Capillary pressure (Pc): buoyancy, height, and pore throat radius

Exploring for Oil and Gas Traps
Series	Treatise in Petroleum Geology
Part	Predicting the occurrence of oil and gas traps
Chapter	Predicting reservoir system quality and performance
Author	Dan J. Hartmann, Edward A. Beaumont
Link	Web page
Store	AAPG Store

A capillary pressure (P_c) 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_c)
• 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_c curve).

Converting lab capillary pressure data

Follow the steps in the table below to convert P_c 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).

Step	Action	Equation
1	Rescale Pc from one lab system to a common technique (i.e., air–brine to air–mercury).	$P_{\text{c system1}}=P_{\text{c system2}}\left({\frac {\gamma \cos \Theta {\text{ of system1}}}{\gamma \cos \Theta {\text{ of system2}}}}\right)$
2	Convert lab Pc to reservoir Pc (i.e., air– mercury to water–oil).	$P_{\text{c res}}=P_{\text{c lab}}\left({\frac {\gamma \cos \Theta _{\text{res}}}{\gamma \cos \Theta _{\text{lab}}}}\right)$
3	Convert reservoir Pc to height ( h ′).	$h'={\frac {P_{\text{c res}}}{({\text{water gradient }}-{\text{ hydrocarbon gradient}})}}$ Typical gradients in psi/ft: Water = 0.433 – 0.45, Oil = 0.33, Gas = 0.07 (range = 0.001–0.22)
4	Convert lab Pc to pore throat radius ( r ) in microns.	$r={\frac {-2\gamma \cos \Theta }{P_{\text{c lab}}}}{\text{ or }}{\frac {C(\gamma \cos \Theta _{\text{lab}})}{P_{\text{c lab}}}}$ where C is the constant 0.29

Example

The following is an example of applying the conversion of lab P_c data to reservoir conditions.

Use these assumptions:

• Maximum air–brine P_c 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_c (P_{c Hg})
• Equivalent oil P_c (buoyancy pressure in the reservoir)
• Height above the free water (h′)
• Pore throat radius for P_{c Hg} as determined at A

Answers (refer to the table below for values)

• ${\mbox{P}}_{\rm {c\ Hg}}={\mbox{P}}_{\rm {c\ brine}}\left({\frac {\gamma \cos \Theta {\mbox{ for Hg}}}{\gamma \cos \Theta {\mbox{ for brine}}}}\right)={\mbox{P}}_{\rm {c\ brine}}\left({\frac {367}{72}}\right)=40(5.1)=204{\mbox{ psi}}$
• ${\mbox{Equivalent oil P}}_{\rm {c}}={\mbox{P}}_{\rm {c\ lab}}\left({\frac {\gamma \cos \Theta _{\rm {res}}}{\gamma \cos \Theta _{\rm {lab}}}}\right)={\mbox{P}}_{\rm {c\ lab}}\left({\frac {26}{367}}\right)={\mbox{P}}_{\rm {c\ lab}}(0.071)=204(0.071)=14.5{\mbox{ psi}}$
• ${\mbox{h}}'={\frac {{\mbox{P}}_{\rm {c\ res}}}{({\mbox{water gradient}}-{\mbox{hydrocarbon gradient}})}}={\frac {14.5}{(0.45-0.33)}}=120{\mbox{ ft}}$
• ${\mbox{r at P}}_{\rm {c\ Hg}}=\displaystyle {\frac {-2\gamma \cos \Theta }{{\mbox{P}}_{\rm {c\ lab}}}}{\mbox{ or C}}\left({\frac {\gamma \cos \Theta _{\rm {lab}}}{{\mbox{P}}_{\rm {c\ lab}}}}\right)=0.29\times {\frac {367}{204}}=0.52\mu$
• ${\mbox{P}}_{\rm {c\ Hg}}{\mbox{ is equivalent to P}}_{\rm {c\ lab}}$

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.

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

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