ALlClAN V. QUINLAN" Department of Mechanical Engineering Massachusetts Institute of Technology Cambridge, Massachusetts INTRODUCTION

Transcription

1 The Influence of Dilution Rate, Temperature, and Influent Substrate Concentration on the Efficiency of Steady-State Biomass Production in Continuous Microbial Culture ALlClAN V. QUINLAN" Department of Mechanical Engineering Massachusetts Institute of Technology Cambridge, Massachusetts INTRODUCTION The maximum achievable biomass concentration in continuous culture equals the influent substrate concentration So times a yield coefficient Y. This is the biomass concentration that would be produced were all the substrate entering the culture vessel permanently incorporated into biomass. However, microbial biomass production in continous culture is inherently inefficient. Some of the influent substrate is flushed unchanged out of the culture vessel, and some is converted into extracellular metabolites within the culture vessel. As a result, only a fraction of the maximum possible biomass concentration is ever actually achieved. This fraction is a direct measure of the efficiency of biomass production. Hence, whatever factors affect this fraction also directly affect the efficiency of biomass production. The purpose of this paper is to identify these factors and determine how they can be manipulated to increase the efficiency of steady-state biomass production in continuous microbial culture. The results obtained apply to nonattached microbial populations whose growth rate saturates in substrate concentration according to a Monod rate law. MONOD BIOMASS PRODUCTION KINETICS Reaction Mechanism A simple Monod reaction mechanism for microbial growth in continuous culture is schematized in FIGURE 1. Its rationale is given in Reference 1. According to it, the total biomass concentration B may be partitioned into two portions: B,, capable of consuming substrate; B,, not capable. Substrate at a concentration S is consumed at a rate csb,/y. For each unit of substrate consumed, Y units of biomass are produced. Substrate consumption causes B, to become saturated and converted to B, at a rate 'Present address: Department of Mechanical Engineering and Materials Science, Duke University School of Engineering, Durham, NC

2 198 ANNALS NEW YORK ACADEMY OF SCIENCES ssb,. Eventually, B, may become unsaturated and converted back to B, at a rate ub,. Production of extracellular metabolites causes biomass to waste away at rates wb,, wb,, wb. In a constant-volume culture vessel, inflow of substrate at a concentration So and a dilution rate d causes substrate and biomass to be flushed out at rates ds, db,, db,, db. Rate Laws If B, is assumed to respond to changes in S much more slowly than B, does, then the familiar differential equations for substrate depletion and biomass production may be derived from the reaction mechanism shown in FIGURE 1.' MICROBIAL GROWTH IN OPEN SYSTEMS A MONOD REACTION MECHANISM FIGURE 1. Reaction mechanism assumed to govern the rate of microbial biomass production in batch (d - 0) and continuous (d > 0) culture. Symbols defined in text and legend of symbols. The differential equation obtained for substrate depletion is: where S = d(s0 - S ) - p,(b/y)s/(k + S ) (1) The second term of Equation 1 represents the rate of substrate consumption. It saturates in substrate concentration according to a Monod rate law. The macroscopic coefficient pm represents the maximum specific growth rate; K, the substrate concentration at which half this rate is achieved. The ratio pm/ Y gives the maximum specific rate of substrate consumption.

3 QUINLQN: STEADY-STATE BIOMASS PRODUCTION 199 The differential equation found for biomass production is: B ICI p,bs/(k + S ) - (W + d)b VBB(S - S,)/(S + K ) where (C - s)k + u ST (W + d)k/vb The net rate of biomass production is given by Equations 4. From Equation 4b, the net rate can be seen to saturate in substrate concentration with a maximum net specific growth rate VB and a threshold substrate concentration S, that must be exceeded for net growth.' The first term in Equation 4a is the Monod rate law for gross biomass production. Steady -State Conditions At steady state,.. S E B E O (7) Under these conditions, the steady-state substrate concentrations 9 may be found from Equation 4b to be: s = s, (8) Similarly the steady-state biomass B may be found from Equations 1, 4a, and 8 to be: B = yso[l - (st/sll)l/[l + (w/d)l (9) As &/so and w/d both become small relative to unity, the steady-state biomass approaches the maximum achievable biomass in value. Efieiency of Steady-State Biomass Production The efficiency of steady-state biomass production 4- may be defined as the ratio of the biomass actually produced at steady state B to the maximum achievable biomass YS,,. Thus, 71ss = B/YS, A simple rearrangement of Equation 9 shows the efficiency of steady-state biomass production depends on the ratios S,/S,, and w/d as follows: So, whatever makes ST/S, and w/d decrease also makes the efficiency increase. Elevating So will obviously improve the efficiency until So >> S,. It is not at all obvious,

4 ) 200 ANNALS NEW YORK ACADEMY OF SCIENCES TABLE 1. Experimental Data Used to Estimate Y, w, s, u as Functions of Temperature T d so s so - s B ( C) (Khr ~ (PP4 (PPd (PPd (PPd (55) * (92) (291) (106) a (54) (16) (97) 77 Washout occurred. bdata in parentheses not used to estimate coefficient values. a a a I (899) 87 1 (380) 428 (921) 854 (416) though, from theory alone how changes in w and d will actually affect the efficiency because ST is a complicated function of w and d (see Equations 6,5,3,2). EVALUATION OF COEFFICIENTS To shed light on how changes in wand d can affect S, and thereby the efficiency of steady-state biomass production, experimental data were analyzed. Experimental Data TABLE 1 gives the experimental data used to evaluate s, u, w, Y, and from them c, wrn, K, ST. The data describe the growth of a nonattached community of microorganisms obtained from the primary clarifier effluent of a municipal sewage treatment plant. The experiments were performed under carbon-limited conditions with glucose as the sole carbon source in a mineral salts medium. The culture vessel was an aerated, TABLE 2. Procedure Used to Estimate Values of Y and w (1) Linearize Equation 9: [(So - S)/dl = (1/Y) + (~/Y)[l/dl (2) Evaluate [(So- S)/b] and [I/d] from TABLE 1 (3) Regress [(So- &/dl on [l/d]: Obtain Yfrom intercept; *Obtain w from slope

5 ~ QUINUN: STEADY-STATE BIOMASS PRODUCTION 20 1 TABLE 3. Procedure Used to Estimate Values of s and u (1) Assumec-s. (2) Substitute Equations 6,5b, 3, and 2 into 8 and linearize the result: [S /(w 41 = (l/s) + (l/su) [w + dl 1 and 4. (3) Evaluate [>/(w + d)] and [w + d] from TABLES (4) Regress [S/(w + d)] on [w + d]: *Obtain s from intercept. *Obtain u from slope. baffled, single-pass cylindrical, one-liter continuous stirred-tank reactor (CSTR). The values of influent and steady-state substrate concentration, respectively So and S, represent biologically available carbon measured in ppm COD; they were calculated from TABLE 2 of Reference 2 by subtracting nondegradable COD from respectively influent COD and reactor soluble COD. The steady-state biomass values B were measured in ppm dry cell weight; they were taken directly from the reactor suspended solids column in Table 2 of Reference 2. Microscopic Rate Coeflcients If each substrate consumption site becomes saturated when one substrate molecule occupies it, then the microscopic saturation and consumption rate coefficients are equal. This case was assumed to apply here, and c was set equal to s. The values of the microscopic rate coefficients s, u, and w were then estimated as functions of temperature by applying the procedures outlined in TABLES 2 and 3 to the data given in TABLE 1. The values thus obtained are presented in TABLE 4. The temperature dependencies of these coefficients are shown in FIGURE 2. Each coefficient rises exponentially with temperature and can be shown3 to have an Arrhenius temperature dependence with a constant apparent activation energy, namely, E,, E,, and E,. The values of w obtained here are close to those given in Table 3 (5th column) of Reference 2. The remaining microscopic rate coefficients were not evaluated in Reference 2. Macroscopic Coefficients The yield coefficient Y was estimated by applying the procedure outlined in TABLE 2 to the data given in TABLE 1. Its values (units: ppm dry cell weight/ppm COD) are reported as a function of temperature in TABLE 4. These values average out to roughly TABLE 4. Coefficient Values Estimated by Applying Procedures Outlined in Tables 2 and 3 to Data Given in Table 1 ~- T Y W S U ( C) (PPm/PPm) (Khr-I) (Khr- ppm- ) (Khr- ) 10, (28.7) , , b b Omitted from linear regression of In w on Tin FIGURE 2. bwashout occurred.

6 202 ANNALS NEW YORK ACADEMY OF SCIENCES 0.5 and show a maximum of at 20OC. They agree well with the yield coefficient values listed in Table 3 of Reference 2. With the assumption c = s, the maximum specific growth rate coefficient pm (Equation 2) reduces to: pm = u + w + d (12) Its dependence on both temperature and dilution rate is illustrated in FIGURE 3. AS I I I I I MICROSCOPIC RATE COEFFICIENTS v' / u-1.13 exp(t/4.06) Khr-l,/' / E,- 36,500 cavmot [r=o.b6. n.3) / /' E," 11,500 cal/mol ( r = n ~ 3) t---- CESN 1.76exp (T/27.58) Khr-lpprn-' Ec'Elm cal/mol (r=0.991.n=3) I I I I I I' Ib T ("C I FIGURE 2. Log-linear relationships between microscopic rate coefficients and temperature. Solid lines represent interpolations of data; dashed lines, extrapolations. Data points tabulated in TABLE 4. temperature rises or dilution rate falls, pm approaches a pure Arrhenius temperature dependence. The influence of dilution rate is strongest at low temperatures where d dominates u and w. The values of pm obtained here agree well with those given in TABLE 3 of Reference 2, which did not consider the influence of d on pm. The influence of temperature and dilution rate on the half-saturation coefficient K (Equations 3, 2) is displayed in FIGURE 4. Again, dilution rate exerts its strongest

7 - I 1 I I MAXIMUM SPECIFIC GROWTH RATE COEFFICIEN' AS A FUNCTION OF TEMPERATURE AND DILUTION RATE c(u+w+d) Pm' 5 c 1s u = 1.13 exp(ti4.06) Khr-' w = 1.94 exp (T/12.89)Khr-' I I I I I I T("C) FIGURE 3. Thermal sensitivity of the maximum specific growth rate coefficient in batch (d - 0) and continuous (d > 0) culture with the microscopic coefficients specified in FIGURE 2. Crosses mark values reported in Table 3 of Reference 2. D a r I I 1 I I HALF - SATURATION COEFFICIENT AS A FUNCTION OF TEMPERATURE AND DILUTION RATE E -/ - - O~ATCH w = 1.94 exp (T/12.89)Khr-'?L s 176 nrn IT/37CIAlYhr-'nnm'l r,., -..--,... rr... I I I I T("C1 FIGURE 4. Thermal sensitivity of the half-saturation coefficient in batch (d - 0) and continuous (d 0) culture with the microscopic coefficients specified in FIGURE 2. Crosses mark values reported in Table 3 of Reference 2.

8 204 ANNALS NEW YORK ACADEMY OF SCIENCES effects at low temperature. As temperature rises or dilution rate falls, K also tends to approach a classic Arrhenius temperature dependence. As was found forb,,,, the values of K obtained here agree well with those listed in Table 3 of Reference 2. The threshold substrate concentration coefficient ST was evaluated by setting c = s and combining Equations 6, Sb, 3,2, with the result: ST (w + d)(u + w + d)/us The dependence of ST on temperature and dilution rate is illustrated in FIGURE 5. Both temperature and dilution rate strongly affect ST across their ranges of variation. In continuous culture (d > 0), S, increases as dilution rate rises, but falls as temperature rises. Over the temperature range studied, S, does not follow an Arrhenius temperature dependence. For the most part, the values of ST calculated from Equation 13 and FIGURE 2 agree with the experimental data presented in Reference 2. (13) SENSITIVITY ANALYSIS As shown by Equation 1 1, decreasing w/d and S,/S,, should improve the efficiency of steady-state biomass production. To decrease w/d, the dilution rate should be raised I ' I 1 I I I THRESHOLD SUBSTRATE CONCENTRATION AS C FUNCTION OF TEMPERATURE AND DILUTION RATE 5t - BATCH I I I I I Ilo T("C1 FIGURE 5. Thermal sensitivity of the threshold, or steady-state, substrate concentration in batch (d - 0) and continuous (d > 0) culture with the microscopic coefficients specified in FIGURE 2. Data points represent S (= S,) values given in TABLE 1.

9 QUlNL4 N: STEA DY-STA TE BIOMASS PRODUCTION 205 I I I 1 I I EFFICIENCY OF STEADY STATE BIOMASS PRODUCTION AS A FUNCTION OF - DILUTION RATE AND TEMPERATURE DILUTION RATE d (Khr-l) FIGURE 6. Influence of dilution rate on the efficiency of steady-state biomass production with temperature as a parameter. Curves were generated from equations for w and ST shown in FIGURE 5. Points were calculated from values of S (= S,) given in TABLE 1 and w given in TABLE 4 and FIGURE 2. Note shift of optimum dilution rate to higher values with rising temperature. and/or the temperature should be lowered (see FIGURE 2). Unfortunately, for microbial cultures with coefficient values similar to those specified in FIGURE 5, either action would at the same time elevate S,, which is counterproductive. As a consequence, the efficiency of steady-state biomass production in such microbial cultures cannot be a monotonic rising function of dilution rate or temperature. Indeed, FIGURES 6-9 show the efficiency passes through a single peak as either dilution rate or temperature increases. When efficiency is plotted versus dilution rate, the peak can be seen to shift toward higher dilution rates as either the temperature or influent substrate concentration rises (FIGS. 6 and 7, respectively). In other words, the optimum dilution rate for steady-state biomass production rises with both temperature and influent substrate concentration. Furthermore, as the peak shifts toward higher dilution rates, it broadens. The peak efficiency is fairly insensitive to temperature changes (FIG. 6), but improves considerably as influent substrate concentration increases (FIG. 7). In contrast, plots of efficiency versus temperature show that raising the dilution rate shifts the peak toward higher temperatures (FIG. 8), but elevating influent substrate concentration shifts it toward lower temperatures (FIG. 9). This means the

10 206 ANNALS NEW YORK ACADEMY OF SCIENCES 1 I I I I I EFFICIENCY OF STEADY STATE BIOMASS PRODUCTION AS A FUNCTION OF DILUTION RATE AND INFLUENT SUBSTRATE CONCENTRATION So= 10,000 ppm COD So = 1000 ppm COD A - B YSO DILUTION RATE d (Khr-'1 FIGURE 7. Influence of dilution rate on the efficiency of steady-state biomass production with influent substrate concentration as a parameter. Curves generated from equations for w and S, shown in FIGURE 5. Note how increasing influent substrate concentration both raises and broadens the range of optimum dilution rates, and also how it improves the peak efficiency. optimum temperature for steady-state biomass production rises with dilution rate, but falls as influent substrate concentration increases. The breadth of the peak is not strongly affected by changes in either dilution rate or influent substrate concentration. However, the peak efficiency can be significantly improved by elevating the influent substrate concentration (FIG. 9), but it is relatively insensitive to dilution rate. DISCUSSION AND CONCLUSIONS With the information presented in FIGURES 6-9, a strategy may be devised for manipulating d, T, and So to optimize the efficiency of steady-state biomass production by microbial cultures obeying Monod rate laws with coefficients that behave as those shown in FIGURES 2-5. Suppose, for example, So is 1000 ppm. Then, for a moderate dilution rate of, say, 100 Khr-' (i.e., a hydraulic retention time of 10 hr), the optimum temperature would be close to 2OoC (FIG. 9). Now, suppose So were raised to 10,000 ppm to increase the

11 QUINUN: STEADY-STATE BIOMASS PRODUCTION 207 peak efficiency. The optimum temperature could be kept close to 2OoC by increasing the dilution rate to a value within the range Khr-' (cf. FIGS. 6 and 7). Conversely, the optimum dilution rate could be kept near 100 Khr-' by lowering the temperature roughly 7OC to about 1 3OC (cf. FIGS. 8 and 9). Therefore, for the process under consideration, relatively high influent substrate concentration, low temperature, and moderate dilution rate would be needed to make the steady-state biomass approach the maximum achievable biomass YS,. The applicability of this finding is restricted by the thermal sensitivity of ST. According to Equation 11, the efficiency of steady-state biomass production is a function of S,, So, w, and d. Of these four variables, only the thermal sensitivity of ST may vary significantly from one microbial culture to another.' For the experimental culture considered in this paper, ST was a monotonic decreasing function of temperature under continuous culture conditions (d > 0, FIG. 5). However, for other microbial cultures, ST may also show a minimum as temperature rises, or it may appear to be a monotonic increasing function of temperature.' The influence of these other thermal sensitivity patterns is the subject of continuing research on the topic of this paper. FIGURE 8. Influence of temperature on the efficiency of steady-state biomass production with dilution rate as a parameter. Curves generated from equations for w and ST shown in FIGURE 5. Note how the optimum temperature rises with dilution rate.

12 208 ANNALS NEW YORK ACADEMY OF SCIENCES SUMMARY The efficiency of steady-state biomass production was defined as the ratio of the biomass produced at steady state to the biomass that would be produced if influent substrate were completely and permanently incorporated. The scope of analysis was confined to microbial growth processes described by a Monod reaction mechanism. A thermo-kinetic analysis of this mechanism with coefficient values estimated from experimental data showed: d = 100 Khr-I SO= 10,000 ppm COD So' 1000 ppm COD T("C) FIGURE 9. Influence of temperature on the efficiency of steady-state biomass production with influent substrate concentration as a parameter. Curves generated from equations for w and ST shown in FIGURE 5. Note how the peak efficiency is improved and the optimum temperature lowered by increasing influent substrate concentration. (1) As the dilution rate was increased, the efficiency passed through a single peak. Raising the temperature did not markedly change the peak efficiency, but did broaden and shift the peak toward higher dilution rates. In contrast, elevating the influent substrate concentration significantly improved the peak efficiency while still broadening and shifting the peak toward higher dilution rates. (2) As the temperature was raised, the efficiency also showed a single peak.

13 QUINIAN: STEADY-STATE BIOMASS PRODUCTION 209 Increasing the dilution rate did not significantly alter the peak value or breadth, but did shift the peak to higher temperatures. In contrast, elevating the influent substrate concentration substantially improved the peak efficiency and caused the peak to shift toward lower temperatures without broadening. (3) As the influent substrate concentration was elevated, the peak efficiency improved and asymptotically approached unity. These results suggested that relatively high influent substrate concentrations, low temperatures, and moderate dilution rates would be needed to optimize the efficiency of steady-state biomass production by Monod processes with coefficient values similar to those used in this paper. ACKNOWLEDGMENTS The research reported in this paper was supported by the Department of Mechanical Engineering and the School of Engineering at M.I.T. The figures were drawn by Andy Poynor. REFERENCES 1. QUINLAN, A. V Thermochemical optimization of microbial biomass-production and metabolite-excretion rates. In Foundations of Biochemical Engineering: Kinetics and Thermodynamics in Biological Systems. H. W. Blanch, E. T. Papoutsakis & G. Stephanopoulos, Eds. ACS Symposium Series 207. Washington, DC. pp MUCK R. E. & C. P. L. GRADY, JR Temperature effects on microbial gfpwth in CSTRs. ASCE J. Environ. Eng. Div QUINLAN, A. V The thermal sensitivity of generic Michaelis-Menten processes without catalyst denaturation or inhibition. J. Thermal Biol APPENDIX SYMBOLS B = total biomass concentration in culture vessel; equals sum of B, plus B,; mg dry cell weight per liter. B, = biomass concentration associated with substrate consumption sites capable of consuming substrate; same units as B. B, = biomass concentration associated with substrate consumption sites not capable of consuming substrate; same units as B. b = steady-state biomass concentration in culture vessel; same units as B. E = apparent activation energy; cal/mol. K = half-saturation coefficient; same units as S. S = substrate concentration in culture vessel; ppm COD. So = influent substrate concentration; same units as S. S, = threshold substrate concentration coefficient; steady-state substrate concentration that must be exceeded for a positive net biomass production rate; same units as S. 3 = steady-state substrate concentration in culture vessel; same units as S. T = temperature; OC.

14 210 ANNALS NEW YORK ACADEMY OF SCIENCES V, = maximum possible specific rate of net biomass production in culture vessel; Khr-I. Y = yield coefficient; ppm dry cell weight produced per ppm COD consumed. c = microscopic substrate consumption rate coefficient; ppm COD-' Khr-l. d = dilution rate (flow/volume); rate at which substrate and biomass are displaced from culture vessel; rate at which substrate is added to culture vessel; Khr-I. s = microscopic substrate saturation rate coefficient; ppm COD-' Khr-I. u = microscopic unsaturation rate coefficient; Khr-I. w = microscopic wastage rate coefficient; Khr-l. l)ss = efficiency of steady-state biomass production; dimensionless. p,,, = maximum specific growth rate coefficient; Khr-'.

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