Flow and Displacement of Bingham Non-Newtonian Fluids in Porous Media

Abstract

Abstract There is considerable evidence that the flow of heavy oil in some reservoirs is non-Newtonian and that this behavior can be approximated by a Bingham type fluid. Investigations in the Laboratory and in a few field tests have shown a behavior that is characteristic of a Bingham fluid; the flow of the heavy oil takes place only after the applied pressure gradient exceeds a certain minimum value. Despite the research that has been carried out over the past 20 years on the flow of non-Newtonian fluids in porous media, very little work has been done on single- and multiple-phase flow of Bingham fluids. At present, there is no reliable method of analyzing pressure buildup data from well tests where the reservoir contains a Bingham oil. This work presents a theoretical study of the flow and displacement of a Bingham type fluid in porous media. An integral method of analyzing the single phase flow of this type of fluid has been developed. An approximate analytical solution has been obtained for transient flow problems, and its accuracy is confirmed by comparison with numerical solutions. The flow behavior of a slightly-compressible Bingham fluid is discussed, and a new method of well test analysis has been developed by using the integral solution. To obtain some understanding of the physics of immiscible displacement with Bingham fluids, a Buckley-Leverett type analytical solution with a practical graphic evaluation method has been developed and applied to the problem of displacing a Bingham-type fluid by water. The results reveal how the saturation profile and the displacement efficiency are controlled not only by the relative permeabilities, as in the case of Newtonian fluids, but also by the inherent complexities of Bingham non-Newtonian behavior. In particular, we find that in the displacement process with a Bingham fluid, there exists a limiting maximum saturation, beyond which no further displacement can be achieved. Introduction Flow of non-Newtonian fluids through porous media is encountered in many subsurface systems involving underground natural resource recovery or storage projects. In the past three decades, a tremendous effort has been expended in developing quantitative analysis of flow of non-Newtonian fluids through porous media. Considerable progress has been reported and much information is available in the chemical engineering, rheology and petroleum engineering literature regarding non-Newtonian fluid flow through porous media (Savins, 1969; Gogarty, 1967; van Poollen, 1969; Ikoku and Ramey, 1979; Odeh and Yang, 1979). The theoretical investigations carried out in this field have mainly concentrated on single-phase power-law non-Newtonian fluid flow, while the experimental studies have intended to provide rheological models for non-Newtonian fluids and porous materials of interest. There is considerable evidence from laboratory experiments and field tests that certain fluids in porous media exhibit a Bingham-type non-Newtonian behavior (Bear 1972; Barenblatt et al., 1984). In these cases, flow takes place only after the applied pressure gradient exceeds a certain minimum value, referred to as the threshold pressure gradient. The flow of oil in many heavy oil reservoirs does not follow Darcy's law, but it may be approximated by a Bingham fluid (Mirzadjanzade et al., 1971). For groundwater flow in certain clayey soils, or in strongly argillized rocks, the existence of a threshold hydraulic gradient has also been observed. When the applied hydraulic gradient is below a certain minimum gradient, there is very little flow. This phenomenon was attributed by some authors to clay-water interactions (Bear, 1972; Mitchell, 1976). The flow of foam in porous media is a focus of current research in many fields. P. 339⁁