As the first step, simple model using chemical reaction rates equations was developed and constructed a system of differential equations. Chemical equilibrium equation incorporating reaction rate was included in system for each chemical reaction. A four-factor design was proposed to study the effect of reaction temperature, H2/CO, oil selectivity, and syngas conversion. A mathematical model for flow conditions inside the FT reactor was developed to simulate the chemical reaction process. Values for some of the reaction rates are the uncertainties of the model and the aim of the work is to find optimum values and validate with experimental results.
The solution of the system gives us concentration of all chemical species as a function of time. Final values of the concentrations and convert them to appropriate quantities to compare with experimental data. An objective function is defined as errors between measured and simulated values. Objective function value close to zero indicates a good fit. Optimization problem was setup using MATLAB with the defined objective function to find an optimum set of values for the uncertain reaction rates.
Developed mathematical model with optimized values were evaluated with results obtained for Oil production with temperature. It shows close agreement with experimental data.