Numerical Simulation of Water-Oil Inflow into the Producing Well from Non-uniform Oil Reservoir

Abstract

Mathematical and numerical models of non-stationary mass transfer in a water-oil mixture flowing into the bottom hole of a production well from a layered-heterogeneous oil reservoir are developed. The model consists of two group of differential equations. The first of them simulates a one-dimensional dispersed oil-water flow with discrete oil droplets included in a continuous water phase, and the second one—two-dimensional two-phase isothermal filtration governing by Darcy’s law with taking into account the compressibility of phases and a porous medium. To solve system of equations the finite difference schema is developed. The mass transfer equations in the bottom hole and in the reservoir are approximated upstream by implicit difference equations. The general system of nonlinear algebraic equations is solved iteratively with the use of the original method to calculate the pressure in the reservoir and Newtonian linearization. The developed numerical model is implemented in computer software that allows to carry out the numerical experiments with simultaneous visualization of the results of calculations. The influence of the reservoir structure and its uncovering conditions by the well on the characteristics of the process in the bottom hole of the well and the transition time of mass transfer processes to a quasi-stationary hydrodynamic regime are estimated.