ABSTRACT

Measurement of continuous permeability profiles on a routine basis has become possible through recent advances in wireline logging hardware and software. Continuous permeability profiles allow geologists and reservoir engineers to better characterize their reservoirs and to more efficiently complete and manage the production of the hydrocarbon reserves. One of the most promising methods for the calculation of continuous permeability information is the use of Stoneley wave data acquired using a monopole acoustic device.

This paper presents the results of a case study conducted for Petroleum Development Oman. In this study, permeability was determined from Stoneley wave data from the Sarmad-1H2 and Sarmad-2H1 wells that penetrated the carbonate reservoirs of the Ara Group of Oman. The Stoneley-wave derived profile was compared with permeability data from other sources; such as, cores, wireline pressure tests, and the interpretation of nuclear magnetic resonance measurements. The results demonstrated the validity of the methodology and showed that Stoneley-wave data can be used on a routine basis to obtain a continuous permeability indication for completion evaluation purposes. The method has great potential in permeability prediction.

INTRODUCTION

In the late 1970s to early 1980s, Petroleum Development Oman (PDO) made several oil and gas discoveries in the South Oman Salt Basin (Figure 1). The exploration objectives were the so-called Carbonate Stringers with over-pressured dolomite reservoirs located within the salt of the Ara Group (Mattes and Conway Morris, 1990) (Figure 2).

With the increased success rate of locating oil accumulations in the intrasalt carbonate reservoirs of the South Oman Salt Basin, it has become important to understand the dynamic behavior of their flow units. Obtaining a reliable permeability from well logs would form a powerful aid in the completion decision process and the formulation of well test-programs.

Permeability estimation within the Carbonate Stringers is complicated by the following factors:

  • • wide variation in permeabilities for different facies;

  • • influence of fracturing in enhancing or degrading permeability;

  • • frequent salt plugging of vugs, fractures, and matrix; and

  • • complex well test responses.

GEOLOGICAL SETTING

The Ara Carbonate Stringers are of late Precambrian/Early Cambrian age. Within the overall hypersaline and restricted setting of the basin, the carbonates mark cyclic sea-level highstands (i.e. episodes of basin freshening), when salt deposition ceased and carbonate production was possible. The consequence of this setting is that the carbonates form isolated bodies (‘Stringers’) within the salt. The salt acts as a seal and the carbonates act as their own source rock (Figure 3).

The facies analysis from core and image logs reveals that the main facies present in these carbonates are grainstone, mudstone, and vuggy thrombolite. Grainstones and vuggy thrombolites form the main reservoir facies (Reinhardt et al.,1999).

STONELEY WAVES

The borehole acoustic waveform can be separated into compressional, shear, and Stoneley wave components. Figure 4 shows a typical waveform measured by a monopole acoustic tool. Compressional and shear waves, which are abbreviated as P-waves and S-waves, are body waves that travel within the formation. In contrast, Stoneley waves are surface waves guided by the borehole fluid at the borehole wall (Figure 5a). They are excited at low frequencies, typically 200 to 2,500 Hz. For all frequencies, Stoneley wave velocity is less than borehole fluid velocity. Their wave motion is axially symmetrical and can be regarded as expanding/contracting borehole waves (Figure 5b).

The first attempt to estimate permeability from acoustic data in hydrocarbon wellbores was made by Rosenbaum (1974) using the theory established by Biot (1962) to model a porous rock. Although this work had some limitations (e.g. frequencies restricted to 20 kHz; assumption of rigid mudcake), that made the results less sensitive to permeability, it recognized the potential of using borehole acoustic data to estimate permeability.

Williams et al. (1984) published the first convincing examples showing the possibility of obtaining reliable permeability indication from Stoneley wave data. Several developments, including the design of new tools that excite Stoneley waves at lower frequencies, have led to the practical application of permeability estimation from Stoneley wave data. Tang et al. (1991) used a simple parametric model of a porous rock developed by Johnson et al. (1987) instead of the full porosity-elastic wave theory. In the model of Tang et al. (1991), Stoneley wave propagation is broken down into its non-permeable and permeable components. The non-permeable part is obtained from modeling, whereas the permeable contribution is calculated from Johnson et al. (1987).

The Tang et al. (1991) model proves that Stoneley waves are most sensitive to formation permeability in the low-frequency range. Permeability influences both Stoneley wave velocity and attenuation as a function of frequency. Figure 6 illustrates this phenomenon by showing several theoretical curves of the response of Stoneley wave attenuation and dispersion as a function of pore-fluid mobility (defined as quotient of pore-fluid permeability over pore-fluid viscosity) and frequency. Increasing permeability, and therefore mobility, increases both attenuation and dispersion, and the lower the frequency, the higher the attenuation and the dispersion.

Over the years, the Tang et al. (1991) model has been further developed to account for tool effect (Tang and Cheng, 1993a), and soft formation effects (Tang and Cheng, 1993b). Separation of permeable and non-permeable effects in the Stoneley wave data remains a challenge. Meeting this challenge is the critical component in this permeability estimation approach.

METHOD

The approach to permeability estimation from Stoneley waves consists of (1) processing, (2) modeling, and (3) comparison/inversion (Figure 7).

Processing

As discussed in the background section, theoretical studies have demonstrated that Stoneley waves contain permeability information. However, Stoneley waveform data measured in the field are contaminated by Stoneley wave reflections and noise. Both reflections and noise can be removed by a wave separation procedure, giving a direct Stoneley wave (wave traveling from transmitter directly to receiver) and a reflectance map that shows the position and strength of different borehole/formation reflectors (fractures or lithological boundaries). Note that the direct Stoneley wave obtained from this processing contains both permeability and non-permeability effects (e.g., borehole caliper changes, formation changes, formation intrinsic damping, and borehole fluid attenuation).

Modeling

This procedure models the non-permeability part of the Stoneley wave excitation and propagation. The synthetic modeling assumes that the formation is an equivalent elastic medium that has the properties of a poro-elastic medium (e.g. formation wave speeds of P- and S-waves and density) but with zero permeability. Variations in borehole diameter and the presence of the logging tool are also accommodated in the method (Tang and Cheng, 1993a; Tezuka et al., 1994). The model propagates the Stoneley wave excited in this elastic formation through a stack of horizontal layers. Each layer has a thickness equal to the logging depth increment, which is typically 6 inches (Figure 8). The elastic wave response at all logged depths is convolved with a reference waveform derived from the measured Stoneley waves at a non-permeable depth in order to account for the source signature. Note that the properties, density, and compressional and shear slowness, are directly measured from the formation, and thus already contain the effects of lithology, porosity, and fluid saturation.

Comparison, Inversion, and Permeability Estimation

After wave-separation processing, the measured Stoneley waves account for all attributes, whether permeability or non-permeability related, whereas modeled Stoneley waves account for only non-permeability attributes. Permeability estimation is based on a comparison between the modeled and the measured Stoneley waves. As a modeled Stoneley wave contains, in principle, all the effects unrelated to permeability, the difference between the modeled and the recorded Stoneley wave should relate to permeability. This difference is evaluated from two wave attributes—travel time-delay (a measure of Stoneley wave dispersion), and centroid frequency shift. The centroid frequency shift takes place because some frequencies are attenuated more than others; thus it is a meaningful measure of permeability-related attenuation. Figure 6 illustrates that both dispersion and attenuation are related to permeability, and can therefore be used to indicate permeability-induced effects and estimate permeability.

The basis of the inversion method is a fast modeling procedure based on the simplified Biot-Rosenbaum theory (Tang and Cheng, 1996), which is a simple and effective model that describes the interaction of the Stoneley wave with a porous formation. The permeability estimation is made by simultaneously fitting the time-delay and frequency-shift data using the model theory.

In permeable formations, Stoneley wave attenuation and travel-time delay, in addition to being sensitive to pore-fluid mobility as shown in Figure 6, are also a function of pore-fluid compressibility. Essentially, the method measures a parameter combination given by:

 

M=kμKf
(1)

where k is the permeability, Kf is the pore-fluid bulk modulus, and μ is the pore-fluid viscosity. The calibration process determines the value of μKf, enabling permeability to be calculated.

Calibration

For calibration purposes, reference permeabilities are required. Calibration may be either a singlepoint calibration or a multiple-point calibration, depending on the available data. Single-point calibration is typically used if other reference information (e.g. core permeabilities and formationtester permeabilities) is not available. In that case, as a rule of thumb, the reference depth is selected in a section where both time delay and the frequency shift have a minimum value such as in a non-permeable shale interval. For single-point calibration, the best estimate of effective pore-fluid parameters and the porosity are used, and permeability is adjusted to match the measured travel-time delay and centroid frequency shift. The best fitting permeability value is taken as formation permeability.

Multiple-point calibration is used in cases where other reliable permeability values are available at several depths (preferably at least two, one located in a non-permeable and another in a highly permeable zone). Through least squares fitting, the pore-fluid parameters are adjusted to fit the permeability values at the reference depths, thereby becoming part of the calibration process.

In summary, the reference depth controls the permeability profile whereas the pore-fluid parameters control the permeability magnitude. Thus, different pore-fluid values will affect the magnitude of the permeability without changing the shape of its profile significantly. If there are multiple fluid phases, the method senses the mobility of the most movable phase, including relative permeability effects. In the absence of calibration data, the estimation method presented here should primarily be used to obtain the variability and an order-of-magnitude estimate of formation permeability. The validity range of Stoneley permeability is, in part, dependent on the saturating formation fluid/gas (Table 1).

Quality Control

The following procedures ensure quality control for the above described method:

  • (1) Evaluation of whether the measured Stoneley wave attenuation and dispersion (measured traveltime delay and measured frequency shift) are responding to permeability variations. The degree of correlation in character between the travel-time delay and centroid frequency shift serves as a unique quality indicator in assessing that the variation in attenuation and dispersion present in the measured Stoneley waves is caused by permeability changes. The wave modeling is aimed at removing non-permeability related wave propagation effects so that both the relative time delay and frequency shift reflect the effects of permeability; hence, if these two curves are indeed controlled by permeability they should exhibit correlation.

  • (2) Consideration of the misfit between the measured and modeled travel-time delay and frequency shift. If theory cannot fit the data, then other factors are playing a role. Misfits due to data quality can be caused by poor-quality wave data, inaccurate caliper and/or shear slowness logs. In many cases, the cause of the misfit can be attributed to the presence of mudcake or excessively high pore-fluid mobility (for example, gas).

RESULTS

The results of Sarmad-1H2 (SAR-1) and Sarmad-2H1 (SAR-2) Stoneley permeability analyses are presented in Figures 9a and 9b, respectively. In both figures, the left track shows the calculated and inversion fitted travel-time delay and centroid frequency shift. The computed Stoneley permeability is shown in the right track. The Stoneley waveform data used in this analysis ranges from 500 to 2,500 Hz for SAR-1 and from 200 to 2,800 Hz for SAR-2. The mud slowness and density were 660 μm/m and 2.1 g/cm3 for SAR-1, and 600 μm/m and 1.5 g/cm3 for SAR-2.

Sarmad-1H2 (SAR-1)

In SAR-1, two sectors were defined and calibrated separately. They are Sector 1 from the top of the log at 3,652 m to 3,720 m, and Sector 2 from 3,720 m to the bottom of the log at 3,800 m.

Sector 1

This was calibrated against permeabilities derived from wireline pressure tests. A viscosity of 0.5 centipoise was used to calculate permeability from the test mobilities. In Sector 1, the inversion fit of the time delay is typically slightly lower, whereas the fitted frequency shift is typically higher than their measured values. This phenomenon can result when a mudcake build-up inhibits the exchange of fluid between the borehole and the formation (Tang et al., 1998). In this case, the Stoneley method may underestimate the permeability.

Within Sector 1, two relatively permeable intervals were identified by the analysis. These were as follows: (1) the interval from 3,664 to 3,673 m, with an arithmetic average and maximum permeability values of 2.8 mD and 27.5 mD (located at 3,665 m) respectively; and (2) the interval from approximately 3,682 to 3,710 m, where the average permeability value was 0.6 mD. The rest of Sector 1 was considered to be tight.

Sector 2

As pressure tests were not available at appropriate depths for calibration of Sector 2, core-plug permeabilities were used instead. The match between inverted and measured time delay and frequency shifted curves was good. Calculated results indicated a permeable interval from 3,721 to 3,762 m that exhibited average and maximum permeabilities of 1.3 mD and 5.5 mD (located at 3,753 m), respectively. The section below 3,762 m was considered to be tight with the exception of a few thin intervals at approximately 3,783 m, 3,788 m, and 3,797 m, where the permeability was 4 mD and 2.5 mD, respectively. The latter interval coincided with a fracture cluster identified from image logs. It is possible that the Stoneley method was sensing some fracture-related permeability, either from open fractures or from fractures that have had their salt filling washed away by the borehole fluid.

Sarmad-2H1 (SAR-2)

In general SAR-2 has a low permeability. The overall correspondence between measured and inverted time delay and frequency-shift curves indicated a reliable permeability profile. The inversion fit of the time delay and the frequency shift was very good. The frequency shift and travel-time delay showed the following two intervals of relatively high permeability: (1) from the top of the stringer (about 4,028 m) to 4,050 m with an arithmetic average permeability value of 0.2 mD; and (2) from 4,105 to 4,125 m, with the highest permeability value being 1.6 mD.

COMPARISON WITH OTHER PERMEABILITY MEASUREMENTS

Figures 10a and 10b compare the results of Stoneley and Nuclear Magnetic Resonance (NMR) derived permeabilities with core plug and build-up Wireline Pressure Test (WPT) permeabilities. In each figure, the left track shows the computed Stoneley permeability, and the right track the NMR permeability. Also shown are Zones 1 to 5 (Figure 10a) and Zones 1 to 6 (Figure 10b) that relate to the compatibility or variability of Stoneley permeability with core-plug, NMR, and WPT permeabilities.

Before discussing the agreement and discrepancies between measurements, it is useful to review the factors that need to be taken into account when making comparisons. Measured permeabilities are a function of (1) scale dependence, (2) directionality/flow geometry, (3) saturation state, and (4) nature of measurement (direct or indirect).

Comparison Factors

Scale Dependence

Permeability is a scale-dependent property in the sense that large-scale permeability depends on the spatial distribution of permeability within the volume being considered. As a consequence, measurement techniques that sample different volumes within a heterogeneous formation will give different answers.

Directionality/Flow Geometry

Permeability is a tensor property with a magnitude that differs depending on the direction of the measurement. The direction in which a flow measurement is made, or the flow geometry associated with a measurement, influences the result obtained.

Saturation State

The saturation state of a rock influences its flow behavior both in terms of the viscosity of the saturating fluids, and in terms of relative permeability effects where an effective rather than an absolute measurement is made. The near-well region often has a different saturation state (flushed zone) from that deeper in the formation, and thus measurements with different depths of investigation will be affected to a different degree.

Nature of Measurement

Measurements of permeability can be direct or indirect. Direct methods are those that measure how the flow influences some measurable property, such as pressure. Indirect methods are based on empirical correlations of some property that has been shown to be related to permeability.

Stoneley permeability is an intermediate-scale measurement with a depth of investigation of between 2.5 and 5 ft. It measures an azimuthally averaged permeability orthogonal to the borehole axis. The depth of investigation is such that it typically measures permeability mostly within the flushed zone, implying that the measured quantity is the effective permeability to water in the presence of residual oil. Calibrating Stoneley permeability will, of course, make it susceptible to any problems inherent in the measurement it is calibrated against.

Core-plug permeabilities are small-scale measurements that are normally made either in a direction parallel to, or orthogonal to, bedding. Typically, core permeabilities are absolute values for a single saturating fluid. They are direct measurements but are subject to any changes in core that result in bringing the rock to surface and preparing the core plugs.

Permeabilities derived from WPT are typically based on two types of measurement; namely (1) drawdown (pseudo-steady state) permeabilities, and (2) buildup permeabilities. Drawdown permeabilities are typically most heavily influenced by properties very close to the well, within a few probe radii for a probe test.

Buildup measurements have a depth of investigation that is dependent on the properties of the rock and saturating fluids but are typically on a far larger scale than drawdown permeabilities. They give a spherical permeability that is a geometric average of the permeability in different directions. Calculation of build-up permeabilities also requires knowledge of the porosity of the rock and compressibilities of the saturating fluids. The examples given in this paper are entirely based on the analysis of build-up data acquired using a dual packer tool, and therefore represent an average over more than 3 ft vertically.

Nuclear Magnetic Resonance logs (NMR) can be used to calculate permeabilities. The method is an indirect one relying on empirical correlations based on pore geometry and bound-fluid volumes. The method is non-directional. It is independent of saturation fluid and is typically based on correlation to core permeabilities. The scale of the measurement is similar to Stoneley permeability though with a higher vertical resolution. In this study, the NMR permeability was derived from an internal Shell correlation based on core samples from three separate wells in the carbonates.

Comparison of Permeabilities for SAR-1

In Zones 2 and 5 (Figure 10a), the Stoneley permeability curve matched the core data better than the NMR permeability. Zone 2 also had a WPT permeability that was in good agreement with both core and Stoneley permeability. In Zone 4, however, the NMR calculations matched the variation in permeabilities better than the Stoneley method. In this case, the difference in the measurements could be partly a scale of measurement effect in that the scatter in the core values showed that permeabilities varied on a scale of less than a meter. The NMR curve that had a higher vertical resolution was better able to track these changes. At the top of Zone 4, the core values ranged from 0.05 mD to 60 mD within a few meters. Stoneley and WPT permeabilities both fell well within this range, though the WPT value was considerably higher (7 mD as opposed to 0.8 mD). In Zone 1, the WPT permeability was also considerably higher than both Stoneley and NMR permeability. Zone 3 showed very low Stoneley permeabilities of approximately 0.01 mD, whereas NMR permeabilities typically ranged between 0.1 mD and 1 mD. Unfortunately, no other measurements were available in this interval for comparison. In Zone 5, the core permeabilities were higher than both Stoneley and NMR measurements, though Stoneley permeabilities did reach similar magnitudes at two depths.

Ten separate intervals were perforated on wireline, and a successful production test was conducted on this stringer. A Production Logging Tool (PLT) flow log gave some indication of the permeable intervals, though the multiple perforated intervals complicated the interpretation. A comparison of cumulative permeability curves with station PLT measurements is given in Figure 11. The Stoneley curve correctly shows that almost 40 percent of production enters through the lowest set of perforations.

Comparison of Permeabilities for SAR-2

In SAR-2, the match of the Stoneley permeability to the core data was excellent in Zones 4, 5, and 6 (Figure 10b). Furthermore, both the core and Stoneley permeabilities were confirmed by the wireline pressure-derived permeability values as shown in Zone 5. Some high core permeabilities were visible from 4,114 m to 4,120 m. Examination of the core and image logs showed that salt-filled vugs and fractures were common in this interval (Figure 12). It is highly likely that the core values were artificially enhanced through the inadvertent dissolution of salt during cleaning. Evidence from comparative cleaning studies on other Stringer wells supports this hypothesis.

The NMR showed rapid variation from values similar to the lower core permeability values, to extremely low permeabilities (<0.01 mD) over all three zones. This did not appear to be caused by differences in vertical resolution between the methods, because the fine-scale core data did not confirm the NMR values (Figure 13). It is unlikely that salt dissolution would universally affect all the core permeability measurements and, therefore, if the low NMR values were real, one would expect the lower core permeabilities to have similar values.

In Zone 1, where no core measurement was available, Stoneley permeability appeared to read less than NMR permeabilities, but agreed more closely with WPT.

In Zones 2 and 3, neither Stoneley nor NMR permeability was in agreement with the highest core permeability values. NMR permeabilities occasionally reached permeability values similar to the lowest core values, but Stoneley permeability values were often an order of magnitude lower. The few WPT points within these zones did not confirm the high permeability values seen by the core. Several of the attempted WPT tests in these intervals were unsuccessful, giving further evidence that the actual in-situ permeabilities are orders of magnitude lower than the core. Furthermore, the well, when subjected to production testing, produced small amounts of water before the tubing was plugged-off by the salt dropping out of solution, which was also not consistent with the high core permeability values.

In order to explain the discrepancies encountered in Zones 2 and 3, a closer examination of data and review of existing studies based on core and image analysis were conducted. Observations that may be related to these discrepancies were as follows:

  1. the problematic intervals showed a particularly high degree of drilling-induced fracturing on image logs (Figure 14);

  2. the formation is deep (approximately 4,000 m below surface) and highly over-pressured;

  3. the predominant facies is a laminated mudstone, which is not typically regarded as a reservoir facies in these Carbonate Stringers;

  4. many of the core permeabilities fell outside the porosity permeability trend defined from other Stringer wells;

  5. numerous hairline fractures were typical of the laminated mudstone facies, most of which were mineralized, in some cases filled with salt;

  6. larger fractures and dilatational jogs were invariably salt-filled.

Given these observations and the discussion above it is highly probable that the higher core values are not representative of the in situ permeability. The most likely explanation is that core permeabilities in these intervals were also enhanced through the dissolution of salt during core cleaning.

An alternative explanation is that micro-fracturing of the core had taken place, either during the drilling process or during pressure release at surface. This would erroneously increase the measured core permeability values. The deep and over-pressured nature of this formation implies considerable stress release and fluid expansion at surface, both of which could potentially lead to core damage. Furthermore, the problem intervals were probably more brittle than the rest of the stringer, as indicated by the induced fractures, and could therefore be expected to be more prone to these problems. Microscopic examination of the core plugs, in addition to permeability measurement of both cleaned and non-cleaned plugs, is needed to confirm these hypotheses.

It is also possible that the induced fracturing had created considerable near-well formation damage by promoting the invasion of drilling fines. This would be sensed by the Stoneley method, but not by the NMR, thus explaining the discrepancy between these measurements. One might imagine that induced fractures would have created a near-well enhancement of permeability, leading to the Stoneley method overestimating the true formation permeability. This is, however, in direct contrast to our observations that Stoneley permeability typically read less than all other methods in the intervals that had particularly high levels of induced fractures. Thus, if anything, the Stoneley method was underestimating permeability in these intervals. One explanation is that a layer of mudcake between the fracture faces had sealed these fractures. This could occur, if the fracture aperture reduced significantly subsequent to formation by the drilling process. It is unlikely that natural fractures, which have a significant aperture before drilling, would be subject to the same effects.

DISCUSSION

The results presented here show that there is no single existing method that provides a completely reliable measurement of permeability in the Carbonate Stringers of the South Oman Salt Basin. Comparison between the measurements is complicated by factors such as the nature of the measurement, scale dependence, and associated flow geometry. In addition, there is no absolute permeability reference for comparison. Typically, core data is regarded as such a reference, but salt plugging of the matrix and salt-plugged fractures cause core permeabilities to be often anomalous, or at least not representative of larger-scale in situ permeabilities.

In spite of these difficulties, the case study shows that the Stoneley method provides a useful and valuable additional source of permeability information. In many cases, Stoneley-derived permeabilities are in better agreement with other measurements than the only other continuous permeability measurement, namely NMR permeabilities.

In places where both NMR-derived permeability (model calculations on a static measurement) and Stoneley-wave derived permeability (modeled dynamic measurements) profiles agree, confidence in the presented permeability values can be high.

In places where Stoneley measurements agree with core data, but not with NMR results, vertical resolution differences in both methods cannot be the direct cause of the discrepancy. More likely, the NMR method—which is based on calibration of core data from three Carbonate Stringer wells—may not be applicable to this particular facies and/or rock fabric.

Differences between the Stoneley and NMR permeability can also be caused by fractures contributing to the overall permeability. The acoustic logging tool will detect fracture-induced permeability effects since it measures the loss of acoustic energy at the borehole wall, regardless of whether the loss is into pores or a fractures system. In contrast, core measurements that are performed on material from non-fractured parts of the rock will not measure fracture permeability. Similarly, the NMR method will not detect fracture permeability because (1) NMR signal responds predominantly to the pore space of the formation matrix, and (2) the transform of the static NMR measurement to the dynamic permeability is made through calibration on core data that lacks fracture-permeability information.

WPT buildups provide an in-situ measurement of permeability and are therefore useful for calibration of the Stoneley permeabilities and assessing the reliability of other permeability methods. In some cases, the WPT confirm that the Stoneley method is correctly sensing the in-situ formation permeability. Some caution is necessary when using WPT measurements, however, as they may be influenced by assumptions regarding the saturating fluid and degree of permeability anisotropy.

CONCLUSIONS

Reliable permeability determination in the Carbonate Stringers of the South Oman Salt Basin is extremely difficult. None of the existing techniques can be regarded as being universally successful. The results of this case study clearly demonstrate the potential of using Stoneley wave analysis for permeability prediction. In several instances, the method gives better results than the NMR calculations when compared with independent WPT estimates and/or core measurements. In other cases, the method has proved to be more reliable than core values and to give results that are more consistent with production tests. The additional strength of the acoustic method is that it is a direct physical measurement. In contrast to the NMR method that derives permeability based on an empirical model, the Stoneley method derives permeability from direct interaction of acoustic wave with the in-situ flow properties of the formation.

ACKNOWLEDGMENTS

An earlier version of this paper was presented at the Society of Petroleum Engineers conference in Dallas, October 2000. The authors wish to thank the Ministry of Oil and Gas of Oman, Petroleum Development Oman LLC, and Baker Atlas for permission to publish this work. In addition, we would like to acknowledge the assistance provided by members of the PDO Stringer team and Baker Atlas Geoscience staff in the Middle East in providing data, original figures, reviewing text, and discussing findings. Dr. J.E. Amthor and three anonymous reviewers are gratefully acknowledged for the critical reading of the manuscript. The design and drafting of the final graphics was by Gulf PetroLink.

ABOUT THE AUTHORS

Latifa Qobi is a Senior Geoscientist with Baker Atlas Geoscience in Bahrain. She has an MSc in Applied Geophysics from Pierre et Marie Curie University, Paris. She joined Baker Atlas in 1994 as a Geophysicist. In 1995, she was assigned to Hasi-Messaoud in Algeria, where she established a Log Analysis Center. In 1997, she moved to Baker Atlas Geoscience in Bahrain and has worked on various projects, mainly related to borehole image analysis. Since 2000, Latifa has worked on, and promoted, advanced acoustic products in the Middle East area. Her current interest is Geomechanics.

E-mail: latifa.qobi@bakeratlas.com

André de Kuijper is Section Head Petrophysics in the Fahud/Lekhwair Asset Team in Petroleum Development Oman (PDO). He was awarded a PhD in Theoretical Physics (Computer Simulations of Molecular Systems) by the University of Amsterdam in 1991. He then joined Shell Research in Rijswijk, The Netherlands, and worked on the development of saturation models. Andre moved to PDO in 1997 to become Senior Exploration Petrophysicist responsible for Carbonate Stringers. Since 2000, he has worked on the Fahud, Lekhwair, and Natih fields.

E-mail: Andre.A.deKuijper@pdo.co.om

Xiao Ming Tang is a Senior Staff Scientist in the Houston Technology Center of Baker Atlas/INTEQ and is Project Leader for acoustic processing and interpretation development. He has a DSc from the Massachusetts Institute of Technology (1990). After graduation, he worked for New England Research, Inc. until 1994 when he joined Baker Atlas. His current interests include borehole acoustics, petrophysics, and rock mechanics. Xiao Ming has been an author or co-author of more than 50 technical publications and ten patents. He is member of SPWLA and SEG.

E-mail: xiaming.tang@aws.waii.com

Jonathan Strauss is a Reservoir Engineering Consultant with Baker Atlas Geoscience in Bahrain. He has a BSc (Hons.) in Physics from the University of Natal, South Africa. He joined Baker Atlas in 1997. Prior to that, he was employed by SOEKOR E&P in South Africa and by PGS Reservoir in the UK. Jonathan’s professional interests are fractured reservoirs, reservoir simulation, well test analysis and simulation, probabilistic methods, and wireline formation.

E-mail: jonathan.strauss@bakeratlas.com