Kinetic prediction of biochemical methane potential of pig slurry

A ailable online a www.sciencedi ec .com ScienceDi ec Ene gy Repo s 8 (2022) 159–165 www.else ie .com/loca e/egy The 8 h In e na ional Con e ence on Ene gy and En i onmen Resea ch ICEER 2021, 13–17 Sep embe Kine ic p edic ion o biochemical me hane po en ial o pig slu y And eia D. San osa,∗, João R. Sil ab, Luis M. Cas oa,b,c, Rosa M. Quin a-Fe ei aa aCIEPQPF – Chemical Enginee ing P ocesses and Fo es P oduc s Resea ch Cen e , Depa men o Chemical Enginee ing, Facul y o Sciences and Technology, Uni e si y o Coimb a, Po ugal bIns i u o Poli écnico de Coimb a, Ins i u o Supe io de Engenha ia de Coimb a, Rua Ped o Nunes, Quin a da No a, 3030-199 Coimb a, Po ugal cIns i u o Poli écnico de Coimb a, Ins i u o de In es igação Aplicada, Labo a ó io SiSus, Rua Ped o Nunes, Quin a da No a, 3030-199 Coimb a, Po ugal Recei ed 20 Decembe 2021; accep ed 17 Janua y 2022 A ailable online xxxx Abs ac Empi ical Kine ic Models ha e been used o desc ibe and es ablish he Anae obic Diges ion kine ics o pig slu y’s (8% TS) Biochemical Chemical Po en ial. A wide selec ion o Empi ical Kine ic Models we e i ed o he expe imen al da a collec ed in ba ch assays o di e en Subs a e o Inoculum a ios, 0.65 (BMP1) and 1 (BMP2). Fo he selec ion o he mos sui able model o each BMP assay, he s a is ical ools R2and he RMSE, along wi h he In o ma ion C i e ion AIC and BIC, we e aken in o conside a ion. F om all he s udied models, he Weibull model p o ed o be he mos sui able o kine ic pa ame e p edic ion o bo h BMP1 and BMP2 assays. This model p esen ed he lowes alues o AIC and BIC, along wi h he highes alue o R2and he lowes RMSE. In his ega d, a R2=0.998, and a RMSE=0.004, was ob ained o BMP1, and a R2=0.999 and a RMSE=0.008 o BMP2. © 2022 The Au ho (s). Published by Else ie L d. This is an open access a icle unde he CC BY license (h p://c ea i ecommons.o g/licenses/by/4.0/). Pee - e iew unde esponsibili y o he scien i ic commi ee o he 8 h In e na ional Con e ence on Ene gy and En i onmen Resea ch, ICEER, 2021. Keywo ds: Anae obic diges ion; Biome hane po en ial es ; Kine ic e alua ion; Kine ic s udy; Nume ical compu a ion; Pig slu y 1. In oduc ion Anae obic Diges ion (AD) is a na u al p ocess ha allows mic oo ganisms o decompose o ganic ma e in he absence o oxygen. This p ocess can be di ided in o ou s ages, hyd olysis, whe e he long ca bon chains a e sho ened; acidogenic when bac e ia con e he suga s and amino acids in o ca bon dioxide, hyd ogen and ammonia; ace ogenesis, in which he sho chains a e con e ed in o ace ic acid; and me hanogenesis, whe e he ace ic acid is con e ed in o me hane [1]. To e alua e he biodeg adabili y o a gi en subs a e, he Biochemical Me hane Po en ial (BMP) assay is widely employed. I is de ined as a simple ba ch p ocedu e ha decomposes he subs a e anae obically. The biogas p oduced du ing he expe imen al pe iod is measu ed and he me hane con en ∗Co esponding au ho . E-mail add ess: [email p o ec ed] (A.D. San os). h ps://doi.o g/10.1016/j.egy .2022.01.128 2352-4847/© 2022 The Au ho (s). Published by Else ie L d. This is an open access a icle unde he CC BY license (h p://c ea i ecommons. o g/licenses/by/4.0/). Pee - e iew unde esponsibili y o he scien i ic commi ee o he 8 h In e na ional Con e ence on Ene gy and En i onmen Resea ch, ICEER, 2021. A.D. San os, J.R. Sil a, L.M. Cas o e al. Ene gy Repo s 8 (2022) 159–165 is e alua ed [2]. This es can only p o ide he maximum p oduc ion o a gi en subs a e. Howe e , using Empi ical Kine ic Models (EKM), o he pa ame e s such as he adap a ion ime o he subs a e o he a e ha he subs a e is con e ed in o biogas can be p edic ed. AD p ocess, being a biological sys em, can be modeled as a cellula g ow h p ocess. Fi s , an adap a ion pe iod is equi ed o allow mic oo ganisms o acclima e o he subs a e and lou ish, designa ed as he Lag Phase pe iod. The nex phase, known as he g ow h phase, con empla es a apid g ow h, whe e he me hane p oduc ion inc eases each day un il eaching a s a iona y phase. The o me phase will las un il he o ganic ma e in he subs a e is deple ed, leading hen o a dec ease in biogas p oduc ion un il, e en ually, he p oduc ion s ops, co esponding o he so-called dea h phase. Hence, he Empi ical Kine ic models o AD a e based on mic obial g ow h, including s a is ical dis ibu ion and enzyma ic o chemical kine ics [1,3]. The Empi ical Kine ic Models a e in cons an de elopmen and adjus men o p omo e an adap a ion o a gi en ope a ion o expe imen al da a obse a ion. Fo AD analysis, he cu e o he me hane accumula ion o e ime ob ained om he BMP is he c ucial poin o he kine ic e alua ion. Once he BMP cu e desc ibes an exponen ial unc ion, a ma hema ical equa ion is equen ly used o desc ibe he AD kine ics unde di e en models such as he Exponen ial model, T ans e ence o T ans e unc ion o he Fi s -O de kine ic [3]. Fo ins ance, he Gompe z model used o desc ibe he human demog aphy was modi ied o adjus o all phases o he AD p ocess [1]. Some p obabili y dis ibu ions, such as in he Weibull and Cauchy models, a e also applied o desc ibe he AD p ocess, along wi h he Cone model ha was p ima ily used o e alua e he gas p oduc ion in umina es diges i e sys em [4]. This s udy p esen s an e alua ion o he kine ic pe o mance o AD o BMP assays o Pig Manu e (PM) a 8% concen a ion (on a To al Solid (TS) basis), aiming o he de e mina ion o kine ic pa ame e s o his subs a e. The expe imen al BMP assay was pe o med in wo es s a wo di e en Subs a e o Inoculum Ra ios (SIR), 0.65 (BMP1), and 1.0 (BMP2). 2. Ma e ials and me hods 2.1. Expe imen al da a collec ion The expe imen al se o da a was acqui ed om a BMP assay a Lab-scale. The BMP assay was conduc ed a mesophilic condi ions (37 ±1◦C and 1 a m), using pig slu y as subs a e a 8% TS and inoculum om a municipal was ewa e ea men s a ion. The wo Subs a e o Inoculum Ra io (SIR) employed we e 0.65 and 1.0 named as BMP1 and BMP2, espec i ely. The expe imen al da a allowed o de e mining he expe imen al accumula ed me hane p oduc ion as a unc ion o ime. 2.2. Kine ic models o da a i The kine ic pe o mance o he BMP was e alua ed using he EKM p esen ed in Table 1. Whe e, BM P ( )is he Cumula i e me hane yield (L CH4/gVS), BM P0 he Me hane po en ial o he subs a e (L CH4/gVS), kis Me hane p oduc ion a e (1/d), is he hyd aulic e en ion ime (d), Rmax he maximum me hane p oduc ion a e (L CH4/gVS .d), λ he lag phase (1/d), eis he Eule ’s numbe , µmax . The maximum speci ic g ow h a e (1/d). 2.3. Model compa ison and selec ion The e alua ion o he mos sui able model equi es no only an assessmen o he coe icien o de e mina ion, deno ed R2and he Roo -Mean-Squa e E o (RMSE), bu also he second-o de Akaike In o ma ion C i e ion (AIC) es [7], Eq. (1), along wi h he Bayesian In o ma ion C i e ion (BIC) es , Eq. (2) [8]. The eason behind his assump ion is based on he ac ha a good R2 i ing does no ansla e in o a alid model. The de e mina ion o AIC and BIC be ween he models allows in e ing i he es ima ion o a gi en e o and he eby he ela i e quali y o he s a is ical models a e adequa e o he da a se [9]. Bo h R2and RMSE pa ame e s we e de e mined by nonlinea eg ession, applying he ” i nlm” unc ion 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. San os, J.R. Sil a, L.M. Cas o e al. Ene gy Repo s 8 (2022) 159–165 Table 1. Empi ical-Kine ic models o Anae obic Diges ion es ed in his wo k. Model Name Model Equa ion Re e ence Fi s -o de Kine ic BM P ( )=BM P0×[1−e−k( − lag )][1,3,5,6] Modi ied Gompe z BM P ( )=BM P0×e−e−e×µmax BM P0( lag − )+1 [3–5] Logis ic BM P ( )=BM P0 1+e2−µmax BM P0( − lag )[1,3,5,6] Felle BM P ( )=2BM P0 πa c an (ek( − lag ))[1,3–5] Cone BM P ( )=BM P0 1+(k×( ))−n[1,3,5,6] Chen–Hashimo o BM P ( )=BM P0×(1−kC H µmax ×( − lag )+kC H −1)[2,3] Weibull B M P ( )=BM P0×[1−e−(k( − lag ))γ][3,4] F ance BM P ( )=BM P0×[1−ek1( lag − )+k2(√ lag −√ )][3,6] Cauchy BM P ( )=2BM P0 πa c an (k( − lag )) [3,4] BIC =N×ln (RSS N)+Kln (N)(2) Whe e he RSS is he Residual Sum o Squa es, Nis he numbe o da a poin s and K is he numbe o pa ame e s es ima ed by he model. 3. Resul s and discussion 3.1. Model i ing Using he “ i nlm” unc ion o MATLAB®, i is possible o ob ain he es ima ed pa ame e o e e y model along wi h he s a is ical ool o e alua e he model when adjus ed o he expe imen al da a. Fig. 1 ep esen s he i ing o all models o BMP1, likewise, he i ing o allmodels o BMP2 is p esen ed in Fig. 2. The g aphic ep esen a ion allows o conclude ha mos models a ain a good i ing wi h he da a. In he exponen ial zone Logis ic, Cone, F ance, and Cauchy models p esen ed a be e i ing. S ill, only F ance and Weibull models ollow he expe imen al da a beha io when he s a iona y egion is achie ed. To be e unde s and he model i ing, Table 2 p esen s he p edic ed pa ame e s by each model and he s a is ical ools, R2and RMSE. Table 2. P edic ed pa ame e s o each model and s a is ical ools ob ained o BMP1. Model Fi s -O de Gompe z Logis ic Felle Cone Chen and Hashimo o Weibull F ance 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 Di (%) 2.40 0.737 0.191 0.538 6.66 21.9 0.538 1.61 12.6 F om Table 2, he Weibull model adjus ed be e o he da a, since i p esen ed he lowes alue o RMSE and he highes alue o R2, which can be ansla ed in o a lowe de ia ion be ween he p edic ed alues and he expe imen al da a. I is also ep esen ed he di e ence be ween he expe imen al alue o BMP0and he one p edic ed by each model, di ided by he expe imen al alue o BMP0(Di %). Addi ionally, i is possible o no ice ha only Chen and Hashimo o, and Cauchy models p esen ed a de ia ion highe han 10%. Fo his eason, hose we e no conside ed as alid kine ic models o BMP1 [10]. 161 A.D. San os, J.R. Sil a, L.M. Cas o e al. Ene gy Repo s 8 (2022) 159–165 Fig. 1. Models i ing o BMP1. Fig. 2. Model i ing o BMP2. Once he s a iona y phase is achie ed, only he F ance model kep adjus ing o he da a. Con a y o wha was obse ed in he BMP1, he Logis ic and he Gompe z models also i ed he s a iona y phase. Table 3 desc ibes he p edic ed pa ame e s by each model and he co esponding s a is ical coe icien s, R2and RMSE. This second expe imen , ca ied ou unde a highe Subs a e o Inoculum Ra io, con i med ha he Weibull model was he model ha be e i s he expe imen al da a since i p esen s he highes de e mina ion coe icien , R2 (0.999), and he lowes RMSE o all es ed models. Simila o he beha io de ec ed in BMP1, in Table 3, can be obse ed ha Gompe z, Logis ic, Felle , Weibull, and F ance models we e conside ed alid o his assay, because Fi s -o de , Cone Chen, and Hashimo o, and Cauchy p esen ed once mo e a de ia ion highe han 10%. When compa ing he expe imen al BMP0(0.643 L CH4/g VS) wi h he p edic ed one, bo h Gompe z and Logis ic models p edic ed he BMP0wi h he same de ia ion (0.937%). Howe e , Gompe z achie ed he closes BMP0 o he expe imen al alue wi h he highes R2. Vel´ azquez-Ma ´ ı e al. [1] employed Gompe z, i s -o de kine ic, ans e ence, and Cone models o e alua e he kine ic models o be used in AD unde mesophilic condi ions. The au ho s ound ha all p o ided high R2, bu p esen ed signi ican di e ences in he RMSE. Rega ding hei s udies, he ans e model and he i s -o de kine ic model gene ally p oduce highe RMSE, so he modi ied Gompe z model and he Cone model make mo e accu a e 162 A.D. San os, J.R. Sil a, L.M. Cas o e al. Ene gy Repo s 8 (2022) 159–165 Table 3. P edic ed pa ame e s o each model and s a is ical ools ob ained o BMP2. Model Fi s -O de Gompe z Logis ic Felle Cone Chen and Hashimo o Weibull F ance 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 Di (%) 10.4 0.933 0.933 6.22 13.1 51.9 2.33 3.42 23.6 es ima ions. In his s udy, he p e ious was no e i ied, wi h he R2 alue being con o mable wi h he RMSE. This means ha o he highes R2co esponds he lowes RMSE achie ed. The o me occu s due o he limi a ions o he EKM, which a e only alid unde speci ic ope a ional condi ions [11]. Fo he same subs a e, as soon as he SIR is changed, he p e ious alid model migh no be applied in he new SIR. The same occu s when he eac o con igu a ion is di e en , wi h he kine ic pa ame e s changing as well. 3.2. Model selec ion Table 4 p esen s he c i e ia analysis o BMP1 and BMP2, allowing o he selec ion o he mos sui able model. Table 4. C i e ia analysis o he bes i o BMP1 and BMP2. Model RSS AIC ∆AIC Akaike weigh BIC ∆BIC BMP1 Fi s -O de 0.000959 −137.44 −20.09 2.40E+07 −136.15 −20.06 Gompe z 0.000369 −153.74 −3.79 1.80E+04 −152.25 −3.96 Logis ic 0.000777 −138.86 −18.67 1.46E+07 −137.37 −18.84 Felle 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 Hashimo o 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 F ance 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 Fi s -O de 0.011569 −146.24 −56.19 1.37E+14 −143.88 −54.54 Gompe z 0.004557 −171.71 −30.72 1.03E+09 −168.43 −29.99 Logis ic 0.012372 −141.75 −60.68 1.21E+15 −138.46 −59.96 Felle 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 Hashimo o 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 F ance 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 epo ed in Pe e a e al. [3], unde s anding he in o ma ion c i e ia allows a oiding o e i ing. The au ho s pe o med a c i ical e iew o a ious BMP es s o a ious publica ions. The main conclusion is ha a gene al model canno be es ablished, wi h each model being unique o each si ua ion. The e o e, he e is no ma hema ical model capable o desc ibing he biome hane o ma ion kine ics p ecisely. To selec he bes model, he lowe alue o he AIC and BIC mus be conside ed. The Weibull model p esen s he lowes AIC and BIC alues o bo h essays, p o iding he pe spec i e ha his model p oduced he bes i . Rega ding BMP2, he Weibull model showed he lowes AIC and BIC. Consequen ly, i is he bes model o i he BMP2 da a. Thus, he c i e ia alida ed he e iciency o he s a is ical ool R2as a good indica o o he model i ing. 163 A.D. San os, J.R. Sil a, L.M. Cas o e al. Ene gy Repo s 8 (2022) 159–165 4. Conclusion A kine ic pe o mance o a BMP assay o Pig Slu y was s udied using wo di e en Subs a e o Inoculum Ra ios (0.65 and 1). In his s udy, a wide a ie y o Empi ical Kine ic Models (EKM) a e es ed, such as he ones based on mic obial g ow h, enzyma ic o chemical kine ic and s a is ical dis ibu ion. The Empi ical Kine ic Models p o ed o be e y use ul ools o p edic he kine ic pa ame e s o a speci ic g ow h p o ile in biological sys ems. The low de ia ions ob ained be ween he heo e ical and expe imen al alues (nea ly equal o o lowe han 10%) we e achie ed o he Fi s -O de , Modi ied Gompe z, Logis ic, Felle , Cone, Weibull, and F ance models in he BMP1 es . Fo he BMP2, low de ia ions we e obse ed in he Modi ied Gompe z, Logis ic, Felle , Weibull, and F ance models. S a is ical ools, such as he R2and he RMSE, along wi h he In o ma ion C i e ia AIC and BIC a e employed o selec he mos sui able model o each BMP assay. The Weibull model is shown o be he mos sui able model o p edic he kine ic pa ame e s o bo h essays, p esen ing he lowes AIC and BIC alues. Rega ding he s a is ical ools, his model in he BMP1 p esen ed he highes alue o R2(0.998) and he lowes RMSE (0.004). I was es ima ed a me hane p oduc ion a e o 0.088 L CH4/ g VS.d. Likewise, in he BMP2, his model was he one eaching he highes alue o R2(0.999) and he lowes RMSE (0.008), wi h an es ima ed µmax o 0.075 LCH4/gVS.d. CRediT au ho ship con ibu ion s a emen And eia D. San os: In es iga ion, Da a cu a ion, Concep ualiza ion, Fo mal analysis, Valida ion, W i ing - o iginal d a . Jo˜ ao R. Sil a: Da a cu a ion, W i ing – e iew & edi ing. Luis M. Cas o: Concep ualiza ion, Supe ision, Valida ion, W i ing – e iew & edi ing. Rosa M. Quin a-Fe ei a: Concep ualiza ion, Supe ision, W i ing – e iew & edi ing, P ojec adminis a ion, Funding acquisi ion. Decla a ion o compe ing in e es The au ho s decla e ha hey ha e no known compe ing inancial in e es s o pe sonal ela ionships ha could ha e appea ed o in luence he wo k epo ed in his pape . Acknowledgmen s Au ho s g a e ully acknowledge o P oyec o 0745 SYMBIOSIS II 3 E, co inanciado po el FEDER a a ´ es del P og ama INTERREG V A Espa˜ na – Po ugal (POCTEP). Funding INTERREG V-A Espanha-Po ugal (POCTEP) Re e ences [1] Velázquez-Ma í Bo ja, Meneses-Quelal O lando W, Gaibo -Cha ez Juan, Niño-Ruiz Zulay. Re iew o ma hema ical models o he anae obic diges ion p ocess. Anae ob. Diges . 2019;1–20. h p://dx.doi.o g/10.5772/in echopen.80815. [2] File Jameson, Ding Huihuang H, Chang Sheng. Biochemical me hane po en ial (BMP) assay me hod o anae obic diges ion esea ch. Wa e (Swi ze land) 2019;11(5). h p://dx.doi.o g/10.3390/w11050921. [3] Pe e a Yeho , Mille Cha les D, Sims Ronald C. Exis ing empi ical kine ic models in biochemical me hane po en ial (BMP) es ing, hei selec ion and nume ical solu ion. Wa e 2020;12(6):1831. h p://dx.doi.o g/10.3390/w12061831. [4] Pi RE, C oss TL, Pell AN, Scho ield P, Doane PH. Use o in i o gas p oduc ion models in uminal kine ics. Ma h Biosci 1999;159(2):145–63. h p://dx.doi.o g/10.1016/S0025-5564(99)00020-6. [5] Nguyen Dinh Duc, Jeon Byong Hun, Jeung Jae Hoon, Rene Eldon R, Banu J Rajesh, Ra ind an Balasub amani, e al. The mophilic anae obic diges ion o model o ganic was es: E alua ion o biome hane p oduc ion and mul iple kine ic models analysis. Bio esou Technol 2019;280(2018):269–76. h p://dx.doi.o g/10.1016/j.bio ech.2019.02.033. [6] Pi RE, C oss TL, Pell AN, Scho ield P, Doane PH. Use o in i o gas p oduc ion models in uminal kine ics. Ma h Biosci 1999;159(2):145–63. h p://dx.doi.o g/10.1016/S0025-5564(99)00020-6. [7] Akaike Hi o ugu. A new look a he s a is ical model iden i ica ion. IEEE T ans Au oma Con ol 1974;19(6):716–23. h p://dx.doi.o g/ 10.1109/TAC.1974.1100705. 164 A.D. San os, J.R. Sil a, L.M. Cas o e al. Ene gy Repo s 8 (2022) 159–165 [8] Schwa z Gideon. Es ima ing he dimension o a model. Ann S a is 1978;6(2):461–4. [9] P o illidis VA, Bo zo is GN. T end p ojec ion and ime se ies me hods. 2019. [10] Raposo F, Bo ja R, Ma ín MA, Ma ín A, de la Rubia MA, Rincón B. In luence o inoculum-subs a e a io on he anae obic diges ion o sun lowe oil cake in ba ch mode: P ocess s abili y and kine ic e alua ion. Chem Eng J 2009;149(1–3):70–7. h p: //dx.doi.o g/10.1016/j.cej.2008.10.001. [11] Rasmuson Ande s, Ande sson Beng , Olsson Louise, Ande sson Ronnie. Empi ical model building. In: Ma hema ical modeling in chemical enginee ing. Camb idge: Camb idge Uni e si y P ess; 2014, p. 40–52. 165