Optimization of Hydrogen Production in Anaerobic Digesters with Input and State Estimation and Model Predictive Control

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Optimization of Hydrogen Production in Anaerobic Digesters with Input and State Estimation and Model Predictive Control


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1 Abstract—This paper addresses the problem of optimization of hydrogen production in continuous anaerobic digesters utilizing an model predictive control (MPC) strategy. The process is described by a dynamic nonlinear model. The influent COD concentration together with the effluent substrate and product concentrations are considered as state variables and estimated by an asymptotic online observer from measurements of gas composition and gas flow rate. It is experimentally demonstrated that a 75% increase of the hydrogen production can be obtained using the influent flow rate as the main control variable while keeping the conversion of the influent COD concentration higher than 95 %. Index Terms—Anaerobic digestion, hydrogen production, modeling, asymptotic observer, model predictive control. I. INTRODUCTION One of the great challenges of the new century is to obtain a new source of renewable energy, capable of replacing fossil fuels. Hydrogen is a promising hope because of its great calorific value, i.e., 122 kJ.g-1 . Unfortunately, even though biological processes have shown strong potentialities for sustainable H2 production, hydrogen is presently mainly produced from the reforming of fossil materials (90% of world production, 45 billion tons) with a high level of pollution generated, i.e., 10 tons CO2.ton-1 [1]. Hydrogen can be produced by micro-organisms using two enzymes (i.e., hydrogenase and nitrogenase) active in their metabolic pathways [2]. However, up to now, the microbial production of hydrogen has still a low efficiency for substrate conversion in anaerobic digestion, ranging between 16 and 45% [3, 4]. The involved processes can be classified into three main classes [5]: biophotolysis, photodecomposition and acidogenic fermentation of carbohydrates (i.e., acidogenesis). The two first processes are photobiological (i.e., light is needed) while the acidogenesis step presents several advantages such as a production yield higher than those obtained with photobiological processes and the capacity of working all day long (i.e., even with no light) [5]. Until now, almost all the studies dedicated to optimization of the anaerobic hydrogen production have been focused on the C. A. Aceves-Lara, E. Latrille, N. Bernet, P. Buffière, J. P. Steyer , they are with INRA, UR050, Laboratoire de Biotechnologie de l’Environnement, Avenue des Etangs, Narbonne, F-11100, France (email: [aceves, latrille, bernet, buffiere, steyer]@supagro.inra.fr) determination of the best operational conditions in steady state [3, 5-7]. In this work, we propose a closed loop optimization of the biohydrogen production using an MPC strategy. The practical implementation requires the measurement of the state variables (i.e., COD and individual volatile fatty acids VFAs) in the input and in the reactor. Because of the lack of cheap and reliable on-line sensors for these variables, we thus propose an asymptotic observer (AO) which estimates these state variables from the measurements of the biogas flow rate and its composition. Experiments were performed to demonstrate the usefulness of this approach. The observer was tested alone over 60 hydraulic retention times (HRT) and the combined AO-MPC strategy was tested for 50 HRTs which is significant to evaluate their performances. II. MATERIALS AND METHODS A. Medium Molasses resulting from the industrial sugarbeet production were used as feeding substrate. They were diluted to concentrations ranging from 5 to 11 g.L-1 by adding a nutritional medium rich in minerals and containing (in mg.L-1 ): MgCl2.6H20, 150; NaCl, 1000; ZnCl2, 10; FeSO4.7H2O, 25; NH4Cl, 1000; CoCl2.5H2O, 5; CuCl2, 5; CaCl2.2H2O, 10; K2HPO4, 150; NiCl2.6H2O, 20; MnCl2.6H2O, 20. B. Reactor design Experiments were carried out in a continuous stirred tank reactor (Setric) with a useful volume of 1270 ml. The reactor was equipped with a stirring system made of a Rushton turbine and a marine propeller in order to ensure a homogeneous mixture and an important agitation. A revolution counter was connected to access to the measurement of the stirring velocity. Stirring velocity was maintained at 300 rpm. Two additional sensors were connected to the reactor for measuring the redox potential (Pt4805 - DXK-S8/225, Mettler Toledo) and pH (4010/120/Pt100, Mettler Toledo). The pH-meter (2300, Ingold) and the transmitter for redox potential (Mettler Toledo) were connected to a computer for on-line data acquisition. The pH was controlled at 5.5 by adding NaOH (2 M) with a peristaltic pump. Temperature in the reactor was also controlled using a platinum probe Pt100 and a heating electric resistance. The temperature of the culture media was Optimization of Hydrogen Production in Anaerobic Digesters with Input and State Estimation and Model Predictive Control C. A. Aceves-Lara, E. Latrille, N. Bernet, P. Buffière, J. P. Steyer e-STA copyright © 2008 by see Volume 5 (2008), N°2 pp 47-51 2 maintained at 37°C. The volume of NaOH added and the temperature were also recorded on-line. C. Off-line measurements Gas composition was analyzed using a gas chromatograph (GC-14A, Shimadzu, colon CTR I, Alltech). Operating conditions were: carrier gas, nitrogen; pressure of 335 KPa; temperature of the injector, 250°C; temperature of the detector, 275°C; temperature gradient for heating, 80 to 120 °C with levels of 10°C per minute. Composition of volatile fatty acids (VFA) in the liquid phase, i.e., acetic (Ace), propionic (Pro), butyric (Bu) and valeric acids, were determined by liquid injection into a gas chromatograph (3900 GC, Varian Inc.). The residual absence or presence of sugar and other bioproducts such as organic acids (lactate), ethanol or acetone was confirmed by a HPLC (colon HPx 87H, BioRad). Operating conditions were: temperature of column, 35°C; temperature of refractometer, 40°C. The biomass concentration was determined through the volatile suspended solid (VSS) concentration measured according to the standard method (APHA, 1995). D. Inoculum preparation The inoculum was prepared with 1 L of sludge taken from a 1m3 pilot-scale fixed bed digester used for several years for the anaerobic treatment of wine distillery wastewater. The sludge was centrifuged for 15 minutes at 17700 g. The reactor was stripped with nitrogen for 15 minutes before continuous feeding with diluted molasses during four days with a retention time of 6 h and a pH equal to 5.5. Finally, it was heated at 98°C during 30 min. III. MATHEMATICAL MODEL A. Structure of biochemical reactions A general mass balance model of a continuous stirred tank reactor fed with glucose, (i.e. molasses containing only sugars like sucrose, fructose and glucose are considered as glucose because of the fast hydrolysis of sucrose[8, 9]) and producing acetate, propionate, butyrate, biomass, carbon inorganic (i.e., CO2, HCO- 3, etc.) and hydrogen from glucose uptake performed by a single micro-organism can be written according to equation (1): ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ − ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ − −⋅= ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ 2 2 2 2 2 2 0 0 0 0 0 H CO in q q H CO X Bu Pro Ace GluGlu DrW H CO X Bu Pro Ace Glu dt d (1) where Glu, Ace, Pro, Bu, X, CO2 and H2 represent, respectively, the concentrations in g.L-1 of glucose, acetate, propionate, butyrate, biomass, carbon dioxide (in mol.L-1 ) and dissolved hydrogen in the liquid phase. The vector r=[r1 r2]t describes the kinetics of the involved biological reactions (in g.L-1 .h-1 ), D is the dilution rate (h-1 ) and qC02 and qH2 the gas flow rates of carbon dioxide and hydrogen expressed in g.L- 1 .d-1 . W represents the matrix of pseudo-stoichiometric coefficients. Pseudo-stoichiometric matrix for our specific case was determined in a previous work [10]. This matrix could be expressed in a Petersen matrix form (TABLE I). TABLE I. Pseudo-stoichiometric matrix of hydrogen production expressed in Petersen matrix form. Component (i) → 1 2 3 4 5 6 7 Rate ↓ (j) Process Glu Ace Pro Bu X CO2 H2 g.(L.h)-1 1 Hydrogen Production -1 w41 w51 w61 w71 X GluK Glu Glu +1 1max,ρ 2 Acid Production -1 w21 w32 w42 w61 X GluK Glu Glu +2 2max,ρ The dynamical model was validated in a previous work [11] and the pseudo-stoichiometric coefficients estimated are: w41=0.3345, w51=0.2510, w61=0.0180, w71=0.0285, w22=0.2421, w32=0.0047, w42=0.1984 and w62 = 0.0037. Finally, kinetics type Monod were used like reaction rates (TABLE I) and its constants values are : ρmax1 = 1.8296 h–1 , ρmax2=1.547 h–1 , KGlu1 = 0.18 g.L-1 and KGlu2 = 0.22 g.L-1 . B. Physicochemical Processes The physicochemical processes (i.e., ions exchange and gas- liquid transfer) are represented, like in the IWA-ADM1 model [12] by a system of differential equations and their parameters were taken from IWA-ADM1 model. However, this model has some differences with respect to acidogenesis of carbohydrates in structured models such as IWA-ADM1. Only one biomass is indeed here assumed for the two biological reactions while in IWA-ADM1, a specific biomass is responsible of each reaction. Moreover, the specific growth rate is assumed not to be affected by pH nor by inorganic nitrogen limitation. Finally, valeric acid is not considered since it was always measured as very close to 0 during the course of the performed experiments. IV. OPTIMISATION Closed loop optimization has been extensively discussed by several workers [13-15]. In biological processes, it was mainly applied for fed-bath reactors [13, 16]. In the present study, the formulation of the closed loop optimization problem is expressed as a model predictive controller using the dynamic model previously described and rewritten as: ),,,( tQGluf ininξξ =& (2) whereξ are the state variables, Gluin is the disturbed input variable and Qin (Qin=D/Vr where Vr is the reactor volume) is the control variable. The objective function to be maximized is: ( )tQGluJmax inin ,,,ξ (3) e-STA copyright © 2008 by see Volume 5 (2008), N°2 pp 47-51 3 In this case, the criteria ∑= + = Ht tu uqHtJ )()( 2 is subject to the following constraints: • ),,,( tQGluf ininξξ =& , i.e., the process dynamics can be represented by the model showed above, • inGluGlu ⋅≤ 05.0 , meaning that 95% of the substrate is converted, because there is no interest to have a high hydrogen gas flow rate without a high conversion of subtract, • 05.7≤inQ mL.min-1 (HRT ≥ 3h), in order to avoid a wash-out. A predictive horizon of 3.5 hours was used. This problem was solved every fifteen minutes, requiring the knowledge of the initial conditions, that is the values of states and process input at time t. The lack of sensors led us to use an asymptotic observer. V. THE NON-LINEAR ASYMPTOTIC OBSERVER In order to estimate the influent concentration together with the compound concentrations in the bioreactor, a state transformation based on the methodology described by Bastin and Dochain [17] was used. To this end, the model needs to fulfill all the structural conditions for the observer design. This is obtained by reducing the model to its biochemical structure and by assuming that the gas phase is close to the chemical equilibrium. Then, the dissolved gas in the liquid phase is calculated from the gas phase concentrations: )( 2, 2,2, 2, 2, OHvapatm HTCOT HT Hgas pPp − + = ρρ ρ )( 2, 2,2, 2, 2, OHvapatm HTCOT COT COgas pPp − + = ρρ ρ 2,2,22,2 2/ HgasHHHLHT pKakH += ρ 2,2,22,2 2/ COgasCOHCOLCOT pKakCO += ρ where pgas,i is the partial pressure of compound i (bar), ρT,i the specific mass transfer rate of gas i, and pvap,H2O the water pressure (bar). Assuming that the dilution rate, the gas flow rate and the gas composition are measured on-line, the following asymptotic observer is proposed: bao EEAZ += (4) where ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ = 2 2 H CO Ea ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ = X Bu Pro Ace Glu Eb and Ao*Ka+Kb=0. This leads to: ( ) DGluDGluQDEA dt dE A dt dGlu inaao a o −++−−= ** (5) where 2,1,1 * =∀= jAA jo ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ = 2 2 H CO a q q Q . In addition, the terms Glu and dGlu/dt can be neglected compared to the other terms because they are very close to zero in most of the experiments. Equation(5) then leads to: ( ) DQDEA dt dE AGlu aao a oin /** ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ ++= Finally, the asymptotic observer for the acetate, propionate, butyrate and biomass concentrations is: ( )ao QADZ dt dZ ' −−= with 2,1&5,...,2, ' =∀=∀= jiAA jio aob EZ - AE ' = VI. RESULTS Fig. 1 shows the feed flow, the estimated inlet glucose concentration and the available off-line glucose measurements. The first fifteen days were used to assess the performance of the observer without controller (i.e., MPC was turned off). The input flow rate was kept constant (HRT = 6 h) and the influent concentrations were varied (i.e., Sin close to 11 gCOD.L-1 during days 1-2, 4-8 and 11-15 and close to 6 gCOD.L-1 during days 2-4 and 8-11). This duration is equal to 60 times the HRT which is long enough to assess AO performance. In order to test the combined AO-MPC strategy, the closed loop controller was then turned on during the last 10 days (i.e., 50 HRTs) and additional input perturbations were applied. HRT was automatically adjusted by the MPC and varied between 3.6 h and 6 h. It is interesting to see that, during days 22 and 23 (i.e., when Sin was decreased to 6 gCOD.L-1 ), the input flow rate was automatically decreased by the MPC. This is explained by the non linear constraints included in the algorithm (and in particular the fact that 95% of the influent substrate should be treated) that allow the controller to avoid wash-out of the reactor. Fig. 2 shows the increase of the hydrogen gas flow rate qH2. It can be seen that when MPC was applied (i.e., after day 15), qH2 was increased by almost 75% , from 360 to 630 ml-H2.h-1 , when Sin was 11 gCOD.L-1 (days 15-20 and 23-25) and by almost 30% when Sin was 6 gCOD.L-1 (days 21-22). The acetate, butyrate, propionate and biomass concentrations measured and estimated by the observer over the whole experiment (i.e., with and without MPC) are shown in Figures 3 to 6 respectively. Qin(mL.min-1) Time (Days) 0 5 10 15 20 25 0 5 10 15 20 25 30 Sin(gDCO.L-1) 3 3.5 4 4.5 5 5.5 6 Sin Obs Sin Exp Qin Fig. 1. Substrate (--) and inflow (-) applied during the course of the experiments e-STA copyright © 2008 by see Volume 5 (2008), N°2 pp 47-51 4 0 5 10 15 20 25 0 100 200 300 400 500 600 700 qH2(ml.min-1) Time (Days) Fig. 2. Hydrogen gas flow rate measured (-)during the course of the experiment 0 5 10 15 20 25 0 0.5 1 1.5 2 2.5 3 Time (days) Aceg.L-1 Exp Obs Fig. 3. Dynamic estimation (-) and (•) off-line measurements of the acetic acid. 0 5 10 15 20 25 0 0.5 1 1.5 2 2.5 3 3.5 4 Time (days) Butg.L-1 Exp Obs Fig. 4. Dynamic estimation (-) and (•) off-line measurements of the butyric acid. Except for biomass where one can notice a similar trend but a constant offset, the estimations are very close to the experimental data, the best results being obtained for butyrate. In order to further validate the observer in a broad range of situations, the MPC was turned off for the last day (from 25 to 27 day) and the input flow rate was set at a high value (i.e., 9.92 mL.min-1 corresponding to HRT = 2.1 h). One can notice that again, the input observer estimated well the experimental data despite a situation very close to wash-out. During this period the hydrogen gas flow rate was higher than during the period 21-22 day, but the substrate conversion was lower than 90% which didn’t respect the constraint of 95%. 0 5 10 15 20 25 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 Time (days) Prog.L-1 Exp Obs Fig. 5. Dynamic estimation (-) and (•) off-line measurements of the propionic acid 0 5 10 15 20 25 0 0.5 1 1.5 2 2.5 3 Time (days) Xg.L-1 Fig. 6. Dynamic estimation (-) and (•) off-line measurements of the biomass. VII. CONCLUSION This paper presented an approach of dynamic optimization of hydrogen production from wastewater by combining an optimal closed loop control together with states and input estimations. The design and performance of the proposed method were applied in a reactor during 27 days. Compared to open loop (i.e., uncontrolled) situations, this led to an increase of 75% of the hydrogen production, from 360 to 630 ml-H2.h- 1 , while keeping removal efficiency of glucose higher than 95%. It is also to be emphasized that only cheap and reliable sensors were needed (i.e., gas flow and composition). VIII. ACKNOWLEDGEMENTS The authors gratefully acknowledge CONACyT in Mexico for the financial support of C.A. Aceves-Lara and Dr. Grégory François for his useful comments. IX. REFERENCES [1] J. Maddy, S. Cherryman, F.R. Hawkes, D.L. Hawkes, R.M. Dinsdale, A.J. Guwy, G.C. Premier, and S. Cole, HYDROGEN 2003 Report Number 1 ERDF part-funded project entitled: “A Sustainable Energy Supply for Wales: e-STA copyright © 2008 by see Volume 5 (2008), N°2 pp 47-51 5 Towards the Hydrogen Economy”. University of Glamorgan, (2003). [2] Y. Asada and J. Miyake, Photobiological hydrogen production, J. Biosci. Bioeng., 88(1999) 1-6. [3] S.W. Van Ginkel and B. Logan, Increased biological hydrogen production with reduced organic loading, Water Res., 39(2005) 3819-3826. [4] J. Woodward, K.A. Cordray, R.J. Edmonston, M. Blanco- Rivera, S.M. Mattingly, and B.R. Evans, Enzymatic hydrogen production: Conversion of renewable resources for energy production, Energy & Fuels, 14(2000) 197-201. [5] D. Das and T.N. Veziroglu, Hydrogen production by biological processes: a survey of literature, Int. J. Hydrogen Energy, 26(2001) 13-28. [6] F. Hawkes, R. Dinsdale, D. Hawkes, and I. Hussy, Sustainable fermentative hydrogen production: challenges for process optimisation, Int. J. 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