A Fractional Flow Theory for Unstable Immiscible Floods

Abstract

Abstract Conventional fractional flow theories such as the Buckley-Leverett analysis have benefited reservoir engineers greatly for many decades. Although being simple, these analyses provide prompt and decent estimations of water breakthrough and oil bank height/duration in the experiments and the fields. However, their intrinsic inaccuracy in estimating unstable immiscible floods due to the existence of viscous fingering has long been ignored. With increasing non-thermal immiscible floods developed for heavy oil reservoirs, an essential improvement for such a theory is desirable. The intrinsic residual oil saturation can never be achieved for strong unstable immiscible floods within a finite time. The fraction of the bypassed oil at a time is highly dependent on the viscosity ratio, flow velocity, interfacial tension, wettability, permeability and the geometry of the rock. Extensive experimental data and numerical studies have indicated that the strength and growth rate of viscous fingering are correlated to a dimensionless number, i.e., the viscous finger number, which is an integration of those factors aforementioned. Such a discovery enables a quantitative establishment of two-phase pseudo relative permeabilities, which are functions of fluid saturations and the viscous finger number. The fractional flow for unstable floods can hence be obtained by use of such pseudo relative permeabilities. The new fractional flow theory extended from the Buckley-Leverett analysis was applied to several groups of heavy-oil water coreflood experiments under various conditions. The new fractional flow analysis was able to predict very well the breakthrough time and oil recovery of these experiments. We further applied the new fractional flow analysis to a slab experiment of viscous oil with a waterflood followed by a polymer flood, and achieved a very good agreement with the oil recovery data. The analysis reproduced that the water cut increased very rapidly and the remaining oil saturation was much larger than the intrinsic residual oil saturation after several pore volumes of waterflood. The subsequent polymer flood altered the pseudo relative permeability curves due to the change of viscosity ratio and brought in a considerable amount of mobile oil to be displaced. This process happens to be similar to the fractional flow of low-tension immiscible flow. Such a scenario is different from what the conventional fractional flow analysis suggests, which neglects the fact that the subsequent polymer flood is able to greatly improve the oil cut by mitigating the viscous fingers originally created by waterflood. The new theory has extended the original fractional flow theories to unstable immiscible floods, a major progress. It can also serve as a critical guideline to estimate and predict the water/polymer breakthrough and the oil production in viscous-oil benchscale experiments and field projects.