Relative Permeability

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Relative permeability (definition): In multiphase flow in porous media, the relative permeability of a phase is a dimensionless measure of the effective permeability of that phase to the absolute permeability.  It can be viewed as an adaptation of Darcy's law to multiphase flow.

Relative permeability is an important parameter in reservoir simulation when determining producible reserves and estimating ultimate recovery. Laboratory measurements of relative permeability should be representative of flow behavior in the reservoir. Lab corefloods should represent the various production scenarios implemented in the field.


Steady-state relative permeability:

This process simulates the two-phase flow behind the flood front at a series of different saturations.


Advantages: Generates two curves and Kr ratio. Early incremental data is available, works well with all samples and even heterogeneous samples, and tests tend to include the effects of weak wetting forces.

Unsteady-state relative permeability:

During this process, one phase is injected, resulting in breakthrough followed by increasing water or gas fractions, yielding a residual oil or gas saturation.


Advantages: Moderate in cost, quick turnaround time, generates two curves and Kr ratio, and at times provides more data at a high fraction of water.

Testing Methods Compared - Steady State versus Unsteady State Relative Permeability

The steady-state testing method involves two fluids injected simultaneously at a constant rate or pressure for extended durations until equilibrium is reached. By changing the ratio of injection rates and repeating the measurements as equilibrium is attained, it is possible for saturations, flow rates, and pressure gradients to be measured and used in Darcy's law to obtain the effective permeability for each phase. The steady-state methods are inherently time-consuming because equilibrium may require several hours or days at each saturation level.  However, this method has greater reliability and the ability to determine relative permeability for a wider range of saturation levels, establishing capillary equilibrium between fluids and reducing or eliminating end effects.

The unsteady-state testing method involves displacing in situ fluids by constant‐rate or constant‐pressure injection of a single fluid while monitoring the effluent volumes continuously. The production data are analyzed, and a set of relative permeability curves is obtained using various mathematical methods. The Johnson‐Bossler‐Naumann (JBN) and Jones‐Roszelle methods are most commonly used for analysis.
The unsteady-state method is the quickest laboratory method of obtaining relative permeability data. However, many difficulties are inherent in unsteady‐state methods. Operational problems such as capillary end effects, viscous fingering, and channeling in heterogeneous cores are difficult to monitor and account for properly.


Reservoir Engineers Use of Relative Permeability Data

In order to generate reserves estimates, engineers perform the following: numerical reservoir modeling, production forecasting, well testing, well drilling, economic modeling, and PVT analysis of reservoir fluids. All of these responsibilities allow the engineer to better make well predictions or determine how the field will produce. Financial planning is optimized and production planning is better assessed. Relative permeability allows the reservoir engineers to determine how much water or gas injection is required to maximize oil production. Additionally, relative permeability data also provides information to determine the amount of surface equipment required to handle the produced fluids. 

Field simulations guided with relative permeability data aid in well design, placement, and performance prediction.