Wettability Literature Survey- Part 4: Effects of Wettability on Capillary Pressure
Authors: Anderson W.G. 
Published: December 2007

Wettability Literature Survey- Part 4: Effects of Wettability Part 4: Effects of Wettability on Capillary Pressure

Summary.
The capillary-pressure/saturation relationship depends on the interaction of wettability, pore structure, initial saturation, and saturation history. No simple relationship exists that relates the capillary pressures determined at two different wettabilities. Therefore, the most accurate measurements are made with cores that have native reservoir wettability.
In a uniformly wetted porous medium, pore geometry effects and the extremely rough surfaces of the porous medium make the capillary pressure curve insensitive to wettability for small contact angles (less than about 50 deg.[0.87 rad] for drainage capillary pressure curves and less than about 20 deg. [0.35 rad] for spontaneous-imbibition capillary pressure curves). When the porous medium has fractional or mixed wettability, both the amount and distribution of the oil-wet and water-wet surfaces are important in determining the capillary pressure curve, residual saturations, and imbibition behavior. Imbibition also depends on the interaction of wettability, pore structure, initial saturation, and saturation history. Because of these interactions, there is a large range of contact angles where neither oil nor water will imbibe freely into a uniformly wetted reservoir core. In contrast, it is sometimes possible for both fluids to imbibe freely into a core with fractional or mixed wettability.

Contact Angles, Capillary Pressure, and Wettability
This paper is the fourth in a series of literature surveys covering the effects of wettability on core analysis. Changes in the wettability of cores have been shown to affect electrical properties, capillary pressure, waterflood behavior, relative permeability, dispersion, simulated tertiary recovery, irreducible water saturation (IWS), and residual oil saturation (ROS).
When oil and water are placed together on a surface, a curved interface between the oil and water is formed, with a contact angle at the surface that can range from 0 to 180 deg. [0 to 3.15 rad]. By convention, the contact angle, 0, is measured through the water. Generally, when 0 is between 0 and 60 to 75 deg. [0 and 1.05 to 1.31 rad], the system is defined as water-wet. When 0 is between 180 and 105 to 120 deg. [3.15 and 1.83 to 2.09 rad], the system is defined as oil-wet. In the middle range of contact angles, a system is neutrally or intermediately wet.
It can be shown that whenever an oil/water interface is curved, the pressure will abruptly increase across the interface to balance the interfacial tension (IFT) forces. This pressure jump, which is the capillary pressure, is given by Laplace's equation :
(1)
where sigma = IFT, P = capillary pressure, p = pressure in the oil, p = pressure in the water, and r1, r2 = radii of curvature of the interface, measured perpendicular to each other.
By convention, the capillary pressure is defined as po-pw. Because of this definition, a radius of curvature po-pw. Because of this definition, a radius of curvature directed into the oil is positive, while one directed into the water is negative. Depending on the curvature of the surface, the capillary pressure can be positive or negative. When the interface is flat, the capillary pressure is zero. When fluids other than oil and water are used, the capillary pressure is usually defined as
(2)
where pNW is the pressure in the nonwetting fluid and pWET is the pressure in the wetting fluid. pWET is the pressure in the wetting fluid. The radii of curvature of the interface, and hence the capillary pressure, are determined by local pore geometry, wettability, saturation, and saturation history. For most porous media, the equations for the interfacial curvature are much too complicated to be solved analytically, and capillary pressure must be determined experimentally. In these cases, a simple relationship between contact angle and capillary pressure cannot be derived.
One geometry where capillary pressure can be calculated as a function of geometry, wettability, and IFT is a capillary tube. Laplace's equation can be used to solve for the capillary pressure as a function of IFT, contact angle, and rt, the radius of the tube.
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