Correlation of Capillary Number Relationships for Sandstone

Abstract

Abstract Capillary number relationships are presented for displacement of both residual and initially continuous oil from water-wet consolidated sandstones having permeabilities that varied over about two orders of magnitude. It was found that the critical displacement ratio, (APILa)cr, for the onset of mobilization could be correlated with sample permeability. Relationships between nominalized reduced residual oil saturation and capillary number (taken as kwAP/Lo) also were correlated satisfactorily. For sandstones, capillary numbers for displacement of continuous oil were lower than values for mobilization of discontinuous oil for down to 50% of normal waterflood residual. Thereafter, capillary number relationships for the two types of displacement were indistinguishable. Conditions for complete recovery of residual oil correspond to values of (kwAP/Lo) of about 1.5 × 10–3 as compared with about 2x 10 -5 for onset of mobilization. Introduction Capillary forces acting within pore networks are responsible for entrapment of one phase by another during immiscible displacements in porous media. Laboratory studies have shown that residual oil can be recovered if the displacing phase causes viscous forces acting on trapped residual oil blobs to exceed the capillary retaining forces. The magnitude of the capillary forces is set by the oil/water interfacial tension (IFT), wettability conditions, and the pore geometry in which trapped oil blobs exist. The apparent magnitude of the viscous forces acting on a trapped oil blob is set by the fluid dynamics of the displacing phase. The ratio of viscous to capillary forces is often called the "capillary number." More than a dozen expressions have been used in the literature to express this ratio," many of which are equivalent. They include the following expressions, which are used also in this paper. (1) (2) and (3) where v, is the Darcy velocity and u is the viscosity of the displacing phase, a is the IFT, and AP/L is the imposed pressure gradient across the sample of length L. ka and kw are specific permeabilities of the sample to air and to the aqueous phase, respectively. In this paper, the term capillary number" implies generic reference to the ratio of viscous to capillary forces. The experimental data found in the EOR literature are still rather limited as far as capillary number results for the immiscible displacement of continuous oil and the mobilization of residual oil from rock samples having widely different transport properties are concerned. In this paper, results and correlations are presented for water-wet sandstones that have comprehensive ranges of permeability and porosity. Theory of Mobilization Consider a water-wet porous medium that has been flooded to normal waterflood residual (ROS). A modified form of Darcy's equation for flow of aqueous phase in linear core flooding is (4) where kw = absolute permeability, krw = relative permeability, u = viscosity, andAP/L = the overall pressure gradient. An expression for capillary number, vu/o, is obtained from Eq. 4 as (5) The so-called "Jamin effect," discovered more than a century ago, provided the basic concept required for the development of a mechanistic interpretation of mobilization of residual oil blobs from water-wet reservoir rocks. The phenomenon of the high pressures required to force nonwetting phase blobs through a periodically constricted capillary is described well by Gardescu, who investigated the resistance to flow observed when an isolated bubble of gas in a liquid was forced into a capillary construction. SPEJ P. 555^