Capillary Pressure Curve: Definition, MICP, and Saturation Height

A capillary pressure curve is a laboratory-derived or theoretically calculated relationship that describes the capillary pressure (Pc) required to achieve a given wetting-phase saturation in a porous rock sample. In petroleum reservoir engineering, the wetting phase is typically formation water and the non-wetting phase is oil or gas, with the curve expressing the pressure difference across the fluid interface inside a pore throat as a function of water saturation. The capillary pressure curve is one of the most consequential petrophysical measurements available to the explorationist and reservoir engineer: it directly controls the vertical distribution of fluids in a reservoir column, the location of the free water level and oil-water contact, the irreducible water saturation, the residual oil saturation after waterflooding, and the seal capacity of cap rocks. A thorough understanding of capillary pressure curves is inseparable from any serious reservoir characterization model and underpins the saturation-height functions that populate volumetric calculations from the wellbore out to the full three-dimensional field model.

Key Takeaways

• Capillary pressure (Pc) is defined by the Young-Laplace equation: Pc = 2 x gamma x cos(theta) / r, where gamma is interfacial tension, theta is contact angle, and r is pore throat radius. Smaller pore throats require higher capillary pressure for non-wetting phase entry.
• Mercury injection capillary pressure (MICP) is the standard laboratory method for measuring the full Pc-Sw curve, using the high interfacial tension of mercury-air (485 mN/m) and a contact angle of 140 degrees to characterize pore throat size distributions across six or more orders of magnitude in pressure.
• Drainage curves (non-wetting phase displacing wetting phase) and imbibition curves (wetting phase displacing non-wetting phase) are distinct due to pore geometry; the difference between them, called hysteresis, controls residual saturations and is critical for enhanced recovery design.
• Water saturation versus height above the free water level (FWL) is calculated directly from the capillary pressure curve: h = Pc / (delta-rho x g), where h is height in metres, delta-rho is fluid density contrast in kg/m3, and g is 9.81 m/s2.
• The Leverett J-function normalizes capillary pressure curves from multiple samples and wells to a single dimensionless curve, enabling field-wide saturation-height functions that are essential for volumetric estimation in heterogeneous reservoirs.

How the Capillary Pressure Curve Works

At the microscale, capillary pressure arises because fluid interfaces are curved when two immiscible fluids occupy the same pore space. The curvature of the interface creates a pressure difference between the non-wetting and wetting phases, with the non-wetting phase always at higher pressure. The radius of curvature of the interface is determined by the geometry of the pore throat it occupies, which is why the pore throat size distribution of a rock directly determines its capillary pressure behaviour. In a rock with a wide range of pore throat sizes (heterogeneous pore system), the non-wetting phase first enters the largest pore throats (lowest capillary entry pressure) and progressively invades smaller and smaller pore throats as pressure is increased. The result is the characteristic sigmoidal shape of the capillary pressure curve on a semi-logarithmic plot: a nearly flat entry pressure plateau followed by a steeply rising section as the inflection of the pore throat size distribution is crossed, then a final flat region representing the irreducible wetting-phase saturation (Swirr), which is the minimum water saturation achievable regardless of how high the applied capillary pressure is raised.

In the reservoir context, capillary pressure is directly related to the height of a hydrocarbon column above the free water level (FWL). The FWL is defined as the depth at which capillary pressure equals zero, meaning the pressure in the oil or gas phase equals the pressure in the water phase. Above the FWL, buoyancy causes the hydrocarbon pressure to exceed the water pressure by an amount that increases linearly with height according to Pc = delta-rho x g x h. This increasing Pc with height means that progressively smaller pore throats are invaded by hydrocarbons as height above the FWL increases. Conversely, near the FWL, only the very largest pore throats contain hydrocarbons, resulting in high water saturations. The capillary pressure curve translates this depth-pressure relationship into a water saturation-height relationship, which is the saturation-height function (SHF) used to assign water saturation to every cell in a reservoir simulation grid based on its depth relative to the FWL.

Mercury Injection Capillary Pressure Testing

The mercury injection capillary pressure (MICP) test is performed by first drying a small rock plug (typically 1 to 5 cubic centimetres) under vacuum to remove all original fluids, then placing it in a mercury porosimeter. The sample is surrounded by mercury at progressively increasing pressures, typically from near-atmospheric (about 3.4 kPa or 0.5 psi) up to 207 MPa (30,000 psi) in modern high-pressure instruments. At each pressure step, a precise volume of mercury injected into the pore space is recorded after equilibration. By converting the injection pressure to an equivalent pore throat radius using the Young-Laplace equation (r = 2 x gamma x cos(theta) / Pc, with gamma = 485 mN/m and theta = 140 degrees for mercury-air), a complete pore throat size distribution is obtained ranging from approximately 200 micrometres at the lowest pressure to about 0.003 micrometres at the highest pressure achievable with standard instruments.

The raw MICP output is a plot of mercury saturation (Shg, expressed as a percentage of pore volume) versus injection pressure (psi or MPa), or equivalently versus equivalent pore throat radius (micrometres). The shape of this curve encodes a wealth of petrophysical information: the entry pressure (threshold pressure or displacement pressure) below which no mercury enters indicates the size of the largest connected pore throat in the sample; the slope of the curve through the main invasion region indicates the breadth of the pore throat size distribution; and the plateau at high pressures indicates the irreducible water saturation (100% - maximum Hg saturation). For reservoir quality assessment, the pore throat radius corresponding to the median mercury saturation (r35, the pore throat radius at 35% Hg saturation by convention from Winland's method) is widely used as a single-number quality indicator that correlates well with in-situ permeability. Permeability can also be estimated directly from MICP data using Kozeny-Carman type models or empirical transforms calibrated to core data from the same formation.

Converting MICP Data to Reservoir Conditions

Because mercury-air conditions in the laboratory bear no physical resemblance to the oil-water or gas-water conditions in a petroleum reservoir, the MICP capillary pressure values must be converted before they can be used in saturation-height modelling. The conversion is based on the ratio of the product of interfacial tension and cosine of contact angle between the two systems:

Pc(reservoir) = Pc(Hg-air) x [sigma(res) x cos(theta-res)] / [sigma(Hg-air) x cos(theta-Hg-air)]

For an oil-water system in a strongly water-wet sandstone (sigma-ow = 30 mN/m, theta-ow = 0 degrees), compared to mercury-air (sigma = 485 mN/m, theta = 140 degrees), the conversion factor is approximately (30 x 1.0) / (485 x -0.766) = 30 / 371.6. The negative cosine of 140 degrees (-0.766) means the conversion factor is numerically (30) / (485 x 0.766) = 30 / 371.6 = 0.0807, giving a reservoir Pc roughly 12 times lower than the laboratory mercury Pc for the same water saturation. This conversion factor is highly sensitive to the assumed interfacial tension and contact angle values, which vary with reservoir temperature, pressure, oil composition, and mineralogy. Best practice is to measure IFT and contact angle on reservoir fluids and core samples under reservoir conditions, though literature values are commonly used where direct measurements are unavailable.

Once converted to reservoir conditions, the Pc-Sw data can be expressed as a height-Sw relationship using h = Pc / (delta-rho x g). The density contrast delta-rho between reservoir water and the hydrocarbon phase is a critical input: for a medium-gravity crude oil with density 800 kg/m3 and formation water density 1080 kg/m3, delta-rho = 280 kg/m3; for natural gas with density 180 kg/m3 and the same water, delta-rho = 900 kg/m3. The higher density contrast for gas means that a given capillary pressure corresponds to a greater height above the FWL in a gas system than in an oil system, which is why gas reservoirs tend to have lower water saturations at equivalent heights above their contacts compared to oil reservoirs in the same rock. Dual unit reporting is standard: heights are given in both metres and feet (1 metre = 3.281 feet) and pressures in both MPa and psi (1 MPa = 145.04 psi).

Drainage and Imbibition: Hysteresis and Residual Saturation

A complete capillary pressure characterization requires measurement of both the drainage curve and the imbibition curve. The drainage curve represents the process in which the non-wetting phase (oil or gas) displaces the wetting phase (water) from the pore space, increasing non-wetting saturation from zero. In the reservoir context, primary drainage corresponds to the initial charging of the reservoir with hydrocarbons during geological time, as migrating oil or gas displaces formation water downward and outward from the accumulation. The imbibition curve represents the reverse process, in which the wetting phase (water) re-invades the pore space, displacing the non-wetting phase upward. During waterflooding of an oil reservoir (the most common form of secondary recovery), imbibition is the dominant displacement process as injected water sweeps oil toward producing wells.

Hysteresis refers to the fact that the drainage and imbibition capillary pressure curves are different for the same rock sample, reflecting the fundamentally different physics of pore filling and pore draining in complex pore geometries. In particular, the imbibition curve shows that when capillary pressure is reduced to zero (or reversed, in the case of spontaneous imbibition), not all of the non-wetting phase is expelled from the pore space. The saturation remaining at Pc = 0 on the imbibition curve is the residual oil saturation (Sor, typically ranging from 0.15 to 0.40 of pore volume in sandstones, and up to 0.50 in carbonates), which is a direct measure of the oil that cannot be recovered by conventional waterflooding. This residual saturation is trapped in pore throats by snap-off (where the advancing water film pinches off isolated ganglia of oil) and in large pore bodies that have been bypassed by the invading water front. Enhanced oil recovery (EOR) methods such as chemical flooding (surfactant injection to reduce IFT), miscible gas injection, and thermal methods target the reduction or mobilization of this residual phase.

The magnitude of hysteresis and the resulting residual saturation depend strongly on the pore geometry (pore-to-throat aspect ratio), wettability, and the history of prior drainage and imbibition cycles. In mixed-wettability or oil-wet systems (common in deeply buried, oil-stained carbonates and some aged sandstones), the imbibition capillary pressure can be negative, meaning that spontaneous imbibition of oil rather than water occurs in the oil-wet pore network while water spontaneously imbibes into the water-wet fraction of the pore space. These wettability effects significantly complicate the interpretation of capillary pressure data and require careful sample preparation and laboratory protocols to avoid altering the wettability state of core plugs during cleaning and preparation steps prior to testing.