A Complex Core-Log Case Study of an Anisotropic Sandstone, Originating from Bahariya Formation, Abu Gharadig Basin, Egypt

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1 PETROPHYSICS, VOL. 50 NO. 6 (DECEMBER 2009); Page ; 21 Figures; 7 Tables A Complex Core-Log Case Study of an Anisotropic Sandstone, Originating from Bahariya Formation, Abu Gharadig Basin, Egypt Matthias Halisch 1,2, Andreas Weller 1, Carl-Diedrich Sattler 3, Wolfgang Debschütz 1 and Abdel Moktader El-Sayed 4 Bahariya Formation sandstones represent important Cretaceous oil and gas reservoirs for Egypt. The formation has been investigated by innumerable well logging activities. The previous focus of petrophysical research has been on Bahariya Oasis where the formation is exposed at the surface and serves as the type locality. In this study, over one hundred core samples from a deep borehole located in the Abu Gharadig Basin within the Western Desert of Egypt have been investigated. From the 35 m thick section where samples have been taken, several logging curves were available to enable a complex core-log data comparison. Owing to a conspicuous flaser bedding of these sandstones, an anisotropy effect was expected. Samples ABSTRACT were collected in two different orientations for each sampling depth: perpendicular and parallel to foliation. From the core, the degree of anisotropy was determined for electrical resistivity, gas permeability, p-wave velocity and thermal conductivity. A novel definition of the coefficient of anisotropy of permeability is presented. Using this definition, the degree of anisotropy of electrical and hydraulic conductivity becomes comparable. Fractures in the direction of the flasered structures cause an increased horizontal permeability and consequently a considerable anisotropy. The anisotropy of p-wave velocity is less sensitive to the flasered structures. Key Words: anisotropy, Bahariya Formation, core logging, petrophysics, sandstone, well logging INTRODUCTION Owing to the fact that the Bahariya Formation is one of Egypt s important onshore oil and gas reservoirs (Sestini, 1995), many geological as well as mineralogical and sedimentological studies have been carried out in the past decades but only sparse petrophysical research. Focus of these research efforts has been mostly on Bahariya Oasis (e.g. Khalifa and Catuneanu, 2008; Al- Wakeel and Abd el Rahman, 2006; Catuneanu et al., 2006; El Bassyony, 2004; Ismail et al., 1989; El Sayed, 1991, Mücke und Aghte, 1988; Dominik, 1985), the Manuscript received by the Editor June 2, 2009; revised manuscript received October 21, Institute of Geophysics, Clausthal University of Technology, D Clausthal-Zellerfeld, Germany; s: matthias.halisch@liag-hannover.de, andreas.weller@tu-clausthal.de, and wolfgang.debschuetz@tu-clausthal.de. 2 Leibniz Institute for Applied Geophysics, Stilleweg 2, D Hannover, Germany; matthias.halisch@liag-hannover.de. 3 Institute of Geology and Palaeontology, Clausthal University of Technology, D Clausthal-Zellerfeld, Germany; carl-diedrich.sattler@tu-clausthal.de. 4 Department of Geophysics, Faculty of Sciences, Ain Shams University, Cairo, Egypt; e.m.moktader76@yahoo.com Society of Petrophysics and Well Log Analysts. All Rights Reserved. December 2009 PETROPHYSICS 478

2 A Complex Core-Log Case Study of an Anisotropic Sandstone, Originating from Bahariya Formation, Abu Gharadig Basin, Egypt type locality of the Bahariya Formation and located in the Western Desert of Egypt, about 370 km southwest of Cairo. Only limited detailed petrophysical reservoir characterizations of the Bahariya Formation made in close combination with geological and mineralogical investigations have been reported in the literature (except El Sayed et al., 1993, Athmer, 2006). This paper presents some results of a complex study using logs and more than 100 core samples from a deep Bahariya Formation penetration in the northwestern part of the Abu Gharadig Basin, approximately 300 km north of the Bahariya Oasis (Figure 1). The investigated section of the Bahariya Formation is located at a measured depth (MD) of about 3500 m below ground level and has an apparent thickness of about 35 m. As Catuneanu et al. (2006) have pointed out, the Bahariya Formation exhibits significant lateral and vertical changes of facies. As a result of their sedimentological studies in the Bahariya Oasis, they specified three major lithological units: unit one consists of interbedded siltstones and sandstones (lower unit), unit two is formed by crossbedded amalgamated sandstone bodies (middle unit) and unit three is characterized by dark-coloured ferruginous sandstones (upper unit). Catuneanu et al. (2006) described the Bahariya depositional environment as an overall transgression with coastal backstepping comprising several coarseningupward cyclothems and the deposition of fossiliferous glauconitic siltstones and sandstones. Hence, the environment was shallow marine with tidal flat to marine shelf settings. In nearly all previous studies outcrops from Bahariya Oasis have been the target of investigations. Their samples are heavily affected by weathering processes, and, the data acquired are partially altered by these processes. Especially in case of petrophysical research, it is therefore not advisable to use such surface data for comparison and interpretation of well log data. In addition, the already mentioned significant lateral and vertical changes of facies make it nearly impossible to tie core data back to log data, considering needed accuracy and resolution. Hence, over one hundred core samples from Bahariya Formation were collected from a drilling site located in the Badr El Din concession area in the northwestern part of the Abu Gharadig Basin. At each depth, a pair of cylindrical plug samples with a diameter of about 2.5 cm and an average length of 4 cm were extracted from the original whole core. So-called H-samples were taken parallel and so-called V-samples perpendicular to the layering. The sample set can be subdivided into two major types of samples as shown in Figure 2. Samples of the first type are characterized by visual indications of flaser bedding or lamination structures. Independent of the intensity of flaser bedding structures, all samples of this type are regarded as laminated samples (+L samples). Samples of the second type show no obvious flaser bedding or lamination structures. This type will be referred to as samples without lamination ( L samples). According to a visual inspection, the sandy part of both types can be regarded as sandstones containing 5-15% glauconite, minor amounts of detrital muscovite, and diagenetic kaolin as a cementation mineral. Additional clay minerals do not occur. Fig. 1 Location map of the well in the Abu Gharadig Basin (star) and of the Bahariya Oasis (triangle). Fig. 2 Classification of the cylindrical sandstone samples into horizontal and vertical samples and into laminated (+L) and non-laminated (-L) samples. December 2009 PETROPHYSICS 479

3 Halisch et al. Sampling depths range from approximately 3512 m to 3547 m, equivalent to an average sampling interval of more than two sample pairs per meter. Using this set of samples, it became possible to perform a complete petrophysical, geological and mineralogical characterization of this deeply buried part of Bahariya Formation. The conspicuous flaser bedding implicates a distinct anisotropy effect on relevant directional reservoir parameters such as permeability, electrical resistivity and seismic velocity. Most logging tools usually yield integrated values of a much larger volume than laboratory measurements without respect to a preferred orientation. Consequently, the deduced directional reservoir parameters can only be assumed to be correct if the investigated formation is isotropic and homogeneous. An interpretation becomes much more difficult if the formation is anisotropic and heterogeneous. Parameters may vary over several value-decades if the orientation of an anisotropic sample is considered. Therefore, it was the main aim of this study to determine the influence of anisotropy on logging data as well as the origin of Logging Tools Table 1. Logging techniques used for investigation of Bahariya Formation. Table 2. Mineralogical investigation techniques for Bahariya Formation samples. anisotropy of the investigated Bahariya sandstones. Logging techniques and laboratory investigations The selected well offers favourable conditions for a complex core-log case study in the investigated depth interval. Eight logs and more than 2500 laboratory data from about 100 core samples are available. The well log consists of standard logging techniques extending from caliper (CAL) and gamma ray (GR) to various electrical and acoustic methods. Table 1 gives an overview of all downhole techniques and determined parameters. A petrophysical laboratory investigation was carried out to determine standard parameters for reservoir characterization, such as porosity, density and permeability, as well as additional parameters such as specific surface area, complex electrical resistivity and thermophysical rock properties. In contrast to well logging activities, laboratory investigations enable a detailed study of anisotropy. Table 2 summarizes the mineralogical investigations. The large variety of Tool Abbreviation Parameter Physical unit GammaRay GR natural gamma radiation of the bedrock API Caliper CAL borehole diameter inch Gamma-Gamma LDEN formation bulk density g/cm³ Compensated Neutron NPHI formation porosity fraction - Micro Spherical Focussed Log MSFL mud cake resistivity Ωm LateroLog Shallow LLS flushed zone resistivity Ωm LateroLog Deep LLD formation resistivity Ωm Borehole Compensated Sonic Log BCSL Interval transit time µs/m Mineralogical tools Technique Abreviation # Samples Thin sectioning 9 Transmitted-light microscopy 9 Reflected-light microscopy 5 Scanning electron microscopy SEM 5 Electron micro probe analysis EMPA 3 Raman laser spectroscopy RLS PETROPHYSICS December 2009

4 A Complex Core-Log Case Study of an Anisotropic Sandstone, Originating from Bahariya Formation, Abu Gharadig Basin, Egypt petrophysical measurements carried out, are compiled in Table 3. We combined the knowledge and data of geology, mineralogy, borehole geophysics and petrophysics to get access to form a detailed reservoir description. The first step was to examine the complex mineralogy of the samples, especially of the flaser beddings, and to study, if and how changes in the mineralogical content influence laboratory and logging data. Contemporaneously, well logging data were interpreted, and a detailed investigation of anisotropy effects on different petrophysical parameters was carried out. In this particular case, it was possible to identify the causes of anisotropy. Section A The upper section has a thickness of approximately 22.5 m. CAL exhibits five minor areas with borehole breakouts, located at ~ 3516 m, ~ m, ~ 3523 m, ~ Well log interpretation Various open hole logging data were available in addition to core sample investigation. For a detailed study, CAL, GR, LDEN, NPHI (run with a quartz sand matrix), MSFL, LLS, LLD and BCSL the abbreviations of the tools are compiled in Table 1 within a target depth range from 3515 m to 3547 m MD (measured depth) were used. A quick look interpretation of all logs (Figure 3) leads to the conclusion that the investigated depth interval of Bahariya Formation in the subject well can be separated into two sections: an upper section A from 3515 m to 3537 m and a lower section B ranging from 3537 m to 3547 m. Note that this is a different classification compared to the geological units described in literature. Table 3. Petrophysical investigation techniques used for Bahariya Formation samples. Fig. 3 Logging curves of the Bahariya Formation in a well in the Abu Gharadig Basin, Egypt. Applied petrophysical methods Applied methods / devices Parameter and symbol Physical unit # of Samples Archimedic weighing grain density: d grain g/cm³ 116 porosity: Φ % 117 Gas-pycnometry - Ultrapycnometer grain density: d grain g/cm³ 117 Magnetic properties - Kappabridge KLY 2 volumetric magnetic susceptibility: χ - 95 Spectral induced polarization - SIP Fuchs complex resistivity: R Ωm 53 Ultrasonic inspection - Krautkramer USLT p-wave velocity: v p m/s 85 Nitrogen adsorption - BET specific internal sample surface: S por m²/kg 57 Gas-permeametry - Hassler-cell permeameter gas permeability: k md 112 Thermal conductivity scanning - TCS thermal conductivity: λ W/(m K) 20 Calorimetry - Setaram C80 DSC specific heat capacity: c J/(kg K) 7 December 2009 PETROPHYSICS 481

5 Halisch et al m and ~ 3532 m. The breakouts do not significantly affect the readings of LDEN, NPHI and MSFL. LDEN shows only small variations from a mean value of 2.5 g/ cm³ and five intervals with higher values of about 2.6 g/ cm³. It is remarkable that these five areas with higher density correlate with the locations of the breakout zones. NPHI readings show only minor variations in porosity (10 16 %). Several indications of gas effects (equal to porous, permeable zones) are observed in the intervals between the breakout zones. GR values are quite low within these permeable zones (< 50 API) and greatly increase at the five breakout zones and high density locations reaching values of nearly 75 API. LLD, LLS and MSFL curves are separated and indicate a porous part of Bahariya Formation. MSFL readings are disturbed through the breakout zones, whereas LLS and LLD readings are of good quality, although some data indicate tool sticking (three indications < 1 m are visible). BCSL is nearly constant (~250 µs/m) and only interrupted by several anomalies (so called cycle skipping caused by the occurrence of gas and/or breakouts and fractures within the formation). Up to this point, section A of Bahariya Formation could be interpreted as porous sandstone interlayered with mudstone or shale. Section B The lower section B covers a depth interval of about 10 m. In this section, CAL indicates massive variations and breakouts. Consequently, NPHI, LDEN, MSFL and BCSL data are not usable, except for a small interval ranging from m to 3541 m where no breakouts occur. In this area, LDEN reads values equal to those from the five anomaly areas from section A (~ 2.6 g/ cm³). NPHI reads parallel to LDEN curve and indicates an average porosity of approximately 8 %. LLS and LLD are overlapping within the entire section, which indicates a (hydraulic) tight formation. In the lower part, LLS and LLD values decrease but still overlay as a result of the massive caliper changes (breakouts are doubling borehole diameter). BCSL is severely affected by some of the changes in borehole diameter but we believe the BCSL would show the same interval transit time (~ 250 µs/m) for this section as in section A if the data could be corrected. Again, high GR values from 65 to 88 API correlate to CAL and LDEN values and anomalies as observed in section A, indicating a quite dense and tight mudstone or shale layer at the bottom of the investigated depth interval. Table 4 summarizes the derived parameters of the CAL, GR, LDEN, NPHI and BCSL tools, compiling minimum, maximum and mean values of both sections. Mineralogical investigations As shown, the Bahariya Formation in the subject well consists of sandstone with shaly interlayers, which are indicated by higher GR and increased LDEN values. The sedimentary structures identified in the sample thin sections of the Bahariya Formation show characteristic features of deposition in a relatively low-energy, sub- to intertidal zone, as Athmer (2006) has described the results Quick look logging results Tool Physical unit Section A Section B Minimum Maximum Mean Minimum Maximum Mean GR API CAL inch > LDEN g/cm³ NPHI % MSFL Ωm 4 30 ~ 11 < ~ 5 LLS Ωm ~ ~ 7 LLD Ωm ~ ~ 7 BCSL µs/m Table 4. Parameter ranges for different logging tools for section A and section B. Bold and italicized values are heavily influenced by caliper variations. 482 PETROPHYSICS December 2009

6 A Complex Core-Log Case Study of an Anisotropic Sandstone, Originating from Bahariya Formation, Abu Gharadig Basin, Egypt of her mineralogical and geological investigations. Flaser bedding develops on tidal flats during the turn from flood to ebb tide, when transport energy reaches its lowest level so that fine material like clay and silt sinks down and gets deposited between sand ripples. The fine sandy layers of the sandstones are mainly composed of quartz (70-80%), glauconite (5-15%), feldspar (1-2%), muscovite (1-2%), and rutile (1-2 %). Apatite, zircon, and hornblende are present as accessory minerals. Cementation minerals are kaolinite and subordinate calcite as well as quartz overgrowths. The angular to subrounded quartz grains show concave-convex contacts which indicate a deep burial (Figure 4). Feldspar appears as plagioclase and microcline which often are heavily etched or totally decomposed to honeycomb structures. Muscovite is mostly aligned along the sedimentary beddings. The mica minerals have a fibrous shape and are lightly twisted, which is another indication for deep burial (Figure 5). Several samples contain oval to tuber-like shaped intraclasts up to several millimeters in size and composed of clay minerals as well as fine sandy to silty quartz. Furthermore, pyrite can be found in the center or as seam. The occurrence of such zonated structures is typical for the intertidal zone. Concerning the contribution to anisotropy effects, the flaser bedding could play the decisive role, especially when it is abundant and creates a barrier for vertical permeability due to the high amount of clay minerals. On the other hand, Figure 6 shows stress related secondary fracture porosity occurring in the laminated samples parallel to the flaser layers. These fractures mainly appear within the flaser layers but also close by. The type of propagation that also affects quartz grains shows that the fractures were not created by core handling, although the core (the plugs) was photographed at surface pressure. This might be a considerable contribution to increase the horizontal permeability. The flaser bedding is composed of clayey-silty, partly carbonaceous layers that contain many small pyrite framboids and minor rutile. Figure 7 shows framboidal pyrites that appear mostly aligned like in a pearl necklace. Such a pyrite framboid embedded in a clay matrix is shown in Figure 8. Due to oxidation, the layers contain minor limonite or other iron hydroxides. Petrophysical investigation Petrophysical parameters are determined under ambient Fig. 5 Thin section image of sample 43 H showing a twisted mica (red arrow) within a sandy layer, sandwiched between two flaser layers. (CP - Crossed polarizers). Fig. 4 Thin section image of sample 74 H with contact to flaser bedding. The red arrow points at a concave-convex contact of quartz grains. (CP - Crossed polarizers). Fig. 6 Thin section images of two different sandstone samples (left-hand side 31 H; right-hand side 43 H) showing secondary fracture porosity (blue) parallel to flaser layers. (PPL: Plane-polarized light). December 2009 PETROPHYSICS 483

7 Halisch et al. conditions for both types of samples (+L and L) and for both orientations of the sample (H horizontal, V vertical). The petrophysical study was designed to determine to what extent the flaser bedding and lamination cause differences in the petrophysical parameters and in the anisotropic behaviour. Table 3 summarizes the petrophysical devices and techniques used. Regarding the parameters determined, we differentiate between the so called scalar properties, which yield a single quantity for each sample, and the directional parameters which depend on the spatial orientation of the specimen and measurement. The determined values of scalar parameters like porosity, density, specific internal surface or magnetic susceptibility should be close to each other for a pair of horizontal (H) and vertical (V) samples. The comparison of the directional parameters like electrical conductivity, permeability, seismic velocity, and thermal conductivity for a pair of samples will indicate the degree of anisotropy. The minima, maxima, average values and standard deviations of all measured parameters are compiled in Tables 5 and 6. Scalar parameters Porosity and density Porosity and density are standard petrophysical parameters that have been determined for all specimens. Averaging all porosity values yields a mean porosity Fig. 7 Microscopic image of sample 43 H under reflected light showing high reflective framboidal pyrites which are aligned like a pearl necklace within a flaser layer. Fig. 8 SEM micrograph of sample 43 H showing pyrite crystals within a framboid (red arrow) in a clay matrix. Compilation of scalar petrophysical parameters Parameter All samples +L samples -L samples min max mean std. dev. min max mean std. dev. min max mean std. dev. Φ d grain [g/cm³] d dry [g/cm³] χ [10-6 SI] S por [1/µm] Table 5. Compilation of minimum, maximum, average value, and standard deviation of scalar petrophysical parameters of all samples, +L, and L samples (Φ = porosity, d grain = grain density, d dry = dry bulk density, χ = magnetic susceptibility, S por = specific internal surface). 484 PETROPHYSICS December 2009

8 A Complex Core-Log Case Study of an Anisotropic Sandstone, Originating from Bahariya Formation, Abu Gharadig Basin, Egypt Compilation of directional petrophysical parameters Parameter All samples H samples V samples min max mean std. dev. min max mean std. dev. min max mean Std. dev. R [Ωm] k [md] v p [m/s] λ [W/(mK)] Parameter +L samples H +L samples V +L samples min max mean std. dev. min max mean std. dev. min max mean Std. dev. R [Ωm] k [md] v p [m/s] λ [W/(mK)] Parameter -L samples H -L samples V -L samples min max mean std. dev. min max mean std. dev. min max mean Std. dev. R [Ωm] k [md] v p [m/s] Table 6. Compilation of minimum, maximum, average value, and standard deviation of directional petrophysical parameters of all samples, H and V samples, +L and L samples. December 2009 PETROPHYSICS 485

9 Halisch et al. of 10.8 %. Considering only +L samples, the mean value decreases to 8.9 %, whereas L samples show a significantly higher porosity average with 13.5 % (Figure 9). Porosity values for +L samples spread over a relatively wide interval, ranging from 3.6 to 15.3 %, while for L samples this interval becomes narrower (9 17 %). High resolution grain density measurements show that +L and L samples cannot be differentiated by their average values (Figure 10). Both values differ from each other only by g/cm³ (2.643 g/cm³ for +L and g/cm³ for L samples). The resulting values closely compare to the grain density of quartz with g/cm³ (Schön, 1996). Consequently, the calculated bulk density, which includes the pore space filling fluid (note: pore Fig. 9 Frequency plot of lab derived porosity values for +L and L samples. Fig. 10 Frequency plot of lab derived grain density values for +L and L samples. 486 PETROPHYSICS December 2009

10 A Complex Core-Log Case Study of an Anisotropic Sandstone, Originating from Bahariya Formation, Abu Gharadig Basin, Egypt space was saturated with tap water) shows a similar trend as porosity (Figure 11). There is only a slight difference in the average bulk density values with 2.46 g/cm³ for +L and 2.40 g/cm³ for L samples. Magnetic susceptibility Results from volumetric magnetic susceptibility measurements are a little more promising. Though there is a broad overlapping interval between the susceptibility values of +L and L samples, a clear distinction is apparent (Figure 12). +L samples exhibit an average value of 148*10-6 SI, in general, a higher susceptibility value than L samples with an average of only 60*10-6 SI. A majority of the +L samples shows susceptibility Fig. 11 Frequency plot of calculated bulk density values for +L and L samples. Fig. 12 Frequency plot of lab derived magnetic susceptibility values for +L and L samples. December 2009 PETROPHYSICS 487

11 Halisch et al. values larger than 60*10-6 SI, but only a small number of L samples exceeds this limit. Though no difference in grain density has been observed, the changes in the mineral content of the strongly flaser bedded samples obviously cause an increase in magnetic susceptibility. Specific surface area The measured specific surface area has been normalized to the volume of pore space. It becomes obvious that L samples are characterized by a smaller surface area with an average value of about 4.5 µm -1. The +L samples reach an average value of about 19.8 µm -1 (Figure 13). Though the average values indicate a remarkable difference, the surface ranges broadly overlap. Directional properties Electrical resistivity The electrical resistivity of all samples has been derived from measurements of the induced polarization spectra in a frequency range from 750 khz to 1 mhz. Only the resistivity amplitudes at a frequency of 1.4 Hz have been used in this study. The measurements were performed under ambient conditions at a constant temperature of about 20 C. The samples were fully saturated with a sodium-chloride solution of 0.56 g/l resulting in a water conductivity of 0.1 S/m. The low salinity solution was chosen in order to enable a comparison of the measured spectra with those of other authors (e.g. Börner and Schön, 1991, Lesmes and Frye, 2001). Resistivity values of both horizontal and vertical samples were determined in the axial direction. Since a horizontal layering can be observed in the +L samples, the measurement of the V-samples provides the transverse resistivity R t (R V = R t ), the resistivity perpendicular to the layering. For the measurements of the H-samples, the current flow is parallel to the planes of layering. The resulting quantity is called longitudinal resistivity R l (R H = R l ). As generally expected for layered structures, the average transverse resistivity of 507 Ωm is slightly higher than the longitudinal resistivity of 369 Ωm. But the intervals that range for the H-samples from 213 to 675 Ωm and for V-samples from 228 to 914 Ωm largely overlap. The comparison between +L samples and L samples, without any reference to orientation, shows that the L samples are less resistive than the +L samples with average values of 355 Ωm and 520 Ωm, respectively. While the average longitudinal and transversal resistivity values for L samples do not differ notably with values of 333 Ωm and 378 Ωm, the directional differences become larger for the +L samples with an average longitudinal resistivity R l of 405 Ωm and an average transversal resistivity R t of 626 Ωm. The dependence of resistivity on the direction of current flow is referred to as anisotropy. According to a definition given by Keller and Frischknecht (1966) Fig. 13 Frequency plot of lab derived specific internal surface values for +L and L samples. 488 PETROPHYSICS December 2009

12 A Complex Core-Log Case Study of an Anisotropic Sandstone, Originating from Bahariya Formation, Abu Gharadig Basin, Egypt the coefficient of anisotropy is determined by taking the square root of the ratio of resistivities measured in the two principal directions, across the bedding planes (R V = R t ) and along the bedding planes (R H = R l ): A R t R = = Rl (1) Since for layered structures the transverse resistivity in general exceeds the longitudinal resistivity, the coefficient of anisotropy A R can be assumed to be larger than one. In our case, the two resistivity values were not determined at the same sample. The longitudinal resistivity results from the measurement at the H sample R R V H. and the transverse resistivity from the V sample. In order to guarantee that both samples can be regarded as twin samples, only those pairs of samples have been included in the anisotropy study that show similar values in the scalar properties (porosity, grain density, and magnetic susceptibility). The coefficient of anisotropy A R of all included samples averages to The average coefficient of anisotropy of +L samples reaches 1.23 and for L samples only 1.06 (Figure 14). The anisotropy data of the directional parameters are compiled in Table 7. Gas permeability Analogous to the electrical resistivity, the permeability Fig. 14 Frequency plot of anisotropy of resistivity for +L and L samples. Compilation of anisotropy coefficients Parameter All samples +L samples -L samples min max mean std. dev. min max mean std. dev. min max mean std. dev. A R A k A v A λ Table 7. Compilation of anisotropy coefficients of all samples. +L-samples and L-samples. sorted by min / max / average value and standard deviation. December 2009 PETROPHYSICS 489

13 Halisch et al. measured for H samples in the axial direction is equivalent to the longitudinal permeability k l. V samples provide the transverse permeability k t. The permeability values range from k 0.01 md for tight to k 50 md for the more permeable parts of the investigated depth interval of Bahariya Formation. The large variation in permeability requires the consideration of the geometric average. For the longitudinal permeability, it reaches a value of 0.74 md compared to 0.27 md for the transverse permeability. If the types of samples are considered, the average permeability of L is, at 6.3 md, a factor of about 65 larger than the permeability of the +L samples, which show only an average permeability of about md. Anisotropy of permeability could be expressed by several formulas. A simple approach (Tiab and Donaldson, 2004) considers the quotient of horizontal (k H = k l ) and vertical permeability (k V = k t ): A * k l = = kt (2) In the case of strong anisotropy, this ratio becomes quite large and cannot easily be compared to coefficients of anisotropy of other petrophysical parameters. Using the Kozeny equation describing a capillary model of electrical and hydraulic conduction in porous media, the following relationship between permeabilities and formation factors measured in two different directions can be derived (Wyllie and Spangler, 1952): k k Considering the definition of the formation factor w k (3) with R w being the resistivity of the saturation fluid, a relation between A k * and A R (see equation 1) can be established: k k H V 2 l F t = t Fl Rt Rl Ft = or Fl =, (4) R R k R A = = = * l t 4 k AR. kt Rl 2.. w (5) Consequently, a power law exponent of 4 has to be applied to the electrical coefficient of anisotropy A R to predict A k*. A better comparability of electrical and hydraulic anisotropy can be achieved if the coefficient of anisotropy for permeability is defined according to the following formula: A k = l 4. (6) Using equation (6), the average coefficient of anisotropy for all samples reaches Considering only +L samples the coefficient increases to 1.46, whereas the coefficient of anisotropy of L-samples is significantly lower at 1.16 (Figure 15). P-wave velocity The seismic p-wave velocities (v p ) have been determined under ambient conditions (temperature and pressure) in the axial direction on dry samples. Therefore, only a relative comparison between sonic log and laboratory velocity has been possible. The measured velocity values of all samples vary within the expected interval for sandstones around an average value of 3225 m/s. H-samples indicate with 3464 m/s a higher average velocity than V-samples, which provide an average value of 2949 m/s. It is interesting to note that the average seismic velocity of +L samples with 3373 m/s is similar to the value of the H-samples. For L samples, the average velocity with 3079 m/s approaches the average value of the V-samples. A seismic anisotropy ratio is defined using the measured values parallel (v H ) and perpendicular (v V ) to the stratification (Schön, 1996): (7) The average anisotropy ratio considering all samples reaches The average value for the L samples is, at 1.12, slightly lower than that for the +L samples at Thermal conductivity Thermal conductivity values have been determined on a subset of 20 samples with 19 samples being classified as +L. Thermal conductivity scanning has been performed on dry and fully water saturated samples (Popov et al., 1999). Each sample has been scanned at the plug mantle k k v Av = v t H V. 490 PETROPHYSICS December 2009

14 A Complex Core-Log Case Study of an Anisotropic Sandstone, Originating from Bahariya Formation, Abu Gharadig Basin, Egypt and the plug face surface. Two measurements for each plane took place so that in total four thermal conductivity values are available for each sample. Considering all values determined on dry samples, an average thermal conductivity of 3.07 Wm -1 K -1 is determined. The average value increases to 4.14 Wm -1 K -1 for the water saturated samples. Considering that heat propagation is perpendicular to scanning direction, the different measured values at core mantle and face surface cannot be easily classified as longitudinal or transverse thermal conductivity. It can be assumed that the thermal scanning in axial direction at the core mantle of the V samples provides the thermal conductivity along the bedding planes or the longitudinal conductivity λ l : λ mv = λ. (8) The scanning of the H samples in axial direction at the core mantle results in the geometric average of longitudinal and transverse thermal conductivity: λ = λ λ. mh l t l (9) The degree of anisotropy is determined by taking the ratio of thermal conductivities in the two principal directions, along the bedding planes λ l and across the bedding planes λ t (Schön, 1996): 2 λl λmv A λ = =. 2 λt λmh (10) Considering the thermal conductivity determined along the core mantle of eight pairs of dry samples, an average coefficient of anisotropy has been determined to be 1.35 with a variation from 1.00 to For the saturated samples, the average coefficient of anisotropy decreases to DISCUSSION The determined downhole and laboratory parameters are directly or indirectly influenced by mineral composition and structural properties of the Bahariya sandstones. Caliper measurement shows zones of strongly increased borehole diameter. These caliper extensions can be interpreted as breakout zones that are related to structural weakness of the sandstone formation. Microscopic investigation of thin sections has revealed fractures in direction of layering or flaser beddings that cause structural weakness (see Figure 6). Observations in Fig. 15 Frequency plot of anisotropy of permeability for +L and L samples. December 2009 PETROPHYSICS 491

15 Halisch et al. the laboratory have shown that +L samples easily break apart along the flasered structures while saturating. CAL data clearly indicate the degree of the structural weakness in the two previously defined sections. Section A consists of interlayers of pure and slightly flasered sandstones. It only exhibits slim to moderate caliper increase in the flasered intervals of the formation. Section B, which mostly consists of flasered sandstones, is characterized by strong breakouts. The caliper extensions are clearly correlated with intervals of increased gamma ray readings. In general, this effect is related to the occurrence of shale and clay minerals within the formation. Based on common logging experience, the intervals of increased gamma ray activity would be interpreted as more or less massive clay or shale barriers. The mineralogical investigation has confirmed a high degree of clay and mica within the flaser beddings. In addition, glauconite and potassium feldspar minerals contribute to the increased gamma ray activity. But quartz remains the main constituent and the lithology represents shaly sandstone. Thin section microscopy has shown that the flaser beddings contain pyrite, limonite, and other iron hydroxides. These iron minerals cause an increased magnetic susceptibility of most +L samples. Iron minerals are also observed in the micritic intraclasts that can be found in a few L samples. This might be the explanation of higher susceptibility for those samples. Since the breakout zones severely affect density and porosity logs, the readings can only be used in the intervals without strong caliper extensions. Bulk density shows only a low variation. Considering that grain density is more or less constant across the investigated interval, bulk density only reflects the changes in porosity. Laboratory investigation has shown that the pure sandstone may be characterized by a porosity of 9 to 17 %. The flaser bedding and the pore space filling clay minerals cause a gradual decrease in porosity for +L samples down to 4 %. The cross plot in Figure 17 summarizes the effects of flasered structures on porosity and magnetic susceptibility. These two parameters, which show the most significant effect amongst scalar parameters, can be used for a rough classification. The upper left quadrant with high porosity and low magnetic susceptibility is exclusively occupied by L samples. The lower right quadrant only contains +L samples. The lower left quadrant remains empty while the upper right is filled with +L samples with porosity larger than 9 % and L samples with higher magnetic susceptibility. Beside gamma ray activity that is recorded by well logging, porosity and magnetic susceptibility are suitable parameters for a rough lithological discrimination of laminated sections. The petrophysical investigation of directional parameters has confirmed that in general the +L samples show a distinct anisotropy. A comparison between the coefficients of anisotropy should reveal whether the Fig. 16 Frequency plot of anisotropy of p-wave velocity for +L and L samples. 492 PETROPHYSICS December 2009

16 A Complex Core-Log Case Study of an Anisotropic Sandstone, Originating from Bahariya Formation, Abu Gharadig Basin, Egypt anisotropy of resistivity, permeability and seismic p-wave velocity are related to each other. Figure 18 compares the coefficients A R and A k which have been determined by equations (1) and (6), respectively. The exponent of the root in equation (6) has been chosen to be 4 in order to get a good agreement between the two coefficients of anisotropy. The diagonal line in Figure 18 represents the ideal agreement of the two coefficients. The data points scattering around the ideal line confirm the general trend and show that +L samples are characterized by a higher degree of anisotropy for both electrical resistivity and permeability. The assumption that electrical and hydraulic conduction is restricted to a capillary pore space has been the precondition to equalize the two sides of equation (3). It can be observed that some +L samples are located at a considerable distance above the ideal line. This indicates a higher degree of anisotropy in permeability. This effect is supposed to be caused by fracture porosity along the flaser bedding (see Figure 6) that increases permeability of H samples. The presence of abundant clay minerals in the samples causes additional electrical conductive paths beside the electrolytic conduction in the pore space. This conduction effect can be amplified by the flasered structures containing pyrite necklaces as shown in Figure 7. It can be assumed that the conductive flaser beddings increase the electrical coefficient of anisotropy A R. Since +L samples are missing below the diagonal line, it can be concluded that the increase of electrical conduction is of minor importance. Using anisotropy data of several Appalachian sandstone formations (Sawyer et al., 2001), a similar trend can be found. Permeability shows a higher degree of anisotropy for a considerable amount of samples while the coefficient of anisotropy of electrical resistivity does not exceed a value of 1.3. The coefficient of anisotropy determined by resistivity data can only be regarded as the lower limit of the anisotropy of permeability. A higher root exponent than 4 in equation (6) should be applied to get a better agreement between hydraulic and electrical anisotropy. In order to determine empirically this exponent by our data, the logarithms of the ratio between longitudinal and transversal permeability and the ratio between transversal and longitudinal resistivity are displayed in Figure 19. According to the following equation k l R t log = a log, kt Rl (11) the factor a = 3.29 is determined by a linear regression in double logarithmic scale and has a coefficient of Fig. 17 Cross plot showing the relation between magnetic susceptibility and porosity of laminated (+L) and nonlaminated ( L) Bahariya sandstone samples. Fig. 18 Comparison between electrical (A ρ ) and hydraulic (A k ) anisotropy of laminated (+L) and nonlaminated ( L) Bahariya sandstone samples. December 2009 PETROPHYSICS 493

17 Halisch et al. determination R² of Considering the definition of the electrical coefficient of anisotropy in equation (1), the root exponent in equation (6) should be increased. We considered an increase from 4 to 2a = 6.58 to equalize the numerical values of both coefficients of anisotropy. As shown in Figure 19, not only the anisotropy of laminated Bahariya samples but also of the Appalachian sandstones (Sawyer et al., 2001) can well be described by the same fitting line. Figure 20 displays a comparison between anisotropy of permeability and seismic p-wave velocity. For L samples, the degree of anisotropy represented by A v and A k stays at low level. The higher degree of anisotropy of the +L samples is only reflected by permeability while the seismic anisotropy ratio, A v, hardly increases. The comparison between anisotropy of electrical resistivity and p-wave velocity which is presented in Figure 21 shows a similar behaviour. The L samples are characterized by low anisotropy. The increase of anisotropy for +L samples is only observed in A R. Though there is a slight increase of p-wave velocity observed for +L samples, the effect of flaser bedding and directional fractures on the anisotropy of seismic velocity can be ignored. Fig. 20 Comparison between hydraulic (A k ) and seismic anisotropy (A v ) of laminated (+L) and non-laminated ( L) Bahariya sandstone samples. Fig. 19 Comparison between electrical (Log(ρ t /ρ l )) and hydraulic (Log(k l /k t )) anisotropy of Bahariya (+L) and Appalachian sandstone samples. Fig. 21 Comparison between electrical (A ρ ) and seismic anisotropy (A v ) of laminated (+L) and non-laminated ( L) Bahariya sandstone samples. 494 PETROPHYSICS December 2009

18 A Complex Core-Log Case Study of an Anisotropic Sandstone, Originating from Bahariya Formation, Abu Gharadig Basin, Egypt CONCLUSIONS Since permeability varies over several orders of magnitude, the sandstone samples originating from the deeply buried Bahariya Formation provide an interesting opportunity to investigate the influence of anisotropy on different directional petrophysical parameters. The depositional environment, which can be described as shallow marine with tidal flat to marine shelf setting, enables the formation of flaser bedding and convoluted bedding structures. The investigated depth interval shows an alternate bedding of pure sandstone ( L) and laminated sandstone (+L) layers. The lamination is dominated by flaser bedding structures that mainly consist of clay minerals. The laminated interlayers are reflected in the logs by higher gamma ray activity and increased bulk density. Since grain density is not affected by the lamination, the increasing bulk density is caused by reduced porosity. Caliper extensions are related to the structural weakness of the laminated intervals caused by fractures along the flasered structures. Most logging curves are affected by breakout zones. The laboratory investigations confirmed a reduction in porosity of the +L samples. Additionally, increased magnetic susceptibility has proven to be a suitable indicator for flaser bedding structures. The assumption that the anisotropy of the Bahariya sandstone samples depends on the occurrence of flaser beddings was verified. The degree of anisotropy in permeability and electrical resistivity remarkably increases for +L samples. Based on the capillary model, a novel definition of the coefficient of anisotropy of permeability is given that enables a better comparability of anisotropy of electrical resistivity and permeability. Regarding the +L samples, the permeability shows a higher degree of anisotropy compared to the electrical resistivity. These results fit quite well to the results of past studies like the one from Schön et al. (2003), although a conventional type of coefficient of anisotropy has been used. In summary and in agreement to older data we can declare that A k > A R > A v. Fractures in direction of lamination were identified to be the reason of the increased permeability in horizontal direction. The anisotropy of p-wave velocity is less sensitive to the flasered structures. The average seismic anisotropy ratio only slightly increases for the +L samples. Last, but not least, some questions have arisen in this study which may offer the possibility of further and new types of investigation for anisotropic formations in general and for the Bahariya Formation in particular. In this case, it may be interesting to take a closer look at how the results might change with variations in clay mineralogy and type. Furthermore, it could be illuminating to investigate how results might change if graded bedding occurs, how multi-salinity resistivity measurements might help to gain new information on resistivity anisotropy, how pressure dependent resistivity and permeability measurements in the laboratory might change the results, and whether it may be possible to derive anisotropy directly from the log data of strongly anisotropic and complex formations. ACKNOWLEDGEMENTS The joint research project between the Department of Geophysics at Ain Shams University Cairo, Egypt, and the Institute of Geophysics at Clausthal University of Technology, Germany, was supported by a grant (WE 1557/10) of the German Research Foundation (DFG) and the Federal Ministry for Economic Cooperation and Development (BMZ). We are grateful to two anonymous reviewers whose constructive comments and remarks helped to improve the manuscript. We thank Wiebke Athmer, Esther Vogt, Sven Nordsiek, and Henning Schröder for their extensive work in laboratory as well as Juliane Herrmann for the appropriation and creation of detailed figures. December 2009 PETROPHYSICS 495

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