Characterisation of deep bed filtration system from laboratory pressure drop measurements

Abstract

During the injection of sea/produced water, permeability decline occurs, resulting in well impairment. Solid and liquid particles dispersed in the injected water are trapped by the porous medium and may increase significantly the hydraulic resistance to the flow. We formulate a mathematical model for deep bed filtration containing two empirical parameters—the filtration coefficient and the formation damage coefficient. These parameters should be determined from laboratory coreflood tests by forcing water with particles to flow through core samples. A routine laboratory method determines the filtration coefficient from expensive and difficult particle concentration measurements of the core effluent; then, the formation damage coefficient is determined from inexpensive and simple pressure drop measurements. An alternative method would be to use solely pressure difference between the core ends. However, we prove that given pressure drop data in seawater coreflood laboratory experiments, solving for the filtration and formation damage coefficients is an inverse problem that determines only a combination of these two parameters, rather than each of them. Despite this limitation, we show how to recover useful information on the range of the parameters using this method. We propose a new method for the simultaneous determination of both coefficients. The new feature of the method is that it uses pressure data at an intermediate point of the core, supplementing pressure measurements at the core inlet and outlet. The proposed method furnishes unique values for the two coefficients, and the solution is stable with respect to small perturbations of the pressure data.