A Dynamic Model for Anaerobic Digestion of Microalgae

Preprints of the 18th IFAC World Congress Milano (Italy) August 28 - September 2, 2011

A Dynamic Model for Anaerobic Digestion of Microalgae ⋆ Francis Mairet ∗,∗∗ Olivier Bernard ∗ Monique Ras ∗∗∗ Laurent Lardon ∗∗∗ Jean-Philippe Steyer ∗∗∗ COMORE-INRIA, BP93, 06902 Sophia-Antipolis Cedex, France (e-mail:{francis.mairet, olivier.bernard} @inria.fr). ∗∗ Departamento de Matem´ atica, Universidad T´ecnica Federico Santa Mar´ıa, Valpara´ıso, Chile (e-mail: [email protected]). ∗∗∗ INRA, UR050, Laboratoire de Biotechnologie de l’Environnement, Avenue des Etangs, Narbonne F-11100, France (e-mail: {rasm, lardonl, jean-philippe.steyer} @supagro.inra.fr) ∗

Abstract: The coupling between a microalgal pond and an anaerobic digester is a promising alternative for sustainable energy production by transforming carbon dioxide into methane (which is a biofuel). In this paper, a dynamic model for anaerobic digestion of microalgae is developed with the objective of helping in the coupled process management. This model includes the dynamics of ammonium and volatile fatty acids since both can lead to inhibition and process instability. Three reactions are considered: two hydrolysis-acetogenesis steps in parallel for the sugars-lipids and for the proteins, and a methanogenesis step. Simulation results were compared with experimental data for Chlorella vulgaris digestion. The model fits the data of the considered 140 day experiment. Keywords: Bioprocess, anaerobic digestion, microalgae, kinetic model, Chlorella vulgaris 1. INTRODUCTION Microalgae culture are of growing interest as a sustainable supplier of biomass for energy production (Chisti, 2007). Anaerobic digestion of microalgae can be used to convert this biomass into biogas. This process also leads to ammonium and phosphate release, which can be source of nutrients for the microalgae culture. Coupling microalgae culture and anaerobic digestion is therefore a promising process to convert solar energy into methane, but it also faces many hurdles (Sialve et al., 2009; Mussgnug et al., 2010) due to its inherent complexity. A dynamic model can therefore be of crucial help for managing this promising process and for identifying optimal working strategies. As a first step towards a coupled model, we propose here a dynamic model for anaerobic digestion of microalgae. Modelling of anaerobic digestion has been widely developed since the seventies (Lyberatos and Skiadas, 1999), from simple models (e.g. considering one limiting reaction) (Graef and Andrews, 1974) to more realistic representation (e.g. ADM1 (Batstone et al., 2002) with 12 reactions). Nevertheless, none of them has been applied for microalgae digestion. Our goal is to develop a model that accurately represents the key variables of the process trying to keep a low level of complexity so that it can be mathematically tractable and suitable for the calibration step and for optimal control problem resolution (Bernard and Queinnec, 2008). Our approach is based on the model proposed by Bernard ⋆ This work benefited from the support of the Symbiose research project founded by the French National Research Agency (ANR).

Copyright by the International Federation of Automatic Control (IFAC)

et al. (2001) (that we will call AM2) for wastewater digestion. In AM2, the anaerobic digestion is represented by two steps: first, the acidogenic bacteria consume the organic substrate and produce CO2 and volatile fatty acids (VFA). Then, the methanogenic bacteria consume VFA and produce CO2 and methane. With two reactions, this model is a good trade-off between realism and simplicity so it has been widely used for analysis, monitoring and control (Steyer et al., 2006; Hess and Bernard, 2009; Rincon et al., 2009). However, AM2 in its present form is not suitable to the anaerobic digestion of microalgae and should therefore be modified. The ammonium release due to the high nitrogen content of microalgae can lead to inhibition, particularly for the methanogenic bacteria (Koster and Lettinga, 1984). Ammonium concentration is therefore a key variable of the process and it must be included in the model. As the inorganic nitrogen production is not correlated to the methane production (Ras et al., 2011), we assume that the substrate made of the harvested microalgae can be divided between a substrate S1 , mainly composed of sugars and lipids, and a substrate S2 , mainly composed of proteins (which therefore contains nitrogen). Each substrate is degraded into VFA by a specific bacterial population. Finally, as in AM2, a third population converts VFA into methane. Note that, contrarily to ADM1 (Batstone et al., 2002), we do not separate lipid and sugar to keep a low level of model complexity. The different kinetics between S1 and S2 degradations will define variations between nitrogen release and methane production. We also consider that a

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Daily averaged dilution rate (d-1)


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chromatography), VFA concentrations (by gas chromatography), ionic concentrations (by ion chromatography), pH and chemical oxygen demand (by colorimetric method). For more details on the experiment protocol see Ras et al. (2011).

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3. MODEL DESIGN

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The model includes three main biological reactions, two hydrolysis-acetogenesis steps in parallel for the sugarslipids (S1 ) and for the proteins (S2 ), and a methanogenesis step. Each reaction is performed by a specific bacterial population Xi .

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Substrate additions (gCOD.L-1)

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• The hydrolysis - acidogenesis of sugars-lipids (S1 ) produces VFA (S3 ):

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µ1 X 1

α1 S1 + α2 NH + (1) 4 −→ X1 + α3 S3 + α4 CO2 • The hydrolysis - acidogenesis of proteins (S2 ) produces VFA (S3 ) and ammonium (NH + 4 ):

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α5 S2 −→ X2 + α6 S3 + α7 NH + (2) 4 + α8 CO2 • The methanogenesis converts VFA (S3 ) into dissolved methane (CH4 ):

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Fig. 1. Operating conditions for the anaerobic digestion of Chlorella vulgaris. fraction of microalgae is inert (SI ) as it has been observed in batch experiments (data not shown). The article is structured as follows: after a material and methods section, the model assumptions are detailed and then the resulting model equations are presented. Finally, we describe the calibration procedure and we compare the model with experimental data of anaerobic digestion of the microalgae Chlorella vulgaris (Ras et al., 2011). 2. MATERIALS AND METHODS 2.1 Experimental device Anaerobic digestion of microalgae was performed over 140 days in a continuously mixed reactor at 35◦ C without pH control. The reactor was fed by daily additions with a concentrated stock of Chlorella vulgaris, harvested after settling. The amount of organic biomass introduced in the digester per day was fixed by the harvesting rate and was maintained constant at 1 g COD.L−1 .d−1 . In order to undergo constant and controlled hydraulic retention times (HRT) over long periods, the concentration of the influent was standardised with demineralised water. For each addition, the same liquid volume was withdrawn in order to maintain a constant reactor liquid volume. Figure 1 shows a daily average of the dilution rate and the substrate additions. At the end of the experiment (from day 100 to 120), the microalgae substrate loaded in the digester was increased by successive inputs of 1, 2, 4 and 6 g COD in order to provide a further insight into the dynamics of microalgae degradation. 2.2 Measurements The following measurements were performed: biogas volume (by water displacement), biogas composition (by gas

µ3 X3

α9 S3 + α10 NH + 4 −→ X3 + α11 CH4 + α12 CO2 (3) In the following, Si and Xi will be expressed in g COD.L−1 −1 while NH + (M ). 4 , CO2 and CH4 in mol.L 3.2 Biological kinetics For the hydrolysis - acidogenesis reactions (1) and (2), the specific growth rates are taken as a Michaelis-Menten function of the corresponding substrate: Si for i = 1, 2 (4) µi (Si ) = µ ¯i Si + KSi A Haldane function is used to represent the methanogenesis specific growth rate in order to incorporate VFA inhibition (Bernard et al., 2001), associated to an ammonia inhibition function (Koster and Lettinga, 1984): KINH 3 S3 µ3 (S3 , NH 3 ) = µ ¯3 (5) 2 S3 + KS3 + S3 /KI3 KINH 3 + NH 3 3.3 Physico-chemical processes In order to compute pH, we consider that all the acid base pairs are in equilibrium. Assuming a pH range of operation less than 8, the carbonate concentration can be neglected so the total inorganic carbon concentration C is equal to the sum of the dissolved carbon dioxide concentration CO2 and the bicarbonate concentration HCO3− . Considering the dissociation conH + HCO −

3 stant KC = for the couple HCO3− /CO2 , the CO2 bicarbonate concentration reads: KC C (6) HCO3− = + H + KC

Similarly, dissociation of the total inorganic nitrogen between free ammonia and ammonium (N = NH 3 + NH + 4)

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and the VFA between un-ionized VFAH and ionized VFA− (S3 = VFAH + VFA− ) leads to: H+ N KN + H + KVFA VFA− = S3 KVFA + H +

NH + 4 =

with KN =

(7)

H + NH 3 NH + 4

+ VFA− and KVFA = HVFAH the dissociation + couples NH 3 /NH 4 and VFA− /VFAH .

constant for the Assuming that VFA are mainly composed of acetate, the dissociation constant of acetate is used for VFA (note that the dissociation constants of the different VFA as propionate and butyrate are very close). We define z as follows: X X z= CatIn − AnIn

(8)

where CatIn and AnIn are the molar concentrations weighted by their valence of cations and anions which are not affected by the digestion (N a+ , K + , Cl− , ...). This leads to the following charge balance: − ˜ − + − z + NH + 4 + H = OH + HCO3 + VFA /MVFA (9)

˜ VFA (using acetate’s The division by the COD content M value: 64 g COD.mol−1 ) is used to convert g COD.L−1 in mol.L−1 . OH − concentration is computed as follows: OH − = KH2 O /H +

(10)

Gathering equations (6) to (10), we obtain: KC KVFA KH2 O S3 − z + + C+ + ˜ H H + KC MVFA (KVFA + H + ) (11) H+ + − N − H = 0 KN + H + where H + is the unknown concentration (pH = − log10 H + ) expressed as a function of the model variables z, N, C and S3 . Equation (11) is solved using a numerical solver (funcR tion fzero under Matlab ) initialised with H + = 10−7 M . The liquid-gas transfer rate of CO2 (in mol.L−1 .d−1 ) is defined as follows: ρCO2 = kL a(CO2 − KH,CO2 PCO2 ) H+ (12) C − KH,CO2 PCO2 ) = kL a( KC + H + where PCO2 is the partial pressure of CO2 in the headspace, KH,CO2 the Henry’s constant and kL a the liquid-gas transfer coefficient. Because of its very low solubility, we consider that all the methane produced is transfered to the headspace, i.e.: ρCH4 = α11 µ3 X3 (13) The gas flow rate can be computed assuming an overpressure in the headspace: (14) qgas = max 0; kp (PCH4 + PCO2 − Patm )

with kp the pipe resistance coefficient (Batstone et al., 2002).

The dynamics of the partial pressures are:   ˙ = −PCO qgas + ρCO Vliq RTop   PCO 2 2 2 Vgas Vgas q V RTop gas liq  ˙ = −PCH  + ρCH4  PCH 4 4 Vgas Vgas

(15)

where Top is the operating temperature and Vliq and Vgas are the volumes of the liquid and gas phases. Finally, the methane content (%CH4 ) of the gas flow is: PCH4 (16) %CH4 = PCH4 + PCO2

3.4 Model equations Now we consider a perfectly mixed reactor fed with microalgae characterized by its content of sugars-lipids β1 , of proteins β2 , and of inert βI . Gathering the biological and physico-chemical elements together, the resulting model reads:   S˙1 = D(β1 Sin − S1 ) − α1 µ1 X1     X˙ 1 = (µ1 − D) X1     S˙2 = D(β2 Sin − S2 ) − α5 µ2 X2     X˙ 2 = (µ2 − D) X2     S˙3 = −DS3 + α3 µ1 X1 + α6 µ2 X2 − α9 µ3 X3     X˙ 3 = (µ3 − D) X3     ˙   N = D(Nin − N ) − α2 µ1 X1 +α7 µ2 X2 − α10 µ3 X3 (17)  ˙ = D(Cin − C) + α4 µ1 X1 C     +α8 µ2 X2 + α12 µ3 X3 − ρCO2     z˙ = D(zin − z)     S˙I = D(βI Sin − SI )    Vliq RTop qgas   ˙  + ρCO2  PCO2 = −PCO2 V  Vgas gas    Vliq RTop qgas  ˙  + ρCH4  PCH4 = −PCH4 Vgas Vgas

where D is the dilution rate, Sin , Nin , Cin and zin are respectively the influent concentrations of microalgae, inorganic nitrogen, inorganic carbon and inert cation menus anion (as defined by equation (8)). The specific growth rates µi are defined by equations (4) and (5), with NH 3 = KN KN +H + N . The liquid-gas transfer rates ρ are given in equations (12) and (13); H + is estimated solving equation (11); the gas flow rate and composition are computed using equations (14) and (16). 4. COMPARISON WITH EXPERIMENTAL DATA The experiment was carried out with feeding impulses. In order to avoid numerical error due to the impulses, simulations were reinitialized after each substrate addition. The effect of each addition (at time ti ) on the concentrations (gathered in vector ξ) are computed from a mass balance as follows: Vin (ti ) − ξin (ti ) − ξ(t− (18) ξ(t+ i ) i ) = ξ(ti ) + Vliq

where Vin and ξin are the volume and the concentrations of the feed additions. Then, the system (17) is solved with − D = 0 until the next impulse (from t+ i to ti+1 ) and so on.

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4.1 Input characterisation Total COD (g.L-1)

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VFA (g COD.L-1)

The input characterisation is a critical step in modelling anaerobic digestion (Kleerebezem and Van Loosdrecht, 2006). The algae composition is species dependent but it can also vary with the environmental conditions (Harrison et al., 1990; Mairet et al., 2011). In non-limited growth, the average biochemical composition (in dry weight (DW)) for Chlorella vulgaris is: protein 60%, lipid 20% and sugar 20% (Becker, 2007; Pruvost et al., 2011). Using approximate elemental compositions for protein (C4.43 H7 O1.44 N1.16 S0.019 ), lipid (C40 H74 O5 ) and sugar (C6 H12 O6 ) (Geider and Roche, 2002), this biochemical composition leads to a C/N ratio of 5.9, which is in line with the measured ratio of 6. The conversion from g DW to g COD is computed for protein (1.76 g COD.g DW −1 ), lipid (2.83 g COD.g DW −1 ) and carbohydrate (1.07 g COD.g DW −1 ) using the approximate elemental compositions. The inert part is computed from the experimental data of batch experiments (data not shown). Assuming that the inert part composition is equal to the algae’s one, we can finally compute the algae composition parameters β1 , β2 and βI . pH in the influent was not monitored but it ranges between 9 and 10 (this high pH results from CO2 uptake by microalgae in the settler). pH and inorganic carbon content in the influent are computed assuming CO2 in equilibrium with its atmospheric atm partial pressure: knowing CO2 (= KH,CO2 PCO ) and zin 2

Table 1. Input characterisation Parameter Value β1 0.3 g COD.g COD−1 β2 0.4 g COD.g COD−1 βI 0.3 g COD.g COD−1 zin 0.017 M pHin 9.6 Cin 0.019 M Nin 0.011 M

Meaning Sugar-lipid content of microalgae Protein content of microalgae Inert content of microalgae Inert Cation - Anion concentration

8 6 4 2

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can be (measured), equation (11) (with C = solved numerically. The input characterisation results are given in table 1.

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Fig. 2. COD, VFA and inorganic nitrogen concentrations: comparison between model prediction (blue lines) and experimental data (green dots) of Chlorella vulgaris digestion. conditions of the digester, total biomass concentration should be in the range 1 to 2 g COD.L−1 and substrate concentrations should be relatively low. Therefore, we assume X1 (0) = X2 (0) = X3 (0) = 0.6g COD.L−1 and S1 (0) = S2 (0) = 0.3g COD.L−1 (SI (0) is computed to reproduce the total COD).

Inorganic carbon concentration Inorganic nitrogen concentration

4.2 Parameter identification The values of the stoichiometric coefficients αi are deduced from Batstone et al. (2002), verifying that they fulfil the conservation law for COD, carbon and nitrogen. The kinetic parameters were identified with a minimization algoR

rithm (function lsqnonlin underPMatlab P ) using the following measurements: COD (= S + X), gas flow rate, methane content, VFA and ammonium. This algorithm is used to find the set of parameters that minimizes an error criterion J between the model and the measurements: !2 p X n X yje (ti ) − yjm (ti ) J= (19) y¯jm j=1 i=1 where yjm (ti ) and yje (ti ) are respectively the measurement and the model estimation for each measured variable j at time ti , and y¯jm is the average value of yjm . As only the total COD is measured, the initial substrate and biomass concentrations are unknown. Given the initial operating

As the experiment was performed with a low loading rate, no inhibition was observed. Nevertheless, inhibition terms were however included in the kinetics since they may play an important role in the future use of the model (control, optimization...). Therefore, inhibition parameter values were taken from Batstone et al. (2002) for ammonia (KINH 3 ) and Bernard et al. (2001) for VFA (KI3 ). Parameter values are given in table 2. Note that Cameron et al. (2011) have applied a new systematic procedure with the same model and dataset for the selection and estimation of optimal parameter combinations providing confidence intervals of the selected parameter estimates. 4.3 Simulation This model describes accurately the experimental data (see Fig.2, 3 and 4). In particular, the good representation of COD and inorganic nitrogen concentrations (Fig.2) is a first hint that the model catches the complex dynamics of microalgae degradation. In accordance with the experimental data, the model predicts a low VFA concentration,

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α2

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g COD.g COD−1

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0.083 mol.g COD −1

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13.1 g COD.g COD−1 mol.g COD −1

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0.19 mol.g COD −1

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0.12 mol.g COD −1

Kinetic parameters µ ¯1 0.2 d−1 KS1 µ ¯2 KS2 µ ¯3

0.29 g COD.L−1 0.053 d−1 0.046 g COD.L−1 0.11 d−1

KS3

0.003 g COD.L−1

KI3

16.4 g COD.L−1

MeaningSource yield for sugar-lipid degradation (acidogenesis of sugar-lipid)a yield for NH + 4 consumption (acidogenesis of sugar-lipid)a yield for VFA production (acidogenesis of sugar-lipid)a yield for CO2 production (acidogenesis of sugar-lipid)a yield for protein degradation (acidogenesis of protein)a yield for VFA production (acidogenesis of protein)a yield for NH + 4 production (acidogenesis of protein)a yield for CO2 production (acidogenesis of protein)a yield for VFA consumption (methanogenesis)a yield for NH + consumption 4 (methanogenesis)a yield for methane production (methanogenesis)a yield for CO2 production (methanogenesis)a

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Parameter Value Stoichiometric parameters α1 12.5 g COD.g COD−1

Gas flow rate (L.d-1.L-1)

Table 2. Parameter values

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Fig. 3. Gas flow rate and composition: comparison between model prediction (blue lines) and experimental data (green dots) of Chlorella vulgaris digestion. of the input (mainly Cin , which can be computed from input pH measurements) should improve the predictions of the reactor pH and the methane content.

Maximum specific growth rate of sugar-lipid acidogenic bacteriab Half saturation constant of sugar-lipid acidogenic bacteriab Maximum specific growth rate of protein acidogenic bacteriab Half saturation constant of protein acidogenic bacteriab Maximum specific growth rate of methanogenic bacteriab Haldane half saturation constant of methanogenic bacteriab Haldane substrate inhibition constant of methanogenic bacteriac Ammonia inhibition constanta

As each bacterial population and substrate was not measured separately, estimations of their dynamic can be obtained by model simulation (Fig. 5). From the 50th day, a high dilution rate produces a washout of protein degrader population X2 and therefore an accumulation of protein S2 . On the other hand, sugars and lipids are almost completely degraded because of a higher maximal growth rate of X1 . This phenomenon leads to a nitrogen release not correlated to the methane production, as it was observed experimentally (Ras et al., 2011). 5. CONCLUSION

KINH 0.0018 M 3 Physico-chemical parameters KC 4.9e-7 M Dissociation constant for the couple HCO3− /CO2 a KN 1.1e-9 M Dissociation constant for the a couple NH 3 /NH + 4 KVFA 1.7e-5 M Dissociation constant for the couple VFA− /VFAH a KH 2 O 2.1e-14 M Dissociation constant for the couple H2 O/OH − a KH,CO2 2.7e-2 M.bar −1 Henry’s constant for CH4 a R 8.31e-2 bar.M −1 .K −1 Gas law constant a kL a 5 d−1 Gas-liquid transfer coefficient kp 5e4 L.d−1 .bar−1 Pipe resistance coefficienta Vliq 1L Reactor liquid volume Vgas 0.1 L Reactor gas volume Top 308.15 K Reactor temperature a : from Batstone et al. (2002), b : from the minimization procedure, c : from Bernard et al. (2001)

In this work, we have proposed a model for anaerobic digestion of microalgae. As the methane and ammonium productions are not correlated, the distinction between sugar-lipid and protein degradations is necessary to obtain a good fitting of the experimental data. As a future work, we expect to validate the model with high load experiments (i.e. with ammonia inhibition). This model will then be used to optimize the coupling between anaerobic digestion and microalgae culture. REFERENCES

except during transients after the successive increasing inputs at the end of the experiment (after day 100). The gas flow rate is well predicted (Fig. 3), and the methane content also except for the successive increasing inputs. This discrepancy in the methane content is probably due to pH underestimation (Fig.4). A better characterisation

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Fig. 4. pH and inert cation - anion concentration: comparison between model prediction (blue lines) and experimental data (green dots) of Chlorella vulgaris digestion.

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Fig. 5. Model prediction of substrate and bacteria population dynamics. The legend indicates each substrate and its associated bacteria population. The high dilution rate at the end of the experiment produces a washout of protein degrader bacteria.

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