kinetic model for anaerobic digestion of livestock manure

6
Kinetic model for anaerobic digestion of livestock manure F. Garcı ´a-Ochoa a, *, V.E. Santos a , L. Naval b , E. Guardiola a , B. Lo ´pez a a Departamento de Ingenierı ´a Quı ´mica, Facultad de Ciencias Quı ´micas, Universidad Complutense, 28040 Madrid, Spain b Universidade do Tocatins, Centro Universitario de Palmas, Palmas, Brasil Received 13 May 1998; received in revised form 3 January 1999; accepted 14 January 1999 Abstract Two unstructured segregated kinetic models to describe the anaerobic digestion of livestock manure are developed and experimental batch data obtained from beef cattle in a 2.0-l work volume digestor fitted to both proposed kinetic models to obtain the values of the parameters. The results obtained by fitting show that the second model proposed has both statistical and physical meaning in the parameter values obtained. The model takes into account a simplified reaction scheme formed by six reactions. Several simplifications have been made (lumping, pseudo-steady state for one compound, first order kinetics, etc.) yielding four key compounds to be analysed and fitted to the model as production-rates expressions (total biomass, chemical oxygen demand (COD), volatile acids, and methane). The model considers three main stages in the process: enzymatic hydrolysis of the waste, growth of ‘acetogenic’ microorganisms (production of acids nongrowth associated), and growth of ‘methanogenic’ microorganisms associated with methane production; the two last processes are accompanied by substrate consumption for maintenance. A non-linear multiple-response regression technique coupled to a fourth-order Runge–Kutta algorithm has been employed to obtain the values of the ten parameters. The model is able to reproduce the experimental data obtained for beef manure anaerobic digestion with more accuracy than experimental error. © 1999 Elsevier Science Inc. All rights reserved. Keywords: Anaerobic digestion; Kinetic model; Livestock manure; Beef cattle 1. Introduction The livestock manure is a complex substrate containing nondissolved and dissolved organic matter such as polysac- charides, lipids, proteins, and volatile fatty acids (VFAs) as well as a high number of inorganic compounds of impor- tance for the environment. Large-scale anaerobic digestion of livestock manure has received growing attention during the recent years as a technology for energy production using manure and other organic wastes in a more efficient way [1]. Therefore, the kinetic modelling of the anaerobic degradation of complex wastes is increasingly needed for a better understanding of the performance of these systems. It is essential for the rational design and operation of biological waste-treatment systems to predict the system stability, effluent quality, and waste stabilization [2]. The anaerobic conversion process of a biological waste to methane gas involves several biological reaction steps, some authors propose only two stages [3], but there are other authors that propose from three to nine stages in the process [4 – 6]. In this work, three stages have been consid- ered: (1) the complex biopolymers are hydrolytically con- verted to lower-molecular-weight compounds able to be used as substrates by cells [4 – 6], in this work called ‘ac- cessible substrate’; (2) the hydrolyzed waste is converted to volatile organic acids by an anaerobic microflora (aceto- genic microorganisms); and (3) finally, methane is produced from volatile organic acids by methanogenic microorgan- isms. Some authors [6,7] propose that the time required for complete digestion is large because the waste dissolution and its hydrolysis to lower-molecular-weight compounds are the rate-limiting steps in the anaerobic digestion process. The development of mathematical models to describe the anaerobic digestion of animal waste began in the 60s [8]. Some of the first works using dynamic models were re- ported by Hill and Barth [9]. These early works were fol- lowed by the development of a model for digestion of swine waste [10] and a description of the techniques used in biological processes modelling [11]. Other models that have contributed to the understanding of animal waste digestion * Corresponding author. Tel.: 134-91-394-4176; fax: 134-91-394- 4171. E-mail address: [email protected] (F. Garcı ´a-Ochoa) Enzyme and Microbial Technology 25 (1999) 55– 60 0141-0229/99/$ – see front matter © 1999 Elsevier Science Inc. All rights reserved. PII: S0141-0229(99)00014-9

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Page 1: Kinetic Model for Anaerobic Digestion of Livestock Manure

Kinetic model for anaerobic digestion of livestock manure

F. Garcı´a-Ochoaa,*, V.E. Santosa, L. Navalb, E. Guardiolaa, B. Lopeza

aDepartamento de Ingenierı´a Quımica, Facultad de Ciencias Quı´micas, Universidad Complutense, 28040 Madrid, SpainbUniversidade do Tocatins, Centro Universitario de Palmas, Palmas, Brasil

Received 13 May 1998; received in revised form 3 January 1999; accepted 14 January 1999

Abstract

Two unstructured segregated kinetic models to describe the anaerobic digestion of livestock manure are developed and experimentalbatch data obtained from beef cattle in a 2.0-l work volume digestor fitted to both proposed kinetic models to obtain the values of theparameters. The results obtained by fitting show that the second model proposed has both statistical and physical meaning in the parametervalues obtained. The model takes into account a simplified reaction scheme formed by six reactions. Several simplifications have been made(lumping, pseudo-steady state for one compound, first order kinetics, etc.) yielding four key compounds to be analysed and fitted to themodel as production-rates expressions (total biomass, chemical oxygen demand (COD), volatile acids, and methane). The model considersthree main stages in the process: enzymatic hydrolysis of the waste, growth of ‘acetogenic’ microorganisms (production of acids nongrowthassociated), and growth of ‘methanogenic’ microorganisms associated with methane production; the two last processes are accompanied bysubstrate consumption for maintenance. A non-linear multiple-response regression technique coupled to a fourth-order Runge–Kuttaalgorithm has been employed to obtain the values of the ten parameters. The model is able to reproduce the experimental data obtained forbeef manure anaerobic digestion with more accuracy than experimental error. © 1999 Elsevier Science Inc. All rights reserved.

Keywords:Anaerobic digestion; Kinetic model; Livestock manure; Beef cattle

1. Introduction

The livestock manure is a complex substrate containingnondissolved and dissolved organic matter such as polysac-charides, lipids, proteins, and volatile fatty acids (VFAs) aswell as a high number of inorganic compounds of impor-tance for the environment.

Large-scale anaerobic digestion of livestock manure hasreceived growing attention during the recent years as atechnology for energy production using manure and otherorganic wastes in a more efficient way [1]. Therefore, thekinetic modelling of the anaerobic degradation of complexwastes is increasingly needed for a better understanding ofthe performance of these systems. It is essential for therational design and operation of biological waste-treatmentsystems to predict the system stability, effluent quality, andwaste stabilization [2].

The anaerobic conversion process of a biological wasteto methane gas involves several biological reaction steps,

some authors propose only two stages [3], but there areother authors that propose from three to nine stages in theprocess [4–6]. In this work, three stages have been consid-ered: (1) the complex biopolymers are hydrolytically con-verted to lower-molecular-weight compounds able to beused as substrates by cells [4–6], in this work called ‘ac-cessible substrate’; (2) the hydrolyzed waste is converted tovolatile organic acids by an anaerobic microflora (aceto-genic microorganisms); and (3) finally, methane is producedfrom volatile organic acids by methanogenic microorgan-isms.

Some authors [6,7] propose that the time required forcomplete digestion is large because the waste dissolutionand its hydrolysis to lower-molecular-weight compoundsare the rate-limiting steps in the anaerobic digestion process.

The development of mathematical models to describe theanaerobic digestion of animal waste began in the 60s [8].Some of the first works using dynamic models were re-ported by Hill and Barth [9]. These early works were fol-lowed by the development of a model for digestion of swinewaste [10] and a description of the techniques used inbiological processes modelling [11]. Other models that havecontributed to the understanding of animal waste digestion

* Corresponding author. Tel.:134-91-394-4176; fax:134-91-394-4171.

E-mail address:[email protected] (F. Garcı´a-Ochoa)

Enzyme and Microbial Technology 25 (1999) 55–60

0141-0229/99/$ – see front matter © 1999 Elsevier Science Inc. All rights reserved.PII: S0141-0229(99)00014-9

Page 2: Kinetic Model for Anaerobic Digestion of Livestock Manure

include the first order models of Morris [12] and Grady et al.[13] and the modified Contois model developed by Chenand Hashimoto [14]. However, assumptions made in theirderivation often reduce their accuracy, and they are not ableto predict optimal operational conditions or failure.

There are three main tendencies in anaerobic digestionmodelling: Hashimoto et al. [14–19] propose an unstruc-tured nonsegregated model based on kinetic equations suchas Monod or Contois, studying the influence of temperatureand waste concentration on model parameter values (m [16]and K [19]). On the other hand, Hill [20–22] proposed anunstructured segregated kinetic model involving six equa-tions and ten parameters, taking into account two differenttypes of biomass. Other authors [2,23–26] have modelledthe anaerobic digestion process based on the Hashimotomodel. Most authors do not obtain the values of the kineticparameters by regression of the experimental data intomodel equation, except Hashimoto [19], who employs aregression to fit the values of the K parameter of his modelwith the temperature and the substrate concentration.

Angelidaki et al. [2] propose a metabolic structured ki-netic model, with a simplified reaction scheme for substrateconsumption, with four reactions: enzymatic hydrolysis,acidogenesis, acetogenesis, and methane production. Thekinetic equations proposed are Monod-type taking into ac-count different inhibition effects. Kinetic parameters are notobtained by fitting and the model is employed to simulatethe process, but it is not able to predict biomass concentra-tion.

The aim of this work is the development of a kineticmodel for anaerobic digestion of livestock manure able todescribe the evolution of total biomass, chemical oxygendemand (COD), organic acids (butyric, propionic, acetic),and methane production. The calculation of the parametersof the model will be made by fitting of experimental data ofanaerobic digestion of beef cattle to the set of differentialequations.

2. Kinetic model

The kinetic model proposed is an unstructured segre-gated model. The model is unstructured because microor-ganism metabolism is not involved in the model, and it is asegregated model because two different biomass types areconsidered: acetogenic and methanogenic bacteria.

The observation of the experimental data yields severalreactions (both serial and parallel) that are involved in theprocess. The six reactions considered are the following:(1) hydrolysis of the waste to obtain an ‘accessible sub-strate’ for the biomass; (2) growth of acetogenic bacteriaemploying the ‘accessible substrate’; (3) production of or-ganic acids by acetogenic bacteria from the ‘accessiblesubstrate’; (4) consumption of the ‘accessible substrate’ foracetogenic bacteria maintenance; (5) growth of methano-genic bacteria and production of methane from organic

acids; and (6) organic acids or ‘accessible substrate’ con-sumption for methanogenic bacteria maintenance.

The last reaction considered involves the proposal of twodifferent reaction schemes, depending on the substrate em-ployed for methanogenic bacteria maintenance:

reaction rate

SOO3 Sacc

Y2 z Sacc1 XagbOO3 2 z Xagb

SaccOO3 Y3 z VA

SaccOO3 Y4 z CO2

Y5 z VA 1 XmetOO3 2 z Xmet1 Y95 z P

VAOO3 Y6 z CO2

r1

r2

r3

r4

r5

r6

6 (1)

reaction rate

SOO3 Sacc

Y2 z Sacc1 XagbOO3 Xagb

SaccOO3 Y3 z VA

SaccOO3 Y4 z CO2

Y5 z VA 1 XmetOO3 2 z Xmet1 Y95 z P

SaccOO3 Y6 z CO2

r1

r2

r3

r4

r5

r6

6 (2)

whereS 5 substrate,Sacc 5 accessible substrate,Xagb 5biomass with acetogenic bacteria,y 5 stoichiometric coef-ficient, VA 5 volatile acids, andXmet 5 methanogenicbacteria biomass.

The kinetic equations considered are the same for bothreaction schemes. All the kinetic equations have been as-sumed to be first order on reactant concentration and theconcentration of biomass involved in the process, but main-tenance reaction rates (r4 and r6) have been assumed to beonly influenced by the concentration of the kind of biomassinvolved in the reaction, as follows:

r2 5 k2 z CSaccz CXagb (3)

r3 5 k3 z CSaccz CXagb (4)

r4 5 mSagbz CXagb (5)

r5 5 k5 z CVA z CXmet (6)

r6 5 mSmetz CXmet (7)

whereC 5 concentration of the compound subscripted,k 5kinetic coefficient of the reaction subscripted,r 5 reactionrate of subscripted reaction; andms 5 maintenance coeffi-cient.

Different growth phases of the two biomass types havebeen considered. Thus, expressions for r2 and r5 have beenassumed to change during fermentation time as follows:

r2 5 k2 z CSaccz CXagb for 0 # t # 12 (8)

r2 5 0 for 12# t # 22 (9)

56 F. Garcıa-Ochoa et al. / Enzyme and Microbial Technology 25 (1999) 55–60

Page 3: Kinetic Model for Anaerobic Digestion of Livestock Manure

r2 5 keagb for 22 # t (10)

r5 5 k5 z CVA z CXmet for 0 # t # 22 (11)

r5 5 0 for 22# t (12)

The concentration of the ‘accessible substrate’ is neededto be known along the digestion time, this concentration isassumed to be at a pseudo-steady state; thus, the kineticequations of reactions 2 and 3 become:

r2 5 k92 z CXagb (13)

r3 5 k93 z CXagb (14)

wherek9 5 kinetic coefficient of the subscripted reactionincluding the value of the concentration of the accessiblesubstrate.

The kinetic equation for reaction 1 is obtained from thepseudo-steady state approximation for the ‘accessible sub-strate’ as following:

for the first reaction scheme:r1 5 Y2 z r2 1 r3 1 r4 (15)

for the second reaction scheme:

r1 5 Y2 z r2 1 r3 1 r4 1 r6

(16)

The resulting two sets of production rate equations forthe two kinetic models proposed are the following:

Kinetic Model 1 (first reaction scheme):

dS

dt5 2r1 5 2@Y2 z r2 1 r3 1 r4# (17)

dXagb

dt5 r2 (18)

dVA

dt5 Y3 z r3 2 Y5 z r5 2 r6 (19)

dXmet

dt5 r5 (20)

dP

dt5 Y95 z r6 (21)

dX

dt5

dXagb

dt1

dXmet

dt(22)

Kinetic Model 2 (second reaction scheme):

dS

dt5 2r1 5 2@Y2 z r2 1 r3 1 r4 1 r6# (23)

dVA

dt5 Y3 z r3 2 Y5 z r5 (24)

wheret 5 time (days).The other four equations for Kinetic Model 2 are iden-

tical to Eqs. (18) and (20) to (22) employed for KineticModel 1.

3. Materials and methods

The beef cattle was obtained from several farms from theComunidad Auto´noma de Madrid (Spain), and it was usedas digestion substrate with a concentration in the effluent of125 g/l. The waste was inoculated with a culture of bacteriafrom waste water secondary treatment. A bench-scale an-aerobic digestor stirred tank with 2 l working volume wasused.

3.1. Experimental procedure

During each experiment the following parameters weremeasured: pH, volatile fatty acids, organic matter, methaneproduction, and biomass. The biogas obtained was collectedin a gasometer by means of a hydraulic closure formed bya saturated aqueous solution of sodium chloride and 10%sulphuric acid. The anaerobic digestor was operated on a40-day retention time at 35°C. The digestor was continu-ously stirred at 1000 rev./min to ensure complete mixing.These variable values were optimised in previous experi-ments by means of a factorial design of experiments [27].

The analytical methods used were those given by theStandard Methods for the Examination of Waters and WasteWaters (APHA, 1990). Volatile fatty acids concentrationwas calculated from supernatant obtained after centrifuga-tion of the mixed liquor at 1000 rev./min for 5 min. Thengas-chromatography was used to determine the fatty acidconcentrations, using a column of stainless steel, packedwith 10% of FFAP plus H3PO4 in W-AW Chromosorb(100/200 mesh), 2.0 m long and 0.0032 m in diameter. Thetotal nitrogen was determined by Kjeldhal method and sub-strate concentration was determined by the COD (mg/l) forup-flow digestion dichromate at 150°C (a variant of theMohr method), and also calculated on the basis of thevolatile solids by gravimetry. Biomass concentration wasdetermined as cell/l by plate counting on YM agar, inocu-lated with 0.1 ml in aliquots of 1.0 ml of supernatant dilutedin 300 ml of sterilized distilled water. Finally, biogas com-position was analyzed by gas chromatography, using astainless steel column 0.0032 m in diameter and 2.0 m longpacked with PORAPAK N (80/100 mesh). Gas chromato-graphic columns supplied by Teknokroma (San Cugat delValles, Spain).

3.2. Parameter calculation methods

Experimental data have been fitted to the kinetic modelusing the Marquardt multiple-response nonlinear regressionalgorithm [28]. The set of differential equations must beintegrated, because the data obtained are integral data (con-centration evolutions with time), the integration has beencarried out using a fourth-order Runge–Kutta algorithmcoupled to the regression to integrate the equations at thesame time.

57F. Garcıa-Ochoa et al. / Enzyme and Microbial Technology 25 (1999) 55–60

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4. Results and discussion

4.1. Experimental results

Biomass, organic acids, substrate (waste), and methanewere analyzed during the fermentation time. Fig. 1 showstotal biomass production; two overlapped growth curves canbe seen; therefore, two kinds of biomass can be considered:acetogenic and methanogenic. Fig. 2 shows the experimen-tal results of substrate (as COD), total acids, and methane.It can be seen that methane would be the final product of aserial reaction scheme.

Fig. 3a shows the experimental data obtained for theorganic acids: both acetic and propionic acids show a max-imum in production and the production of butyric acid is notimportant compared to the other acids produced. The ratiosof the three acids to the total acid concentration were cal-

culated (see Fig. 3b), showing that these ratios can beconsidered constant during the experiment: 56% acetic acid,34% propionic acid, and 10% butyric. Therefore, it is rea-sonable to apply lumping of these species: all the organicacids (acetic, propionic, and butyric acids) are considered asa single compound that shows a maximum of production.This compound is called ‘total acids’ (VA), and it seems tobe the intermediate compound in a serial reaction scheme.

The first growth curve (acetogenic bacteria growth)reaches the stationary phase after 10 fermentation days (seeFig. 1) and the production of total acids begins approxi-mately at this fermentation time (see Fig. 2). The secondgrowth curve (methanogenic bacteria growth) and methaneproduction begin around the 15th fermentation day. After20 days of fermentation the second growth curve reachesthe stationary phase and the microorganisms of the firstgrowth curve begin the death phase (see Fig. 1). This facthas been taken into account by Eqs. (8) to (12).

Fig. 1. Total biomass experimental data and reproduction obtained bymeans of the Kinetic Model 2 (Eqs. (18) and (20) to (24)), with theparameter values from Table 2. (}) Total biomass experimental data; (—)model prediction.

Fig. 2. Experimental results obtained for the substrate (COD) (}), totalacids (■) and methane (E) and reproduction obtained by means of theKinetic Model 2 (Eqs. (18) and (20) to (24)), with the parameter valuesfrom Table 2. (}) Total biomass experimental data; (—) model prediction.

Fig. 3. Experimental results of acid concentration evolution: (a) concen-tration of the three main acids detected in the process; and (b) ratios of theindividual acid concentrations to total acid concentration.

58 F. Garcıa-Ochoa et al. / Enzyme and Microbial Technology 25 (1999) 55–60

Page 5: Kinetic Model for Anaerobic Digestion of Livestock Manure

Experimental data show that the process study can bedivided into three steps: hydrolytic, acetogenic, and metha-nogenic stages. The experimental concentration-time curvesshow that the process is carried out in a serial way. Thehydrolytic stage is assumed to be achieved during the wholeprocess, transforming the waste into an ‘accessible sub-strate’ (Sacc) able to be taken up by the microorganisms.This ‘accessible substrate’ has not been analyzed; therefore,a pseudo-steady state for this compound has to be assumed.The ‘accessible substrate’ is employed for acetogenic mi-croflora growth, production of organic acids (not associatedwith growth) and maintenance of both acetogenic andmethanogenic microorganisms. The growth of methano-genic microflora is associated to methane production andthe organic acids formed by the acetogenic bacteria are thesubstrates employed; these acids are lumped into a singlecompound called VA, as indicated above.

The values of the parameters of the model and the sta-tistical parameters obtained by the first kinetic model areshown in Table 1, and the parameters for the second kineticmodel are summarized in Table 2.

Parameters obtained by means of the first kinetic modelhave no physical meaning because one parameter is nega-tive and the zero-value for two others is included inside theconfidence interval. Parameters obtained by fitting of thesecond kinetic model to the experimental data show bothphysical and statistical meaning, for 95% of confidence.Figs. 1 and 2 show the very good experimental data repro-duction by the second kinetic model proposed.

5. Conclusions

Anaerobic digestion of livestock manure can be de-scribed as a three-step process: hydrolytic, acetogenic, andmethanogenic stages.

Two kinetic models have been checked to describe theanaerobic digestion of beef cattle process. Experimental

data have been obtained in batch. The Kinetic Model 2 wasfinally chosen; this model is formed by Eqs. (18) and (20) to(24), using the reaction rates provided by Eqs. (3) to (16).This kinetic model is able to describe with high accuracy theexperimental results obtained for the anaerobic digestion ofbeef cattle process, as shown by Figs. 1 and 2, using thekinetic and stoichiometric parameter values given by Table2. This model takes into account a reaction scheme assum-ing the following considerations: organic matter is hydro-lyzed to an ‘accessible substrate’ by an enzymatic process;acetogenic bacteria maintenance is carried out using the‘accessible substrate’; total volatile acids production is car-ried out by acetogenic bacteria, and it is a partially growth-associated process; methanogenic bacteria maintenance iscarried out using the ‘accessible substrate’; and methaneproduction is associated with the growth of methanogenicbacteria.

Acknowledgments

This work has been supported by Comunidad Auto´nomade Madrid, under Contract No. 00227-92 and by ComisionInterministerial de Ciencia y Tecnologı´a (CICYT) underContract No. BIO-97-0596.

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Table 1Values of the kinetic and stoichiometric parameters obtained byregression using the first kinetic model, Eqs. (17) to (22) (first reactionscheme) and the values of the statistical parameters obtained byregressiona

Parameter Value tS Lower limit Upper limit F

k92 0.0854 2.763 105 0.0853 0.0855k93 1.090 1.243 104 1.089 1.091mSagb 0.713 1.363 102621.093 106 1.093 106

k5 0.04954 7.73 104 0.04955 0.04953mSmet 4.082 115.5 4.01 4.15 1273Y2 0.976 1.533 102721.273 107 1.273 107

Y3 0.620 6.983 103 0.620 0.621Y5 24.018 49.8 24.179 23.857Y95 10.36 61.5 10.02 10.69keagb 0.0504 2.053 104 0.0504 0.0505

a Statistical parameters for 95% confidence level:tS 5 1.96 andF 51.88.

Table 2Values of the kinetic and stoichiometric parameters obtained byregression using the second kinetic model, Eqs. (18) and (20) to (24)(second reaction scheme) and the values of the statistical parametersobtained by regressiona

Parameter Value tS Lower limit Upper limit F

k92 0.0839 4.13 104 0.0838 0.0840k93 0.454 718.0 0.452 0.455mSabg 0.713 20.97 0.981 1.187k5 0.0151 6.803 104 0.0150 0.0152mSmet 0.551 4.26 0.292 0.809Y2 2.548 2.208 2.888 15.00 692.1Y3 1.758 213.4 1.741 1.775Y5 7.885 27.71 7.288 8.422Y95 19.76 41.48 18.81 20.71keagb 0.0601 7.193 103 0.0601 0.0602

a Statistical parameters for 95% confidence level:tS 5 1.96 andF 51.88.

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