Second-order isothermal reaction in a semi-batch reactor: modeling, exact analytical solution, and experimental verification

Mathematical modeling of semi-batch reactors (SBRs) can help to control the reaction conditions and product properties through tuning the concentration or flow rate of the external feed of reactants. In the present work, an isothermal SBR behavior with irreversible bimolecular type second-order reactions was investigated both mathematically and experimentally. The governing non-linear differential equation was solved analytically using hypergeometric Whittaker functions. The obtained analytical results were compared with numerical and approximate solutions to verify the correctness and accuracy of the exact solution. In order to determine the validity of the mathematical model, a set of experiments were performed in the reactor and the results were compared with the mathematical solution over a wide range of operating conditions by varying the model parameters. It was observed that the analytical solutions are in good agreement with the experimental data. The relative error between the experimental data and the exact analytical solution in the calculation of the reactant concentration inside the reactor was 0.1–0.3% and that for the feed solution was in the range of 0.7–15%. The obtained exact solution can be beneficial to chemical reactor design and control.