This document discusses rock-fluid interactions in petroleum reservoirs, including capillary pressure and capillary rise. It notes that reservoirs contain immiscible fluids like oil, water and gas in microscopic pores, leading to significant surface forces due to the high fluid-rock and fluid-fluid contact area. Capillary pressure arises from relative adhesion and cohesion forces at fluid-fluid and fluid-solid interfaces, affecting wettability and contact angle. Capillary rise results from capillary pressure differences and can be modeled using equations that relate capillary pressure to surface tension, pore radius and height of rise. Mercury injection is discussed as a method to determine capillary pressure curves and pore size distributions in cores.

1. 21 Rock Fluid Interactions Capillary Rise, Capillary Pressure, J
Functions.pdf
107
Petr 3520: Rock-Fluid Interactions (such as capillary rise,
capillary pressure…) Class 21
etc.) and fluid properties. But reservoir
engineers must also understand immiscible fluid-fluid
interactions and rock-fluid interactions.
In petroleum reservoirs we have:
1. Microscopic-sized pores + two or more (immiscible) fluids
(oil-water, gas-water, or oil-gas-
water) which typically do not mix (they are immiscible, not
miscible). The rocks are water-wet or oil-wet
(which means that the rock is preferentially wetted by water or
oil).
Because the pores are so small, the surface area (fluid-rock
contact, and fluid-fluid contact (for example,
oil to water)) to volume (of fluid and/or rock) is very high, thus
surface forces become significant.
Example Calculation: 1 ft

2. 3
cube of rock, assume to be bundle of 1 mm dia tubes each 1 ft
= 304.8 mm
long. There are 300
2
= 90,000 tubes in this cube. Surface area in mm
2
, convert to ft
2
: A = 1000 ft
2
.
2. What are surface forces? Surface forces exist at
(immiscible) liquid-liquid and liquid-solid interfaces.
Surface forces arise due to relative Adhesion vs. Cohesion.
Cohesion (“stick or stay together”) is a property of a fluid
whose molecules have high intermolecular
attraction. The fluid’s molecules would rather stick to
themselves rather than another fluid or nearby
surface.
Adhesion is the degree to which a fluid will “stick” to a nearby
solid surface.
3. Wetting, Contact Angle: These are the result of the relative
cohesion vs. adhesion of two fluids and a

3. solid surface.
Fluid “wets” a surface: Adhesion > Cohesion. The fluid’s
molecules preferentially attracted to
surface.
Fluid does not “wet” the surface: Cohesion > Adhesion. The
fluid’s molecules preferentially
attracted to fluid.
solid surface, measured through the fluid.
interaction with a solid surface:
-X on automobile windshields
-stick fry pans
5. Examples of a fluid’s cohesion vs. adhesion (relative
affinity of a fluid’s molecules to itself or to a solid
surface)
-stick frying pans (for a
fluid to form drops like this, the
fluid’s molecules would rather cohere with other fluid
molecules than adhere to a solid surface)

4. Units: [work/area] = [dyne-cm/cm
2
] A fluid
wants to minimize its free surface. It takes work or energy to
create additional surface area.
108
il and
water.
8. Capillarity or capillary action, wicking.
fittings
9. Capillary rise (in a small diameter tube called a capillary

5. tube)
glass rather than Hg)
10. Capillary pressure: Pressure difference across a curved
interface between two fluids (water-oil, water-
air, etc.)
11. Leverett’s capillary pressure experiments with long tubes
of sand. (See next page.)
Hysteresis.
-Function.
12. Capillary pressure curves (pc vs. Sw). (Note: These curves
make it appear that pc = function of Sw,
but the opposite is true. Chemistry (contact angle, wetting,
surface tension, adhesion) produce capillary
rise, which determines Sw and capillary pressure.
13. How create or determine experimentally a capillary
pressure vs. Sw curves? Threshold pressure
(pore entry pressure). Curve shape is a function of pore size
distribution. A reservoir as a “bundle of
capillary tubes.” Use of mercury injection to determine pore
size distribution.

6. 14. Transition zone in reservoir.
Capillary Pressure and J-Function Equations:
144
c o w
h
p p p
3
], h [ft], 144 [in
2
/ft
2
]
2 cos
c o w
p p p gh h
r

7. 109
0.2166
cos
c
p k
J
21 Surface Tension, Molecular Forces, High Energy at Surface
1.pdf
106
Petr 3520: Surface Tension, Molecular Interactions, Higher
Energy at Surface Class 21
If a fluid has a surface tension (fluid-air) or an interfacial
tension (between that fluid and another
immiscible fluid), molecules (within a few molecules thickness)

8. near the surface will have a higher
energy (due to molecular interactions) and thus the surface will
act like a “skin.”
22 Two Capillary Pressure Equations.pdf
114
Petr 3520: Reservoir Engineering Lecture 22: Two Capillary
Pressure Equations
Capillary pressure is important to petroleum engineers because
reservoirs typically have:
gas, etc.)
a “bundle of capillary tubes”
1. Because of capillary pressure effects, we rarely see sharp
saturation changes in a reservoir. Instead, we see “transition”
regions or
zones. The capillary pressure phenomenon “smears” saturation
changes. Examples:
-oil contact is not sharp. Water saturation (Sw) does

9. not go from 100% water to Swc (in 15-25% range) in one sharp
step.
Instead it varies over a few feet to 50 ft or more in a region
called a “transition zone.”
-oil contact can have a small transition zone.
not a perfect piston, unfortunately. It can slump due to gravity
effects, and the
sharp saturation front can smear due to capillary pressure.
2. One more key role of the capillary pressure (pc) vs. water
saturation (Sw) curve (equation) is in reservoir simulation. A
reservoir
simulator is a computer program which models complex
behavior in a reservoir. It takes steps in time (called time
steps), and at each step it
solves a system of equations (pressure equation, saturation
equations, and others) for all cells in the model. It turns out
that the apparently
simple, lowly capillary pressure equation (pc vs. Sw) is a
valuable independent equation which relates saturation and
pressure.
115

10. Petr 3520 Homework 21: Capillary Pressure, J Function
Name:
Capillary Pressure Equations
This equation was derived for the capillary rise of a fluid in a
capillary tube. The pressure difference across the meniscus =
the free surface.
pc = po – pw = difference in phase pressures
– –
capillary tube
(Equation pC 1)
This equation was derived from a force balance on the fluid
meniscus in a capillary tube. The upward force is the vertical
component of the fluid surface tensile force, and the downward
force is the weight of the fluid in the tube.
-water surface tension [dyne/cm]

11. r = radius of capillary tube
(Equation pC 2)
Use this equation to convert a pc vs. Sw curve to height above
the water-oil-contact (100% water).
(Equation pC 3) (pC 1 rearranged)
This the dimensionless Leverett J-Function. It was devised to
be a dimensionless function to correlate capillary pressure
curves from different regions in the same reservoir.
[unitless]
1. Look up “Capillary Action” on www.wikipedia.org and read
the entry. List three things you learned about capillarity.
2. In 1940, Leverett placed 10 ft long sand-packed tubes into
water and measured saturations along the length of the tube.
(This was water-air capillarity, different from the water-oil case
in a reservoir.) Explain his two tests (a) dry sand in tube in
water, and (b) water-saturated tube in water. Draw a picture of
these two curves (on the same h vs. Sw axes). Label the
imbibition and drainage curves. At a given height, h, which
curve has the larger water saturation, Sw?

12. 3. Explain the mercury injection method for measuring
capillary pressure. A capillary pressure vs. saturation curve can
indicate the pore size distribution in the core. How? Draw two
examples and explain them.
4. What is the “threshold pressure” (also called “pore entry
pressure”). Give an example of a field case when we need to be
concerned about pore entry pressure.
5. For this equation: Briefly explain how it is derived. How
is it used? What are po a

13. 6. For this equation: Briefly explain how it is derived (in
these affect capillary pressure?
7. A capillary pressure curve shows pc vs. Sw. This suggests
that pc is a function of Sw. But is it? What is (are) the most
foundational scientific principle(s) that cause(s) capillary rise?
8. Color in the capillary rise in various sizes of capillary tubes
and draw the resulting h vs. Sw curve from the average Sw at a
particular height from the “bundle of capillary tubes” model.

14. 9. What other ways do you, as a reservoir engineer, have to
determine the height of the transition zone (saturations vs.
height)?
10. How does the existence of a water-oil transition zone
affect:
(a) Where you complete wells? Why?
(b) Calculation of the volume of oil in place?

15. 11. A special core analysis provided the capillary pressure
curve given below for a reservoir
wh
following:
(a) Convert the pc vs. Sw curve to a height vs. Sw curve.
[Answer: At pc = 0.8 psi, h = 9.6 ft, etc.]
(b) Sketch the water-oil transition zone on the figure below by
carefully drawing construction lines (it’s best to use a ruler)
from the curve to the reservoir. Label the heights h and the
saturations at those heights.
12. Convert the capillary pressure curve given above to a J
0.0608 (unitless)]
http://www.digitalformation.com/Documents/CPRP.pdf
Notes and Terms
Equations
Capillary pressure (pc) equation (developed for a capillary tube
(liquid-air)) as a function of (in consistent units):
Capillary pressure (pc) in [dyne/cm2]

16. Liquid-
Liquid-
Capillary tube radius (r) in [cm]
For pressure in [psi] and r in [microns]:
Capillary pressure (pc) in [psi]
Liquid-
Liquid-
Capillary tube radius (r) in [micron = 10-
Note: 1 psi = 68,947.6 dyne/cm2 and 1 cm = 10-
To find pore throat diameter (r) vs. pc from
mercury injection test:
Capillary pressure (pc) in [psi]
Mercury-
Mercury-
Capillary tube radius (r) in [micron = 10-
The use of Hg injection to determine pore throat size
distribution is well established. However, the capillary pressure
vs. saturation curve obtained by Hg injection cannot directly be
used for a reservoir. The Hg-air pc data should be converted to
oil-water, gas-oil, gas-water, or whatever the actual system is
by using the following equation:

17. where,
Term
Typical Value(s)
pc(o-w) = oil-water capillary pressure
n/a
pc(air-Hg) = air-mercury capillary pressure
n/a
-w = oil-water interfacial tension
-w = 48 [dyne/cm]
-Hg = air-mercury surface tension
-Hg = 480 [dyne/cm]
-w = oil-water contact angle
-w = 30°
-Hg = air-mercury contact angle
-Hg = 140°
-w = gas-water interfacial tension
-w = 72 [dyne/cm]
-o = gas-oil interfacial tension
-o = 24 [dyne/cm]
-w = gas- -o = gas-oil contact angle
- -o = 0°
1. Explain why all oil and/or gas reservoirs have a minimal
water saturation (Swc (“connate”) or
Swi (“interstitial”), usually ranging from 10-30%) throughout
the reservoir?

18. 2. Explain the mercury injection method for measuring
capillary pressure. A capillary pressure vs. saturation curve can
indicate the pore size distribution in the core. How? What
equation applies to Hg injection?
3. What are the advantages/disadvantages to the Hg injection
method for determining a capillary pressure curve?
4. Once a capillary pressure curve is determined from Hg
injection data, can this be used directly for an oil reservoir?
Why or why not? If not, how can it be converted to a suitable
capillary pressure curve?

19. 5. What is the “threshold pressure” (also called “pore entry
pressure”). Give an example of a field case when we need to be
concerned about pore entry pressure.
6. For each capillary tube bundle size distribution given below,
draw the corresponding capillary pressure curve shape.
223
g
D
×
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c
p

20. h
144
(
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c
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23. cos
)
(
)
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144
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gh
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