Analytical Solution of the Mathematical Model of Anaerobic Fermentation in a Flow Bioreactor for Biogas Production

The article briefly considers the current state and prospects for the development of biogas (biomethane) production technologies during organic waste recycling. The relevance of the problem is determined by the fact that the experience of operating biogas complexes in the conditions of the Republic of Belarus during biogas generation only from organic waste has shown low economic efficiency. Atthesametime, solving the importanttaskofrecyclingindustrialandhouseholdwaste while simultaneouslyobtaining an energyresourceandorganicfertilizerisnotonlynecessary,butalso an attractiveresult from boththeenvironmentalandenergy production points. The state of this problem abroad shows the presence of potential for the development of biotechnology in our country both in the technological and in the system-constructive design of biogas complexes. The implementation of this potential in practice presupposes that the developers have an adequate mathematical apparatus describing the transfer processes in bioreactors. An analytical solution of the mathematical model of the organic waste fermentation process is given, which is supposed to be used to study the transfer processes in flow-type biotanks when designing hybrid energy-technological systems for biogas generation using alternative energy sources. It is shownthat the mathematicalmodelobtained as aresult of the analyticalreviewfor the studyis in goodagreementwith the empirical data obtainedtodescribe the continuousoperationof a flow-through bioreactor,andisingoodagreementwith the results of numericalcalculationsofanalyticalmodels by anumber of otherresearchers. Thisanalyticalsolution makes it possible to determine the characteristicdependences of the biogasproductionrate, the dynamics of itsgenerationrate,changes in the concentration of nutrientabsorbed by bacteria,and the concentration of bacteriain a flow-typebioreactordependingon the rate of nutrientsupply to thebioreactor. The obtainedsolutionsareexpected to be usedin the synthesis of controlalgorithms for the developed multi-resourcehybridenergy technology systemforgeneratingandenrichingbiogas of a flow-storagetypeusingalternativeenergysources.