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Capillary pressure (Pc) curves: pore throat size determination (view source)
Revision as of 17:05, 31 January 2014
, 17:05, 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
}}
[[Capillary pressure]] (P<sub>c</sub>) curves are a rock property measurement that relates the volume of pore space controlled by pore throats of a given size (usually given in microns) to a given [[capillary pressure]].
==What is capillary pressure?==
P<sub>c</sub> is the resistant force to hydrocarbon [[migration]]. It is a function of the interfacial tension (γ), the [[wettability]] (Θ), and pore throat radius (r). P<sub>c</sub> increases with decreasing pore throat size, increasing interfacial tension, and increasing contact angle (greater oil wetting). It can be expressed as follows:
:<math>\mbox{P}_{\rm c} = \frac{2\gamma \cos \Theta}{\mbox{r}}</math>
This expression assumes the capillary phenomenon occurs within a tube with a circular cross section. Real pores only approximate this, and then only if they are intergranular or intercrystalline (Coalson, personal communication, 1997).
==Capillary test procedure==
In a mercury capillary pressure test, a rock with a measured [[porosity]] is immersed in a mercury pressure cell. The pressure in the cell is raised to a predetermined pressure level (P1, figure below). When the cell comes to equilibrium, the volume of injected mercury is measured (V2). Since the porosity of the test sample is known prior to the test, the volume of injected mercury can be converted to the percent of the total pore volume filled with mercury (for example, 10% at [[pressure::10 psi]] for point M1). All the pores filled with mercury at this point in the test have at least one 10μ pore throat radius or larger and represent 10% of the sample's pore volume. This procedure is repeated several more times at different pressures (for example, points M2 through M5).
==Pore throat profiles==
A curve is drawn through the measured points at test completion. This capillary pressure curve also represents a pore throat size profile for the tested sample. It relates a given pore throat size to its capillary resistance (P<sub>c</sub>). The diagram below shows the curve drawn through the points in Figure 9-11.
[[file:predicting-reservoir-system-quality-and-performance_fig9-11.png|thumb|{{figure number|9-11}}See text for explanation.]]
[[file:predicting-reservoir-system-quality-and-performance_fig9-12.png|thumb|{{figure number|9-12}}See text for explanation.]]
==Converting capillary pressure to pore throat size==
Capillary pressure curves are converted to profiles of pore throat size by solving the previous equation for ''r'':
:<math>\mbox{r} = \frac{2\gamma \cos \Theta}{\mbox{P}_{\rm c}}</math>
Capillary pressure for a given S<sub>w</sub> can also be converted to an approximation of height above free water (''h'') within a reservoir system. From a capillary pressure curve at a given S<sub>w</sub>, we read the capillary pressure and multiply it by a factor that converts P<sub>c</sub> to [[buoyancy pressure]] (P<sub>b</sub>). If the conversion factor is not known, we use 0.4 for gas and 0.7 for oil.
==Using p<sub>c</sub> to estimate ''h'' and ''r''==
Use the table below to estimate height above free water (''h'') and pore throat radius (''r'') from a mercury capillary pressure curve.
{| class = "wikitable"
|-
! To estimate
! Follow this procedure
|-
| Pore throat size ( ''r'' ) from S<sub>w</sub>
| * <table-wrap id="ch09utbl12a" position="float"> <table frame="hsides"> <colgroup> <col align="left"></col> <col align="left"></col> </colgroup> <thead> <tr> <th align="left"> Step </th> <th align="center"> Action </th> </tr> </thead> <tbody> <tr> <td align="center"> 1 Enter the X-axis at percent pore volume (S<sub>w</sub> value). </td></tr> <tr> 2 At the intersectionof grid line and P<sub>c</sub> curve, read the corresponding value for ''r'' on the Y-axis </tr> </tbody> </table> </table-wrap>
|-
| <th align="left"> Step</th>
| <th align="center"> Action</th>
|-
| 1
| Enter the X-axis at percent pore volume (S<sub>w</sub> value).
|-
| 2
| At the intersectionof grid line and P<sub>c</sub> curve, read the corresponding value for ''r'' on the Y-axis
|}
<tr><td align="left" valign="top">Height above free water level (''h'') from S<sub>w</sub></td><td align="center">
*
{| class = "wikitable"
|-
! Step
! Action
|-
| 1
| Enter the X-axis at percent pore volume (S<sub>w</sub> value).
|-
| 2
| At the intersection of grid line and P<sub>c</sub> curve, read the corresponding value for P<sub>c</sub> on the left Y-axis.
|-
| 3
| Multiply P<sub>c</sub> by the appropriate gradient (as a rule of thumb, use 0.7 for oil, 0.4 for gas).
|}
</td></tr>
==Example==
Using the curve in the diagram below, if S<sub>w</sub> = 20% (point 1), then the mercury capillary pressure (P<sub>c</sub>) that must be overcome to enter pore throats at that point on the curve is [[pressure::200 psi]] (point 2). Converting mercury P<sub>c</sub> to hydrocarbon column height (''h''):
:<math>\mbox{h} = 200 \mbox{ psi} \times 0.7 = 140 \mbox{ ft of oil column}</math>
:<math>&=200 \mbox{ psi} \times 0.4 = 50 \mbox{ ft of gas column}</math>
The minimum pore throat radius entered when S<sub>w</sub> is 20% and P<sub>c</sub> is [[pressure::200 psi]] is 0.5μ.
[[file:predicting-reservoir-system-quality-and-performance_fig9-13.png|thumb|{{figure number|9-13}}See text for explanation.]]
==See also==
* [[Classifying pore systems]]
* [[Pore system fundamentals]]
* [[Pore system shapes]]
* [[Pore and pore throat sizes]]
* [[Connectivity and pore throat size]]
* [[Classifying pore systems]]
==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
}}
[[Capillary pressure]] (P<sub>c</sub>) curves are a rock property measurement that relates the volume of pore space controlled by pore throats of a given size (usually given in microns) to a given [[capillary pressure]].
==What is capillary pressure?==
P<sub>c</sub> is the resistant force to hydrocarbon [[migration]]. It is a function of the interfacial tension (γ), the [[wettability]] (Θ), and pore throat radius (r). P<sub>c</sub> increases with decreasing pore throat size, increasing interfacial tension, and increasing contact angle (greater oil wetting). It can be expressed as follows:
:<math>\mbox{P}_{\rm c} = \frac{2\gamma \cos \Theta}{\mbox{r}}</math>
This expression assumes the capillary phenomenon occurs within a tube with a circular cross section. Real pores only approximate this, and then only if they are intergranular or intercrystalline (Coalson, personal communication, 1997).
==Capillary test procedure==
In a mercury capillary pressure test, a rock with a measured [[porosity]] is immersed in a mercury pressure cell. The pressure in the cell is raised to a predetermined pressure level (P1, figure below). When the cell comes to equilibrium, the volume of injected mercury is measured (V2). Since the porosity of the test sample is known prior to the test, the volume of injected mercury can be converted to the percent of the total pore volume filled with mercury (for example, 10% at [[pressure::10 psi]] for point M1). All the pores filled with mercury at this point in the test have at least one 10μ pore throat radius or larger and represent 10% of the sample's pore volume. This procedure is repeated several more times at different pressures (for example, points M2 through M5).
==Pore throat profiles==
A curve is drawn through the measured points at test completion. This capillary pressure curve also represents a pore throat size profile for the tested sample. It relates a given pore throat size to its capillary resistance (P<sub>c</sub>). The diagram below shows the curve drawn through the points in Figure 9-11.
[[file:predicting-reservoir-system-quality-and-performance_fig9-11.png|thumb|{{figure number|9-11}}See text for explanation.]]
[[file:predicting-reservoir-system-quality-and-performance_fig9-12.png|thumb|{{figure number|9-12}}See text for explanation.]]
==Converting capillary pressure to pore throat size==
Capillary pressure curves are converted to profiles of pore throat size by solving the previous equation for ''r'':
:<math>\mbox{r} = \frac{2\gamma \cos \Theta}{\mbox{P}_{\rm c}}</math>
Capillary pressure for a given S<sub>w</sub> can also be converted to an approximation of height above free water (''h'') within a reservoir system. From a capillary pressure curve at a given S<sub>w</sub>, we read the capillary pressure and multiply it by a factor that converts P<sub>c</sub> to [[buoyancy pressure]] (P<sub>b</sub>). If the conversion factor is not known, we use 0.4 for gas and 0.7 for oil.
==Using p<sub>c</sub> to estimate ''h'' and ''r''==
Use the table below to estimate height above free water (''h'') and pore throat radius (''r'') from a mercury capillary pressure curve.
{| class = "wikitable"
|-
! To estimate
! Follow this procedure
|-
| Pore throat size ( ''r'' ) from S<sub>w</sub>
| * <table-wrap id="ch09utbl12a" position="float"> <table frame="hsides"> <colgroup> <col align="left"></col> <col align="left"></col> </colgroup> <thead> <tr> <th align="left"> Step </th> <th align="center"> Action </th> </tr> </thead> <tbody> <tr> <td align="center"> 1 Enter the X-axis at percent pore volume (S<sub>w</sub> value). </td></tr> <tr> 2 At the intersectionof grid line and P<sub>c</sub> curve, read the corresponding value for ''r'' on the Y-axis </tr> </tbody> </table> </table-wrap>
|-
| <th align="left"> Step</th>
| <th align="center"> Action</th>
|-
| 1
| Enter the X-axis at percent pore volume (S<sub>w</sub> value).
|-
| 2
| At the intersectionof grid line and P<sub>c</sub> curve, read the corresponding value for ''r'' on the Y-axis
|}
<tr><td align="left" valign="top">Height above free water level (''h'') from S<sub>w</sub></td><td align="center">
*
{| class = "wikitable"
|-
! Step
! Action
|-
| 1
| Enter the X-axis at percent pore volume (S<sub>w</sub> value).
|-
| 2
| At the intersection of grid line and P<sub>c</sub> curve, read the corresponding value for P<sub>c</sub> on the left Y-axis.
|-
| 3
| Multiply P<sub>c</sub> by the appropriate gradient (as a rule of thumb, use 0.7 for oil, 0.4 for gas).
|}
</td></tr>
==Example==
Using the curve in the diagram below, if S<sub>w</sub> = 20% (point 1), then the mercury capillary pressure (P<sub>c</sub>) that must be overcome to enter pore throats at that point on the curve is [[pressure::200 psi]] (point 2). Converting mercury P<sub>c</sub> to hydrocarbon column height (''h''):
:<math>\mbox{h} = 200 \mbox{ psi} \times 0.7 = 140 \mbox{ ft of oil column}</math>
:<math>&=200 \mbox{ psi} \times 0.4 = 50 \mbox{ ft of gas column}</math>
The minimum pore throat radius entered when S<sub>w</sub> is 20% and P<sub>c</sub> is [[pressure::200 psi]] is 0.5μ.
[[file:predicting-reservoir-system-quality-and-performance_fig9-13.png|thumb|{{figure number|9-13}}See text for explanation.]]
==See also==
* [[Classifying pore systems]]
* [[Pore system fundamentals]]
* [[Pore system shapes]]
* [[Pore and pore throat sizes]]
* [[Connectivity and pore throat size]]
* [[Classifying pore systems]]
==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]]