Permeability (earth sciences)

The permeability (Latin: permeare "let through ", from Latin: by " passing " and Latin: meare " pass " ) is used in geotechnical engineering to quantify the permeability of soils and rock for liquids or gases (for example, ground water, oil or natural gas ) used. With her ​​very closely linked is the same here explained permeability.

• 4.1 Metrologically
• 4.2 Computationally from the particle distribution curve

• 5.1 production of oil and natural gas

Definition

The permeability is derived from Darcy 's law and is defined as:

Where:

• K = permeability in m²
• Q = Flow rate in m³ / s
• η = dynamic viscosity of the fluid medium in Ns / m
• L = length of the porous body through which flow in m
• A = cross-sectional area flowed through the porous body in m²
• Ap = pressure difference in N / m, which occurs after the streams.

The permeability depends only on the properties of the medium through which flow from ( material parameter ), because the product of the flow rate Q and viscosity η remains constant:

Since permeability is not affected by the density, which depends on the pressure in gases, it is well suited for gases and is therefore often used in the oil and gas industry. The dynamic viscosity is independent in the range of validity of the Gas Act from the pressure, the temperature dependence is always given.

As a SI unit for permeability results m². Another common unit is the Darcy, named after the French scientist Henry Darcy (1803-1858), who in 1856 studied the flow of water through Kiesbettungen:

Since 1 Darcy is a relatively high permeability, the millidarcy ( mD ) or the SI unit ( microns ) ² are used in geotechnical engineering and mining often.

Coefficient of permeability

Also, the coefficient of permeability (or hydraulic conductivity ) quantified the permeability of soil or rock, but go here, the density and viscosity of the fluid flowing through a:

Where:

• Kf = permeability in m / s
• ρ = density of the fluid, in water 1000 kg / m³
• G = acceleration due to gravity = 9.81 m / s ²
• η = dynamic viscosity of the fluid, water at 10-3 Ns / m.

The permeability coefficient is usually used for flowing liquids (water ), ie in the areas of water management and water. Since in ( incompressible ) fluids can be assumed to be the permeability also simplifies write as:

Through which the flow takes place with the height difference.

Unless otherwise stated, the values ​​given in the literature for kf usually refer to water. If the hydraulic conductivity is known for a traversed with water medium, then can the permeability of this medium for other substances calculate (see " Determination of permeability ").

Value ranges

The boundary between a permeable and an impermeable bottom is about 10-6 m / s

Properties and variables

The permeability of soils depends primarily on its porosity. Of rock on its porosity and / or its Klüftigkeit The porosity of soils in turn depends on the particle size, its distribution, and thus the pore volume of the soil.

Permeability and permeability coefficient quantified in a similar manner, the flow rate Q through a permeable medium in dependence on the pressure difference AP, different units thereof are:

• In transmission, there is an area (m²)
• The coefficient of permeability, it is a speed (m / s).

Both variables can be dependent on the direction and are then represented as tensors.

In addition, both variables constant over the flow rate Q, if the following conditions are met:

Determination

Metrologically

In petrophysical laboratories permeability is routinely determined on cylindrical specimens having a diameter of 30 mm and a length of 40 to 80 mm; in the United States for routine measurements of samples 1 inch x 1 1 /2 inch in use. For studies in which it comes to a large pore volume (for example, relative permeability ), and specimen diameter of 40 mm are usual. The orientation of the samples is by default parallel to the stratification.

A special case is the determination of Permeabilitätsanisotropie on cubes of 30 or 40 mm edge length. They are so to work out from the core material, in that two surfaces are oriented parallel to the layers and thus the data can be determined on a sample parallel to and perpendicular to the layering.

With the outlined measurement arrangement kf is determined for water:

K can then be on the dynamic viscosity η of water and its density ρ calculate:

If the coefficient of permeability kf determined for the flow-through water medium experimentally, as can be seen from the aforementioned relationship to hydraulic conductivity of this medium to other fluids, such as oil, by inserting the density and dynamic viscosity calculated:

Or by using the kinematic viscosity:

Calculated from the particle size distribution curve

For soils is possible, the permeability coefficient kf for water in m / s from the particle distribution curve estimate ( Hazen, 1893):

Where:

• Dw = Effective grain diameter in mm
• D10 = grain diameter for the weight fraction of m = 10 % of the grain size distribution curve.

This estimate is only valid under the assumption that the non-uniformity is ( uniform soil).

According Beyer

C is a coefficient that depends on the non-uniformity: For certain, C = 0.0116, so that the formula corresponds to the Hazen.

Application

These material parameters are applied when soil or rock of liquids or gases are flowed through: groundwater flow, drinking water, extraction of oil or natural gas, calculations of water huge intake of buildings and tunnels, determining the tightness of dams and dikes, even in contaminated soils and the pressing of carbon dioxide.

Production of oil and natural gas

For the efficiency of the production of oil and natural gas production rate is an important factor. It depends inter alia on the permeability of the geological formations from which these raw materials are conveyed. However, since the world market price on the economy decides not here permanently valid values ​​can be specified.

Transmissibility and transmissivity

The transmissibility is defined as the product of permeability K and the cardinality M of water leading soil or rock layer ( aquifer ):

Similarly, the transmissivity is defined as the product of permeability kf and thickness:

If the aquifer from i layers with different permeabilities and thicknesses, then the respective products are added:

From the last formula, the purpose of the two variables is clear: they are the integrals of the respective permeability values ​​(K or k f ) of the aquifer thickness dar. This takes into account that the permeability is not over the entire height of the aquifer is usually the same: is the aquifer inhomogeneous with respect to its permeability.

Because the common factor M between the two variables have the same relationship as between kf and K:

The more common of the two variables is the transmissivity in accordance with DIN, since as drinking water plays an important role in the extraction of groundwater.

The transmissivity is usually determined via a pumping test. It only gives the total transmissivity and no information on the above Inhomogeneities in the Durchlässigleit the aquifer.

Notes:

• The transmissibility is also used in the optical industry as a permeability measurement for contact lenses. Here it indicates how much oxygen (in cm ³ / s) on both sides at 1 mmHg pressure an area of ​​1 cm ² flows through a membrane. See: permeability ( solid ), Barrer.
• Often ( scientific and casual ) is called the degree of transmission used in physics as transmissivity.