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Capillary pressure (Pc): buoyancy, height, and pore throat radius (view source)
Revision as of 20:24, 31 January 2014
, 20:24, 31 January 2014Initial import
{{publication
| image = exploring-for-oil-and-gas-traps.png
| width = 120px
| series = Treatise in Petroleum Geology
| title = Exploring for Oil and Gas Traps
| part = Predicting the occurrence of oil and gas traps
| chapter = Predicting reservoir system quality and performance
| frompg = 9-1
| topg = 9-156
| author = Dan J. Hartmann, Edward A. Beaumont
| link = http://archives.datapages.com/data/specpubs/beaumont/ch09/ch09.htm
| pdf =
| store = http://store.aapg.org/detail.aspx?id=545
| isbn = 0-89181-602-X
}}
A [[capillary pressure]] (P<sub>c</sub>) curve is generated in the lab using a mercury pressure cell, a porous plate, or a centrifuge. Fluid systems used in these techniques include air–water (brine), oil–water, air–mercury, or air–oil. Data generated by these techniques cannot be compared directly to each other or to reservoir conditions. Below, we demonstrate how to convert pressures measured in the lab to
* Standard pressure scale (mercury P<sub>c</sub>)
* Reservoir pressure
* Height above free water
* Pore throat size
If true reservoir conditions are at least partially oil wet, then the water saturation–height plot shifts away from the pore volume–height plot (P<sub>c</sub> curve).
==Converting lab capillary pressure data==
Follow the steps in the table below to convert P<sub>c</sub> to [[buoyancy pressure]], pore throat size (''r''), or hydrocarbon column height (''h''′). Assume water-wet conditions in the reservoir (γ = interfacial tension, Θ = contact angle).
{| class = "wikitable"
|-
! Step
! Action
! Equation
|-
| 1
| Rescale P<sub>c</sub> from one lab system to a common technique (i.e., air–brine to air–mercury).
| P<sub>c system1</sub> = P<sub>c system2</sub> (γcosΘ of system1/γcosΘ of system2)
|-
| 2
| Convert lab P<sub>c</sub> to reservoir P<sub>c</sub> (i.e., air– mercury to water–oil).
| P<sub>c</sub><sub>res</sub> = P<sub>c</sub><sub>lab</sub> (γcosΘ<sub>res</sub> /γcosΘ<sub>lab</sub> )
|-
| 3
| Convert reservoir P<sub>c</sub> to height ( ''h'' ′).
| h′ = P<sub>c</sub><sub>res</sub> /(water gradient – hydrocarbon gradient) <break> </break> Typical gradients in psi/ft: Water = 0.433 – 0.45, Oil = 0.33, Gas = 0.07 (range = 0.001–0.22)
|-
| 4
| Convert lab P<sub>c</sub> to pore throat radius ( ''r'' ) in microns.
| r = –2γcosΘ/P<sub>c</sub><sub>lab</sub> or C(γcosΘ<sub>lab</sub> )/P<sub>c</sub><sub>lab</sub> where C is the constant 0.29
|}
==Example==
The following is an example of applying the conversion of lab P<sub>c</sub> data to reservoir conditions.
'''Use these assumptions:'''
* Maximum air–brine P<sub>c</sub> value for a sample is [[pressure::40 psi]].
* Air–mercury is the base data set.
* The reservoir is oil filled.
'''Determine these parameters:'''
* Equivalent air–mercury P<sub>c</sub> (P<sub>c</sub> <sub>Hg</sub>)
* Equivalent oil P<sub>c</sub> (buoyancy pressure in the reservoir)
* Height above the free water (''h''′)
* Pore throat radius for P<sub>c</sub> <sub>Hg</sub> as determined at A
'''Answers''' (refer to the table below for values)
* <math>\mbox{A.\quad P}_{\rm c\ Hg} = \mbox{P}_{\rm c\ brine} \left(\frac{\gamma \cos \Theta \mbox{ for Hg}}{\gamma \cos \Theta \mbox{ for brine}}\right) = \mbox{P}_{\rm c\ brine} \left(\frac{367}{72}\right) = 40 (5.1) = 204 \mbox{ psi}</math>
* <math>\mbox{B.\quad Equivalent oil P}_{\rm c} = \mbox{P}_{\rm c\ lab} \left(\frac{\gamma \cos \Theta_{\rm res}}{\gamma \cos \Theta_{\rm lab}}\right) = \mbox{P}_{\rm c\ lab} \left(\frac{26}{367}\right) = \mbox{P}_{\rm c\ lab} (0.071) = 204 (0.071) = 14.5 \mbox{ psi}</math>
* <math>\mbox{C.\quad h}' = \frac{\mbox{P}_{\rm c\ res}}{(\mbox{water gradient} - \mbox{hydrocarbon gradient})} = \frac{14.5}{(0.45 - 0.33)} = 120 \mbox{ ft}</math>
* <math>\begin{array}{c@{\quad}l}\mbox{D.} amp;\mbox{r at P}_{\rm c\ Hg} = \displaystyle\frac{-2\gamma \cos \Theta}{\mbox{P}_{\rm c\ lab}} \mbox{ or C} \left(\frac{\gamma \cos \Theta_{\rm lab}}{\mbox{P}_{\rm c\ lab}}\right) = 0.29 \times \frac{367}{204} = 0.52 \mu</math>
:<math>[12pt]&\mbox{P}_{\rm c\ Hg} \mbox{ is equivalent to P}_{\rm c\ lab}\end{array}</math>
==Conversion variables==
The conversion from one lab system to another requires values for the contact angle of the fluids to the grain surfaces (Θ) and interfacial tension (γ) between the two fluids. Theta is a reflection of [[wettability]]. This information is also required to determine an equivalent buoyancy pressure in the reservoir. Some typical lab and reservoir values are shown in the table below.
{| class = "wikitable"
|-
|-
| ''' Laboratory Measurements '''
|-
| System
| Θ
| cosΘ
| γ
| γcosΘ
|-
| Air–water
| 0
| 1.0
| 72
| 72
|-
| Oil–water
| 30
| 0.866
| 48
| 42
|-
| Air–mercury
| 40
| 0.766
| 480
| 367
|-
| Air–oil
| 0
| 1.0
| 24
| 24
|-
| ''' Reservoir Measurements '''
|-
| System
| Θ
| cosΘ
| γ
| γcosΘ
|-
| Water–oil
| 30
| 0.866
| 30
| 26
|-
| Water–gas
| 0
| 1.0
| 50
| 50
|}
==See also==
* [[Pore–fluid interaction]]
* [[Hydrocarbon expulsion, migration, and accumulation]]
* [[Characterizing rock quality]]
* [[Pc curves and saturation profiles]]
* [[What is permeability?]]
* [[Relative permeability and pore type]]
==External links==
{{search}}
* [http://archives.datapages.com/data/specpubs/beaumont/ch09/ch09.htm Original content in Datapages]
* [http://store.aapg.org/detail.aspx?id=545 Find the book in the AAPG Store]
[[Category:Predicting the occurrence of oil and gas traps]]
[[Category:Predicting reservoir system quality and performance]]
| image = exploring-for-oil-and-gas-traps.png
| width = 120px
| series = Treatise in Petroleum Geology
| title = Exploring for Oil and Gas Traps
| part = Predicting the occurrence of oil and gas traps
| chapter = Predicting reservoir system quality and performance
| frompg = 9-1
| topg = 9-156
| author = Dan J. Hartmann, Edward A. Beaumont
| link = http://archives.datapages.com/data/specpubs/beaumont/ch09/ch09.htm
| pdf =
| store = http://store.aapg.org/detail.aspx?id=545
| isbn = 0-89181-602-X
}}
A [[capillary pressure]] (P<sub>c</sub>) curve is generated in the lab using a mercury pressure cell, a porous plate, or a centrifuge. Fluid systems used in these techniques include air–water (brine), oil–water, air–mercury, or air–oil. Data generated by these techniques cannot be compared directly to each other or to reservoir conditions. Below, we demonstrate how to convert pressures measured in the lab to
* Standard pressure scale (mercury P<sub>c</sub>)
* Reservoir pressure
* Height above free water
* Pore throat size
If true reservoir conditions are at least partially oil wet, then the water saturation–height plot shifts away from the pore volume–height plot (P<sub>c</sub> curve).
==Converting lab capillary pressure data==
Follow the steps in the table below to convert P<sub>c</sub> to [[buoyancy pressure]], pore throat size (''r''), or hydrocarbon column height (''h''′). Assume water-wet conditions in the reservoir (γ = interfacial tension, Θ = contact angle).
{| class = "wikitable"
|-
! Step
! Action
! Equation
|-
| 1
| Rescale P<sub>c</sub> from one lab system to a common technique (i.e., air–brine to air–mercury).
| P<sub>c system1</sub> = P<sub>c system2</sub> (γcosΘ of system1/γcosΘ of system2)
|-
| 2
| Convert lab P<sub>c</sub> to reservoir P<sub>c</sub> (i.e., air– mercury to water–oil).
| P<sub>c</sub><sub>res</sub> = P<sub>c</sub><sub>lab</sub> (γcosΘ<sub>res</sub> /γcosΘ<sub>lab</sub> )
|-
| 3
| Convert reservoir P<sub>c</sub> to height ( ''h'' ′).
| h′ = P<sub>c</sub><sub>res</sub> /(water gradient – hydrocarbon gradient) <break> </break> Typical gradients in psi/ft: Water = 0.433 – 0.45, Oil = 0.33, Gas = 0.07 (range = 0.001–0.22)
|-
| 4
| Convert lab P<sub>c</sub> to pore throat radius ( ''r'' ) in microns.
| r = –2γcosΘ/P<sub>c</sub><sub>lab</sub> or C(γcosΘ<sub>lab</sub> )/P<sub>c</sub><sub>lab</sub> where C is the constant 0.29
|}
==Example==
The following is an example of applying the conversion of lab P<sub>c</sub> data to reservoir conditions.
'''Use these assumptions:'''
* Maximum air–brine P<sub>c</sub> value for a sample is [[pressure::40 psi]].
* Air–mercury is the base data set.
* The reservoir is oil filled.
'''Determine these parameters:'''
* Equivalent air–mercury P<sub>c</sub> (P<sub>c</sub> <sub>Hg</sub>)
* Equivalent oil P<sub>c</sub> (buoyancy pressure in the reservoir)
* Height above the free water (''h''′)
* Pore throat radius for P<sub>c</sub> <sub>Hg</sub> as determined at A
'''Answers''' (refer to the table below for values)
* <math>\mbox{A.\quad P}_{\rm c\ Hg} = \mbox{P}_{\rm c\ brine} \left(\frac{\gamma \cos \Theta \mbox{ for Hg}}{\gamma \cos \Theta \mbox{ for brine}}\right) = \mbox{P}_{\rm c\ brine} \left(\frac{367}{72}\right) = 40 (5.1) = 204 \mbox{ psi}</math>
* <math>\mbox{B.\quad Equivalent oil P}_{\rm c} = \mbox{P}_{\rm c\ lab} \left(\frac{\gamma \cos \Theta_{\rm res}}{\gamma \cos \Theta_{\rm lab}}\right) = \mbox{P}_{\rm c\ lab} \left(\frac{26}{367}\right) = \mbox{P}_{\rm c\ lab} (0.071) = 204 (0.071) = 14.5 \mbox{ psi}</math>
* <math>\mbox{C.\quad h}' = \frac{\mbox{P}_{\rm c\ res}}{(\mbox{water gradient} - \mbox{hydrocarbon gradient})} = \frac{14.5}{(0.45 - 0.33)} = 120 \mbox{ ft}</math>
* <math>\begin{array}{c@{\quad}l}\mbox{D.} amp;\mbox{r at P}_{\rm c\ Hg} = \displaystyle\frac{-2\gamma \cos \Theta}{\mbox{P}_{\rm c\ lab}} \mbox{ or C} \left(\frac{\gamma \cos \Theta_{\rm lab}}{\mbox{P}_{\rm c\ lab}}\right) = 0.29 \times \frac{367}{204} = 0.52 \mu</math>
:<math>[12pt]&\mbox{P}_{\rm c\ Hg} \mbox{ is equivalent to P}_{\rm c\ lab}\end{array}</math>
==Conversion variables==
The conversion from one lab system to another requires values for the contact angle of the fluids to the grain surfaces (Θ) and interfacial tension (γ) between the two fluids. Theta is a reflection of [[wettability]]. This information is also required to determine an equivalent buoyancy pressure in the reservoir. Some typical lab and reservoir values are shown in the table below.
{| class = "wikitable"
|-
|-
| ''' Laboratory Measurements '''
|-
| System
| Θ
| cosΘ
| γ
| γcosΘ
|-
| Air–water
| 0
| 1.0
| 72
| 72
|-
| Oil–water
| 30
| 0.866
| 48
| 42
|-
| Air–mercury
| 40
| 0.766
| 480
| 367
|-
| Air–oil
| 0
| 1.0
| 24
| 24
|-
| ''' Reservoir Measurements '''
|-
| System
| Θ
| cosΘ
| γ
| γcosΘ
|-
| Water–oil
| 30
| 0.866
| 30
| 26
|-
| Water–gas
| 0
| 1.0
| 50
| 50
|}
==See also==
* [[Pore–fluid interaction]]
* [[Hydrocarbon expulsion, migration, and accumulation]]
* [[Characterizing rock quality]]
* [[Pc curves and saturation profiles]]
* [[What is permeability?]]
* [[Relative permeability and pore type]]
==External links==
{{search}}
* [http://archives.datapages.com/data/specpubs/beaumont/ch09/ch09.htm Original content in Datapages]
* [http://store.aapg.org/detail.aspx?id=545 Find the book in the AAPG Store]
[[Category:Predicting the occurrence of oil and gas traps]]
[[Category:Predicting reservoir system quality and performance]]