# Capillary pressure (Pc) curves: pore throat size determination

Series Exploring for Oil and Gas Traps Treatise in Petroleum Geology Predicting the occurrence of oil and gas traps Predicting reservoir system quality and performance Dan J. Hartmann, Edward A. Beaumont Web page AAPG Store

Capillary pressure (Pc) curves are a rock property measurement that relates the volume of pore space controlled by pore throats of a given size (usually given in microns) to a given capillary pressure.

## What is capillary pressure?

Pc is the resistant force to hydrocarbon migration. It is a function of the interfacial tension (γ), the wettability (Θ), and pore throat radius (r). Pc increases with decreasing pore throat size, increasing interfacial tension, and increasing contact angle (greater oil wetting). It can be expressed as follows:

${\mbox{P}}_{{{\rm {c}}}}={\frac {2\gamma \cos \Theta }{{\mbox{r}}}}$

This expression assumes the capillary phenomenon occurs within a tube with a circular cross section. Real pores only approximate this, and then only if they are intergranular or inter crystalline.[1]

## Capillary test procedure

Figure 1 Example of a mercury capillary pressure test.

In a mercury capillary pressure test, a rock with a measured porosity is immersed in a mercury pressure cell. The pressure in the cell is raised to a predetermined pressure level (P1, Figure 1). When the cell comes to equilibrium, the volume of injected mercury is measured (V2). Since the porosity of the test sample is known prior to the test, the volume of injected mercury can be converted to the percent of the total pore volume filled with mercury (for example, 10% at 10 psi68.948 kPa
0.0689 MPa
0.68 atm
for point M1). All the pores filled with mercury at this point in the test have at least one 10μ pore throat radius or larger and represent 10% of the sample's pore volume. This procedure is repeated several more times at different pressures (for example, points M2 through M5).

## Pore throat profiles

Figure 2 Curve drawn through the points in Figure 1.

A curve is drawn through the measured points at test completion. This capillary pressure curve also represents a pore throat size profile for the tested sample. It relates a given pore throat size to its capillary resistance (Pc). Figure 2 shows the curve drawn through the points in Figure 1.

## Converting capillary pressure to pore throat size

Capillary pressure curves are converted to profiles of pore throat size by solving the previous equation for r:

${\mbox{r}}={\frac {2\gamma \cos \Theta }{{\mbox{P}}_{{{\rm {c}}}}}}$

Capillary pressure for a given Sw can also be converted to an approximation of height above free water (h) within a reservoir system. From a capillary pressure curve at a given Sw, we read the capillary pressure and multiply it by a factor that converts Pc to buoyancy pressure (Pb). If the conversion factor is not known, we use 0.4 for gas and 0.7 for oil.

## Using pc to estimate h and r

Use the table below to estimate height above free water (h) and pore throat radius (r) from a mercury capillary pressure curve.

To estimate Follow this procedure
Pore throat size ( r ) from Sw
1. Enter the X-axis at percent pore volume (Sw value).
2. At the intersectionof grid line and Pc curve, read the corresponding value for r on the Y-axis
Height above free water level (h) from Sw
1. Enter the X-axis at percent pore volume (Sw value).
2. At the intersectionof grid line and Pc curve, read the corresponding value for Pc on the left Y-axis
3. Multiply Pc by the appropriate gradient (as a rule of thumb, use 0.7 for oil, 0.4 for gas).

## Example

Figure 3 Example of a mercury capillary pressure test.

Using the curve in Figure 3, if Sw = 20% (point 1), then the mercury capillary pressure (Pc) that must be overcome to enter pore throats at that point on the curve is 200 psi1,378.951 kPa
1.379 MPa
13.609 atm
(point 2). Converting mercury Pc to hydrocarbon column height (h):

${\mbox{h}}=200{\mbox{ psi}}\times 0.7=140{\mbox{ ft of oil column}}$
${\mbox{h}}=200{\mbox{ psi}}\times 0.4=50{\mbox{ ft of gas column}}$

The minimum pore throat radius entered when Sw is 20% and Pc is 200 psi1,378.951 kPa
1.379 MPa
13.609 atm
is 0.5μ.