Progress on the theory of flow in geologic media with threshold gradient

Abstract

Abstract Several experimental studies have indicated that the traditional Darcy law is not valid at low filtration velocities. These results do not represent rare exceptions, but rather the ordinary behavior of certain fluid‐porous media geosystems, such as water and gas flowing through soils containing wet clays. In addition, viscoplastic fluids, such as oils containing paraffin, asphaltene and wax, flowing under low temperature in porous media exhibit similar deviations from the Darcian behavior. The common conclusion of these studies, which are summarized in the first part of this paper, is that non‐Darcian fluid flow, in many cases, may be described by a filtration law with threshold gradient: there is no flow for forced pressure gradient values below the threshold gradient and there is a linear relationship between flow velocity and pressure gradient above the threshold gradient value. The second part of this paper deals with the theoretical aspects of fluid flow with threshold gradient. Solutions to several two‐dimensional steady‐state horizontal flow problems are discussed. The solutions show that the typical characteristic of the flow regime is stagnation zones which appear in the vicinity of the critical points of the flow. When water is injected into the reservoir to displace the non‐Newtonian fluid, the stagnation zones change and achieve a final limiting configuration. The size of the stagnation zones at that time determines the loss of the displaced fluid, which may be minimized by increasing the flow rate of the displacing liquid (water). The last section of this paper deals with nonsteady flow situations and introduces methods to estimate field scale reservoir parameters, particularly the field scale threshold gradient. A number of publications available only in Russian are critically presented and compared to the western literature.