Development and Application of a New Technique for Upscaling Miscible Displacements

Summary To better design and manage miscible gas injection, a fast and accurate coarse-scale miscible simulation capability is required. In this paper, we present a new technique for the upscaling of first-contact miscible displacements. The method comprises two components: effective flux boundary conditions (EFBCs) and the extended Todd and Longstaff with upscaled relative permeabilities (ETLU) formulation. The former accounts approximately for the effects of the global flow field on the local upscaling problems, while the latter modifies the way that effective fluid properties and upscaled relative permeabilities are computed so that effectively residual oil is properly represented. For a sequence of partially layered, synthetic 2D permeability fields, the technique is shown to be successful in reproducing reference fine-scale solutions. The method is also shown to outperform other upscaling techniques over a wide range of coarsening factors. The upscaling procedure is then applied to a 3D simulation of a miscible gas-injection field study. A near-well upscaling technique is also incorporated into the methodology. We show that the new approach provides coarse-scale simulation results that match the reference solutions closely. In addition, the technique is shown to be very efficient computationally. Introduction In many oil fields with significant amounts of associated gas, miscible gas injection is a potentially attractive recovery method because it can yield high local displacement efficiencies and may also offer a solution for gas handling. For an accurate estimation of the displacement efficiency, complex phenomenalike viscous fingering need to be modeled properly. There are two broad categories of approaches to modeling miscible displacements: fully compositional (FC) and limited compositional (LC). For multicontact miscible processes, FC simulations are generally required. However, fine-scale FC simulations of miscible processes are prohibitively time-consuming. While compositional streamline techniques may eventually address many of the computational difficulties, several issues (e.g., gravity, compressibility, and streamline updating) have yet to be fully resolved. When first-contact miscibility is applicable, the LC formulation may be preferable because of its computational efficiency. The LC formulation allows the simulator to model miscibility within a black-oil framework and empirically accounts for viscous fingering by modifying the fluid properties of the pseudophases. However, because fine-scale LC simulations are still computationally demanding, there remains a clear need for a robust miscible upscaling technique. In this work, we present a novel upscaling technique for the fast and accurate coarse-scale simulation of first-contact miscible displacements. Our method is an LC approach that has two components: the use of EFBCs for the calculation of upscaled (pseudo-) relative permeabilities and the ETLU formulation. EFBCs incorporate some approximate global flow information into the local upscaling calculations and appropriately suppress the flux through high-permeability streaks that are not continuous throughout the domain. As a result, EFBCs address the problem of premature breakthrough of injected fluid, which can occur because of the overestimation of flux that results from the use of standard boundary conditions. Our ETLU formulation extends the Todd and Longstaff method by accounting for the fact that, within reservoir-simulation length scales, there exists an amount of oil that is practically immobile and not available for mixing (Sorb). The computation of effective fluid properties and upscaled relative permeabilities, therefore, should not include this Sorb. This concept in fact leads to the improved behavior of the upscaled relative permeabilities. Previous miscible upscaling approaches entailing upscaled relative permeabilities neither included the Sorb concept nor used any specialized boundary conditions such as EFBCs.