Transient Behavior of Water-Oil Interface in an Upward Flow in Porous Media

Abstract

A numerical study is performed to analyze unsteady flow of two immiscible fluids, water and oil, in a vertical cell filled with a porous medium. Injection of water from the bottom face perturbs the water-oil interface, which ceases being horizontal. The fluid motion in the porous medium is described by the transient Darcy model and continuity equation. A fully implicit, strongly coupled mathematical model is adopted to handle rapid water-oil interface changes. Effects of dimensionless parameters such as gravity-viscosity number N, dimensionless flow rate, Darcy number, and porosity are investigated and thoroughly documented. Their effects on evolution of the water-oil interface, on water breakthrough time, and on oil recovery are presented and discussed. A significant development of water-oil interface occurs, as the gravity-viscosity parameter and the porosity of the reservoir rock decrease. Results show that the breakthrough time is shorter for very dense, viscous oils (low values of N) and in the case of low Darcy number. High permeability can be beneficial in practical situations if the flow rate is maintained constant, since it permits considerable delay of water breakthrough, mainly at high values of N. A new coning correlation is presented to predict water breakthrough time and oil recovery, based on the flow equations and regression analysis using the data from numerical simulations.