Application of mass and energy balance regularities in

Application of Mass and Energy Balance Regularities in Fermentation

L. E. ERICKSON,* I. G. MINKEVICH, and V. K. EROSHIN, Institute of Biochemistry and Physiology of Microorganisms, U.S.S.R. Academy of Sciences, 142292 Pushchino, Moscow

Region, U .S .S . R .

Summary Material and energy balances for fermentation processes are developed based on

the facts that the heat of reaction per electron transferred to oxygen for a wide variety of organic molecules, the number of available electrons per carbon atom in biomass, and the weight fraction carbon in biomass are relatively constant. Mass- energy balance equations are developed which relate the biomass energetic yield coefficient to sets of variables which may be determined experimentally. Organic substrate consumption, biomass production, oxygen consumption, carbon dioxide production, heat evolution, and nitrogen consumption are considered as measured variables. Application of the balances using direct and indirect methods of yield coefficient estimation is illustrated using experimental results from the literature. Product formation is included in the balance equations and the effect of product formation on biomass yield estimates is examined. Application of mass-energy balances in the optimal operation of continuous single-cell protein production facil- ities is examined, and the variation of optimal operating conditions with changes in yield are illustrated for methanol as organic substrate.

INTRODUCTION

Material and energy balances are widely used in science and engineering. In biotechnology and bioengineering, material and energy balances have also been widely used; however, because of the large number of biochemical processes involved in cell growth and product formation, application of material and energy balances is frequently not fully exploited in analyzing experimental data. In some cases only very approximate material and energy balances are used with growth processes because of the complexity of the process.

Improvements in instrumentation for measuring important vari-

* Present address: Kansas State University, Manhattan, Kansas 66506.

Biotechnology and Bioengineering, Vol. XX, Pp. 1595- 1621 (1978) @ 1978 John Wiley & Sons, Inc. 0006-3592/78/0020- 1595$01 .OO

1596 ERICKSON, MINKEVICH, AND EROSHIN

ables in fermentation processes and the use of on-line computers with fermentors provide new opportunities for application of material and energy balances in fermentation. Organic substrate consumption, biomass production, nitrogen consumption, oxygen consumption, carbon dioxide production, and heat evolution are some of the variables which may be estimated from experimental measurements and used in material and energy balance calculations. Frequently, for rapid estimation only some of the above variables are available because of the time required for analysis. Moreover, under dynamic conditions (e.g., batch growth) some measured variables respond more rapidly than others to changes in the rate of cultivation.

In this paper methods for rapid estimation of yield coefficients from sensors frequently used in laboratory and production fermentors are presented. Once yield coefficients have been estimated, values of other variables can also be estimated. Procedures which allow the accuracy of the yield coefficients to be estimated are also presented and discussed. The possibility of product formation is also considered, and methods to estimate the quantity of products are described. Only heterotrophic growth is considered; that is, the organic substrate is the source of energy for cellular production of biomass. Only ammonia is considered as a source of nitrogen.

Since mass and energy balances have been employed widely in biochemical engineering, literature on their application is not re- viewed here. Unique aspects in this work are the application of certain regularities which are very useful when mass and energy balances are applied to aerobic fermentation processes and the use of reductance degree or equivalents of available electrons in mass and energy balance calculations.

MASS-ENERGY BALANCES

The mass-energy balance method employed in this work is based on the earlier work of Minkevich, Eroshin, and co-workers.1-16 Their approach utilizes the fact that the heat of reaction per electron transferred to oxygen is relatively constant for oxidation of a wide variety of organic molecules .131071'-1g Minkevich, Eroshin, and co- workers1.l0 showed that relatively constant and similar values are obtained for oxidation of dried biomass according to the balance equation

MASS-ENERGY BALANCES IN FERMENTATION 1591

where CH,O,N, denotes the elemental composition of the biomass calculated per atom of carbon and where

Yb = 4 + p - 2n - 3 q ( 2 )

is the reductance degree' of the biomass; that is, yb is the number of equivalents (equiv) O2 requiredquantity of biomass containing 1 g atom carbon for oxidation of the biomass to CO, , H 2 0 , and NH3. Note that the oxidation according to eq. (1) results in nitrogen in the NH3 form. Ammonia is used in eq. (1) because the nitrogen in biomass and in the feed has a reductance degree N = -3. The influence of the nitrogen fraction in the energy balance is minimized when calculations are made on this basis.

Another important aspect of the approach of Minkevich and Eroshin is the use of reductance degree, y , in mass and energy balance calculations. 1*4*5~13-15 From the experimental results sum- marized by Minkevich, Eroshin, and coworkers,l*10 it is seen that the value of Yb is relatively constant and that the relative variance is less than the relative variances in the elemental composition of carbon, hydrogen, oxygen, and nitrogen. When the chemical composition of the biomass is known, it may be used to calculate Yb according to eq. ( 2 ) . When it is not known, the average value (Yb = 4.2) may be employed.'.'O

In order to illustrate the method, the balance equation of microbial growth' CH,Oi + u N H ~ + bO2

= ycCH,O,N, + zCH,O,N, + (1 - y c - z)COZ + cHZO (3)

will be considered. In this equation CH,Oi denotes the elemental composition of the organic substrate, CH,O,N, gives the elemental composition of the biomass, and CH,O,N, gives the elemental composition of the product. When more than one product is present in significant quantity, CH,O,N, may be taken as the average elemental composition of the products. The subscripts denote numbers of atoms of hydrogen, oxygen, and nitrogen per carbon atom. The coefficients yc and z are the fraction of substrate carbon converted to biomass and product, respectively. Equation (3) is relatively general since many organic substrates and products may be written in this form. Ethanol for example, may be written as CH300.5.

The reductance degree, y s , of the organic substrate (or number of equivalents of available electrons in that quantity of organic substrate which contains 1 g atom carbon) is

y s = 4 + m - 2 1 (4)


and, similarly, for the product

y p = 4 f r - 2s - 3 t

where the number of equivalents of available electrons is taken as 4 for carbon, 1 for hydrogen, -2 for oxygen, and -3 for nitrogen. (For the values of reductance degree C = 4, H = 1, 0 = -2, and N = -3, there are no available electrons in COz, HzO, and NH:,.) The oxygen requirement is directly related to the available electrons to be transferred to oxygen; thus, a balance may be written based on the available electrons in eq. (3)

( 5 )

Y S + b(-4) = Y c Y b + Z Y P (6)

b = - Y c Y b - Z Y P ) (7)

Thus, the oxygen requirement in eq. (3) is given by eq. (6) as

Equation (7) may also be obtained from balancing eq. (3) with respect to nitrogen, hydrogen, and oxygen. Rearranging eq. (7) to reflect the fractional allocation of available electrons in the organic substrate gives

The first term is the fraction of available electrons transferred to oxygen, the second term is the fraction of available electrons transferred to biomass, and the third term is the fraction of available electrons transferred to product.

Since the heat of reaction per electron transferred to oxygen is assumed to be constant for all the organic molecules included in eq. (8), the first term gives the fraction of energy of the organic substrate that is evolved as heat. For eq. (3), the heat of reaction is directly related to the oxygen consumption. The heat evolved per unit of organic substrate containing 1 g atom carbon, Q, is

(9)

where Qo is approximately 27 kcaVequiv available electrons transferred to oxygen. l,l0 Cooney et aLZ0 experimentally measured the oxygen consumption and heat evolution in fermentation and found a similar value in these experiments.

It is important to realize that the constant Qo allows the mass and energy balances to be coupled together into a mass-energy balance. Thus, eq. (8) is a mass balance relating the oxygen consumption, b , biomass carbon yield, y c , and product yield, z , and also an energy balance.

Q = Q O ( ~ ~ / Y S ) Y S = 4Q&


The second term in eq. (8) is equal to the fraction of energy of the organic substrate contained in the biomass; that is,

is the energetic yield coefficient for biomass production. The energetic yield coefficient, 7, is the ratio of the heat of oxidation of the produced biomass to the heat of oxidation of the utilized substrate where the oxidations are to the products CO,, H 2 0 , and NH, . This definition of the energetic yield coefficient is a convenient one for computational purposes when NH, is used as the source of nitrogen; however, it is important to realize that energy-associated yield coefficients have also been defined in other way~.'l- '~

The third term in eq. (8) may also be interpreted as the fraction of the chemical energy of the organic substrate which is contained in the product or products, f p ; that is,

t P = Z Y P / Y S (1 1)

Equation ( 3 ) is based on the analytical method in which oxygen in the biomass is estimated by difference such that the estimate does not include, for example, the oxygen in phosphate because it is reported as ash (P'O,). If the oxygen in phosphate is included in the chemical formula CH,O,N,P,, then the reductance degree may be written

Y b = 4 + p - 2n - 3 q + 5k (12)

From eq. ( l o ) , one can see that the energetic yield coefficient, q, is related to the mass yield coefficient based on organic substrate, Y , , according to the

where us and ffb are the weight fractions of carbon in the organic substrate and biomass, respectively.

The energetic yield coefficient may also be related to the mass yield coefficient based on oxygen, Yo (g biomass produced/g oxygen c ~ n s u m e d ) . ' ~ ~ The oxygen requirement in eq. ( 3 ) is b mol 0, or 32 b g O,, while the produced biomass contains y c g atoms carbon which corresponds to 12yC / a b g biomass. From eqs. (7), (lo), and ( I I ) , the ratio, yo (g atoms carbon in biomass/g mol O,), may be written

or, the biomass-to-oxygen ratio on a mass basis as


For heterotrophic microbial growth, because of the laws of ther- modynamics, only part of the energy in the organic substrate is contained in the synthesized biomass. Thus, the thermodynamic range for the biomass energetic yield coefficient is from zero to one for every organic substrate; however, in actual practice, values of r ) are less than 0.7. From eq. (15) it is easy to see that the values of the biomass yield with respect to oxygen, Y o , may range from zero when r ) = 0 to infinity when 7 = 1 and tP = 0. The specific oxygen requirement decreases as the energetic yield increases for constant values of t p . For both r ) and Y o , the thermodynamic range of yields is independent of the source of organic substrate; however, the range of the mass yield coefficient with respect to organic substrate, 0 < Ys < y s u s / y b u b , and carbon yield, 0 < y c < ys / y b , depends on the energy in the organic substrate. Table I shows values of the theoretical maximum mass yield, Y , , and the maximum carbon yield, y c , for a variety of organic substrates for 7) = 1.0, Y b = 4.2, and (Tb = 0.48. Table I shows that raw materials in which the energy content as indicated by y, is high have a high theoretical yield. For methane in which y, = 8 is high, Ys = 3.0 when r ) = 1.0. On the other hand for oxalic acid in which ys = 1 is small, Ys = 0.1 when r ) = 1.0.

For heterotrophic growth, the organic substrate is a source of some nutrients as well as the source of energy. In Table I the maximum yields with respect to carbon are larger than one when ys > Y b . For these conditions carbon dioxide is required as a source of carbon and the term ( 1 - y c - z ) in eq. (3) has negative values.

Equations (10) and (13)-( 15) relate the biomass energetic yield coefficient to other yield coefficients. It is convenient to select the energetic yield coefficient for estimation because of its fundamental importance and because this leads to a better conceptual or physical understanding of the results. The energetic yield also has the convenient range from zero to one for all organic substrates. From the energetic yield, other yield coefficients may be estimated using eqs. (10) and (13)-(15).

When nitrogen consumption is measured, it may be used as one of the variables in estimating 77. In eq. (3), the molar nitrogen consumption (a) per unit quantity of consumed organic substrate containing 1 g atom carbon is

a = y c q + z t

a = YS4r)IYb + Y S f t P I Y P

(16)

(17)

or from eqs. (10) and ( 1 1)

When tP = 0, estimates of r ) may be obtained using eq. (17).


TABLE I Mass Yields of Biomass on Organic Substrate Corresponding

to the Thermodynamic Maximum Energetic Yield

Substrate

Thermodynamic Equiv available yield

in corresponding to 7 = 1.0 organic

substrate containing 1 g carbon weight atom carbon yield yield

Ys Y C Y S

Alkanes Methane Hexane Hexadecane

Methanol Ethanol Hexadecanol Ethylene glycol Glycerol

Formaldehyde Glucose Sucrose Starch, cellulose

Formic acid Acetic acid Propionic acid Lactic acid Fumaric acid Oxalic acid

Alcohols

Carbohydrates

Organic acids

8.0 6.3 6.1

6.0 6.0 6.0 5.0 4.7

4.0 4.0 4.0 4.0

2.0 4.0 4.7 4.0 3.0 1 .o

1.9 3.0 1.5 2.65 1.5 2.6

1.4 1 . 1 1.4 1.55 1.4 2.4 1.2 1 .o 1 . 1 0.9

0.95 0.8 0.95 0.8 0.95 0.85 0.95 0.9

0.5 0.3 0.95 0.8 1 . 1 1.15 0.95 0.8 0.7 0.6 0.25 0.1

Carbon dioxide production measurements may be used with substrate consumption data to obtain the fraction of carbon in the organic substrate evolved as carbon dioxide, d. This ratio may be related to q by using eq. (3) to obtain

d = 1 - yc - z (18)

andeqs. (10),(11),and(l8)togive

d = 1 - ( Y s / Y a h - (YS/YP)tP (19)

Similarly, the ratio of oxygen consumption to organic substrate consumption measurements may be related to q. Combining eqs. (7), (lo), and (11) gives


Equations (9) and (20) may be combined to give

Q = Q o ~ s ( 1 - 7 - 5 ~ ) (21)

which may be used when heat evolution measurements and substrate consumption data are available.

From eqs. (lo), (14), (17) and (19)-(21) other expressions relating measured variables and q may be obtained. For example, from eqs. (19) and (20) the respiratory quotient or COz/02 ratio is

Similarly, eqs. (17) and (20) may be combined to relate r ) to the ammonia-to-oxygen mole ratio; that is,

Equations (17) and (19) may be combined to relate r ) to the ammonia-to-carbon dioxide mole ratio. Thus,

When the product term, t p , is zero or small enough to be neglected, the biomass energetic yield, q, may be estimated from any one of the ratios presented in eqs. (lo), (14), (17) and (19)-(24). Such estimates are considered in the next section. When products are present, more than one ratio is required to estimate q except when the biomass yield is directly measured. However, it is important to stress that ratios based on NH3, Oz, and COz very quickly follow a change in r ) during fermentation while it is difficult to experimentally measure the corresponding small changes in biomass concentration.

BIOMASS PRODUCTION

Yield Estimation

Figures 1 and 2 have been constructed to illustrate how various sets of measured values may be used to quickly estimate yield coefficients. Graphical representation also enables one to visually appreciate the relative accuracy with which r ) may be estimated when values of the variance of the measurements are known. In Figures 1 and 2 , Y b = 4.2 is used for the reductance degree of the


Fig. 1 . Ratios of a = NH3/Sc, b = Oz/Sc, d = COz/Sc, and y c as a function of the energetic yield, 7, for ys = 4.0 (-) and ys = 6.0 (---). S, is the number of g atoms carbon in the consumed organic substrate.

biomass and q = 0.16 is employed for the ratio of nitrogen atoms to carbon atoms in the biomass. Product formation is assumed to be absent; i.e., tP = 0. Equations (lo), (17), (19), and (20) are illustrated in Figure 1 , while eqs. (22)-(24) are illustrated in Figure 2.

Figures 1 and 2 show results for ys = 4.0 (solid lines) and ys = 6.0 (dashed lines). As may be seen from Table I, ys = 4.0 for glucose and other carbohydrates, acetic acid, and formaldehyde. Methanol, ethanol, and all other alcohols of this aliphatic series have values of ys = 6.0. Long-chain alkanes, such as hexadecane, have values of ys only slightly larger than 6. For example, ys = 6.125 for hexadecane. Since the value of ys does not influence the


Fig. 2. Mole ratios of (NHJO,), (COz/Oz), and (NH3/C02) as a function of energetic yield, 7, for ys = 4.0 (-) and ys = 6.0 (---); except for NH3/02 which is identical to that for ys = 4.0.

nitrogen-to-oxygen ratio in eqs. (23), this solid line in Figure 2 is for all values of ys .

As shown earlier, only one ratio from Figures 1 and 2 is needed to estimate the energetic yield, r); however, by employing more than one ratio, it may be possible to obtain a more accurate estimate of 77. If the differences between estimates of r) from two or more ratios are large, this may be due to product formation, measurement errors, or an incorrect assumption such as in the nitrogen content of the biomass. Agreement of estimates of r) from two or more ratios should generally be expected to be good, since the agreement reflects the accuracy of the material and energy balances.

The ratio of heat evolution to oxygen consumption should be constant and approximately equal to 27 kcaVg equiv O2 consumed. When both of these quantities are measured, the accuracy of the


measurements may be checked by computing this ratio. Similarly, the nitrogen consumption-to-biomass production ratio may be calculated and checked against measured or average values of biomass nitrogen fraction. l,lo Since nitrogen may be associated with products, when this ratio is not in agreement, this may be due to measurement errors or the involvement of nitrogen with product formation.

The variance of the reductance degree, Y b , and elemental composition of the biomass has been investigated.'*'O The biomass reductance degree, yb , has a relative variance of about 4%. The mass fraction carbon in the biomass, ( + b , has a relative variance of about 5%. The relative variance is larger for nitrogen; it is about 20%. These results are for 28 yeast and 12 bacteria determinations with growth under industrial and laboratory conditions. For repeated work with a particular organism, the elemental composition may be determined and used to estimate yb , ub , and 4.

Figure 1 shows the linear relationships which exist between energetic yield and the ratios of ammonia to organic substrate (a), oxygen to organic substrate (b), carbon dioxide to organic substrate (4, and biomass carbon yield on organic substrate (y,). When organic substrate utilization is known, any of these ratios may be used to estimate energetic yield. Where good estimates of oxygen utilization are available, the oxygen-to-organic substrate ratio (b), has the advantage of not requiring estimates of Y b , ( + b , or 4; however, it provides a good estimate of r ] only when no other products are formed. Both the oxygen-to-organic substrate ratio (b) and carbon dioxide-to-organic substrate ratio (4 are estimates of r] by difference, and as shown by eqs. (19) and (20), estimates of r ] , when tP = 0 is assumed, will be correct only if this assumption is valid. On the other hand, the carbon yield (u,) provides a direct estimate of the energetic yield that is not influenced by product formation. The ammonia-to-organic substrate ratio (a) may also be influenced by product formation as shown in eq. (17).

Figure 2 shows several ratios using the variables: CO, production, 0, consumption, and NH3 consumption. These variables may be measured continuously or frequently and can be quickly used to estimate yield coefficients when no other products are formed. For both y s = 4 and ys = 6, the ammonia-to-oxygen and ammonia-to- carbon dioxide ratios should give good estimates of the energetic yield from accurately measured values of NH3 consumption, 0, consumption, and CO, evolution.

In Figure 2, the dashed lines are for y s = 6.0 (methanol, ethanol,


and long-chain hydrocarbons); however, the solid line for the ammonia-to-oxygen ratio is for both ys = 4.0 and ys = 6.0. For ys = 6.0, all of the ratios should give good estimates of the energetic yield coefficient in the region of practical interest; i.e., for q = 0.3- 0.6. The choice of which ratio to use can be based on the experimental conditions and which values can be most accurately measured. If all three variables are measured, three estimates of the energetic yield coefficient may be obtained and compared to gain insight about the accuracy of the estimates.

For ys = 4.0 (glucose and other carbohydrates), the solid lines in Figure 2 should give good estimates of the energetic yield coefficient only for the ammonia-to-oxygen and ammonia-to-carbon dioxide ratios. The carbon dioxide-to-oxygen ratio (respiratory quotient) is almost constant for small values of 7) and increases only very slowly as 71 increases in the region of practical interest (q = 0.4-0.7). The respiratory quotient may be examined to gain insight into the accuracy of the O2 and COz measurements and the assumption of no product formation. If this ratio differs significantly from the correct value, this may be due to either measurement errors or product formation. For example, if ethanol is being formed as product, the value of the respiratory quotient will be higher.

Application to Continuous Operation

In this section an application of material and energy balances to the operation of continuous single-cell protein (SCP) production is illustrated. In the production of biomass for SCP, a continuous process is employed. In order to optimize economic efficiency, the process should be operated close to the point of simultaneous organic substrate and oxygen substrate growth limitation (with con- trolled ammonia addition).8 Since changes in the yield coefficients may occur during continuous production, it is important to be able to quickly estimate the yield coefficients, identify the factor which is limiting growth, and to change the rate of organic substrate addition to follow the point of simultaneous limitation by both organic substrate and oxygen.

In an earlier work,' equations were developed to relate the organic substrate feed rate, oxygen-transfer rate, and nitrogen feed rate under conditions of continuous operation with simultaneous organic substrate, oxygen, and nitrogen growth limitation. For example, the relation between organic substrate consumption and oxygen utilization is given by the ratio


which is easily obtained from eqs. (13) and (15) when tP = 0. This yield ratio is shown in Figure 3 for methanol. Note that the ratio increases in value as 7) increases. For a continuous fermentor in which the oxygen-transfer rate is equal to KLa(CL - C ) and the consumed substrate is D(So - S ) ,

(26) yo - 3 - - m o - S ) - _ Y s 2 ~ s m s ( l - 7)) K L ~ ( C L- C )

D = KLa(C L - C ) Y , / ( S 0 - S ) Y s

So = KLa(CL - C ) Y o / D Y s + S

This equation may be solved for D to obtain8

(27)

(28)

Equation (26) may also be solved for S o to obtain

For the maximum oxygen-transfer rate, KLaCL, and utilization of all the organic substrate, DSo ,

DSoIKLa CL = Y o / Y s (29)

Equations (27)-(29) and Figure 3 show that either the dilution rate, D , or the organic substrate feed concentration, S o , should vary in direct proportion to ( Y o / Y s ) when the energetic yield coefficient varies. An increase in energetic yield coefficient will

0 05

Fig. 3. Variation of 1) biomass weight yield based on organic substrate, Y s ; 2) biomass weight yield based on oxygen, Y o , and 3) the ratio ( Y 0 / Y , ) with the energetic yield, q, for methanol.

I608 ERICKSON, MINKEVICH, AND EROSHIN

result in an increased biomass concentration in the fermentor because Ys increases as q increases. Since the oxygen requirement decreases as q increases for a given organic substrate feed rate (see the oxygen-to-organic substrate ratio in Fig. l) , the oxygen-transfer capability of the fermentor will be fully used only if D or S o is increased in direct proportion to (Yo / Y s ) . If D or S o is not increased, the dissolved oxygen concentration in the fermentor will increase so that eq. (26) is satisfied.

When the energetic yield decreases, the yield on oxygen will decrease and it is necessary to decrease D or So in direct proportion to (Yo / Y s ) . If D and So remain constant, under oxygen-limited conditions, the organic substrate concentration will increase and eq. (26) will be satisfied. Furthermore, the biomass concentration in the fermentor will be directly proportional to Yo under oxygen- limited conditions; that is, the biomass concentration will decrease in direct proportion to curve 2 in Figure 3 as q decreases under oxygen-limited conditions when the unused substrate is not converted to extracellular products.

Based on eqs. (27) and (28) and the above analysis, it appears that operation under organic-substrate-limited conditions with almost full use of the oxygen-transfer capacity of the fermentor can be maintained by varying either D or So using dissolved oxygen concentration level control; i.e., if the dissolved oxygen concentration decreases, either D or So can be decreased to a point where the dissolved oxygen returns to the desired concentration. This method of control assumes that the dissolved oxygen concentration can be accurately measured and that operation is at a sufficiently high dissolved oxygen concentration to allow observable decreases in dissolved oxygen concentration under organic-substrate-limited conditions. If D or S o is varied by means of dissolved oxygen concentration level control, then the dissolved oxygen concentration will be maintained constant, and the oxygen-transfer rate will be constant provided K L a and CL also remain constant. Under these conditions, as the energetic yield changes, the productivity of the fermentor will vary according to curve 2 in Figure 3.

Dissolved oxygen level control may be useful in laboratory and pilot-plant operation; frequently however, for industrial biomass production, the dissolved oxygen concentration is too low to use dissolved oxygen concentration level control. When it is not possible to vary D or So based on dissolved oxygen level control, the value of (Yo / Y s ) may be estimated from the estimated value of q. Since ( Y o / Y s ) is the ratio of carbon substrate consumption to


oxygen consumption, this value can be compared to the ratio of the carbon substrate feed rate to the maximum rate of oxygen transfer DSo / K L a C L . If these two ratios are equal, the operation is at the desired condition; however, if

DSO IKL aCL ' yo I ys (29')

an excessive amount of organic substrate may be entering the fermentor. The value of D or S o can be reduced to achieve equality in eq. (29'). An increase in dissolved oxygen concentration will result if the organic substrate feed rate is too low.

When the dissolved oxygen level is very low and organic substrate may not be limiting growth, then the ratios presented in Figure 1 should be used to estimate the energetic yield coefficient only if information on the dissolved organic substrate concentration is available. The ratios in Figure 2 should be used when the dissolved organic substrate concentration is not known.

Either D or So or some combination of D and So may be varied to keep the process close to the optimal operating condition of simultaneous oxygen and organic substrate growth limitation. When So is constant and D is varied according to eq. (27), X = Ys(S,, - S ) and the cell concentration variation is directly proportional to Ys (curve 1 in Fig. 3) for constant values of S. On the other hand, if D is constant and So is vaned according to eq. (28), the cell concentration variation is directly proportional to productivity. Thus, the variation of cell concentration will follow the yield with respect to oxygen (curve 2 in Fig. 3) whenever the productivity follows this curve (constant rate of oxygen consumption). Thus, by varying the dilution rate the variation in cell concentration will be smaller for yields of practical interest.

PRODUCT FORMATION

When product formation is present or the possibility of product formation must be considered, the accurate estimation of yield coefficients by indirect methods requires more experimental data than when product formation may be neglected. Direct measurement of biomass, organic' substrate, and product concentrations leads directly to biomass yield coefficients and product yield coefficients; however, when product formation is not the main objective, usually product concentrations are not measured. In this section the estimation of yield coefficients is considered where biomass

1610 EFUCKSON, MINKEVICH, AND EROSHIN

production is the primary goal, but product formation may be present. When products may be present, one may assume that they are absent and estimate the value of the biomass energetic yield coefficient, r ) , from several different sets of variables. Comparison and analysis of these estimates may indicate whether product formation is significant. Good agreement of direct and indirect methods will generally occur only if the assumption of negligible product formation is valid.

From measured values of biomass production and organic substrate consumption, eq. (13) gives a direct estimate of r). Similarly, if t = 0 in eq. (17) (no nitrogen associated with products), ammonia and organic substrate consumption give a direct estimate of r). If the nitrogen consumption term is large because product formation has resulted in ammonia consumption for acid neutralization, direct incorporation into products, or both, the estimate of r ) from eq. (17) (assuming t p = 0) may be considerably larger than the expected value, and this may serve as an indication that products are present.

If oxygen consumption and organic substrate consumption measurements are available, the sum ( r ) + t p ) may be estimated from eq. (20). When f p = 0, this gives an estimate of r). If this sum is larger than estimates of r ) from biomass and organic substrate or nitrogen and organic substrate, this may be due to product formation. The difference between the ( r ) + t p ) estimate from oxygen and organic substrate and r ) from biomass and organic substrate is an estimate of t p , the fraction of the energy in the organic substrate which is converted to products; i.e., from eqs. (13) and (20):

Oxygen consumption and biomass production measurements may be used to estimate the biomass energetic yield using eq. (14) or eq. (15) and the assumption that t p = 0. Estimates of r ) from these equations using the assumption t p = 0 give an estimate of the energetic yield based on the fraction of the substrate energy which is associated with the first and second terms of eq. (8); that is, eq. (14) may be written in the form

Substrate energy contained in products is not included in estimating the energetic efficiency. Thus, this estimate of r) also has an important physical meaning: it gives the energetic yield based on the sum of the fractions of substrate energy converted to heat and

MASS-ENERGY BALANCES IN FERMENTATION I61 1

biomass. When products are present in significant quantity, this estimate of q indicates the biomass energetic yield which could be achieved if the products would also be converted to biomass with similar energetic efficiency.

When carbon dioxide evolution, organic substrate consumption, and biomass production are measured, these may be used in eq. (18), which is a carbon balance, to estimate z, the fraction of the carbon incorporated into products. Alternately, estimates of 7) from eq. (13) and (1 - d)yb /y s from eq. (19) may be compared. The quantity (1 - d)yb / y s is an estimate of 7) when there is no product formation. When it is significantly larger than direct estimates of 77, this is an indication of product formation; i.e., eqs. (13) and (19) may be combined to give an estimate of product formation; namely,

For a given value of 7) (i.e., a given amount of biomass production on a particular organic substrate) any product formation that is present will be at the expense of carbon dioxide evolution from the point of view of a carbon balance, and the quantity of available electrons in the product is directly related to the reduction in oxygen consumption. Ammonia consumption will be either equal to that required for biomass production or if ammonia is associated with product formation it will be greater than that required for biomass production. Thus, it is easy to see that the two ratios, ammonia-to- oxygen and ammonia-to-carbon dioxide, given by eqs. (23) and (24), respectively, will both be larger than those for the correct value of q when product formation is present. Figure 2 and eqs. (23) and (24) show that both of these ratios increase monotonically as 7) increases. Thus, if one assumes product formation is absent and estimates 7) using Figure 2, the estimate of 7) should be larger than the correct value when products are present.

The respiratory quotient or COz/Oz ratio should also be examined when these measurements are available. The value of the respiratory quotient for substrates in which ys is of similar magnitude to Y b is frequently useful in estimating product formation. Figure 4 illustrates for ys = 4 how the value of the respiratory coefficient changes when products with different energy contents are formed. In each case tp = 0.2; i.e., 20% of the energy in the organic substrate is converted to product. For ethanol formation or any product with y p = 6 , the respiratory quotient has a higher value as shown in Figure 4 for S p = 0.2 or z = 0.133. When acetic acid or any product with y p = 4 is formed, the value of the respiratory


0 3 7

Fig. 4. Respiratory quotient ( C 0 2 / 0 2 ) vs. energetic efficiency, 7, for ys = 4.0 under conditions of: 1) no product formation; 2) ethanol formation (yp = 6.0, tp = 0.2); 3) acetic acid or lactic acid formation (yp = 4.0, tP = 0.2), and 4) citric acid formation (yp = 3.0, tp = 0.2). If the product is utilized as organic substrate for biomass production, the respiratory quotient is: 5) ethanol (ys = 6.0); 1) acetic or lactic acid ( y s = 4.0), and 6) citric acid ( y s = 3.0).

quotient does not change significantly. For y p = 3 or citric acid, for example, the respiratory quotient has lower values as shown in Figure 4 for t p = 0.2 or z = 0.267. Frequently in fermentations, products are formed and later utilized as an organic substrate. Figure 4 also shows values of the respiratory quotient for biomass production for ys = 6 (ethanol), ys = 4 (carbohydrates, acetic acid), and ys = 3 (citric acid). For ys > Y e , values of the respiratory quotient are less than one for no product formation, and for ys < Y b , they are greater than one. For product formation when ys = 4, where y p > y s , the respiratory quotient increases as tp increases for a given value of 7; similarly, for y p < y s , the respiratory quotient decreases as t p increases for a particular value of 7.


In estimating the biomass energetic yield coefficient, r), from different sets of measured values, there are conditions which may give similar estimates of r) even when products are present. For example, when nitrogen is not associated with products, ratios of ammonia consumption to oxygen consumption may give estimates of r) identical to those from biomass production and oxygen consumption because nitrogen consumption and biomass production are directly related. Similarly, oxygen consumption and heat evolution are directly related. The physical interpretations given earlier in this section can also be extended using heat evolution in place of oxygen and/or nitrogen in place of biomass when nitrogen is not associated with products.

ANALYSIS OF EXPERIMENTAL RESULTS

As shown in the equations and figures presented earlier, the energetic yield coefficient may be estimated from several sets of measured values. Estimates by different methods may be compared to check the consistency of the results when the experimental measurements are sufficient to allow more than one estimate. For example, if three variables are measured, three different estimates of r) may be obtained using each of the available combinations of two measured values.

The work of BattleyZ4 provides an example in which several estimates of the energetic yield may be calculated. Using Saccha- romyces cerevisiae and glucose as organic substrate, Battley measured cellular carbon, substrate carbon, CO, , and 0, consumption. The chemical composition of the biomass was also measured. Using Battley’s experimental results,24 the following estimates were obtained: Y b = 4.28, r) = 0.36 from 0, and glucose consumption, r)

= 0.36 from biomass production and glucose consumption, r) = 0.34 from CO, production and glucose consumption, and r) = 0.36 from biomass production and 0, consumption. From these results, we see that consistent estimates of r) are obtained from 0, consumption, glucose consumption, and biomass production.

With ethanol as the organic substrate, BattleyZ4 measured organic substrate consumption, CO, production, 0, consumption, and biomass composition. Using the available data, we obtained Y b = 4.45, r) = 0.40 from 0, and ethanol consumption, r) = 0.39 from CO, production and ethanol consumption, and r) = 0.37 from CO, production and 0, consumption.

battle^^^ also used acetic acid as the organic substrate. For this


case, we obtained Y b = 4.29, r ) = 0.32 from oxygen and acetic acid consumption, and r ) = 0.33 from CO, production and acetic acid consumption. As shown in Figure 2 for ys = 4.0, the C0,/02 ratio does not give an accurate estimate of r ) because the ratio is nearly constant for values of q in the 0-0.4 range. Therefore, we did not try to estimate r ) from CO, production and 0, consumption.

The work of Hernandez and Johnsonz5 may also be used to estimate several values of the energetic yield. In this work, organic substrate consumption, cell production, and 0, consumption were measured using glucose, ethanol, and acetic acid as organic substrates. Cell composition was not reported; therefore, we assumed c b y b = 2.0 in our calculations and estimates of r). For glucose, values of r ) = 0.64 were obtained from each of the three sets of experimental data. For ethanol, r ) = 0.46 from 0, and ethanol consumption, 7) = 0.44 from biomass production and ethanol consumption, and q = 0.45 from biomass production and 0, consumption. For acetic acid as organic substrate, q = 0.52 from 0, and acetic acid Consumption, r ) = 0.45 from biomass production and acetic acid consumption, and r) = 0.48 from biomass production and 0, consumption.

From the results presented above using the data of BattleyZ4 and Hernandez and we see that good agreement of the values of r ) from different measured values can be obtained. The results of Hernandez and Johnsonz5 for acetic acid show that good agreement is not always obtained in estimating r ) from several sets of data. The differences in this case may be due to measurement errors, product formation, or an incorrect assumption such as in the composition of the biomass.

KanazawaZ6 has measured 0, consumption, heat evolution, biomass production, and cell composition in pilot-scale equipment with a working volume of 100 m3 for SCP production with n-paraffins as organic substrate. Values of biomass yield based on organic substrate, Y , , are also reported; however, KanazawaZ6 does not state whether the concentration of hydrocarbons in the effluent was measured or assumed to be negligible in determining Ys . The results of KanazawaZ6 obtained from continuous-culture studies will be used here as an example to illustrate the application of mass-energy balances in SCP applications. Sufficient measurements were made to estimate the energetic yield from different sources of data. The results of KanazawaZ6 and our estimates of energetic yield r) are shown in Tables I1 and 111. In Table I1 the values of Y s , X, and DX were used to determine the values of substrate consumption

5

X

DX

0,

upta

ke

from

0,

and

from

0,

and

s E I/) rn Z M

TA

BL

E I

1 4"

Estim

ated

val

ues

of r

) w

Estim

ated

Val

ues

of E

nerg

etic

Yie

ld C

oeff

icie

nt f

rom

Oxy

gen

Con

sum

ptio

n, B

iom

ass

Prod

ucti

on, a

nd O

rgan

ic S

ubst

rate

a

W

Exp

t. N

o.

YS

(bio

mas

s, %

) (k

g/m

s hr)

(k

g m

ol/m

3 hr)

YO

subs

trat

e pr

oduc

tivity

fr

om Y

s

z 1

1.12

4

1.01

2.

97

0.15

4 0.

60

0.47

0.

43

0.39

2

1.13

1.

28

3.07

0.

159

0.60

0.

46

0.43

0.

40

0

4 1.

14

2.04

2.

66

0.18

4 5

1.09

1.

17

3.00

0.

187

0.50

0.

36

0.38

0.

38

6 1.

18

1.43

3.

24

0.17

2 0.

59

0.42

0.

42

0.42

8 1.

04

1.37

3 1.

06

1.58

3.

22

0.16

3 0.

62

0.51

0.

43

0.37

!2

0.45

0.

28

0.36

0.

40

2 m" 7

1.14

1.

52

3.20

0.

146

0.69

0.

52

0.46

0.

40

E 3.

11

0.15

2 0.

64

0.53

0.

44

0.37

Z

A

vera

ge

1.11

0.

59

0.45

0.

42

0.39

4

% 0" M

a D

ata

from

Kan

azaw

a.26

Z


TABLE 111 Estimated Values of the Energetic Yield Coefficient from Heat Evolution, Biomass

Productivity, and Organic Substrate Consumptiona

Estimates of 7)

Y S AHIDX from AH and from AH and Expt. No. (kg/kg) (kcaVkg) substrate productivity from Ys

1 1.25 4&10 0.49 0.47 0.44 2 1.03 6060 0.45 0.40 0.36 3 1.09 5830 0.44 0.41 0.38

Average 1.12 5510 0.46 0.43 0.39

a Data from Kanazawa.26

(a backward calculation to obtain the original data). In Table 111, Kanazawa's measured values of 11,400 kcaUkg for the heat of combustion of hydrocarbon substrate were used in the equation*

(32) to estimate the energetic yield from (AH), the heat evolutiodkg biomass produced, and substrate consumption. In Table 111, the energetic yield using biomass production and heat evolution was obtained using the experimental value of heat evolutiodkg biomass produced (AH) together with the estimated energy content of the biomass. The energy content of the biomass was obtained using = 4.19 and (Tb = 0.436 from Kanazawa's experimental determina- tion of cell composition,26 together with the mean value of the heat of reaction for biomass oxidation of 27 kcaVequiv available electrons.'~'O Thus, for the biomass

7) = 1 - (AH)Y,/11,400

AHb = 1000(27YbCrb 112) (33) which yields 4110 kcaVkg biomass. Thus, the estimates of 7 from biomass production and heat evolution may be obtained from

7 = AHb/(AHb + A H ) (34) The value of 41 10 kcaVkg biomass is less than the measured value of 4700 kcal/kg reported for the heat of combustion by Kanazawa26 because the heat of combustion of NH3 to N, and H,O is not

* Equation (32) utilizes the heat evolved per unit of energy in the consumed organic substrate to estimate 7. The product (AHY,) does not depend on the accuracy of biomass measurements. Equation (32) is analogous to eq. (20); it is obtained by combining eqs. (&(I 1) to give Q/Qoys = 1 - q - t p . Assuming t p = 0, and noting that the ratio Q/Qors = AHYs/11,400, eq. (32) is obtained.


included in our calculation, while it is present in Kanazawa’s experimental measurement. In order to use the mass-energy balance equations consistently as developed in the earlier part of this work, the heat of reaction upon oxidation of the biomass to NH,, CO,, and H20 must be employed in eq. (34).

From Tables I1 and 111, we can see that there are differences in the estimates of r ) using the different sources of data in each table. We also see that the estimates of r) from oxygen and from heat evolution give rather similar results when used with either organic substrate or biomass productivity (the average values are 0.45 and 0.46 using organic substrate and 0.42 and 0.43 using biomass productivity). Since 0, consumption and heat evolution are directly related, this suggests that the 0, consumption and heat evolution measurements are consistent with each other.

The source of the deviation of the values of 77 from one another may be due to hydrocarbon substrate which is not completely consumed or is converted to products such as fatty acids. It is also possible that the amount of biomass produced was actually more than the measured values. If the biomass measurements are incorrect and the other measurements are correct, the energetic efficiency predicted from oxygen and organic substrate would be the correct value, and biomass production would be about 15% larger than reported. However, if the organic substrate utilization measurement is in error, the correct energetic efficiency is obtained from 0, consumption and biomass production, and about 7% of the energy in the organic substrate is contained in unutilized substrate or products.

We also examined several other possibilities as to why these results are not in agreement. Kanazawa’s reported value for oxygen in biomass may include the oxygen in phosphate. It is not difficult to use Kanazawa’sZ6 measured value of weight fraction of phosphorus in biomass and recalculate y b using P = 5 to obtain -yb = 4.31 instead of y b = 4.19. This correction increases the value of r)

estimated from Y , by about 2.8% so the average value is about 0.40 rather than 0.39. The estimate of r ) from 0, consumption and biomass productivity is increased slightly (about 1%) while the estimate from 0, and substrate consumption is unaffected.

We also noted that the fraction of carbon in the biomass as determined by Kanazawa26 is lower than the average value. l,l0 When mb = 0.48 is used instead of 0.436, the energetic yield estimated from Y , is about 0.43, which is much closer to the value obtained from consumption of 0, and organic substrate that is unaffected by


the value of ( T b . If the cell composition data are from the final product from the pilot plant, removal of unutilized hydrocarbon and lipids in the separation process would lead to a smaller value of crb .

In order to further examine the possibility of incomplete substrate utilization, the respiratory quotient was estimated from the average values of biomass yield from organic substrate and from oxygen ( Ys = 1 . 1 1 and Yo = 0.59). The fraction of substrate carbon incorporated into biomass is

Y c = Y S f l b / U S (35)

If no products other than biomass, C 0 2 , and water are formed, the fraction of substrate carbon converted to C02 is (1 - yc) . Thus, the g mol C02 producedg mol O2 utilized is

Substituting numerical values into eq. (36) yields C 0 2 / 0 2 = 0.53. If eq. (22) is used with tP = 0 to estimate the energetic yield from this ratio, q = 0.29 is obtained. Alternately, using eq. (22) for tp = 0 and the average estimates of q in Table 11, one obtains respiratory quotients of 0.41, 0.44, and 0.46 for energetic yield coefficients equal to 0.45, 0.42, and 0.39, respectively. These estimates of the respiratory quotient are considerably smaller than the value of 0.53 obtained from eq. (36). If part of the substrate is unutilized or converted to fatty acids, the respiratory quotient would be lower than the value of 0.53 estimated from Y, and Y o . For example, if 7% of the organic substrate is unutilized, the value of the respiratory quotient as estimated from

using average values for Ys and Yo is reduced to 0.45. Equation (30) may be used to estimate the fraction of energy in

the organic substrate converted to products. Equation (30) is also equal to the difference between the estimate of r ) from O2 and organic substrate consumption and the estimate of r ) from biomass and organic substrate consumption. From Table 11, using average values of r), tP = 0.45 - 0.39 = 0.06. Similarly, from Table 111, using average values, t p = 0.46 - 0.39 = 0.07 where r ) = 0.46 is from heat evolution and organic substrate consumption. For long- chain fatty acids, this corresponds to about 1 g/liter in the effluent stream.


The work of KanazawaZ6 is used here to illustrate how mass- energy balances may be used to examine experimental results and check their consistency. In this example, one may conclude that the values of the energetic yield, q, estimated from oxygen and heat evolution give consistent results when employed with either biomass production or organic substrate consumption. One may also conclude that the estimates of energetic yield from: 1) oxygen and organic substrate, 2) oxygen and biomass, and 3) biomass and organic substrate are inconsistent. Furthermore, when data from heat evolution are used in place of the 0, consumption data, the results are also inconsistent, but the differences are similar to those observed when oxygen is used in place of heat evolution. Exami- nation of the respiratory quotient suggests that at least part of the inconsistency is due to unutilized organic substrate or formation of products such as long-chain fatty acids.

In the work of KanazawaZ6 material and energy balances are also employed; however, in the material balances to estimate 0, consumption, the hydrogen in NH, is not considered in the material balances. Similarly, the heat of combustion of NH, is not properly considered in the energy balance of Kanazawa.26

CONCLUSIONS

Mass-energy balances may be used advantageously in analyzing experimental results and in the operation of fermentation processes. Characterization of organic materials using their reductance degree greatly simplifies material and energy balance computations and allows one to advantageously use the facts that the reductance degree of biomass is relatively constant and that the energy evolved per equivalent of electrons transferred to oxygen is relatively constant. The definition of the biomass energetic yield coefficient as the fraction of the energy in the organic substrate which is converted to biomass based on oxidation to CO,, HzO, and NH, provides a useful parameter which may be directly related to various mass yield coefficients using the reductance degree. Equations are developed which relate ratios of a number of these variables to the biomass energetic yield coefficient. Organic substrate consumption, biomass production, O2 consumption, NH, consumption, CO, production, and heat evolution are measured variables which may be effectively used in mass-energy balance calculations.

Examination of available experimental results shows that good agreement of estimates of the biomass energetic yield coefficient

I620 ERICKSON, MINKEVICH, AND EROSHIN

can be obtained from different sets of measured variables. Analysis of other experimental results shows that the procedures may be used to detect when products may be present, and to estimate the possible amount of products.

a

b

C CL C

D d

AH

KLa k 1 m n P Q

Qo 4 r S s c

SO

mb

S t X Y O

Y S

Y C

Y o Z

Y b

Y P

Y s

Nomenclature mol NHJquantity of organic substrate containing 1 g atom carbon (g moVg atom carbon) mol OJquantity of organic substrate containing 1 g atom carbon (g moVg atom carbon) concentration of dissolved 0, (kg/m3) equilibrium or saturation dissolved 0, concentration (kg/m3) mol H,O/quantity of organic substrate containing 1 g atom carbon (g moYg atom carbon) dilution rate (hr-l) mol COJquantity of organic substrate containing 1 g atom carbon (g moVg atom carbon) heat evolution/kg biomass produced (kcdkg) heat of reaction for biomass oxidation to CO, , H,O, and NH3 (kcaYkg) oxygen-transfer coefficient (hr-l) atomic ratio of phosphorus to carbon in biomass (dimensionless) atomic ratio of oxygen to carbon in organic substrate (dimensionless) atomic ratio of hydrogen to carbon in organic substrate (dimensionless) atomic ratio of oxygen to carbon in biomass (dimensionless) atomic ratio of hydrogen to carbon in biomass (dimensionless) heat evolution in fermentation per quantity of organic substrate containing 1 g atom carbon (kcaVg atom carbon) heat evolution per equivalent of oxygen (kcaUg equiv) atomic ratio of nitrogen to carbon in biomass (dimensionless) atomic ratio of hydrogen to carbon in products (dimensionless) organic substrate concentration in the fermentor (kg/m3) number of g atoms carbon in the consumed organic substrate (g atoms carbon) organic substrate concentration in the feed to the fermentor (kg/m3) atomic ratio of oxygen to carbon in products (dimensionless) atomic ratio of nitrogen to carbon in products (dimensionless) biomass concentration in the fermentor (kg/m? biomass mass yield based on oxygen (dimensionless) biomass mass yield based on organic substrate (dimensionless) biomass carbon yield (fraction of organic substrate carbon in biomass) (dimensionless) biomass yield per mol 0, (g atoms carbon in biomass/g mol 0,) fraction of organic substrate carbon in products (dimensionless) reductance degree of biomass as defined by eq. (2) (equiv available electrondg atom carbon) reductance degree of products (equiv available electrondg atom carbon) reductance degree of organic substrate (equiv available electrondg atom carbon)


tP

7 )

ub us

fraction of energy in organic substrate which is converted to products (dimensionless) fraction of energy in organic substrate which is converted to biomass weight fraction carbon in biomass (dimensionless) weight fraction carbon in organic substrate (dimensionless)

References 1. I. G. Minkevich and V. K. Eroshin, Folia Microbiol., 18, 376 (1973). 2. V. K. Eroshin and A. I. Belyanin, Prikl. Biokh. Mikrobiol., 4, 704 (1968) (in

3. I. G. Minkevich, G. P. Popkov, and V. K. Eroshin, Prikl. Biokh. Mikrobiol.,

4. I. G. Minkevich and V. K. Eroshin, Izvestiya AN SSSR, Ser. Biol. N2, 245

5 . I. G. Minkevich and V. K. Eroshin, Izvestiya AN SSSR, Ser. B i d . , N3, 414

6. I. G. Minkevich and V. K. Eroshin, Mikrobiol. Promishlennost, 1(109), 10

7. I. G. Minkevich -and V. K. Eroshin, Mikrobiol. Promishlennost, 2(110), 1

8. I. G. Minkevich and V. K. Eroshin, Mikrobiol. Promishlennost, 7(115), 1

9. I. G. Minkevich and V. K. Eroshin, Usp. Sovremennoi Biol., 82, 103 (1976)

10. I. G. Minkevich, V. K. Eroshin, T. A. Alekseeva, and A. P. Tereshchenko,

11. I. G. Minkevich and V. K. Eroshin, Stud. Biophys., 49,43 (1975). 12. I. G. Minkevich and V. K. Eroshin, Stud. Biophys., 59, 67 (1976). 13. I. G. Minkevich and V. K. Eroshin, Biotechnol. Bioeng. Symp., 4, 21 (1973). 14. V. K. Eroshin,Biotechnol. Bioeng. Symp., 4, 995 (1974). 15. V. K. Eroshin, Proc. Biochem., 12(6), 29 (1977). 16. G. K. Skryabin, S. V. Chepigo, and V. K. Eroshin, Proceedings of the 9th

World Petroleum Congress, review paper 14, 121, Applied Science Publishers, Essex, England, 1975.

Russian).

8, 160 (1972) (in Russian).

(1972) (in Russian).





(in Russian).

Mikrobiol. Promishlennost. 2(144), 1 (1977) (in Russian).

17. W. M. Thornton, Philos. Mag., 33, 1% (1917). 18. M. S. Kharasch, Bur. Stand. J. Res., 2 , 359 (1929). 19. M. S. Kharasch and B. Sher, J. Phys. Chem., 29, 625 (1925). 20. C. L. Cooney, D. I. C. Wang, and R. I. Mateles, Biotechnol. Bioeng., 11,269

21. W. J. Payne,Ann. Rev. Microbiol., 24, 17 (1970). 22. V. 0. Tauson, Mikrobiol., 2(1), 19 (1933); see also V. 0. Tauson, Basic

Aspects of Plant Bioenergetics, Publishing House of the USSR Academy of Sciences, Moscow, 1950, in Russian, p. 201.

(1969).

23. E. F. Terroine and R. Wurmser, Bull. Soc. Chim. Biol., 4, 519 (1922). 24. E. H. Battley, Physiol. Plantarum, 13(2), 192 (1960). 25. E. Hernandez and M. J. Johnson, J. Bacreriol., 94, 996 (1967). 26. M. Kanazawa, in Single Cell Protein I I , S . R. Tannenbaum and D. I. C.

Wang, Eds., M.I.T. Press, Cambridge, Mass., 1975, p. 438.

Accepted for Publication February 14, 1978

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