Title 05 Capillary Pressure 202.0 KB 15
##### Document Text Contents
Page 1

Capillary Pressure 1

Capillary Pressure

Instructional Objectives:

- List four uses of capillary pressure data.
- Define hysteresis.
- Sketch capillary pressure curves for typical drainage and imbibition processes.
- Explain the relation between capillary pressure data and reservoir fluid saturation.
- Define oil-water and gas-oil transition zones.
- Convert capillary pressure lab data to reservoir conditions.
- Define the J-function.
- List four different methods for measuring capillary pressure in the lab.

Uses of Capillary Pressure Data:

- Determine initial water saturation in the reservoir.
- Determine fluid distribution in the reservoir.
- Determine residual oil saturation for water flooding applications.
- Determine pore size distribution index.
- May help in identifying zones or rock types.
- Input for reservoir simulation calculations.

Capillary pressure measurements determine the initial water saturation. This is the saturation at
which the increase in capillary pressure does not affect the saturation.
Capillary pressure data can also determine the vertical fluid distribution in the reservoir by
establishing the relation between the capillary pressure and height above the free water level.
Imbibition capillary pressure measurements determine the residual oil saturation in water flooding
operation.
We can infer the pore size distribution index, , from capillary pressure data. This index can be
used to calculate relative permeability using industry correlations.
Capillary pressure curves are similar for the same rock type. The shape also gives indication
Capillary pressure curves are used to initialize simulation runs and in flow calculations between
grid blocks.

Capillary Pressure Concept:

A B

o

w
1

2

3
Pc = 0

Pressure

D
ep

th

w
o

Water exists at all levels below 2, and both water and oil exist at all levels above 2.

Page 2

Capillary Pressure 2

Oil and water pressure gradients are different because their density is different.
At level 2, pressure in both the water and oil phases is the same.
At any level above 2, such as level 3, water and oil pressures are different.
This difference in pressure is called the capillary pressure.

Capillary Pressure Definition:

- The pressure difference existing across the interface separating two immiscible fluids.
- It is usually calculated as:

Pc = pnwt - pwt
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.

Example:
Define capillary pressure in the following systems:

- Water-gas system.
- Water-wet water-oil system.
- Oil-gas system.

Solution:

- water-gas system:
Pc = pg - pw

- water-wet water-oil system:
Pc = po - pw

- oil-gas system:
Pc = pg - po

Relation between Capillary Pressure and Fluid Saturation:

Free Water Level

Pc

Pd
Water-oil contact

Hd

H
e
ig

h
t

A
b

o
ve

F
re

e
W

a
te

r
L

e
ve

l
(F

e
e
t)

0 50 100
Sw (Percent)

0 50 100
Sw (Percent)

0

Page 7

Capillary Pressure 7

L

LL
cL

r
P

cos2

R

RR
cR

r
P

cos2

Pc = capillary pressure, psia
= interfacial tension, dynes/cm
= contact angle, degrees

r = radius of pore throat, cm
Subscripts L and R refer to laboratory and reservoir conditions, respectively.

Setting rL = rR and combining equations yields:

cR

RR

cL

LL
RL

PP
rr

cos2cos2

Therefore, capillary pressure at reservoir conditions is given by:

cL
LL

RR
cR PP cos

cos

Example:
Convert the laboratory capillary pressure data for sample 28 in the attached capillary pressure
curve (obtained using mercury injection method) to reservoir conditions for a formation containing
oil and water.
Calculate reservoir capillary pressure data for mercury saturations of 70, 60, 50, 40, 30, 20, and
10 percent.
Laboratory Data: Hg = 480 dynes/cm, Hg = 140

o
Reservoir Data: ow = 24 dynes/cm, ow = 20

o
Note: The reservoir data are very difficult to obtain. The reservoir data above are representative
values based upon industry literature.

0

400

800

1200

1600

2000

020406080

Mercury Saturation, percent pore space

In
je

ct
io

n
P

re
ss

u
re

,
p

si
a

Page 8

Capillary Pressure 8

Solution:
Steps:

- Solve the equation that relates lab capillary pressure data to reservoir capillary pressure
data for the conditions we have.

- Obtain laboratory capillary pressure data from the curve for Sample 28.
- Convert the lab numbers to reservoir capillary pressure.

Mercury

Saturation
(SHg)

%

PcL
psia

PcR
psia

70 1,320 80.5
60 820 50.0
50 560 34.2
40 410 25.0
30 310 18.9
20 240 14.6
10 200 12.2

cL

ccL
LL

RR
cR

P

PPP
L

061.0
140cos480
20cos24

cos
cos

Drainage and Imbibition Capillary Pressure Curves:

Drainage (1)

Imbibition (2)

Si Sm

Sw

Pd

Pc

0 0.5 1.0

Page 14

Capillary Pressure 14

= 72 dynes/cm. k = 47 md.
= 0o. = 19.4 %

A v e ra g e d A ir /B r in e C a p illa ry
P re s s u re D a ta

P c
p s ia

S w
%

1 9 8 .3
2 9 8 .3
4 9 6 .8
8 5 9 .0

1 5 3 6 .3
3 5 2 5 .4

5 0 0 1 5 .3

Solution:

Calculated
J-Functions

Sw
%

0.22*
J(Sw)

98.3 0.22
98.3 0.43
96.8 0.86
59.0 1.73
36.3 3.24
25.4 7.57
15.3 108.1

In the table above, we have not multiplied through by the conversion factor 0.22.

120

100

80

60

40

0

20

0 20 40 60 80 100

0.
22

*
J

(S
w

)

Sw , %

Page 15

Capillary Pressure 15

Example: Estimating Pc from the J-Function:
Estimate capillary pressures from Leverett J-function calculated in the previous example for a
different core sample.
Properties of core sample:
k = 100 md.
= 10 %

Solution:

Estimated Capillary
Pressures for the 100-md
Permeability Core Sample

Sw,
%

Pc,
psia

98.3 2.27
98.3 4.45
96.8 8.91
59.0 17.91
36.3 36.90
25.4 78.18
15.3 1118.63

Laboratory Methods for Measuring Capillary Pressure:

- Porous diaphragm method
- Mercury injection
- Centrifuge method
- Dynamic method