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Acoustic wave velocity behavior for some Jurassic carbonate samples, north Sinai, Egypt
Journal of African Earth Sciences 111 (2015) 14e25
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Journal of African Earth Sciences journal homepage: www.elsevier.com/locate/jafrearsci
Acoustic wave velocity behavior for some Jurassic carbonate samples, north Sinai, Egypt Nahla A. El Sayed, Hesham Abuseda*, Mohamed A. Kassab Egyptian Petroleum Research Institute, Naser City 11727, Cairo, Egypt
a r t i c l e i n f o
a b s t r a c t
Article history: Received 21 January 2015 Received in revised form 9 July 2015 Accepted 14 July 2015 Available online 16 July 2015
Seismic data of reservoir rocks use for understand of risk reduction. Acoustic laboratory measurements have been carried out for 75 carbonate rock samples for both dry and fully saturated collected from Jurassic deposits exposed in the north Sinai at Gebel El-Maghara. This study has been carried out to know more about the behavior of compression wave velocity and shear wave velocity in carbonate rock samples for both dry and fully saturated conditions and to investigate the effect of porosity, permeability and density on both dry and fully saturated acoustic velocities. The compressional wave velocities at dry and fully saturated carbonate rock samples increased with increasing the bulk density and decreasing the porosity, while the porosity decreasing with increasing bulk density, the relationships between the porosity as well as shear wave velocity in dry and fully saturated are in cloud points, with no clear relationships. The relationships between the permeability and both the compressional wave and the shear wave velocities at dry and fully saturated cases could not be identified. The statistical analyses indicate that the compressional wave in the fully saturated is higher than the compressional wave in dry case. The compressional wave velocity of the fully saturated carbonate rock samples were strongly correlated with the compressional wave velocity of the dry rock samples and the derived equation can be used for prediction of the compressional wave velocity of fully saturated rock from the compressional wave velocity of dry rock. The shear wave of the fully saturated carbonate rock samples is a fair correlated with the shear wave of the dry rock samples. © 2015 Elsevier Ltd. All rights reserved.
Keywords: Compressional wave velocity Shear wave velocity Density Poisson's ratio
1. Introduction The studied carbonate rock samples were collected form some of Jurassic deposits exposed at Gebel El-Maghara in the north Sinai. Gebel El-Maghara section is located between longitudes 33 180 e 33 270 E. and latitudes 30 380 e 30 440 N., Fig. 1. All the studied samples representing the exposure section were collected from Masajid Formation, Safa Formation, Bir Maghara Formation, Shusha Formation, Rajabia Formation and Mashaba Formation, which is assigned to Jurassic age, Fig. 2. Said (1990), mentioned that the complete Jurassic section in north Sinai is exposed at Gebel El-Maghara (1980 m.) and during the Jurassic and Cretaceous periods there was not a great change in deposition framework. The dominant rocks are limestones and dolomites. The use of seismic waves for determining reservoir rock properties is of great value to hydrocarbon zonation and exploration.
* Corresponding author. E-mail address: [email protected] (H. Abuseda). http://dx.doi.org/10.1016/j.jafrearsci.2015.07.016 1464-343X/© 2015 Elsevier Ltd. All rights reserved.
The acoustic properties of rocks control the relations between an alternating stress of various frequencies and corresponding strains. Seismic waves velocities for gas, water and oil reservoirs are early discussed by many investigators (e.g. Hughes and Kelly 1952, Brandt 1955, Hicks and Berry 1956, Wyllie et al., 1958, Nur and Simmon 1969, Elliot and Wiley 1975, Gregory 1976, Minear 1982, Han et al., 1986, El Sayed et al., 1998, Vernik and Nur 1992a, b, Salah 2001 and Kassab, M. A., 2011. Compressional and shear waves have different behavior in rocks depending on difference in porosity, fluid saturation, fluid viscosity, density, laminations, fracturing, clay content, mineralogy, compaction and pore space framework. Biot (1956) investigated the seismic wave propagation at high frequencies in an isotropic, liquid saturated porous medium. Two main conclusions may be drawn from Biot's analysis. First, the shear wave velocity values in a liquid saturated porous material will always be less than that in the dry material based on an assumption that micro cracks are negligible. Second, the compressional wave velocity values in the liquid saturated porous material will generally be higher than that in the dry case, except
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Fig. 1. Geological map of Egypt (Schlumberger, 1984).
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Fig. 2. Lithostratigraphic section of Gebel El Maghara, (after Kassab, 2004).
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for material having low bulk compressibility. The technique used to measure acoustic wave velocity is the pulse first arrival technique, in which the travel time is determined for a pulse of compressional or shear waves to pass a known measured thickness of the rock (sample length). Numerous theoretical models have been proposed to describe elastic wave propagation in two phase sedimentary rocks of finite porosity. Perhaps the most successful of these is the model of Biot (1962). The Biot model requires knowledge on the elastic properties of the matrix material, pore fluid saturation, and the elastic properties of the frame or skeleton composing the matrix. The elastic properties of the frame are determined empirically, with little theoretical consideration given to the pore geometry creating the non-uniform porosity. Gregory (1976) stated that the experimental data support Biot's theory for all porosities at confining pressures above 62,000 kPa. However, as pressure declines, the data for low porosity rocks begin to depart from the theory. The interpretation of velocity behavior is slightly difficult due to the effect of many parameters such as rock compressibility, density of matrix and pore fluids, rigidity and rock porosity. Poisson's ratio is defined as the ratio of relative lateral strain to longitudinal strain of uniaxial stress applied to a unit cube of the rock. It is computed from compressional wave velocity Vp and shear wave velocity Vs by the following relation:
2 Vp VS
2 y ¼ 2 Vp 1 2 VS
(1)
with: Vp is compression wave velocity (m/sec), Vs is shear wave velocity (m/sec), and y is Poisson's ratio. Poisson's ratio varies over a range 0.0 < y < 0.5 for all types of dry and saturated rocks (Nur and Simmon, 1969, Gregory, 1976). In addition, Poisson's ratio has been used as an indicator for fracture height determination in charged reservoir rocks (Gregory, 1976). Poisson's ratio varies over a wide range of possible values including negatives values (Gregory, 1976). Negatives Poisson's ratio is observed for real sedimentary rock. High values of the compressional wave velocity are obtained for saturated samples and low values are obtained for dry samples (compressional wave velocity (dry) < compressional wave velocity (saturated) Boulanouar et al. (2013). The shear wave velocity decreases as the water saturation increasing until it reaches 70%e75% and then starts to increase again El Sayed et al. (1998) and Abuseda (2010). Compressional wave velocity of saturated rock can predicted from the compressional wave velocity of dry rock Kahraman (2007). The present work aims to learn more about the behavior of both compressional and shear wave velocity in samples for both dry and fully saturated conditions and to investigate the effect of porosity, permeability and density for both dry and fully saturated acoustic velocities. 2. Material and methods All samples were measured at the Ain Shams University and the Egyptian Petroleum Research Institute, Egypt. Density and porosity of rock samples are closely related. The volumetric mass density of a substance is defined by the ratio of mass (m) and volume (V). In the case of rock samples, a differentiation into bulk density (natural raw density) and grain density becomes evident. The natural raw density considers the total mass and the total volume (V) of the sample. If the sample is dry, the mass (m) is only related to the solid
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constituents or the mineral grains (mg). The dry density is determined by the equation:
db ¼
mg V
(2)
The grain density, which considers the mass of the solid constituents and only the volume of the solid phase (Vg), is determined in a similar way:
dg ¼
mg Vg
(3)
It becomes evident that the grain density is larger than the dry density for porous media with V > Vg. The volume of the pore space (Vp) results from the difference between the total volume (V) and the volume of the solid phase (Vg). Porosity (Ф) is the most important parameter for evaluating the storage capacity of a porous medium. Porosity was measured by use of helium porosimeter. The porosity of a rock is defined as the ratio of the rock void spaces to its bulk volume, multiplied by one hundred to express it in percent Amyx et al. (1960). This can be expressed in mathematical form as;
F ¼ Vb Vg Vb
(4)
with Ф being the porosity fraction, Vb the bulk volume, cm3, and Vg the grain volume, cm3 The permeability (k) of all samples was measured by a gas permeameter using nitrogen as the flowing fluid. Permeability of a rock is controlled by many factors such as rock pore geometry, cementation, rock texture, grain size, grain shape, and roundness. The permeability (K) in mD was measured by use of core lab permeameter. The Darcy's equation relating permeability to compressible fluids is;
K ¼ ½2000*m*q*L*Pa
i .h A* P12 P22
(5)
with K being the permeability (mD), m the viscosity of air, centipoises, q the gas volume flow rate cm3/sec, P1 the upstream pressure (atmosphere), P2 the downstream pressure (atmosphere) and Pa the atmospheric pressure (atmosphere). Compressional wave velocity and shear wave velocity were measured at room temperature and ambient pressure on cylindrical samples using two channels Sonic Viewer (OYO-170) in the petrophysical lab of the Department of Geophysics at Ain Shams University, Cairo. The compressional and shear wave velocities have been measured at ultrasonic frequencies of 63 kHz and 33 kHz, respectively. Compressional wave velocity (Vp) and shear wave velocity (Vs) measurements were made with the samples in both dry and fully water saturated state, both of them can be computed from the elastic moduli by the following formulas;
Vp ¼
Vs ¼
ðk þ 4m=3Þ 1=2 d
m1=2 d
(6)
(7)
with к being the bulk modulus, m the shear modulus, and d the density. Petrophysical laboratory investigations were carried out to determine compressional wave velocity and shear wave velocity of dry and fully saturated rock samples as well as additional standard parameters for reservoir characterization such as, bulk density, porosity, and permeability. All the petrophysical parameters were
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Table 1 Compilation of minimum, maximum, average values and standard deviations of measured petrophysical parameters for some Jurassic carbonate samples, at Gebel El-Maghara Section. Parameters
dbulk F (%) K, (mD) Vp dry, (m/s) Vs dry, (m/s) Vp/Vs dry Poisson's ratio (y) dry Vp, saturated (m/s) Vs saturated, (m/s) Vp/Vs saturated Poisson's ratio (y) saturated
Carbonate samples Minimum
Maximum
Mean
Std. dev.
2.42 1.00 0.01 4400 1160 1.46 0.06 4120 1310 1.55 0.14
2.74 8.64 4.33 6450 3410 4.37 0.47 7210 3510 4.40 0.47
2.58 3.82 1.14 5382 2134 2.66 0.39 5604 2169 2.75 0.40
0.07 1.76 1.31 520 515 0.64 0.08 641 564 0.74 0.07
with; dbulk in g/cm3 is the bulk density, F % is the porosity, K, mD is the permeability, Vp is compression wave velocity (m/sec), Vs is shear wave velocity (m/sec), Vp/Vs is a ratio between compression and shear wave velocity and y is Poisson's ratio.
determined under ambient conditions. Minimum, maximum, average and standard deviation of porosity, permeability, bulk density, compressional and shear wave velocity of dry and fully saturated rock samples are listed in Table 1.
3. Results and discussion 3.1. Mineralogical investigations of the studied samples The mineralogical investigation of this study has been done in more details by Gomaa et al. (2014). The present carbonate microfacies were classified according to the depositional textures classification of Folk (1959, 1962), the nomenclature and classification of pore spaces were carried out following Choquette and Pray's classification (1970). Based on the mineralogical composition, texture, structure, and faunal content, the present carbonate samples can be classified into five carbonate microfacies, biomicrite (Fig. 3A and B), fossiliferous biomicrite (Fig. 3C), sandy biomicrite, (Fig. 3D), Oobiosparite (Fig. 3E) and foraminiferal biomicrite, (Fig. 3F). Thin sections revealed that, most of the carbonate samples are tight with no visible porosity. In the case of the studied carbonate samples, partial dissolution of the calcitic matrix can be noticed in some parts, caused some vugs which were filled later by sparite cement (Fig. 3B). The dissolution of fossil skeletons and remains increased the pore volume due to particle moldic porosity after leaching of foraminifera skeletons (Fig. 3F). Microfractures filled with silica are noticed through the ground mass (Fig. 3C), and through the shell fragments
Fig. 3. Photomicrograph of the microfacies of carbonate rock samples.
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(Fig. 3F). Calcite cement is the most common cement either as micrite to microsparite matrix and/or as pseudo sparite cement, cementation of the fossil remains and skeletons by micrite cement (Fig. 3A and C), and by sparite cement (Fig. 3B) that reduced and obliterated the present vugy and moldic porosity. The iron oxides are noticed in most of the studied samples. Aggrading neomorphism can be assigned as uniform crystal size patches maintained within the ground mass (Fig. 3A, C, and D), where there is a patch of spary calcite crystals surrounded by patches of microspary calcite. 3.2. Petrophysical relationship Petrophysical parameters porosity, permeability, bulk density and seismic wave velocity of Gebel El-Maghara carbonate rock samples were performed and determined under ambient conditions. To obtain the petrophysical data to learn more about the behavior of compression wave velocity and shear wave velocity in rock samples for both dry and fully saturated conditions and to investigate the effect of porosity, permeability and density on both dry and fully saturated acoustic velocities. 3.2.1. Density, porosity and permeability The obtained bulk density values vary from 2.42 to 2.74 g/cm3 with mean values 2.58 g/cm3 and standard deviation 0.07 g/cm3. The measured porosity values vary from 1.00% to 8.64% with mean values 3.82% and standard deviation 1.76%, while the permeability values distribution varies from 0.01 mD to 4.33 mD, with mean values 1.14 mD and standard deviation 1.31 mD. 3.2.1.1. Density-porosity relationship. The bulk density and the porosity relationship for the studied rock samples, was studied and shown in Fig. 4, this relationship indicates a decrease of porosity with increasing bulk density and characterized by a good correlation coefficient (R ¼ 0.78) between porosity and bulk density for limestone samples. This relationship displays a linear inverse relationship and controlled by the following equation:
Fig. 4. Porosity versus bulk density for carbonate rock samples.
Fig. 5. Porosity versus permeability for carbonate rock samples.
db ¼ 2:70 0:03F
(8)
3.2.1.2. Porosityepermeability relationship. The relationship between the permeability and the porosity in Fig. 5, for the studied rock samples is indicated by a positive trend, the correlation coefficient (R ¼ 0.58) between the porosity and the permeability, means that the porosity is not the main contributor for the rock permeability. The resulting fitting equation read:
k ¼ ½10ð0:27F1:50Þ
Fig. 6. Porosity versus Vp(dry) for carbonate rock samples.
(9)
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The relationship of compressional wave of dry rock samples and permeability, which is shown in Fig. 7, illustrates that the data points are cloudy without any clear trend. The relationship between compressional wave velocity of dry rock samples and bulk density, which is displayed in Fig. 8, shows a fair direct proportional relationship with correlation coefficient of (R ¼ 0.47) and controlled by the following equation:
VpðdryÞ ¼ 3700:50db 4182:54
(11)
The relationships of the compressional wave velocity of dry rock samples with the porosity, permeability and bulk density, indicate that porosity and bulk density has effects on compressional wave velocity of dry rock samples to some extent, while permeability seems very weak related to compressional wave velocity.
3.2.3. Compressional wave velocity of saturated rock samples The measured the compressional wave values of saturated samples (Vpsaturated) vary from 4120 to 7210 m/s, with mean values 5604 m/s and standard deviation 641 m/s. The relationship between the compressional velocity of saturated rock samples and the porosity was plotted in Fig. 9, the correlation coefficient (R ¼ 0.43), displays a linear inverse relationship and controlled by the following equation:
Fig. 7. Permeability versus Vp(dry) for carbonate rock samples.
VpðsaturatedÞ ¼ 6207:95 157:99F 3.2.2. Compressional wave velocity of dry rock samples The measured compressional wave values of dry rock samples (Vpdry) vary from 4400 to 6450 m/s with a mean value of 5382 m/s and a standard deviation 520 m/s. The relationship between the compressional wave velocity of dry rock samples and the porosity is displayed in Fig. 6, it shows a fair inverse relationship with correlation coefficient (R ¼ 0.53), the relationship is a linear inverse relationship and controlled by the following equation:
VpðdryÞ ¼ 5984:25 157:54F
Fig. 8. Bulk density versus Vp(dry) for carbonate rock samples.
(10)
(12)
The relationship of the compressional of saturated rock samples and the permeability, which is displayed in Fig. 10, illustrates that the data points are cloudy without any clear trend. The relationship between the compressional of saturated rock samples and the bulk density, which is displayed in Fig. 11, correlation coefficient decreases to 0.27, and controlled by the following equation:
VpðsaturatedÞ ¼ 2619:82db 1167:27
(13)
The relationships of the compressional velocity of saturated rock samples with the porosity, the bulk density and the permeability show approximately similar behavior compared to the
Fig. 9. Porosity versus Vp(saturated) for carbonate rock samples.
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Fig. 10. Permeability versus Vp(saturated) for carbonate rock samples.
compressional velocity of the dry samples, but the correlation coefficients at the dry state is higher than the correlation coefficients at the saturation state, which mean that the state of saturation has effects on the behavior of the relationships between compressional velocity and the standard parameters for reservoir characterization (e.g. bulk density, porosity, and permeability).
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Fig. 12. Porosity versus Vs(dry) for carbonate rock samples.
samples and the porosity is displayed in Fig. 12, the resulting data points are flocked together in a cloud of points without any clear trend. The relationship of the shear wave of dry rock samples and the permeability, which is displayed in Fig. 13, does not show any trend. The relationship between the shear wave velocity of dry rock samples and the bulk density, which is plotted in Fig. 14, exhibits a scatter of data points without clear trend.
3.2.4. Shear wave velocity of dry rock samples The measured shear wave velocity values of dry rock samples (Vsdry) vary from 1160 to 3410 m/s with a mean value of 2134 m/s and standard deviation 515 m/s. The relationship between the shear wave velocity of dry rock
3.2.5. Shear wave velocity of saturated rock samples The shear wave velocity values of saturated rock samples Vs(saturated) vary from 1310 to 3510 m/s with a mean value of 2169 m/s and a standard deviation 564 m/s.
Fig. 11. Bulk density versus Vp(saturated) for carbonate rock samples.
Fig. 13. Permeability versus Vs(dry) for carbonate rock samples.
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Fig. 14. Bulk density versus Vs(dry) for carbonate rock samples.
The relationship between the shear wave velocity of saturated rock samples and the porosity, which is displayed in Fig. 15, does not show any trend. The comparison of the shear wave of saturated rock samples and the permeability, which is shown in Fig. 16, does not show any clear trend. The cross plot of the shear wave velocity of saturated rock samples and the bulk density in Fig. 17, exhibits a scatter of data points that is similar to the cross plot of shear wave velocity against the dry density in Fig. 14, the two plots indicate no clear trend.
Fig. 15. Porosity versus Vs(saturated) for carbonate rock samples.
Fig. 16. Permeability versus Vs(saturated) for carbonate rock samples.
3.2.6. Compressional wave velocity of dry rock samples and compressional wave velocity of saturated rock samples relationship The comparison between the compressional velocity of the dry rock samples and compressional velocity of the saturated rock samples, which is displayed in Fig. 18, shows a very good direct proportional relationship with a correlation coefficient of (R ¼ 0.65), which means that the compressional velocity of the saturated rock samples can be predicted from the compressional velocity of the dry rock samples.
VpðsaturatedÞ ¼ 0:80VpðdryÞ þ 1295:11
Fig. 17. Bulk density versus Vs(saturated) for carbonate rock samples.
(14)
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calculated if the shear wave velocity values of the dry rock samples known. 3.2.8. Relationships between compressional wave velocity and shear wave velocity of both dry saturated rock samples The comparison between the compressional velocity and the shear wave velocity of the dry rock samples has been shown in Fig. 20, the graph exhibits that the data points are cloudy without any clear trend, as well as the comparison between the compressional velocity and the shear wave velocity of saturated rock samples (Fig. 21). The relationships of compressional velocity and shear wave velocity of both the dry and the fully saturated rock samples show approximately similar behavior, which means that there are no relationships between compressional velocity and shear wave velocity in the cases of both dry and saturated carbonate samples.
Fig. 18. Vp(dry) versus Vp(saturated) for carbonate rock samples.
3.2.7. Shear wave velocity of dry rock samples and shear wave velocity of saturated rock samples relationship The comparison between the shear wave velocity of the dry rock samples and the shear wave velocity of the saturated rock samples, which is plotted in Fig. 19, indicates a fair direct proportional relationship with a correlation coefficient of (R ¼ 0.52) and controlled by the following equation:
3.2.9. Vp/Vs ratio with shear wave velocity of dry and saturated rock samples Vp/Vs ratio for samples filled with gas (dry rock) is with mean value of 2.66, and for the rock samples filled with water (fully saturated) is with mean value of 2.75, which means that the Vp/Vs ratio of the dry samples is lower than the Vp/Vs ratio of the fully saturated samples. The plots in Figs. 22 and 23 show the relationships between the Vp/Vs ratio and the shear wave velocity for both the dry and the fully saturated rock samples respectively. The data points have a negative trend, which means that the Vp/Vs ratio increases with decreasing the shear wave velocity for both the dry and the fully saturated rock samples.
Eq. (15) means that the shear wave velocity of the saturated rock samples can be linked to the shear wave velocity of the dry rock samples and the shear wave of the saturated rock samples can be
3.2.10. The effect of saturation on Poisson's ratio relations The Poisson's ratio of saturated samples is between 0.14 and 0.47 and the Poisson's ratio of dry samples is between 0.06 and 0.47. The Poisson's ratio of some samples was very low values, may be due to the presence of clay or fine particles to bridge the gaps between grains, where the Poisson's ratios decrease. The studied carbonate rock samples were classified into five carbonate microfacies, biomicrite, fossiliferous biomicrite, sandy
Fig. 19. Vs(dry) versus Vs(saturated) for carbonate rock samples.
Fig. 20. Vp(dry) versus Vs(dry) for carbonate rock samples.
VsðsaturatedÞ ¼ 0:56VsðdryÞ þ 964:98
(15)
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Fig. 21. Vp(saturated) versus Vs(saturated) for carbonate rock samples. Fig. 23. Vs(saturated) versus Vp/Vs(saturated) for carbonate rock samples.
biomicrite, Oobiosparite and foraminiferal biomicrite. Thin sections investigations revealed that, most of carbonate samples are tight with no visible porosity. Diagenesis processes (e.g. cementation, dissolution and neomorphism) have highly effects on the porosity values of the studied carbonate rock samples. The porosity of the studied carbonate rock samples has linked to bulk density. The permeability of most samples increases with increasing the porosity. The compressional velocities at the dry and the fully saturated increased with increasing the bulk density and decreasing the porosity, this means that the behavior of seismic wave (P-wave) velocity through the rock samples was
Fig. 22. Vs(dry) versus Vp/Vs(dry) for carbonate rock samples.
affected by both the porosity and the bulk density. The increasing of the compressional velocity with decreasing the porosity of both the dry and the fully saturated carbonate samples may be due to increase in the rigidity of the rock which are caused by low porosity and then lead to increasing the compressional velocity. The resulting data points between the shear wave velocity and porosity for both the dry and the fully saturated samples are flocked together in a cloud of points without any clear trend, while the porosity decreasing with increasing bulk density this means that the porosity and the bulk density have effects on the behavior of the shear wave velocity through the dry and the fully saturated rock samples. The relationships between permeability and seismic velocities (compressional and shear wave) could not be identified. This means that permeability has no impact in the behavior of seismic velocity through both dry and fully saturated rock samples. The statistical analysis indicate that the compressional velocity is higher in the fully saturated state, where the average value of compressional of saturated rock samples is 5604 m/s and compressional of dry rock samples is 5382 m/s. this means that water saturation has a highly effect on the behavior of the compressional velocity through rock samples, which is in agreement with Gassmann's (1951) theory. The relationships indicate that the compressional velocity of fully saturated rock samples were strongly correlated with the compressional velocity of dry rock samples, and the derived equation can be used for the prediction of the compressional velocity of fully saturated rock from the compressional velocity of dry rock. The shear wave velocity of fully saturated rock samples is a fair correlated with the shear wave velocity of dry rock samples. The Vp/Vs ratio increases with increasing saturations, where the Vp/Vs ratio of dry samples (filled with gas) is lower than the Vp/Vs ratio of saturated samples (filled with water) and the data points have a negative trend between Vp/Vs ratio and shear wave velocity of dry and fully saturated rock samples, which means the Vp/Vs ratio increases with decreasing shear wave. Poisson's ratio sometimes goes to very low values, which may be due to the presence of clay or fine particles that build bridges between grains.
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4. Conclusions Diagenesis processes (e.g. cementation, dissolution and neomorphism) have highly effects on the porosity values of the studied carbonate rock samples. The porosity of the studied carbonate rock samples has linked to the bulk density. The permeability of most samples increases with increasing the porosity. The porosity and the bulk density have highly effects on the behavior of the compressional velocity at the dry and the fully saturated rock samples. The porosity and the bulk density have slightly effects on the behavior of the shear wave velocity through the dry and the fully saturated rock samples. The permeability has no impact in the behavior of the seismic velocity (compressional and shear wave) through both the dry and the fully saturated rock samples. The compressional velocity is higher in the fully saturated state. The compressional velocity of the fully saturated rock can be predicted from the compressional velocity of dry rock. The shear wave velocity of the fully saturated rock samples is a fair correlated with the shear wave velocity of the dry rock samples. The Vp/Vs ratio increases with increasing saturations. Poisson's ratio sometimes goes to very low values, which may be due to the presence of clay or fine particles that build bridges between grains. Acknowledgments The authors would like to thank the reviewers for their great comments that improved and reconstructed the manuscript. Thanks are also due to the editor, whose patience and insightful suggestions have led to a concise revised version. References Abuseda, H., 2010. Petrophysical Modeling of Formation Factor, Porosity and Water Saturation of Bahariya Formation Western Desert, Egypt. Ph.D. Thesis. Ain Shams University, p. 134. Amyx, J.W., Bass Jr., D.M., Whiting, R.L., 1960. Petroleum Reservoir Engineering. Mc Graw Hill Publ. Co., New York, p. 601. Biot, M.A., 1956. Theory of propagation of elastic waves in a fluid saturation porous solid II: high frequency range. J. Acoust. Soc. Am. 28, 179e191. Biot, M.A., 1962. Generalized theory of ultrasonic propagation in porous dissipative media. J. Acoust. Soc. Am. 34, 1254e1264. raud, Y., Harnafi, M., Sebbani, J., Boulanouar, A., Rahmouni, A., Samaouali, M., Ge 2013. Determination of thermal conductivity and porosity of building stone
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from ultrasonic velocity measurements. Geomaterials 3, 138e144. Published Online October 2013. Brandt, H., 1955. A study of the speed of sound in porous granular media. ASME J. Appl. Mech. 22, 479e486. Choquette, P.W., Pray, L.C., 1970. Geologic nomenclature and classification of porosity in sedimentary carbonates. AAPG Bull. 54, 207e250. El Sayed, A.A., El Batanony, M., Salah, A., 1998. Poisson's ration and reservoir fluid saturation: upper cretaeceous, Egypt. In: MinChem '98, 27e30 September, Siofok, Hungary, pp. 9e14. Elliot, S.E., Wiley, B.F., 1975. Compressional velocities of partially saturated unconsolidated sands. Geophysics 40, 949e954. Folk, R.L., 1959. Practical petrographic classification of limestones. Bull. Am. Ass. Petrol. Geol. 43, 111. Folk, R.L., 1962. Spectral subdivision of limestone types. Am. Ass. Petrol. Geol. Mem. 1, 62. Gassmann, F., 1951. Elasticity of porous media. Vierteljahr. Naturforschenden Gesselschaft 96, 1e23. Gomaa, M.M., Kassab, M.A., EleSayed, N.A., 2014. Study of electrical properties and petrography for carbonate rocks in the Jurassic formations: Sinai Peninsula, Egypt. Arab. J. Geosci. http://dx.doi.org/10.1007/s12517-014-1543-3. Gregory, A.R., 1976. Fluid saturation effects on dynamic elastic properties of sedimentary rocks. Geophysics 41, 895e921. Han, D.H., Nur, A., Morgan, D., 1986. Effect of porosity and clay content on wave velocities in sandstones. Geophysics 51, 2093e2107. Hicks, W.G., Berry, J.E., 1956. Application of continuous velocity logs to determination of fluid saturation of reservoir rocks. Geophysics 21, 739e754. Hughes, D.S., Kelly, J.L., 1952. Variation of elastic wave velocity with saturation in sandstone. Geophysics 17, 739e752. Kahraman, S., 2007. The correlations between the saturated and dry compressional velocity of rocks. Ultrasonics 46, 341e348. Kassab, M.A., 2004. Petrophysical Studies on Jurassic Rocks in Gulf of Suez and North Sinai and its Implementations for Hydrocarbon Exploration. Ph. D. thesis. Ain Shams University, Cairo, Egypt. Kassab, M.A., 2011. The behavior of acoustic wave velocity in some Paleozoic sandstone samples. Petroleum Sci. Technol. 29, 260e270. Minear, M.J., 1982. Clay models and acoustic velocities. In: Presented at the 57th Ann. Mtg., Am. Inst. Min. Metall. Eng., New Orleans. Nur, A., Simmons, G., 1969. The effect of saturation on velocity in low porosity rocks. Earth Planet Sci. Lett. 7, 183e193. Said, R., 1990. The Geology of Egypt. Published for EGPC, Conoco and Repsol. A. A. Balkema Publishers, Brookfield, USA, p. 734. Salah, A., 2001. Effects of Fluids Saturation on the Acoustic Properties of the Upper Cretaceous Reservoirs, Western Desert, Egypt. M.Sc. Thesis. Ain Shams University, p. 175. Schlumberger, 1984. Well Evaluation Conference of Egypt, p. 64. Schlumberger Middle East Service. Vernik, L., Nur, A., 1992a. Petrophysical classification of siliciclastics for lithology and porosity prediction from seismic velocities. AAPG 79, 1295e1309. Vernik, L., Nur, A., 1992b. Ultrasonic velocity and anisotropy of hydrocarbon source rocks. Geophysics 57, 727e735. Wyllie, M.R.J., Gregory, A.R., Gardnet, L.W., 1958. An experimental investigation of factors effecting elastic wave velocities in porous media. Geophysics 23, 450e493.
Contents lists available at ScienceDirect
Journal of African Earth Sciences journal homepage: www.elsevier.com/locate/jafrearsci
Acoustic wave velocity behavior for some Jurassic carbonate samples, north Sinai, Egypt Nahla A. El Sayed, Hesham Abuseda*, Mohamed A. Kassab Egyptian Petroleum Research Institute, Naser City 11727, Cairo, Egypt
a r t i c l e i n f o
a b s t r a c t
Article history: Received 21 January 2015 Received in revised form 9 July 2015 Accepted 14 July 2015 Available online 16 July 2015
Seismic data of reservoir rocks use for understand of risk reduction. Acoustic laboratory measurements have been carried out for 75 carbonate rock samples for both dry and fully saturated collected from Jurassic deposits exposed in the north Sinai at Gebel El-Maghara. This study has been carried out to know more about the behavior of compression wave velocity and shear wave velocity in carbonate rock samples for both dry and fully saturated conditions and to investigate the effect of porosity, permeability and density on both dry and fully saturated acoustic velocities. The compressional wave velocities at dry and fully saturated carbonate rock samples increased with increasing the bulk density and decreasing the porosity, while the porosity decreasing with increasing bulk density, the relationships between the porosity as well as shear wave velocity in dry and fully saturated are in cloud points, with no clear relationships. The relationships between the permeability and both the compressional wave and the shear wave velocities at dry and fully saturated cases could not be identified. The statistical analyses indicate that the compressional wave in the fully saturated is higher than the compressional wave in dry case. The compressional wave velocity of the fully saturated carbonate rock samples were strongly correlated with the compressional wave velocity of the dry rock samples and the derived equation can be used for prediction of the compressional wave velocity of fully saturated rock from the compressional wave velocity of dry rock. The shear wave of the fully saturated carbonate rock samples is a fair correlated with the shear wave of the dry rock samples. © 2015 Elsevier Ltd. All rights reserved.
Keywords: Compressional wave velocity Shear wave velocity Density Poisson's ratio
1. Introduction The studied carbonate rock samples were collected form some of Jurassic deposits exposed at Gebel El-Maghara in the north Sinai. Gebel El-Maghara section is located between longitudes 33 180 e 33 270 E. and latitudes 30 380 e 30 440 N., Fig. 1. All the studied samples representing the exposure section were collected from Masajid Formation, Safa Formation, Bir Maghara Formation, Shusha Formation, Rajabia Formation and Mashaba Formation, which is assigned to Jurassic age, Fig. 2. Said (1990), mentioned that the complete Jurassic section in north Sinai is exposed at Gebel El-Maghara (1980 m.) and during the Jurassic and Cretaceous periods there was not a great change in deposition framework. The dominant rocks are limestones and dolomites. The use of seismic waves for determining reservoir rock properties is of great value to hydrocarbon zonation and exploration.
* Corresponding author. E-mail address: [email protected] (H. Abuseda). http://dx.doi.org/10.1016/j.jafrearsci.2015.07.016 1464-343X/© 2015 Elsevier Ltd. All rights reserved.
The acoustic properties of rocks control the relations between an alternating stress of various frequencies and corresponding strains. Seismic waves velocities for gas, water and oil reservoirs are early discussed by many investigators (e.g. Hughes and Kelly 1952, Brandt 1955, Hicks and Berry 1956, Wyllie et al., 1958, Nur and Simmon 1969, Elliot and Wiley 1975, Gregory 1976, Minear 1982, Han et al., 1986, El Sayed et al., 1998, Vernik and Nur 1992a, b, Salah 2001 and Kassab, M. A., 2011. Compressional and shear waves have different behavior in rocks depending on difference in porosity, fluid saturation, fluid viscosity, density, laminations, fracturing, clay content, mineralogy, compaction and pore space framework. Biot (1956) investigated the seismic wave propagation at high frequencies in an isotropic, liquid saturated porous medium. Two main conclusions may be drawn from Biot's analysis. First, the shear wave velocity values in a liquid saturated porous material will always be less than that in the dry material based on an assumption that micro cracks are negligible. Second, the compressional wave velocity values in the liquid saturated porous material will generally be higher than that in the dry case, except
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Fig. 1. Geological map of Egypt (Schlumberger, 1984).
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Fig. 2. Lithostratigraphic section of Gebel El Maghara, (after Kassab, 2004).
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for material having low bulk compressibility. The technique used to measure acoustic wave velocity is the pulse first arrival technique, in which the travel time is determined for a pulse of compressional or shear waves to pass a known measured thickness of the rock (sample length). Numerous theoretical models have been proposed to describe elastic wave propagation in two phase sedimentary rocks of finite porosity. Perhaps the most successful of these is the model of Biot (1962). The Biot model requires knowledge on the elastic properties of the matrix material, pore fluid saturation, and the elastic properties of the frame or skeleton composing the matrix. The elastic properties of the frame are determined empirically, with little theoretical consideration given to the pore geometry creating the non-uniform porosity. Gregory (1976) stated that the experimental data support Biot's theory for all porosities at confining pressures above 62,000 kPa. However, as pressure declines, the data for low porosity rocks begin to depart from the theory. The interpretation of velocity behavior is slightly difficult due to the effect of many parameters such as rock compressibility, density of matrix and pore fluids, rigidity and rock porosity. Poisson's ratio is defined as the ratio of relative lateral strain to longitudinal strain of uniaxial stress applied to a unit cube of the rock. It is computed from compressional wave velocity Vp and shear wave velocity Vs by the following relation:
2 Vp VS
2 y ¼ 2 Vp 1 2 VS
(1)
with: Vp is compression wave velocity (m/sec), Vs is shear wave velocity (m/sec), and y is Poisson's ratio. Poisson's ratio varies over a range 0.0 < y < 0.5 for all types of dry and saturated rocks (Nur and Simmon, 1969, Gregory, 1976). In addition, Poisson's ratio has been used as an indicator for fracture height determination in charged reservoir rocks (Gregory, 1976). Poisson's ratio varies over a wide range of possible values including negatives values (Gregory, 1976). Negatives Poisson's ratio is observed for real sedimentary rock. High values of the compressional wave velocity are obtained for saturated samples and low values are obtained for dry samples (compressional wave velocity (dry) < compressional wave velocity (saturated) Boulanouar et al. (2013). The shear wave velocity decreases as the water saturation increasing until it reaches 70%e75% and then starts to increase again El Sayed et al. (1998) and Abuseda (2010). Compressional wave velocity of saturated rock can predicted from the compressional wave velocity of dry rock Kahraman (2007). The present work aims to learn more about the behavior of both compressional and shear wave velocity in samples for both dry and fully saturated conditions and to investigate the effect of porosity, permeability and density for both dry and fully saturated acoustic velocities. 2. Material and methods All samples were measured at the Ain Shams University and the Egyptian Petroleum Research Institute, Egypt. Density and porosity of rock samples are closely related. The volumetric mass density of a substance is defined by the ratio of mass (m) and volume (V). In the case of rock samples, a differentiation into bulk density (natural raw density) and grain density becomes evident. The natural raw density considers the total mass and the total volume (V) of the sample. If the sample is dry, the mass (m) is only related to the solid
17
constituents or the mineral grains (mg). The dry density is determined by the equation:
db ¼
mg V
(2)
The grain density, which considers the mass of the solid constituents and only the volume of the solid phase (Vg), is determined in a similar way:
dg ¼
mg Vg
(3)
It becomes evident that the grain density is larger than the dry density for porous media with V > Vg. The volume of the pore space (Vp) results from the difference between the total volume (V) and the volume of the solid phase (Vg). Porosity (Ф) is the most important parameter for evaluating the storage capacity of a porous medium. Porosity was measured by use of helium porosimeter. The porosity of a rock is defined as the ratio of the rock void spaces to its bulk volume, multiplied by one hundred to express it in percent Amyx et al. (1960). This can be expressed in mathematical form as;
F ¼ Vb Vg Vb
(4)
with Ф being the porosity fraction, Vb the bulk volume, cm3, and Vg the grain volume, cm3 The permeability (k) of all samples was measured by a gas permeameter using nitrogen as the flowing fluid. Permeability of a rock is controlled by many factors such as rock pore geometry, cementation, rock texture, grain size, grain shape, and roundness. The permeability (K) in mD was measured by use of core lab permeameter. The Darcy's equation relating permeability to compressible fluids is;
K ¼ ½2000*m*q*L*Pa
i .h A* P12 P22
(5)
with K being the permeability (mD), m the viscosity of air, centipoises, q the gas volume flow rate cm3/sec, P1 the upstream pressure (atmosphere), P2 the downstream pressure (atmosphere) and Pa the atmospheric pressure (atmosphere). Compressional wave velocity and shear wave velocity were measured at room temperature and ambient pressure on cylindrical samples using two channels Sonic Viewer (OYO-170) in the petrophysical lab of the Department of Geophysics at Ain Shams University, Cairo. The compressional and shear wave velocities have been measured at ultrasonic frequencies of 63 kHz and 33 kHz, respectively. Compressional wave velocity (Vp) and shear wave velocity (Vs) measurements were made with the samples in both dry and fully water saturated state, both of them can be computed from the elastic moduli by the following formulas;
Vp ¼
Vs ¼
ðk þ 4m=3Þ 1=2 d
m1=2 d
(6)
(7)
with к being the bulk modulus, m the shear modulus, and d the density. Petrophysical laboratory investigations were carried out to determine compressional wave velocity and shear wave velocity of dry and fully saturated rock samples as well as additional standard parameters for reservoir characterization such as, bulk density, porosity, and permeability. All the petrophysical parameters were
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Table 1 Compilation of minimum, maximum, average values and standard deviations of measured petrophysical parameters for some Jurassic carbonate samples, at Gebel El-Maghara Section. Parameters
dbulk F (%) K, (mD) Vp dry, (m/s) Vs dry, (m/s) Vp/Vs dry Poisson's ratio (y) dry Vp, saturated (m/s) Vs saturated, (m/s) Vp/Vs saturated Poisson's ratio (y) saturated
Carbonate samples Minimum
Maximum
Mean
Std. dev.
2.42 1.00 0.01 4400 1160 1.46 0.06 4120 1310 1.55 0.14
2.74 8.64 4.33 6450 3410 4.37 0.47 7210 3510 4.40 0.47
2.58 3.82 1.14 5382 2134 2.66 0.39 5604 2169 2.75 0.40
0.07 1.76 1.31 520 515 0.64 0.08 641 564 0.74 0.07
with; dbulk in g/cm3 is the bulk density, F % is the porosity, K, mD is the permeability, Vp is compression wave velocity (m/sec), Vs is shear wave velocity (m/sec), Vp/Vs is a ratio between compression and shear wave velocity and y is Poisson's ratio.
determined under ambient conditions. Minimum, maximum, average and standard deviation of porosity, permeability, bulk density, compressional and shear wave velocity of dry and fully saturated rock samples are listed in Table 1.
3. Results and discussion 3.1. Mineralogical investigations of the studied samples The mineralogical investigation of this study has been done in more details by Gomaa et al. (2014). The present carbonate microfacies were classified according to the depositional textures classification of Folk (1959, 1962), the nomenclature and classification of pore spaces were carried out following Choquette and Pray's classification (1970). Based on the mineralogical composition, texture, structure, and faunal content, the present carbonate samples can be classified into five carbonate microfacies, biomicrite (Fig. 3A and B), fossiliferous biomicrite (Fig. 3C), sandy biomicrite, (Fig. 3D), Oobiosparite (Fig. 3E) and foraminiferal biomicrite, (Fig. 3F). Thin sections revealed that, most of the carbonate samples are tight with no visible porosity. In the case of the studied carbonate samples, partial dissolution of the calcitic matrix can be noticed in some parts, caused some vugs which were filled later by sparite cement (Fig. 3B). The dissolution of fossil skeletons and remains increased the pore volume due to particle moldic porosity after leaching of foraminifera skeletons (Fig. 3F). Microfractures filled with silica are noticed through the ground mass (Fig. 3C), and through the shell fragments
Fig. 3. Photomicrograph of the microfacies of carbonate rock samples.
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(Fig. 3F). Calcite cement is the most common cement either as micrite to microsparite matrix and/or as pseudo sparite cement, cementation of the fossil remains and skeletons by micrite cement (Fig. 3A and C), and by sparite cement (Fig. 3B) that reduced and obliterated the present vugy and moldic porosity. The iron oxides are noticed in most of the studied samples. Aggrading neomorphism can be assigned as uniform crystal size patches maintained within the ground mass (Fig. 3A, C, and D), where there is a patch of spary calcite crystals surrounded by patches of microspary calcite. 3.2. Petrophysical relationship Petrophysical parameters porosity, permeability, bulk density and seismic wave velocity of Gebel El-Maghara carbonate rock samples were performed and determined under ambient conditions. To obtain the petrophysical data to learn more about the behavior of compression wave velocity and shear wave velocity in rock samples for both dry and fully saturated conditions and to investigate the effect of porosity, permeability and density on both dry and fully saturated acoustic velocities. 3.2.1. Density, porosity and permeability The obtained bulk density values vary from 2.42 to 2.74 g/cm3 with mean values 2.58 g/cm3 and standard deviation 0.07 g/cm3. The measured porosity values vary from 1.00% to 8.64% with mean values 3.82% and standard deviation 1.76%, while the permeability values distribution varies from 0.01 mD to 4.33 mD, with mean values 1.14 mD and standard deviation 1.31 mD. 3.2.1.1. Density-porosity relationship. The bulk density and the porosity relationship for the studied rock samples, was studied and shown in Fig. 4, this relationship indicates a decrease of porosity with increasing bulk density and characterized by a good correlation coefficient (R ¼ 0.78) between porosity and bulk density for limestone samples. This relationship displays a linear inverse relationship and controlled by the following equation:
Fig. 4. Porosity versus bulk density for carbonate rock samples.
Fig. 5. Porosity versus permeability for carbonate rock samples.
db ¼ 2:70 0:03F
(8)
3.2.1.2. Porosityepermeability relationship. The relationship between the permeability and the porosity in Fig. 5, for the studied rock samples is indicated by a positive trend, the correlation coefficient (R ¼ 0.58) between the porosity and the permeability, means that the porosity is not the main contributor for the rock permeability. The resulting fitting equation read:
k ¼ ½10ð0:27F1:50Þ
Fig. 6. Porosity versus Vp(dry) for carbonate rock samples.
(9)
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The relationship of compressional wave of dry rock samples and permeability, which is shown in Fig. 7, illustrates that the data points are cloudy without any clear trend. The relationship between compressional wave velocity of dry rock samples and bulk density, which is displayed in Fig. 8, shows a fair direct proportional relationship with correlation coefficient of (R ¼ 0.47) and controlled by the following equation:
VpðdryÞ ¼ 3700:50db 4182:54
(11)
The relationships of the compressional wave velocity of dry rock samples with the porosity, permeability and bulk density, indicate that porosity and bulk density has effects on compressional wave velocity of dry rock samples to some extent, while permeability seems very weak related to compressional wave velocity.
3.2.3. Compressional wave velocity of saturated rock samples The measured the compressional wave values of saturated samples (Vpsaturated) vary from 4120 to 7210 m/s, with mean values 5604 m/s and standard deviation 641 m/s. The relationship between the compressional velocity of saturated rock samples and the porosity was plotted in Fig. 9, the correlation coefficient (R ¼ 0.43), displays a linear inverse relationship and controlled by the following equation:
Fig. 7. Permeability versus Vp(dry) for carbonate rock samples.
VpðsaturatedÞ ¼ 6207:95 157:99F 3.2.2. Compressional wave velocity of dry rock samples The measured compressional wave values of dry rock samples (Vpdry) vary from 4400 to 6450 m/s with a mean value of 5382 m/s and a standard deviation 520 m/s. The relationship between the compressional wave velocity of dry rock samples and the porosity is displayed in Fig. 6, it shows a fair inverse relationship with correlation coefficient (R ¼ 0.53), the relationship is a linear inverse relationship and controlled by the following equation:
VpðdryÞ ¼ 5984:25 157:54F
Fig. 8. Bulk density versus Vp(dry) for carbonate rock samples.
(10)
(12)
The relationship of the compressional of saturated rock samples and the permeability, which is displayed in Fig. 10, illustrates that the data points are cloudy without any clear trend. The relationship between the compressional of saturated rock samples and the bulk density, which is displayed in Fig. 11, correlation coefficient decreases to 0.27, and controlled by the following equation:
VpðsaturatedÞ ¼ 2619:82db 1167:27
(13)
The relationships of the compressional velocity of saturated rock samples with the porosity, the bulk density and the permeability show approximately similar behavior compared to the
Fig. 9. Porosity versus Vp(saturated) for carbonate rock samples.
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Fig. 10. Permeability versus Vp(saturated) for carbonate rock samples.
compressional velocity of the dry samples, but the correlation coefficients at the dry state is higher than the correlation coefficients at the saturation state, which mean that the state of saturation has effects on the behavior of the relationships between compressional velocity and the standard parameters for reservoir characterization (e.g. bulk density, porosity, and permeability).
21
Fig. 12. Porosity versus Vs(dry) for carbonate rock samples.
samples and the porosity is displayed in Fig. 12, the resulting data points are flocked together in a cloud of points without any clear trend. The relationship of the shear wave of dry rock samples and the permeability, which is displayed in Fig. 13, does not show any trend. The relationship between the shear wave velocity of dry rock samples and the bulk density, which is plotted in Fig. 14, exhibits a scatter of data points without clear trend.
3.2.4. Shear wave velocity of dry rock samples The measured shear wave velocity values of dry rock samples (Vsdry) vary from 1160 to 3410 m/s with a mean value of 2134 m/s and standard deviation 515 m/s. The relationship between the shear wave velocity of dry rock
3.2.5. Shear wave velocity of saturated rock samples The shear wave velocity values of saturated rock samples Vs(saturated) vary from 1310 to 3510 m/s with a mean value of 2169 m/s and a standard deviation 564 m/s.
Fig. 11. Bulk density versus Vp(saturated) for carbonate rock samples.
Fig. 13. Permeability versus Vs(dry) for carbonate rock samples.
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Fig. 14. Bulk density versus Vs(dry) for carbonate rock samples.
The relationship between the shear wave velocity of saturated rock samples and the porosity, which is displayed in Fig. 15, does not show any trend. The comparison of the shear wave of saturated rock samples and the permeability, which is shown in Fig. 16, does not show any clear trend. The cross plot of the shear wave velocity of saturated rock samples and the bulk density in Fig. 17, exhibits a scatter of data points that is similar to the cross plot of shear wave velocity against the dry density in Fig. 14, the two plots indicate no clear trend.
Fig. 15. Porosity versus Vs(saturated) for carbonate rock samples.
Fig. 16. Permeability versus Vs(saturated) for carbonate rock samples.
3.2.6. Compressional wave velocity of dry rock samples and compressional wave velocity of saturated rock samples relationship The comparison between the compressional velocity of the dry rock samples and compressional velocity of the saturated rock samples, which is displayed in Fig. 18, shows a very good direct proportional relationship with a correlation coefficient of (R ¼ 0.65), which means that the compressional velocity of the saturated rock samples can be predicted from the compressional velocity of the dry rock samples.
VpðsaturatedÞ ¼ 0:80VpðdryÞ þ 1295:11
Fig. 17. Bulk density versus Vs(saturated) for carbonate rock samples.
(14)
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calculated if the shear wave velocity values of the dry rock samples known. 3.2.8. Relationships between compressional wave velocity and shear wave velocity of both dry saturated rock samples The comparison between the compressional velocity and the shear wave velocity of the dry rock samples has been shown in Fig. 20, the graph exhibits that the data points are cloudy without any clear trend, as well as the comparison between the compressional velocity and the shear wave velocity of saturated rock samples (Fig. 21). The relationships of compressional velocity and shear wave velocity of both the dry and the fully saturated rock samples show approximately similar behavior, which means that there are no relationships between compressional velocity and shear wave velocity in the cases of both dry and saturated carbonate samples.
Fig. 18. Vp(dry) versus Vp(saturated) for carbonate rock samples.
3.2.7. Shear wave velocity of dry rock samples and shear wave velocity of saturated rock samples relationship The comparison between the shear wave velocity of the dry rock samples and the shear wave velocity of the saturated rock samples, which is plotted in Fig. 19, indicates a fair direct proportional relationship with a correlation coefficient of (R ¼ 0.52) and controlled by the following equation:
3.2.9. Vp/Vs ratio with shear wave velocity of dry and saturated rock samples Vp/Vs ratio for samples filled with gas (dry rock) is with mean value of 2.66, and for the rock samples filled with water (fully saturated) is with mean value of 2.75, which means that the Vp/Vs ratio of the dry samples is lower than the Vp/Vs ratio of the fully saturated samples. The plots in Figs. 22 and 23 show the relationships between the Vp/Vs ratio and the shear wave velocity for both the dry and the fully saturated rock samples respectively. The data points have a negative trend, which means that the Vp/Vs ratio increases with decreasing the shear wave velocity for both the dry and the fully saturated rock samples.
Eq. (15) means that the shear wave velocity of the saturated rock samples can be linked to the shear wave velocity of the dry rock samples and the shear wave of the saturated rock samples can be
3.2.10. The effect of saturation on Poisson's ratio relations The Poisson's ratio of saturated samples is between 0.14 and 0.47 and the Poisson's ratio of dry samples is between 0.06 and 0.47. The Poisson's ratio of some samples was very low values, may be due to the presence of clay or fine particles to bridge the gaps between grains, where the Poisson's ratios decrease. The studied carbonate rock samples were classified into five carbonate microfacies, biomicrite, fossiliferous biomicrite, sandy
Fig. 19. Vs(dry) versus Vs(saturated) for carbonate rock samples.
Fig. 20. Vp(dry) versus Vs(dry) for carbonate rock samples.
VsðsaturatedÞ ¼ 0:56VsðdryÞ þ 964:98
(15)
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Fig. 21. Vp(saturated) versus Vs(saturated) for carbonate rock samples. Fig. 23. Vs(saturated) versus Vp/Vs(saturated) for carbonate rock samples.
biomicrite, Oobiosparite and foraminiferal biomicrite. Thin sections investigations revealed that, most of carbonate samples are tight with no visible porosity. Diagenesis processes (e.g. cementation, dissolution and neomorphism) have highly effects on the porosity values of the studied carbonate rock samples. The porosity of the studied carbonate rock samples has linked to bulk density. The permeability of most samples increases with increasing the porosity. The compressional velocities at the dry and the fully saturated increased with increasing the bulk density and decreasing the porosity, this means that the behavior of seismic wave (P-wave) velocity through the rock samples was
Fig. 22. Vs(dry) versus Vp/Vs(dry) for carbonate rock samples.
affected by both the porosity and the bulk density. The increasing of the compressional velocity with decreasing the porosity of both the dry and the fully saturated carbonate samples may be due to increase in the rigidity of the rock which are caused by low porosity and then lead to increasing the compressional velocity. The resulting data points between the shear wave velocity and porosity for both the dry and the fully saturated samples are flocked together in a cloud of points without any clear trend, while the porosity decreasing with increasing bulk density this means that the porosity and the bulk density have effects on the behavior of the shear wave velocity through the dry and the fully saturated rock samples. The relationships between permeability and seismic velocities (compressional and shear wave) could not be identified. This means that permeability has no impact in the behavior of seismic velocity through both dry and fully saturated rock samples. The statistical analysis indicate that the compressional velocity is higher in the fully saturated state, where the average value of compressional of saturated rock samples is 5604 m/s and compressional of dry rock samples is 5382 m/s. this means that water saturation has a highly effect on the behavior of the compressional velocity through rock samples, which is in agreement with Gassmann's (1951) theory. The relationships indicate that the compressional velocity of fully saturated rock samples were strongly correlated with the compressional velocity of dry rock samples, and the derived equation can be used for the prediction of the compressional velocity of fully saturated rock from the compressional velocity of dry rock. The shear wave velocity of fully saturated rock samples is a fair correlated with the shear wave velocity of dry rock samples. The Vp/Vs ratio increases with increasing saturations, where the Vp/Vs ratio of dry samples (filled with gas) is lower than the Vp/Vs ratio of saturated samples (filled with water) and the data points have a negative trend between Vp/Vs ratio and shear wave velocity of dry and fully saturated rock samples, which means the Vp/Vs ratio increases with decreasing shear wave. Poisson's ratio sometimes goes to very low values, which may be due to the presence of clay or fine particles that build bridges between grains.
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4. Conclusions Diagenesis processes (e.g. cementation, dissolution and neomorphism) have highly effects on the porosity values of the studied carbonate rock samples. The porosity of the studied carbonate rock samples has linked to the bulk density. The permeability of most samples increases with increasing the porosity. The porosity and the bulk density have highly effects on the behavior of the compressional velocity at the dry and the fully saturated rock samples. The porosity and the bulk density have slightly effects on the behavior of the shear wave velocity through the dry and the fully saturated rock samples. The permeability has no impact in the behavior of the seismic velocity (compressional and shear wave) through both the dry and the fully saturated rock samples. The compressional velocity is higher in the fully saturated state. The compressional velocity of the fully saturated rock can be predicted from the compressional velocity of dry rock. The shear wave velocity of the fully saturated rock samples is a fair correlated with the shear wave velocity of the dry rock samples. The Vp/Vs ratio increases with increasing saturations. Poisson's ratio sometimes goes to very low values, which may be due to the presence of clay or fine particles that build bridges between grains. Acknowledgments The authors would like to thank the reviewers for their great comments that improved and reconstructed the manuscript. Thanks are also due to the editor, whose patience and insightful suggestions have led to a concise revised version. References Abuseda, H., 2010. Petrophysical Modeling of Formation Factor, Porosity and Water Saturation of Bahariya Formation Western Desert, Egypt. Ph.D. Thesis. Ain Shams University, p. 134. Amyx, J.W., Bass Jr., D.M., Whiting, R.L., 1960. Petroleum Reservoir Engineering. Mc Graw Hill Publ. Co., New York, p. 601. Biot, M.A., 1956. Theory of propagation of elastic waves in a fluid saturation porous solid II: high frequency range. J. Acoust. Soc. Am. 28, 179e191. Biot, M.A., 1962. Generalized theory of ultrasonic propagation in porous dissipative media. J. Acoust. Soc. Am. 34, 1254e1264. raud, Y., Harnafi, M., Sebbani, J., Boulanouar, A., Rahmouni, A., Samaouali, M., Ge 2013. Determination of thermal conductivity and porosity of building stone
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