Petroleum Engineering 311

Petroleum Engineering 311

Reservoir Petrophysics

Homework 5 – Capillary Pressure

1 November 2000 — Due: Wednesday 8 November 2000

5.1Determination 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 WO-1 / Core WO-2

Core Length, in

/ 1.699 / 1.632
Dry Weight of Core, gm / 46.476 / 45.314
Core Porosity, fraction / 0.1911 / 0.1752
Core Permeability, md / 290 / 266
Water (Brine) Density, gm/cc / 1.05 / 1.05
Oil (Kerosene) Density, gm/cc / 0.7891 / 0.7891
Interfacial Tension, dyne/cm / 25 / 25
Long radius, in / 6.1 / 6.1
Core WO-1 / Core WO-2

Saturated

Weight
(gm) / Centrifuge
Speed
(RPM) /

Saturated

Weight
(gm) / Centrifuge
Speed
(RPM)
50.761 / 0 / 49.333 / 0
50.738 / 476 / 49.297 / 476
50.477 / 975 / 49.041 / 975
50.328 / 1500 / 48.907 / 1500
50.232 / 2000 / 48.824 / 2000
50.159 / 2500 / 48.765 / 2500
50.101 / 3000 / 48.719 / 3000
50.012 / 4000 / 48.652 / 4000

Air-Oil System:

Properties

/ Core AO-1 / Core AO-2

Core Length, in

/ 1.601 / 1.721
Dry Weight of Core, gm / 44.205 / 47.423
Core Porosity, fraction / 0.1819 / 0.1846
Core Permeability, md / 242 / 275
Oil (Kerosene) Density, gm/cc / 0.7891 / 0.7891
Air Density, gm/cc / 0.00122 / 0.00122
Interfacial Tension, dyne/cm / 50 / 50
Long radius, in / 6.1 / 6.1
Core AO-1 / Core AO-2

Saturated

Weight
(gm) / Centrifuge
Speed
(RPM) /

Saturated

Weight
(gm) / Centrifuge
Speed
(RPM)
47.238 / 0 / 50.719 / 0
46.058 / 476 / 49.841 / 476
45.592 / 975 / 49.178 / 975
45.376 / 1500 / 48.795 / 1500
45.240 / 2000 / 48.532 / 2000
45.185 / 2500 / 48.472 / 2500
45.089 / 3000 / 48.353 / 3000
45.020 / 4000 / 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.aDetermine the "corrected" capillary pressure function using the capillary pressure-average saturation plot (pc versus Savg). Use an individual plot for each case.

5.1.bPlot capillary pressure versus wetting phase saturation on a single plot (pc versus S).

5.1.cConvert all capillary pressure data to the Leverett J-function, and plot all cases on single plot (J(S) versus S).

Governing Equations:

Capillary Pressure

where,

r1=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

pc=Capillary pressure, psia

gc=Gravitational constant, 32.2 lbm-ft/lbf-sec2

Average Saturation

where,

Wt=Sat. Weight-Dry Weight, gmw=Water density, gm/cc

w=Water density, gm/cco=Oil density, gm/cc

=Avg. Water saturation, fractiona=Air density, gm/cc

=Avg. Oil saturation, fractionVp=Pore volume, cc

Saturation Correction (for centrifuge effects)

where,

pc=Capillary pressure, psia

=Average saturation, fraction

S=Corrected saturation, fraction

Petroleum Engineering 311

Reservoir Petrophysics

Homework 5 – Capillary Pressure

1 November 2000 — Due: Wednesday 8 November 2000

5.2Determination 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 Hg-1

Core Length, in

/ 1.1695
Core Diameter, in / 1.0050
Core Porosity, fraction / 0.2250
Core Permeability, md / 315
Mercury Density, gm/cc / 13.59
Air Density, gm/cc / 0.00122
Core Hg-1

Injected

Mercury
Volume
(cc) / Cell
Pressure
(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.aDetermine 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.bConvert 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)

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

5.3Brooks-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.aFor 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.bFor 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

where,

pc=Capillary pressure, psia

pd=Displacement (or threshold) pressure, psia

Sw=Wetting phase saturation, fraction

Swi=Irreducible wetting phase saturation, fraction

=Brooks-Corey exponent, dimensionless