Simulation of Time-Lapse Resistivity Logging During Two-Phase Well Testing in Petroleum Reservoirs

Abstract

Abstract Well testing methods are widely used in petroleum industry to identify reservoir parameters in-situ, at real reservoir flow conditions. Two-phase tests with water injection extend capabilities of well testing to evaluation of oil-water flow characteristics through the solution of an inverse problem based on well measurements during the test. Near-wellbore water saturation is used as one of the informative measured parameters. However, water saturation is actually not directly measured on wells. Instead, it is interpreted from time-lapse well logging data, with resistivity logging being one of the options. This means that forward and inverse problems are to be extended to incorporate direct simulations of resistivity logging. In this paper we address the forward problem. It is formulated and solved for different types of logging tools, both for open hole and through the casing. A numerical algorithm and software implementation have been developed for repeated solution of an axisymmetric forward problem of resistivity logging – a 2D elliptical partial differential equation for electrical potential. Distributions of formation resistivity at the moments of logging are calculated from distributions of water saturation and salinity. The latter are computed through numerical solution of the forward problem of well testing – a two-phase oil-water flow in the reservoir with changing salinity of the water phase, with full account for real fluid and reservoir properties. The software implementation of the resistivity logging problem has been tested in comparison with the known theoretical solutions. Examples are presented to show how time-lapse changes in resistivity logging data reflect the specifics of the two-phase flow with changing water salinity during the well test.