The goal of reservoir characterization is to distribute petrophysical properties in 3-D. Porosity, permeability, and saturation values have no intrinsic spatial information and must be linked to a 3-D geologic model to be distributed in space. This link is provided by relating petrophysical properties to rock fabrics. The vertical succession of rock fabrics was shown to be useful in constructing a geologic framework for distributing porosity, permeability, and saturation in 3-D. Permeability is perhaps the most difficult petrophysical property to obtain and image because its calculation from wireline logs requires the estimation of pore-size distribution. In this study of the Arab-D reservoir, rock fabric and interparticle porosity were used to estimate pore-size distribution. Cross-plots of water saturation and porosity, calibrated with rock-fabric descriptions, formed the basis for determining the distribution of rock fabric and pore size from resistivity and porosity logs. Interparticle porosity was obtained from travel-time/porosity, cross-plot relationships. A global porosity-permeability transform that related rock fabric, interparticle porosity, and permeability was the basis for calculating permeability from wireline logs. Calculated permeability values compared well with core permeability. In uncored wells, permeability was summed vertically and the horizontal permeability profile compared with flow-meter data. The results showed good correlation in most wells.
A key aspect in constructing a reservoir model is distributing petrophysical properties in 3-D space. Because petrophysical data contain no intrinsic spatial information, this process requires not only measuring the petrophysical properties of core samples and calculating properties from wireline logs, but also of linking them to the stratigraphy.
This paper illustrates a method of calculating matrix permeability profiles and rock-fabric successions using some common wireline logs, such as gamma ray, neutron, density, acoustic, deep resistivity, and induction. Core and log data from the Haradh area (Figure 1) of the Ghawar Arab-D (Jurassic) reservoir (Figure 2) were used as follows:
(1) To link petrophysics and stratigraphic-related petrophysical measurements to rock fabrics.
(2) To calibrate rock-fabric petrophysical class and interparticle porosity to wireline-log responses.
(3) To calculate permeability from common wireline logs using a global rock-fabric interparticle porosity permeability transform.
Numerous ways of calculating permeability from wireline logs have been tried. The most popular has been the porosity-permeability transform. This approach fails because permeability is a function of interparticle porosity and pore size, not simply of porosity (Pittman, 1992). Another approach is to relate permeability to water saturation, porosity, and capillary pressure (Timur, 1968; Saner et al., 1997). Although this method has been used successfully in siliciclastic reservoirs, it is difficult to apply to carbonate reservoirs because of the complexity of the pore space. Several statistical approaches are in vogue to calibrate core data with log responses, including various statistical regression methods (Neo et al., 1998), cluster analysis, neural networks (Mohaghegh, 2000), and fuzzy logic (Cuddy, 2000).
The rock-fabric approach of this study used interparticle porosity and rock-fabric petrophysical class to characterize pore size. A single porosity-permeability transform can be used in those reservoirs that are characterized by interparticle porosity and a uniform rock fabric. Most carbonate reservoirs, however, are more complex, being composed of varying amounts and types of vugs, as well as variable interparticle porosity and several petrophysically significant rock fabrics.
Once permeability values have been calculated from wireline logs, they must be distributed into 3-D space to form a reservoir model. Several methods have been used. The most common approach has been to construct a correlation framework and interpolate permeability between wells constrained by the correlation surfaces. No link between permeability and geologic description is required, and the correlation structure may be based simply on gamma-ray and porosity logs. This method tends to average high- and low-permeability values and results in a reservoir model that is unrealistically uniform. A more realistic permeability distribution can be obtained by using modern spatial statistical methods, such as variography (Jenson et al., 1997). However, if not constrained by a geologic model, the resulting permeability model may also be unrealistic. Geologic models typically consist of facies distributed within a sequence stratigraphic framework (Kerans and Tinker, 1997). Permeability values from core data are linked to facies by using various rock-typing methods, such as regression analysis and cluster analysis. In this paper, permeability is linked to rock-fabric facies, and the rock fabrics are an integral part of the permeability calculations.
The principal ways of distributing petrophysical properties in 3-D space are as follows:
(1) Calculation of a reasonable vertical permeability profile for each well.
(2) Linking the permeability profile to the vertical succession of rock fabrics that can be incorporated within a sequence stratigraphic model to distribute the data in the interwell space.
This is not a two-step process, such as defining petrophysical rock-types first and then attempting to find stratigraphic links, or of developing the stratigraphic model first and then characterizing the facies petrophysically. It is an iterative process, with geological and petrophysical interpretations being done in concert.
The approach was in two parts as follows:
(1) Develop the methodology for calculating permeability and rock fabric using data from two cored wells.
(2) Test the method by using core data from other cored wells and flow-meter data from uncored wells.
The first step was to relate core measurements to rock-fabric descriptions using the classification described by Lucia (1995). This resulted in a relationship between rock-fabric petrophysical class, interparticle porosity, and permeability that was the basis for calculating permeability from wireline logs. A similar approach to characterizing Arab-D reservoirs was presented by Wilson (1981), Munn and Jubralla (1987), and Saner and Sahin (1999). The second step was to develop a method for estimating rock fabric and interparticle porosity from common wireline logs. This resulted in a relationship between rock fabric/water saturation/porosity and interparticle porosity/acoustic transit time/porosity.
The method was tested on three cored wells by comparing rock fabric and permeability results with core data, and on eight uncored wells by comparing calculated permeability with flow-meter data. The stratigraphic implications of the calculated rock-fabric successions were examined by correlating the vertical succession of rock fabrics.
Database and Analyses
Core descriptions, core analyses, and thin sections were provided by Saudi Aramco. Boyles Law porosity and permeability measurements were made on 1.25-inch-diameter horizontal core plugs. No capillary-pressure curves were available. Rock fabrics were identified from thin sections cut from the ends of the core plugs used for the petrophysical measurements. The samples were impregnated with blue dye to simplify pore-space identification. Sample density was 0.5 ft but, in most intervals, thin sections were described every 1 ft. A total of 421 thin sections were described. Percentages of pore types and minerals were determined by 300 point counts per thin section using a mechanical stage. Grain and crystal sizes were measured by means of an optical micrometer.
Total porosity from core analysis was divided into interparticle, separate-vug, and touching-vug pore types. No touching-vug porosity or large vuggy pore spaces were seen in thin sections or in core slabs. Separate vugs were found within fossil fragments (forams and Cladocoropsis), and as grain molds and skeletal dolomite crystals. In a few thin sections of grain-dominated fabrics, intragrain microporosity was identified by the presence of a blue tint from the impregnating dye. The porosity could not be determined because the pore size was too small. However, the number of grains with a blue tint was recorded and used to estimate the effect of intragrain microporosity on permeability.
Interparticle porosity was obtained by subtracting visible, separate-vug porosity obtained from thin sections, from total porosity obtained from core measurements. Core porosity was used for total porosity instead of visible porosity. This was because not all interparticle pore space was seen when using an optical microscope, whereas separate-vug porosity was normally visible. Intergrain and interdolomite-crystal pores were often visible, but microporosity in micrite was not. This procedure assumed that the separate-vug porosity measured from thin sections was an average value for the core sample. For this assumption to be valid, the thin section must have a relatively uniform fabric. At best, the large difference in scale between thin sections and core samples made this assumption an approximation.
Particle size and sorting were characterized according to the Lucia classification (Figure 3) (Lucia, 1995). In this classification, grainstone is well sorted, grain-dominated packstone is moderately sorted, mud-dominated packstone is poorly sorted, and wackestone and mudstone are considered to have well- to moderately sorted, fine-particle-size fabrics. Dolomite crystals range in size from 90 micrometers (μm) to 500 μm and are generally well sorted.
Saudi Aramco provided porosity and water saturation calculations for each well together with a basic suite of porosity and resistivity logs. No nuclear magnetic resonance logs were available. The authors did no log analyses. All core data were depth-shifted to match porosity-log depths. This step had to be done as accurately as possible to ensure that descriptions of thin sections and core data were linked closely to log responses.
Saudi Aramco had measured porosity and permeability on core plugs. Studies had shown that in the Arab-D there is little difference between porosity values measured at ambient conditions and under confining pressure (Harari et al., 1995). However, samples with well-developed stylolites commonly have higher than expected permeability values, probably because of the opening of pore spaces along stylolites when the pressure is reduced on bringing the core to the surface. Such samples were discarded. No tension-gash fractures were seen in the data set.
A large difference in scale existed between wireline-log measurements, core measurements, and thin-section descriptions. Wireline logs average data over intervals of several feet, petrophysical measurements are made on 1.25-inch core plugs or 6-inch whole-core samples, and thin-section descriptions are made on slices of core samples 30 μm thick. To scale rock-fabric descriptions to wireline-log measurements the following conditions were necessary:
• Thin sections with a relatively uniform fabric so as to be representative of the core sample.
• Rock fabrics being relatively uniform over the logged interval so that core samples were representative of the log responses.
A major concern of our study was the degree to which thin sections represented the fabric of the core sample. Small-scale heterogeneity within the core sample could cause the thin section to be unrepresentative; some examples of heterogeneity (Figure 4) are as follows:
• The patchy distribution of calcite cement or dolomite crystals.
• Particles that are large relative to the core sample, such as large fossil fragments.
• Mixtures of rock fabrics, such as wackestone, with burrows containing grain-dominated packstone.
Changes in rock fabric across stratal surfaces are another example of small-scale heterogeneity observed in some core plugs. Patchy distribution of calcite cements, dolomite crystals, and rock fabrics, often results in large differences between thin-section porosity and core porosity. It can also cause permeability values to be either too high or too low for the measured porosity and rock fabric. For example, one grainstone sample had a visible porosity of 5 percent and a measured porosity of 19 percent. The permeability was 3 millidarcies (mD), which was too low for a grainstone with 19 percent porosity but was reasonable for a porosity of 5 percent. This measurement suggested the presence of patchy calcite cement and so the sample was not included in the analysis. Many thin sections that contained large fragments of Cladocoropsis, or had mixed fabrics due to burrowing, or had irregularly distributed calcite cement and replacement dolomite crystals, were judged to be unrepresentative of the core sample and were not used in the analysis.
The rock fabric must be relatively uniform over the sampling interval in order to get a proper log response to the fabric. Porosity and resistivity logs typically sample a vertical interval of about 2 ft. Beds less than this are too thin for porosity and resistivity tools to give a unique response, and the tools record a mixed response. Therefore, only intervals having a uniform fabric more than 3 ft thick were used to calibrate log data with core descriptions.
The first step in the rock-fabric method was to divide the pore space into interparticle, separate-vug, and touching-vug pore types. No touching vugs were seen in the thin sections or the core descriptions. Step two was to describe particle size and sorting, as proposed by Lucia (1995) (Figure 3). The third step was to develop interparticle porosity/permeability transforms, and porosity/saturation/capillary-pressure transforms for various particle-size and particle-sorting groups.
Lithology is an important consideration, and for the purposes of this study, the samples were divided into limestone (0%-10% dolomite), dolomitic limestone (10%-80% dolomite), and dolomite (80%-100% dolomite) for analysis. The 80-percent limit was chosen because Powers (1962) reported an increase in porosity and permeability in samples having between 80 and 100 percent dolomite. Figure 5 shows photomicrographs of limestone fabrics.
Limestone (0–10 percent dolomite)
The grainstones contained well-sorted, coated grains 200 μm to 400 μm in size, with isopachous calcite cement on multicrystalline grains, and syntaxial-overgrowth cement on single-crystal echinoderm fragments (Figure 5a). Compaction effects included grain interpenetration, grain crushing, and the spalling of isopachous cement. Moldic porosity ranged from 0 to 7 percent. The sample set consisted of only 15 grainstone samples and 4 of them were discarded because the thin sections appeared to be unrepresentative of the core plug based on criteria discussed in Scaling Concerns. The porosity and permeability values of the 11 remaining samples plotted (Figure 6) in the class 1 field of Lucia (1995).
The grain-dominated packstones (Figures 5b-d) showed a wide variety of fabrics. In the more even-textured samples, intergrain lime mud ranged from a few percent to 40 to 50 percent of the bulk volume (Figure 5b). However, some samples had an uneven texture from a mixture of wackestone and grain-dominated packstone (Figure 5f). These samples plotted in the class 2 field when most of the sample was a grain-dominated fabric. There were 100 samples of grain-dominated packstones, most of which were porous and permeable. Of these, 29 were discarded—20 for having large Cladocoropsis grains and 9 for the presence of stylolites—and the remaining 71 samples plotted within the class 2 field (Figure 7).
Grains were mostly peloids or micritized grains in the size range of 150 μm to 300 μm and the lime mud components were less than 20 μm in size. The only cement observed was syntaxial overgrowths on echinoderm fragments (Figures 5b and 5c). The interpenetration of grains suggested compaction. Interparticle porosity was the most common pore type visible by means of an optical microscope. Few separate vugs were visible and grains with intragrain microporosity were present only locally.
The mud-dominated fabrics were as follows:
• Mud-dominated packstone with grains as a supporting fabric but with the intergrain space filled with micrite (Figure 5g).
• Wackestone having micrite clearly as the supporting fabric.
• Mudstone with few observable grains (Figure 5h).
Of the 52 samples of mud-dominated fabrics, 6 were discarded because they contained large Cladocoropsis fragments and 7 because of stylolites. Of the remaining 39, only 10 were permeable and all but 3 plotted in the petrophysical class 3 field (Figure 8). Mud-dominated fabrics have little separate-vug pore space.
The affect of stylolites and large fossil fragments was to increase permeability for a given porosity mainly in mud-dominated fabrics because they had the lowest permeability. However, this effect was probably related to measurements made at ambient rather than restored pressure conditions. A porosity-permeability plot of mud-dominated fabrics containing large Cladocoropsis fragments and stylolites (Figure 9), showed that these samples had anomalously high permeabilities for a class 3 fabric; therefore, they were not included in the analysis.
Dolomitic Limestones (10-80 percent dolomite)
Dolomitic, Grain-dominated Packstones
There were 27 samples of dolomitic grain-dominated packstone (Figure 5d). The samples were divided into groups of 10 to 25 percent, 25 to 50 percent, and 50 to 80 percent dolomite, for analysis. All but four samples had less than 50 percent dolomite. The dolomite crystal size ranged between 80 μm and 200 μm. Most of the samples plotted within the petrophysical class 2 field (Figure 10). No relationship appeared to exist between the amount of dolomite and porosity or permeability, which suggested that the partial replacement by large dolomite crystals had not altered the porosity or pore-size distribution.
Dolomitic, Mud-dominated Fabrics
Similarly, the 63 dolomitic, mud-dominated samples were divided into dolomite-content groups (10%-25%, 25%-50%, and 50%-80% dolomite) for analysis. No clear relationship existed between the amount of dolomite and the porosity. However, all but 4 samples with less than 9 percent porosity had permeabilities of less than 0.1 mD, whereas all 30 samples having more than 9 percent porosity were permeable (Figure 11). Permeable samples with 10 to 25 percent dolomite tended to plot in the petrophysical class 3 field along with other mud-dominated fabrics. Permeable samples of the 25 to 80 percent dolomite, however, plotted within the class 2 field with the grain-dominated packstones, and samples having the most dolomite (50%-80%) tended to be the most permeable for a given porosity.
The reason that some partly dolomitized, mud-dominated fabrics plotted in the class 2 field rather than in class 3 was because pore size has been increased by the dissolution of intercrystal lime mud. Figure 12 shows photomicrographs of dolostone and dolomitic wackestone. Thin-section analysis of the permeable samples suggested that dissolution of intercrystal mud had produced pore space and highly porous intercrystal mud, probably as part of the dolomitization process. Figure 12a illustrates a thin section in which intercrystal mud has been partly dissolved to create pore space in half of the view, whereas lime mud fills intercrystal areas in the other half. The porosity is 18 percent and permeability 47 mD. The high permeability results from the large pore spaces between the dolomite crystals. The sample illustrated in Figure 12b has 17 percent porosity and 15 mD permeability, a permeability that is higher than would be expected for a mud-dominated fabric. The pore space is within the mud fraction between the dolomite crystals, a slight blue tint being visible in thin section. A calculated porosity of 58 percent for the mud fraction accounted for the higher-than-expected permeability.
Dolomite crystals more than 100 μm in size characterized the dolostone samples. Most dolostones were permeable and all plotted in the class 1 field together with grainstones (Figure 13). The dolomite-crystal size varied from 100 μm to 500 μm, and the fabrics were typically uniform (Figure 12c). However, some samples had a slightly bimodal dolomite crystal distribution. In these cases, tight areas of coarse (250 μm-350 μm), cloudy crystals were mixed with porous zones of smaller (150 μm-250 μm) crystals having cloudy centers and clear rims (Figure 12d). Several thin sections contained separate vugs in the form of skeletal dolomite. Other minerals in the dolostone were small amounts of chert, a green clay mineral (probably chlorite), and laths of anhydrite. Samples with abundant chert or green clay were discarded from the data set as being unrepresentative.
Samples were divided into three crystal size groups; namely, 100 μm to 200 μm, 200 μm to 300 μm, and 300 μm to 500 μm. The porosity-permeability crossplot showed that permeability tended to increase as dolomite-crystal size increased (Figure 13). The petrophysical class 1 field defined by the dolostones was somewhat larger than that defined by Lucia (1995).
Average core and thin-section porosity values showed that most porosity was interparticle, and separate-vug porosity was less than 1.5 percent (Table 1). In class 1 dolostones and grainstones, most pore space was visible, indicating that there was very little microporosity in these fabrics (microporosity being defined as pore space that was not visible with an optical microscope). The proportion of microporosity increased in class 2 grain-dominated packstones and accounted for about 70 percent of the pore space. In mud-dominated fabrics, pore space was dominated by microporosity.
Statistical analysis of porosity data from limestone fabrics indicated that porosity decreased as the mud content increased (Figure 14). Grainstones and grain-dominated packstones had similar mean values (15% and 17%, respectively) but different ranges. With one exception, grainstones had porosity values higher than 9 percent, whereas grain-dominated packstones ranged from 1 to 28 percent porosity. Mud-dominated packstones had a lower mean value of 12 percent. The porosity range was similar to that of the grain-dominated packstone. Values, however, were clearly skewed to the low range, whereas those of the grain-dominated packstone were skewed to the high range. Wackestones had a mean value of 10 percent, and 80 percent of the values were less than 15 percent. The mean value for mudstones was 7 percent, and 80 percent of the values were less than 10 percent.
The reduction in porosity values with increasing lime mud suggested that the mud was more easily compacted than was the lime sand. Very little calcite cement, which could provide a resistance to compaction, was visible in the samples. It was limited to isopachous cement in a few grainstones and to syntaxial cement on echinoderm fragments. Differential compaction of mud-dominated fabrics over grain-dominated fabrics is a common feature of limestone reservoirs and was observed in compaction experiments (Goldhammer, 1997).
GLOBAL ROCK-FABRIC/POROSITY/PERMEABILITY TRANSFORM
Analyses of thin section and core data demonstrated that rock fabrics could be grouped into petrophysical fields defined by interparticle porosity and permeability (Figure 15). This conclusion was tested against thin-section descriptions from three additional cores in the Haradh area. The relationships between rock-fabric descriptions and petrophysical properties were similar to those developed from the first two cores (Figure 15a). However, grain sizes in the grain-dominated packstone samples covered a much larger range than in cores 1 and 2, with grain sizes larger than 500 μm being common in the lower interval (Figure 5e).
Data from the five wells were combined and are presented in Figure 15b. The three generic rock-fabric-specific porosity-permeability transforms developed by Lucia (1995) can be used to calculate permeability for this suite of rocks. Dividing these fabrics into three classes was somewhat arbitrary because there was a continuum of fabrics from mudstone to grainstone and from 5 μm- to 500 μm-dolostones. Thus, there was also a complete continuum of rock-fabric-specific porosity-permeability transforms instead of just three possibilities.
Samples were sorted by grain size and plotted on the porosity-permeability plot (Figure 16). Samples containing grains larger than 0.5 mm plotted in the class 1 field whereas those having grain sizes between 0.1 and 0.2 mm clustered at the boundary between class 2 and 3. All other samples plotted in a scatter between these two groups, suggesting that pore size increased with grain size in grain-dominated packstones.
Combining Haradh data with data presented by Lucia (1995) and with data from Shu’aiba (Cretaceous) reservoirs in the Middle East, resulted in a robust description of the relationship between rock fabric, interparticle porosity, and permeability (Figure 17). The lower limit of class 3 was defined by data from porous mudstone and wackestone fabrics from the Shu’aiba (Cretaceous) reservoir in the Idd el Shargi field (Lucia, 1998). The particle size of this fabric was 5 μm. The lower limit of class 3 was named class 4, and the upper limit was class 2.5 (Figure 18a). The permeable class 3 fabrics in this study were principally mud-dominated packstones and wackestones with higher permeability values than the Shu’aiba mudstones. These observations suggested that the permeability increased with increasing grain content in mud-dominated fabrics (Figure 18b). Permeability increased with increasing dolomite-crystal size from 5 μm to 20 μm in mud-dominated dolostones because pore size was directly related to dolomite-crystal size (Figure 18c).
Grain-dominated packstone; fine- to medium-crystalline, grain-dominated dolopackstone; and medium-crystalline mud-dominated dolostone occupy class 2 (Figure 18c). The permeability of grain-dominated packstones increased with decreasing amounts of intergrain micrite and with increasing grain size because pore size is directly related to grain size and the volume of intergrain lime mud. As illustrated previously, grain-dominated packstones having grains larger than 0.5 mm commonly overlapped into the class 1 field. Cruz (1997) also demonstrates this overlapping for an oncoid grain-dominated packstone from a Cretaceous reservoir in offshore Brazil. The permeability of medium-crystalline, mud-dominated dolostone increased with increasing dolomite crystal size from 20 μm to 100 μm. The upper limit of class 2 was named class 1.5 (Figure 18a).
Grainstones, dolograinstones, and large crystal dolostones occupied class 1 (Figures 18b and 18c). Permeability increased with an increase in grain size (100 μm-500 μm) and dolomite crystal size (100 μm-500 μm), because of the relationship between particle size and pore size. The upper limit of class 1 was named class 0.5, defined by the 500 μm-dolostones of the Ghawar field (Figure 18a).
Using porosity-permeability equations for each class and class boundary, we developed by multilinear regression an equation relating permeability to a continuum of rock-fabric petrophysical classes and interparticle porosity. The resulting global transform was
k = permeability
Class = rock-fabric petrophysical class ranging from 0.5 to 4
ϕip = fractional interparticle porosity
A = 9.7982; B = 12.0838; C = 8.6711; D = 8.2965.
This relationship was useful because it required only two values to characterize the pore-size distribution needed to estimate permeability. One value was petrophysical (interparticle porosity) and the other was a geologic description (rock fabric). As a result, this equation provided a direct link between numeric values for interparticle porosity and permeability, and a geologic description with stratigraphic implications.
PERMEABILITY AND ROCK FABRIC FROM COMMON WIRELINE LOGS
Interparticle porosity and the rock-fabric petrophysical class are required for estimating permeability using the global permeability transform. However, no wireline logs measure interparticle porosity or describe rock fabric. Instead, these attributes are estimated by using empirical relationships between them and wireline-log values. Interparticle porosity is determined by estimating separate-vug porosity from acoustic-log algorithms and subtracting it from the log-derived total porosity. The rock-fabric petrophysical class is estimated from porosity, water saturation, and reservoir height relationships.
Rock-fabric specific relationships for these parameters were derived from mercury capillary-pressure curves by Lucia (1995), and are adequate for estimating original water saturation. No mercury capillary-pressure data were available for this study, but saturation and porosity data provided by Saudi Aramco were used to develop a relationship between rock fabric, water saturation, and porosity. Water saturation is a function of capillary pressure (reservoir height) as well as porosity and rock fabric. It changes rapidly in the transition zone between the zero capillary pressure level and the zone of irreducible water saturation. However, all wells in this study appeared to be sufficiently high in the reservoir to warrant the assumption of irreducible water saturation.
Rock-Fabric Petrophysical Class
The rock-fabric petrophysical class was determined from crossplots of water saturation and porosity calibrated to rock-fabric descriptions (Figure 19). Calibrating log response with thin-section and core-slab descriptions presented a major problem in scaling data. As discussed earlier, the core sample must be relatively uniform before a thin-section description from that sample could be assumed to be representative. Likewise, the rock fabric had to be relatively uniform over the interval sampled by the wireline log before a core description could be considered representative. In this study, it was assumed that the rock fabrics must be constant for at least 3 ft in order that resistivity and porosity logs could present a unique response.
Class 1 large-crystal dolostones and grainstones form a field characterized by low water saturation, and with the coarser dolostones tending to have the lowest water saturation (Figure 19). The lower limit of the field was assigned as a class of 0.5 and the upper limit to class 1.5, to conform to the class values of the global transform. Most of the data points that formed a prominent high-porosity trend on the crossplot (Figure 19), were class 2 grain-dominated packstones. The class 2 values that overlap into the class 1 field may have responded to large-grain fabrics. Included in this trend were dolomitic, mud-dominated fabrics having more than 9 percent porosity. The upper boundary of this trend was assigned a class limit of 2.5. Class 3 mud-dominated fabrics and class 3 low-porosity, dolomitic mud-dominated fabrics formed a trend above the class 2 fabrics. Most class 3 data had less than 5 percent porosity and were not used to define the class; the data used had less than 10 percent porosity. Class 3 samples that overlapped into the class 2 field may have been from intervals that contained burrows filled with grain-dominated packstone. The upper limit of mud-dominated fabrics was spaced above the class 3 group and labeled class 4.
The distinction between the classes was less apparent in the low-porosity range. Class 1 fabrics remained in the class 1 field, but class 2 fabrics tended to move down into the class 1 field, and class 3 fabrics tended to move down into the class 2 field. There are many possible explanations for this, but it may indicate a nonlinear relationship between log porosity and log saturation for a given fabric. Below 5 percent porosity, the method was unreliable. However, 80 percent of the samples with less than 5 percent porosity were mud-dominated fabrics, or petrophysical class 3 (see Figure 14). Therefore, intervals having porosity of less than 5 percent were assigned to petrophysical class 3.
A relationship between rock-fabric petrophysical class, water saturation, and porosity was developed by multilinear regression using the equations for the class boundaries. The relationship was
Class = rock-fabric petrophysical class ranging from 0.5 to 4
Sw = water saturation
A = 3.1107, B = 1.8834, C = 3.0634, D = 1.4045.
Figure 20 and Figure 21 show the results of wireline-log calculation for calibration wells A and B. A comparison between the calculated and observed petrophysical class for the two calibration wells is illustrated by Figures 20a and 21a. In general, reservoir zones 1 and 2 are dominated by class 1 and 2 grain-dominated fabrics and large-crystal dolostone, whereas reservoir zone 3 contains more class 3 mud-dominated fabrics. The difference in presentation made comparisons difficult. The calculated class values formed a continuum, whereas the class values obtained from core description were constrained to three numbers. However, the calculated classes plotted generally within the range of the three classes as determined from thin-section descriptions.
The difference between foot-by-foot core descriptions and log-calculated fabrics is illustrated in zones 1 and 2 of calibration well A (Figure 20a). Core descriptions showed thin beds of class 3 mud-dominated fabrics intercalated with class 2 grain-dominated packstones. The thin class 3 beds were not resolved by the log calculations, most likely because the log was responding primarily to low water saturation in the class 2 fabric and only partly to higher water saturation in the class 3 fabric. The petrophysical class was thus understated. The problem of sample scaling was present in the data from zone 3 as well. Here, the core descriptions showed thin beds of class 2 grain-dominated packstone, some with large grains and intraclasts, intercalated within class 3 mud-dominated fabrics.
The continuum of petrophysical classes showed subtle changes in the vertical succession of rock fabrics that may be useful for stratigraphic analysis. In calibration well A, the vertical succession of fabrics in the limestone interval of reservoir zones 1 and 2 could be interpreted as representing four upward-coarsening cycles (Figure 20a). The two beds of class 1 were dolostone and could not be used for cycle analysis. Zone 3 limestone also exhibited cycles. These may be valuable in constructing a chronostratigraphic geologic framework because upward-coarsening cycles are frequently used as a eustatic signal in the analysis of vertical facies successions (Kerans and Tinker, 1997). In calibration well B (Figure 21a), the presence of dolostone (class 1) masked the vertical succession of rock fabrics in zones 1 and 2 because the dolostone precursor fabric could not be determined. Zone 3 limestone again exhibited cyclicity.
An anomalously high petrophysical class of between 2 and 3 was calculated for the 6,580-6,590 ft interval of calibration well B (Figure 21a). The values were anomalous because no core was available from the interval itself, and the core from above and below the interval consisted of large-crystal dolostone of class 1.5 to 0.5. The reason for the erroneously high class value was an anomalously low resistivity value for the very high porosity value of 30 percent. The low resistivity may have resulted from deep invasion of drilling fluid into a highly permeable interval. The high permeability was evidenced by the flow meter, which showed 60 percent of flow occurring from a 10-ft interval from 6,575 to 6,585 ft (Figure 21c).
Interparticle porosity was calculated by subtracting separate-vug porosity from total porosity. An acoustic-porosity algorithm was used to calculate the separate-vug porosity. The amount of separate-vug porosity, typically less than 2 percent (see Table 1), did not have a large impact on permeability calculations. Therefore, it was reasonable to substitute total porosity for interparticle porosity when acoustic logs were not available.
When acoustic logs were available, separate-vug porosity (svug) was estimated from a relationship between lithology, transit time, and total porosity (Lucia and Conti, 1987; Wang and Lucia, 1993). This relationship takes the form of
variable ‘a’ is a function of lithology
variable ‘b’ accommodates site-specific data
Δt = transit time
ϕ = porosity.
The Arab-D Formation in the Haradh area is composed of calcite, dolomite, and minor amounts of anhydrite, and the variable ‘a’ was replaced by a function that depends on the dolomite fraction. The dolomite fraction was estimated from a simple relationship between neutron and density logs. The following equation was used in this study to estimate separate-vug porosity from total porosity and transit time:
D = dolomite fraction from neutron and density logs
Δt = transit time
ϕ = total porosity fraction.
The algorithm will calculate erroneously high separate-vug values (1) if porosity and acoustic logs are not properly depth matched, (2) if large changes in porosity occur abruptly, and (3) if the acoustic or porosity logs show an anomalous response. These spikes must be removed before interparticle porosity is calculated.
Comparing calculated separate-vug porosity with thin-section values (Figure 22) was difficult because of the large difference in scale between thin sections and wireline-log measurements, as discussed previously. In calibration well A, calculated and described values were similar up to, and including, the 85 percentile (Figure 22a). Above 85 percent, the values diverged with thin sections having the higher amounts of separate vugs. This divergence resulted from the wireline logs averaging values over sections about 2 ft long, whereas the thin sections showed small-scale variations. Separate-vug porosity, however, was less than 2 percent in 85 percent of both the thin-section and the log data, indicated that it did not have a large impact on permeability calculations (see Table 1).
In calibration well B, 90 percent of the thin sections had less than 2 percent separate-vug porosity (Figure 22b). The log-calculated values were higher, as only 70 percent of the values had fewer than 2 percent vugs. None of the thin sections had more than 6 percent vugs, whereas 5 percent of the log values were above 6 percent, and some values were more than 10 percent. This well contained considerable amounts of dolostone, and the acoustic response to the dolostone in this well was erratic, resulting in anomalously high values for separate-vug porosity. To compensate, total porosity values were used as interparticle porosity in the dolostone intervals because core descriptions show that vuggy porosity was not a significant pore type.
Permeability was calculated from wireline logs by substituting petrophysical class and interparticle porosity into the global permeability transform. Permeability estimates calculated using this method compared well with core-plug permeability in reservoir zones 1 and 2 (Figures 20b and 21b). Core-plug values show more variability than calculated values because wireline logs average out small-scale variability. Scattered, high core-plug permeability values were present in zone 3, but were not matched by wireline-log calculations. The high permeability was caused by large-grain, grain-dominated packstones in thin beds within an overall mud-dominated interval, but the resistivity logs did not resolve them. The porosity values were reasonable, but the petrophysical class tended to be overstated, resulting in permeability values that were much too low.
Calculated and core permeability values from zones 1 and 2 are compared in the two wells (Figure 23). It shows a low correlation coefficient of 0.3 (Figure 23a), partly because of the different measurement scales and inaccuracies in matching core and log depths. The reduced major axis (RMA) fit shows a tendency to underestimate high permeability and overestimate low permeability. Most of the values lie within a factor of 5 of the RMA regression, which is a reasonable fit when comparing small-scale and large-scale permeability data.
The method was blind tested on additional cored wells with a similar result (Figure 23b). Core and calculated permeability values from zones 1 and 2 show a similar trend and a low correlation coefficient of 0.4. There is a similar tendency to overestimate the low permeability but less of a tendency to underestimate high permeability. Again, most of the values lay within a factor of 5 of the RMA fit.
Flow-meter Comparisons and Super-permeability
In a recent paper, Meyer et al. (2000) reported on their investigation into the geologic characteristics of super-permeability (super-k) using core data. They compared rock fabrics from core and thin section descriptions with flow rates calculated from flow-meter data. Super-k was defined as intervals having flow rates exceeding 500 barrels of fluid per day per foot of vertical section.
In our study, we compared calculated permeability values with flow-meter data, and referred super-k to intervals where a large portion of the flow (more than 50 percent) is from a few feet of vertical section. The calculated permeability values were summed vertically, and the vertical profile was compared with flow-meter data from the two calibration wells. Although this process does not test the magnitude of the permeability values, it does provide insight into the accuracy of the method. The flow meter and cumulative horizontal permeability (kh) profile should be in good agreement if the vertical permeability profile is representative of the reservoir permeability. There is a good comparison in calibration well A, suggesting that the calculated values capture the flow characteristics of this well (Figure 20c). Importantly, there is little flow from zone 3, although core analysis shows thin, high-permeability intervals. This observation suggests that these thin intervals do not extend far from the well bore and that the calculated permeabilities are more representative of the reservoir than are the core data.
The flow-meter data and kh profile from calibration well B did not match. In the upper interval, the flow meter showed 60 percent of the flow occurring from a 10-ft interval that was defined by Saudi Aramco as a super-k interval (Figure 21c). There is no core from the high-flow interval, but thin sections from above and below it are composed of large-crystal class 1 dolostone. Porous large-crystal dolostone is one of the fabrics described as contributing to super-k behavior by Meyer et al. (2000). As discussed previously, petrophysical class is overstated because of anomalously high water saturation calculated for this interval. However, if a class 1 dolostone is assumed, sufficient permeability can be calculated to account for the high flow rate. Adding 750 mD/ft to the 5-ft super-k interval provided a good match between log data and flow-meter data (Figure 21c). This was not an exceptionally high permeability value. In addition, 15 percent of the flow was from zone 3 (Figure 21c). Importantly, this flow originated from one interval at about 6,700 ft that has a core permeability of between 100 and 1,000 mD. Core descriptions showed that this interval was a large-grained, grain-dominated packstone having large intraclasts. Assuming a petrophysical class of 1.25 for this fabric (see Figure 16) and using the calculated porosity values for this interval, the result was permeability ranging from 90 to 200 mD. A match between flow meter and cumulative kh was obtained by inserting these values over the 5-ft interval from 6,695 to 9,700 ft (Figure 21c). The rest of the high-permeability beds in zone 3 did not contribute to the flow.
Permeability Calculations Compared with Flow-meter Data in Uncored Wells
The method was tested in eight uncored wells by summing permeability vertically and comparing the resulting kh profile with flow-meter data. No sonic logs were available from these wells, and permeability calculations were based on the assumption that total porosity was equal to interparticle porosity. This assumption was reasonable because thin-section studies showed that separate-vug porosity was of only minor importance in this area.
Comparing the cumulative kh with flow meters showed that three wells have excellent comparisons (Figure 24a), and one of them contained a super-k interval. There was no flow from zone 3 in these wells. Four wells had poor comparisons because of flow from zone 3 where little permeability had been calculated (Figure 24b). Adding sufficient permeability to the lower inflow zone to match the flow meter improved the match in zones 1 and 2 significantly. One well had a super-k interval that could not be matched by the kh profile, suggesting the presence of a touching-vug pore system (karst and/or fracture porosity) to account for the high flow rate (Figure 24c).
Correlation of Rock-fabric Successions
The vertical succession of rock fabrics was evaluated by correlating upward-coarsening successions between four wells (Figure 25). Only wells containing small amounts of dolostone were used in the correlation test because the precursor fabrics of the large-crystal dolostones could not be determined. The origin of the dolostones was recently discussed by Cantrell et al. (2001) and is outside the scope of this paper. The Figure 25 cross-section suggests that in zones 1 and 2, four upward-coarsening, high-frequency cycles can be correlated between the four wells. Zone 3 appears to be divided by a zone of class 2 fabrics that can be correlated between the four wells and may represent a longer-term cycle.
Considerable variability remains after grouping the fabrics into petrophysical classes because of the following variables:
• variations in crystal size, grain size, and sorting of the fabrics within the class group,
• scale differences between the size of the core sample and the thin sections, and
• small-scale variability.
Permeability varies with the size of the dolomite crystals as explained previously. Many of the grain-dominated packstones are burrowed mixtures of wackestone and grain-dominated packstone, and the permeability of the sample depends on how these two fabrics are mixed. Class 2 samples that overlap into the class 1 field had grains larger than 500 μm. Small-scale variability most likely accounted for much of the scattering of data within the petrophysical classes. Senger et al. (1993) and Jennings et al. (2000) have made recent studies of the distribution of permeability in outcrop-reservoir analogs and in subsurface core material. They showed that much of the variance (normally one to two orders of magnitude) was at the scale of inches to feet and was nearly randomly distributed in space. Small-scale variability can account for as much as 80 percent of the variance and masks the part of the variance that is spatially correlated. The larger-scale variance is often spatially correlated and can be linked to the distribution of rock-fabric facies (Kerans et al., 1994).
The rock-fabric method for estimating permeability described earlier is subject to the following conditions:
• That rock fabrics are reasonably uniform vertically for 3 ft or more.
• That accurate values for water saturation and porosity are available.
• That major touching-vug pore systems are not present.
• That the logs have not been affected by injected water, bottom water, or edge-water encroachment.
• That good acoustic logs are available if the volume of separate-vug porosity is large.
Calculating rock-fabric petrophysical class is important because it provides the link between petrophysical properties and the stratigraphic framework necessary to display permeability, porosity, and water saturation in 3-D. The global transform and the rock-fabric petrophysical-class equation could be combined to produce an equation relating permeability to porosity and water saturation without the petrophysical-class variable. The tie to rock fabrics, however, provides a basis by which log-calculated petrophysical properties can be realistically distributed in 3-D space. Vertical fabric successions from mud-dominated to grain-dominated can be used to define high-frequency cycles. These successions provide information for constructing a sequence stratigraphic, high-frequency-cycle framework for distributing petrophysical properties in 3-D.
Thin-section descriptions from the Arab-D reservoir in the Haradh area of the Ghawar field showed that the dominant pore types were intergrain and intercrystal. Separate-vug porosity was generally less than 2 percent, and no touching-vug pores were observed in the thin sections or core slabs. Using only samples with a relatively uniform fabric, we could group rock fabrics into petrophysical classes defined by interparticle porosity and permeability, as demonstrated by Lucia (1995).
Grainstones and large-crystal dolostones fell within petrophysical class 1 field. Most class 1 fabrics in this study were dolostones, and permeability increased with increasing dolomite-crystal size from 100 μm to 500 μm. Grain-dominated packstones were within petrophysical class 2 field. Mud-dominated fabrics were grouped into class 3. Most mud-dominated samples had less than 0.1 mD permeability and less than 9 percent porosity but, when permeable, they plotted in the class 3 field. Mud-dominated fabrics with 25 to 80 percent dolomite and greater than 9 percent porosity, plotted in class 2. This mud-dominated fabric had class 2 characteristics because progressive dolomitization had increased the pore size by increasing porosity in the intercrystal mud and by creating intercrystal pore space.
Thin-section descriptions supported the concept that there was a continuum of rock fabrics that created a continuum of petrophysical classes. Thus, a global porosity-permeability transform was developed that was based on the interrelationships of rock-fabric petrophysical class, interparticle porosity, and permeability. This transform could be used for all carbonates that do not have a touching-vug pore system.
The global porosity-permeability transform was the basic equation for calculating permeability from wireline logs using the rock-fabric method. Petrophysical class was determined by crossplots of water saturation and porosity calibrated with rock-fabric descriptions from beds that were 3 ft or more feet thick. Interparticle porosity could be estimated by subtracting separate-vug porosity (estimated from transit-time/porosity crossplots) from total porosity. In most cases, values from calculated separate-vug porosity were similar to those obtained from thin-section descriptions. However, separate-vug porosity was generally less than 2 percent and was not a major factor. Therefore, total porosity was a reasonable substitute for interparticle porosity in this study.
The Arab-D reservoir is divided into reservoir zones 1 and 2, characterized by grain-dominated packstone and large-crystal dolostone, and reservoir zone 3, composed of mud-dominated fabrics and thin beds of large-grain, grain-dominated packstone. In zones 1 and 2, the calculated permeability was typically within a factor of 5 of core permeability. Core permeabilities were measured on core plugs and were more variable than log permeabilities that were based on measurements over a 2-ft interval. This difference in scale accounted for most of the scatter.
In zone 3, thin, high-permeability intervals in the core data were not duplicated by log calculations. Judging from flow-meter data, many of these thin, permeable beds did not contribute to flow-suggesting that the log permeabilities were representative of the reservoir. However, a few intervals did contribute, and the log permeabilities were grossly understated. Water saturation was too high over these intervals, resulting in a petrophysical class that was also too high and a permeability that was much too low. The reason for water saturation being overstated was because the resistivity log did not respond uniquely to thin, grain-dominated packstone beds but was averaging the thin beds together with the dominant mud-dominated fabric.
Calculated permeability values were summed vertically and compared with flow-meter profiles to test the accuracy of permeability calculations in the eight uncored wells and four cored wells. Kh and flow-meter profiles provided good correlations in wells that showed no flow from the lower interval. If the flow meter indicated flow from the lower interval, a match between kh and flow-meter profiles was obtained by adding sufficient permeability to the lower interval to match the flow meter.
Super-k was present in three wells, and the kh profiles in two of them matched the flow meter. In these two wells, the high-flow intervals were associated with a high-porosity, large-crystal dolostone, suggesting that the high flow rate was from intercystalline pore spaces. No match was obtained in the third well because the super-k interval did not have a corresponding high porosity zone. A touching-vug pore system (karst and/or fracture porosity) was most likely present in this well.
The examination of the vertical successions of rock fabrics calculated in this study suggested that they could be used to correlate high-frequency cycles and define chronostratigraphic surfaces for the construction of a sequence stratigraphic framework. However, this would be possible only in limestone intervals. Replacement of limestone by large-crystal dolomite would complicate the analysis of vertical fabric-stacking patterns because the dolostone precursor fabrics cannot be determined.
This research was done at the Bureau of Economic Geology, The University of Texas at Austin, Texas. Saudi Aramco funded the research and provided the data. The authors wish to thank Saudi Aramco and the Saudi Arabian Ministry of Petroleum for permission to publish these results. The authors benefited from discussions with Charles Kerans and Stephen C. Ruppel of the Bureau of Economic Geology. Patrick J. Mickler assisted in describing the numerous thin sections. Anonymous reviewers and GeoArabia’s editorial staff are thanked for their professional treatment of this publication. The drafting of the final graphics was by Gulf PetroLink staff.
ABOUT THE AUTHORS
F. Jerry Lucia is a Senior Research Fellow at the Bureau of Economic Geology, The University of Texas at Austin. He was awarded a BSc in Engineering in 1952 and MSc in Geology in 1954 from the University of Minnesota. Before joining the Bureau in 1985, he was a Consulting Geological Engineer for Shell Oil Company assigned to the Head Office. Jerry retired from Shell in 1985 with 31 years experience in research and operations as a Geological Engineer. His technical expertise includes the origin and distribution of carbonate strata, petrophysics, and petroleum geology. He is currently co-principal investigator of the Characterization Research Laboratory of the Bureau of Economic Geology. Project areas include the Permian Basin and the Middle East. He has received awards for Best Paper from the American Association of Petroleum Geologists Wallace E. Pratt Memorial in 1994 and 1995, and Distinguished Service Award from the West Texas Geological Society in 1993. Jerry is an active member of AAPG, SPE, and is a Fellow of the Geological Society of America.
James W. Jennings is a Research Scientist at the Bureau of Economic Geology, The University of Texas at Austin where he conducts research on carbonate reservoir characterization and modeling. He has a BS degree from the University of Wyoming and an MS and PhD from Texas A&M University, all in Petroleum Engineering. Before joining the Bureau of Economic Geology, he was a Senior Research Engineer at Arco, and a Reservoir Engineer at Sohio where he researched various aspects of geostatistics, reservoir characterization, and reservoir modeling.
Michael Rahnis has a BA in Geology from Franklin & Marshall College in 1992 and an MA from the University of Texas at Austin in 1995. He has specialized in the study of carbonate diagenesis, and early marine cementation in particular. Michael is currently undertaking a geological mapping project for the GIS Department of Lancaster County in Pennsylvania.
Franz O. Meyer is a Geological Specialist with Saudi Aramco. He has a BS in Geology from State University College of New York, New Pulz, and an MS and PhD from the University of Michigan. He joined Shell as an Exploration Geologist and later became a Carbonate Specialist at Shell’s Belair Research Laboratory in Houston, Texas. Franz joined Saudi Aramco in 1991 and has been involved in various Jurassic carbonate reservoir and outcrop studies in eastern and central Saudi Arabia. His work includes research into reservoir characterization, sequence stratigraphy, and dolomite sedimentology, as well as teaching.