NASA Technical Memorandum TM 102151

A Simple, Mass Balance Model Of

Carbon Flow In A Controlled Ecological

Life Support System

Jay L. Garland

Department Of Environmental

Sciences, Clark Hall

University Of Virginia

Charlottesville, VA. 22903

March 1989

The Bionetics Corporation

Kennedy Space Center, Florida

Contract NAS 10-10285

National Aeronautics and

Space Administration

John F. Kennedy Space Center

I IASA

TABLE OF CONTENTS

Abstract ............................................................................................................................... 1

Introduction ...................................

.....................................................................................

Methods .............................................................................................................................. 2

Results .............................................................................................................................. 19

Conclusions .................................................................................................................... 31

Literature Cited ............................................................................................................... 32

LIST OF TABLES

Table 1............................................................................................................................. 20

Table 2............................................................................................................................. 25

Table 3 ............................................................................................................................. 28

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

LIST OF FIGURES

............................................................................................................................... 3

.............................................................................................................................. 8

............................................................................................................................ 17

............................................................................................................................ 21

............................................................................................................................ 22

6............................................................................................................................ 24

..o

......................................................................................................................... 7

8 ............................................................................................................................ 30

ABSTRACT

Internal cycling of chemical elements is a fundamental aspect of a

Controlled Ecological Life Support System (CELSS). Mathematical models are

useful tools for evaluating fluxes and reservoirs of elements associated with

potential CELSS configurations. A simple mass balance model of carbon flow

in CELSS was developed based on data from the CELSS Breadboard project

at Kennedy Space Center. All carbon reservoirs and fluxes were calculated

based on steady state conditions and modelled using linear, donor-controlled

transfer coefficients. The linear expression of photosynthetic flux was replaced

with Michaelis-Menten kinetics based on dynamical analysis of the model which

found that the latter produced more adequate model output.

Sensitivity analysis of the model indicated that accurate determination of

the maximum rate of gross primary production is critical to the development of

an accurate model of carbon flow. Atmospheric carbon dioxide was particularly

sensitive to changes in photosynthetic rate. The small reservoir of CO2 relative

to large CO2 fluxes increases the potential for volatility in CO2 concentration.

Feedback control mechanisms regulating CO2 concentration will probably be

necessary in a CELSS to reduce this system instability.

Examination of alternative food production subsystems demonstrated

that enzymatic conversion of inedible plant material has the potential to

significantly increase human food supply. Aquaculture systems are much less

efficient food producers, and should be considered for their qualitative rather

than quantitative role in human nutrition.

INTRODUCTION

Life support is currently a major limitation to man's long term presence in

space. The Controlled Ecological Life Support System (CELSS) program is a
long range NASA effort of research and engineering whose goal is the

development of an operative regenerative life support system. A CELSS would

be closed to all external material supplies except energy (sunlight). The

Kennedy Space Center's (KSC) current CELSS Breadboard project involves

the study of plant growth in a large sealed unit called the Biomass Production

Chamber (BPC). Future efforts at KSC will focus on integrative, manned testing

of waste management, biomass processing, and biomass production

subsystems.

Carbon is the key element of life. Knowledge of the carbon cycle,

therefore, is fundamental in understanding a biologically-based regenerative

life support system like CELSS.

A simple mass balance model of carbon flow in CELSS could be used

for several purposes in the KSC-CELSS Breadboard project; 1) quantify

approximate carbon reservoir and flux values, 2) identify "data poor" areas,

3) identify potential instabilities in the system, and 4) determine the sensitivity of

the system to uncertainty in system variables. This knowledge could increase

the effectiveness of management decisions involving future research efforts.

Resources could be focused on the accurate determination of parameters which

have the greatest influence over system behavior. Control mechanisms could

be developed to deal with system instabilities. Future engineering projects

could be scaled based on pool and flux sizes. For these reasons, a model was

developed based on a general conceptualization of a CELSS system with

consideration of the specific areas of research in CELSS at KSC.

METHODS

A box and arrow diagram was made showing the selected carbon

reservoirs and flows into and out of each compartment (Figure 1). Each box in

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carbon/square meter of plant growth area, and the arrows represent the

appropriate carbon flows in gC/m2/day.

Values for all reservoirs and fluxes were calculated based on assumed

steady state conditions (i.e., - input=output for all reservoirs). The source of

these values are described below.

A Fortran computer program was written to describe the changes in

carbon reservoirs over time. All energy fluxes were modelled as linear, donorcontrolled fluxes. Coefficients for these parameters were calculated by dividing

the energy flow for a flux by the reservoir size in the donor box at steady state

conditions. Models containing equations describing biological processes within

the system would be more flexible than the model described here. For

example, equation-based models could be adjusted to account for crop-specific

differences in plant growth by changing equation parameters. While the mass

balance, donor-controlled nature of this model does not allow for such flexibility,

it is the simplest methodology which will serve the purposes outlined in the

introduction.

Numerical solutions to the system of differential equations describing

reservoir sizes in the system were obtained using the fifth-order Runge-Kutta

technique (DVERK program in the IMSL library of the CDC computer at the

University of Virginia).

Model Structure

Vascular plant growth is assumed to be fundamental for food production

and gas exchange in this system. Harvested edible plant material is classified

into edible, soluble inedible, and insoluble inedible fractions.

4
Edible material production is assumed to be completely consumed by

humans without any losses due to food processing. Food processing is not

evaluated in this model for any edible products.

Significant amounts (35%) of the inedible fraction of potential CELSS

crops like wheat are readily soluble in water. This fraction contains significant

quantities of both organic compounds and inorganic plant nutrients. Recent

work at KSC evaluating the direct use of this "leachate" fraction as a source of

nutrients for hydroponic plant growth found that biological pretreatment to

remove organics significantly increased its effectiveness (Garland et al. 1988).

This pretreatment would involve concomitant production of microbial biomass

which can be used as feed for aquaculture production systems.

The insoluble fraction of agricultural residues are largely composed of

the biopolymers cellulose and hemicellulose (Alexander 1977). Enzymatic

conversion of these polymers to their monosaccharide subunits (glucose and

xylose/arabinose, respectively) produces a readily available energy source for

the production of single cell food suitable for human consumption. Glucose

could also be consumed directly by humans, but this model has all

monosaccharide production passing into single cell food production.

The common method of enzymatic conversion involves separate enzyme

production and hydrolysis steps (KSC-AIBS Biomass Processing Panel Report

1986). A relatively small amount of insoluble material is used for enzyme

induction in selected microbial strains which produce significant quantities of

extracellular enzyme. The enzyme is then harvested and transferred to a

hydrolysis reactor where a large fraction of the insoluble material is converted to

monosaccharides.

A key advantage to enzymatic hydrolysis is the decoupling of enzymatic

breakdown and microbial production in the decomposition pathway. This

5
should maximize production of edible material since the monosaccharide can

be isolated and used to grow microbial strains which have high production

rates, pallatibility, and nutritional value. At present, the organisms with optimal

production of the cellulase and hemicellulase enzymes do not also possess

optimal features for food production. Furthermore, separation of the

monosaccharide from the residual, non-decomposed plant material allows for a

more readily purified single-cell food.

An advantage of enzymatic hydrolysis of polymers compared to chemical

methods is the production of high protein "wastes" (microbial biomass from

enzyme production phase and spent enzyme) suitable for consumption by

intermediate consumer organisms such as fish in the CELSS system.

Tilapia, a native African species, is a suitable candidate for food

production in CELSS because of its resistance to poor water quality and

disease, tolerance of a wide range of environmental conditions, and ability to

utilize organic wastes as food (Baladn and Hailer 1982). The potential for

space conservation and containment in combined aquaculture/hydroponic

systems are added advantages of aquatic versus non-aquatic animal

production systems.

Model Parameters

Plant Production

Plant standing crop and production values are based on continuous

culture of dwarf wheat, Triticum aestivum L. cv. Yecora roja, using the nutrient

film technique hydroponic system in the BPC at KSC. The BPC contains 64 tray

positions (0.24 m2/tray) for nutrient film technique (NFT) culture. Since the life

cycle of Y. roja is approximately 64 days it was assumed that one tray would be

harvested per day. It is estimated that the maximal yield of wheat under BPC
conditions will be 1000 g dry wt/tray (Cheryl Mackowiak, pers. comm.). This

production rates corresponds to a daily areal value of 65.10 g dry wt/m2/day

(1000 g/day/[64 trays x 0.24 m2/tray]). If the carbon content of plant material is

estimated as 40% (Alexander 1977), then a total of 26.04 gC/m2/day will be

produced.

The standing crop of plant material was estimated by determining the

mean plant wt/tray from plant growth curves for Y. roja (Figure 2). The growth

curve was generated from experiments performed as part of the microbiological

research group at KSC (unpublished data). The average weights for five day

intervals in the life cycle were estimated. These values were converted to the

percent of the total biomass at harvest and multiplied by the 1000 g/tray

estimates. These values were then multiplied by five, summed, and adjusted for

growing area and carbon content ([34660 g/{15.35 m2 }] x 40% C). This

represents the plant standing crop with the system in steady state when one tray

is harvested and planted per day.

The rates of carbon fixation (gross primary production [GPP]) and plant

respiration (gross primary production - net primary production [NPP]) were

estimated based on the calculated daily production of respired C from other

sources in the system of 25.89 gC/m2/d (see below for details). If the system is

in steady state, the rate of carbon fixation must be equivalent to the sum of plant

respiration and respiration from other sources (25.89). Net primary production

is often estimated as 50% of GPP (Odum 1959), which would make NPP

equivalent to 25.89 gC/m2/d and GPP equivalent to 2 x 25.89 gC/m2/d in this

steady state model.

The present state of this model ignores loss of photosynthetically fixed

carbon through the roots of plants via exudation. While this is known to

represent a significant (12-18% of NPP) flow of carbon (Barber and Martin
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1976) for the purposes of this model, it is assumed that practically all exuded

carbon is respired by the rhizosphere microbial community and, therefore,

included in the plant respiration value. Future measurements of bacterial

production and turnover rates in the hydroponic system would allow for the

modelling of carbon associated with plant root exudation.

Leachate Bioreactor

Work at KSC has shown that approximately 35% of the dry weight of

inedible wheat residues is readily soluble in water. Preliminary studies were

performed at densities of 50 g straw/L water. At this concentration, 3 g/L of

dissolved organic carbon was measured, indicating that 17% of the leachate is

carbon by weight (3/[50 x 0.35]). The harvest yield (edible dry weight/total dry

weight) of Y. roja is approximately 40%. Therefore, of the 62.10 g dry weight of

aerial production of plant material, inedible material constitutes 37.26 g, and the

soluble fraction of the inedible material will total 13.04 g. Finally, soluble

carbon will comprise 17% of that fraction or 2.22 g/m2/d.

Experiments at KSC with bacterial treatment of leachate found that 60%

of the soluble carbon was metabolized after four days incubation (Garland,

unpubl, data). Recalcitrant carbon production, therefore, would equal 0.888

g/m2/d (2.22 x 0.40).

Microbial biomass, as estimated by total viable counts and protein

content, reached near maximal levels in the reactor at day 1 and remained

constant until day 4 when numbers declined. This was the major criteria for

selecting a four day residency time of soluble organic carbon in the bioreactor.

Protein content of the particulate material at day 4 was 0.222 mg/ml. If a N

content for protein of 20% and a C/N ratio of bacterial cells of 10/1 are assumed

(Alexander 1977) the carbon concentration in microbial biomass harvested at

9
day 4 will be 0.444 mgC/ml. At the substrate concentration of 50 g/L stated

above, the daily loading volume (which will be equivalent to the daily harvest

volume in a steady state system) will equal (37.26/50) 0.774 L. Daily areal

production of microbial carbon, therefore, will be 0.330 gC/m2/d (0.444 mg C/ml

x 0.744 L/day).

Respiration was calculated from the difference between input of

dissolved carbon and output of microbial biomass and recalcitrant carbon.

The changing levels of microbial carbon and dissolved organic carbon

were averaged over the four day residency time to determine the reservoir of

carbon in the reactor. A constant daily rate of degradation based on 60%

reduction in four days (15%/day) was assumed. Average microbial biomass

was estimated as half of maximal for day 1 and maximal for days 2, 3, and 4.

Garland et al. (1988) found that half of the remaining carbon is

metabolized by bacteria in the hydroponic system after 30 days of plant growth.

It is questionable to assume a constant rate of degradation over such a

relatively long period of time, especially since the remaining carbon may be

increasing in recalcitrance with time. Until more data is available on rates of

decay and the residency time of carbon in the hydroponic system (i.e., - how

often will the hydroponic system be "cleansed" of its organics?) recalcitrant

carbon will be treated as if it is completely combusted at an instantaneous rate.

Enzyme Production

The remaining inedible carbon production ([26.02 g/m2/d x 0.60%] -2.32

g/m2/d) is 13.29 g/m2/d, and will largely consist of cellulose and hemicellulose.

Part of this material will be needed to induce the cellulase and hemicellulase

enzymes for biopolymer saccharification. A reasonable substrate concentration

for optimal enzyme production is 2% (per. obs.). The crude enzyme suspension

10
produced in this manner can convert approximately 100 g of wheat straw.

Therefore, for every 20 g used for enzyme production, 100 g of straw can be

hydrolyzed. In a steady state system, then, 17% of insoluble residue

production, or 2.26 g/m2/d will be used for enzyme production and 83%, or

11.03 g/m2/d will be added to the hydrolysis reactor.

The daily input of material on a dry weight basis equals 5.65 g/m 2

(2.26/0.40). Assuming a substrate concentration of 2% for enzyme induction a

volume of 282 ml will be needed for the daily input. Enzyme production in

Trichoderma reesei cultures, typically is maximal after seven days (Mandels

and Andreotti 1978), so total volume allocated for enzyme production would be

1.97 L (282 ml x 7 days). Data from Acebal et al. (1986) of the percent weight

remaining in T. reesei cultures was used to estimate standing crop and loss

Day % remaining Weight remaining (g C)

1 119 2.69

2 100 2.26

3 76 1.72

4 67 1.51

5 57 1.29

6 57 1.29

7 48 1.08

11.84

values.

The standing crop of the enzyme production system will be the sum of the

carbon content at each of the seven days. Production of waste carbon

(undigested wheat straw, fungal mycelium) will 1.08 g/m2/d since 48% of the dry

weight is left at harvest. These estimates assume that dry weight loss is highly

correlated with loss of C. This may not be entirely true since dry weight

l!
remaining at different days contains varying percentages of fungal biomass

which may contain a higher proportion of carbon/unit weight than plant material.

Direct measurements are needed to determine more accurate values.

Total carbon transfer of 0.211 gC/m2/d to the hydrolysis reactor was

calculated assuming a harvest volume of 282 mL, a protein content of harvest

enzyme suspension of 1.5 mg/ml (Mandels and Andreotti 1978), and a 50%

carbon content for protein. The latter value was obtained by examining the

average carbon content of amino acids.

Since the level of soluble carbon in the enzyme production system is

very low compared to the insoluble residue and microbial biomass it was

excluded from the calculation of the carbon reservoir.

Respiration was estimated by subtracting the soluble and insoluble loss

rates from the input.

Biopolymer Saccharification Reactor

A reactor volume of 551 mL was estimated as above by adjusting the

carbon input to a dry weight basis and assuming a substrate concentration of

5% ([11.03/0.4]/0.05). If enzymatic conversion efficiency is 70%, then 7.72 g of

monosaccharide C will be produced on an daily areal basis. This value should

be adjusted to account for the addition of water in the hydrolysis reaction by

multiplication by 0.9 (6.95 g/m2/d), because conversion efficiency is usually

defined on a weight rather than carbon basis. Waste output (spent enzyme,

undigested wheat straw) is the difference between inputs and monosaccharide

output ([11.03+.211]-6.95=4.29). Since the optimal hydrolysis time is

approximately two days and no carbon losses through respiration are present

over time, the carbon reservoir of the reactor is sum of the daily inputs multiplied

by a factor of two.

]2
A 70% conversion efficiency is within the range found in recent work at

KSC involving enzymatic conversion of cellulose in wheat straw (Garland and

Strayer, in prep).

Microbial Protein Production

The yield coefficient (g biomass produced/g substrate) of most potentially

edible microorganisms grown on monosaccharides range between 0.4 to 0.5

(Gottschalk 1986). Assuming an intermediate yield coefficient of 0.45, daily

areal production of microbial C would be 3.13 gC/m2/d given the

monosaccharide production rate of 6.95 gC/m2/d. This direct estimate of

microbial carbon from monosaccharide carbon is possible because both

monosaccharide and yeast or fungi are approximately 40% carbon by weight.

Respiration was estimated by taking the difference between input and

output.

Maximum growth yield in batch culture of many edible fungi, including a

patented fungi (U.S. Patent 3,937.654) used for mycoprotein production, is

usually reached after 24-36 hr. The average turnover time would be 30 hr, or

1.2 days. Turnover rate, the inverse of turnover time, is equivalent to the

production/standing crop ratio. Therefore, standing crop of the single cell food

production unit is equal to 3.13/0.833 or 3.75 g/m 2.

Aquaculture System

The energy conversions in the aquaculture production system are based

on a poikilothermic animal grazing on a variety of food sources, some of low

food quality. Production rate was calculated assuming a 50% assimilation rate

of ingested food, 80% respiration of assimilation energy, and an edible index

(filet wt/total wt) of 40% (Balarin and Hailer 1982, Majowski and Warwood 1981,

]3
Patrice Owens, pers. comm.). While these values are in the range of reported

values, they are speculative. More research is needed in the physiology of

Tiliapia fed CELSS-derived materials to more accurately define these values.

It is assumed that Tilapia waste is of little nutritive value since it already

has passed through the digestive tract. However, microbial conditioning of this

material in a biofilter integrated with the aquaculture system may significantly

increase food quality of the waste material. Such a biofilter may be a necessary

component of the aquaculture system to reduce ammonia levels. Due to the

paucity of available data, however, fish waste is assumed to undergo complete

combustion to regenerate CO2.

Fish production influences the level of human ingestion, and,

correspondingly, human egestion. Since the latter is an input to the

aquaculture reservoir, flux values were run through the model with iterative

adjustments until equilibrium in all the aquaculture and human fluxes were

reached.

Annual production/biomass (P/B) ratio for young of the year sunfish,

which should closely approximate Tilapia in growth characteristics, have been

estimated in the field at 1.174. (Gerking 1962). This converts to a ratio of 0.0033

on a daily basis. Standing crop biomass therefore, was estimated as

1.35/0.0033, or 409.1 g/m 2.

Human

A human egestion rate of 50% was assumed based on a average value

of a vertebrate homeotherm eating a vegetable diet (Heal and Maclean 1975).

An adult crew is expected in a CELSS system for the near term so all

assimilated carbon is respired.

]4
The reservoir of human carbon was estimated by determining the amount

of biomass that could be supported by the available energy. Total carbon input

to humans is 14.24 g/m2/d. Assuming a 40% carbon content, this corresponds

to 35.6 g dry wt/m2/d. Since a reasonable estimate of caloric content of

biomass is 4.5 kcal/g dry weight, this converts to 160.2 kcal/m2/d. Total kcal

available for the BPC growing area is 2460.7 kcal/d, which is the approximate

maintenance caloric value for an active 54.5 kg adult between age 25-34.

Adjusted to an areal basis, and assuming an 18% percent carbon content for

humans (Starr and Taggart 1988), the reservoir of human biomass is 609

gC/m 2.

In an actual CELSS system food reserves would probably be used to

offset short term energy deficits in humans. This would mean that the human

reservoir and related fluxes (i.e., - ingestion, respiration, and egestion rates)

would stay constant despite fluctuations in the rest of the system. However,

such food supplements are ignored in this model so that the dynamic effects of

changes in the system on human carbon can be observed.

Atmospheric CO2

All respired CO2 is assumed to completely enter the atmospheric pool,

even though dissolved gas and carbonate will represent a separate pool in

aquatic subsystems. This pool and related fluxes should be addressed as the

model grows in complexity.

Since elevated CO2 concentrations increase plant growth, it is expected

that CO2 concentrations of 1000 ppm will be maintained in the BPC. The BPC

is a cylinder of 3.5 m diameter and 7.5 m height (73 m 3 volume). Additional

duct work brings the total chamber volume to 112 m3 or 112000 L. Assuming

an air density of 1.2 g/L, the chamber will contain 134400 g of air CO2

]5
concentration of 1000 ppm corresponds to 134.4 g of CO2, and, accordingly,

36.39 g C. Adjusted on the growing area basis, 36.29/15.36, or 2.36 gC/m 2, will

be present in the system.

Changes in Description of Photosynthetic Flux

Donor control flux is a reasonable assumption for all flows in the model

except photosynthesis. Donor control implies that photosynthesis is linearly

dependent only on available carbon, and ignores the major influences of

available radiance and nutrients. An alternative linear model of photosynthetic

flux, recipient control, may be a more realistic expression since CO2 uptake

would be directly dependent on plant biomass. Nonlinear Michaelis-Menten

kinetics may be an even more realistic description of photosynthetic flux.

Results of experiments performed at KSC with soybean (Figure 3) show the

asymptotic relationship between photosynthesis and CO2 predicted by such

kinetics.

The difficulty in using the Michaelis-Menten equation arises from the

need to quantify coefficients within the expression. The equation states that:

V = (Vmax * S)/(Km + S) where V equals reaction velocity, Vmax equals

maximum velocity reaction, S is substrate concentration, and Km is the

substrate concentration at half maximum velocity. The CO2 concentration is

considered the substrate concentration in photosynthesis. Given the model

assumption that NPP-1/2GPP, then Km is equivalent to the CO2 concentration

when NPP is zero. A graph of NPP versus CO2 concentration measured under

various light levels was developed from measurements taken at KSC (Figure 3).

The x intercept on this graph, which is called the CO2 compensation point and

is analogous to Km when NPP=I/2GPP, is approximately 50-100 ppm. The

approximated mean of 75 ppm is equivalent to 0.177 gC/m 2. As discussed

]6
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above, the maximum velocity is the flux at steady state (51.86 gC/m2/d) since

the model assumed a maximum areal production rate of 1000 g/tray. To

maintain steady state mass balance, 51.86 was used as the value for V, and the

equation was solved for Vmax using the steady state S value (2.36) and the Km

value of 0.177. Vmax can be expressed as a constant (A) times the amount of

plant biomass. Using the steady state value for plant standing crop of 903.23, A

becomes 0.06172.

The response of the model to perturbation from steady state was

compared for the three different expressions of photosynthetic flux; donor

control, recipient control, and Michaelis-Menten. The perturbation was a 33%

reduction in plant standing crop. This simulates in a general sense some type

of failure in the plant growth system (i.e., plant disease, pump failure, etc.). The

purpose of this exercise, however, was not to accurately model a particular

perturbation in the system, but to evaluate the validity of the expression for

photosynthetic flux.

Model Analysis

Model parameters were also adjusted to examine the system's sensitivity

to selected functions. It would be useful to know the extent of changes caused

in the system by uncertainty in certain system functions. Near term research

efforts would be more productive if emphasis was placed on accurate

estimation of those parameters which cause the most significant effects in

system function.

The sensitivity of the model to changes in the Vmax and Km parameters

was analyzed to further evaluate the carbon fixation transfer term. Model runs

were performed with Vmax values 10% greater than and less than that in the

steady state model. Separate model runs were performed assuming CO2

]8
compensation points of 100 and 50 ppm, which represents the approximate

range found in Figure 3.

The effects of altered enzyme conversion efficiency and fish assimilation

rate were also addressed. In these cases, concomitant adjustment in

parameters relating the biopolymer saccharification reactor and aquaculture

reservoirs were made. For example, a 10% increase in enzyme conversion

efficiency would cause a 10% reduction in waste production from the reactor.

The original and adjusted values of all parameters altered in these model runs

are shown in Table 1.

RESULTS

Comparison of Different Models of Photosynthetic Flux

The relative responses of the three models to decreased plant biomass

were evaluated with respect to expected system behavior. Changes with time

were evaluated for three carbon reservoirs: plant, human, and CO2. It is

reasonable to assume that plant biomass would return to or near the original

steady state value after the perturbation, while human carbon levels would

decline in response to lower food availability. Levels of CO2 would probably

rise initially due to the relatively high turnover rate of carbon in the microbial

and aquaculture subsystems. Respiratory and waste CO2 production rates

would be based on steady state levels in these reservoirs while CO2 uptake

rate would be significantly reduced due to the lower plant biomass. However,

CO2 levels should return to near steady state values as plant biomass

increased.

The responses of the models including donor and recipient control of

photosynthesis do not agree with this intuitive system behavior (Figures 4, 5).

The donor control model output shows the expected rebound in plant biomass

19
Table 1. Parameter adjustments used in sensitivity analyses.

Term Steadv State 10% increase 10% Decrease

Vmax 0.06171 0.06789 0.0555

Km O.177 0.236* O.118*

Enzyme efficiency

A45

(CH20 prod)

A46

(waste prod)

0.309 0.3447 0.260

0.191 0.1552 0.2399

Assimilation efficiency

A66 0.00198 0.00238 0.00146

(inedible prod)

A67 0.00132 0.00159 0.000997

(edible prod)

A68 0.0132 0.015878 0.01058

(respiration)

A68W 0.0165 0.01323 0.01985

feaestionl

* - values were adjusted based on 002 compensation point of 100 ppm and 50

ppm.

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and decline in human biomass, but little change in CO2. In the recipient control

model human carbon declines, but plant biomass carbon remains constant and

CO2 rises asymptotically. The linear dependence of photosynthetic rate on

plant biomass causes the lack of responsiveness in the plant reservoir.

Accordingly, CO2 levels never decrease because photosynthetic rate remains

low.

The non-linear model captures the expected changes in all three carbon

reservoirs (Figure 6). Carbon dioxide increases 30 fold by day 25 and then

declines to the original steady state level by day 70. The new steady state

levels of plant and human carbon are lower than those in the originial steady

state. This is reasonable since 300 g of carbon were removed from the system

as part of the perturbation.

This exercise has shown that the non-linear model is probably a more

adequate model since it duplicates more of the expected system behavior than

the linear models. Adequacy is defined as the fraction of the actual system

behavior which is correctly modelled (Mankin et al. 1975). The non-linear

model, therefore, was used in the sensitivity analyses described below.

The recovery time of the system to perturbation (i.e., - time to new steady

state) is approximately 70 days, or the time it takes wheat to pass through an

entire life cycle.

Sensitivity of the Model to Changes in Vmax and Km

A decrease in Vmax causes significant effects in all carbon reservoirs

while an increase does not significantly affect any reservoir except CO2 (Table

2). This asymmetry is probably a result of the asymptotic nature of the

Michaelis-Menten equation. Changes in Km cause little effect in any carbon

23
o o o o o

.c

0

m=

.__ 0

_U

_c

LU_

(l:l::lJ_-qN :II:IVrIOSISMVEIO) NOBHVO

LL

24
Table 2. Results of sensitivity analysis

Carbon Reservoir Parameter

Km Vmax

-I- - -I- -

Plant 0.2+ 0.1 + 0.1 + 32.3-

SPCB 0.0 0.1+ 0.1+ 32.0-

EPB 0.0 0.08+ 0.1+ 1.7-

BSB 0.4- 0.04+ 0.1 + 32.2-

SCFPB 0.0 0.0 0.03 1.0-

Aquaculture System 0.6+ 0.25+ 0.2+ 24.0-

Human 0.2+ 0.001- 0.1+ 25.9-

CO,z_ 31.3+ 34.3- 59.3- 241 gO.O+

SPCB = Soluble Plant Carbon Bioreactor

EPB -- Enzyme Production Bioreactor

BSB = Biopolymer Saccharification Bioreactor

SCFPB= Single Cell Food Production Bioreactor

+ = increase in parameter (see test)

- = decrease in parameter (see test)

All values are percent change in carbon reservoir from steady state level after

200 day model run.

25
reservoir except CO2. Since Km lies well below the asymptotic region of the

Michaelis-Menten curve, the CO2 response is symmetrical.

These results reveal several important features of the model and, hence,

the system. First, the accurate determination of Vmax is critical to the effective

modelling of the system. A 10% decline in Vmax causes 30% reductions in

most carbon reservoirs. The human reservoir has not reached steady state

even after 200 days (Figure 7). Secondly, the CO2 reservoir is particularly

sensitive to changes in photosynthetic rate. Carbon dioxide was the only

reservoir to be significantly effected by all changes in Km and Vmax.

Concentration of CO2 increased 24100% to a level of 241000 ppm with a 10%

change in Vmax.

The relatively small CO2 pool and large CO2 fluxes are the probable

cause of this volatility in CO2 concentration. To prevent large fluctuations in

CO2 concentrations, feedback control of photosynthesis may be necessary.

This could require that the baseline plant growth rate is less than the maximum

rate so that increasing CO2 can be corrected for by increasing CO2 uptake.

Alternative CO2 "trapping" methods may also be effective. Varying the rate at

which solid wastes are combusted is one potential alternative, although it

represents a much smaller flux than photosynthesis.

Sensitivity of the Model to Changes in Enzyme Efficiency

The greatest effects of altered enzyme efficiency are found in the

reservoirs directly influenced by products of the biopolymer saccharification

reactor; the single cell food production reactor and the aquaculture subsystem

(Table 3). The asymmetrical responsiveness of the system described above is

also apparent in these results. Decreases in enzyme efficiencies cause almost

twice the change in reservoir sizes as do increases. Human carbon decreases

26
O uJ

_- g g (J') _.- v-

(I:I=IJ.=IN 3uvnos/SNVI:IO) NOSI:IVO NVl_lrtN

O

O

Od

O

O

O

>.

,<

a

"O

O

E

"10

u)

tO

X

>

e-

(n

c_

(.-

t_

to

0_

O

I'="

O

(n

LU

r_

LL

27
Table 3. Results of sensitivity analysis.

Carbon Reservoir Test

Enzyme

Efficiency

-I- - O

Plant 0.3+ 0.4- 2.1-

SPCB 0.3+ 0.4- 2.0-

EPB 0.3+ 0.4- 2.1-

BSB 0.2+ 0.4- 2.1-

SCFOB 11.9+ 22.8- 100.0-

Aquaculture System 4.6- 9.3+ 40.5+

Human 2.4+ 5.2- 22.3-

1.3- 1,_- 1.2-

Fish

Assimilation

-!-

0.5- 0.7+

0.5- 0.8+

0.5 0.7+

0.5- 0.7+

0.5- 0.8+

1.0+ 1.0-

0.1+ 0.5-

1,3+ 1.3-

SPCB = Soluble Plant Carbon Bioreactor

EPB = Enzyme Production Bioreactor

BSB -- Biopolymer Saccharification Bioreactor

SCFPB= Single Cell Food Production Bioreactor

+ = increase in parameter (see text)

- = decrease in parameter (see text)

0 = paramter set to 0

All values are percent change in carbon reservoir from steady state level after

200 day model run.

28
by 5.2% and increases by 2.4% with a 10% decrease and increase,

respectively, in enzyme efficiency. This asymmetry reflects the dominant role of

photosynthetic flux in the system.

The relatively small change in the human reservoir caused by altered

enzyme efficiency suggests that enzymatic biomass conversion may not be an

efficient means of food production in CELSS. To test this hypothesis a model

run was performed with an enzyme efficiency of 0%. This elimination of

enzymatic conversion causes a 22% reduction in human carbon (Table 3,

Figure 8). Based on these results it can be concluded that enzymatic

conversion provides a substantial augmentation of food production for humans.

Accurate determination of enzyme conversion efficiency, however, is not of

critical importance in modelling the system.

Sensitivity of the Model to Changes in Assimilation Efficiency of Fish

The model is very insensitive to changes in fish assimilation efficiency.

No reservoir changes by more than 1% with a 10% increase or decrease in

efficiency. This not only indicates that accurate determination of flux rates in the

aquaculture system are not critical for system modelling, but suggests that the

aquaculture system may not be an effective means of significantly increasing

the rate of food production. Substantially greater assimilation and respiratory

efficiencies could increase production rates, as could utilization of aquaculture

waste products. It appears that single cell food production is a much more

efficient means of processing inedible plant material. The difference in

palatability and nutritional value between single cell food and fish, however, is

an important consideration when comparing the separate food production

techniques.

29
o

o

r_

i

i

! !

o o

o

8

(EI:I13W 31:IVI"IOS/SI_IYEIO) NO8EIYO NVINI'IH

o

o

,qE

(D

,,- a o

r-

'3

_>,

o ">

(/)

C

0

in

80
CONCLUSIONS

1) A CELSS model containing a non-linear expression of photosynthetic

flux (Michaelis-Menten kinetics) seems to produce more adequate model output

compared to models using donor or recipient control of photosynthesis.

2) The accurate determination of the maximum rate of gross primary

production (Vmax term in Michaelis-Menten equation) is critical for modelling

carbon flow in CELSS.

3) Feedback control mechanisms are probably necessary in a CELSS in

order to prevent severe fluctuations in atmospheric CO2 concentrations.

4) Enzymatic conversion of inedible material has the potential to

significantly increase the amount of food energy available for human

consumption. Near-term research efforts in accurate determination of enzyme

conversion efficiency, however, are not critical.

5) Aquaculture does not appear to be an efficient means of producing

food energy unless fish are substantially more efficient energy converters than

assumed in this model.

3]
LITERATURE CITED

Acebal, C., M.P. Castillon, P. Estrada, I. Mata, E. Costa, J. Aguadu, D. Romero,

and F. Jimenez. 1986. Enhanced cellulase production from Tnchoderma

reesei QM 9414 on physically treated wheat straw. Appl. Microb.

Biotechnol. 24:218-223.

Alexander, M. 1977. Introduction to soil microbiology. John Wiley & Sons,

New York.

Balarin, J.D. and R.D. Hailer. 1982. The intensive culture of Tilapia in tanks,

raceways, and cages. In: (J.F. Muir and R.J. Roberts, eds.). Recent

advances in aquaculture. Westview Press, Boulder, CO.

Barber, D.A. and J.K. Martin. 1976. The release of organic substances by

cereal roots into soil. New Phyto. 76:69-80.

Garland, J.L., C.L. Mackowiak, and R.F. Strayer. 1988. Utilization of the soluble

fraction of inedible wheat biomass in a Controlled Ecological Life Support

System (CELSS). Poster presented at the annual meeting of the American

Society For Gravitational and Space Biology, October 1988.

Garland, J.L. and R.F. Strayer. 1989. The effect of inoculum size and starch

concentration on cellulase production in cocultures of fungi. Submitted to

Biotech. and Bioeng. (In preparation).

Gerking, S.D. 1962. Production and food utilization in a population of bluegill

sunfish. Ecol. Mon. 32:31-78.

Gottschalk, G. 1986. Bacterial Metabolism. Springer-Verlag, New York.

Heal, O.W. and S.F. Maclean. 1975. Comparative productivity in ecosystems--

secondary productivity. Pp. 89-103 in: W.H. Van Dobben and R.H. LoweMcConnell (eds.). Unifying Concepts in Ecology. Junk, The Hague.

Kennedy Space Center-American Institute of Biological Sciences CELSS

Biomass Processing Technical Panel Report. 1986.

32
Majowski, E. and A. Warwood. 1981. A bioenergetic model of the rainbow

trout, Salmo gairdneri. Can. J. Fish. Aquatic Sci. 38:1199-1208.

Mandels, M. and R.E. Andreotti. 1978. Problems and challenges in the

cellulose to cellulase fermentation. Proc. Biochem. 13:6-13.

Mankin, J.B., R.V. O'Neill, H.H. Shugart, and B.W. Rust. 1975. The importance

of validation in ecosystem analysis.

the analysis of ecological systems.

Jolla, CA.

In: G. Inness (ed.). New directions in

Society for Computer Simulation, La

Odum, E.P. 1959. Fundamentals of ecology. W.B. Saunders, Philadelphia.

Starr, C. and R. Taggart. 1988. Biology: The unity and diversity of life.

Wadsworth.

33

Report Documentation Page _°tl,.Tkli _O'aul(:S and

1. Report No.

TM 102151

2. Government Accession No.

4. Title and Subtitle

A simple, mass balance model of carbon fl(_ in a

controlled ecological life support system

7. Author(s)

_ay L. Garland I

9. Performing Organization Name and Address

the Bionetics Corporation IDepartment of Enviror_ental

IJohn F. Kennedy Space Sciences, Clark Hall

_nter, Florida 32899 University of Virginia

/ Char]otte_vi I 1p. V"A 22c!133

12. Sponsoring Agency Name and Address . "

John F. Kennedy Space Center, NASA

Florida 32899

3. Recipient's Catalog No.

5. Report Date

darch 1989

6. Performing Organization Code

BIO

8. Performing Organization Report No.

10. Work Unit No.

11. Contract or Grant No.

NASI0-10285

13. Type of Report and Period Covered

14. Sponsoring Agency Code

15. Supplementary Notes

16. Abstract

Internal cycling of chemical elements is a fundamental aspect of a Controlled

Ecological Life Support System (CELSS). Mathematical models are useful tools for

evaluating fluxes and reservoirs of elements associated with potential CELSS

configurations. A simple mass balance model of carbon flow in CELSS was developed

based on data from the CELSS Breadboard project at Kennedy Space Center. All carbon

reservoirs and fluxes were calculated based on steady state conditions and modelled

using linear, donor-controlled transfer coefficients. The linear expression of I

photosynthetic flux was replaced with Michaelis-Menten kinetics based on dynamical .

analysis of the model which found that the latter produced more adequate model output

Sensitivity analysis of the model indicated that accurate determination of the

maxim_n rate of gross pr_ary production is critical to the development of an accurate

model of carbon flow. Atmospheric carbon dioxide was particularly sensitive to

changes in photosynthetic rate. The shall reservoir of CO 2 relative to large CO 2

fluxes increases the potential for volatility in CO 2 concentration. Feedback control

mechanisms regulating COp concentration will probabIy be necessary in a CELSS to

reduce this system instaSility.

17. Key Words (Suggested by Author(s))

Carbon, CELSS, Model

19. Security Classif. (of this report)

nclassified

NASA FORM 1626 OCT 86

18. Distribution Statement

20. Security Classif. (of this page)

classified

Price
16. Abstract (oontinued)

Examination of alternative food production subsystems demonstrated that enzymatic

conversion of inedible plant material has the potential to significantly increase

human food supply. Aquaculture systems are n_/ch less efficient food producers, and

should be considered for their qualitative rather than quantitative role in human

nutrition.