Development of Mathematical Models and Application of the Modified Gompertz Model for Designing Batch Biogas Reactors

Biogas is a combustible gas produced by the anaerobic digestion of organic matter (biomass) in the absence of oxygen. In this study, mathematical models for the design of batch anaerobic biogas reactors for digesting cattle dungs at ambient temperatures (30 +/- A 3 A degrees C) were developed. Biogas productions from five (5) reactors with varying mass of total solids were monitored for a period of 42 days. It was observed that optimal biogas yield (y (t) ) occurred at volatile solids concentration in the range of 60.0-80.0 g VS/L, which corresponds to 8.0-10.0 % total solids. Optimum biogas yield rates were between 1.44 and 1.64 ml/g VS/day. The modified Gompertz model was used in predicting maximum biogas yield (y (m) ), maximum biogas yield rate (R (m) ), the minimum time taken to produce biogas (lambda), and these were found respectively to be between 68 and 86 ml/g VSloaded, 2.50-2.97 ml/g VSloaded/day and 9.7-12.0 days with goodness of fit ranging from 0.996 to 0.999. A relationship between maximum biogas yield potential and volatile substrate concentration was established to be y(m) = -0.0266[VS](2) + 4.8396[VS] + 129.1. An appropriate application of the developed models would lead to an optimal design of a biogas plant digesting cattle/livestock dungs with biogas and organic fertilizers production for farmers and gardeners alike.