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
CHAPTER ONE
1.0 INTRODUCTION
1.1 Background to the Study
Ethanol, a volatile, colorless, flammable chemical produced from petroleum via chemical transformation of ethylene and also by anaerobic fermentation of glucose (known as simple sugar) gotten from starch using yeast or other microorganisms. The primary source of ethanol is grain containing sugar, waste from woods and organic substances (Egwim et al.,2015). Bioethanol (C2H5OH) is derived from hydrolysis and fermentation of glucose from cellulose biomass. It can be produced from the distillation of ethanolic waste gotten from fermentation of cellulosic biomass (Graeme, 2010, Egwim et al., 2015). Understanding the dynamics and inert behavior in the production of ethanol helps to optimisation the product. Fathoming the dynamic and static behavior of ethanol formed in order to control and improve the production of ethanol made from lignocellulosic resources such as agricultural residues (wheat straw, corncob, and paddy straw) (Par and Cardona, 2011). Lignocellulose, contain 10 – 20% lignin, 25 – 30% hemicellulose and 30% – 35% cellulose. They also contain water, protein and lipids (Achinas and Euverink, 2016). Biomass contains approximately 70% of cellulosic and hemicellulosic polymers and are linked to the lignin component through a variety of covalent bonds that give the lignocellulosic biomass significant strength and resistance to biochemical or physical treatment (Achinas and Euverink, 2016).
Ethanol from sugar cane biomass, bagasse, straw and other lignocellulosic materials offer unique environmentally sustainable energy sources, economic strategic benefits and are considered as a safe and cleanest liquid fuel substitute to fossil fuels. lignocellulose biomass can be a cheap raw material with constant supply as a substrate for bioconversion to fuel ethanol (Chin et. al., 2011).
Energy crops such as switch grass and fast-grow trees, and forest resources have been recognized as renewable for industrial applications to produce ethanol and other biofuels (Chin et. al., 2011) Banana trunk biomass is useful as a raw material for ethanol production because it contains sugar with high level of glucose or precursors to glucose (Badger, 2002; Egwim et al., 2015). Historically, fermentation products were mainly food products, but in recent years an increased interest has been observed in the production of bulk chemicals, such as, ethanol and other solvents, specialty chemicals (Pharmaceuticals, industrial enzymes), biofuels and food additives (flavor modifiers). Ethanol from biomass reduces the dependency of the government and industry on fossil fuels; it is cost effective, a cheap alternative for domestic cooking and reduces greenhouse emission (Evans et. al., 2021a).
Computational Engineers apply mathematical optimization in a systematic and efficient way to obtain the best solution for a given problem. In biochemical systems, optimization models are used to simulate results (Evans et. al., 2021a). The two important applications of computational optimization are parameter estimation and design problem (Mendes and Kell, 1998).
1.1.3 Parameter Estimation Method
This is the determination of the optimal parameter as well as calculating the real values of unidentified parameters in a dynamic system centered on experiential input and output data of a system. The experimental results for a set of data are replicated by adjusting the model to obtain the best ways to achieve the set objectives
1.1.4 Experimental Design Problem
Useful in metabolic engineering and biochemical evolution studies, to maximize the variability of interesting products. Experimental design improved metabolic pathways in order to optimize the production of unwanted bye-products.
1.2 Statement of The Research Problem
The rising demand for ethanol either as fuel or for industrial purpose calls for higher production and more efficient bioprocesses. One of the challenges facing human development is sustainable energy crisis. The over dependency on crude oil as source of energy in Nigeria has put the country at a disadvantaged in harnessing or exploring other energy sources. Currently, there are trends in hydrolyzing banana trunk polymers, using enzyme processes to produce fermentable sugars and the fermentable sugar is further converted into ethanol making it a cheap renewable fuel. However, the mathematical model for the optimization of the various parameters leading to the production of cheap ethanol from this abundant and renewable polymer has not been achieved.
1.3 Aim and Objectives
The research aims at determining the rate at which the optimal ethanol production can be achieved for revenue generation.
The objectives are to:
ii. Formulate mathematical models for the kinetics of ethanol production.
iii. Analytically determine the optimal rate constant of ethanol produced from banana trunk biomass.
iv. Optimize the cost of ethanol production.
v. Apply Lagrange multiplier technique to obtain the extreme cost of the revenue subject to a constraint.
1.4 Justification of the Study
Banana trunk biomass is a renewable polymer abundant in nature particularly in Nigeria, as Nigeria is ranked among the highest producers of banana in West Africa Egwim et al., 2015). Banana trunk is a lignocellulosic biomass that is not directly linked to food production (thus avoids food insecurity) and contains high level of cellulose that can be hydrolyzed to simple sugars, so can serve as a potential source of ethanol. The increasing demand in consumption of energy and the attending constituents of price fluctuation necessitates the need to look for alternative source of energy especially from Biomass sources. The development of an applicable mathematical model for ethanol production from cheap agro wastes will encourage greatly the production of ethanol from renewable energy which can complement or substitute the production of ethanol from other sources with comparative cost.
This material content is developed to serve as a GUIDE for students to conduct academic research
MATHEMATICAL MODELS FOR THE KINETICS AND OPTIMISATION OF BANANA TRUNK BIOMASS HYDROLYSIS FOR ETHANOL PRODUCTION
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