Introduction toCapillary Pressure

• Determine fluid distribution in reservoir (initial conditions)

• Accumulation of HC is drainage process for water wet reservoirs (max

possible HC saaturation)

• 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

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, 981 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, dyne/cm2

ow = Interfacial tension between oil and water, dyne/cm

= Oil/water contact angle, degrees

r = Radius of capillary tube, cm