Full text loading...
-
Dynamic Saturation Reconstruction for Multiphase Flow by Time-Of-Flight Fill Functions
- Publisher: European Association of Geoscientists & Engineers
- Source: Conference Proceedings, ECMOR XVII, Sep 2020, Volume 2020, p.1 - 19
Abstract
Summary
The hyperbolic nature of transport equations makes multiphase simulations sensitive to numerical diffusion or smearing due to insufficient grid resolution or long time -steps, in particular for cases with linear or weakly nonlinear displacement fronts. The number of grid cells is often limited by the available computational resources, and is tightly coupled to the geological description.
Apart from increasing the grid resolution, several approaches have been taken to remedy the problem. The first is to use a more accurate scheme for the transport equations, e.g., in the form of a high-resolution finite-volume scheme, or by adding more degrees of freedom in the form of higher-order finite elements. Such schemes are well developed on rectilinear and curvilinear grids, but more challenging to formulate on general polytopal grids. A second approach is to use some form of upscaling to generate new pseudo-relative permeability/mobility functions, since the simulation grid in many cases is formed by upscaling an underlying finer geocellular grid.
Herein, we present a novel approach to two-phase flow, based on dynamic reconstruction of saturations, that combines the two approaches. The key idea is to solve the transport on a coarser grid, but use a set of numerically computed filling functions to reconstruct fine-scale saturation variations. These fill functions are computed by solving local flow and time-of-flight problems before the simulation. Each fill- function accounts for the local velocity field by a simple superposition of solutions, and ensures that any 1D solution can be mapped onto the underlying fine-scale cells while preserving the average saturation within the containing coarse block. By assuming that the local solution is a self-similar solution of a Riemann problem, we can approximate the fine-scale saturation distribution at any point in the coarse block. We demonstrate that this can give highly accurate results for both linear and Buckley-Leverett type flux functions for a range of heterogeneous test cases. A comparison is made with different levels of implicitness and a WENO scheme at both coarse and fine scales.
© EAGE Publications BV