Simulation of an integrated system for the production of methane and single cell protein from biomass

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Simulation of an integrated system for the production of methane and single cell protein from biomass
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viii, 146 leaves : ill. ; 28 cm.
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Thomas, Michael Vernon, 1950-
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Farm manure in methane production -- Computer simulation   ( lcsh )
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Methane   ( lcsh )
Agricultural Engineering thesis Ph. D
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Thesis:
Thesis (Ph. D.)--University of Florida, 1988.
Bibliography:
Includes bibliographical references.
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by Michael Vernon Thomas.
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Typescript.
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Vita.

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Full Text










SIMULATION OF AN INTEGRATED SYSTEM
FOR THE PRODUCTION OF METHANE AND
SINGLE CELL PROTEIN FROM BIOMASS








By

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

1988


U OE F LIBRARIES














To my wife, Laurie, without whose love

and encouragement this would never have

been accomplished.














ACKNOWLEDGMENTS


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.


iii








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

Biomass Project.
















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 . .


iii

vii


. 1

. 4
. 4
. 4
. 4
. 10
. 15
. 15
. 17
. 20
. 20
. 22
. 24
. 26
. 26
. 26
. 36
. 36
. 38
. 39
. 41
. 42


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 . .


100

118

119


. 121

. 136

. 140

. 144

. 146


~I-I






















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

By

MICHAEL VERNON THOMAS

December 1988


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

various strategies.

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

vii


--- -------








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

cattle manure.

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-

puters.


viii














INTRODUCTION


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








2
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

system.

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.

















LITERATURE REVIEW

Unit Processes
Anaerobic Digestion

Anaerobic microbiology

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=








5
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

methane.

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





SHORT CHAIN
ORGANIC
ACIDS





II. METHANOGENIC
ORGANISMS


Figure 2. The two-population model of anaerobic digestion.


CH4, CO2


f_









7

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

reaction proceed.

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

Clostridium aceticum.

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


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II. HYDROGEN PRODUCING-
ACETOGENIC BACTERIA


I. HYDROLYTIC BACTERIA


IV. METHANOGENIC BACTERIA


Figure 4. The four-population model of anaerobic digestion
presented by Hashimoto et al. (1980). Reprinted by .
permission.


4

________________________________________^________________________' ^










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









11

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

practiced.

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


4








12
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

content:

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


- L,








13

(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








15
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

several disadvantages.










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.








17

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

treatment systems:

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

80%.








18

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

90%.

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.








19

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








20

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

al. 1985).


Alaae Production

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


_ I








22

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


__I__








23

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.



Integrated Systems
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

examined first.

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,


I










managerial, and environmental constraints must be identified

(Walker, 1984).

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


___A








26

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

viewpoint.



Mathematical Modeling

Kinetics of Anaerobic Digestion

General kinetics

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

research.

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).


dM dS
= a bM
dt dt
and
dS kMS

dt Kg + S


where

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

microorganisms, time-1,

Kg = half velocity coefficient for substrate utilization.

Combining these equations yields:


(dM/dt) akS
= b
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,


_ _i










is frequently used to represent a-k, yielding the more

familiar form of the Monod equation:


mu S
mu =
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-

cal techniques.

Contois (1959) proposed the following modification to

the Monod equation:

A
mu S
mu =
BP + S


where B is a constant growth parameter, and P is the bac-

terial density.

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








29

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

presented.

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

follows:











A
mu
mu =
Ks S
1 + -- + -
S Ki


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:

A
mu
mu =
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









31
mass transfer coefficients were determined for a number of

parameters.

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

where

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









32

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,

1978):


S


A
mu = mu [


( 1 K ) S
K +


It should be noted again that this model was derived

for steady state conditions. Under dynamic conditions it
A
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




I_










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








34

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
and
Rd VFA
Kd =
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








35

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

available data.

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).











CSTR modeling

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

Hashimoto, 1978):


dX 1
dt = ( mu )X
and
dS so -S Amu*X
dt h Y


where,

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

is achieved.



FBR modeling

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









37

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

involved.

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
es


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









38

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,


dX 1
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,

1985).



CER modeling

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

present.

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








39

tended to be protracted and to take place at lower than

actual temperatures.

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


__








40
models of algal growth. When developed, these models may be

applicable to a wider range of species than currently

available models.

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:


[Sub]
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

rate.

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








41
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:


dW
dt = (Pg Rm) E ] D

where

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








42
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

hyacinths.


Systems Modeling

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








43

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.








44
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

engine-generator.

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.














METHODOLOGY

Model Development

General

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

system variables.














48


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

and

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)
fl


S21 = Sin VS%2


__


(kg)












S21 = S21 (kg/m3)
f21

=3 Si VS%3 (kg/m3)
f3

Sdl = Sin s1 fl S21 s3 f3 (kg)


f2 = f21 + f2h (m3/d)


s2 = S21 + S2h (kg/m3)
f2

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
where

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
fa


shr fl fhl silout + f3 h3 S3out (kg/m3
5hr = (kg/mn3)
fhr

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









51

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


1









52
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

follows:


M1 + M2 + M3 + Ms = Mt

G1 + G2 + G3 + Gg = Gt

Mt 100 = Qt
Gt

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

was:



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.








53

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-

site uses.

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








54
greater than the ambient temperature as defined by input

data the heat losses were calculated by :


Area (T -T
SArea (Treactor ambient)
R

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

efficiency.



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








55

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

current dollars.

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

equation:

Cost = $6906 Volume 0.494

approximated (r2 = 0.97) the data of Vernick and Walker

(1981).










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.


I









57
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
2475

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








58
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

communication).

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
Capital Cost

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

this work.



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








60
factors, the biodegradability factor (BO) and the acid

factor (ACFACT).

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.








61

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,

kg/m3.

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

as follows:



(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:


dmc
dt


= (muc kdc (1-BRC)flow )mc[k] + (1-BRC)flow mc[k-1]
volk volk


(3) Rate of change of lignified COM:

dlcom = (lcom[k-1] Icom[k])flow Icombkd
dt volk


(4) Rate of change of readily degradable COM:


drdcom = (rdcom[k-l] rdcom[k])flow

dt volk


+ Icombkd rdcombkd


(5) Rate of change of soluble organic:


dSO = rdcombkd + (SO[k-l] SO[k])flow + kd*m[k]
dt volk

+ kdc-mc[k] mu*m[k]
y








63

(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

follows.

(1) Rate of change of acetogens:

dm
dm = (mu kd)*m
dt


(2) Rate of change of methanogens:

dmc = (muc kdc)*mc
dt


(3) Rate of change of lignified COM:

dlcom = (Icomin) flow lcombkd
dt volk








64

(4) Rate of change of readily degradable COM:


drdcom = (rdcomin) flow + Icombkd rdcombkd
dt volk

(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
A
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









65

equations were used to calculate specific growth and death

rates.

A
mu =mu


muc =


1+ ks + VFAk]
SO(k] ki

A
muc


+ ksc + VFA[k]
VFA[k] kic


kd= ___
1 + ki
VFA[k]


kdc = kac
1 + kic
VFA[k]

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








66
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

al. (1984).

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









67

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

methanogens produced.

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

(1984).

Substrate composition has a marked effect on digester

operation. The values of BO and ACFACT used to describe








68

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

retention time.

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

(kg/m3) form.

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








70
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.









71

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

procedure.

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


I









72

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

(1981).

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

form:


usub Substrate

kssub Substrate


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.


1










A (T-25)
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

production system.

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)
where

Pgmax = 22.318 + 0.102 S S > 100
= 0.32 S S < 100

and S = incident solar radiation in Langleys / day.


i








75
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

efforts.

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:









76

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

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.









78
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)











79





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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

waste.

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

shown.



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









81

Table 3. Sources for FBR model


validation data


Waste Temp. HRT VS CH4 Reference
type (C) (days) (g/L) (L/L-d)


Bolte

Bolte

Bolte

Bolte

Bolte

Bolte

Brumm

Brumm

Brumm

Brumm


et al.

et al.

et al.

et al.

et al.

et al.

(1980)

(1980)

(1980)

(1980)


Swine

Swine

Swine

Swine

Swine

Swine

Swine

Swine

Swine

Swine

Swine

Swine

Swine

Swine

Swine

Swine

Swine

Swine

Swine

Bean

Bean

Bean


(1985)

(1985)

(1985)

(1985)

(1985)

(1985)


35

35

35

55

55

55

24

24

24

24

35

35

35

35

35

35

35

35

35

35

35

35


Whey 32 2.0 5.6


5

2.5

1.5

2.5

1.5

1.0

1.0

2.0

3.0

6.0

1.0

3.0

3.0

3.0

3.0

1.7

2.7

1.0

3.7

19

8.8

5.5


9.8

9.3

10.3

10.4

9.6

10.0

4.0

3.8

3.3

3.9

4.0

1.5

3.0

6.0

12.0

17.3

17.8

18.7

17.0

25

25

25


.84

1.38

2.0

1.84

2.68

3.29

.81

.66

.51

.44

.98

.16

.35

.66

1.25

2.6

2.2

3.8

2.1

.35

.86

1.25


& 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)


Hasheider

Hasheider

Hasheider

Hasheider

Hasheider

Kennedy &

Kennedy &

Kennedy &

Kennedy &

Stevens &

Stevens &

Stevens &


.52 Thomas (1984)


























































































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83
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

(Figure 12).

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












89







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92

curves may have been due to differences between actual

conditions and the average climatological data used for the

simulation.



Table 4. Algae model validation sources


Location

Belfast, N. Ireland

Singapore

Haifa, Israel

Jerusalem, Israel

Haifa, Israel

Gainesville, Florida

Roswell, New Mexico

Taiwan

Taiwan

Tokyo, Japan

Tokyo, Japan

Trebon, Czeckoslovakia

Rupite, Romania


Source

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)

Goldman (1979a)

Tsukada et al. (1977)

Tsukada et al. (1977)

Goldman (1979a)

Goldman (1979a)

Goldman (1979a)


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