Two Optimization Methods to Determine the Rate Constants of a Complex Chemical Reaction Using FORTRAN and MATLAB

Abstract

Problem statement: For chemical reactions, the determination of the rate constants is both very difficult and a time consuming process. The aim of this research was to develop computer programs for determining the rate constants for the general form of any complex reaction at a certain temperature. The development of such program can be very helpful in the control of industrial processes as well as in the study of the reaction mechanisms. Determination of the accurate values of the rate constants would help in establishing the optimum conditions of reactor design including pressure, temperature and other parameters of the chemical reaction. Approach: From the experimental concentration-time data, initial values of rate constants were calculated. Experimental data encountered several types of errors, including temperature variation, impurities in the reactants and human errors. Simulations of a second order consecutive irreversible chemical reaction of the saponification of diethyl ester were presented as an example of the complex reactions. The rate equations (system of simultaneous differential equations) of the reaction were solved to get the analytical concentration versus time profiles. The simulation results were compared with experimental results at each measured point. All deviations between experimental and calculated values were squared and summed up to form a new function. This function was fed into a minimizer routine that gave the optimal rate constants. Two optimization techniques were developed using FORTRAN and MATLAB for accurately determining the rate constants of the reaction at certain temperature from the experimental data. Results: Results showed that the two proposed programs were very efficient, fast and accurate tools to determine the true rate constants of the reaction with less 1% error. The use of the MATLAB embedded subroutines for simultaneously solving the differential equations and minimization of the error function was very fast in solving such problems, as compared to the FORTRAN program, which, although resulting in fast and accurate results, yet, requiring the use of a library of external subroutines. Conclusion: Any of the two proposed methodologies could be used to determine the rate constants of any complex reaction at a certain temperature. The proposed programs were independent of the nature of the reaction, only the rate equations and the initial conditions had to be modified for any new reaction.