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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|left|thumb|{{figure number|1}}Modified schematic diagram of Darcy's experimental apparatus. (Modified from <ref name=pt05r56>Folk, R. L., 1959, 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:

:<math>q = KA \frac{\Delta h}{L}</math>

:<math>q = KA \frac{\Delta h}{L}</math>

* ''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.

[[file:permeability_fig2.png|thumb|{{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.)]]

==Factors controlling permeability==

==Factors controlling permeability==

[[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===

Directional and local variations of permeability generally exist in reservoirs. Permeability perpendicular to bedding planes (vertical permeability) is typically lower than horizontal permeability (parallel to the bedding planes).

Directional and local variations of permeability generally exist in reservoirs. Permeability perpendicular to bedding planes (vertical permeability) is typically lower than horizontal permeability (parallel to the bedding planes).

===[[Porosity]]===

===Porosity===

Several attempts have been made in the past to derive a general relationship between porosity and permeability. Prominent among these relationships is the work of Kozeny<ref name=pt05r98>Kozeny, J. S., 1927, Uber Kapillare Leitung des Wassers im Boden (Aufstieg, Versickerung und Anwendung auf die Bewasserung): S.-Ber. Wiener Akad. Abt. II a, v. 136, p. 271–306.</ref>, which considered the porous media as a bundle of capillary tubes of equal length. Modifications to account for tortuosity of flow paths in the porous media have been proposed, including the Carman-Kozeny model (1938). Unfortunately, only qualitative results have been obtained using these permeability-porosity relationships because of the complexity of the geometry of the porous media.

Several attempts have been made in the past to derive a general relationship between porosity and permeability. Prominent among these relationships is the work of Kozeny,<ref name=pt05r98>Kozeny, J. S., 1927, Uber Kapillare Leitung des Wassers im Boden (Aufstieg, Versickerung und Anwendung auf die Bewasserung): S.-Ber. Wiener Akad. Abt. II a, v. 136, p. 271–306.</ref> which considered the porous media as a bundle of capillary tubes of equal length. Modifications to account for tortuosity of flow paths in the porous media have been proposed, including the Carman-Kozeny model (1938). Unfortunately, only qualitative results have been obtained using these permeability-porosity relationships because of the complexity of the geometry of the porous media.

Berg<ref name=pt05r25>Berg, R. R., 1970, Method for determining permeability from reservoir rock properties: Transactions Gulf Coast Association of Geological Societies, v. 20, p. 303–317.</ref> suggested that a better understanding of the properties of the rock that control size, shape, and continuity of the rock is the key to relating fluid flow properties to reservoir rock properties. Qualitatively, it is reasonable to assume that permeability should increase with increase in porosity in unfractured reservoirs without significant diagenetic alterations. In fact, it has been shown that there is a relationship between porosity and permeability within units with the same hydraulic properties<ref name=pt05r8>Amaefule, J. O., Keelan, D. K., Kersey, D. G., Marschall, D. M., 1988, Reservoir description—a practical synergistic engineering and geological approach based on analysis of core data: 63rd SPE Annual Technical Conference and Exhibition of the Society of Petroleum Engineers, Houston, TX, October 2–5, SPE 18167.</ref>. (For more on porosity, see the chapters on “Porosity” and “Core-Log Transformations and Porosity-Permeability Relationships” in Part 5.)

Berg<ref name=pt05r25>Berg, R. R., 1970, Method for determining permeability from reservoir rock properties: Transactions Gulf Coast Association of Geological Societies, v. 20, p. 303–317.</ref> suggested that a better understanding of the properties of the rock that control size, shape, and continuity of the rock is the key to relating fluid flow properties to reservoir rock properties. Qualitatively, it is reasonable to assume that permeability should increase with increase in porosity in unfractured reservoirs without significant diagenetic alterations. In fact, it has been shown that there is a relationship between porosity and permeability within units with the same hydraulic properties.<ref name=pt05r8>Amaefule, J. O., Keelan, D. K., Kersey, D. G., Marschall, D. M., 1988, Reservoir description—a practical synergistic engineering and geological approach based on analysis of core data: 63rd SPE Annual Technical Conference and Exhibition of the Society of Petroleum Engineers, Houston, TX, October 2–5, SPE 18167.</ref> (For more on porosity, see [[Porosity]] and [[Core-log transformations and porosity-permeability relationships]].)

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

===Confining pressure===

===Confining pressure===

[[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.

When gas is used to determine permeability at low mean pressure, the resistance to flow from drag is very low, resulting in “gas slip conditions.” Consequently, permeability calculated from Darcy's law will be too high and must be corrected using the Klinkenberg<ref name=pt05r97>Klinkenberg, L. J., 1941, The permeability of porous media to liquid and gases, in Drilling and Production Practices: Washington, D., C., American Petroleum Institute, p. 200–211.</ref> model. When gas permeability is corrected for slippage effects at the fluid/pore wall interface, it is called equivalent, nonreactive, liquid permeability or Klinkenberg permeability.

When gas is used to determine permeability at low mean pressure, the resistance to flow from drag is very low, resulting in “gas slip conditions.” Consequently, permeability calculated from Darcy's law will be too high and must be corrected using the Klinkenberg<ref name=pt05r97>Klinkenberg, L. J., 1941, The permeability of porous media to liquid and gases, in Drilling and Production Practices: Washington, D., C., American Petroleum Institute, p. 200–211.</ref> model. When gas permeability is corrected for slippage effects at the fluid/pore wall interface, it is called equivalent, nonreactive, liquid permeability or Klinkenberg permeability.

At high flow rates, gas flowing through porous media accelerates at pore throats and decelerates in pore bodies, giving rise to what is called inertial effects. Non-Darcy flow has been described by Forchheimer<ref name=pt05r58>Forchheimer, P. H., 1901, Wasserbewegung durch Boden: Zeitschrift Verein Deutscher Ingenieure, v. 45, n. 50, p. 1781–1788.</ref>, who presented modifications.

At high flow rates, gas flowing through porous media accelerates at pore throats and decelerates in pore bodies, giving rise to what is called inertial effects. Non-Darcy flow has been described by Forchheimer,<ref name=pt05r58>Forchheimer, P. H., 1901, Wasserbewegung durch Boden: Zeitschrift Verein Deutscher Ingenieure, v. 45, n. 50, p. 1781–1788.</ref> who presented modifications.

===Laboratory methods for permeability determination===

===Laboratory methods for permeability determination===

Liquid and gas permeability can be determined on core samples in the laboratory. However, gas permeability is determined most frequently because sample preparation is simplified and the analytical procedure is fairly rapid. Two methods currently exist for gas permeability determination: steady-state and unsteady-state.

Liquid and gas permeability can be determined on core samples in the laboratory. However, gas permeability is determined most frequently because sample preparation is simplified and the analytical procedure is fairly rapid. Two methods currently exist for gas permeability determination: steady-state and unsteady-state.

[[file:permeability_fig4.png|thumb|{{figure number|4}}Schematic diagram of (a) steady-state and (b) unsteady-state apparatus.]]

===Gas permeability by steady-state method===

===Gas permeability by steady-state method===

[[file:permeability_fig4.png|thumb|300px|{{figure number|4}}Schematic diagram of (a) steady-state and (b) unsteady-state apparatus.]]

A simplified schematic diagram of the steady-state apparatus is shown in [[:file:permeability_fig4.png|Figure 4a]]. The apparatus includes a pressurized gas cylinder, a Hassler core holder, and a flowmeter. The apparatus is designed to ensure that no restrictions exist in flow lines that could cause a pressure drop between the core face and the pressure gauges. To determine air permeability, a clean, dried core sample is first placed in the core holder and pressure is applied to the rubber sleeve to seal it to the core. Air is then injected at a constant pressure until gas production rate and pressure stabilize. The pressure differential between the two ends of the core and flow rate are recorded for permeability calculation using the integrated form of Darcy's law for a compressible fluid. Thus,

A simplified schematic diagram of the steady-state apparatus is shown in [[:file:permeability_fig4.png|Figure 4a]]. The apparatus includes a pressurized gas cylinder, a Hassler core holder, and a flowmeter. The apparatus is designed to ensure that no restrictions exist in flow lines that could cause a pressure drop between the core face and the pressure gauges. To determine air permeability, a clean, dried core sample is first placed in the core holder and pressure is applied to the rubber sleeve to seal it to the core. Air is then injected at a constant pressure until gas production rate and pressure stabilize. The pressure differential between the two ends of the core and flow rate are recorded for permeability calculation using the integrated form of Darcy's law for a compressible fluid. Thus,

Measurements are usually made at several gas flow rates to ensure that flow conditions satisfy Darcy's law. In practice, gas permeability is calculated from the slope of the plot of ''V''_a versus (''p''₁² - ''p''₂²)/''L'', which results in a straight line passing through the origin as long as the conditions for Darcy's flow are maintained. The steady-state method has been the industry standard for many years because it is a convenient technique and the equipment is easy to operate.

Measurements are usually made at several gas flow rates to ensure that flow conditions satisfy Darcy's law. In practice, gas permeability is calculated from the slope of the plot of ''V''_a versus (''p''₁² - ''p''₂²)/''L'', which results in a straight line passing through the origin as long as the conditions for Darcy's flow are maintained. The steady-state method has been the industry standard for many years because it is a convenient technique and the equipment is easy to operate.

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

===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 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), 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>

A schematic diagram of the unsteady-state Klinkenberg permeameter (Jones, 1990) is shown in [[:file:permeability_fig4.png|Figure 4b]]. The permeameter works on the principle of transient analysis of pressure pulse decay in which Klinkenberg permeability is determined as a function of gas (ideally helium) pressure decay. This equipment consists of a reference cell of known volume that charges the core sample with gas. A downstream valve vents the gas pressure, and pressure change as a function of time is recorded. A typical pressure drawdown plot (Jones, 1990) is shown in [[:file:permeability_fig5.png|Figure 5]]. Advantages of the unsteady-state method include the ability to determine simultaneously (from Figure 5) the Klinkenberg permeability (''k''_∞ helium slippage factor (β_He), and the inertial coefficient (β). A comparison of the steady-state method to the unsteady-state method is presented in Table 1.

A schematic diagram of the unsteady-state Klinkenberg permeameter [[(Jones, 1990)]]{{citation needed}} is shown in [[:file:permeability_fig4.png|Figure 4b]]. The permeameter works on the principle of transient analysis of pressure pulse decay in which Klinkenberg permeability is determined as a function of gas (ideally helium) pressure decay. This equipment consists of a reference cell of known volume that charges the core sample with gas. A downstream valve vents the gas pressure, and pressure change as a function of time is recorded. A typical pressure drawdown plot [[(Jones, 1990)]]{{citation needed}} is shown in [[:file:permeability_fig5.png|Figure 5]]. Advantages of the unsteady-state method include the ability to determine simultaneously (from Figure 5) the Klinkenberg permeability (''k''_∞ helium slippage factor (β_He), and the inertial coefficient (β). A comparison of the steady-state method to the unsteady-state method is presented in Table 1.

{| class = "wikitable"

{| class = "wikitable"

|+ {{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 chapter, therefore, interested readers are referred to the paper by <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===

It is necessary to average permeability determined for each pay zone to obtain permeability distribution. The most commonly used method to average horizontal permeability is the arithmetic average. Comparison of core permeabilities shows that arithmetic average permeabilities values generally agree with well test permeabilities.

It is necessary to average permeability determined for each pay zone to obtain permeability distribution. The most commonly used method to average horizontal permeability is the arithmetic average. Comparison of core permeabilities shows that arithmetic average permeabilities values generally agree with well test permeabilities.

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>

 

* [https://www.onepetro.org/search?q=Dinwiddie&peer_reviewed=&published_between=on&from_year=2005&to_year=2005&rows=10  In situ minipermeameter measurements]

==See also==

==See also==

* [[Core description]]

* [[Core description]]

* [[Porosity]]

* [[Porosity]]

* [[Relative permeability]]

* [[Relative permeability]]

* [[Wettability]]

* [[Wettability]]

[[Category:Laboratory methods]]

[[Category:Laboratory methods]]