Methods and apparatus for dynamically estimating the location of an oil-water interface in a petroleum reservoir

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. As new measurements are acquired, posterior pdfs, updated for expected temporal variations, become prior pdfs for the new measurements. According to a third method, uncertainty about the reservoir parameters is represented by Gaussian pdfs. The relationship between measurements and reservoir parameters is locally approximated by a linear function. Uncertainties are quantified by a posterior covariance matrix.