kinetics of anaerobic digestion

Energy Convers. Mgmt Vol. 28, No. 4, pp. 335-337, 1988 0196-8904/88 $3.00+0.00 Printed in Great Britain. All rights reserved Copyright © 1988 Pergamon Press plc

TECHNICAL NOTE

KINETICS OF ANAEROBIC DIGESTION

JUGAL KISHOR and S. P. SINGtt Centre of Energy Studies, Indian Institute of Technology, Hauz Khas, New Delhi-1 l0 016, India

(Received 9 March 1987; received for publication 29 September 1988)

Abstract--The basic chemical kinetic equations for anaerobic digestion have been solved to get closed form solutions for the substrate concentration and the concentration of anaerobes. Numerical calculations have been performed to obtain quantitative estimates for their time behaviour.

Anaerobic digestion Organic waste Continuous-flow completely mixed digester Substrate and microorganism concentrations

NOMENCLATURE

Cs = Substrate concentration (mg/1) C o = Initial substrate concentration (mg/1) C~ = Microorganism concentration (mg/l) C O = Initial microorganism concentration (mg/l) K S = Half velocity coefficient equal to the substrate

concentration when (dCJdt)= ½1~ax (mg/l) P = Coefficient for growth yield of microorganisms Q = Decay coefficient for microorganisms (day -I) t = Time (day)

/Z~max=Maximum rate of waste utilization per unit weight of microorganisms at high substrate concentration (day- i )

INTRODUCTION

The anaerobic digestion process has been in oper- ation for the production of biogas and also for improving environmental conditions by the control of various parameters for different kinds of waste materials, such as municipal waste, cattle dung, agri- cultural residues, slaughter waste and industrial waste [1]. In the early practice of anaerobic digestion, the level of control was primitive, being primarily that of simple storage. Consequently, the rates of anaerobic digestion were correspondingly low. With time, various parameters, including maintenance of optimum digester temperature and pH-value, nutri- ents and trace metals, were controlled to enhance the fermentation process. The process configuration was adapted to the feedstocks and solids retention time control to improve methane conversion and process stability.

Anaerobic digestion has been employed for a variety of purposes, for example to convert biomass crop to methane, to produce saleable methane from cattle dung and to deodorize pig waste. In some places, chlorinated wood pulping waste water is also detoxified by anaerobic digestion.

Anaerobic treatment of complex waste material, however, presents a set of problems to scientists for improving treatment technology. Simulation of the kinetics for microbial growth and substrate utiliza-

tion is an important area in which intensive research work is required. The kinetics of the chemical reac- tion determines the residential time for the substrate in the reactor, hence the size of the reactor.

Degradation of organic matter takes place in three consecutive step reactions: (a) hydrolysis of the long chain compounds, (b) formation of volatile fatty acids and (c) methane conversion, Lawrence and McCarty [2] first attempted to model the kinetics of the methane fermentation phase. The purpose of the investigation was to study experimentally the kinetics of utilization of the most prevalent volatile fatty acids, which are the precursors of methane, and evaluate the experimental results in the context of widely used kinetic models for substrate utilization. Another study on the kinetics of anaerobic treatment at reduced temperature has been made by O'Rourke [3]. He has concluded that, in the consecutive chain reactions, the slowest step could govern the overall kinetics. A sound theoretical basis for the rate of growth of anaerobics related with the substrate utilization has, however, not been attempted to the best of our knowledge. The purpose of the present study is, therefore, to formulate the basics of the chemical kinetics involved in the process of anaerobic digestion. The formulations has been presented in dimensionless form and numerical calculations performed for the time dependent behaviour of anaerobic population and basic substrate concentration.

THEORY

According to Heukelekian et al. [4] and Weston and Eckenfelder [5], the net rate of microorganism growth per unit volume of the digester in a continuous flow, completely mixed anaerobic digester can be expressed by the following rate equations:

dC x {dCs\

335

336 KISHOR and SINGH: TECHNICAL NOTE

where

dCddt- rate of substrate consumption per unit volume of the digester (mass/volume-time)

P---coefficient for the growth yeild of the microorganisms (time- x )

Q =decay coefficient for microorganisms (time-l).

The substrate utilization rate in any waste treatment process is a function of the substrate and microorganisms concentration. This relationship was first reported by Monod [6] for bacterial growth rate and the growth limiting nutrient concentration in the following manner, i.e.

dC, C at = # .... Ks + C-----~ C~ (2)

where ~smax =

=

maximum rate of waste utilization per unit weight of mocroorganisms at high substrate concentration (time -~) and half velocity coefficient equal to the substrate concentration when dC~/dt t (mass/volume).

Combining equations (1) and (2)

dC~ C~ -dt = P#sm~ K,'-+ C, Cx - QC~"

From equations (3) and (2), one obtains

QK, 1

(3)

Q (4) dCx(p- u dC, .... ) - # .... Cs "

Integrating the above equation with the boundary condition Cx = C o and Cs = C o at t = 0, one obtains:

c0 ) ( c ) co Q c_~, c_~, ,, , . .~

QK, C~ - - In W6. ( 5 )

q C~m~, # .... C~

Substituting for C~ from equation (5) in equation (2), one gets

- - 0 0 d(Cs/C°) IAm,,(CdC,) ~C~ dt (KJC °) + (a/co)

+ ( P - u s ~ Q ~ ) ( 1 -~s°~) + C~,#QK' .... Inc~. (6)

The above equatioin is a transcendental equation which can be numerically solved for different values of C~ to get the corresponding value of t, which is a measure of the retention time.

RESULTS AND DISCUSSION

The values of various parameters used for calculations have been taken from Ref. [2] for the acetate;

0.9

0.8

0.7 /t

! I / 2co=2 m,,, 0.6 /k

G' 0.5

0.3

0.2

O A I I I

0 '10 20 30 40 50 60 70 80 90 Time t (days)

Fig. I. Time behaviour of dimensionless quantities C,/C ° and C~/C~,~ for different values of C~.

these are:

P = 0.054 mg/mg

Q = 0.037 day- l

# ~ = 4.8 mg/mg-day

Ks = 333 mg/l.

The calculated values of the substrate concentration and anaerobe population as a function of time are plotted in Fig. 1 for different values of C °. It is seen that for increasing values of C °, C~ tends to zero in relatively shorter periods of time.

Parameter Q is dependent on the environmental conditions and genetic properties of the anaerobes.

,3,35oo,,

09 X / \ ~.o :o.os / ~ 2.o .o.1

0 2 0.8 " : •

0,7

E 0.6

G' 0,5 1 °~= 0.4

0.5

0.2

0.1 /

~ , . ~ a ~ I I I l 20 40 60 80 100 120 140 160

Time t (days)

Fig. 2. Time behaviour of dimensionless quantities C,/C ° and Cx/Cx~ ~ for CO= 1 mg/l and Q =0.05, 0.1, 0.2 day -I.

KISHOR and SINGH: TECHNICAL NOTE 337

0.9

o.ai-

0.7

0.6

u" 0.5

0.3

0.2 l

0.1

I 0 20

~ 2 1 C ° = 3 1 3 5 m g / l C ° = 2 m9/I. 1.0 =0.05 2.0 =0.1

.2

40 60 80 100 120 140

Time t (doys)

I 160

Fig. 3. Time behaviour of dimensionless quantities CJC ° and C~/C ..... for C o = 2 mg/l and Q = 0.05, 0.1, 0.2 day -t.

Hence we have studied the variation of C~ and Cx for different values of Q in Figs 2-4. As Q increases, the growth kinetics of the anaerobes is slower, thereby decreasing the fermentation rate and increasing the retention time correspondingly. The death rate of anaerobes is much faster than the growth rate when Cs tends to zero. Therefore, it is obvious that, for larger values of Q, the digester feeding time interval for two consecutive batches has to be less in order to maintain the constant bacterial population. Equat ion (5) shows that, if the substrate concentrat ion tends to zero, the value of microorganisms concentration approaches

C+ P-,x C - . . . .

For COx to be non-negative, keeping all other parameters constant, one gets the following limiting

1.0

0 . 9

Cs 0 = 3135 mg/L 0.8 ¢o, 5 m g / t

1.o -o.o5 0.7 2.0 =0.1

3 .0 - 0 . 2

~,~ 0 . 6

~ 0.5

~= 0.3

0 .2

0.1

' I I I I I I 0 20 40 60 80 100 120 140 160

Time t (days)

Fig. 4. Time behaviour of dimensionless quantities Cb/C ° and Cx/C . . . . for C o = 5 mg/l and Q = 0.05, O. l, 0.2 day-t.

value for the initial substrate concentration

CO > K,Q P#,m~ - Q

R E F E R E N C E S

1. R. E. Spcece, Environmental requirements for anaerobic digestion of biomass. In Advances in Solar Energy (Edited by K. W. Boer and J. A. Duffle), Vol. 2, Chap. 2. Plenum Press, New York.

2. A. W. Lawrence and P. L. McCarty, J. Wat. Pollut. Control Fed. 41, RI (1969).

3. J. T. O'Rourke, Ph.D. dissertation, Stanford Univer- sity, Calif. (1968).

4. H. Heukdekian, H. E. Oxford and R. Managaneli, Sewage Ind. Wastes 23, 945 (August 1951).

5. R. F. Wester and W. W. Eckenfelder, Sewage Ind. Wastes 27, 802 (July 1955).

6. J. Monod, Researches sur la Croissance des Cuttures Bacteriennes. Hermann and Ci¢, Paris (1942).

kinetics of anaerobic digestion

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