Effect of the finite difference solution scheme in a free boundary convective mass transfer model

摘要

Moving boundary mass transfer inside a cylindrical capillary tube was properly represented in a previous work [1], considering no convective effects for the liquid phase. The technique for solving the model was the methodology developed by Illingworth and Golosnoy [2], which transformed the moving boundaries in fixed ones. That model was not adequate to represent the mass transfer inside square capillaries, because convective flow patterns generated by tube corners were not considered. In this work, the convective term was considered in the liquid phase and in the interface equations. Discretisation in liquid phase and interface equations was modified due the inclusion of the new term. Two different solution schemes were used for the finite difference method, applied to the liquid phase. A semi-implicit model, where the terms in the coefficient matrix associated to the concentration (diffusion coefficient and convective term) were evaluated in the previous concentration value; in this way, the finite difference matrix has constant coefficients. A fully implicit model, with those terms evaluated at the present concentration value. In this case, the finite difference matrix has variable coefficients and an additional iterative calculation must be solved until there is no variation in concentration profiles. Results showed that simulation time (10 min), relative error (7.53%) and molar flux ratio (2.98) for semi-implicit model is bigger than the simulation time (6 min), relative error (4.54%) and molar flux ratio (2.2) for fully implicit model. It was concluded that finite difference solution scheme strongly affects the predicted molar flux ratio, but it is not very important for the interface displacement prediction.