Mathematical Modeling of Gas Adsorption Processes in Packed Bed: The Role of Numerical Methods on Computation Time

Rigorous mathematical modeling of adsorption processes in packed beds involves time-consuming computations which are considered as the fundamental weakness of such thorough mathematical models. Thus, reducing the computation time was a key factor in improving adsorption mathematical models. In order to achieve this goal, an attempt was made to know how much using different numerical methods influenced the accuracy and time of these computations. For this purpose, the adsorption process of gas mixture consisting of H2O, CO2, CH4 and N2 in a tower packed with Zeolite 5A was considered to be modeled. The mathematical model was simplified based on the fact that neglecting the variations of pressure and temperature had no significant effect on the results of the model. This fact has been confirmed through previous research (M. Gholami & Talaie, 2009). The main objective of this study was to compare the capabilities of two important numerical methods in terms of their computation time and stability. Finite difference and orthogonal collocation were the numerical methods that were taken into account to be examined in solving the governing equations. The results obtained in this study revealed that orthogonal collocation was the best to solve pellet equations, while finite difference was more appropriate for bed equations. As a result, a combined method was suggested to be proper, i.e. orthogonal collocation for solving pellet equations and finite difference for solving bed equations. The results demonstrated that the combined method required half as much computation time as the one in which finite difference method was employed to solve the whole equations.