Permeability

Permeability: is a measure of a rock’s ability to conduct fluids.

A fluid of known viscosity is pumped through a rock sample of known cross-sectional area and length. The pressure drop across the sample is measured through pressure gauges.

The unit of permeability is the Darcy. A rock having a permeability of one Darcy allows a fluid of one centipoises (CP) viscosity to flow at a velocity of one centimeter per second for a pressure drop of one atmosphere per centimeter. The formula for Darcy’s Law as formulated by Muskat and Botset is as follows:

Where:
q = rate of flow
k = permeability
(P1 – P2) = pressure drop across the sample
A = cross-sectional area of sample
µ = viscosity of fluid
L = length of the sample

Since most reservoirs have permeabilities that are much less than a Darcy, the millidarcy (one thousandth of a Darcy) is commonly used for measurement. Permeability is generally referred to by the letter k.

In the form shown above, Darcy’s law is only valid when there is no chemical reaction between the fluid and rock, and when there is only one fluid phase present completely filling the pores. The situation is far more complex for mixed oil or gas phases, although we can apply a modified Darcy-type equation. Average permeabilities in reservoirs commonly range from 5 to 500 millidarcies. Some reservoirs, however, have extremely high permeabilities. Some of the Cretaceous sandstone reservoirs of the Burgan field in Kuwait, for example, have permeabilities of 4,000 millidarcies (Greig, 1958).
Since flow rate depends on the ratio of permeability to viscosity, gas reservoirs may be able to flow at commercial rates with permeabilities of only a few millidarcies. However, oil reservoirs generally need permeabilities in the order of tens of millidarcies to be commercial. Fanall, you must note that the permeability is a property of a rock not of the fluid.

Classification of permeability

Absolute Permeability (k): is Permeability of a rock to a fluid when the rock is 100% saturated with that fluid.

Effective Permeability (ke):

It has been found that in sand containing more one fluid the presence of one materially impedes the flow of the other. This has given rise to the use of the term effective permeability impedes, which may be defined as the apparent permeability to a particular phase (oil, gas or water) or saturation with more than one phase. The amount that flow is
impeded depends upon the saturation of the fluids in the sand. The lower the saturation of a particular fluid in the sand, the less readily that fluid flows; or, stated in another way, the lower the saturation of particular fluid in sand, the lower is the effective permeability to that fluid.

Relative Permeability (kr):

Relative permeability is another term used in reservoir calculation. Relative permeability is the ratio of the effective permeability to a particular phase to the normal (absolute) permeability of the sand. The unit of effective permeability is the Darcy while the relative permeability is being a ratio, has no unit.

Laboratory Measurement of Permeability

Laboratory measurement of permeability usually uses air as the flow fluid and thus the value obtained is permeability to air (K_air). Common device that may used to determining (k) is shown below.

Permeability values may also be obtained from results of the following flow test
1-RFT – repeat formation test.
2- DST – drill stem test.
New methods of quantification of permeability using well logs are also being developed:
1- Resistivity Gradient.
2- Porosity and Water Saturation.