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Understanding the role of thin films in porous media is vital if wettability is to be elucidated at the pore level. The type and thickness of films coating pore walls determines reservoir wettability and whether or not reservoir rock can be altered from its inlial state of wettability. Pore shape. especially pore wall curvature, is an important factor in determining wetting film thickness. Yet, pore shape and the physics of thin wetting films are generally neglected in models of flow in porous rocks. This paper incorporates thin wetting film forces into a collection of capillary tubes model to describe the geological development of so-called mixed-wettability in reservoir rock. Our model emphasizes the remarkable role of thin films. New pore-level fluid configurations arise that are quite unexpected. For example, efficient water displacement of oil (i.e., low residual oil saturation) characteristic of mixed-wettability porous media comes about due to interconnected oil lenses or rivulets which bridge the walls adjacent to a pore corner. Predicted residual oil saturations are found to be approximately 35 percent less in mixed-wet rock when compared to completely water-wet rock. Calculated capillary pressure curves mimic those of mixed-wet porous media in the primary drainage, imbibition, and secondary drainage modes. Amott-Harvey indices range from -0.18 to 0.36 also in good agreement with experimental values1**. References and illustrations at end of paper The wettability of reservoir rock is a critical factor in determining the displacement effectiveness and ultimate oil recovery by drive fluids, such as water. Since the most wetting fluid tends to occupy the smallest and, hence, most hydrodynamically resistive pore channels while the least wetting fluid distributes to the largest and least resistive pore channels, wettability is a prime factor controlling multiphase flow and phase trapping. Therefore, understanding how wettability is established at the pore level is crucial if predictive flow models are to be developed. Wettability in porous media is generally classified as either homogeneous or heterogeneous. For the homogeneous case the entire rock surface has a uniform molecular affinity for either water or oil. Conversely, heterogeneous wettability indicates distinct surface regions that exhibit different affinities for oil or water. Three broad classifications of homogeneous wetting exist: strongly water-wet, strongly oil-wet, and intermediate wet. If smooth representative rock surfaces can be prepared, then contact angles for water-wet surfaces, measured through the water phase, are near zero. Whereas, for oil-wet surfaces they are near 180". In the case of intermediatewetting, the rock has neither a strong affinity for water nor oil, and contact angles range roughly from 45" to 135" 3. Two types of heterogeneous wettability are generally recognized. Mixed-wettability refers to distinct and separate water-wet and oil-wet surfaces which coexist and span a porous medium. Dalmation, also speckled or spotted, wettability refers to continuous water-wet surfaces enclosing A PORE-LEVEL SCENARIO FOR THE DEVELOPMENT OF 2 MIXED-WETTABILITY IN OIL RESERVOIRS SPE 24880 macroscopic regions of discontinuous oil-wet surfaces or vice-versa 4. For many years, it was common petroleumengineering practice to assume that oil reservoirs are strongly water-wet. Because most reservoir rock is highly siliceous and because oil reservoirs evolve by oil migrating into initially brine-occupied pore space, it was thought that the rock surface maintains a strong affinity for water even in the presence of oil5. In 1973, however, Salathie16 established that reservoirs with mixed-wettability display low residual oil (i.e., oil trapped as isolated globules) and consequently high displacement efficiency, as gauged by the ratio of oil recovered after waterflooding to the original oil in place. More recently, Fassi-Fihri et a17 used cryoscanning electron microscopy to confirm that wettability is heterogeneous on the pore scale in actual reservoir media and that mineralogy greatly affects the type of wettability. The purpose of this paper is to develop a porelevel picture of how mixed-wettability might form and evolve in reservoir rock initially filled with brine. Before embarking on this task we briefly explore the relationship between thin films and wettability. Thin Films and Wettability A succinct description of mixed-wettability follows when the effects of thin films which coat and adhere to solid surfaces are considered. Thin-film forces in fact control wettability. Figure 1 displays a schematic diagram of an apparatus used to quantify thin-film forces in liquid films adjacent to a solid surface8. An annular porous disk, which allows flow of wetting fluid, is sealed against a solid substrate. A nonwetting fluid meniscus enters from below the solid substrate disk assembly. Far away from the solid substrate, the meniscus is hemispherical. When the central portion of the meniscus is pressed against the wall, a thin film forms. As the pressure of the nonwetting fluid rises compared to that in the wetting fluid, the film thins and the meniscus or Plateau border recedes into the corner. An experiment proceeds by applying a capillary pressure difference (i.e., PC = Pnw Pw) across the Plateau-border meniscus and measuring the resulting thickness of the film by interferometry or ellipsometry. At equilibrium, the pressure of the wetting fluid in the thin film and the Plateau border are identical. The film is flat, yet the capillary pressure is nonzero. Consequently, the standard Young-Laplace equation of capillarity does not describe the thin film portion of Fig. 1. Rather, thin-film forces must be incorporated into the Young-Laplace equation by adding a term. n(h), referred to as disjoining pressure9-l2 : In the augmented Young-Laplace equation, o refers to the bulk interfacial tension between the wetting and nonwetting phases for an interface with principal radii of curvature rl and r2. Disjoining pressure is a function of film thickness, h. If disjoining pressure is positive, the two interfaces are repelled, whereas if disjoining pressure is negative the two interfaces are attracted. When films are thin (e.g., 100 nm), the disjoining pressure is significant compared to the other terms in Eqn. (1). For the flat film in Fig. 1, the curvature is zero so that at equilibrium PC = ll(h). Equation 1 may be cast in dimensionless form by a characteristic force, o, and a characteristic dimension, am. Representative values of o and am are 50 mN1m and 150 pm respectively. With this scaling, the first term on the right side of Eqn. (1) varies from approximately 113 to 10 whereas a disjoining pressure of 500 Pa makes the second term of order 1. A schematic disjoining pressure isotherm is drawn in Fig. 2. For certain values of disjoining pressure, for example l l1 , there are three possible equilibrium film thicknesses. The outermost films have thicknesses of order 10 to 100 nm. The central portion of the n versus h curve ( i.e., where dnldh is positive) is an unstable region13. A film in this thickness region spontaneously thickens or thins to a new stable configuration. The innermost films are quite thin, possibly on the order of one or several monolayers of solvent molecules. The effective range of the disjoining pressure is denoted by hp. Many factors contribute to the shape of a disjoining pressure isotherm. Three major force components are electrostatic interactions, van der Waals interactions, and hydration forces14. The first, electrostatic forces, originate from the overlap of ionic clouds known as electrical double layers present at each interface. For symmetric charged films, these are repulsive stabilizing forces15. M e l r ~ s e ' ~ and Hallq7 give thorough discussions of double-layer repulsive forces and their effects on film stability. Dispersive van der Waals forces are usually attractive and destabilize thin-aqueous films14. Lastly, strong repulsive hydration forces are important at film thicknesses approaching molecular dimensions1' . Clearly, the mineral content of pore walls has a large effect on thin-film interaction forces. For example, when a drop of crude oil is contacted wlh a brine-covered surface, crude oil adheres more readily (i.e., thick a ueous films break more easily) on calcite than Because calcite has a more positive surface charge, under identical conditions there is lesser stabilizing repulsive action from the electrostatic overlap forces. Oil-drop adhesion tests provide a simple approach to characterize the wetting behavior of crude oils against solid surface^^*'^^^^. When adhesion occurs, it is found that the solidloillwater boundary is fixed or "pinned" at the three-phase contact linela. Accordingly, the contact line of a retracting oil drop does not recede along the solid substrate. In subsequent sections, the importance of contact-angle pinning in mixed-wettability systems will become evident. SPE 214880 A. R. KOVSCEK , H. WONG, AND C. J. RADKE Thin-film forces determine the contact angle. Direct integration of the augmented Young-Laplace equation yields the following relationship between contact angle, 8, and disjoining pressure2' In Eqn, (2), h is the equilibrium film thickness of interest. Implicit in Eqn. (2) is the constraint that hphm cc 1. Integration over the positive purely repulsive portions of Fig. 2 (i.e., the thick outer films) results in zero contact angle. Conversely, nonzero contact angles up to 90° are possible when Eqn. (2) is integratedz1 over the attractive negative portions of Fig. 2. The above equation is derived for a meniscus attached to a flat solid surface. Nevertheless, it still applies for solid curved surfaces as long as the film thickness is much smaller than the radius of curvature of the surface. Consider now films on significantly curved surfaces. Figure 3 displays one

A Pore-Level Scenario for the Development of Mixed Wettability in Oil Reservoirs