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In this study a kinetic model was developed to represent the kinetics of transesterificiation of waste vegetable oil (frying oil) in a batch reactor at different isothermal conditions of 313 K, 323 K, 333 K and 338 K. The reaction occurs in series of 3 steps. Solution to the model was derived using MATLAB the method for solving was done by applying ode solver ode15s which makes use of backward differential formulas known as Gear method was used to solve the equations derived and to simulate kinetic data from literature. The effect of temperature on concentration profile of species and the reaction rate constant was studied for the selected isothermal conditions. Temperature had no effect on formation of triglyceride, alcohol and Methyl ester because the concentration at 313 K, 323 K, 333 K and 338 K were close but temperature favoured the formation of Diglyceride and Monoglyceride. High temperature did not favour formation of glycerol which is the undesired product. The maximum yield of methyl ester for was obtained at 338 K which was 79.97%.and corresponds to what was obtain experimentally from the work of Jisieke (2015).The molar ratio of methanol to oil was held constant at 6:1.the rate constant obtained from the simulation were close to that which is obtainable from the work of Nivea et al. (2008) .The value of the rate constant k2 and k-2 increased as temperature increased.

Transesterificiation is the general term used to describe the important class of organic reactions where an ester is transformed into another ester through interchange of the alcohol to glycerol moiety. This is also described as chemical process by which biodiesel is produced. It is primarily the displacement of alcohol from an ester by another alcohol; the reaction reduces the high viscosity of triglycerides usually present vegetable oil and animal fat. (Orificia et al., 2013). The transesterificiation reaction is an equilibrium reaction and the transformation occurs essentially by mixing the reactants. However, the presence of a catalyst (strong acid, base or alkali metal) accelerates considerably the adjustment of the equilibrium. In order to achieve a high yield of the ester, the alcohol has to be used in excess.
Vegetable oils are oils from feedstock and plants are usually found to contain long chain alkyl (methyl, propyl and ethyl) esters. For this study used frying oil would be used as the oil of interest for the transesterificiation reaction. Some vegetable oils may be in form of a colorless liquid and could be a pale yellow liquid sometimes with distinct taste and odor, their boiling point ranges from 313 0C to 350 and likewise the density is from 800kg/ 961kg/m3 they contain triglyceride in which most of their fatty acids chains are ricinoleate. Oleate and linoleates and other components vegetable oils can be used for domestic purposes and commercial purposes like in the production of soaps, brake fluids and hydraulic, paints, dyes, inks, coatings etc. (Leonor and Forero, 2012).
Vegetable oils are a good source of ricinoleic and oleic acid, this acid is a mono unsaturated, 18-carbon fatty acid ricinoleic acid has a unique characteristic in which its hydroxyl functional……………………

1.1 Aim and Objectives of Study
The aim of this study is to obtain a kinetic model for transesterificiation reaction of frying oil.
The objectives include the following
 Apply model to fit that of a batch reactor at isothermal conditions
 Simulate the reaction using computational software package MATLAB
 Study the effects of temperature on the kinetic rate constant and concentrations of components.
MATLAB is the application applied in this study because it is can be applied to solve complex differential equations It is most suitable for solving differential equations of any kind.
Using MATLAB and the derived model equations can be solved and simulated to obtain results that can be compared to existing results in literature. In obtaining a suitable model of a batch reactor to carry out this reaction certain parameters such as different temperature only at isothermal condition would be considered, therefore to achieve this mass balance equations coupled with rate kinetic rate constants for both the forward and backward reaction will be greatly employed in this study.
1.2 Scope of Work
The scope of this work will cover the following:
 Mass balances on the reacting species
 It will also cover reaction kinetics involved in the transesterificiation reaction of used vegetable oil and methanol.
 Deriving a model which describes the reaction in the batch reactor.

 Use of MATLAB to simulate reaction.
1.3 Justification of Study
This research work is adopted as a result of the increase in need of suitable reactors for reactions like esterification reaction, saponification reaction, hydro-cracking and transesterificiation reaction which is essential in the production of bio fuel.
There has been a major concern about the high rate of exploitation of oil reserves In Nigeria and around the world and the need for alternative fuels arises.
As a new form of energy is been explored, reactors and technology are needed to harness it, this will in turn improve lifestyle of the people, increased productivity in agriculture, improved health care and also a stable economy, therefore there is a need to bring about new reactors that will enhance the exploitation of a new form of energy, .therefore the significance of this study is that it would give a model which describes the reaction in the batch reactor. It would also save the time of carrying out multiple experiments and model would serve a good purpose in the production of biodiesel.
1.4 Problem Statement
The Transesterificiation reaction process of vegetable oil and methanol is applied in the production of Biodiesel, the process is to be optimized to fit the reaction occurring in Batch reactor. The problem to be solved is to obtain the kinetic model and study the effects of temperature on the rate constants (k).

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