Solution of linear differential equations in chemical kinetics through flow graph theory approach

Abstract

A flow graph theory is a method for finding the analytical solution of linear differential equations which arise in chemical kinetics through Cramer's method of determinants. This article presents the applicability of flow graph theory for deriving the analytical solution of kinetic equations which arise in modeling of complex reaction system such as hydrocracking of heavy oils. A discrete lumped model for hydrocracking of heavy oils was developed and analytical solution for the governing model equations was derived using Laplace transforms earlier. In this work, a new method involving flow graph theory was used instead of Laplace transforms. The kinetic equations which describe the performance of a hydrocracker are governed by linear differential equations and a general analytical solution was successfully derived using flow graph theory. The analytical solution obtained through flow graph theory is similar with the reported solution using Laplace transforms for the kinetic equations of hydrocracking of heavy oils. Furthermore, the relative errors between the experimental data and model calculations using analytical solution of the three lump hydrocracker model are reasonable except for few data points.