caillary pressure.pdf
TRANSCRIPT
Introduction to
Capillary Pressure
• 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
Prof. Dr. E
issa M
ohamed Shokir
DRAINAGE AND IMBIBITION
CAPILLARY PRESSURE CURVES
Drainage
Imbibition S
i 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 Prof. D
r. Eiss
a Mohamed Shokir
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
Prof. Dr. E
issa M
ohamed Shokir
Seal
Reservoir rock
Seal
Migration route
Oil/water contact (OWC)
Hydrocarbon accumulation
in the reservoir rock
Top of maturity
Source rock
Fault (impermeable)
Reservoir Seal
Seal
Prof. Dr. E
issa M
ohamed Shokir
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:
Waterflooding an oil reservoir in which the reservoir is
water wet
Accumulation of oil in an oil wet reservoir
Accumulation of condensate as pressure decreases in a
dew point reservoir Prof. Dr. E
issa M
ohamed Shokir
Prof. Dr. E
issa M
ohamed Shokir
• 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. Prof. Dr. E
issa M
ohamed Shokir
Capillary Tube - Conceptual Model
Air-Water System
Water
Air h
• 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. Prof. Dr. E
issa M
ohamed Shokir
• 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 fluids
aw
aw
grh
cos2
CAPILLARY TUBE MODEL
AIR / 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).
Prof. Dr. E
issa M
ohamed Shokir
Rise of Wetting Phase Varies with
Capillary Radius
WATER
AIR
1 2 3 4
Ayers, 2001 Prof. Dr. E
issa M
ohamed Shokir
CAPILLARY TUBE MODEL
AIR/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 Prof. D
r. Eiss
a Mohamed Shokir
• Combining the two relations results in the following
expression for capillary tubes:
rP aw
c
cos2
CAPILLARY PRESSURE – AIR / WATER
SYSTEM
Prof. Dr. E
issa M
ohamed Shokir
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
Prof. Dr. E
issa M
ohamed Shokir
Flow Units
Gamma Ray Log
Petrophysical Data
Pore Types
Lithofacies Core
1
2
3
4
5
Core Plugs
Capillary Pressure
f vs k
Pc vs. Sw Function Reflects Reservoir Quality
Petrophysical analyses of core samples are used to identify reservoir flow units and non-flow units Prof. D
r. Eiss
a Mohamed Shokir
Flow Units
Gamma Ray Log
Petrophysical Data
Pore Types
Lithofacies Core
1
2
3
4
5
Core Plugs
Capillary Pressure
f vs k
Pc vs. Sw Function Reflects Reservoir Quality
High Quality
Low Quality
Function moves up
and right, and
becomes less “L”
shaped as reservoir
quality decreases Prof. Dr. E
issa M
ohamed Shokir
Effect of Permeability on Shape
Decreasing
Permeability,
Decreasing
A B
C
20
16
12
8
4
0 0 0.2 0.4 0.6 0.8 1.0
Water Saturation
Cap
illa
ry P
ressu
re
Modified from NExT 1999, after xx) Prof. D
r. Eiss
a Mohamed Shokir
Effect of Grain Size Distribution on Shape
Well-sorted Poorly sorted
Cap
illa
ry p
ressu
re, p
sia
Water saturation, % Modfied from NExT, 1999; after …)
Decreasing
Prof. Dr. E
issa M
ohamed Shokir
Prof. Dr. E
issa M
ohamed Shokir
Prof. Dr. E
issa M
ohamed Shokir
Prof. Dr. E
issa M
ohamed Shokir
In a gas reservoir having a gas-water contact,
the thickness of the transition zone will be a
minimum since will be large. Also, if all
other factors remain unchanged, a low API
gravity oil reservoir with an oil-water contact
will have a longer transition zone than a high
API gravity oil reservoir.
grh aw cos2
Prof. Dr. E
issa M
ohamed Shokir
Prof. Dr. E
issa M
ohamed Shokir
Capillary Pressure in Reservoirs
A B
Reservoir, o
Aquifer, w
1
2
3
Pc = po-pw = 0
Pressure D
ep
th
dpw=wg/D dh
Free
Water
Level
dpo=og/D dh
Prof. Dr. E
issa M
ohamed Shokir
Fluid Distribution in Reservoirs
Gas & Water
Gas density = g
Oil, Gas & Water
Oil & Water
Oil density = o
Water
Water density = w
‘A’
h1
h2 ‘B’
Free Oil Level
Free Water Level
Capillary pressure difference
between
oil and water phases in core ‘A’
Pc,ow = h1g (w-o)
Capillary pressure difference
between
gas and oil phases in core ‘B’
Pc,go = h2g (o-g)
Fau
lt
Prof. Dr. E
issa M
ohamed Shokir
LEVERETT J-FUNCTION FOR
CONVERSION OF Pc DATA
Reservoir
c
Lab
cw
k
cosθσ
PCk
cosθσ
PC)J(S
ff
Prof. Dr. E
issa M
ohamed Shokir
EXAMPLE J-FUNCTION FOR
WEST TEXAS CARBONATE
0.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
8.00
9.00
10.00
0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00
Water saturation, fraction
J-fu
nction
Jc
Jmatch
Jn1
Jn2
Jn3
Prof. Dr. E
issa M
ohamed Shokir
Sw* Power Law Model
• Having an equation model for capillary pressure
curves is useful
– Smoothing of laboratory data
– Determination of
• The Sw* Power Law Model is an empirical model
that has proven to work well
– Model parameters: Swi, Pd,
1/λ*
wdc SPP
wi
wiw*
wS1
SSS
Prof. Dr. E
issa M
ohamed Shokir
• Sw* rescales x-axis
Sw* Power Law Model
Capillary Pressure vs. Wetting Phase Saturation
0
5
10
15
20
25
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Sw, fraction
Pc, p
sia
Swi=0.20
Pd=3.0
Sw*, fraction Sw*=0 Sw*=1 Prof. D
r. Eiss
a Mohamed Shokir
• Power Law Equations plot as Log-Log straight
line
Sw* Power Law Model
Capillary Pressure Data Plotted vs. Sw* (for Swi=0.20)
1
10
100
0.01 0.1 1
Sw*, fraction
Pc, p
sia slope = -1/ = -1/2.0
Pd=3.0
1
Prof. Dr. E
issa M
ohamed Shokir
Sw* Power Law Model
• Straight line models are excellent for
– Interpolation and data smoothing
– Extrapolation
– Self Study: review Power Law Equations (y=axb) and
how to determine coefficients, a and b given two
points on the straight log-log line
1/λ*
wdc SPP
wi
wiw*
wS1
SSS
Prof. Dr. E
issa M
ohamed Shokir
Sw* Power Law Model
• Pd, can be determined from Log-Log plot
• But, Swi can be difficult to determine from Cartesian plot,
if data does not clearly show vertical assymptote
1/λ*
wdc SPP
wi
wiw*
wS1
SSS
Capillary Pressure vs. Wetting Phase Saturation
0
5
10
15
20
25
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Sw, fraction
Pc, p
sia
Prof. Dr. E
issa M
ohamed Shokir
• Choosing wrong Swi limits accuracy of
determining Pd,
Sw* Power Law Model
Same Capillary Pressure Data Plotted vs. Sw*
1
10
100
0.01 0.1 1
Sw*, fraction
Pc, p
sia
Swi value too small
Swi value too large
Swi value correct
Prof. Dr. E
issa M
ohamed Shokir