A Novel Approach for Incorporating Physical Dispersion in Miscible Displacement

Abstract

TX 75083-3836, U.S.A., fax 01-972-952-9435. AbstractPhysical dispersion is one of the main mechanisms responsible for controlling the gas-oil mixing that occurs in a miscible flood process. Many conventional reservoir simulators do not explicitly account for the physical dispersion and presume that it may be compensated by numerical dispersion arising out of the finite difference scheme with single point upstream weighting of mobilities for the reservoir grid block sizes used in field-scale simulations. This assumption may lead to erroneous results.The multi-point flux approximation (MPFA) schemes developed in recent years provide improved treatment of the convective flux and allow the handling of tensorial permeabilities for non-uniform and skewed grids. These grids are often required for proper representation of the reservoir geometry. The physical dispersion coefficient in the dispersive flux is tensorial in nature and amenable to a treatment similar to the permeability in the convective flux. We have applied a multipoint control-volume method together with a total variation diminishing (TVD) scheme to calculating the dispersive flux in a compositional simulator. The TVD scheme was used to minimize the effect of front smearing caused by numerical dispersion. This paper presents a method for calculating the full physical dispersion tensor in a compositional simulator using corner-point grids. The proposed formulation accurately handles dispersive flux for non-orthogonal grids, and along with the TVD scheme provides a means for distinguishing physical dispersion from numerical dispersion.A number of cases are presented to show the improvements in simulation results that could be obtained with the proposed method.

Upscaling and Simulation of Waterflooding in Heterogeneous Reservoirs Using Wavelet Transformations: Application to the SPE-10 Model

“…Harten and co-workers (Harten 1979;Harten and Osher 1987;Yee and Harten 1987) introduced the total variation diminishing (TVD) method for evaluating the phase mobilities, which is free of the instabilities. It is increasingly being used in reservoir simulation (Rubin and Blunt 1991;Wattenbarger et al 1997), especially when numerical dispersion dominates the physical dispersion (Peddibhotla et al 1997;Sammon et al 2001;Thiele and Edwards 2001;Shrivastava et al 2002;Mallison et al 2003). The method requires a front detection technique based on calculating successive mobility ratios in the neighboring blocks.…”