The Integration of Capillary Pressures and Pickett Plots for Determination of Flow Units and Reservoir Containers
- R. Aguilera (Servipetrol Ltd.) | M.S. Aguilera (Servipetrol Ltd.)
- Document ID
- Society of Petroleum Engineers
- SPE Reservoir Evaluation & Engineering
- Publication Date
- December 2002
- Document Type
- Journal Paper
- 465 - 471
- 2002. Society of Petroleum Engineers
- 4.1.5 Processing Equipment, 5.6.1 Open hole/cased hole log analysis, 5.1 Reservoir Characterisation, 4.6 Natural Gas, 4.1.2 Separation and Treating, 2.2.2 Perforating, 5.2 Reservoir Fluid Dynamics, 5.8.6 Naturally Fractured Reservoir, 5.8.7 Carbonate Reservoir
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This paper shows how to construct lines of constant capillary pressure, process speed, pore-throat aperture, and height above the free water table on a Pickett plot. The integration of these properties allows the determination of flow units and reservoir containers and illustrates the important link between geology, petrophysics, and reservoir engineering.
The concept of flow (or hydraulic) units and reservoir containers has been used in the oil industry with a good deal of success during the past few years. The process or delivery speed k/f can be used in many instances to define a flow unit. Correlation of flow units between wells helps to establish reservoir containers and forecast reservoir performance.
We show that a Pickett crossplot of effective porosity vs. true resistivity should result in parallel straight lines for intervals with constant process speed k/f. The slope of the straight lines is related to the porosity exponent m, the water-saturation exponent n, and constants in the absolute permeability equation. From the straight lines, it is possible to determine capillary pressures and pore-throat apertures directly for each flow unit at any water saturation. Pore throats at 65% water saturation compare very well with Winland r35 values. The method has not been published previously in the literature.
Building lines of constant k/f allows the display of complete capillary pressure curves on the Pickett plot, including regions that are and are not at irreducible water saturation. Previous empirical methods for determining the absolute permeability of a given interval assume that the water saturation is at irreducible conditions. This paper presents a technique that allows us to estimate absolute permeability even if the interval contains moveable water.
The use of this technique is illustrated with previously published data from the Morrow sandstone in the Sorrento field of southeastern Colorado and carbonates from the Mission Canyon formation in the Little Knife field of North Dakota. We conclude that flow units can be determined reliably from the integration within one single log-log graph of Pickett plots, capillary pressures, pore-throat apertures, and Winland r35 values.
Pickett plots1,2 have long been recognized as very useful in log interpretation. The Pickett plot has been extended throughout the years to include many situations of practical importance, including naturally fractured reservoirs,3-5 shaly formations,6 reservoirs with irreducible and moveable water,7,8 formations with variable permeabilities, 8,9 and reservoirs with significant variations in porethroat apertures.10,11
This paper shows how to determine flow units by incorporating lines of constant process speed k/f on a Pickett plot. A schematic of this approach is shown in Fig. 1, where Pc1 and Pc2 are constant capillary pressures, r1 and r2 are constant pore-aperture radii, and (k/f)1 and (k/f)2 are constant process or delivery speeds. The correlation of flow units between wells helps to define reservoir containers.12
Well-log signatures, capillary pressures, Winland r35 pore throats, and/or process (or delivery) speed k/f help to define a flow unit. Hartmann and Beaumont12 have defined a flow unit as a reservoir subdivision characterized by a similar pore type. They define a container as "a reservoir system subdivision consisting of a pore system made up of one or more flow units, which respond as a unit when fluid is withdrawn." The work presented in this paper is based on those definitions. The same parameters mentioned earlier are built on the Pickett plot to facilitate the determination of flow units.
Archie's13 basic formation evaluation equations can be combined as proposed by Pickett1,2 to obtain
Eq. 1 indicates that a crossplot of f vs. Rt on log-log coordinates should result in a straight line with a negative slope equal to m for intervals with constant values of aRw, n, and Sw.
Archie's equation poses the limitation that it would tend to give unrealistically large values of water saturation in shaly formations. To alleviate the problem, it is better to prepare the Pickett plot using a shale correction (Ash) to the resistivity (Rt), as explained by Aguilera.6 This is based on the observation that all equations for evaluation of shaly formations published in the literature, no matter how long they are, become Sw=Ish -1/n.
An empirical equation that has been found to give reasonable estimates of permeability throughout the years has the form14
for the case of a medium-gravity oil. For a dry gas at shallow depth, a constant approximately equal to 79 is used in place of 250. Water saturation in Eq. 2 is at irreducible conditions. The optimum situation is when core data are available and the constants in Eq. 2 can be calibrated to better fit a particular reservoir. In that case, the permeability equation is written as follows:
Eq. 3 can be solved for irreducible water saturation Swi and incorporated into Eq. 1 to obtain
Eq. 4 indicates that a crossplot of Rt vs. f on log-log coordinates should result in a straight line with a slope equal to (-c3n-m+n/c4) for intervals at irreducible water saturation with constant aRw and constant k/f. Extrapolation of the straight line to 100% porosity yields the product [aRw(c2 -n)(k/f)n/c4].
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