Engineering HW....
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lectures.zip21 Rock Fluid Interactions Capillary Rise, Capillary Pressure, J Functions.pdf
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Petr 3520: Rock-Fluid Interactions (such as capillary rise, capillary pressure…) Class 21
So far in this class we have studied rock properties (, k, cf, 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 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
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.
Contact Angle: Angle formed between a fluid drop and a solid surface, measured through the fluid.
4. Examples of wettability, contact angle (): A fluid’s interaction with a solid surface:
Rain-X on automobile windshields
Gore Tex fabric
Non-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)
Round drops on plant leaves, on non-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)
6. Surface tension (): Between a fluid’s surface and air. 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.
Free fluids form drops (minimum surface area)
Round drops on plants (cohesion
Water bugs
Coin or paper clip float on water
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7. Interfacial tension (): Between two fluids, e.g. oil and water.
8. Capillarity or capillary action, wicking.
Paper towels
Sponges
Soldering electronic components or copper plumbing pipe and fittings
Sap (water) moves up into tall trees by capillary action
9. Capillary rise (in a small diameter tube called a capillary tube)
Capillary falls (with mercury vs. air, because air wets the 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.)
Imbibition vs. Drainage capillary pressure curves. Hysteresis.
Leverett’s J-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.
14. Transition zone in reservoir.
Capillary Pressure and J-Function Equations:
144 c o w
h p p p
p [psi], [lb/ft
3 ], h [ft], 144 [in
2 /ft
2 ]
2 cos c o wp p p gh h
r
in consistent darcy units
109
0.2166
cos
cp k J
with pc [psi], [dyne/cm], k [md], and [fraction]
21 Surface Tension, Molecular Forces, High Energy at Surface 1.pdf
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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) 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
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Petr 3520: Reservoir Engineering Lecture 22: Two Capillary Pressure Equations
Capillary pressure is important to petroleum engineers because reservoirs typically have:
Two or more immiscible fluids (e.g. water and oil, water and gas, etc.)
Tiny pores (very high surface area). Can be considered to be 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:
Water-oil contact is not sharp. Water saturation (Sw) does 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.”
Gas-oil contact can have a small transition zone.
Injected water can form a “piston” in a reservoir. But it is 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.
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