ADM1-based modeling of anaerobic codigestion of maize silage and cattle manure – calibration of parameters and model verifi cation (part II)

The aim of this study was to implement ADM1xp model to simulate behavior of anaerobic co-digestion of maize silage and cattle manure. The accuracy of ADM1xp has been assessed against experimental data of anaerobic digestion, performed at OLR = 2.1 gVS dm-3·d-1 and HRT = 45d. Due to the high number of parameters in ADM1xp, it was necessary to develop a customized procedure limiting the range of parameters to be estimated. The best fi tting of experimental to simulated data was obtained after verifi cation of 9 among 105 stoichiometric and kinetic parameters. The values of objective function (JC) ranged between 0.003 (for valerate) and 211 (for biogas production). Unauthenticated Download Date | 6/13/16 11:01 AM ADM1-based modeling of anaerobic codigestion of maize silage and cattle manure – calibration of parameters 21 disintegration constants/hydrolysis rates, the half saturation constants for acids (Ks,i) and the maximum specifi c uptake rates for acids (km,i). The other parameters can be adopted from Batstone et al. (2002). The procedure of estimating a minimal number of a subset of parameters, providing the best fi tting of experimental to simulated data, is a multi-stage process. To fi nd a parameter set with the best fi tting, the possible equifi nality of models should be considered. Equifi nality means that there is no simple of optimal parameter set representing a system, but rather several combinations of parameter values for a chosen model structure. For instance, Ge et al. (2010) and Batstone and Keller (2001) specifi ed a parameter by confi dence regions, not using single values. The results of several combinations led to the creation of a kind of map, consisting of global and local minima and maxima. By equifi nality, the number of modifi ed parameters was reduced to only a few of the most sensitive. To assess the best fi tting of the model to experimental data, several methods can be adopted. The weighted sum of squared errors between model predictions and collected data can be minimized by changing the model parameters (θ). The quality of the model calibration can be evaluated by analyzing the parameter estimation covariance matrix C(θ.). This matrix is calculated by many minimization programs using different techniques (Dochain and Vanrolleghem 2001). The diagonal elements are the variances of the parameter estimates, while the off-diagonal elements are the covariances between different parameters. The covariance matrix can then be used to calculate confi dence intervals, confi dence regions and parameter correlations. Small variances will result in small confi dence regions and more accurate parameter estimations. Wichern et al. (2009) used a genetic algorithm and defi ned a fi tness function as an assessment tool by minimizing the sum of squared differences between the logarithm of measurements and the logarithm of simulated results. Koch et al. (2010) evaluated the agreement between simulated and experimental data using a modifi ed Nash–Sutcliffe coeffi cient. In many papers, the coeffi cients of model fi tting to experimental data are used in analysis of model sensitivity. For that purpose, Kim et al. (2006) used a single step variation method (SVM) to identify the sensitivity of a model for digestion of grass. Wichern et al. (2009) determined the sensitivity index from a procedure in which each parameter was changed several times in increments of 10% above and below the nominal value. In the present study, the genetic algorithm optimization procedure, ga, was used to determine model coeffi cients. Materials and methods Experiments Laboratory fermenter In order to calibrate the ADM1xp, data from laboratory-scale experiments were collected. Anaerobic digestion was performed in a stainless-steel, anaerobic CSTR with a working volume of 100 dm3 (total volume 120 dm3). The reactor was equipped with a stirrer with adjustable rotation speed (76 rpm min.-1) and a water jacket. The fermentor was semicontinuously fed each day. The volume of added feedstock was the same as the digestate withdrawn. The biogas was collected in Tedlar sample bags each day for 1 h and its composition was measured using a GA 2000+ automatic analyser (Geotechnic Instruments, UK). Feedstock preparation and experiment set-up In the experiment, maize silage and cattle manure were used as substrates. These were from a farm in Komorowo (Kujawsko-Pomorskie Region of Poland). The feedstock was composed of maize silage and cattle manure mixed at a ratio of 49:51 (% VS) and diluted with water to obtain a desired concentration of total solids in the infl uent. The feedstock was prepared by weighting 220 g of maize silage and 641 g of cattle manure. The mixture was diluted with 1361 g of water to obtain 113.5 g kg-1 TS and 93.5 g kg-1 VS. Input calculations The input before running the simulations included the following operational conditions: feeding time and volume, temperature of the reactor and the properties of the feedstock. The fermenter was supplied daily with 2.22 dm3 of the prepared feedstock. The HRT was 45d and the OLR was 2.1 gVS dm-3·d-1. Temperature in the fermenter was maintaining at 39°C by water jacket. The characterization of the feedstock was based on chemical oxygen demand (COD), concerned particulate, soluble degradable and inert organic matter. A detailed methodology for calculations of values for the infl uent variables was given in Part I. Some missing values were taken from Batstone et al. (2002) and Rosén and Jeppsson (2006). The values of infl uent variables are given in Table 5 (Part I). The initial values of stoichiometric coeffi cients and kinetic parameters used for the simulation were derived from Batstone et al. (2002). Mathematical model In the present study, the ADM1xp is a modifi ed version of ADM1. The modifi cation concerns incorporation of the Xp value (concentration of particulate products arising from biomass decay (IFAK 2009). This was proposed by Wett et al. (2006) and implemented by ifak system (Germany). The modifi ed model is in the form of a differential (25) and algebraic (34) equation system with 33 steady-state variables (substrates, reaction intermediates and gaseous products, i.e. methane, hydrogen, carbon dioxide in liquid and gaseous phase) and 105 stoichiometric and kinetic parameters. The SIMBA 6.6 software package (ifak system GmbH, Germany), working in a 32-bit environment MATLAB/SIMULINK (MathWork, USA) was used as a simulation tool. Identifi cation of parameters In the ADM1xp model, anaerobic digestion is divided into four basic processes. Each of them is described by specifi c kinetics rate equations (Table 1). All biochemical extracellular processes are assumed to be the fi rst order, whereas all intracellular reactions are Monod-type kinetics. Model calibration and verifi cation In the present study, for calibration of ADM1xp, the genetic algorithm optimization procedure, ga, included in the MATLAB R2012b (MathWork, USA) package was used. Experimental results of biogas/methane production, pH, the concentration of acetate, propionate, and valerate in digestate were used. The fi rst step was to set the initial values of all model parameters to Unauthenticated Download Date | 6/13/16 11:01 AM 22 K. Bułkowska, I. Białobrzewski, Z.M. Gusiatin, E. Klimiuk, T. Pokój be the same as in Batstone et al. (2002). Then, simulations were performed to fi t the model output. The following parameters were adjusted: disintegration constant (kdis), maximum uptake rate for butyrate (km,c4), propionate (km,pro), acetate utilisers (km,ac), half saturation coeffi cients (KS,c4), (KS,pro), (KS,ac) and the coeffi cients describing inhibitory effect (KI h2,c4), (KI,H2,pro), (KI nh3). Other parameters have been used according to Batstone et al. (2002), without any modifi cation. The objective function, JC, (eq. (1)) used to confi rm the accuracy of ADM1xp. It was defi ned as the mean value of the squared differences between the experimental and estimated values of selected fractions (F):