Kinetic prediction of biochemical methane potential of pig slurry

Available online at www.sciencedirect.com ScienceDirect Energy Reports 8 (2022) 159–165 www.elsevier.com/locate/egyr The 8th International Conference on Energy and Environment Research ICEER 2021, 13–17 September Kinetic prediction of biochemical methane potential of pig slurry Andreia D. Santosa,∗, João R. Silvab, Luis M. Castroa,b,c, Rosa M. Quinta-Ferreiraa aCIEPQPF – Chemical Engineering Processes and Forest Products Research Center, Department of Chemical Engineering, Faculty of Sciences and Technology, University of Coimbra, Portugal bInstituto Politécnico de Coimbra, Instituto Superior de Engenharia de Coimbra, Rua Pedro Nunes, Quinta da Nora, 3030-199 Coimbra, Portugal cInstituto Politécnico de Coimbra, Instituto de Investigação Aplicada, Laboratório SiSus, Rua Pedro Nunes, Quinta da Nora, 3030-199 Coimbra, Portugal Received 20 December 2021; accepted 17 January 2022 Available online xxxx Abstract Empirical Kinetic Models have been used to describe and establish the Anaerobic Digestion kinetics of pig slurry’s (8% TS) Biochemical Chemical Potential. A wide selection of Empirical Kinetic Models were fitted to the experimental data collected in batch assays of different Substrate to Inoculum ratios, 0.65 (BMP1) and 1 (BMP2). For the selection of the most suitable model for each BMP assay, the statistical tools R2and the RMSE, along with the Information Criterion AIC and BIC, were taken into consideration. From all the studied models, the Weibull model proved to be the most suitable for kinetic parameter prediction for both BMP1 and BMP2 assays. This model presented the lowest values of AIC and BIC, along with the highest value of R2and the lowest RMSE. In this regard, a R2=0.998, and a RMSE=0.004, was obtained for BMP1, and a R2=0.999 and a RMSE=0.008 for BMP2. © 2022 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Peer-review under responsibility of the scientific committee of the 8th International Conference on Energy and Environment Research, ICEER, 2021. Keywords: Anaerobic digestion; Biomethane potential test; Kinetic evaluation; Kinetic study; Numerical computation; Pig slurry 1. Introduction Anaerobic Digestion (AD) is a natural process that allows microorganisms to decompose organic matter in the absence of oxygen. This process can be divided into four stages, hydrolysis, where the long carbon chains are shortened; acidogenic when bacteria convert the sugars and amino acids into carbon dioxide, hydrogen and ammonia; acetogenesis, in which the short chains are converted into acetic acid; and methanogenesis, where the acetic acid is converted into methane [1]. To evaluate the biodegradability of a given substrate, the Biochemical Methane Potential (BMP) assay is widely employed. It is defined as a simple batch procedure that decomposes the substrate anaerobically. The biogas produced during the experimental period is measured and the methane content ∗Corresponding author. E-mail address: [email protected] (A.D. Santos). https://doi.org/10.1016/j.egyr.2022.01.128 2352-4847/© 2022 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons. org/licenses/by/4.0/). Peer-review under responsibility of the scientific committee of the 8th International Conference on Energy and Environment Research, ICEER, 2021. A.D. Santos, J.R. Silva, L.M. Castro et al. Energy Reports 8 (2022) 159–165 is evaluated [2]. This test can only provide the maximum production of a given substrate. However, using Empirical Kinetic Models (EKM), other parameters such as the adaptation time of the substrate or the rate that the substrate is converted into biogas can be predicted. AD process, being a biological system, can be modeled as a cellular growth process. First, an adaptation period is required to allow microorganisms to acclimate to the substrate and flourish, designated as the Lag Phase period. The next phase, known as the growth phase, contemplates a rapid growth, where the methane production increases each day until reaching a stationary phase. The former phase will last until the organic matter in the substrate is depleted, leading then to a decrease in biogas production until, eventually, the production stops, corresponding to the so-called death phase. Hence, the Empirical Kinetic models for AD are based on microbial growth, including statistical distribution and enzymatic or chemical kinetics [1,3]. The Empirical Kinetic Models are in constant development and adjustment to promote an adaptation to a given operation or experimental data observation. For AD analysis, the curve of the methane accumulation over time obtained from the BMP is the crucial point for the kinetic evaluation. Once the BMP curve describes an exponential function, a mathematical equation is frequently used to describe the AD kinetics under different models such as the Exponential model, Transference or Transfer function of the First-Order kinetic [3]. For instance, the Gompertz model used to describe the human demography was modified to adjust to all phases of the AD process [1]. Some probability distributions, such as in the Weibull and Cauchy models, are also applied to describe the AD process, along with the Cone model that was primarily used to evaluate the gas production in ruminates digestive system [4]. This study presents an evaluation of the kinetic performance of AD for BMP assays of Pig Manure (PM) at 8% concentration (on a Total Solid (TS) basis), aiming for the determination of kinetic parameters for this substrate. The experimental BMP assay was performed in two tests at two different Substrate to Inoculum Ratios (SIR), 0.65 (BMP1), and 1.0 (BMP2). 2. Materials and methods 2.1. Experimental data collection The experimental set of data was acquired from a BMP assay at Lab-scale. The BMP assay was conducted at mesophilic conditions (37 ±1◦C and 1 atm), using pig slurry as substrate at 8% TS and inoculum from a municipal wastewater treatment station. The two Substrate to Inoculum Ratio (SIR) employed were 0.65 and 1.0 named as BMP1 and BMP2, respectively. The experimental data allowed for determining the experimental accumulated methane production as a function of time. 2.2. Kinetic models for data fit The kinetic performance of the BMP was evaluated using the EKM presented in Table 1. Where, BM P (t)is the Cumulative methane yield (L CH4/gVS), BM P0the Methane potential of the substrate (L CH4/gVS), kis Methane production rate (1/d), tis the hydraulic retention time (d), Rmax the maximum methane production rate (L CH4/gVS .d), λthe lag phase (1/d), eis the Euler’s number, µmax . The maximum specific growth rate (1/d). 2.3. Model comparison and selection The evaluation of the most suitable model requires not only an assessment of the coefficient of determination, denoted R2and the Root-Mean-Square Error (RMSE), but also the second-order Akaike Information Criterion (AIC) test [7], Eq. (1), along with the Bayesian Information Criterion (BIC) test, Eq. (2) [8]. The reason behind this assumption is based on the fact that a good R2fitting does not translate into a valid model. The determination of AIC and BIC between the models allows inferring if the estimation of a given error and thereby the relative quality of the statistical models are adequate for the data set [9]. Both R2and RMSE parameters were determined by nonlinear regression, applying the ”fitnlm” function on MATLAB®. AIC ={Nln (RSS N)+2K, when K N≥40 N×ln (RSS N)+2K+2K(K+1) N−K−1, when K N<40 (1) 160 A.D. Santos, J.R. Silva, L.M. Castro et al. Energy Reports 8 (2022) 159–165 Table 1. Empirical-Kinetic models for Anaerobic Digestion tested in this work. Model Name Model Equation Reference First-order Kinetic BM P (t)=BM P0×[1−e−k(t−tlag )][1,3,5,6] Modified Gompertz BM P (t)=BM P0×e−e−e×µmax BM P0(tlag −t)+1 [3–5] Logistic BM P (t)=BM P0 1+e2−µmax BM P0(t−tlag )[1,3,5,6] Feller BM P (t)=2BM P0 πarctan (ek(t−tlag ))[1,3–5] Cone BM P (t)=BM P0 1+(k×(t))−n[1,3,5,6] Chen–Hashimoto BM P (t)=BM P0×(1−kC H µmax ×(t−tlag )+kC H −1)[2,3] Weibull B M P (t)=BM P0×[1−e−(k(t−tlag ))γ][3,4] France BM P (t)=BM P0×[1−ek1(tlag −t)+k2(√tlag −√t)][3,6] Cauchy BM P (t)=2BM P0 πarctan (k(t−tlag )) [3,4] BIC =N×ln (RSS N)+Kln (N)(2) Where the RSS is the Residual Sum of Squares, Nis the number of data points and K is the number of parameters estimated by the model. 3. Results and discussion 3.1. Model fitting Using the “fitnlm” function of MATLAB®, it is possible to obtain the estimated parameter for every model along with the statistical tool to evaluate the model when adjusted to the experimental data. Fig. 1 represents the fitting of all models for BMP1, likewise, the fitting of allmodels for BMP2 is presented in Fig. 2. The graphic representation allows to conclude that most models attain a good fitting with the data. In the exponential zone Logistic, Cone, France, and Cauchy models presented a better fitting. Still, only France and Weibull models follow the experimental data behavior when the stationary region is achieved. To better understand the model fitting, Table 2 presents the predicted parameters by each model and the statistical tools, R2and RMSE. Table 2. Predicted parameters for each model and statistical tools obtained for BMP1. Model First-Order Gompertz Logistic Feller Cone Chen and Hashimoto Weibull France Cauchy BMP0(LCH4/gVS) 0.381 0.375 0.373 0.374 0.397 0.454 0.374 0.378 0.419 µmax (LCH4/gVS.d) N.A. 0.060 0.052 N.A. N.A. −1.11E+09 N.A. N.A. N.A. Tlag (d) N.A. −0.538 −0.875 2.698 N.A. N.A. −0.696 0.028 0.285 K (1/d) 0.286 N.A. N.A. 0.457 0.389 N.A. 0.236 0.348 0.414 KCH N.A. N.A. N.A. N.A. N.A. −3.33E+09 N.A. N.A. N.A. R20.993 0.997 0.994 0.994 0.988 0.956 0.998 0.996 0.984 RMSE 0.007 0.005 0.008 0.006 0.010 0.017 0.004 0.006 0.011 Diff (%) 2.40 0.737 0.191 0.538 6.66 21.9 0.538 1.61 12.6 From Table 2, the Weibull model adjusted better to the data, since it presented the lowest value of RMSE and the highest value of R2, which can be translated into a lower deviation between the predicted values and the experimental data. It is also represented the difference between the experimental value of BMP0and the one predicted by each model, divided by the experimental value of BMP0(Diff %). Additionally, it is possible to notice that only Chen and Hashimoto, and Cauchy models presented a deviation higher than 10%. For this reason, those were not considered as valid kinetic models for BMP1 [10]. 161 A.D. Santos, J.R. Silva, L.M. Castro et al. Energy Reports 8 (2022) 159–165 Fig. 1. Models fitting for BMP1. Fig. 2. Model fitting for BMP2. Once the stationary phase is achieved, only the France model kept adjusting to the data. Contrary to what was observed in the BMP1, the Logistic and the Gompertz models also fitted the stationary phase. Table 3 describes the predicted parameters by each model and the corresponding statistical coefficients, R2and RMSE. This second experiment, carried out under a higher Substrate to Inoculum Ratio, confirmed that the Weibull model was the model that better fits the experimental data since it presents the highest determination coefficient, R2 (0.999), and the lowest RMSE of all tested models. Similar to the behavior detected in BMP1, in Table 3, can be observed that Gompertz, Logistic, Feller, Weibull, and France models were considered valid for this assay, because First-order, Cone Chen, and Hashimoto, and Cauchy presented once more a deviation higher than 10%. When comparing the experimental BMP0(0.643 L CH4/g VS) with the predicted one, both Gompertz and Logistic models predicted the BMP0with the same deviation (0.937%). However, Gompertz achieved the closest BMP0to the experimental value with the highest R2. Vel´ azquez-Mart´ ı et al. [1] employed Gompertz, first-order kinetic, transference, and Cone models to evaluate the kinetic models to be used in AD under mesophilic conditions. The authors found that all provided high R2, but presented significant differences in the RMSE. Regarding their studies, the transfer model and the first-order kinetic model generally produce higher RMSE, so the modified Gompertz model and the Cone model make more accurate 162 A.D. Santos, J.R. Silva, L.M. Castro et al. Energy Reports 8 (2022) 159–165 Table 3. Predicted parameters for each model and statistical tools obtained for BMP2. Model First-Order Gompertz Logistic Feller Cone Chen and Hashimoto Weibull France Cauchy BMP0(LCH4/gVS) 0.710 0.649 0.637 0.683 0.727 0.977 0.658 0.665 0.795 µmax (LCH4/gVS.d) N.A. 0.048 0.045 0.079 N.A. −1.68E+06 N.A. N.A. N.A. Tlag (d) N.A. 0.165 0.048 0.918 N.A. N.A. 0.269 0.361 0.823 K(1/d) 0.096 N.A. N.A. N.A. 0.135 N.A. 0.114 0.171 0.133 KCH N.A. N.A. N.A. N.A. N.A. −1.34E+05 N.A. N.A. N.A. R20.989 0.996 0.988 0.997 0.997 0.978 0.999 0.998 0.995 RMSE 0.020 0.013 0.021 0.012 0.011 0.028 0.008 0.009 0.013 Diff (%) 10.4 0.933 0.933 6.22 13.1 51.9 2.33 3.42 23.6 estimations. In this study, the previous was not verified, with the R2value being conformable with the RMSE. This means that to the highest R2corresponds the lowest RMSE achieved. The former occurs due to the limitations of the EKM, which are only valid under specific operational conditions [11]. For the same substrate, as soon as the SIR is changed, the previous valid model might not be applied in the new SIR. The same occurs when the reactor configuration is different, with the kinetic parameters changing as well. 3.2. Model selection Table 4 presents the criteria analysis for BMP1 and BMP2, allowing for the selection of the most suitable model. Table 4. Criteria analysis of the best fit for BMP1 and BMP2. Model RSS AIC ∆AIC Akaike weight BIC ∆BIC BMP1 First-Order 0.000959 −137.44 −20.09 2.40E+07 −136.15 −20.06 Gompertz 0.000369 −153.74 −3.79 1.80E+04 −152.25 −3.96 Logistic 0.000777 −138.86 −18.67 1.46E+07 −137.37 −18.84 Feller 0.000740 −139.84 −17.70 9.40E+06 −138.35 −17.87 Cone 0.001572 −124.77 −32.76 8.28E+09 −123.28 −32.94 Chen e Hashimoto 0.005336 −100.32 −57.21 4.96E+14 −98.84 −57.38 Weibull 0.000261 −157.53 0.00 3.84E+03 −156.21 0.000 France 0.000542 −142.90 −14.64 2.78E+06 −141.58 −14.64 Cauchy 0.002124 −118.74 −38.79 1.25E+11 −117.26 −38.96 BMP2 First-Order 0.011569 −146.24 −56.19 1.37E+14 −143.88 −54.54 Gompertz 0.004557 −171.71 −30.72 1.03E+09 −168.43 −29.99 Logistic 0.012372 −141.75 −60.68 1.21E+15 −138.46 −59.96 Feller 0.003358 −180.87 −21.55 1.43E+07 −177.59 −20.83 Cone 0.003216 −182.17 −20.25 7.78E+06 −178.89 −19.53 Chen e Hashimoto 0.022453 −123.87 −78.56 5.10E+18 −120.59 −77.83 Weibull 0.001497 −202.42 0.00 6.68E+02 −198.42 0.000 France 0.002069 −192.72 −9.70 6.18E+04 −188.72 −9.70 Cauchy 0.004628 −171.24 −31.18 1.27E+09 −167.96 −30.46 As reported in Pererva et al. [3], understanding the information criteria allows avoiding overfitting. The authors performed a critical review of various BMP tests of various publications. The main conclusion is that a general model cannot be established, with each model being unique for each situation. Therefore, there is no mathematical model capable of describing the biomethane formation kinetics precisely. To select the best model, the lower value of the AIC and BIC must be considered. The Weibull model presents the lowest AIC and BIC values for both essays, providing the perspective that this model produced the best fit. Regarding BMP2, the Weibull model showed the lowest AIC and BIC. Consequently, it is the best model to fit the BMP2 data. Thus, the criteria validated the efficiency of the statistical tool R2as a good indicator of the model fitting. 163 A.D. Santos, J.R. Silva, L.M. Castro et al. Energy Reports 8 (2022) 159–165 4. Conclusion A kinetic performance of a BMP assay for Pig Slurry was studied using two different Substrate to Inoculum Ratios (0.65 and 1). In this study, a wide variety of Empirical Kinetic Models (EKM) are tested, such as the ones based on microbial growth, enzymatic or chemical kinetic and statistical distribution. The Empirical Kinetic Models proved to be very useful tools to predict the kinetic parameters of a specific growth profile in biological systems. The low deviations obtained between the theoretical and experimental values (nearly equal to or lower than 10%) were achieved for the First-Order, Modified Gompertz, Logistic, Feller, Cone, Weibull, and France models in the BMP1 test. For the BMP2, low deviations were observed in the Modified Gompertz, Logistic, Feller, Weibull, and France models. Statistical tools, such as the R2and the RMSE, along with the Information Criteria AIC and BIC are employed to select the most suitable model for each BMP assay. The Weibull model is shown to be the most suitable model to predict the kinetic parameters for both essays, presenting the lowest AIC and BIC values. Regarding the statistical tools, this model in the BMP1 presented the highest value of R2(0.998) and the lowest RMSE (0.004). It was estimated a methane production rate of 0.088 L CH4/ g VS.d. Likewise, in the BMP2, this model was the one reaching the highest value of R2(0.999) and the lowest RMSE (0.008), with an estimated µmax of 0.075 LCH4/gVS.d. CRediT authorship contribution statement Andreia D. Santos: Investigation, Data curation, Conceptualization, Formal analysis, Validation, Writing - original draft. Jo˜ ao R. Silva: Data curation, Writing – review & editing. Luis M. Castro: Conceptualization, Supervision, Validation, Writing – review & editing. Rosa M. Quinta-Ferreira: Conceptualization, Supervision, Writing – review & editing, Project administration, Funding acquisition. Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgments Authors gratefully acknowledge to Proyecto 0745 SYMBIOSIS II 3 E, cofinanciado por el FEDER a trav´ es del Programa INTERREG V A Espa˜ na – Portugal (POCTEP). Funding INTERREG V-A Espanha-Portugal (POCTEP) References [1] Velázquez-Martí Borja, Meneses-Quelal Orlando W, Gaibor-Chavez Juan, Niño-Ruiz Zulay. Review of mathematical models for the anaerobic digestion process. Anaerob. Digest. 2019;1–20. http://dx.doi.org/10.5772/intechopen.80815. [2] Filer Jameson, Ding Huihuang H, Chang Sheng. Biochemical methane potential (BMP) assay method for anaerobic digestion research. Water (Switzerland) 2019;11(5). http://dx.doi.org/10.3390/w11050921. [3] Pererva Yehor, Miller Charles D, Sims Ronald C. 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