Up-scalingof Multipase Flow Functions Using a Steady State Flow Model

摘要

A concept of multiphase up-scaling based on steady-state flow approach was introduced in Ref. 2. It enables efficient calculation of effective properties through a numerical solution of steady-state 2-phase flow equation in 1D. The extension of this concept, i.e. steady-state multiphase flow, on 2 and 3 space dimensions, is studied below. We present a model for efficient direct up-scaling in 2 and 3D. The developed numerical model simulates steady-state multiphase flow in heterogeneous reservoirs with account for viscous, capillary and gravity forces at a given external pressure drop. We utilize the developed model to directly compute effective properties in 2D, and present examples that show the dependence of effective relative permeabilities and capillary pressure on the magnitude of the external pressure deop, and also study the convergence of the effective relative permeabilities and capillary pressures towards the viscous limit functions.