New reliable tools to mathematically model chemical reaction systems.

Graphical abstract Highlights • HPM and EHPM can have broad applications in chemical and petroleum engineering. • Multiple reaction systems and reactive absorption are modelled using new reliable tools. • HPM and EHPM offer simple, easy to use, and reliable solutions in reaction systems. • HPM solution exhibits high deviation from exact solution for complex differential equations. • EHPM provides more accurate modeling results than HPM for complicated chemical processes. Abstract There are a variety of chemical reactions and absorption equipment in chemical production plants across the world. Appropriate modelling of chemical reactors and reactive absorption systems is important for simulation, optimization, and scale-up purposes in the process/chemical engineering discipline. In this study, a chemical reactor and a reactive absorption system are modelled through different mathematical methods. The first case includes two unsteady state first-order reactions in series, and the latter system incorporates a first-order reaction and a diffusive mass transfer phenomenon. The concentration distribution for these two different cases is attained using Homotopy Perturbation Method (HPM) and Enhanced Homotopy Perturbation Method (EHPM) as an efficient, straightforward, and precise technique to solve differential equations. The primary approximation is generally selected with some unknown constant parameters, which can be obtained through applying the initial and boundary conditions. The solution is eventually attained in the form of power series. The modelling results obtained from HPM and EHPM are compared to the outputs attained from the available analytical solutions. The comparison implies that EHPM has a higher capability to provide proper solutions for the governing equations of both reaction cases in this study with a reasonable accuracy. EHPM appears suitable in several cases to obtain approximate analytical solutions where the governing transport phenomena equations in various chemical engineering processes lead to complicated differential equations. This research work introduces a systematic and efficient modelling procedure to properly capture important aspects such as reaction progress, concentration distribution, and phase change in complex transport phenomena systems. [ABSTRACT FROM AUTHOR]