MATHEMATICAL MODELS FOR THE KINETICS AND OPTIMISATION OF BANANA TRUNK BIOMASS HYDROLYSIS FOR ETHANOL PRODUCTION

Abstract

Ethanol is a renewable energy which can be used for domestics, automobile and industrial fuel. There is the need to make ethanol cheap from agro wastes. In this Study, Mathematical models were formulated, for the production of ethanol from unpretreated and pretreated banana trunk biomass using the consecutive reaction models where the product of a reaction will be a substrate of another reaction. The kinetics of the different processes was determined and the optimum rate for the production of ethanol from banana trunk biomass was obtained analytically. The optimum revenue was obtained using the formulated revenue model obtained by modifying the Cobb-Douglass model. Necessary and Sufficient conditions for the optimality of the revenue generated were determined using the Karush-Kuhn-Tucker (KKT) condition and the Enigmatic Bordered Hessian respectively. The results from the initial value problem obtained, shows that there is significant effect of kinetic variables on the optimum ethanol yield from banana trunk biomass. The results for the batch and continuous process of pretreated and unpretreated banana trunk biomass shows that continuous process gives higher yield of ethanol for both pretreated and unpretreated, however the continuous process proves more efficient. The formulated revenue model gives optimum revenue of N 19,082 with a profit of N 15,082. The KKT condition resulted to λ≥0, proving the solution to be an optimal point. The Enigmatic Bordered Hessian matrix with principal minor determinants of – 193.20, 1.399740440 x 106 , – 4.7241, – 1.404622276 x 106 , 1.130920568 x 1011 shows an indefiniteness, which means that the formulated model has a saddle point. The work concludes that increasing hydrolysis rate will increase the glucose yield thereby increasing the ethanol yield. Increase in the rate of fermentation reduces the time taken to obtain optimum ethanol yield of 3800kg/L Pilot plants for the production of ethanol from other agro waste should be developed using these models