Mathematical model of the whey and cow manure co-digestion process

Anaerobna razgradnja (digestija) učinkovita je i ekološki prihvatljiva tehnologija oporabe energije iz biorazgradivog organskog otpada. Osnovni produkt procesa anaerobne razgradnje je bioplin, a proces se u pravilu provodi tako da se kao izvor biorazgradivog organskog otpada upotrebljavaju dva ili više različitih supstrata te u tom slučaju govorimo o kodigestiji. Uobičajeni supstrati u procesu anaerobne digestije koja se provodi u svrhu proizvodnje bioplina su poljoprivredni otpad, otpad iz stočarstva te u zadnje vrijeme možda i najzanimljiviji supstrat – biorazgradiva frakcija komunalnog otpada. U ovom radu analiziran je matematički model procesa kodigestije sirutke i goveđe gnojovke. Ovaj matematički model procesa uzima u obzir specifičan sastav supstrata koji se sastoji od ugljikohidrata, proteina i lipida. Kinetika biokemijskih procesa koji se provode tijekom hidrolize celuloze, proteina i lipida opisana je kinetičkim izrazima za reakciju prvog reda. Kinetika biotransformacija tijekom acidogeneze (fermentacije) šećera i aminokiselina, acetogeneze (anaerobne oksidacije) dugolančanih masnih kiselina, acetogeneze hlapivih masnih kiselina, metanogeneze octene kiseline i metanogeneze vodika opisana je pomoću nestrukturnog Monodovog modela, uključujući razne inhibicijske učinke. Rezultirajući matematički model procesa numerički je riješen pomoću programskog paketa Wolfram Mathematica 10.0. Rezultati simulacije matematičkog modela procesa korišteni su za predviđanje dinamičke promjene koncentracije metana u bioplinu, a metan je izabran kao mjerodavna komponenta jer ima najveći udio u sastavu bioplina dobivenom kodigestijom iz sirutke i goveđe gnojovke. Za određivanje stupnja nesigurnosti predmetnoga kompleksnoga matematičkog modela procesa korištene su metode analize osjetljivosti. Metodama analize osjetljivosti, koje mogu biti lokalne i globalne, određuje se u kolikoj mjeri neodređenost ulaznih čimbenika utječe na neodređenost izlaznih čimbenika matematičkog modela procesa. Analize osjetljivosti matematičkog modela procesa razgradnje sirutke i goveđe gnojovke pokazale su da u pravilu samo jedan kinetički parametar ima dominantan utjecaj na koncentraciju supstrata i brzinu reakcija pojedinih faza anaerobnog procesa.Anaerobic digestion (digestion) is an efficient and environmentally acceptable energy recovery technology where biodegradable organic waste was used as a substrate. The basic product of the anaerobic digestion process is biogas, and the process is generally carried out by using two or more different substrates. In this case we are talking about the codigestion. The conventional substrates in the anaerobic digestion process that are being carried out for the purpose of biogas production are agricultural waste, cattle-breeding waste, and the most interesting one - biodegradable fraction of municipal waste. In this work a mathematical model of the codigestion process of whey and cow manure has been studied. The model takes into account the specific composition of the substrate, which consists of carbohydrates, proteins and lipids. The kinetics of biochemical processes that are carried out during the hydrolysis of cellulose, proteins and lipids are described by kinetic terms for the first order reaction. Kinetics of biotransformation during acidogenesis (fermentation) of sugar and amino acids, acetogenesis (anaerobic oxidation) of long-chain fatty acids, acetogenesis of volatile acids, acetic acid methanogenesis and hydrogen methanogenesis are described by a non-structural Monod model, including various inhibitory effects. The resulting mathematical model of the process is numerically solved using the Wolfram Mathematica 10.0 software package. The results of the simulation of the mathematical model of the process were used to predict the dynamic change of methane concentration in the biogas. Methane was chosen as the relevant component because it has the largest fraction of biogas produced by codigestion of whey and cow manure. Sensitivity analysis methods were used to determine the degree of uncertainty of the complex mathematical model of the process analyzed in this study. Sensitivity analysis methods, which can be local and global, determine to what extent the uncertainty of input factors affects the uncertainty of the output factors of the mathematical model of the process. Based on the simulation of anaerobic codigestion of whey and cow manure, sensitivity analysis was performed. The analysis have shown that mainly the change in the value of a single kinetic parameter affects the substrate concentration and the rate of reaction