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Appendix B
.

PERMEABILITY

Permeability is the measure of the ability of a porous rock to transmit a fluid
under the pressure gradient (differential pressure). The absolute permeability is the
ability of a rock to conduct a fluid (gas, oil, or water) at 100% saturation with that
fluid. Effective/phase permeability is the ability of a rock to conduct one fluid phase
(gas, oil, or water) in the presence of other fluid phases. Relative permeability to a
fluid is the ratio of effective/phase permeability at a given saturation to the
permeability at 100% saturation (the absolute permeability). The terms k ro (k o /k),
k rg (k g /k), and k rw (k w /k) denote the relative permeability to oil, to gas, and to water,
respectively (k is the absolute permeability, often the single-phase liquid
permeability). The relative permeability is expressed in percent or as a fraction. It
ranges from zero at a low saturation to 1 at a saturation of 100%.
Permeability is measured by an arbitrary unit called Darcy, which is named after
Henry d’Arcy, a French engineer, who in 1856 devised a method of measuring the
3
permeability of porous rocks. The permeability is equal to 1 Darcy if 1 cm of fluid
2
per second flows through 1 cm of cross-section of rock under a pressure gradient of
1 atm/cm, the fluid viscosity being 1 cP. Because most reservoir rocks have an
average permeability considerably o1 Darcy, the usual measurement units are
millidarcies (mD).
In the majority of formations there is a simultaneous existence of more than one
phase: (1) oil and gas, (2) oil and water, or (3) oil, gas, and water. The concept of
effective permeability implies that all but one phase are immobile. Inasmuch as a
part of the effective pore space is occupied by another phase, a correction factor
must be used. The magnitude of effective permeability depends on wettability, i.e.,
on whether (1) the immobile phase does not wet the solid surfaces of the rock and,
therefore, occupies the central parts of the pores, or (2) the immobile phase wets the
solid surfaces and thus tends to concentrate in smaller pores. The nature,
distribution, and amount of immobile phase affects effective permeability.
The results of effective/phase permeability measurement are shown graphically in
the triangular diagram, where the apex represents the 100% saturation point of the
respective phase (oil, gas, or water). Contour lines of equal permeability to oil, gas,
and water are drawn in order to evaluate the test results and characteristics of
simultaneous multiphase fluid flow (Fig. B-1). Composition of three-phase flow
through the porous media (after Leverett, 1941) is shown in Fig. B-2.
The diagram of relative permeability to oil and to water versus the oil and water
saturation is constructed and data points for the relative phase permeability to oil
and water in the presence of gas phase are depicted on the diagram. Examples of
curves of relative permeability to oil and to water vs. water saturation are shown in
Figs. B-3–B-5.