Relative Permeability

Introduction

The absolute permeability of a rock is when the permeability when the medium is saturated with a single one-phase fluid and only that fluid is flowing through the medium (I.e, the saturation is 100%). If a second fluid is present, the permeability will be less than the absolute permeability. Absolute permeability can be calculated from the Darcy Equation:

However, commonly reservoirs contain 2 or 3 fluids:

• Water-oil systems

• Oil-gas systems

• Water-gas systems

• Water-gas-oil

A pore containing a single fluid is compared with a pore containing two fluids in the figure below:

Note that the cross-sectional area for flow for each fluid must be less than the cross-sectional area for flow if only one fluid was present. Also, the presence of a fluid-fluid interface increases the total surface area exposed to fluid flow. Therefore the drag is increased for any given volumetric flow rate, and the effective permeability is decreases. The blockage of pore throats by one fluid further reduces the effective permeability.

Effective Permeability

Effective permeability: is a measure of the conductance of a porous medium for one fluid phase when the medium is saturated with more than one fluid.

Relative Permeability Concept

To account for the effect of multiple fluids, relative permeabilities are defined as follows:

Where:

kr= relative permeability

i = “o” for oil, “g” for gas, and “w” for water

k = absolute permeability

Final Comments

• Relative permeability is unique for different rocks and fluids

See Also:

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References:

• Colin Lyle Jordan Course Notes: PETE 616 - Engineering Near Critical Reservoirs

• Richard O. Baker, Harvey W. Yarranton, Jerry Jensen, “Practical Reservoir Engineering & Characterization“, Gulf Publishing, 2015.