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0 2000 4000 6000 8000 0 2000 4000 6000 8000 Vp Lab (m/sec) Vp Predicted (m/sec) The Effects of Internal Pore Structure on Compressional Sonic Velocity in Sandstone and Carbonate Rocks Muhammad Nur Ali Akbar MSc Petroleum Geoengineering, University of Miskolc – Egyetemvaros 3515, Miskolc, Hungary Introduction References Studies examining the relationship between velocity and porosity has been conducted by several researchers, who showed that this relationship is not linear, while at first it was believed that this relationship was linear (Wyllie et al., 1956). This non-linear behavior is certainly expected from the presence of heterogeneity parameters such as clay content (Han et al., 1986) and distribution which in turn affects the size, shape and relationships or connectivity between the pores, uniformity of grain size and grain arrangement, and the different type of mineral compositions and rock compaction. However, the studies corelating velocity and permeability are rarely found in success. Therefore, the complex architecture of porous rock leads us to perform an extensive research for better understanding on how the acoustic wave propagates through the porous medium and how the pore geometric details show the correlation between velocity and porosity- permeability. Data Used Methods Analysis and Results Sandstone – The laboratory data used of sandstone were compiled by Prasad (2003). There are 67 core samples and the data provide the measurements of velocity at similar pressure around 40 MPa and saturated by distilled water along with porosity and permeability. All values used here were measured on fully saturated rocks under varying pressures using the pulse transmission technique (Prasad, 1998). The source of the sample is from several formations in United Kingdom, China, Europe, and USA. The carbonate rock samples were collected from Weger et al. (2009). There are 120 samples with high-quality measurements of the velocity, porosity, permeability and the geological description. The source of the samples is from several formations in the Middle East, Southeast Asia, and Australia. The compressional velocity of the core samples was measured in the saturated condition with distilled water. The pore fluid inside the sleeve at pressure of 2 MPa while the applied effective pressure was 20 MPa. Rock typing of Pore Geometry-Structure is applied in this study by using PGS rock type curve (Wibowo and Permadi, 2013). Pore geometry here is simply an equivalent to mean hydraulic radius (Harmsen, 1955) and pore structure is a pore attribute that is influenced by pore shape, pore tortuosity, and specific internal surface area, which all make up the architecture of the pore system and texture of the rock. The rock type follows the rule of similarity the Kozeny constant (Kozeny, 1927). Following is the Kozeny equation re-written in two forms: where a is a constant and b is the power law exponent. Then, this rock typing method is applied to core analysis data and the grouping result of each relation can be extended to seismic parameters to create strong interrelationships of velocity with pore geometry, and pore structure Nomenclatures Symbols Parameters Units ɸ Porosity Fraction k Permeability mD τ Tortuosity Fraction F s Pore Shape Factor Fraction S b Specific Internal Surface Area Micron 2 V p Compressional Velocity m/s ɸ 0.5 = a ɸ 3 ɸ 0.5 = ɸ 1 2 0.5 ɸ 3 = 1 2 Sandstone Carbonate y = 2231.3x 0.1314 R² = 0.9593 y = 2400.3x 0.1459 R² = 0.9601 y = 2492.5x 0.1786 R² = 0.8306 y = 2791.1x 0.211 R² = 0.8649 y = 3218.2x 0.2144 R² = 0.8479 y = 3668.2x 0.2602 R² = 0.9232 y = 4458.8x 0.3365 R² = 0.9638 y = 4992.4x 0.3869 R² = 0.998 0 1000 2000 3000 4000 5000 6000 7000 8000 0.01 0.1 1 10 100 1000 Vp (m/sec) (k/Ф) 0.5 Vp vs. Pore Geometry y = 2128.1x 0.0586 R² = 0.967 y = 2233.5x 0.0627 R² = 0.9676 y = 2211.2x 0.0743 R² = 0.8475 y = 2396.8x 0.0812 R² = 0.8743 y = 2674.1x 0.0806 R² = 0.8626 y = 2871.6x 0.0909 R² = 0.9227 y = 3072.7x 0.1097 R² = 0.9753 y = 3114.1x 0.1172 R² = 0.9969 0 1000 2000 3000 4000 5000 6000 7000 8000 0.001 0.1 10 1000 100000 10000000 Vp (m/sec) k/Ф 3 Vp vs. Pore Structure V p vs Pore Structure (k/ɸ 3 ) RT Equations d q R 2 3 Vp = 2128.1 (k/ɸ 3 ) 0.0586 2128.0 0.0586 0.9670 4 Vp = 2233.5 (k/ɸ 3 ) 0.0627 2233.5 0.0627 0.9676 5 Vp = 2211.2 (k/ɸ 3 ) 0.0743 2211.2 0.0743 0.8475 6 Vp = 2396.8 (k/ɸ 3 ) 0.0812 2396.8 0.0812 0.8743 7 Vp = 2674.1 (k/ɸ 3 ) 0.0806 2674.1 0.0806 0.8626 8 Vp = 2871.6 (k/ɸ 3 ) 0.0909 2871.6 0.0909 0.9227 9 Vp = 3072.7 (k/ɸ 3 ) 0.1097 3072.7 0.1097 0.9753 10 Vp = 3114.1 (k/ɸ 3 ) 0.1172 3114.1 0.1172 0.9969 General Equation Vp = d( k/ 3 )] q Vp vs. Pore Geometry [(k/ɸ) 0.5 ] RT Equations c p R 2 3 Vp = 2231.3 √(k/ɸ) 0.1314 2231.0 0.1314 0.9593 4 Vp = 2400.3 √(k/ɸ) 0.1459 2400.0 0.1459 0.9601 5 Vp = 2492.5 √(k/ɸ) 0.1786 2492.5 0.1786 0.8306 6 Vp = 2791.1 √(k/ɸ) 0.211 2791.1 0.2110 0.8649 7 Vp = 3218.2 √(k/ɸ) 0.2144 3218.2 0.2144 0.8479 8 Vp = 3668.2 √(k/ɸ) 0.2602 3668.2 0.2602 0.9232 9 Vp = 4458.8 √(k/ɸ) 0.3365 4458.8 0.3365 0.9638 10 Vp = 4992.4 √(k/ɸ) 0.3869 4992.4 0.3869 0.9980 General Equation Vp= c[(k/) 0.5 ] p 0 2000 4000 6000 8000 0 2000 4000 6000 8000 Vp Lab (m/sec) Vp Predicted (m/sec) • Avg. Relative Error : 7.9% • Avg. Absolute Error : 351.85 m/s • Avg. Relative Error : 8.3% • Avg. Absolute Error : 373.60 m/s Conclusions Acknowledgements: The described study was carried out as part of the EFOP-3.6.1-16- 2016-00011 “Younger and Renewing University – Innovative Knowledge City – institutional development of the University of Miskolc aiming at intelligent specialization” project implemented in the framework of the Szechenyi 2020 program. The realization of this project is supported by the European Union, co-financed by the European Social Fund. Thank you too for demonstrator program of Geophysics Department and TEKH University of Miskolc supporting this study and conference. Appreciation to SPE Student chapter University of Miskolc for arranging this attendance to Zagreb, Croatia. Contact Information Tel: +36 203903511 Email: [email protected] Web: www.uni-miskolc.hu This study represents ideal systems where P-wave velocity values are systematically controlled by similarity of internal pore structure which is similarity in both tortuosity and pore shape factor. In the given rock type, either pore geometry or pore structure is increase owing to the decrease specific internal surface area and porosity but increasing mean hydraulic radius, which all give rise to an increase in saturated P-wave velocity in both sandstone and carbonate. The best obtained prediction of P-wave velocity of sandstone was made by the relationship between V p and pore geometry (k/ɸ) 0.5 , giving average relative error of 5.23%. However, the prediction of P-wave velocity of carbonate is showed the best result by the relationship between V p and pore structure (k/ɸ 3 ) with average relative error of 7.9%. Furthermore, estimation of sonic logs can be generated once the well logs analysis provides the corresponding permeability and porosity values. y = 2236.4x 0.1161 R² = 0.9192 y = 2399.6x 0.1236 R² = 0.9237 y = 2562.3x 0.1792 R² = 0.9699 y = 2916.8x 0.2185 R² = 0.9955 y = 3062.4x 0.2302 R² = 0.9962 y = 3698.6x 0.292 R² = 0.9959 y = 4063.6x 0.3109 R² = 0.9235 y = 4899.1x 0.3744 R² = 0.9886 y = 6421.8x 0.4487 R² = 0.9501 0 1000 2000 3000 4000 5000 6000 0.01 0.1 1 10 100 1000 Vp (m/sec) (k/ɸ) 0.5 Vp vs Pore Geometry y = 2109.8x 0.0489 R² = 0.9216 y = 2197x 0.0523 R² = 0.9421 y = 2257.6x 0.0695 R² = 0.9767 y = 2411.3x 0.0792 R² = 0.9924 y = 2467.7x 0.0803 R² = 0.9951 y = 2703.5x 0.0951 R² = 0.9955 y = 2788.9x 0.0943 R² = 0.9226 y = 2954.5x 0.1036 R² = 0.9753 y = 3058x 0.1045 R² = 0.9489 0 1000 2000 3000 4000 5000 6000 7000 0.001 0.1 10 1000 100000 10000000 Vp (m/sec) k/ɸ 3 Vp vs Pore Structure As can be seen in left and right figures, all the data points cover nine rock type lines (RT-4 to RT-13) for sandstone and eight rock types for carbonate (RT-3 to RT-10). Either plot V p versus pore geometry or V p versus pore structure shows that all the data points are separated to form clusters with very strong coefficient of determination R 2 (more than 0.9), each specifically representing a certain rock type. The general formed equations based on these relationships are V p =c [(k/) 0.5 ] p and V p =d [(k/ 3 )] q , where c and d are constants and p and q are exponents, which are all rock type dependent. V p vs. Pore Geometry [(k/ɸ) 0.5 ] RT Equations c p R² 4 Vp = 2236.4 √(k/ɸ) 0.1161 2236.4 0.1161 0.9192 5 Vp = 2399.6 √(k/ɸ) 0.1236 2399.6 0.1236 0.9237 6 Vp = 2562.3 √(k/ɸ) 0.1792 2562.3 0.1792 0.9699 7 Vp = 2916.8 √(k/ɸ) 0.2185 2916.8 0.2185 0.9955 8 Vp = 3062.4 √(k/ɸ) 0.2302 3062.4 0.2302 0.9962 9 Vp = 3698.6 √(k/ɸ) 0.292 3698.6 0.292 0.9959 10 Vp = 4063.6 √(k/ɸ) 0.3109 4063.6 0.3109 0.9235 11 Vp = 4899.1 √(k/ɸ) 0.3744 4899.1 0.3744 0.9886 13 Vp = 6421.8 √(k/ɸ) 0.4487 6421.8 0.4487 0.9501 General Equation Vp= c[(k/) 0.5 ] p V p vs Pore Structure (k/ɸ 3 ) RT Equations d q R 2 4 Vp = 2109.8 (k/ɸ 3 ) 0.0489 2109.8 0.0489 0.9216 5 Vp = 2197.0 (k/ɸ 3 ) 0.0523 2197.0 0.0523 0.9421 6 Vp = 2257.6 (k/ɸ 3 ) 0.0695 2257.6 0.0695 0.9767 7 Vp = 2411.3 (k/ɸ 3 ) 0.0792 2411.3 0.0792 0.9924 8 Vp = 2467.7 (k/ɸ 3 ) 0.0803 2467.7 0.0803 0.9951 9 Vp = 2703.5 (k/ɸ 3 ) 0.0951 2703.5 0.0951 0.9955 10 Vp = 2788.9 (k/ɸ 3 ) 0.0943 2788.9 0.0943 0.9226 11 Vp = 2954.5 (k/ɸ 3 ) 0.1036 2954.5 0.1036 0.9753 13 Vp = 3058.0 (k/ɸ 3 ) 0.1045 3058.0 0.1045 0.9489 General Equation Vp = d( k/ 3 )] q The important finding is that all rock types have the same behavior, V p tends to increase with an increase in Kozeny constant. However, for a given ɸ for all the groups, V p increases remarkably with a decrease in Kozeny constant. These all mean that V p increases with either an increase in the complexity of pore systems or, at the same pore complexity, a decrease in specific internal surface area. V p tends to become higher as pore geometry and pore structure variable increase. As pore geometry here is equivalent to the mean hydraulic radius, V p increases with this radius. Meanwhile, plot V p against pore structure has much similar behavior as the relationship between pore geometry variable and V p . 0 1000 2000 3000 4000 5000 6000 7000 0 1000 2000 3000 4000 5000 6000 7000 Vp Lab (m/s) Vp Predicted (m/s) • Avg. Relative Error : 8.63 % • Avg. Absolute Error : 343.13 m/s 0 1000 2000 3000 4000 5000 6000 7000 0 1000 2000 3000 4000 5000 6000 7000 Vp Lab (m/s) Vp Predicted (m/s) • Avg. Relative Error : 5.23 % • Avg. Absolute Error : 208.92 m/s • Han, D. H., Nur, A. and Morgan, D. [1986] Effects of Porosity and Clay Content on Wave Velocities in Sandstones. Geophysics, 51, 2093–2107. http://dx.doi.org/ 10.1190/1.1442062. • Harmsen, G. J. [1955] The Concept "Hydraulic Radius" in Porous Media. Petroleum Transactions, AIME, 204. 274-277. • Kozeny, J. [1927] Uber kapillare leitung des wassers im boden (Aufstieg Versikerung und Anwendung auf die Bemasserung), Sitzungsber Akad, Wiss, Wein, Math-Naturwiss, KL 136(Ila):271–306. • Prasad, M. [2003] Velocity-permeability relations within hydraulic units. Geophysics, 68:108–117. https://doi.org/10.1190/1.1543198 . • Weger RJ, Eberli GP [2009] Quantification of pore structure and its effect on sonic velocity and permeability on carbonate. AAPG Bull 93(10):1297–1317. https://doi.org/10.1306/05270909001 . • Wibowo, A.S., and Permadi P. [2013] A Type Curve for Carbonates Rock Typing. Proceedings of the IPTC Beijing, China, 26-28 March. IPTC-16663. • Wyllie, M.R.J., Gregory, A.R. and Gardner, I.W. [1956] Elastic wave velocities in heterogeneous and porous media. Geophysics, 12(1):41–70. This poster is prepared for the 6 th Annual Student Energy Congress 2019 (March 4 th –7 th ) in Zagreb, Croatia
