| Permeability (fluid) |
Article Index for Permeability |
Information AboutPermeability (fluid) |
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The Intrinsic permeability of any Porous material is: : where : is the intrinsic permeability {Link without Title} : is a dimensionless constant that is related to the configuration of the flow-paths : is the average, or effective pore Diameter {Link without Title} Permeability needs to be measured, either directly (using Darcy's Law ) or through Estimation using Empirically derived formulas. A common unit for permeability is the '' Darcy '' (D), or more commonly the ''millidarcy'' (mD) (1 darcy 10−12m&2). Other units are cm&2 and the SI m&2. Permeability is part of the proportionality constant in Darcy's Law which relates discharge (flow rate) and fluid physical properties (e.g. Viscosity ), to a pressure gradient applied to the porous media. The proportionality constant specifically for the flow of water through a porous media is the Hydraulic Conductivity ; permeability is a portion of this, and is a property of the porous media only, not the fluid. In naturally occurring materials, it ranges over many orders of magnitude (see table below for an example of this range). For a rock to be considered as an exploitable hydrocarbon reservoir without stimulation, its permeability must be greater than approximately 100 mD (depending on the nature of the hydrocarbon - gas reservoirs with lower permeabilities are still exploitable because of the lower Viscosity of gas with respect to oil). Rocks with permeabilities significantly lower than 100 mD can form efficient ''seals'' (see Petroleum Geology ). Unconsolidated sands may have permeabilities of over 5000 mD. TENSOR PERMEABILITY To model permeability in Anisotropic media, a permeability Tensor is needed. Pressure can be applied in three directions, and for each direction, permeability can be measured (via Darcy's Law in 3D) in three directions, thus leading to a 3 by 3 tensor. The tensor is realized using a 3 by 3 Matrix being both Symmetric and Positive Definite (SPD matrix):
The permeability tensor is always Diagonalizable (being both symmetric and positive definite). The Eigenvectors will yield the principal directions of flow, meaning the directions where flow is parallel to the pressure drop, and the Eigenvalues representing the magnitude of flow along principal directions. RANGES OF COMMON INTRINSIC PERMEABILITIES These values do not depend on the fluid properties; see the table derived from the same source for values of Hydraulic Conductivity , which are specific to water. Source: modified from Bear, 1972 SEE ALSO REFERENCE
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