Multiphase Upscaling Using Approximation Techniques

Abstract

AbstractCoarsening and upscaling are common practices in reservoir simulation for reducing model size to improve computational efficiency. As part of the standard simulation workflow, engineers upscale geological models to simulation models to reduce the CPU time and requirement on computational resources. Coarsening is also an attractive approach for reduced order modeling. In that case, aggressive coarsening is carried out to drastically reduce the size of the simulation model, and hence simulation time. In reduced order modeling, a run is expected to take a small fraction of time required for a typical simulation run. Reduced order modeling plays a crucial role in uncertainty quantification, history matching, and other applications where a large number of simulation models need to be evaluated.This paper proposes a new method for upscaling relative permeability for reduced order modeling and multiphase flow simulation. With this approach, approximations are introduced to eliminate the need for local or global multiphase flow simulations for the purpose of building coarse-scale displacement tables. Instead, the technique is based on global pressure solutions and velocity fields for incompressible two-phase flow. A set of time-of-flight and corresponding saturation solutions are obtained by solving 1st order partial differential equations in space variables using finite difference technique. The partial differential equation for saturations is general and may include gravity effects. Spatial time-of-flight (TOF) and saturation solutions are combined to construct approximate time-dependent saturation functions from which coarse-scale relative permeability functions are generated. To account for mobility differences in the reservoir before and after the reservoir is swept, several coarse relative permeability functions are computed based on a few approximate saturation and velocity distributions. This set of coarse relative permeability functions are then averaged to produce the final coarse permeability functions to be used for coarse-scale flow simulation. The proposed technique has been used to simulate flow on models with challenging horizontal and vertical permeability properties. Test results show that the use of the proposed multiphase upscaling method significantly improves the accuracy of coarse simulation results, while speeding up the run by more than 100 times.