Analytic solution of nonlinear batch reaction kinetics equations

Abstract

The classical nonlinear reaction kinetics equations are solved using an analytic technique for solving nonlinear problems known as the homotopy analysis method. An explicit analytic solution for the concentration of reactants and products that is uniformly valid for all times is presented. Numerical simulations based on Runge--Kutta initial value problem solvers verify our analytic solutions with good agreement. References D. W. T. Rippin, Simulation of single andmultiprod uct batch chemical plants for optimal design and operation, Computers and Chemical Engineering, 7, (3), 1983, 137--156. doi:10.1016/0098-1354(83)85016-9 M. Friedrich and R. Perne, Design and control of batch reactorsó an industrial viewpoint, Computers and Chemical Engineering, 19s, 1995, S357--S368. doi:10.1016/0098-1354(95)87063-6 Y. Kawarasai, T. Kawai, H. Nakano and T. Yamane, A long-lived batch reaction system of a cell-free protein synthesis, Analytical, Biochemistry, 226, 1995, 320--324. M. Fulcher, J. 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