffi-
cient (BRC). The BRC was the fraction of active biomass
that was assumed could not be washed out of the digester.
Bolte worked with swine waste supernatant and assumed
all biodegradeable organic matter was either soluble or so
rapidly degradable as to be of negligible decay time.
The anaerobic digestion submodel created for use within
this system model included a modification of the work of
Bolte (1985) to include slowly degradable substrates and to
provide better estimates of substrate effects on methane
content of the biogas. It was designed to allow most
reactor types to be represented with only minor changes,
most of which could be made by changing parameters in a
reactor specific procedure which called the process model as
a subroutine. Integration was performed by a fourth order
Runge-Kutta integration routine. The models of Hill (1983a)
and Bolte (1985) were defined by only four state variables.
These were the two bacterial populations and their respec-
tive substrates. The generic process model used in this
study adds two additional state variables to account for
varying degradation rates of complex organic matter. The
state variables and their associated parameters are shown in
Table 1. Selected variables used in the digestion model
m = acetogenic bacterial concentration, kg/m3.
mc = methanogenic bacterial concentration, kg/m3.
mu = acetogen growth rate, l/d.
muc = methanogen growth rate, l/d.
kd = acetogen death rate, l/d.
kdc = methanogen death rate, l/d.
loom = lignified, or slowly degradable, complex
organic matter, kg/m3.
rdcom = readily degradable complex organic matter,
Icombkd = breakdown rate of loom, kg/m3-d.
rdcombkd = breakdown rate of rdcom, kg/m3-d.
SO = soluble organic material, kg/m3.
VFA = volatile fatty acids, kg/m3
BRC = bacterial retention coefficient
volk = volume of one compartment of a reactor, m3
flow = volume of liquid added to the reactor, m3/d
y = acetogenic yield coefficient, g org./g substrate
yc = methanogenic yield coefficient, g org./g substrate
yhac = acid yield coefficient, g VFA produced / g
acetogenic bacteria produced
Digesters were divided into a number (k) of equally
sized compartments which were considered to be completely
mixed reactors. The six basic rate equations for k > 1 were
(1) Rate of change of acetogens:
d[k]= (mu kd (1-BRC)flow)m[k] + (1-BRC)flow m[k-l]
dt volk volk
(2) Rate of change of methanogens:
= (muc kdc (1-BRC)flow )mc[k] + (1-BRC)flow mc[k-1]
(3) Rate of change of lignified COM:
dlcom = (lcom[k-1] Icom[k])flow Icombkd
(4) Rate of change of readily degradable COM:
drdcom = (rdcom[k-l] rdcom[k])flow
+ Icombkd rdcombkd
(5) Rate of change of soluble organic:
dSO = rdcombkd + (SO[k-l] SO[k])flow + kd*m[k]
+ kdc-mc[k] mu*m[k]
(6) Rate of change of volatile fatty acids:
dVFA = (VFA[k-1] VFA[k] flow + mu-m[k]-yhac -mucmc[k]
dt volk yc
The equations were modified slightly for the compartment
k = 1. In this case the influent bacterial concentrations
were assumed to be zero, and the substrate [k-1]
concentration was replaced by the influent substrate
concentration (ie. SOin).
The above equations represent the rate equations for
continuous flow reactors. Non-continuous flow reactors such
as the CER were modeled as a single homogeneous reactor with
no effluent flow. The unloading of this type of reactor was
treated as a discrete event and handled outside the diges-
tion routine. The rate equations for the CER were as
(1) Rate of change of acetogens:
dm = (mu kd)*m
(2) Rate of change of methanogens:
dmc = (muc kdc)*mc
(3) Rate of change of lignified COM:
dlcom = (Icomin) flow lcombkd
(4) Rate of change of readily degradable COM:
drdcom = (rdcomin) flow + Icombkd rdcombkd
(5) Rate of change of soluble organic:
dSO = (SOin) flow + kd*m + kdc*mc + rdcombkd mu*
dt volk y
(6) Rate of change of volatile fatty acids:
dVFA = (VFAin)flow + mu-m-yhac muc*mc
dt volk yc
The bacterial growth and death rates were those
proposed by Hashimoto (1980) and have been used extensively
by others (Hill, 1983b; Dwyer, 1984) in validated models.
Hashimoto proposed that a single maximum specific growth
rate (mu) be used which was common to all of the populations
in the digester. He determined this value to be
mu = 0.013-(T) 0.129
where T was the temperature between 20 and 60 degrees C.
The maximum specific bacterial death rate was proposed
to be equal to the maximum growth rate (Hill et al., 1983).
The ka had previously been taken as one tenth of mu.
However, it was shown that this was an insufficient removal
mechanism in CER type reactors where there is no bacterial
washout. The Monod coefficients ki, kic, ks, and ksc were
taken directly from Hill et al. (1983). The following
equations were used to calculate specific growth and death
1+ ks + VFAk]
+ ksc + VFA[k]
1 + ki
kdc = kac
1 + kic
where mu = acetogenic growth rate (d-1), muc = methanogenic
growth rate (d-1), kd = acetogenic death rate (d-1), and kdc
= methanogenic death rate (d-1).
The degradation rates for rdcom and clom were based on
simple first order kinetics. Rdcom was defined as that
material which had an average half-life of two days before
breakdown into soluble organic material. The two day half-
life was determined during calibration and sensitivity
testing using reactors operated at retention times which
varied from 6 days to 9 hours.
Similarly, lcom was defined to have a half-life of 20
days and break down into rdcom. This represented material
which was protected from rapid hydrolytic attack by the
lignocellulosic structures frequently found in crop residues
and other sources of biomass. Calibration of the lcom
breakdown rate was accomplished using data from Chynoweth et
Yield coefficients for the model were obtained from a
variety of sources. The acetogenic and methanogenic yield
coefficients, y = 0.1 grams of acetogenic organisms / gram
substrate, and yc = 0.0315 grams of methanogenic organisms /
gram substrate, were obtained from Hill et al. (1983).
Yield of acetate from soluble organic metabolized
during acetogenesis was derived from the stoichiometry of
Dwyer (1984). This work was done on a model using five
bacterial populations instead of two. Therefore, contribu-
tions from the degradation of propionate and butyrate, and
from the homoacetogenic conversion of CO2 were added to
obtain the proper value. Because neither pH or carbonate
balances nor hydrogen-using methanogens were considered in
this model, it was assumed that approximately 11% of the
available CO2 from acetogenesis was used in homoaceto-
genesis. This was supported by sensitivity analysis during
model calibration. A value of yhac = 6.64 grams VFA / gram
acetogens produced was used in the model.
The volumetric yield of CO2 from acetogenesis was taken
directly from Hill and Barth (1977). The volumetric yields
of methane and CO2 from methanogenesis were modifications of
the Hill and Barth parameters. To adjust the volumetric
yields of Hill and Barth to account for a higher proportion
of hydrogen utilizing methanogenic bacteria when non-
carbohydrate substrates were used, a factor, CH4RAT, was
defined. This was defined as 1.0 for pure carbohydrate sub-
strates but varied down to 0.69 for swine waste. It may be
roughly thought of as having represented the conversion of
CO2 to acetate and the direct reduction of CO2 to methane.
The volumetric yield parameters were as follows:
yvCO2 = 2.35,
yvCH4 = 15.86 / CH4RAT
ycvCO2 = 9.32 [15.86 (1-CH4RAT)],
where yvCO2 = L CO2 / gram acetogens produced, yvCH4 = L CH4
/ gram methanogens produced, and ycvCO2 = L CO2 / gram
Volatile solids reduction was assumed to be through
conversion to CO2 or methane. The following equation
represents this destruction:
VS destroyed = 0.782 (VFA used) + 0.284 (SO used).
The conversion factors were from two sources. The conver-
sion factor for the destruction of VFA by methanogens,
0.782, was taken directly from Bolte (1985). The acetogenic
destruction of SO was calculated from the work of Dwyer
Substrate composition has a marked effect on digester
operation. The values of BO and ACFACT used to describe
beef, dairy, swine, and poultry waste were those of Hill
(1983a). Bolte (1985) described screened swine waste
(ACFACT = 0.10 and BO = 0.95) and protein-carbohydrate waste
(ACFACT = 0.001 and BO = 1.00).
Inherent in the use of only two "lumped" parameters to
describe a substrate was the assumption that the substrate
was instantly available for use by the bacterial population.
This assumption may have been valid for relatively volatile
wastes digested at long retention times. In such a case the
time required for hydrolysis is short compared to the
Where these conditions were not met, as in a fixed bed
reactor operating at a short retention time, or when digest-
ing slowly degradable biomass, it became necessary to devise
a more accurate representation.
To satisfy this need to represent the breakdown of
complex materials, two additional substrate parameters were
defined. These were the readily degradable fraction of the
biodegradable solids (rdf) and the lignified, or slowly
degradable, fraction of the biodegradable solids (lf).
The readily degradable fraction of the waste was
defined to have an average half-life of 2 days. This meant
that there was little effect on reactor operation at
retention times in excess of six to eight days, where most
CSTR's operate. However, it had a very large effect on
FBR's where retention times were much shorter and potential
substrate material could wash out of the reactor before it
could be digested.
Calibration of the rdcom parameter for swine waste was
accomplished using the data of Nordstedt and Thomas (1985b).
Swine waste was determined to have a rdf = 0.69. The
protein carbohydrate waste was found to have a rdf = 0.8.
The lignified component of these wastes was considered
negligible. Beef and poultry wastes were not calibrated for
rdf because low retention time data was unavailable. The
rdf for beef was assumed to be 0.7 in this model based on
similarity with swine waste. However, the lignified
fraction could be significant in some cases where large
amounts of bedding were incorporated. Poultry wastes were
assigned a value for rdf = 0.5 as an estimate of their
degradability, but this has not been tested at the short
retention times needed for validation.
Continuous stirred tank reactor model
This is the conventional continuous flow anaerobic
digester. All state variables were kept in their intensive
The model defines the bacterial retention coefficient
as zero. The number of compartments to be simulated was
defined as 1 since this was a theoretically homogeneous
reactor. The waste type and influent concentration, flow,
reactor volume and temperature were determined from input
data. These values, and those of the state variables at the
end of the last day's simulation, were passed to the general
process model. The returned state variables were stored for
use in the next day's simulation.
Fixed bed reactor model
This model was identical to the CSTR in that it was a
continuous flow reactor model using intensive variables.
Operation was similar to the CSTR except for two parameters.
The FBR model defined an FBR as five compartments in
series, each one-fifth of the total reactor void volume, so
as to create a psuedo plug flow effect. The bacterial
retention coefficient was BRC = 0.995. This resulted in an
active bacterial retention time of 50 days at a hydraulic
retention time of 6 hours. This was a reasonable value for
a well developed biofilm, as evidenced by the stability
exhibited by the number of successful reactors operated at
short hydraulic retention times.
Continuously expanding reactor model
The continuously expanding reactor was treated dif-
ferently from the types previously discussed because it was
not a continuous flow reactor. The effluent term of the
mass balance equation was zero except during discrete
emptying events. The influent term, however, was semi-
continuous. As a result the volume varied with time.
To correctly represent these differences the CER model
stored state variables in their extensive form. Upon
execution, the model calculated the new volume of the CER
and converted the state variables from the extensive form to
the intensive form used by the generic digestion model.
After the digestion routine had simulated the biologi-
cal processes for the day, the returned state variables were
multiplied by the volume to convert them to extensive form.
They were then passed back to the global system model to be
stored until the next execution of the CER simulation
Because there was no effluent, the bacterial retention
coefficient was meaningless. The CER was assumed to be
homogeneous and was simulated with a single compartment.
Because of the limited data available on CER operations
and on hyacinth digestion, water hyacinth characteristics
were specifically calibrated for the CER model. Biodegrad-
ability was taken to be 0.66 based on the work of Chynoweth
et al. (1984). The readily degradable and lignified frac-
tions were calibrated in accordance with the work of
Nordstedt (1988). The parameters were set to rdf = 0.5,
If = 0.4, ch4rat = 0.7, and the acid factor = 0.05.
The discrete emptying event was triggered by the CER
reaching the design maximum volume. First the state
variables were converted to the intensive form. The CER
volume was then reset to a predetermined "seed" volume to
begin the next cycle. Finally the state variables were
returned to their extensive form. Effluent distribution for
land application was also performed at this time.
Algal Growth Model
In general, growth and nutrient uptake kinetics of
microalgae have been modeled using some form of the Monod
relationship. Temperature has historically been used to
modify the growth rate by using a linear or exponential
temperature factor (Bolte et al., 1986). The algal growth
model used here was based on the work of Hill and Lincoln
The model developed by Hill and Lincoln (1981) used
five inputs to determine specific growth rate. These were
temperature, C02, ammonia, orthophosphate, and light. The
temperature effect was modeled as a standard Arrhenius
function. The other nutrients, and light, follow the Monod
The most limiting substrate was used to determine the
overall growth rate for the model at each iteration. A
death rate, kd was included to account for senescence and
predation. The following equation was used to calculate the
net algal growth rate.
mu algae (mu algae mulimit- kd) 1.05
algae algae limit
where mulimit was the most limiting musub.
In experiments using wastewater from a swine lagoon it
was determined that CO2, ammonia and phosphate were present
in excess (Hill and Lincoln, 1981). Since the primary feed
for the algal unit was digester effluent, this model assumed
that these nutrients were present in excess. Tracking the
above nutrients through the system was left for further
research. Only the radiation component was considered
limiting in this model.
The daily radiation was considered to be spread over 13
hours in a sinusoidal pattern from 7 AM to 8 PM. Kg was
determined to be 2.60 MJ/m2-hour. This was equivalent to the
value (1.037 Langleys/minute) used by Hill and Lincoln. The
maximum specific growth rate was 3.0 d-1 as determined by
Hill and Lincoln. In calibrating the model to the published
data, kd was set to 0.25 d-1.
The rate equation d alg/dt = mualgae X was inte-
grated hourly by a 4th order Runge-Kutta integrator to yield
the algal concentration.
Algal yield in g/m2 was determined by the effective
depth of the algal channel. This was the depth to which
adequate light could penetrate to sustain growth. Under
normal conditions it varied between about 0.2 and 0.4 meters
but could be substantially reduced by high turbidity.
Water Hyacinth Growth Model
The growth model for the water hyacinths (Eichornia
crassipes) was taken from the work of Lorber et al. (1984).
The basic physiological equation describing the growth of
water hyacinths was:
dW/dT = (Pg Rm) E D
where W = dry weight, g/m2
Pg = gross photosynthesis, g/m2-day
R, = maintenance respiration, g/m2-day
E = conversion efficiency, dimensionless
D = detrital production, g/m2-day
It was assumed that the plants remained in the vegeta-
tive stage, therefore, phenological growth stages were not
modeled. It was felt that this assumption was valid due to
the frequent harvesting which takes place in a biomass
Gross photosynthesis (Pg) was a function of the amount
of solar radiation intercepted by the plants, the tempera-
ture, and the nutrient levels in the ponds. It was descri-
bed by the following equation:
Pgmax f(dens) f(T) f(P) f(N)
Pgmax = 22.318 + 0.102 S S > 100
= 0.32 S S < 100
and S = incident solar radiation in Langleys / day.
The density function accounted for the inability of the
canopy to intercept all of the incident light at low den-
sities. The function was based on work by Debusk et al.
(1981) and was given by the equation:
f(dens) = W / 1000 W < 1000 g/m2
= 1.0 W > 1000 g/m2
The temperature function used by Lorber et al. (1984)
and reported by Mitsch (1975) was modified slightly to
promote model stability at low temperatures. The modified
function was given as:
f(T) = 1.0 0.0038 (T-29)2 T > 15 C
= 0.255 T < 15 C
In this model, phosphorus and nitrogen were assumed to
be present in excess of the minimum concentrations. There-
fore, f(P) and f(N) were defined as 1.0 in this model. In
fact, the more likely scenario would be inhibition due to
ammonia toxicity. However, this toxic effect is not well
documented. Many other factors should also be considered in
the removal of nutrients from ponds, several about which
little is quantitatively known. Because of this, nutrient
removal by the hyacinths was left for future modeling
The maintenance respiration requirement was extracted
from gross photosynthate (Pg Rm) prior to conversion to
plant material. The respiration function was a linear
function of the existing crop and was given as:
R, = Ro I W
where Ro was the respiration coefficient. In this model, Ro
was set to the value 0.01 recommended by Lorber et al.
(1984). This value was reasonable and in line with those of
soybeans and other crops.
Because only the vegetative growth stages were modeled,
the conversion efficiency (E) was considered a constant.
Lorber et al. reported a conversion efficiency of 0.83,
which was comparable to the 0.73 reported for soybean growth
(Wilkerson et al.,1983).
The formation of detrital material due to overcrowding
was estimated to occur at densities in excess of 2400 g/m2.
At a density of 2600 g/m2 detrital formation was expected to
equal the photosynthetic growth. The following equation
governs detrital production due to overcrowding:
D = dW [1 ((2600 W) / 200)] W > 2400
= 0.0 W < 2400
It should be noted that production of detritus due to poor
growth conditions was reflected in the term (Pg Rm).
Model validation is the process by which the suitabil-
ity of the model is evaluated in light of the purposes for
which it was designed. As was mentioned at the end of the
literature review, a model can never be validated, only
invalidated. The difference between calibration and
validation is that during calibration the parameters of the
model are adjusted to make the model fit the data. In the
validation process the data used is independent of that used
to calibrate the model and no adjustments are made to the
model parameters. Only the model inputs which characterize
the nature of the experiment producing the real data are
manipulated. The output data from the simulation is then
compared to the real data to obtain an indication of the
validity of the model.
Continuous Stirred Tank Reactor Model
The CSTR model was validated by comparing the simulated
methane production with that reported in the literature.
Nineteen studies were evaluated. Swine waste was used as
the substrate in 10 studies, 3 used beef waste, 2 used dairy
waste, and 4 used the waste from poultry layer operations.
The type of waste, operating temperature, hydraulic
retention time, influent volatile solids concentration and
reference are listed in Table 2. The scatter diagram of
predicted vs. actual volumetric methane production for the
CSTR studies is presented in Figure 7. Linear regression was
performed on this data, and the 95% confidence limits are
shown by the envelope bounded by smooth curves on either
side of the diagonal line representing perfect agreement.
Table 2. Sources for CSTR model validation data
Waste Temp. HRT VS CH4 Reference
type (C) (days) (g/L) (L/L-d)
Swine 35 15 50.4 1.22 Hashimoto(1983)
Swine 55 15 50.4 1.45 Hashimoto(1983)
Swine 55 10 50.4 1.80 Hashimoto(1983)
Swine 22.5 40 36 .29 Stevens & Schulte(1979)
Swine 35 15 39.2 1.07 Fischer et al.(1975)
Swine 35 15 60 1.36 Fischer et al.(1975)
Swine 35 15 46.8 1.17 Fischer et al.(1975)
Swine 35 15 43.4 1.08 Fischer et al.(1975)
Swine 35 18 36.0 .71 Lapp et al.(1975)
Swine 35 30 31.4 .49 Kroeker et al.(1975)
Layer 35 44 69.1 .58 Converse et al.(1977)
Layer 35 31 59.5 .74 Converse et al.(1977)
Layer 35 42 81.9 .77 Converse et al.(1977)
Layer 35 52.5 72.5 .67 Converse et al.(1977)
Beef 55 12 62.5 1.59 Hashimoto et al.(1979)
Beef 55 7 82.6 3.57 Hashimoto et al.(1979)
Beef 35 20 47.5 .69 Burford et al.(1977)
Dairy 35 12 76.8 .77 Coppinger et al.(1978)
Dairy 35 15 64.7 .67 Converse et al.(1977a)
+ ) \ 0
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\ \ \ -
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P-i/-i "poaid tH3 lonjiV
Fixed Bed Reactor Model
The fixed bed reactor model was validated by conducting
simulations of 23 fixed bed reactor operations reported in
the literature. Temperatures ranged from 24 to 55 C and
hydraulic retention times from 1 to 19 days. Influent
volatile solids concentrations varied from 1.5 to 25 kg/m3.
Substrates included both swine waste and food processing
The type of waste, operating temperature, hydraulic
retention time, influent volatile solids concentration and
reference are listed in Table 3. A scatter diagram of
predicted vs. actual volumetric methane production for the
FBR studies is presented in Figure 8. Linear regression was
performed on this data, and the 95% confidence limits are
Continuously Expandina Reactor Model
Validation of the system's CER model was limited by
lack of available data. The work of Hill et al. (1983) and
Hill et al. (1985) provided many of the parameters used in
the general digestion model. The only other CER studies
available were those of Young (1979) and Nordstedt (1988).
The data of Nordstedt (1988) was used with the CER
model to characterize the breakdown characteristics of the
water hyacinth biomass. Therefore, this work was more
Table 3. Sources for FBR model
Waste Temp. HRT VS CH4 Reference
type (C) (days) (g/L) (L/L-d)
Whey 32 2.0 5.6
& Sievers (1983)
& Sievers (1983)
& Sievers (1983)
& Sievers (1983)
& Sievers (1983)
van den Berg(1982)
van den Berg(1982)
van den Berg(1982)
van den Berg(1982)
van den Berg(1981)
van den Berg(1981)
van den Berg(1981)
.52 Thomas (1984)
P--i/- '"poad tH0 IonfPV
properly characterized as calibration than validation.
Actual data and predicted digester performance over time are
shown in Figure 9. A scatter diagram of predicted vs.
actual volumetric methane production for this study is
presented in Figure 10. Linear regression was performed,
and the 95% confidence limits are shown.
The work of Young (1979), conducted at 21 and 35 C in
1.4 m3 digesters, was also simulated. Predicted long term
yields of methane correlated very well with the actual data.
Transient behavior was less accurate, particularly at a
temperature of 21 C.
In Young's work, feeding was completely stopped at day
35 and not resumed until day 42, at which time a shock load
of 7 times the normal daily load was fed to the CER. The
model overestimated the effect of this transient. This was
especially pronounced in the 35 C Trial (Figure 11). In
addition, the model failed to predict a plateau in the
methane production after the first 20 days in the 21 C trial
Without additional data, it cannot be said that the CER
model has been validated. However, poor transient response
for a single study cannot be considered to have invalidated
the model. As more work is done with the CER concept,
additional simulations should be conducted to increase the
confidence in the CER model.
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Aloal Growth Model
The algal growth model was based upon the parameters of
Hill and Lincoln (1981) for determining growth and death
rates. The model was calibrated using their published data.
Thirteen hours of daylight was assumed with a half sinusoi-
dal distribution over that period.
Validation of the model was performed by comparison of
reported algal yields from thirteen studies conducted
between 1967 and 1988 (Table 4).
Due to the lack of reported information about solar in-
solation levels and water temperatures in many references,
most simulations were run using climatological data (Lunde,
1980; Landsberg, 1981; and Goldman, 1979b).
Algal yields for the various studies as well as the
predicted value for each latitude are shown in Figure 13.
Latitude was chosen for the X-axis to separate the experi-
ments by location. It should be noted that most of these
experiments were for less than a full year and were used
only for model validation. They should not be taken as an
indication of annual production. A scatter diagram of
predicted vs. actual yields is given in Figure 14. The test
for lack of fit was not significant at the 95% level.
A simulation of one year's production at Haifa, Israel
was compared with actual data from Moraine et al. (1979) and
is shown in Figure 15. The shift between the summer growth
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curves may have been due to differences between actual
conditions and the average climatological data used for the
Table 4. Algae model validation sources
Belfast, N. Ireland
Roswell, New Mexico
Fallowfield and Garrett (1985)
Goh and Lee (1982)
Moraine et al. (1979)
Shelef et al. (1973)
Shelef et al. (1978)
Lincoln et al, (1986)
Johnson et al. (1988)
Tsukada et al. (1977)
Tsukada et al. (1977)
Water Hyacinth Model
The water hyacinth model used the parameters originally
specified by Lorber et al. (1984) with the exception of
modification of the temperature function. As mentioned