Darcy and non-Darcy Flows in Fractured Gas Reservoirs

Abstract In this paper, we discuss the application of Forchheimer’s model in flow problems where high sensitivity to capillary pressure is involved. The Forchheimer equation is basically composed of a Darcy term and a non-Darcy term to account for the inertial effects involved by high flow rates inside porous media. However, the Forchheimer equation does not offer an easy and systematic approach for estimating the flow, given that the β parameter, a non-Darcy flow coefficient, also known as the Forchheimer coefficient, is specific to different reservoir characteristics and must be determined accurately through experiments. It is, therefore, very important, before applying the Forchheimer model, to have an idea of its domain of applicability. It is commonly accepted that non-Darcy flow may occur especially in gas reservoirs, fractured reservoirs, near-wellbore regions, and inside wells. But the limits of the Forchheimer model limits are not clearly defined and its impact at field scale for reservoir engineering purposes is not very well established. This paper presents one possible domain of applicability of the Forchheimer model for a fractured gas reservoir model with water injection. The model has been designed to approach the conditions requiring the use of the Forchheimer model, which are high rates and high permeability. Oil and gas fractured reservoirs with water injection are also known to be very sensitive to capillary pressure data. Capillary pressure is a determinant parameter influencing fluid mobility in two-phase reservoirs. The determining of accurate capillary pressure data is essential to get satisfying results, especially in fractured reservoirs. Therefore, this study investigates the impact of capillary pressure on non-Darcy flows and compares the results with the results predicted by the Darcy model.