Geostatistical Analysis of Permeability Data and Modeling of Fluid-Flow Effects in Carbonate Outcrops

Abstract

Summary Permeability data from Permian dolomitized shallow-water platform carbonate outcrops in west Texas and New Mexico exhibit two to five orders of magnitude variability, most of which occurs within distances of a few feet [1 to 2 m] within single rock-fabric units. A variety of longer-range features are also observed, including vertical interbed average-permeability contrasts, 140- to 180-ft [42- to 54-m] lateral periodicities, and up to 2,700-ft [810-m] lateral trends. The short-range heterogeneities can be modeled with K-Bessel semivariograms having asymptotic power-law behavior at the origin. The periodicities can be modeled with "hole-effect" J-Bessel semivariograms. Stochastic two-dimensional areal and vertical cross-section models explore the effects of these heterogeneities. Fluid-flow simulations demonstrate that some long-range features control overall flow behavior even when short-range variability composes most of the variance. The short-range heterogeneities produce local smearing of displacement fronts. Introduction For more than 10 years the Bureau of Economic Geology (BEG), The U. of Texas, Austin (UT), has been collecting petrophysical data from carbonate outcrops in west Texas and New Mexico to advance knowledge of the geological, petrophysical, geostatistical, and fluid-flow aspects of this important class of hydrocarbon reservoir rocks.1–6 Most of this work has been conducted in Permian dolomitized shallow-water platform carbonate systems of the San Andres, Grayburg, and Victorio Peak (a Clear Fork equivalent) formations. The subsurface equivalents of these outcrop successions contain a majority of the hydrocarbon resources in the Permian Basin of west Texas and New Mexico and more than 17 billion [>2.7 billion?m3] of remaining mobile oil.7 Although particularly applicable to Permian Basin reservoirs, these outcrops provide insight into reservoir architecture and heterogeneity in highly cyclic shallow-water platform carbonate successions around the world. The prolific Permian Khuff carbonate reservoirs of the Middle East, for example, are close analogs. This paper is focused on two outcrops: a San Andres outcrop at Lawyer Canyon, Algerita Escarpment, Guadalupe Mountains, New Mexico, and a Victorio Peak outcrop, Apache Canyon, Sierra Diablo Mountains, Texas (Fig. 1). Outcrops of the San Andres formation in the Guadalupe Mountains form a 17-mile [27-km] continuous exposure along the Algerita Escarpment. Approximately parallel to depositional dip, this section displays a spectrum of cyclic, middle to outer platform carbonate facies successions. Studies of this shallow-water carbonate platform succession based on the application of modern sequence stratigraphic concepts have created a basis for modeling of San Andres reservoirs.4 The Lawyer Canyon area, the locale for most of the measurements described in this article, exposes the ramp-crest segment of the lower San Andres platform. Cycles in the ramp crest comprise basal mudstones and wackestones and capping grainstones and grain-dominated packstones.4 Lawyer Canyon is perhaps the most thoroughly sampled carbonate outcrop in the world, at least in terms of petrophysical measurements relevant to fluid-flow modeling. The earliest known sampling at this location was conducted by Shell Oil Co. in 1969-1971.8 Sampling by the BEG and UT at Lawyer Canyon began in 1988.9 The BEG data set has been augmented with measurements collected by Chevron Petroleum Technology Co.10 and previously unpublished data collected by Mobil Technology Co. in 1992-1993. The combined ramp-crest data set at Lawyer Canyon (there are additional outer ramp data at Lawyer Canyon that we do not discuss here11) includes approximately 5,000 mechanical field permeameter (MFP) measurements, 1,200 plug samples, 830 natural gamma-ray measurements, and a variety of descriptive parameters. In this article we examine four horizontal transects of MFP data designed to reveal patterns of permeability heterogeneity that cannot be observed in vertical wells (Fig. 2). We also consider in less detail six vertical MFP transects. The transects sample three different grainstone units, the highest permeability rock fabric at Lawyer Canyon.4 Each transect is fully contained within a single grainstone unit. Outcrops in Apache Canyon provide a 1.5-mile [2.4-km] continuous exposure of the Victorio Peak formation along an oblique-to-dip section immediately landward of the platform margin. Ongoing studies of the Victorio Peak succession reveal thin cycles packaged into thicker cycle sets and sequences. Petrophysical data for this study were obtained from 414 1-in.-diameter [2.54-cm] plug samples collected in 1997 from a horizontal transect in a single high-frequency cycle at the base of a high-frequency sequence. The transect was designed to investigate petrophysical heterogeneity in a transition from tidal-flat facies updip to subtidal grainstones and grain-dominated packstones downdip. General Observations The MFP data from the four horizontal Lawyer Canyon transects are displayed in Fig. 3. The 414 Apache Canyon samples were each cut into as many 1-in.-long [2.54-cm] pieces as possible, producing 689 plugs. The Apache Canyon permeability transect is shown in Fig. 4. The Apache Canyon porosity transect (not shown) has similar properties. Perhaps the most striking feature of these data is the high degree of variability. The Lawyer Canyon transects have at least two orders of magnitude variation within single grainstone units. One transect, H1, exhibits more than three orders of magnitude variation. The Apache Canyon transect, which spans a transition from subtidal to tidal-flat facies, has five orders of magnitude variability. The larger variability at Apache Canyon is related to the larger range of rock fabrics sampled, but it is also due to the different permeability measurement methods. The lower limit of MFP measurements at Lawyer Canyon is about 1 md [9.87E-04 µm2]; the lower limit of plug permeability data at Apache Canyon is 0.01 md [9.87E-06 µm2]. Table 1 summarizes the permeability data from these five transects. The Apache Canyon transect stands out from the others; it has a smaller geometric average and a larger variance than any of the Lawyer Canyon transects. The smaller mean permeability at Apache Canyon is consistent with the generally muddier rocks sampled in that transect. The Lawyer Canyon averages, especially in transect H2b, might be slightly overestimated because of the inability of the MFP to measure permeabilities less than 1 md [<9.87E-04 µm2].

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“…The outcrop geology is quite similar to the oilfields of West Texas and consists of highly cyclic Permian dolomitized shallow water platform carbonates (Jennings et al, 2000). Figure 1 shows the location of the outcrop and the associated geology.…”

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“…Numerical simulations show that fingering, sweep efficiency and breakthrough time in enhanced oil recovery are sensitive to such variations 2,31,32 . Such effects may also be important for subsurface carbon dioxide sequestration and storage 33 .…”

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“…A typical example of semivariogram with its component is shown in Figure 6. The classical semivariogram is calculated by using the following formula [34] [35].…”

“…( ) where γ is the calculated semivariogram of the variable v at the separation distance and direction specified by the ''lag'' vector h, the x i are the data locations and n is the number of data pairs separated by h [34]. Stable model is a powered exponential variogram calculated as [36].…”

“…where c is the total variance or sill parameter, r is the range parameter, and p is the asymptotic power-law exponent [34]. For additional information on other models and semivariogram components can be found in several textbooks on geostatistic [31] [35].…”