Robust fast recovery of the filtration function for flow of water with particles in porous media

Abstract

Models for deep bed filtration during the injection of seawater with solid inclusions depend on an empirical filtration function that represents the rate of particle retention. This function must be calculated indirectly from experimental measurements of other quantities. The practical petroleum engineering purpose is to predict injectivity loss in the porous rock around wells. This phenomenon is studied in laboratory injection tests, where the effluent particle concentration is measured over time. We presented in a previous work1 a method for determining the filtration function from these measurements. In this work, we improve on this method introducing a data preprocessing technique which makes the algorithm robust, and present numerical results with data which could not be treated before. The main purpose of this paper is to present this complete method for the solution of the inverse problem of determining the filtration function in the classical deep bed filtration theory from injected and effluent particle concentration measurements.