Abstract: Methods for locating an oil-water interface in a petroleum reservoir include taking resistivity and pressure measurements over time and interpreting the measurements. The apparatus of the invention includes sensors preferably arranged as distributed arrays. According to a first method, resistivity and pressure measurements are acquired simultaneously during a fall-off test. Resistivity measurements are used to estimate the radius of the water flood front around the injector well based on known local characteristics. The flood front radius and fall-off pressure measurements are used to estimate the mobility ratio. According to a second method, resistivity and pressure measurements are acquired at a variety of times. Prior knowledge about reservoir parameters is quantified in a probability density function (pdf). Applying Bayes' Theorem, prior pdfs are combined with measurement results to obtain posterior pdfs which quantify the accuracy of additional information.

Abstract: Inception of hydrocarbon extraction from a reservoir causes the oil-water interface to warp and cusp toward the extraction gates along a well. This invention proposes time-lapse DC/AC measurements with an array of permanently deployed sensors in order to detect and estimate the change in geometry and proximity of the oil-water interface as a result of production, and therefore as a function of time. The estimation is carried out with a parametric inversion technique whereby the shape of the oil-water interface is assumed to take the form of a three-dimensional surface describable with only a few unknown parameters. A nonlinear optimization technique is used to search for the unknown parameters such that the differences between the measured data and the numerically simulated data are minimized in a least-squares fashion with concomitant hard bound physical constraints on the unknowns.