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# Single phase permeability

The capacity to flow fluids is one of the most important properties of reservoir rocks. As a result, extensive research has been applied to describe and understand the permeability of rocks to fluid flow. In this page and its associated topics, only single-phase or absolute permeability will be considered. Multiphase relative permeabilities must be derived using relations described in relative permeability and capillary pressure

## Permeability

### Darcy's law

Permeability (k) is a rock property relating the flow per unit area to the hydraulic gradient by Darcy’s law,

(1)

where: p is pressure ρ is fluid density g is gravitational acceleration z is elevation μ is the dynamic viscosity

The ratio q/A has the units of velocity and is sometimes referred to as the "Darcy velocity" to distinguish it from the localized velocity of flow within pore channels. The natural unit of k is length squared; however, petroleum usage casts Eq. 1 in mixed units, so that the unit of k is the darcy, which is defined as the permeability of a porous medium filled with a single-phase fluid of 1-cp viscosity flowing at a rate of 1 cm3/s per cross-sectional area of 1 cm2 under a gradient of 1 atm pressure per 1 cm.[1]

Reservoir rocks are usually characterized in millidarcies (md), a unit that is 1/1000 of a darcy. Conversion factors are:

• 1 darcy = 0.9869×10-12 m2
• 1 md = 0.9869×10 -11 cm2

Bass[2] noted that Darcy’s law holds only for viscous flow and that the medium must be 100% saturated with the flowing fluid when the determination of permeability is made. Furthermore, the medium and the fluid must not react by chemical reaction, absorption, or adsorption; otherwise, the permeability changes as the fluid flows through the sample. Darcy’s law (Eq. 1) has many practical applications, including determination of permeability in the laboratory and wellbore.

### Darcy's law for hydrological applications

In hydrological applications, the fluid is assumed to be water at near-surface conditions. The viscosity of water is factored into the transport term, which is called hydraulic conductivity (K) and has the units of velocity. Darcy’s law is then written as

(2)

This version of Darcy’s law is not useful to the petroleum engineer, but it is sometimes handy to be able to convert from hydraulic conductivity units to permeability. To obtain k in darcies, multiply K in m/s by 1.04×105.

### Property of pore space geometry

Permeability is a property of pore space geometry; specifically, it has been found to be proportional to ()2, where:

• R is a pore throat dimension
• Φ is porosity

However, a measure of R is not available unless capillary pressure determinations have been made, in which case permeability has also been determined in the laboratory. Because permeability can be measured only on a restricted set of samples or from a limited number of well tests, it must often be derived from other properties or measurements. Porosity and permeability are routinely measured on core plugs; necessary corrections to core measurements are covered in NEED TITLE HERE

### Effect of clays and minerals

The topics of fluid sensitivity and stress also deserve consideration. Many rocks contain clays or other minerals that are sensitive to the pore fluid. If an incompatible pore fluid is introduced during a production process, these minerals can:

• Change form
• Swell
• Migrate

Permeability can then decrease by orders of magnitude. As effective pressure is increased, pore space decreases and permeability is lowered. The change in permeability with pressure is greater at low effective pressures. This pressure dependence is also strong in poorly consolidated rocks or rocks where flow is dominated by fractures. As rocks become consolidated or well cemented, the pressure dependence may become negligible.

### Predicting permeability

To quantitatively predict permeability, one needs a physical model and a method of zoning or clustering the data. Models used to predict permeability from porosity and other measurable rock parameters fall into classes based on:

• Grain size
• Mineralogy
• Surface area
• Pore dimension parameters

Zonation techniques include the following types of approaches:

• Database
• Statistical
• Clustering
• Neural networks

Ultimately, the choices of model and zonation method depend on the problem to be solved, the data available, and the resources devoted to the task.

## Models for estimating permeability

Some of these models are:

Additional approaches use data from well logs for estimating permeability. A comparison of available approaches provides practical information for choosing the right approach for a particular situation.

## Nomenclature

 A = area g = gravitational acceleration k = permeability K = hydraulic conductivity p = pressure q = volumetric flow rate z = elevation μ = dynamic viscosity ρ = density Φ = porosity

## References

1. API RP 27, Recommended Practice for Determining Permeability of Porous Media. 1956. Dallas, Texas: API.
2. Bass, D.M. Jr. 1987. Properties of Reservoir Rocks. In Petroleum Engineering Handbook, Ch. 26, ed. H.B. Bradley. Richardson, Texas: Society of Petroleum Engineers.