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