The present study aimed to propose a general model for absorption with a non-elementary chemical reaction. The modeling of the system was conducted within the stagnant liquid film surrounding bubbles in the bubble column reactor. The finite difference method was used to solve the governing differential equations. The model was solved for the general reaction orders of components with a general boundary condition. Therefore, it includes all kinetic regimes based on the film theory and is capable of predicting the absorption system with a complex reversible or irreversible chemical reaction. Further, the effects of different parameters such as the equilibrium constant, the concentration of components, and chemical reaction orders on the absorption enhancement were investigated. The results indicated that the initial concentration and reaction order of components can significantly influence the absorption enhancement. Finally, In order to validate the model, the results were compared with those of the previous studies. (C) 2020 Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.