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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.

Tarballs, which are lumps of oil weathered to solid sticky species, are mainly originated from offshore petroleum activities such as drilling, production, and maintenances. Removing them from water contaminated surfaces is not an easy separation process. Hence, it seems necessary to appropriately characterize them and to find an effective removal method to diminish their concentration in targeted beaches and oceans/seas. Besides the experimental work, a population balance model is developed to obtain the evolution of tarball aggregates size distribution in this study. The model predictions are compared to the experimental results, which are determined by an image analysis technique. The comparison shows a satisfactory agreement, implying the reliability and accuracy of the developed model. The model considers the fractal nature of the tarball aggregates so that the fractal dimension is calculated to be 1.9. The impact of poloxamine copolymer on the evolution of the size distribution of tarball aggregates is investigated. It is found that with increasing the concentration of poloxamine from 0 to 16.67 and 33.33 g/L, the average particle size increases from 90 to 99 and 155 μm, respectively. The number of the particles for an average diameter is determined through an experimental procedure. The average diameter increases with time before the steady state condition is achieved. It then lowers to become almost constant. This study can provide a systematic procedure to characterize tarballs, leading to finding an efficient technique for elimination of tarballs.