RESERVOIR CHARACTERIZATION

Porosity partitioning and permeability quantification in vuggy carbonates

 Porosity-permeability relationships were established for three formations in the Permian basin, West Texas, using wireline logs. 

Duffy Russell* and Jonas Gournay, ExxonMobil; Chunming Xu* and Pete Richter, Schlumberger
 

A pilot study of 13 wells in Means oil field of the Permian basin, West Texas, established porosity-permeability relationships for the Permian Queen, Grayburg and San Andres formations. The optimized workflow used borehole image and conventional log processing with calibration to core data. This approach allowed the quantification of porosity and permeability heterogeneity in vuggy carbonate facies in the field.

INTRODUCTION

Means field was discovered in northeast Andrews County, West Texas, in 1934 with the Humble R. M. Means No. 1 well, Fig. 1. Oil production is from Permian strata, mainly the Guadalupian San Andres, Grayburg and Queen formations, with supporting production from Wolfcampian and Leonardian strata. These formations are predominantly dolomitized marine carbonate platform successions, with the exception of the lower Grayburg, which is a mixed carbonate-siliciclastic reservoir facies. Typical completion strategies are to fracture-stimulate the tighter Grayburg reservoirs and to perforate and acidize the better San Andres reservoirs. Following 31 years of primary recovery with 40-acre well spacing, the field has been developed on 10- to 20-acre well spacing in the active-flank waterflood areas and 10-acre well spacing in the updip areas where tertiary recovery by CO₂ injection is conducted. Recovery efficiencies vary from about 14% in the waterflood area to 42% in the CO₂-flood area.

The original carbonate platform has been structurally modified into a north-trending asymmetric anticline with a steeply dipping eastern limb and a gently dipping western limb. Outer-shelf, shelf-margin and middle-shelf facies dominate the San Andres formation. The Grayburg is predominantly middle-shelf facies characterized by laminated dolomite with interparticle and intraparticle porosity and minimal vuggy porosity. Thin anhydrite horizons may occur, interbedded with finely laminated fluvial and eolian sandstone. Anhydritic dolomite is also a common facies. Permeability in both the dolomite and sandstone is usually less than 1 mD, but can be as high as 10 mD. The lower Grayburg is dominated by middle- to inner-shelf facies. The upper Grayburg is dominated by evaporite and dolomite facies. During deposition of the San Andres formation, shallow-water carbonate sedimentation dominated the central basin platform region, producing a thick carbonate sequence that later became completely dolomitized. The Queen formation is dominated by supratidal evaporite facies (anhydrite and halite) and dolomite interbedded with fluvial and eolian sandstone. The sandstone horizons are the main reservoirs. The Queen and lower Grayburg are mixed siliciclastic-carbonate successions marked by cycles of shallow-water carbonate deposition, subaerial exposure and terrestrial-derived siliciclastic bypass. The resulting stratigraphy is characterized by thin, interbedded carbonates (now dolomitized), anhydrites and fine-grained sandstones and siltstones.

OVERVIEW

Previous studies on outcrop analog sections were combined with conventional wireline log data analysis in order to describe the stratigraphy and reservoir heterogeneity.² However, conventional wireline logs lack the intrinsic vertical and azimuthal resolution to provide adequate characterization of reservoir properties. Image logs are the key to resolving small-scale heterogeneity in complex carbonate reservoir pore systems. Thus a different workflow is used to partition vug porosity and quantify permeability and to characterize reservoir rock types by integrating data from calibrated borehole images and conventional wireline logs.³

A study of 13 wells in Means oil field established porosity-permeability relationships for the Permian Queen, Grayburg and San Andres formations. For example, in different vuggy zones of the San Andres formation, with similar total porosity values of about 8%, permeability is found to vary by 2-3 orders of magnitude. This variation is modeled by an exponential relationship between permeability and the vuggy porosity partitioned from borehole image processing. To apply the methodology to wells without image logs, a vuggy porosity index is estimated from conventional logs through a modified sonic porosity analysis. Permeability estimation uses both the vuggy porosity partitioned from borehole image logs and the vuggy porosity index from conventional logs.

In the San Andres, vugs in thin zones result in layer-cake structures of thin, super-permeable zones sandwiched between thicker, non-vuggy zones containing bypassed oil. The average conventional-log porosity in these thin zones, where the layering is below log resolution, results in an erroneous permeability profile when input to the exponential relationship between vuggy porosity and permeability. Similarly, the thin-bedded Grayburg siliciclastic and dolomite facies rocks, which were generally thought to be poor reservoirs in this field, exhibit significant vertical variation in porosity and permeability.

Petrophysical rock types have been differentiated using image and conventional log data and neural network processing. The integration of log-derived permeability and rock types with production data has provided the basis for interwell heterogeneity prediction and field-wide completion strategies.

METHODOLOGY

Of the 13 wells studied, 8 had been logged with both borehole imaging and conventional tools. Two of these eight imaged wells also had whole core with which to calibrate the interpretation and permeability quantification. Five existing wells in the northern part of the field, in which the imaged wells are most concentrated, had only conventional logs; these five were selected to evaluate the methodology once established.

Borehole image logs have a spatial resolution of about 0.2 in. (5 mm) and 80% azimuthal coverage in an 8-in. borehole. They reveal rock textures that contrast with resistive rock matrix, such as pores invaded by conductive drilling mud, and these produce relative changes in microresistivity, Fig. 2. Thus, image logs are used for various quantitative analyses, such as determining vug connectivity by means of image texture analysis and partitioning primary and secondary porosity through borehole-porosity image analysis.⁴ The terms “vug” and “vuggy” refer to voids that are either visually identifiable as holes on the images (Fig. 2) or recognizable through specific log signatures identified through log data processing. Here “primary porosity” refers to the matrix porosity or microporosity, in contrast to the “secondary porosity,” which is heterogeneously distributed around the borehole. Based on borehole images, cores and sonic log data, the secondary porosity defined from borehole image processing correlates most often with vuggy or moldic porosity.

One critical part of the processing chain is to calibrate the microresistivity image log properly with a shallow laterolog (LLS or equivalent) before any quantitative petrophysical analysis. The calibrated microresistivity image is then converted into a calibrated porosity image based on a modification of the technique described by Newberry et al. (1996) to partition primary and secondary porosity. This method computes the percentage of primary and secondary porosities and not the sizes of the pores.

An algorithm is developed for estimating permeability in wells with borehole image data by analyzing the correlation among partitioned porosity, rock types and core permeability. A method is shown for using porosity data from conventional logs (sonic, neutron and density) to estimate both a vug-porosity index and permeability, after calibration to the borehole image results, for extrapolation to wells without core and image logs.

POROSITY AND PERMEABILITY ANALYSES

Core data from Well MSAU-5508 and the results from elemental composition log data in Well MSAU-5456 confirm a critical assumption that conductivity on borehole image logs primarily results from conductive fluids in the pores rather than from the presence of clays or other conductive minerals, Fig. 3. This confirmation provided the theoretical foundation for the analysis of the pore systems around the borehole using electrical image logs.

After calibration to shallow laterolog resistivity, the calibrated electrical borehole image was transformed into a borehole porosity image, which is displayed as a high-resolution porosity variation map around the borehole using the algorithm:⁵

where is the transformed porosity variation around the borehole, PXND is neutron-density crossplot porosity, LLS is shallow laterolog resistivity or equivalent, and R_image is the microresistivity from the calibrated image log.

The porosity variation around the borehole is quantitatively analyzed with 28-bin porosity spectra calculated over a 1-in. interval spacing along a vertical-moving window. The spectra are displayed as variable-density waveforms in Fig. 2, track 3. A cutoff at the median value plus 4 standard deviations was used to separate primary porosity and secondary porosity, the latter corresponding mostly to vuggy porosity in Means field. Figures 2 and 4 illustrate the wider porosity spectra in the more vuggy zones in the San Andres formation and the narrower spectra in the non-vuggy Queen and Grayburg formations.

The vug connectivity coefficient, a rock-texture parameter extracted from borehole images using texture processing, is a good indicator of permeability in carbonate reservoirs.⁶ However, the image-texture processing data in Means field did not match the core permeability, especially in the San Andres vuggy zones. In the Grayburg formation, an 8%-porosity zone had permeability less than 0.1 mD. In contrast, a zone with 8-10% porosity in the vuggy San Andres formation had more than 100 mD permeability, Fig. 4. The production data demonstrates that nearly 100% of injection took place in the vuggy zones. Both the core permeability and injection data suggest that vugs are well connected and that their contribution to the high permeability is much greater than that indicated by the vug connectivity coefficient. Residual oil saturation does render a lower vug connectivity coefficient from image-texture processing, but it should not be as pessimistic below the oil/water contact. This dramatic increase of permeability due to the increase of vug porosity, without total porosity change, results in the inverse correlation between total porosity and permeability.⁷

Through iterative experimentation, the Klinkenberg-corrected permeability (in mD) from core plugs in Well MSAU-5508 exponentially varies with vug porosity as follows:

where and are the total porosity and vug porosity from borehole image-porosity processing, respectively, and a and b are constants that have been rounded to 10 and 100, respectively. The term is equivalent to permeability in homogeneous rocks (when vug porosity is zero). The constant a was determined by manually matching to the core permeability in intervals with negligible vug porosity (e.g., the interval above 4,500 ft in Fig. 4). In vuggy zones below 4,500 ft, the permeability was dominantly controlled by the product of vug porosity and vug connectivity factor b. We then used the same a and b values in all the study wells in Means field. Constants a and b may be unique for a particular oil field with its characteristic pore system, vug connectivity and fluid content. Therefore, calibration to core permeability data is essential.

To extend the heterogeneity analysis to uncored wells with no borehole image logs, the neutron-density crossplot porosity and Wyllie time-average porosity from the sonic log are used as input for vug porosity prediction. This is based on the assumption that vugs, especially spherical vugs in carbonates, have little effect on compressional sonic waves and cause the Wyllie porosity to read too low.⁸ Therefore, the difference between the neutron-density and sonic porosities can be regarded as a measure of vuggy porosity. For example, the difference between the total porosity and the sonic porosity, referred to hereafter as the sonic vug-porosity index or sonic vug index, correlates well with the secondary or vuggy porosity derived from image processing in almost all of the wells, Figs. 4 and 5. A few discriminators are needed to eliminate vug porosity computation in noncarbonates. In sandstones and within halite washout zones, the Wyllie porosity is larger than the total porosity, thereby yielding negative porosity differences, which have been excluded. The thick, tight dolomite zones are used as a zero baseline to calibrate this vug-porosity index. In Eq. 2, for wells with no image data, the input value foris the neutron-density crossplot porosity and is the sonic vug-porosity index.

Figure 4 demonstrates the good agreement between the three types of porosity and the permeability data. The disagreement at high-and low-porosity points occurs because the total porosity curve, PXND, reflects an average porosity for a borehole interval of about 2-4 ft, whereas core porosity may not always represent the total porosity at a given depth because of its relatively small sampling volume. Moreover, it is often impossible to obtain representative cores from sections with large vugs, thereby creating a sampling bias towards homogeneous rocks. Although variable depth mismatches between the core samples and the 1-in. resolution image-derived data make it difficult to calculate error statistics or display meaningful crossplots, the high-resolution porosity from the borehole images apparently provides a unique solution in heterogeneous dolomites. For example, in the less vuggy interval shallower than 4,500 ft in Well MSAU-5508 (Fig. 4), the total porosity curve from the borehole image almost overlies the core porosity curve, outperforming the PXND. In particular, thin streaks in the Grayburg sandy dolomites with porosity values greater than 10% (e.g., in the 4,400-4,460-ft interval) match well with cores but they are not resolved by conventional logs. Figure 2 demonstrates that vugs in the San Andres formation are developed in thin zones. The total porosity from borehole images varies from 2% to 20%, which correlates with the image texture data, but the openhole log porosity averages the variation to almost a constant 8%. With the exponential factor of vug porosity, the two porosity results yield significantly different reservoir flow characteristics (i.e., permeability).

In the vuggy 4,500-4,580-ft interval, the difference between borehole-image porosity and core-plug porosity is greater. Borehole-image total porosity is equivalent to whole-core porosity. Therefore, greater heterogeneity yields a greater difference between porosity values from borehole images and core plugs. The sonic vug-porosity index is computed from several logs of different resolution and different depths of investigation. For this reason, the sonic vug-porosity index has lower resolution, less accuracy, and needs more calibration than vug porosity derived from borehole images.

The microconductivity response of the borehole image log results primarily from the conductive filtrate in the dolomites. Therefore, the image vug porosity and permeability correlate with the effective vug porosity and permeability. Vugs filled with euhedral sulfur crystals and heavy oil are observed in cores, Fig. 3. These non-effective vugs are invisible on the borehole images due to negligible resistivity contrast between the matrix and infill materials. The partially filled vugs may appear as moldic voids on borehole images, Fig. 2. Although in many intervals of the San Andres formation anhydrite and sulfur content may comprise 25% of the matrix volume based on elemental spectroscopy log results, permeability from the borehole images in these anhydrite-rich zones can still exceed 1,000 mD. The exponential relationship between permeability and vug porosity indicates that pore throats and connectivity increase dramatically as the volume of effective vugs increases. In the well-developed vuggy zones in which core recovery ranges from poor to impossible, borehole image logs may constitute the most valuable data source for continuous permeability measurements along the borehole.

IMPLICATIONS FOR RELATIVE PRODUCTIVITY

The integration of borehole image data and conventional log porosity data explains anomalous zones. Figure 5 illustrates a typical problem in which thin, high-permeability streaks are swept (conductive) while thicker oil zones with as much as 10% porosity contain bypassed hydrocarbons (resistive). The borehole image shows a series of resistive dolomites, each with a thickness of 3-4 ft, separated by thin, high-permeability streaks immediately above the oil/water contact. Conventional logs show about 10-12% total porosity and values of about 5% for sonic vug-porosity index in the resistive zones. The vug porosity from the image is too low in these resistive zones above the oil/water contact due to the anomalous resistivity response. In contrast, the interval below the oil/water contact is much more conductive despite its lower porosity. The vug porosity computed from the image also matches well with the sonic vug index in the lower interval. Core observations suggest heavy oil and sulfur plugging the vugs as a plausible interpretation for these resistive, porous zones above the oil/water contact.

In this case, the highly porous, oil-saturated zone does not produce when it is adjacent to a thief zone that “short circuits” the fluid flow. This observation supports the concept that high-permeability thief zones are the primary cause of early water breakthrough and low sweep efficiency. Relative productivity with continuous permeability profiles should be modeled before production and, especially, before water injection. Quantification of the permeability heterogeneity along the borehole is only the first step; it is equally important to know how these zones are networked in 3D reservoir space.

CONCLUSIONS

Primary and secondary porosities that primarily correspond to matrix and vug porosity in Means field can be partitioned using either borehole porosity-spectrum analysis of electrical images or the sonic vug-porosity index from calibrated sonic porosity and neutron-density crossplot porosity. Synthetic porosity computed from borehole images resolves porosity heterogeneity more effectively than porosity derived from conventional wireline logs. The subject methodology provides quick thief-zone identification to optimize well completion design. Although the discrepancy in depth and resolution between log data and core data causes a crossplot of synthetic permeability to show scatter, the exponential correlation between permeability and vug porosity is clear. Permeability measurements in a heterogeneous rock vary not only azimuthally but also with measured volume.

Three distinct dolomites in the San Andres formation with similar porosity values have permeability values that vary by 2-3 orders of magnitude. Permeability values derived from borehole images resolve small-scale vertical layer heterogeneity that cannot be resolved using conventional logs. Core-derived permeability and borehole-image permeability data have similar trends; however, image-log data provides a continuous record over vuggy intervals that cannot be sampled with core plugs. The permeability relationship is effectively extrapolated from wells with image logs to wells with conventional logs and sonic data. Permeability derived from the sonic vug-porosity index correlates well with core- and image-log permeability.  

ACKNOWLEDGEMENT

This article was prepared from “Porosity partitioning and permeability quantification in vuggy carbonates using wireline logs, Permian Basin, West Texas,” published in the SPWLA journal Petrophysics, 47, No. 1, February 2006, pp. 13-22. The authors thank ExxonMobil Production Company for permission to publish the data. Special thanks go to Bill Newberry with Schlumberger for his help during the project and to Dr. Shin-Ju Ye with ExxonMobil for her recommendations.

LITERATURE CITED

 ¹ Map modified from Pranter, M. J., Hurley, N. F. and T. L. Davis, “Sequence-stratigraphic, petrophysical, and multicomponent seismic analysis of a shelf-margin reservoir: San Andres formation (Permian), Vacuum field, New Mexico, United States,” in Eberli, G. P., Masaferro, J. L. and J. F. Rick Sarg, eds., AAPG Memoir 81: Seismic Imaging of Carbonate Reservoirs and Systems, 2004, pp. 59-89.
² Eisenburg, R. A. et al., “Modeling reservoir heterogeneity within outer ramp carbonate facies using an outcrop analog, San Andres Formation in the Permian Basin,” AAPG Bulletin, 78, No. 9, 1994, pp. 1337-1359; Kerans, C., Lucia, F. J. and R. K. Senger, “Integrated characterization of carbonate ramp reservoirs using Permian San Andres Formation outcrop analogs,” AAPG Bulletin, 78, No. 2, 1994, pp. 181-216; Lucia, F. J. and C. Kerans, “Stratigraphic and operational controls on remaining oil in carbonate-ramp reservoirs,” AAPG Abstracts for the International Conference and Exhibition, Vienna, 1997, pp. 1395-1396; Lucia, F. J., Carbonate Reservoir Characterization, Springer-Verlag, Berlin, 1999, p. 222; Kazatchenko, E. and A. Mousatov, “Primary and secondary porosity estimation of carbonate formation using total porosity and the formation factor,” SPE 77787 presented at the SPE Annual Technical Conference and Exhibition, San Antonio, Texas, Sept. 29-Oct. 2, 2002.
³ Xu, C. and B. M. Newberry, Method for quantifying permeability of vuggy carbonates using wireline logs, U.S. Patent No. 6714871 B1, 2004.
⁴ Russell, S. D., Akbar, M., Vissapragada, B. and G. Walkden, “Rock types and permeability prediction from dipmeter and image logs,” AAPG Bulletin, 86, No. 10, 2002, pp. 1709-1732; Newberry, B. M., Grace, L. M., and D. D. Stief, “Analysis of carbonate dual porosity systems from borehole electrical images,” SPE 35158 presented at the Permian Basin Oil and Gas Recovery Conference, March 27-29, 1996.
⁵ Newberry et al., 1996.
⁶ Russell et al., 2002.
⁷ Ibid. Similarly, two different trends in the porosity-permeability crossplot, with the larger slope attributed to vuggy porosity, were shown by Wang, B. and I. Al-Aasm, “Karst-controlled diagenesis and reservoir development: Example from the Ordovician main-reservoir carbonate rocks on the eastern margin of the Ordos basin, China,” AAPG Bulletin, 86, No. 9, 2002, pp. 1639-1658.
⁸ Brie, A., Johnson, D. L. and R. Nurmi, “Effect of spherical pores on sonic and resistivity measurements,” paper W in 26th Annual Logging Symposium Transactions, Society of Professional Well Log Analysts, 1985.

THE AUTHORS
	Duffy Russell is a geologist for Saudi Aramco specializing in image log and core characterization of the Arab-D reservoir of Ghawar field. He has 28 years’ experience in exploration and production geology. He previously worked for Mobil in Dallas, evaluating ventures in the Middle East, Russia and Australia; for ADCO in Abu Dhabi, working on carbonate production challenges in Cretaceous reservoirs; and at ExxonMobil in Houston, pursuing the characterization of porosity and permeability in West Texas carbonate reservoirs. He earned a BS degree in geology at North Carolina State University, an MS degree in geology at Duke University and a PhD degree in geology from the University of Aberdeen.
	Jonas Gournay earned a PhD degree at the University of Texas at Austin in 1999 for his research on carbonate diagenesis and reservoir characterization. Since joining Mobil in 1999, and then ExxonMobil, he has focused his efforts on stratigraphy and reservoir characterization working mostly in carbonate terrains including the Paradox basin, West Texas, and most recently the Middle East.
	Chunming Xu earned a BS degree in geoscience at Jianhan Petroleum College in China in 1982. He spent 10 years interpreting seismic stratigraphy and thrust tectonics in China and Canada. After joining Schlumberger in 1992, he worked on methodologies for integrated stratigraphic interpretation and reservoir characterization using wireline logs and seismic data. He recently joined Shell in Houston as a geologist.
	Pete Richter is vice president for Schlumberger Data and Consulting Services overseeing European, Caspian and African operations and based in La Defense, France. Mr. Richter has over 20 years� experience in oilfield services and technical management. He joined Schlumberger in 1981 as a wireline field engineer in the US. In 2002, he was assigned to the Data and Consulting Services group for the Arabian market as operations manager. Mr. Richter earned a BS degree in mechanical engineering at South Dakota School of Mines and Technology.