Calculating capillary pressure (Pc) for oil–water and gas–water systems involves fundamental concepts from interfacial phenomena. Generally, Pc is related to the curvature of the interface between the two immiscible fluids, the interfacial tension, and the geometry of the pore space.

Below are the key approaches and equations:

For a simple, idealized interface (e.g., a cylindrical capillary tube), the capillary pressure can be expressed as:

Pc = 2σ cos(θ) / r

where

• σ is the interfacial tension (oil–water or gas–water, respectively),

• θ is the contact (wetting) angle, and

• r is the effective radius of the capillary pore.

This equation is a starting point, especially for understanding pore-scale phenomena.

For more complex pore geometries, the curvature is expressed with two radii (R1 and R2):

Pc = σ (1/R1 + 1/R2)

This form is more suitable when both principal curvatures need to be taken into account.

In reservoir engineering, capillary pressure in a porous medium is often correlated with saturation using a scaling function:

J(S) = Pc * √(k/φ) / σ cos(θ)

where

• k is permeability,

• φ is porosity,

• S is the saturation.

Rearranging, you can derive Pc for a given saturation by:

Pc = [σ cos(θ) / √(k/φ)] * J(S)

This correlation helps account for the heterogeneity of real pore structures.

For an oil–water system, σ reflects the oil–water interfacial tension, and typically, the wettability of the rock may favor water or oil, affecting the contact angle θ.

For a gas–water system, σ is the gas–water surface tension. Often, the wetting behavior is different (usually water-wet), so θ might be lower. The intrinsic properties of the fluids (density and viscosity) further influence the curvature, particularly under hydrostatic conditions.

• Determine the appropriate interfacial tension (σ) for the system, which can be measured experimentally.

• Identify or estimate the contact angle (θ) from wettability tests.

• Define the effective pore radius ® or use pore-size distribution data from core samples or models.

• If needed, use correlations like the Leverett J-function for real porous media to integrate reservoir properties.

• Finally, plug the values into the chosen equation to calculate Pc.

References with Relevant Equations:

• Dullien, F. A. L. (1992). “Porous Media: Fluid Transport and Pore Structure.” (This book is a comprehensive resource on pore geometry and fluid transport, including capillary pressure formulations.)

• Lake, L. W. (1989). “Enhanced Oil Recovery.” (Lake discusses the application of capillary pressure in reservoir engineering and presents practical correlations derived from experimental data.)

• Morrow, N. R. (1970s). “Wettability and Its Effect on Oil Recovery” in Journal of Petroleum Technology. (This paper delves into the role of wettability and how it affects the capillary pressure between phases.)

• Leverett, M. C., et al. (1941). “Capillary Behavior in Porous Solids” in Transactions of the AIME. (Original work that provides the basis for the Leverett J-function, widely used in analyzing capillary pressure data in porous media.)