Dry Anaerobic Digestion Modelling: Parameter Sensitivity

Hassen Benbelkacem,* Julien Bollon, Rémy Gourdon and Pierre BuffièreLaboratoire de Génie Civil et d'Ingénierie Environnementale, Université de Lyon, INSA‐LYON, 20 Avenue Albert Einstein F‐69621,Villeurbanne Cedex, France

Amodel dedicated to dry anaerobic digestion processwas previously developed. Thismodel was based on the ADM1model andmodified to take intoaccount the specificity of dry anaerobicmedia. The objective of thework presented herewas to study the sensitivity to themodel of 2 parameters. Thefirst parameter (kLa) was related to mass transfer of the biodegradation products (CH4, CO2, H2) from liquid phase to gas phase. Two gas productionbehaviours were pointed out, depending on kLa value and corresponding to limiting or non‐limiting transfer rate. A kLa value of 5 d�1 marked thetransition. The second parameter (kmX) was linked to biological kinetic reactions. The sensitivity of kmX was important: a variation of �10 % of itsvalue affected clearly the kinetic consumption of the substrate. A method to determine those parameters was presented. This method was then usedto determine both biological kinetic parameter and mass transfer coefficient from batch experimental data of methane production with acetate asorganic substrate at two different moisture contents.

Keywords: modelling, dry anaerobic digestion, model sensitivity, kinetic parameter, mass transfer

INTRODUCTION

Dryanaerobic digestion is a particularly attractive technolo-gy for the treatment of biowaste and residual municipalsolid waste. Even if, in 2010, dry digestion processes

accounted for 60% of the digestion European capacity,[1] high‐solid anaerobic digestion (AD) is a lessmature technology thanwetAD and it can suffer from biological, physical and chemicalproblems due to excessive amounts of solids. Indeed, at such highsolids content (more than 20%), many questions arise in terms ofrheological behaviour, chemical equilibriums and mass transfer.

The mass transport of soluble and particulate compounds withina high‐solid anaerobic digester is totally misunderstood. Biologicalreactions induced by the microorganisms are sensitive to their localenvironments; however, because of the low water content and thepoor mixing efficiency within a high‐solid digester, soluble com-pounds are transported by diffusive convection, thereby creatingthe potential for pockets of local environment (pH, VFAs, dissolvedH2 and CO2…) which can inhibit the biological activity and moreprecisely the methanogenic stage. As a consequence, high‐solid ADcan thus be driven by local mass transfer phenomena. Diffusivetransport is strongly related to the porosity and the viscosity of themedia and, thus, to the global water content. Only a recent paperdetermined experimentally the diffusion coefficients in high‐soliddigested media by using an innovative experimental method whereiodide was used as a soluble tracer.[2] Abbassi‐Guendouz et al.[3]

have also shown that physical limitation related to liquid/gas masstransfer can affect the global anaerobic digestion performance forhigh solids content. The effect of the total solids (TS) content on ADperformances was experimentally investigated in a batch reactor(TS ranging from 10 to 35%). An inhibition of methanogenic stepwas observed for high solids content (>30% TS).

Many models have been proposed for wet digestion but ADM1was the most used since it was settled in 2002.[4] ADM1 is a verycomplete and complex biological model that introduces manyphysical and biochemical phenomena. However, ADM1 does notseem to be adapted to dry digestion media, in particular because ofthe singular properties of dry media in terms of biological kineticsand mass transfer. A previous article detailed the main modifica-

tions applied to ADM1 to adapt to dry conditions.[5] It was shownthat the model calibration with the fitting of biochemicalparameters only was not sufficient for the full understanding ofthe observed experimental data, especially at high solids content.This is the reason why the liquid to gas mass transfer was believedto be limiting in such cases. It is the purpose of the present paperto study the sensitivity of the model. Two parameters relatedrespectively to mass transfer and biological kinetic reaction werethen tested. Amethod to determine those parameterswas presentedand used for batch experimental data of methane production withacetate as organic substrate at two different moisture contents.

MODEL DESCRIPTION

The model presented was based on the ADM1 model, originallydeveloped for liquid‐phase anaerobic digestion.[4] The ADM1 is astructured biological model that simulates the major conversionmechanisms of complex organic substrates into biogas anddegradation by‐products. 24 state variables and 19 reactions (4hydrolysis steps, 8 substrate uptake reactions, and 7 microbialgrowth reactions) are involved. TheADM1model has beenmodifiedto take into account the specificity of dry anaerobic digestionprocesses. This kinetic model is developed for a homogeneous(completely mixed) system and its structure was already presentedin a previous paper.[5] The main differences are detailed here.

Main Modifications to ADM1

Four main modifications have been made:

� Disintegration, hydrolysis and acidogenesis steps were gath-ered in a single step (called DHA). This step was modelled by afirst‐order kinetic expression.

*Author to whom correspondence may be addressed.E‐mail address: hassen.benbelkacem@insa-lyon.frCan. J. Chem. Eng. 9999:1–5, 2014© 2014 Canadian Society for Chemical EngineeringDOI 10.1002/cjce.22089Published online in Wiley Online Library(wileyonlinelibrary.com).

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� Microbial population was considered as constant. Thisstrong assumption is supported by several justifications:anaerobic digestion has a low biomass yield (below 0.1gCODbiomass/gCODdegraded), and since our tests are performed atlow F/M ratio (5 gCOD added for 90 g volatile solid per kg ofreactor), the expected amount of biomass produced is at amaximum 0.5 g of COD, i.e., 0.5 % of the initial amount ofvolatile solid.

� Only 6 substrates were considered (24 in ADM1): particulatematter (Xsd), total propionate (Spro), total acetate (Sac), solublehydrogen (SH2), soluble methane (SCH4) and soluble inorganiccarbon (SIC).

� Themaximal growth rate (km_i) and the biomass concentrationassociated Xi to each trophic group have been lumped into asingle parameter, kmXi. This parameter, called “maximumsubstrate consumption rate”, represents the activity of themicroorganisms that degrade component i.

A volumetric unit was difficult to apply since the density of themedium may vary depending on the nature of the waste or thedegradation progress. Thus, concentrations were expressed accord-ing to a media wet mass unit and not a volumetric unit. The mainunit was mgCOD.kg

�1, apart for inorganic carbon (mmol.kg�1).Biodegradation products were obtained under a soluble form,

and gaseous substances are then transferred to the gaseous phase.Biogas production (CH4, CO2 and H2) was directly calculated fromsoluble concentrations through dynamic gas‐liquid transferequations (1).

rliq‐gas;i ¼ kLaðSi � KH;i:MC:Pgas;iÞ ð1Þ

where rliq‐gas,i is the specific transfer rate (mgCOD. kg�1.d�1), kLa

is the mass transfer coefficient (d�1), Si is the concentration ofcomponent i in the digestate (expressed in mgCOD. kg

�1), KH,i. isthe Henry’s law coefficient (mmol.L�1.bar�1) and Pgas,i is thepartial pressure (bar) of component i. The moisture content MC(in kg of water per of kg of medium) is thus introduced to obtainedthe appropriate unit for rliq‐gas,i.

The dry digestionmodel proposed is depicted in Figure 1, and themodel structure is described in details in the previous paper.[5]

Model Inputs

Four input categories had to be specified:

� Initial concentrations: soluble degradable (degradable Chemi-cal Oxygen Demand, COD), soluble propionate, soluble acetateand soluble IC (Inorganic Carbon).

� Kinetic parameters: the DHA step was characterized by a firstorder kinetic constant (kDHA), while the other biochemicaldegradations of each component “i” were characterized by 2parameters (kmXi, already seen, and Ksi, the half saturationvalue for component i).

� Mass transfer parameters: in particular, the overall masstransfer coefficient kLa.

� Stoichiometric parameters: for each degradation step, thestoichiometric coefficients were set according to theliterature.[4]

The model was implemented on MATLABTM.

Sensitivity of Model Inputs

The model sensitivity to 2 main input parameters were tested. Thefirst one was the mass transfer coefficient kLa. Indeed, the “pasty”aspect of waste material in dry anaerobic systems inducedsignificant differences fromwet digestion in terms ofmass transfer.Some authors reported that high solids anaerobic digestion mediacould be subjected to complex diffusion phenomena. Theyconcluded that decreasing water content could induce diffusionlimitation.[6] The second parameter was the maximum substrateconsumption rate kmX, described before. The other parameter thatcould have an importance is the half‐saturation constant Ks. It wasshown that the model was less sensitive to its variation.[5]

EXPERIMENTAL SET‐UP

In order to use the model for the determination of kLa and kmX,specific methanogenic activity (SMA) experiments were run withacetate added as a substrate in a digestate.

Characterization of Digestate

The medium used in SMA experiments is a municipal solid wastedigestate, whose main characteristics are total solids (TS) 18%,volatile solid (VS) 48% on a TS basis, density 1.1 kg.L�1. It hasbeen sampled from an industrial mesophilic dry digester located inFrance. The digestate (about 40 kg) was stored at 35 8C beforestarting SMA experiments in order to remove residual organicmatter and limit endogenous activity in order to make sure thatthe measured activity arises from the degradation of the addedcomponents during the tests.

SMA Experiments

The SMA was measured under mesophilic conditions (35� 2 8C)using septum‐capped bottles of 500mL volume as batch reactorscontaining 200 g of medium, without stirring. For each assay,5 gCOD of acetate per kilogram of digestate were added as the singlesource of carbon. SMA experiments were carried out in triplicateand followed by a control (“blank”) which reproduced the testwithout addition of substrate into the digestate.Two series were operated with different TS: 18% and 35%.

For assays at TS of 35%, 200 g of medium was composed bya mix of fresh digestate and dried digestate to adjust the TScontent. Assay at 18% TS does not need any specific prepara-tion as it corresponded to initial moisture of MSW digestate.Bottles were flushed with nitrogen gas to ensure anaerobicconditions. Nutrients and trace elements were added toprevent deficiency during the tests. For all tests, two subsequentadditions of substrate were done in order to insure biomassstability. The results of the second substrate addition werepresented.Figure 1. Simplified dry digestion model proposed.[5]

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Analytical Methods

Biogas production was determined by pressure measurement(manometric method) using a DigitronTM 2085P pressuretransducer whereas biogas composition was analyzed by anAgilentTM gas microchromatograph equipped with a thermal con-ductivity detector (CPG–TCD), a Poraplot U column (8 m�0.320mm ID) for CO2 and H2S separation and a Molsieve 5 8Acolumn (10m �PPU 3m) for O2, N2, and CH4 separation. Heliumwas used as carrier gas.

RESULTS AND DISCUSSION

Parameters Sensitivity

All the results presented in this section were obtained by simula-tion using the model with acetate as the only substrate.

Mass transfer sensitivity

kLa was the most important factor for transfer modelling betweenliquid and gaseous phases. Although this parameter was extremelydifficult to determine experimentally in digestion media, itsconsideration was decisive for the model. Figure 2 shows theinfluence of kLa on the methane production in the gas phase. Onlythe acetate degradation step was considered here and thekinetic biological parameters were kept constant. Two ranges of

kLa where the methane production profile was very different couldbe noticed:

� The first range, for kLa values higher than 5d�1: mass transferwas not limited. Soluble products of the biodegradation (heremethane and carbon dioxide) were immediately transferred tothe gaseous phase. The methane production curves for kLavalues equal to 5 and 10 d�1 were similar.

� For kLa values lower than 5d�1, mass transfer was the limitingstep. A methane accumulation in the liquid phase wasobserved. Thus, if mass transfer limitation occurred, differentcurves of gas methane production could be obtained with thesame kinetic parameters as shown on Figure 2. This commentwas crucial when only gaseous methane production wasfollowed to determine biological kinetic parameters (likeduring experiments of specific methanogenic activity).

Kinetic parameter sensitivity

Two configurations, where mass transfer was limited or not, weretested to evaluate the kinetic parameter sensitivity to the model.

Non‐limiting mass transfer case. For this case, kLa was fixedat 5 d�1. Here again, only the acetate degradation step wasconsidered. Indeed, acetate was the last intermediate substratebefore methane formation and its kinetic degradation had directlyan effect on methane production. Figure 3a shows both acetatedegradation and methane production for three values of kmX with10% variation. As shown on Figure 3a, the sensitivity of the kmXparameterwas important: a variation of� 10%of its value affectedthe kinetic consumption of the substrate. Themethane produced isthen transferredwithout delay to the gas phase and hence, kmX hada significant part in the methane profile obtained.

Limiting mass transfer case. For this case, kLa was fixed at 0.5 d�1.Figure 3b shows the methane production for three values of kmXwith 10% variation. The results of acetate degradation are notshown because they are obviously not modified by the kLa change.The most important thing to point out was the beginning of thecurves where the methane produced by the acetate degradationwas not transferred to the gas phase but still remained in the liquidphase. A supersaturation ofmethane occurred during thefirst days,which is a known phenomena in anaerobic digestion.[4,7] Thissupersaturation was not observed with a high kLa value, as shownin Figure 3a.

Figure 2. Influence of kLa (in d�1) on gas methane production for fixedbiological parameters.

Figure 3. (a) Influence of kmX on acetate degradation kinetic and gas methane production for kLa fixed at 5 d�1 (non‐limiting mass transfer situation).(b) Influence of kmX on gas methane production for kLa fixed at 0.5 d�1 (limiting mass transfer situation).

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DISCUSSION

The model developed here could be used to determine bothbiological kinetic parameters and mass transfer coefficient fromexperimental results. The method to determine those parameterscould be divided in two cases:

First case: gas methane production and intermediate substrates(acetate, propionate) were followed.

� Determination of kmXi with substrate degradation curves.� Adjustment of kLa with the curve of gas methane production.

Second case: only the gas methane production was followed asshown on Figure 4.

� Adjustment of kLa with part 1 of the curve (see Figure 4), at thebeginning of the experiment.

� Determination of kmXi with the quasi‐linear part of theexperimental curve (part 2).

The kLa was thus the first parameter to be calibrated using part 1of the curve, and then the kmX was determined by the slope usingpart 2 of the curve. But as shown in Figure 2, when kmX was keptconstant, the slope in part 2 also depends on the kLa value.

SMA Experiments: Model Results

The methane production of MSW digestate spiked with acetate(5 gCOD per kg of medium) at total solid contents of 18% and 35%

are shown in Figure 5. This production was highly affected by theTS content. Themodel was then used to fit the experimental results(see Figure 5 and Table 1). The adjustment of kLa was done byfitting the beginning of the experimental curve, the kmX by fittingthe quasi‐linear part of the experimental curve.A good fitting was obtained for the two TS contents. Only the kLa

value had been changed: at 35% TS, kLa is seven times lower thanat 18% TS (1.05 and 0.15 d�1 at 18 and 35% TS respectively). Forboth experiments, mass transfer was the limiting step. In ourprevious paper where the mass transfer coefficient was keptconstant, the shape of the simulated curves could not account forthe initial delay between the acetate degradation and the methaneproduction.[5]

This confirms the diffusion limitations, already suspected byBollon et al.[2] Their results showed a strong influence of the TScontent on the diffusion coefficient of iodide in dry anaerobicdigestion: a decrease by a factor 50 and 185 (compared to purewater) was obtained at 8% TS and 25% TS, respectively. Abbassi‐Guendouz et al.[3] also identified that a limitation of the overallmass transfer can clearly reduce the methane production and canresult in a considerably lower cumulative methane production.Moreover, they noticed that 30% TS could be considered as athreshold concentration for an inhibitory effect in high‐solid AD.The last point was not confirmed by our results.If the kmX value, expressed in mgCOD.kg

�1.d�1, was the same forthe 2 TS contents, the specific methanogenic activity (SMA),corresponding to the maximum methane production rate andexpressed in gCOD.kgVS

�1.d�1, is quite different. SMA can beused to assess biomass activity and the results showed that SMA athigh TS content was half than that at low TS content (2.5 and4.9 COD.kgVS

�1.d�1 respectively at 35% and 18 % TS), whichunderlined that using high‐solid content for anaerobic digestionextended the time to complete the reaction. The same results wereobserved by Mora‐Naranjo et al.[8] for waste samples excavatedfrom landfill: they investigated the influence of the water contentfor TS ranging from 17% to 73% and underlined a 6‐fold increaseof the specific methane rate, under thermophilic conditions. LeHyaric et al.[6] described also a linearly relationship between SMAand water content for a dry mesophilic MSW digestate spiked withpropionate.

CONCLUSION

The present work focused on the study of the sensitivity of twoparameters to results provided by a model dedicate to dryanaerobic digestion. A method was described to determine thoseparameters, kLa and kmX, using the model to fit experimentalresults. This method was then put into practice for batchexperiments. The main results were:

� Two ranges of kLa valueswere identified: the first range, for kLavalues higher than 5 d�1 where mass transfer was not limited;the second range, for kLa values lower than 5d�1 where a gasaccumulation in the liquid phase could be observed.

Figure 4. Method to determine both kLa (part 1) and kmX (part 2) whenonly gas methane production curve was available.

Figure 5. Methane production during SMA experiments at 2 TS contents:experimental and modelling results.

Table 1. Fitted mass transfer and kinetic parameters used for modellingmethane production during SMA experiments

TS contentkLa(d�1)

kmX(mg COD.kg

�1.d�1)SMA

(g COD.kgVS�1.d�1)

18% 1.05 420 4.935% 0.15 420 2.5

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� A 10% variation of the maximum substrate consumption ratekmX affected clearly both substrate degradation and methaneproduction curves.

� Even if kLa was extremely difficult to determine experimental-ly, the method developed here may allow the determination ofboth kLa and kmX by fitting experimental results and usingdifferent parts of the experimental methane production curve.

� The model was used to determine kLa and kmX of specificmethanogenic activity experimentswhere acetatewas added asorganic substrate in a MSW digestate. 2 TS contents weretested. A good fitting was obtained with the same value of kmX(420mCOD.kg

�1.d�1) and a kLa 7 times lower at 35% TS thanat 18% TS (1.05 and 0.15 d�1 at 18 and 35% TS respectively).This confirms the strong influence of the water distribution indry anaerobic digestion.

REFERENCES

[1] L. De Baere, B. Mattheeuws, F. Velghe, 12th Int. Congr. onAnaerobic Digestion, IWA, Guadalajara, Mexico, 2010.

[2] J. Bollon, H. Benbelkacem, R. Gourdon, P. Buffiere,Chem. Eng.Sci. 2013, 89, 115.

[3] A. Abbassi‐Guendouz, D. Brockmann, E. Trably, C. Dumas, J.‐P. Delgenes, J.‐P. Steyer, R. Escudie, Bioresour. Technol. 2012,111, 55.

[4] D. J. Batstone, J. Keller, I. Angelidaki, S. Kalyuzhnyi, S. G.Pavlostathis, A. Rozzi, W. Sanders, H. Siegriest, V. A. Vavilin,Water Sci. Technol. 2002, 45, 65.

[5] J. Bollon, R. Le Hyaric, H. Benbelkacem, P. Buffière, Biochem.Eng. J. 2011, 56, 212.

[6] R. LeHyaric, C. Chardin, H. Benbelkacem, J. Bollon, R. Bayard,R. Escudié, P. Buffière, Bioresour. Technol. 2010, 102, 822.

[7] A. Pauss, G. Andre, M. Perrier, S. R. Guiot, Appl. Environ.Microbiol. 1990, 56, 1636.

[8] N. Mora‐Naranjo, J. A. Meima, A. Haarstrick, D. C. Hempel,Waste Manage. 2004, 24, 763.

Manuscript received February 28, 2014; revisedmanuscript receivedMay 20, 2014; accepted for publication May 27, 2014.

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