Petroleum Engineering 311
Reservoir Petrophysics
Homework 5 – Capillary Pressure
1 November 2000 — Due: Wednesday 8 November 2000
5.1 Determination of Capillary Pressure Using the Centrifuge.
You are to determine the capillary pressure (pc) profiles for the centrifuge data
given below.
Input Data:
Water-Oil System:
Properties
Core Length, in
Dry Weight of Core, gm
Core Porosity, fraction
Core Permeability, md
Water (Brine) Density, gm/cc
Oil (Kerosene) Density, gm/cc
Interfacial Tension, dyne/cm
Long radius, in
Core WO-1
Saturated
Centrifuge
Weight
Speed
(gm)
(RPM)
50.761
0
50.738
476
50.477
975
50.328
1500
50.232
2000
50.159
2500
50.101
3000
50.012
4000
Core WO-1
1.699
46.476
0.1911
290
1.05
0.7891
25
6.1
Core WO-2
1.632
45.314
0.1752
266
1.05
0.7891
25
6.1
Core WO-2
Saturated
Centrifuge
Weight
Speed
(gm)
(RPM)
49.333
0
49.297
476
49.041
975
48.907
1500
48.824
2000
48.765
2500
48.719
3000
48.652
4000
Air-Oil System:
Properties
Core Length, in
Dry Weight of Core, gm
Core Porosity, fraction
Core Permeability, md
Oil (Kerosene) Density, gm/cc
Air Density, gm/cc
Interfacial Tension, dyne/cm
Long radius, in
Core AO-1
Saturated
Centrifuge
Weight
Speed
(gm)
(RPM)
47.238
0
46.058
476
45.592
975
45.376
1500
45.240
2000
45.185
2500
45.089
3000
45.020
4000
Core AO-1
1.601
44.205
0.1819
242
0.7891
0.00122
50
6.1
Core AO-2
1.721
47.423
0.1846
275
0.7891
0.00122
50
6.1
Core AO-2
Saturated
Centrifuge
Weight
Speed
(gm)
(RPM)
50.719
0
49.841
476
49.178
975
48.795
1500
48.532
2000
48.472
2500
48.353
3000
48.293
4000
Petroleum Engineering 311
Reservoir Petrophysics
Homework 5 – Capillary Pressure
1 November 2000 — Due: Wednesday 8 November 2000
5.1 (Continued)
Required:
5.1.a Determine the "corrected" capillary pressure function using the capillary
pressure-average saturation plot (pc versus Savg).
Use an individual plot
for each case.
5.1.b Plot capillary pressure versus wetting phase saturation on a single plot (pc
versus S).
5.1.c Convert all capillary pressure data to the Leverett J-function, and plot all
cases on single plot (J(S) versus S).
Governing Equations:
Capillary Pressure
p
c

(62.4)  
(2)(144) g
2
2
2
(r2  r1 )
c
where,
r1


pc
gc
=
=
=
=
=
r2-core length, ft
w = Water density, gm/cc
(w-o) or (o-a), gm/cc
o = Oil density, gm/cc
(/30)xRPM, radians/sec
a = Air density, gm/cc
Capillary pressure, psia
Gravitational constant, 32.2 lbm-ft/lbf-sec2
Average Saturation
Wt
 
o
V
p
S

or
w
(   )
w
o
Wt
 
a
V
p
S

o
(   )
o
a
where,
= Water density, gm/cc
= Oil density, gm/cc
= Avg. Water saturation, fraction
w
o
a
= Avg. Oil saturation, fraction
Vp
= Pore volume, cc
Wt = Sat. Weight-Dry Weight, gm
w = Water density, gm/cc
S
S
w
o
= Air density, gm/cc
Saturation Correction (for centrifuge effects)
S  S  pc dS
dp
c
where,
pc
S
S
= Capillary pressure, psia
= Average saturation, fraction
= Corrected saturation, fraction
Petroleum Engineering 311
Reservoir Petrophysics
Homework 5 – Capillary Pressure
1 November 2000 — Due: Wednesday 8 November 2000
5.2 Determination of Capillary Pressure Using Mercury Injection.
You are to determine the capillary pressure (pc) profile for the Mercury injection
data given below.
Input Data:
Mercury-Air System:
Properties
Core Length, in
Core Diameter, in
Core Porosity, fraction
Core Permeability, md
Mercury Density, gm/cc
Air Density, gm/cc
Core Hg-1
1.1695
1.0050
0.2250
315
13.59
0.00122
Core Hg-1
Injected
Mercury
Cell
Volume
Pressure
(cc)
(psia)
0.000
0.18*
0.053
1.00
0.082
2.00
0.108
3.00
0.143
4.00
0.194
5.00
0.414
6.00
1.313
7.00
1.723
8.00
1.932
9.00
2.067
10.00
2.154
11.00
2.232
12.00
2.279
13.00
2.319
14.00
2.357
15.00
2.487
25.00
2.627
30.00
2.705
40.00
2.780
50.00
2.868
75.00
2.944
100.00
3.020
150.00
3.075
200.00
3.142
300.00
3.192
400.00
3.224
500.00
3.261
600.00
3.288
700.00
3.308
800.00
3.310
900.00
3.350
1000.00
* Minimum pressure in system (i.e., the maximum "vacuum" drawn on the system).
Petroleum Engineering 311
Reservoir Petrophysics
Homework 5 – Capillary Pressure
1 November 2000 — Due: Wednesday 8 November 2000
5.2 (Continued)
"Cell Expansion": (calibration equation valid for this case only)
Vexp = 0.017676(pc)0.338339
Required:
5.2.a Determine the "corrected" air saturation (subtract the cell expansion from
the injected mercury volume) and plot pc,Hg versus Sair on a Cartesian plot.
5.2.b Convert the pc,Hg — Sair capillary pressure data to the Leverett J-function,
and add this trend to the cases from 5.1.c.
Governing Equations:
Air Saturation (Mercury-air system)
S
a

1 (V  V
p
Hg,inj,c )
V
p
where,
VHg,inj
= Injected Mercury volume, cc
VHg,inj,c = (VHg,inj-Vexp) Injected Mercury volume (corrected), cc
Vexp = Cell expansion volume, cc (from calibration equation)
Vp = Pore volume, cc
Sa = Air saturation, fraction
Petroleum Engineering 311
Reservoir Petrophysics
Homework 5 – Capillary Pressure
1 November 2000 — Due: Wednesday 8 November 2000
5.3 Brooks-Corey Model for Representing Capillary Pressure
Using the capillary pressure saturation data obtained from Parts 5.1 and 5.2, you
are to "fit" the Brooks-Corey pc model to each case.
Required:
5.3.a For each pc data set you are to determine the pd, Swi, and  parameters in
the Brooks-Corey pc model using a statistical approach such as least
squares. Be sure to explain ALL steps.
5.3.b For each pc data set you are to determine the pd, Swi, and  parameters in
the Brooks-Corey pc model using the "type curve" approach given in the
notes. The type curve and data grid plot are attached.
Governing Equations:
Brooks-Corey Capillary Pressure Model
1

 S w  S wi  
p
 p 

c
d
 1  S wi 
where,
pc
pd
Sw
Swi

=
=
=
=
=
Capillary pressure, psia
Displacement (or threshold) pressure, psia
Wetting phase saturation, fraction
Irreducible wetting phase saturation, fraction
Brooks-Corey exponent, dimensionless