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Introduction toCapillary Pressure
Some slides in this section are modified from NExT PERF Short Course Notes, 1999.However, many of the slides appears to have been obtained from other primarysources that are not cited by NExT. Some slides have a notes section.
• Determine fluid distribution in reservoir (initial conditions)
• Accumulation of HC is drainage process for water wet res.
• Sw= function of height above OWC (oil water contact)
• Determine recoverable oil for water flooding applications
• Imbibition process for water wet reservoirs
• Pore Size Distribution Index,
• Absolute permeability (flow capacity of entire pore size distribution)
• Relative permeability (distribution of fluid phases within the pore size
distribution)
• Reservoir Flow - Capillary Pressure included as a term of flow potential for
multiphase flow
• Input data for reservoir simulation models
Applications of Capillary Pressure Data
water wet,Z;PD
ZgρpΦ owc,
wow
DRAINAGE AND IMBIBITION CAPILLARY PRESSURE CURVES
Drainage
ImbibitionSi Sm
Swt
Pd
Pc
0 0.5 1.0
Modified from NExT, 1999, after …
DRAINAGE
• Fluid flow process in which the saturation of the nonwetting phase increases
• Mobility of nonwetting fluid phase increases as nonwetting phase saturation increases
IMBIBITION
• Fluid flow process in which the saturation of the wetting phase increases
• Mobility of wetting phase increases as wetting phase saturation increases
Four Primary Parameters
Si = irreducible wetting phase saturation
Sm = 1 - residual non-wetting phase saturation
Pd = displacement pressure, the pressure required to force non-wetting fluid into largest pores
= pore size distribution index; determines shape
DRAINAGE PROCESS
• Fluid flow process in which the saturation of the nonwetting phase increases
• Examples:
• Hydrocarbon (oil or gas) filling the pore space and displacing the original water of deposition in water-wet rock
• Waterflooding an oil reservoir in which the reservoir is oil wet
• Gas injection in an oil or water wet oil reservoir
• Pressure maintenance or gas cycling by gas injection in a retrograde condensate reservoir
• Evolution of a secondary gas cap as reservoir pressure decreases
IMBIBITION PROCESS
IMBIBITION
•Fluid flow process in which the saturation of the wetting phase increases
•Mobility of wetting phase increases as wetting phase saturation increases
Examples:
Accumulation of oil in an oil wet reservoir
Waterflooding an oil reservoir in which the reservoir is water wet
Accumulation of condensate as pressure decreases in a dew point reservoir
FlowUnits
Gamma RayLog
PetrophysicalData
PoreTypes
LithofaciesCore
1
2
3
4
5
CorePlugs
CapillaryPressure
vs k
Pc vs. Sw FunctionReflects Reservoir Quality
High Quality
Low Quality
Function moves up and right, and becomes less “L” shaped as reservoir quality decreases
Effect of Permeability on Shape
Decreasing Permeability,Decreasing
A B
C
20
16
12
8
4
00 0.2 0.4 0.6 0.8 1.0
Water Saturation
Cap
illa
ry P
ress
ure
Modified from NExT 1999, after xx)
Effect of Grain Size Distribution on Shape
Well-sortedPoorly sorted
Ca
pill
ary
pre
ssu
re, p
sia
Water saturation, %Modfied from NExT, 1999; after …)
Decreasing
• The pressure difference existing across the interface separating two immiscible fluids in capillaries (e.g. porous media).
• Calculated as:
Pc = pnwt - pwt
CAPILLARY PRESSURE- DEFINITION -
Where:
Pc = capillary pressure
Pnwt = pressure in nonwetting phase
pwt = pressure in wetting phase
• One fluid wets the surfaces of the formation rock (wetting phase) in preference to the other (non-wetting phase).
• Gas is always the non-wetting phase in both oil-gas and water-gas systems.
• Oil is often the non-wetting phase in water-oil systems.
Capillary Tube - Conceptual ModelAir-Water System
Water
Airh
• Considering the porous media as a collection of capillary tubes provides useful insights into how fluids behave in the reservoir pore spaces.
• Water rises in a capillary tube placed in a beaker of water, similar to water (the wetting phase) filling small pores leaving larger pores to non-wetting phases of reservoir rock.
• The height of water in a capillary tube is a function of:
– Adhesion tension between the air and water
– Radius of the tube
– Density difference between fluidsaw
aw
grh
cos2
CAPILLARY TUBE MODELAIR / WATER SYSTEM
This relation can be derived from balancing the upward force due to adhesion tension and downward forces due to the weight of the fluid (see ABW pg 135). The wetting phase (water) rise will be larger in small capillaries.
h = Height of water rise in capillary tube, cm
aw = Interfacial tension between air and water,dynes/cm
= Air/water contact angle, degrees
r = Radius of capillary tube, cm
g = Acceleration due to gravity, 980 cm/sec2
aw = Density difference between water and air, gm/cm3
Contact angle, , is measured through the more dense phase (water in this case).
Rise of Wetting Phase Varies with Capillary Radius
WATER
AIR
1 2 3 4
Ayers, 2001
CAPILLARY TUBE MODELAIR/WATER SYSTEM
Air
Water
pa2
h
pa1
pw1
pw2
Water rise in capillary tube depends on the density difference of fluids.
Pa2 = pw2 = p2
pa1 = p2 - a g h
pw1 = p2 - w g h
Pc = pa1 - pw1
= w g h - a g h
= g h
• Combining the two relations results in the following expression for capillary tubes:
rP aw
c
cos2
CAPILLARY PRESSURE – AIR / WATER SYSTEM
CAPILLARY PRESSURE – OIL / WATER SYSTEM
• From a similar derivation, the equation for capillary pressure for an oil/water system is
rP ow
c
cos2
Pc = Capillary pressure between oil and water
ow = Interfacial tension between oil and water, dyne/cm
= Oil/water contact angle, degrees
r = Radius of capillary tube, cm