| Even though this research is concerned with the mathematical modelling and computer simulation of fluid displacement in porous media, the techniques behind the computer simulation can be applied to both steady and transient problems in linear and nonlinear systems in fluid flows, heat transfer, and chemical reactor modelling. Moreover, most chemical reactors are cylindrical tubes, so the three-dimensional model was used to simulate the cylindrical reactor. The model selected for multiphase flow through porous media results in two, second-order, nonlinear partial differential equations for which no analytical solution has been found. The weak formulation of the model equations and the algorithm for solving the equations are given. Two numerical techniques are used: The first one, three-dimensional model (TDM), is a quite general type of three-dimensional finite element method. The second one, plug flow model (PFM), is a combination of finite element and finite difference methods. The second technique was developed to reduce the CPU time and memory storage of the first technique. In the three-dimensional model, the manipulations and computer implementations of the three-dimensional finite element is much more complicated than those of the two-dimensional finite element, so the approximate solution by the second technique is shown.; No numerical solution and experimental data for three-dimensional systems of fluid displacement were found in a survey of the literature. Comparisons of computed results of two techniques are shown in this work. The results show that the agreement of two models is acceptable. It requires the interpolation functions for PFM to plot saturation profiles, so the use of the weak formulation of TDM is more feasible. Since the test and trial functions used in PFM are assumed to be functions of x and y only for a three-dimensional system, the solutions of the TDM are more realistic than those from the PFM. When the CPU time and memory storage are being considered, the PFM is recommended for practical and economic reasons. |
