A Numerical Study of the Performance of Unstable Displacements in Heterogeneous Media
Creators: name: Khataniar, Santanu
Publisher: name: The University of Texas at Austin
Year: 1991
Subjects: Heterogeneous media
Finite element method

description: The finite difference method (FDM) and the finite element method (FEM) are the commonly used numerical methods in reservoir simulation. The first objective of this study was to perform a detailed comparison of the two methods for simulating multiphase flow in porous media. The FDM with three point central differencing and the Galerkin FEM were used to simulate both non-compositional and compositional unstable displacements in homogeneous and heterogeneous porous media. The performance of the two methods was compared on the basis of accuracy and computational efficiency. The results showed that in homogeneous media, the FEM with Gaussian quadrature was more accurate than the FEM with Lobatto quadrature and the FDM. In heterogeneous media, the FEM with Gaussian quadrature suffered from numerical oscillations. The FEM with Lobatto quadrature was stable in heterogeneous media, but it produced results nearly identical to those obtained by the FDM. The FEM was slower than the FDM to varying extents, depending on the problem being simulated. Thus, the FDM was found to be superior to the FEM for simulating multiphase flow in heterogeneous media. The second objective of this study was to investigate the effects of reservoir heterogeneity, viscosity ratio, and gravity segregation on the performance of unstable displacements by suitable numerical methods. Several heterogeneous media were generated geostatistically and characterized systematically by a set of heterogeneity parameters. Immiscible, first-contact miscible (FCM), and multi-contact miscible (MCM) displacements were then simulated in these porous media with different viscosity ratios and different conditions of gravity segregation. The simulation results showed that heterogeneity always reduced the efficiency of a displacement. The severity of this detrimental effect depended on the character of the heterogeneity. The effect of heterogeneity was more pronounced in the adverse viscosity ratio displacements than in the favorable viscosity ratio displacements. Gravity segregation was found to have a detrimental effect on the displacement performance only when the heterogeneity levels were low. In all cases, FCM displacements performed the best, immiscible displacements performed the worst, and MCM displacements were intermediate between the two. Thus, the ultimate goal of designing a reservoir displacement should be to achieve total miscibility as quickly as possible. The final objective of this study was to make a preliminary comparison of the simulated and the experimental results. Immiscible and FCM displacement experiments were conducted in unconsolidated sandpacks. The spatial fluid distributions inside the sandpacks were obtained by computed tomography (CT} imaging. A comparison of the experimental fluid distributions and recovery curves with their simulated counterparts showed good qualitative agreement. This indicates the feasibility of using the simulation methods of this study to effectively duplicate the characteristic features of reservoir displacements.