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G. Donald Hill, Ph.D.
Consulting Petrophysicist
The World is My District
California Registered Geophysicist 170 California Registered Geologist 6043 Kentucky Registered Professional Geologist 1624 Texas Licensed Professional Geophysicist 6289
Petrophysics, Borehole Geophysics, and Subsurface Geology Planning, Oversight, and Interpretation
1012 Hillendale Ct. Walnut Creek, CA 94596 e-mail: dgwhill@aol.com http://www.hillpetro.com Office: FAX: Home: Cell: (510) (781) (925) (925) 450-6102 240-6208 947-1541 437-5748
DRAFT - Memorandum
Subject: Leverett J-Function Date: May 17, 2004
------------------------------------------------------------------------------------------------------------------
ABSTRACT Converting capillary pressure data to the (dimensionless) Leverett J-Functions facilitates facies identification and comparison of potential reservoir performance, as well as providing independent verification of wireline petrophysical analyses. LEVERETT J-FUNCTION The Leverett J-Function (Leverett, 1941; Craig, 1971) is a normalized (dimensionless) representation of capillary pressure (Pc) measurement data, which attempts to eliminate some of the dependencies upon measurement protocol and conditions, making it easier to compare measurements from multiple core samples. The J-Function representations are claimed to be dependent only upon: pore size distribution, radius of the largest pore(s), fluid wettability, and interfacial tension of the fluid pair involved BASIC DEFINITIONS The Leverett J-Function is defined by:
J sw =
Pc Cos
K
,
1)
where: Jsw is the Leverett J-Function (dimensionless normalized capillary pressure). Pc is (measured) capillary pressure. is interfacial tension between the two fluids. is the contact angle of the wetting phase. K is the permeability of the sample. is the porosity of the sample.
Leverett J-Function
Page 2
If Pc is in pounds/sq. in (psi), becomes:
is in dyne/cm, K is in mD, and
is fractional, Equation 1
J sw =
0.22Pc Cos
K
.
1a)
Other sets of units require a change in the (0.22) constant of Equation 1a. If Equation 1 (1a) is used for laboratory measurements, and are for the fluids actually used for the measurements and Pc is the measured capillary pressure. If Equation 1 (1a) is used for field data, and are for the reservoir fluids and Pc is given by:
Pc =
where:
gh ,
2)
is fluid density difference g is gravitational acceleration. h is height above the water contact. should be from restored net overburden routine (KPS)
In either case, K and measurements,
Equation 2 can be further simplified if the fluid densities are converted to pressure gradients (e.g., psi/ft), which removes the need for g. If is in psi/ft and h is in ft, Equation 1a is the form to use. If other density/pressure gradient, and/or height above the water contact units are used, the 0.22 coefficient in Equation 1a must be changed to accommodate the units used. EXAMPLES OF J-FUNCTION USAGE Facies Comparison Figure 1 shows Leverett J-Function for four clean-sand reservoirs. Multiple JFunction curves for the same reservoir are different from samples and provide an illustration of (potential) facies variability, within the reservoir. This indication of heterogeneity can be used to zone the reservoir for wireline analysis.
Figure 1. Comparison of Four Selected Clean-Sand Reservoir J-Functions.
Leverett J-Function
Page 3
Reservoir Comparison Figure 2 shows Leverett J-Functions for two Danish North Sea Chalk Reservoirs. The different J-functions mandated that different petrophysical models be used for wireline evaluation. It is also obvious that one of the reservoirs will have a much higher recovery factor. As a result, these reservoirs, even when encountered in a single well should be produced separately.
Figure 2. Comparison of Two Danish North Sea Chalk Reservoir Leverett J-Functions.
Confirmation of Wireline Predicted High Recovery Factor Figure 3 shows Leverett J-Functions for a shallow Niger Delta sand reservoir. Wireline analysis had estimated very low irreducible water saturations, Swir, indicating a very high recovery factor (low residual oil saturation, Sor). While the J-Function data, in Figure 3 show some heterogeneity, the low Sor < 5%, confirms the wireline prediction of a very high recovery factor.
Leverett J-Function
Page 4
Figure 3. Niger Delta Leverett J-Function Data for Clean-Sand Reservoir With High-Gravity Crude.
Independent Verification of Wireline Saturation Estimates Figure 4 shows a comparison of wireline (modified Archie) and Leverett JFunction water saturation, Sw, estimates, for a Danish North Sea well. The J-Function Sw estimates (based on capillary pressure measurements, restored net over burden KPS measurements, and height above the O/W contact, in a long transition zone) agree very well with the wireline Sw estimates (based upon density, neutron, gamma ray, and induction resistivity logs). This close agreement increases confidence, in both sets of measurements.
Figure 4. Comparison of Wireline and Leverett J-Function Estimates, in a Transition Zone.
Leverett J-Function
Page 5
CONCLUSIONS AND SUMMARY Converting capillary pressure data to the (dimensionless) Leverett J-Functions facilitates facies identification and comparison of potential reservoir performance, as well as providing independent verification of wireline petrophysical analyses. REFERENCES Amyx, J. W., Bass, D. M., and Whiting, R. L., 1960, Petroleum Reservoir Engineering Physical Properties, McGraw-Hill Book Company, New York. Craig, F. F., 1971, The Reservoir Engineering Aspects of Waterflooding, SPE. Hill, D. G., 1984, "XXXXXXXXXXXXXXXXXX, Offshore Denmark: Leverett JFunction Water Saturation Estimates", Internal Memorandum from D. G. Hill to R. M. White, Chevron Overseas Petroleum, Inc. Leverett, M. C., 1941, " Capillary Behavior in Porous Solids", Trans., AIME, v. 142, pp. 152 - 169. Moore, C. V., 1978, "Integrating Capillary Pressure and Other Core Measurements with Wireline Log Data to Determine Fluid Saturations in North Sea Chalk Reservoirs", Formation Evaluation Committee Minutes, Standard Oil Company of California.

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