A Well Test for In-Situ Determination of Relative Permeability Curves

Abstract

Summary We propose a novel well-test for in-situ estimation of relative permeabilities under two-phase (oil/water) flow conditions. The test consists of three periods: injection of water into an oil reservoir operating above bubblepoint pressure, a falloff test, and a producing period. The producing period is critical because it yields production data that reflect changes in sandface mobility and thus is highly sensitive to the parameters used to model relative permeability curves, whereas our results indicate that injection/falloff pressure data by themselves are not as reliable for defining relative permeability curves. We have developed optimization code based on the Levenberg-Marquardt algorithm and coupled it with a commercial reservoir simulator to obtain a procedure for data analysis wherein the reservoir simulator is used as the forward model. By matching data by minimization of a weighted least-squares objective function, we generate estimates of absolute permeability, relative permeability, and the well skin factor. We show the method can be applied with either power-law models or B-splines. We introduce a variable transformation that can be used to ensure that the estimated relative permeabilities are monotonic and concave up when B-splines are used.