Energy Vol. 12, No. 6, pp. 497-500, 1987 0360.!%42/87 $3.00 -60.00 Printed in Great Britain Pergainon Journatf Ltd

KINETICS OF ANAEROBIC COWDUNG DIGESTION

S. C. BHA~ACHARYA and PHAM QUANG KHAI

Division of Energy Technology, Asian Institute of Technology, Bangkok 10501, Thailand

(Received 16 June 1986)

Abstract-Expressions are presented for the concentration of substrate in the eIIluents of an anaerobic digestor for the Monod and Contois kinetic equations. The calculations are compared with experimental results of Morris. The comparison suggests that Contois’ equation is the better relation for modelling cowdung digesters.

INTRODUCTION

The design of anaerobic digestors for organic wastes such as cowdung generally involves a large degree of empiricism. Better knowledge of the kinetics involved is necessary to optimize process performance. The Monod kinetic equation, which has been successfully used in studying the kinetics of pure cultures of bacteria utilizing simple substrates, is often used to study the anaerobic digestion of complex organic materials. Chen and Hashimoto’ reported that a number of authors have found that this relation did not predict volatile solids reduction during anaerobic fermentation, whereas the Contois kinetic equation2 yields satisfactory prediction of biomass utilization in anaerobic fermenters.

ANALYSIS

For a continuous-flow, stirred-tank (CFST) reactor, the net growth of micro-organism at the steady state is zero and

Y(ds/dt) - KIX = 0 (1)

where ds/dt = rate of substrate utilization per unit volume, Y = growth yield coefficient, K, = micro-orga~sm decay coefficient. An expression for the substrate utilization rate canbe derived that depends on the form of the expression for the specific growth rate of the micro-organisms.

(A) Mono&s kinetic relation

Monod3 proposed that the specific growth rate of micro-organisms varies with substrate concentration as follows:

where p = specific growth rate, hsx = maximum possible specific growth rate attained at high substrate concentration, K = saturation constant, S = substrate concentration.

Using Eqs. (1) and (2), it may be shown that the effluent biodegradable substrate concentration for a CFST reactor is given by

s = K(1 + I&6)/[& Yq, - &) - 1] (3)

where q,,, = maximum specific substrate utilization rate = &,,/Y and 0 = hydraulic reten- tion time. Equation (3) can be simplified to

S = (A + BO)/(CO - 1) (4) 497

498 S. C. BHATTACHARYA and PHAM QUANG KHAI

where A, B and C are kinetic parameters. The total effluent substrate concentration, S, consists of a biodegradable part S and a non-biodegradable part S,. Thus,

s, - s, = (A + Be)/(ce - l),

s, = (A + Be)/(ce - 1) + s,,

S, = f(O) + S,

(5)

wheref(8) is a function of 0 only. Thus, the total effluent concentration depends on the retention time 0 and on S,, which depends on total influent concentration and the nature of the substrate, i.e.

(6)

where R is the non-biodegradable fraction of the substrate.

(B) Contois’ kinetic equation

Contois2 proposed that the specific growth of micro-organisms is given by

P = PnlaxSM~X + 9. (7)

Using Eqs. (7) and (l), it can be shown that the effluent biodegradable substrate concentration for a CFST reactor is

s = s&r/( yq,e - i - Kde + IX). (8)

Equation (8) may be simplified to

S/S, = M/(NO - 1 + M), (9)

where M and N are kinetic parameters. The effluent/influent total substrate concentration ratio is

ws,, = (S + w&l = w&l + cv&)~ w%A S,/S,, = R + (1 - R)M/(NB - 1 + M).

(10)

RESULTS AND DISCUSSION

The suitability of Eqs. (5) or (10) for predicting concentration of effluents from an anaerobic digestor was examined by using experimental results of Morris4 for anaerobic cowdung digestion. His results for an influent volatile solids (VS) concentration of 69.89 g/l were used to obtain a polynomial fit of the ratio St/Stovs hydraulic retention time by a least-square method. The value of R (i.e. the value of S/S,, at very large retention time) was estimated to be 0.592. The polynomial fit and the value of R were used to obtain prediction of S,/S,, at different hydraulic retention times for other influent vs concentrations (87.2, 52.3 and 34.9g/l).

Predictions from Monad’s relation were obtained by using Eq. (6) and the estimated value of R. The value off(e) at a given value of 8 was estimated from the polynomial fit given in Eq. (6).

Kinetics of anaerobic cowdung digestion 499

Experimental vobes of .S, /St,

Fig.1. Comparisons of predictions from Monod’s equation with experimental values of Morris for different influent volatile solids concentrations (in g/1):0, 87.2; A, 52.3; V, 34.9.

According to Contois’ relation [e.g. Eq. (lo)], the ratio S/S,, for a given substrate (i.e. a given value of R) depends only on retention time. Predictions for different values of influent substrate concentrations and different values of retention were again obtained from the polynomial fit of Eq. (10).

Figure 1 shows a comparison of experimental values for S,/S,, of Morris with the predictions obtained from Monad’s equation. Deviations are significant. The discrepancy between experimental and theoretical values was estimated by calculating the relative root mean square error defined as

rms = i

112

e l/n c/ImIkJex,t - (~*l~r,),,>/(~rI~,~)~,12 ” I

which was found to be 12.5%. Figure 2 shows a comparison of experimental and predicted values of S,/S,, obtained from Contois’ equation. The deviations are much smaller with a relative root mean square error of 4.3%. Thus, the comparisons of experimental values of S,/S,, with .theoretical values suggest that Contois’ equation is more appropriate for modelling anaerobic cowdung digestion than Monod’s.

1.0

0.6 0.7 0.6 0.9 1.0

Experimental values of S, /St,

Fig.2. Comparison of predictions from Contois’ equation with experimental values of Morris for different influent volatile solids concentration (in g/l): 0, 87.2: A, 52.3; 0.

500 S. C. BHATTACHARYA and PHAM QUANG KHAI

REFERENCES

1. Y. R. Chen and A. G. Hashimoto, Biotechnol. Bioengng 22, 2081 (1980). 2. D. E. Contois, J. Microbial. 21, 40 (1959). 3. J. Monad, A. Rev. Microbial. 3, 371 (1949). 4. G. R. Morris, MS. Thesis, Cornell Univ., Ithaca, N.Y. (1976).