Development of a Resistivity Model That Incorporates Quantitative Directional Connectivity and Tortuosity for Enhanced Assessment of Hydrocarbon Reserves
- Artur Posenato Garcia (University of Texas at Austin) | Zoya Heidari (University of Texas at Austin)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- October 2018
- Document Type
- Journal Paper
- 1,552 - 1,565
- 2018.Society of Petroleum Engineers
- Hydrocarbon Reserves, Electrical Measurements, Rock Fabric, Directional Pore Connectivity
- 8 in the last 30 days
- 171 since 2007
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Success of the strategies to exploit hydrocarbon reservoirs depends on the availability of reliable information about pore structure and spatial distribution of fluids within the pore space. Reliable quantification of directional pore-space connectivity and characterization of pore architecture are, however, challenging. The objectives of this paper include (1) quantifying the directional connectivity of pore space [connected pore volume (PV)] and rock components, (2) identifying geometry-defined fabric features that contribute to the pore-connectivity variations within the same formation (e.g., tortuosity, constriction factor) and introducing analytical/numerical methods and mechanistic models to estimate them, and (3) improving assessment of hydrocarbon saturation by introducing a new resistivity model that incorporates the directional pore-space-connectivity factor.
We introduce a new resistivity model that minimizes calibration efforts and improves assessment of hydrocarbon saturation in complex formations by incorporating a directional connectivity factor. The directional pore-space connectivity is defined as the geometry and texture of the porous media resulting from sedimentary and diagenetic processes, and is estimated with pore-scale images. The directional connectivity factor is a function of electrical tortuosity, and, therefore, we introduce a mechanistic equation that incorporates geometrical features of the pore space to accurately estimate electrical tortuosity. Then, we validate the new tortuosity model against results obtained from a semianalytical streamline algorithm in 3D pore-scale images from each rock type of interest in the formation. The actual electrical tortuosity obtained from numerical simulations is calculated with the geometry of the streamlines associated with the electric current and the corresponding time of flight (TOF) of electric charges.
We successfully applied the introduced method to two carbonate formations. The results confirm that the introduced directional-connectivity factor can detect rock-fabric features, through quantifying the connected PV and tortuosity, and that it is a function of the directional-diffusivity coefficient. The quantification of rock fabric and pore-space connectivity improves the estimation of hydrocarbon saturation by 43% compared with conventional methods. The use of such a parameter for rock-fabric characterization from pore-scale images helps to decrease the need for calibration efforts in the interpretation of borehole geophysical measurements. Just a few cuttings from different rock types are sufficient for the proposed method.
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Archie, G. E. 1942. The Electrical Resistivity Log as an Aid in Determining Some Reservoir Characteristics. Trans. of the AIME 146 (1): 54–62. SPE-942054-G. https://doi.org/10.2118/942054-G.
Barrett, R., Berry, M., Chan, T. F. et al. 1994. Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods, second edition. Philadelphia, Pennsylvania: Society for Industrial and Applied Mathematics (SIAM).
Batycky, R. P., Blunt, M. J., and Thiele, M. R. 1997. A 3D Field-Scale Streamline-Based Reservoir Simulator. SPE Res Eval & Eng 12 (4): 246–254. SPE-36726-PA. https://doi.org/10.2118/36726-PA.
Batycky, R. P. 1997. A Three-Dimensional Two-Phase Field-Scale Streamline Simulator. PhD dissertation, Stanford University, Stanford, California (January 1997).
Berg, C. F. 2012. Re-Examining Archie’s Law: Conductance Description by Tortuosity and Constriction. Physical Review E 86 (4): 046314. https://doi.org/10.1103/PhysRevE.86.046314.
Berg, C. F., Herrick, D., and Kennedy, D. 2016. Geometrical Factor of Conductivity in Rocks: Bringing New Rigor to a Mature Model. Presented at the SPWLA 57th Annual Logging Symposium, Reykjavik, Iceland, 25–29 June. SPWLA-2016-M.
Chen, H. and Heidari, Z. 2016. Quantifying the Directional Connectivity of Rock Constituents and Its Impact on Electrical Resistivity of Organic-Rich Mudrocks. Mathematical Geosciences 48 (3): 285–303. https://doi.org/10.1007/s11004-015-9595-9.
Chi, L. and Heidari, Z. 2016. Directional-Permeability Assessment in Formations With Complex Pore Geometry With a New Nuclear-Magnetic-Resonance-Based Permeability Model. SPE J. 21 (4): 1436–1449. SPE-179734-PA. https://doi.org/10.2118/179734-PA.
Clennell, M. B. 1997. Tortuosity: A Guide Through the Maze. In Developments in Petrophysics, ed. Lovell M. A. and Harvey P. K., Vol. 122, pp. 299–344. London: Special Publications, Geological Society.
Cordazzo, J., Maliska, C. R., and Silva, A. F. C. 2002. Interblock Transmissibility Calculation Analysis for Petroleum Reservoir Simulation. Presented at the 2nd Meeting on Reservoir Simulation, Universidad Argentina de la Empresa, Buenos Aires, 5–6 November.
Datta-Gupta, A. and King, M. J. 1995. A Semi-Analytic Approach to Tracer Flow Modeling in Heterogeneous Permeable Media. Advances in Water Resources 18 (1): 9–24. https://doi.org/10.1016/0309-1708(94)00021-V.
Datta-Gupta, A. and King, M. J. 2007. Streamline Simulation: Theory and Practice. Richardson, Texas: Textbook Series, Society of Petroleum Engineers.
Dong, H. 2007. Micro-CT Imaging and Pore Network Extraction. PhD thesis, Imperial College, London (December 2007).
Ertekin, T., Abou-Kassen, J. H., and King, G. R. 2001. Basic Applied Reservoir Simulation. Richardson, Texas: Textbook Series, Society of Petroleum Engineers.
Garcia, A. P., Heidari, Z., and Rostami, A. 2017. Improved Assessment of Hydrocarbon Saturation in Mixed-Wet Rocks With Complex Pore Structure. Presented at the SPWLA 58th Annual Logging Symposium, Oklahoma City, Oklahoma, 17–21 June. SPWLA-2017-LL.
Heidari, Z. and Garcia, A. P. 2016. Austin Chalk. Digital Rocks Portal, 4 March 2016, https://doi.org/10.17612/P73011 (accessed 18 September 2017).
Herrick, D. C. and Kennedy, W. D. 1994. Electrical Efficiency—A Pore Geometric Theory for Interpreting the Electrical Properties of Reservoir Rocks. Geophysics 59 (6): 918–927. https://doi.org/10.1190/1.1443651.
Herrick, D. C. and Kennedy, W. D. 2009. A New Look at Electrical Conduction in Porous Media: A Physical Description of Rock Conductivity. Presented at the SPWLA 50th Annual Logging Symposium, The Woodlands, Texas, 21–24 June. SPWLA-2009-10142.
Kozeny, J. 1927. Uber kapillare Leitung der Wasser in Boden. Sitzungsber Akad. Wiss., Wien 136 (2a): 271–306.
Lucia, F. J. 1995. Rock-Fabric/Petrophysical Classification of Carbonate Pore Space for Reservoir Characterization. Bull. of the American Association of Petroleum Geologists 79 (9): 1275–1300.
Nunes, J. P., Bijeljic, B., and Blunt, M. J. 2015. Time-of-Flight Distributions and Breakthrough Curves in Heterogeneous Porous Media Using a Pore-Scale Streamline Tracing Algorithm. Transport in Porous Media 109 (2): 317–336. https://doi.org/10.1007/s11242-015-0520-y.
Owen, J. E. 1952. The Resistivity of Fluid-Filled Porous Body. J Pet Technol 4 (7): 169–174. SPE-952169-G. https://doi.org/10.2118/952169-G.
Oyewole, E., Garcia, A. P., and Heidari, Z. 2016. A New Method for Assessment of Directional Permeability and Conducting Pore Network Using Electric Conductance in Porous Media. Presented at the SPWLA 57th Annual Logging Symposium, Reykjavik, Iceland, 25–29 June. SPWLA-2016-TT.
Pollock, D. W. 1988. Semi-Analytical Computation of Path Lines for Finite-Difference Models. Ground Water 26 (6): 743–750. https://doi.org/10.1111/j.1745-6584.1988.tb00425.x.
Prodanovic, M., Esteva, M., Hanlon, M. et al. 2015. Digital Rocks Portal: A Repository for Porous Media Images, https://doi.org/10.17612/P7CC7K (accessed 18 September 2017).
Revil, A., Woodruff, W. F., Torres-Verdi´n, C. et al. 2013. Complex Conductivity Tensor of Anisotropic Hydrocarbon-Bearing Shales and Mudrocks. Geophysics 78 (6): D403–D418. https://doi.org/10.1190/geo2013-0100.1.
Rosenfeld, A. and Pfaltz, J. L. 1968. Distance Functions on Digital Pictures. Pattern Recognition 1 (1): 33–61. https://doi.org/10.1016/0031-3203(68)90013-7.
Schindelin, J., Arganda-Carreras, I., Frise, E. et al. 2012. Fiji: An Open-Source Platform for Biological-Image Analysis. Nature Methods 9 (7): 676–682. https://doi.org/10.1038/nmeth.2019.
Shabro, V., Kelly, S., Torres-Verdi´n, C. et al. 2013. Pore-Scale Modeling of Electrical Resistivity and Permeability in FIB-SEM Images of Hydrocarbon-Bearing Shale. Presented at the SPWLA 54th Annual Logging Symposium, New Orleans, 22–26 June. SPWLA-2013-AA.
Verma, S. and Aziz, K. 1996. Two- and Three-Dimensional Flexible Grids for Reservoir Simulation. Presented at the 5th European Conference on the Mathematics of Oil Recovery, Leoben, Austria, 3–6 September. https://doi.org/10.3997/2214-4609-201406874.
Verma, S. and Aziz, K. 1997. A Control Volume Scheme for Flexible Grids in Reservoir Simulation. Presented at the SPE Reservoir Simulation Symposium, Dallas, 8–11 June. SPE-37999-MS. https://doi.org/10.2118/37999-MS.
Winsauer, W. O., Shearin Jr., H. M., Masson, P. H. et al. 1952. Resistivity of Brine-Saturated Sands in Relation to Pore-Geometry. AAPG Bulletin of the American Association of Petroleum Geologists 36 (2): 230–252. https://doi.org/10.1306/3D9343F4-16B1-11D7-8645000102C1865D.
Wyllie, M. R. J. and Rose, W. D. 1950. Some Theoretical Considerations Related to the Quantitative Evaluation of the Physical Characteristics of Reservoir Rock From Electrical Log Data. J Pet Technol 2 (4): 105–118. SPE-950105-G. https://doi.org/10.2118/950105-G.
Zhang, X. and Knackstedt, M. A. 1995. Direct Simulation of Electrical and Hydraulic Tortuosity in Porous Solids. Geophysical Research Letters 22 (17): 2333–2336. https://doi.org/10.1029/95GL02230.