Mathematical Modelling of Zinc-Induced Inhibition on Fermentative Biohydrogen Production by Granular Sludge
DOI:
https://doi.org/10.54987/jebat.v8i1.1126Keywords:
Biohydrogen, Anaerobic granular sludge, Predictive models, MOORA, MMF modelAbstract
Biohydrogen production in anaerobic granular sludge reactors has led to the development of stable microbial communities that enhance substrate conversion rates. The fermentation process of sucrose by these microbial communities is a sustainable approach to hydrogen production, making biological dark fermentation an effective method for renewable biohydrogen generation. This study analyzed biohydrogen production data from granular sludge in a packed-bed upflow reactor processing sucrose-containing wastewater at 26 °C for more than 500 days, using multiple predictive kinetic models. The biohydrogen production data were converted to natural logarithms to improve linearity and reduce variance. The Morgan–Mercer–Flodin (MMF) model, coupled with the Multi-Objective Optimization by Ratio Analysis (MOORA) approach, achieved the best statistical results among nine tested predictive models based on error functions, including the highest adjusted R² value and the lowest RMSE, AICc, BIC, and HQC values. The MMF model successfully predicted all stages of hydrogen production sigmoidal growth while also modeling zinc-induced stimulation and inhibition effects. The combination of multi-criteria analysis (MOORA) with classical error-function analyses improved model discrimination, enabling a deeper understanding of microbial growth patterns under different environmental conditions to optimize biohydrogen production systems.
References
Elbeshbishy E, Dhar BR, Nakhla GF, Lee HS. A critical review on inhibition of dark biohydrogen fermentation. Renew Sustain Energy Rev. 2017;79:656-68.
Zheng H, Zeng RJ, Angelidaki I. Biohydrogen production from glucose in upflow biofilm reactors with plastic carriers under extreme thermophilic conditions (700C). Biotechnol Bioeng. 2008;100(5):1034-8.
Levin DB, Carere RC, Çiçek N, Sparling RR. Challenges for biohydrogen production via direct lignocellulose fermentation. Int J Hydrog Energy. 2009;34(17):7390-403.
Bielen AAM, Verhaart MRA, van der Oost J, Kengen SWM. Biohydrogen production by the thermophilic bacterium Caldicellulosiruptor saccharolyticus: Current status and perspectives. Life. 2013;3(1):52-85.
Tunca B, Kutlar FE, Kas A, Yilmazel YD. Enhanced biohydrogen production from high loads of unpretreated cattle manure by cellulolytic bacterium Caldicellulosiruptor bescii at 75 °C. Waste Manag. 2023;171:401-10.
Pachapur VL, Sarma SJ, Brar SK, Le Bihan Y, Buelna G, Verma M. Biohydrogen production by co-fermentation of crude glycerol and apple pomace hydrolysate using co-culture of Enterobacter aerogenes and clostridium butyricum. Bioresour Technol. 2015;193:297-306.
Goud RK, Raghavulu SV, Mohanakrishna G, Naresh K, S. VM. Predominance of Bacilli and Clostridia in microbial community of biohydrogen producing biofilm sustained under diverse acidogenic operating conditions. Int J Hydrog Energy. 2012;37(5):4068-76.
García-Depraect O, Rene ER, Diaz-Cruces VF, León-Becerril E. Effect of process parameters on enhanced biohydrogen production from tequila vinasse via the lactate-acetate pathway. Bioresour Technol. 2019;273:618-26.
Sarkar O, Rova U, Christakopoulos PF, Matsakas L. Continuous biohydrogen and volatile fatty acids production from cheese whey in a tubular biofilm reactor: Substrate flow rate variations and microbial dynamics. Int J Hydrog Energy. 2024;59:1305-16.
El-Dalatony MM, Zheng Y, Ji M, Li X, Salama ES. Metabolic pathways for microalgal biohydrogen production: Current progress and future prospectives. Bioresour Technol. 2020;318.
Monlau F, Aemig Q, Trably E, Hamelin J, Steyer JP, Carrère H. Specific inhibition of biohydrogen-producing Clostridium sp. after dilute-acid pretreatment of sunflower stalks. Int J Hydrog Energy. 2013;38(28):12273-82.
Rai P, Pandey AC, Pandey A. Optimization of sugar release from banana peel powder waste (BPPW) using box-behnken design (BBD): BPPW to biohydrogen conversion. Int J Hydrog Energy. 2019;44(47):25505-13.
Brynjarsdóttir H, Scully SM, Örlygsson J. Production of biohydrogen from sugars and lignocellulosic biomass using Thermoanaerobacter GHL15. Int J Hydrog Energy. 2013;38(34):14467-75.
Zheng G, Kang Z, Qian Y, Wang L, Zhou Q, Zhu H. Biohydrogen production from tofu wastewater with glutamine auxotrophic mutant of Rhodobacter sphaeroides. In: AIP Conference Proceedings. 2008. p. 143-8.
García AB, Cammarota MC. Biohydrogen production from pretreated sludge and synthetic and real biodiesel wastewater by dark fermentation. Int J Energy Res. 2019;43(4):1586-96.
Park J hoon, Yoon JJ, Park H, Kim Y, Lim D jung, Kim SH. Feasibility of biohydrogen production from Gelidium amansii. Int J Hydrog Energy. 2011;36(21):13997-4003.
van Ginkel SW, Logan BE. Inhibition of biohydrogen production by undissociated acetic and butyric acids. Environ Sci Technol. 2005;39(23):9351-6.
Tang J, Yuan Y, Guo W, Ren N. Inhibitory effects of acetate and ethanol on biohydrogen production of Ethanoligenens harbinese B49. Int J Hydrog Energy. 2012;37(1):741-7.
Alam M, Mostafa A, Dhar BR. Impact of petroleum versus bio-based nano/microplastics on fermentative biohydrogen production from sludge. Int J Hydrog Energy. 2024;94:959-70.
Tratzi P, Ta DT, Zhang Z, Torre M, Battistelli F, Manzo E, et al. Sustainable additives for the regulation of NH3 concentration and emissions during the production of biomethane and biohydrogen: A review. Bioresour Technol. 2022;346.
Salerno MB, Park W, Zuo Y, Logan BE. Inhibition of biohydrogen production by ammonia. Water Res. 2006;40(6):1167-72.
Chae KJ, Choi M, Kim KY, Ajayi FF, Chang IS, Kim IS. Selective inhibition of methanogens for the improvement of biohydrogen production in microbial electrolysis cells. Int J Hydrog Energy. 2010;35(24):13379-86.
Hafez H, Elbeshbishy E, Nakhla GF, El Naggar HM. Simulating the impact of suppression of methanogenesis in continuous flow biohydrogen reactors. Int J Hydrog Energy. 2011;36(10):5885-94.
Nemestóthy N, Bakonyi P, Rózsenberszki T, Kumar G, Koók L, Kelemen G, et al. Assessment via the modified gompertz-model reveals new insights concerning the effects of ionic liquids on biohydrogen production. Int J Hydrog Energy. 2018;43(41):18918-24.
Frascari D, Cappelletti M, Mendes JDS, Alberini A, Scimonelli F, Manfreda C, et al. A kinetic study of biohydrogen production from glucose, molasses and cheese whey by suspended and attached cells of Thermotoga neapolitana. Bioresour Technol. 2013;147:553-61.
Mohanty K, Das D. Kinetics of biohydrogen production by dark fermentation processes. 2012;127-36.
Halmi MIE, Syed MA, Shamaan NA, Shukor MY. Mathematical Modeling of Molybdenum Reduction to Molybdenum Blue by Burkholderia sp. Strain Dr.Y27 and Model Selection Using the MOORA Method. J Environ Bioremediation Toxicol. 2024 Dec 26;7(2):17-24.
Barik T, Parida S, Pal K. Optimizing Process Parameters in Drilling of CFRP Laminates: A Combined MOORA-TOPSIS-VIKOR Approach. Fibers Polym. 2024 May 1;25(5):1859-76.
Brauers W. Multi-objective seaport planning by MOORA decision making. Ann Oper Res. 2013 July 1;206.
Brauers WKM, Zavadskas EK, Peldschus F, Turskis Z. Multi?objective decision?making for road design. Transport. 2008 Jan 1;23(3):183-93.
Li C, Fang HHP. Inhibition of heavy metals on fermentative hydrogen production by granular sludge. Chemosphere. 2007 Mar;67(4):668-73.
Motulsky HJ, Ransnas LA. Fitting curves to data using nonlinear regression: a practical and nonmathematical review. FASEB J. 1987;1(5):365-74.
Ross T. Indices for performance evaluation of predictive models in food microbiology. J Appl Bacteriol. 1996;81(5):501-8.
Akaike H. A New Look at the Statistical Model Identification. IEEE Trans Autom Control. 1974;19(6):716-23.
Burnham KP, Anderson DR. Multimodel inference: Understanding AIC and BIC in model selection. Sociol Methods Res. 2004;33(2):261-304.
Schwarz G. Estimating the Dimension of a Model. Ann Stat. 1978;6(2):461-4.
Hannan EJ, Quinn BG. The Determination of the Order of an Autoregression. J R Stat Soc Ser B Methodol. 1979;41(2):190-5.
Ezekiel M. The Sampling Variability of Linear and Curvilinear Regressions: A First Approximation to the Reliability of the Results Secured by the Graphic 'Successive Approximation' Method. Ann Math Stat. 1930;1(4):275-333.
Marquardt DW. An Algorithm for Least-Squares Estimation of Nonlinear Parameters. J Soc Ind Appl Math. 1963;11(2):431-41.
Seidel A, Gelbin D. On applying the ideal adsorbed solution theory to multicomponent adsorption equilibria of dissolved organic components on activated carbon. Chem Eng Sci. 1988 Jan 1;43(1):79-88.
Porter JF, McKay G, Choy KH. The prediction of sorption from a binary mixture of acidic dyes using single- and mixed-isotherm variants of the ideal adsorbed solute theory. Chem Eng Sci. 1999;54(24):5863-85.
Karel W, Brauers W, Zavadskas E. The MOORA method and its application to privatization in a transition economy. Control Cybern. 2006 Jan 1;35.
Shukor MY. Chitosan-Silica Composite Aerogel for the Adsorption of Cupric Ions: Isothermal Remodeling and MOORA-Based Model Selection. J Environ Microbiol Toxicol. 2024 Dec 26;12(2):53-62.
McClure PJ, Cole MB, Davies KW. An example of the stages in the development of a predictive mathematical model for microbial growth: the effects of NaCl, pH and temperature on the growth of Aeromonas hydrophila. Int J Food Microbiol. 1994;23(3-4):359-75.
Karthic P, Joseph S, Arun N, Varghese LA, Santhiagu A. Biohydrogen production using anaerobic mixed bacteria: Process parameters optimization studies. J Renew Sustain Energy. 2013;5(6).
Baranyi J, Roberts TA. A dynamic approach to predicting bacterial growth in food. Int J Food Microbiol. 1994;23(3-4):277-94.
Agarry SE, Audu TOK, Solomon BO. Substrate inhibition kinetics of phenol degradation by Pseudomonas fluorescence from steady state and wash-out data. Int J Environ Sci Technol. 2009;6(3):443-50.
Othman AR, Bakar NA, Halmi MIE, Johari WLW, Ahmad SA, Jirangon H, et al. Kinetics of molybdenum reduction to molybdenum blue by Bacillus sp. strain A.rzi. BioMed Res Int. 2013;2013:Article number 371058.
Abubakar A, Uba G, Biu HA. Kinetics Modelling of Pseudomonas stutzeri strain DN2 Growth Behaviour in Tributyltin Chloride. J Environ Microbiol Toxicol. 2021 Dec 31;9(2):13-8.
Arroyo-López FN, Bautista-Gallego J, Durán-Quintana MC, Garrido-Fernández A. Modelling the inhibition of sorbic and benzoic acids on a native yeast cocktail from table olives. Food Microbiol. 2008 June 1;25(4):566-74.
Baty F, Delignette-Muller ML. Estimating the bacterial lag time: Which model, which precision? Int J Food Microbiol. 2004;91(3):261-77.
Buchanan RL. Developing and distributing user-friendly application software. J Ind Microbiol. 1993;12(3-5):251-5.
Morgan PH, Mercer LP, Flodin NW. General model for nutritional responses of higher organisms. Proc Natl Acad Sci. 1975 Nov 1;72(11):4327-31.
Santos SA, Souza G da S e, Oliveira MR de, Sereno JR. Uso de modelos não-lineares para o ajuste de curvas de crescimento de cavalos pantaneiros. Pesqui Agropecuária Bras. 1999 July;34(7):1133-8.
Topal M, Bolukbasi ?C. Comparison of nonlinear growth curve models in broiler chickens. J Appl Anim Res. 2008 Dec 1;34(2):149-52.
Tariq M, Iqbal F, Eyduran E, Bajwa M, Huma Z, Waheed A. Comparison of nonlinear functions to describe the growth in Mengali sheep breed of Balochistan. Pak J Zool. 2013 June 1;45:661-5.
Augustine A, Imelda J, Paulraj R, David NS. Growth kinetic profiles of Aspergillus niger S14 a mangrove isolate and Aspergillus oryzae NCIM 1212 in solid state fermentation. Indian J Fish. 2015;62(3):100-6.
Kemper CM. Growth and development of the brush-tailed rabbit-rat (Conilurus penicillatus), a threatened tree-rat from northern Australia. Aust Mammal. 2020 June 5;
Yahuza S, Sabo IA. Mathematical Modelling of the Growth of Bacillus cereus Strain wwcp1on Malachite Green Dye. J Biochem Microbiol Biotechnol. 2021 Dec 31;9(2):25-9.
Giacon TG, de Gois e Cunha GC, Eliodório KP, Oliveira RP de S, Basso TO. Homo- and heterofermentative lactobacilli are distinctly affected by furanic compounds. Biotechnol Lett. 2022 Dec 1;44(12):1431-45.
Tomulescu C, Moscovici M, Stoica R, Albu G, Sevcenco C, Vamanu A. Investigation of culture conditions by Response Surface Methodology and kinetic modeling for exopolysaccharide production by Klebsiella oxytoca ICCF 419 strain, using lactose as substrate. Romanian Biotechnol Lett. 2020 Aug 18;25:2033-44.
Carvalho ÂR, Genz Bazana LC, Ferrão MF, Fuentefria AM. Curve fitting and linearization of UV-Vis spectrophotometric measurements to estimate yeast in inoculum preparation. Anal Biochem. 2021 July 15;625:114216.
Khamis A, Ismail Z, Haron K, Mohammed AT. Nonlinear Growth Models for Modeling Oil Palm Yield Growth. J Math Stat. 2005 Sept 30;1(3):225-33.
Germec M, Turhan I. Ethanol production from acid-pretreated and detoxified tea processing waste and its modeling. Fuel. 2018 Nov 1;231:101-9.
Aisami A, Shukor MYA. Predictive Mathematical Modelling of the Total Number of COVID-19 Cases for the Kingdom of Saudi Arabia. J Environ Microbiol Toxicol. 2020 July 31;8(1):11-5.
Yahuza S, Sabo IA, Dan-Iya BI, Shukor MYY. Prediction of Cumulative Death Cases in Nigeria Due to COVID-19 Using Mathematical Models. Bull Environ Sci Sustain Manag. 2020 July 31;4(1):20-4.
Shukor MYA, Sabo IA, Yahuza S, Dan-Iya BI, Wada SA. Prediction of Cumulative Death Cases in The United States Due to COVID-19 Using Mathematical Models. J Environ Microbiol Toxicol. 2020 July 31;8(1):37-41.
Uba G, Yakasai HM, Abubakar A, Shukor MYY. Prediction of Cumulative Death Cases in Brazil Due to Covid-19 Using Mathematical Models. Bull Environ Sci Sustain Manag. 2020 July 31;4(1):13-9.
Yakasai HM, Shukor MYA. Predictive Mathematical Modelling of the Total Number of COVID-19 Cases for The United States. Bioremediation Sci Technol Res. 2020 July 31;8(1):11-6.
Aisami AB, Umar AM, Shukor MYA. Prediction of Cumulative Death Cases in Indonesia Due to COVID-19 Using Mathematical Models. Bioremediation Sci Technol Res. 2020 July 31;8(1):32-6.
Rusnam, Syafrawati S, Khayat ME, Nasution FI, Yakasai HM, Abubakar A. Primary Mathematical Modeling of the Growth of SDS by a bacterium Isolated From a Paddy Field. J Environ Microbiol Toxicol. 2024 July 31;12(1):23-30.
Wijeratne AW, Karunaratne JA. Morgan-Mercer-Flodin model for long term trend analysis of currency exchange rates of some selected countries. Int J Bus Excell. 2013 Dec 2;7(1):76-87.
Manogaran M, Othman AR, Shukor MY, Halmi MIE. Modelling the Effect of Heavy Metal on the Growth Rate of an SDS-degrading Pseudomonas sp. strain DRY15 from Antarctic soil. Bioremediation Sci Technol Res. 2019 July 31;7(1):41-5.
Shukor MS, Shukor MY. Bioremoval of toxic molybdenum using dialysis tubing. Chem Eng Res Bull. 2015;18(1):6-11.
Sevinç P, Gündüz U, Eroglu I, Yücel M. Kinetic analysis of photosynthetic growth, hydrogen production and dual substrate utilization by Rhodobacter capsulatus. Int J Hydrog Energy. 2012;37(21):16430-6.
Dalgaard P. Modelling of microbial activity and prediction of shelf life for packed fresh fish. Int J Food Microbiol. 1995;26(3):305-17.
Beckers L, Masset J, Hamilton C, Delvigne F, Toye D, Crine MD, et al. Investigation of the links between mass transfer conditions, dissolved hydrogen concentration and biohydrogen production by the pure strain Clostridium butyricum CWBI1009. Biochem Eng J. 2015;98:18-28.
Mamimin C, Prasertsan P, Kongjan P, O-Thong S. Effects of volatile fatty acids in biohydrogen effluent on biohythane production from palm oil mill effluent under thermophilic condition. Electron J Biotechnol. 2017;29:78-85.
Khanna N, Kotay SM, Jose Gilbert J, Das D. Improvement of biohydrogen production by Enterobacter cloacae IIT-BT 08 under regulated pH. J Biotechnol. 2011;152(1-2):9-15.
Song Y, Lu Y, Yu L. Stoichiometry and Thermodynamic Analysis on Biohydrogen Production from Xylose by Klebsiella oxytoca GS-4-08. Energy Fuels. 2019;33(1):356-61.
Luxem KE, Nguyen AJ, Zhang X. Biohydrogen production relationship to biomass composition, growth, temperature and nitrogenase isoform in the anaerobic photoheterotrophic diazotroph Rhodopseudomonas palustris. Int J Hydrog Energy. 2022;47(66):28399-409.
Zheng G, Kang Z, Qian Y, Wang L. Enhanced biohydrogen generation from organic wastewater containing NH4+ by phototrophic bacteria Rhodobacter sphaeroides AR-3. Front Environ Sci Eng China. 2009;3(4):387-92.
Ho K, Chen Y, LEE DJ. Biohydrogen production from cellobiose in phenol and cresol-containing medium using Clostridium sp. R1. Int J Hydrog Energy. 2010;35(19):10239-44.
Hsieh P, Lai YC, Chen K, Hung CH. Explore the possible effect of TiO2 and magnetic hematite nanoparticle addition on biohydrogen production by Clostridium pasteurianum based on gene expression measurements. Int J Hydrog Energy. 2016;41(46):21685-91.
Dreschke G, Papirio S, Sisinni DMG, Lens PNL, Esposito G. Effect of feed glucose and acetic acid on continuous biohydrogen production by Thermotoga neapolitana. Bioresour Technol. 2019;273:416-24.
Ciranna A, Ferrari R, Santala VP, Karp MT. Inhibitory effects of substrate and soluble end products on biohydrogen production of the alkalithermophile Caloramator celer: Kinetic, metabolic and transcription analyses. Int J Hydrog Energy. 2014;39(12):6391-401.
Dhar BR, Elbeshbishy E, Nakhla GF. Influence of iron on sulfide inhibition in dark biohydrogen fermentation. Bioresour Technol. 2012;126:123-30.
Zheng G, Wang L, Kang Z. Feasibility of biohydrogen production from tofu wastewater with glutamine auxotrophic mutant of Rhodobacter sphaeroides. Renew Energy. 2010;35(12):2910-3.
Pakpour F, Mohammadi M, Najafpour-Darzi G. Effect of ferric citrate on biohydrogen production from syngas using rhodopseudomonas palustris PT. Middle East J Sci Res. 2013;14(9):1242-6.
Pekgöz G, Gündüz U, Ero?lu I, Yücel M, Kovács KL, Ra´khely G. Effect of inactivation of genes involved in ammonium regulation on the biohydrogen production of Rhodobacter capsulatus. Int J Hydrog Energy. 2011;36(21):13536-46.
Knutson CM, Plunkett MH, Liming RA, Barney BM. Efforts toward optimization of aerobic biohydrogen reveal details of secondary regulation of biological nitrogen fixation by nitrogenous compounds in Azotobacter vinelandii. Appl Microbiol Biotechnol. 2018;102(23):10315-25.
Oh YK, Seol E, Kim J, Park S. Fermentative biohydrogen production by a new chemoheterotrophic bacterium Citrobacter sp. Y19. Int J Hydrog Energy. 2003;28(12):1353-9.
Goud RK, Sarkar O, Chiranjeevi P, S. VM. Bioaugmentation of potent acidogenic isolates: A strategy for enhancing biohydrogen production at elevated organic load. Bioresour Technol. 2014;165(C):223-32.
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