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''Permeability'' is a property of porous media that characterizes the ease with which fluid can flow through the media in response to an applied pressure gradient. It is a measure of fluid conductivity of porous material. This article discusses specific issues relating to the factors influencing the accuracy and precision of permeability determination.

''Permeability'' is the capacity of a rock layer to transmit water or other fluids, such as oil. The standard unit for permeability is the Darcy (d) or, more commonly, the millidarcy (md). Relative permeability is a dimensionless ratio that reflects the capability of oil, water, or gas to move through a formation compared with that of a single-phase fluid, commonly water. If a single fluid moves through rock, its relative permeability is 1.0. Two or more fluids generally inhigit flow through rock compared with that of a single phase of each component.<ref name=Petersetal_2012>Peters, Kenneth E., David J. Curry, and Marek Kacewicz, 2012, [http://archives.datapages.com/data/specpubs/hedberg4/INTRODUCTION/INTRODUCTION.HTM An overview of basin and petroleum system modeling: Definitions and concepts], ''in'' Peters, Kenneth E., David J. Curry, and Marek Kacewicz, eds., Basin modeling: New horizons in research and applications: [http://store.aapg.org/detail.aspx?id=1106 AAPG Hedberg Series no. 4], p. 1-16.</ref>

==Theoretical background==

==Theoretical background==

[[file:permeability_fig1.png|300px|thumb|{{figure number|1}}Modified schematic diagram of Darcy's experimental apparatus. (Modified from <ref name=pt05r56>Folk, R. L., 1959, [http://archives.datapages.com/data/bulletns/1957-60/data/pg/0043/0001/0000/0001.htm Practical petrographic classification of limestones]: AAPG Bulletin, v. 43, p. 1–38.</ref>.)]]

[[file:permeability_fig1.png|300px|thumb|{{figure number|1}}Modified schematic diagram of Darcy's experimental apparatus. (Modified from Folk.<ref name=pt05r56>Folk, R. L., 1959, [http://archives.datapages.com/data/bulletns/1957-60/data/pg/0043/0001/0000/0001.htm Practical petrographic classification of limestones]: AAPG Bulletin, v. 43, p. 1–38.</ref>)]]

The fundamental relationship given by Henry<ref name=pt05r44>Darcy, H., 1856, Les Fontaines Publiques de la Ville de Dijon: Paris, Victor Dalmont, p. 590–594.</ref> is the basis for permeability determination. Darcy's law originates from the interpretation of the results of the flow of water through an experimental apparatus, shown in [[:file:permeability_fig1.png|Figure 1]]. In this experiment, water was allowed to flow downward through the sand pack contained in an iron cylinder. Manometers located at the input and output ends measured fluid pressures, which were then related to flow rates to obtain the following fundamental Darcy's law:

The fundamental relationship given by Henry<ref name=pt05r44>Darcy, H., 1856, Les Fontaines Publiques de la Ville de Dijon: Paris, Victor Dalmont, p. 590–594.</ref> is the basis for permeability determination. Darcy's law originates from the interpretation of the results of the flow of water through an experimental apparatus, shown in [[:file:permeability_fig1.png|Figure 1]]. In this experiment, water was allowed to flow downward through the sand pack contained in an iron cylinder. Manometers located at the input and output ends measured fluid pressures, which were then related to flow rates to obtain the following fundamental Darcy's law:

* ''L'' = length (cm)

* ''L'' = length (cm)

The units in which permeability is typically expressed are the ''darcy'' (d) and ''millidarcy'' (md). A permeability of 1 d allows the flow of 1 cm³ per second of fluid with 1 cP (centipoise) viscosity through a cross-sectional area of 1 cm² when a pressure gradient of 1 atm/cm is applied. This definition unfortunately contains nonconsistent units, as pressure is expressed in atmospheres rather than in fundamental units. Lowman et al.,<ref name=pt05r104>Lowman, S. W., 1972, Definition of selected groundwater terms—revisions and conceptual refinements: U. S. Geological Survey Water Supply Paper 1988, 21 p.</ref> however, have redefined the darcy unit in the mks system in which square meters represents the standard dimension of permeability. The millidarcy, which is one-thousandth of a darcy, is commonly used in core analysis and oilfield operations.

The units in which permeability is typically expressed are the ''darcy'' (d) and ''millidarcy'' (md). A permeability of 1 d allows the flow of 1 cm³ per second of fluid with 1 cP (centipoise) [[viscosity]] through a cross-sectional area of 1 cm² when a pressure gradient of 1 atm/cm is applied. This definition unfortunately contains nonconsistent units, as pressure is expressed in atmospheres rather than in fundamental units. Lowman et al.,<ref name=pt05r104>Lowman, S. W., 1972, Definition of selected groundwater terms—revisions and conceptual refinements: U. S. Geological Survey Water Supply Paper 1988, 21 p.</ref> however, have redefined the darcy unit in the mks system in which square meters represents the standard dimension of permeability. The millidarcy, which is one-thousandth of a darcy, is commonly used in [[Overview of routine core analysis|core analysis]] and oilfield operations.

==Factors controlling permeability==

==Factors controlling permeability==

[[file:permeability_fig2.png|thumb|300px|{{figure number|2}}Relationship among permeability, sorting, and grain size. (From <ref name=pt05r124>Pettijohn, F. J., 1975, Sedimentary rocks, 3rd ed.: New York, Harper and Row, p. 628.</ref>; after Krumbein and Monk, 1942.)]]

[[file:permeability_fig2.png|thumb|300px|{{figure number|2}}Relationship among permeability, sorting, and [[grain size]]. (From Pettijohn;<ref name=pt05r124>Pettijohn, F. J., 1975, Sedimentary rocks, 3rd ed.: New York, Harper and Row, p. 628.</ref> after Krumbein and Monk.<ref name=KandM1943>Krumbein, W. C., and G. D. Monk, 1943, Permeability as a function of the size parameters of unconsolidated sands: American Institute of Mining and Metallurgical Engineers, Technical Publication 1492. 11 p.</ref>)]]

===Pore geometry===

===Pore geometry===

Permeability is a function of the geometry of the pore structure of the porous media. Permeability is controlled in sandstone by grain size, grain orientation, packing arrangement, cementation, clay content, bedding, and grain size distribution and sorting. In carbonates, permeability is a function of the degree of mineral alteration (such as dolomitization), [[porosity]] development, and fractures. [[:file:permeability_fig2.png|Figure 2]] shows the relationship among permeability, sorting, and grain size.

Permeability is a function of the geometry of the pore structure of the porous media. Permeability is controlled in sandstone by grain size, grain orientation, packing arrangement, cementation, clay content, bedding, and grain size distribution and sorting. In carbonates, permeability is a function of the degree of mineral alteration (such as dolomitization), [[porosity]] development, and fractures. [[:file:permeability_fig2.png|Figure 2]] shows the relationship among permeability, [[Core_description#Maturity|sorting]], and grain size.

===Bedding===

===Bedding===

===Confining pressure===

===Confining pressure===

[[file:permeability_fig3.png|300px|thumb|{{figure number|3}}Effect of net confining stress on permeability. (After <ref name=pt05r8 />.)]]

[[file:permeability_fig3.png|300px|thumb|{{figure number|3}}Effect of net confining stress on permeability. (After Amaefule et al.<ref name=pt05r8 />)]]

Permeability decreases with increasing confining pressure. Unconsolidated or poorly lithified rock undergoes much greater permeability reduction under confining pressure than well-consolidated rock. As shown in [[:file:permeability_fig3.png|Figure 3]], a greater percentage of permeability reduction is typically observed in lower permeability rock than in higher permeability rock. To determine permeability-stress relationships, which are representative of ''in situ'' reservoir conditions, permeability measurements should be made on selected samples at a series of confining pressures. Jones<ref name=pt05r86>Jones, S. C., 1988, Two-point determinations of permeability and PV versus net confining stress: Society of Petroleum Engineer Formation Evaluation, v. 3, p. 235–241.</ref> has recently presented a method that allows a two-point determination of a permeability-stress model that reduces the required number of permeability measurements under confining stress for permeability-stress prediction.

Permeability decreases with increasing confining pressure. Unconsolidated or poorly lithified rock undergoes much greater permeability reduction under confining pressure than well-consolidated rock. As shown in [[:file:permeability_fig3.png|Figure 3]], a greater percentage of permeability reduction is typically observed in lower permeability rock than in higher permeability rock. To determine permeability-stress relationships, which are representative of ''in situ'' reservoir conditions, permeability measurements should be made on selected samples at a series of confining pressures. Jones<ref name=pt05r86>Jones, S. C., 1988, Two-point determinations of permeability and PV versus net confining stress: Society of Petroleum Engineer Formation Evaluation, v. 3, p. 235–241.</ref> has recently presented a method that allows a two-point determination of a permeability-stress model that reduces the required number of permeability measurements under confining stress for permeability-stress prediction.

===Gas permeability by unsteady-state method===

===Gas permeability by unsteady-state method===

[[file:permeability_fig5.png|300px|thumb|{{figure number|5}}Typical pressure drawdown plot. (Modified from <ref name=pt05r85 />.)]]

[[file:permeability_fig5.png|300px|thumb|{{figure number|5}}Typical pressure drawdown plot. (Modified from Jones.<ref name=pt05r85 />)]]

Aronofsky<ref name=pt05r21>Aronofsky, J. S., 1954, Effect of gas slip on unsteady flow of gas through porous media: Journal of Applied Physics, v. 25, n. 1, p. 48–53., 10., 1063/1., 1721519</ref> has discussed the theory of transient permeability measurements, and the development of transient state permeameters has been discussed by Wallick and Aronofsky,<ref name=pt05r160>Wallick, G. C., Aronofsk, J. S., 1954, Effects of gas slip on unsteady flow of gas through porous media—experimental verification.: Transactions of the American Institute of Mining and Engineering, v. 201, p. 322–324.</ref>, [[Champlin (1962)]]{{citation needed}}, Morris,<ref name=pt05r115>Morris, W. L., 1953, Assignor, Philips Petroleum Co. Portable Permeameter: U., S. Patent No. 2,633,015, March 23.</ref> and Jones.<ref name=pt05r85>Jones, S. C., 1972, Rapid accurate unsteady-state klinkenberg permeameter: Society of Petroleum Engineers Journal, v. 12, p. 383–397., 10., 2118/3535-PA</ref>

Aronofsky<ref name=pt05r21>Aronofsky, J. S., 1954, Effect of gas slip on unsteady flow of gas through porous media: Journal of Applied Physics, v. 25, n. 1, p. 48–53., 10., 1063/1., 1721519</ref> has discussed the theory of transient permeability measurements, and the development of transient state permeameters has been discussed by Wallick and Aronofsky,<ref name=pt05r160>Wallick, G. C., Aronofsk, J. S., 1954, Effects of gas slip on unsteady flow of gas through porous media—experimental verification.: Transactions of the American Institute of Mining and Engineering, v. 201, p. 322–324.</ref>, [[Champlin (1962)]]{{citation needed}}, Morris,<ref name=pt05r115>Morris, W. L., 1953, Assignor, Philips Petroleum Co. Portable Permeameter: U., S. Patent No. 2,633,015, March 23.</ref> and Jones.<ref name=pt05r85>Jones, S. C., 1972, Rapid accurate unsteady-state klinkenberg permeameter: Society of Petroleum Engineers Journal, v. 12, p. 383–397., 10., 2118/3535-PA</ref>

|+ {{table number|1}}Comparison of steady-state and unsteady-state techniques

|+ {{table number|1}}Comparison of steady-state and unsteady-state techniques

|-

|-

! Steady-State

! Steady-State || Unsteady-State

! Unsteady-State

|-

|-

| Industry standard for 30 years

| Industry standard for 30 years || Determines more representative permeability ''k''_∞ instead of ''k''_air at reservoir conditions

| Determines more representative permeability ''k''_∞ instead of ''k''_air at reservoir conditions

|-

|-

| Convenient to use

| Convenient to use || Enhanced accuracy results from measurement of pressure versus time instead of rate

| Enhanced accuracy results from measurement of pressure versus time instead of rate

|-

|-

| Permeability is determined at low confining pressures

| Permeability is determined at low confining pressures || Measures additional reservoir description parameters: β and ''b''

| Measures additional reservoir description parameters: β and ''b''

|-

|-

|

| || Develops practical link with historical data

 

| Develops practical link with historical data

|}

|}

===Liquid permeability by unsteady-state method===

===Liquid permeability by unsteady-state method===

A technique based on pulse decay analysis<ref name=pt05r6>Amaefule, J. O., Masuo, S. T., 1986, Use of [[capillary pressure]] data for rapid evaluation of formation damage or [[stimulation]]: Society of Petroleum Engineers Paper No. 12475.</ref> has been developed recently to determine effective permeability to liquid for low quality reservoir rocks. The authors reviewed computational techniques and experimental protocols for liquid permeability determination. A technique that allows the simultaneous determination of liquid permeability and compressibility was also developed. A detailed discussion of this technique is beyond the scope of this article, therefore, interested readers are referred to<ref name=pt05r6 />.

A technique based on pulse decay analysis<ref name=pt05r6>Amaefule, J. O., Masuo, S. T., 1986, Use of capillary pressure data for rapid evaluation of formation damage or stimulation: Society of Petroleum Engineers Paper No. 12475.</ref> has been developed recently to determine effective permeability to liquid for low quality reservoir rocks. The authors reviewed computational techniques and experimental protocols for liquid permeability determination. A technique that allows the simultaneous determination of liquid permeability and compressibility was also developed. A detailed discussion of this technique is beyond the scope of this article, therefore, interested readers are referred to Amaefule and Masuo.<ref name=pt05r6 />

===Permeability averaging and uncertainty determination===

===Permeability averaging and uncertainty determination===

Systematic and/or random errors may affect the accuracy of permeability determined from any method, whether laboratory core or well test analysis. Uncertainty in the models used for permeability determination and input variables can result only in random errors if the same analytical technique, equipment calibration, and quality control scenario are considered. Amaefule and Keelan<ref name=pt05r5>Amaefule, J. O., Keelan, D. K., 1989, Stochastic approach to computation of uncertainty in petrophysical properties: SC Conference Paper No. 8907.</ref> have shown that random errors can be addressed through stochastic modeling in which uncertainty can be assigned to the independent variables by multiple measurements and statistical calculations. Typically, accuracy of measured permeabilities decline at low and high values and are usually within ±5%.<ref name=pt05r89>Keelan, D. K., 1971, A critical review of core analysis techniques: 22nd Annual Technical Meeting of the Petroleum Society of the Canadian Institute of Mining, Calgary, Banff, Alberta, June 2–5, Paper No. 7612, p. 1–13.</ref>

Systematic and/or random errors may affect the accuracy of permeability determined from any method, whether laboratory core or well test analysis. Uncertainty in the models used for permeability determination and input variables can result only in random errors if the same analytical technique, equipment calibration, and quality control scenario are considered. Amaefule and Keelan<ref name=pt05r5>Amaefule, J. O., Keelan, D. K., 1989, Stochastic approach to computation of uncertainty in petrophysical properties: SC Conference Paper No. 8907.</ref> have shown that random errors can be addressed through stochastic modeling in which uncertainty can be assigned to the independent variables by multiple measurements and statistical calculations. Typically, accuracy of measured permeabilities decline at low and high values and are usually within ±5%.<ref name=pt05r89>Keelan, D. K., 1971, A critical review of core analysis techniques: 22nd Annual Technical Meeting of the Petroleum Society of the Canadian Institute of Mining, Calgary, Banff, Alberta, June 2–5, Paper No. 7612, p. 1–13.</ref>

==See also==

==See also==

* [[Core description]]

* [[Core description]]

* [[Porosity]]

* [[Porosity]]

* [[Relative permeability]]

* [[Relative permeability]]

* [[Wettability]]

* [[Wettability]]

[[Category:Laboratory methods]]

[[Category:Laboratory methods]]