3D Reconstruction of Porous Media From a 2D Section and Comparisons of Transport and Elastic Properties
- Morteza Elahi Naraghi (University of Texas at Austin) | Kyle Spikes (University of Texas at Austin) | Sanjay Srinivasan (Pennsylvania State University)
- Document ID
- Society of Petroleum Engineers
- SPE Reservoir Evaluation & Engineering
- Publication Date
- May 2017
- Document Type
- Journal Paper
- 342 - 352
- 2017.Society of Petroleum Engineers
- Transport Properties, Digital Rock Physics, 3-D Reconstruction of Porous Media, Elastic Properties
- 1 in the last 30 days
- 547 since 2007
- Show more detail
- View rights & permissions
|SPE Member Price:||USD 12.00|
|SPE Non-Member Price:||USD 35.00|
High-resolution, 3D microstructure images of rocks can be used to compute the transport and elastic properties of those samples by use of a digital rock-physics approach. Those properties are complex functions of the pore-size distribution, geometry, and morphology, and necessitate the use of accurate 3D volumes. Because of the limited availability of 3D microstructure images of rocks, several attempts to construct 3D images from 2D images have been made.
In this study, we propose a new stochastic method to reconstruct a 3D image of the rock by use of only a 2D section of the imaged rock sample. Our method is derived from a simple observation that the pores are gradually deformed from one section to the next. Therefore, the first step is to generate multiple independent realizations by performing multiple-point-statistics (MPS)-based stochastic simulations. These simulations represent independent 2D scans through the rock volume. Next, a succession of images is generated spanning two adjacent independent sections. These images consist of gradually morphed features from one section to those in the next independent section. Juxtaposing these 2D images results in the reconstructed 3D image.
We implement the algorithm on a Berea sandstone rock for which the 3D high image was available for comparison. We calculate the spatial connectivity in the third direction, and confirmed that the proposed method can retrieve the connectivity in the third direction accurately. We also compute transport and elastic properties from the reconstructed image and from the original image to verify that this method reproduces the appropriate spatial statistics and pore-size distribution, geometry, and morphology. We also compare the numerical results with laboratory measurements performed on the sample. The results obtained by use of the reconstructed image reveal that the numerically calculated properties are similar to the measured values. We compare the mismatch of transport and elastic properties with the original measurements with that of the previous reconstruction algorithm. These comparisons show that the proposed simulation method has the same accuracy as previous ones. However, the proposed method is much more computationally efficient than the other algorithms, which are dependent on simulation of all 2D layers, mainly because of the faster MPS algorithm and the fact that the simulation is being performed only for the independent layers instead of all the layers.
The proposed methodology is an accurate method to reconstruct a 3D representative sample of a rock given only one 2D thin section. The algorithm is computationally efficient and faster than the previously introduced algorithm, and can easily be used to characterize samples for which 3D images are difficult to obtain in terms of both time and expense.
|File Size||1 MB||Number of Pages||11|
Adler, P. M., Jacquin, C. G. and Quiblier, J. A. 1990. Flow in Simulated Porous Media. Int. J. Multiphas. Flow 16 (4): 691–712. https://doi.org/10.1016/0301-9322(90)90025-E.
Al-Kharusi, A. S. and Blunt, M. J. 2007. Network Extraction from Sandstone and Carbonate Pore Space Images. J. Pet. Sci. Eng. 56 (4): 219–231. https://doi.org/10.1016/j.petrol.2006.09.003.
Andrä, H., Combaret, N., Dvorkin, J. et al. 2013. Digital Rock Physics Benchmarks—Part I: Imaging and Segmentation. Comput. Geosci. 50 (January): 25–32. https://doi.org/10.1016/j.cageo.2012.09.005.
Caers, J. 2003. History Matching Under Training-Image-Based Geological Model Constraints. SPE J. 8 (3): 218–226. SPE-74716-PA. https://doi.org/10.2118/74716-PA.
Caers, J. 2007. Comparing the Gradual Deformation with the Probability Perturbation Method for Solving Inverse Problems. Meth. Geol. 39 (1): 27–52. https://doi.org/10.1007/s11004-006-9064-6.
Daly, C. 2005. Higher Order Models using Entropy, Markov Random Fields and Sequential Simulation. In Geostatistics Banff 2004, Vol. 1, ed. O. Leuangthong and C. V. Deutsch, 215–224. Dordrecht, The Netherlands: Springer.
Dong, H. and Blunt, M. J. 2009. Pore-Network Extraction from Micro-Computerized-Tomography Images. Phys. Rev. E 80 (3): 036307. https://doi.org/10.1103/PhysRevE.80.036307.
Dong, H., Touati, M. and Martin, J. B. 2007. Pore Network Modeling: Analysis of Pore Size Distribution of Arabian Core Samples. Presented at the SPE Middle East Oil and Gas Show and Conference, Manama, Bahrain, 11–14 March. SPE-105156-MS. https://doi.org/10.2118/105156-MS.
Drach, B., Drach, A. and Tsukrov, I. 2013. Characterization and Statistical Modeling of Irregular Porosity in Carbon/Carbon Composites based on X-Ray Microtomography Data. ZAMM 93 (5): 346–366. https://doi.org/10.1002/zamm.201100190.
Drach, A., Drach, B. and Tsukrov, I. 2014. Processing of Fiber Architecture Data for Finite Element Modeling of 3D Woven Composites. Adv. Eng. Softw. 72 (June): 18–27. https://doi.org/10.1016/j.advengsoft.2013.06.006.
Eskandaridalvand, K. and Srinivasan, S. 2010. Reservoir Modelling of Complex Geological Systems--A Multiple-Point Perspective. J Can Pet Technol 49 (8): 59–69. SPE-139917-PA. https://doi.org/10.2118/139917-PA.
Gao, M., He, X., Teng, Q., et al. 2015. Reconstruction of Three-Dimensional Porous Media from a Single Two-Dimensional Image using Three-Step Sampling. Phys. Rev. E 91 (1): 013308. https://doi.org/10.1103/PhysRevE.91.013308.
Hajizadeh, A. and Farhadpour, Z. 2012. An Algorithm for 3D Pore Space Reconstruction from a 2D Image Using Sequential Simulation and Gradual Deformation with the Probability Perturbation Sampler. Transport Porous Med. 94 (3): 859–881. https://doi.org/10.1007/s11242-012-0028-7.
Hajizadeh, A., Safekordi, A. and Farhadpour, F. A. 2011. A Multiple-Point Statistics Algorithm for 3D Pore Space Reconstruction from 2D Images. Adv. Water Resour. 34 (10): 1256–1267. https://doi.org/10.1016/j.advwatres.2011.06.003.
Hastings, W. K. 1970. Monte Carlo Sampling Methods Using Markov Chains and Their Applications. Biometrika 57 (1): 97–109. https://doi.org/10.2307/2334940.
Hazlett, R. D. 1995. Simulation of Capillary-Dominated Displacements in Microtomographic Images of Reservoir Rocks. Transport Porous Med. 20 (1–2): 21–35. https://doi.org/10.1007/BF00616924.
Hazlett, R. D. 1997. Statistical Characterization and Stochastic Modeling of Pore Networks in Relation to Fluid Flow. Math. Geol. 29 (6): 801–822. https://doi.org/10.1007/BF02768903.
Hu, L. Y., Blanc, G. and Noetinger, B. 2001. Gradual Deformation and Iterative Calibration of Sequential Stochastic Simulations. Math. Geol. 33 (4): 475–489. https://doi.org/10.1023/A:1011088913233.
Kashib, T. and Srinivasan, S. 2006. A Probabilistic Approach to Integrating Dynamic Data in Reservoir Models. J. Pet. Sci. Eng. 50 (3–4): 241–257. https://doi.org/10.1016/j.petrol.2005.11.002.
Imperial College London. 2016. Petroleum Engineering and Rock Mechanics group image repository of the Imperial College London, http://www3.imperial.ac.uk/earthscienceandengineering/research/perm/porescalemodelling.
Keehm, Y., Mukerji, T. and Nur, A. 2004. Permeability Prediction from Thin Sections: 3D Reconstruction and Lattice-Boltzmann Flow Simulation. Geophys. Res. Lett. 31 (4). https://doi.org/10.1029/2003GL018761.
Kirkpatrick, S., Gelatt, C. D. and Vecchi, M. P. 1983. Optimization by Simulated Annealing. Science 220 (4598): 671–680. https://doi.org/10.1126/science.220.4598.671.
Lesmes, D. P. and Frye, K. M. 2001. Influence of Pore Fluid Chemistry on the Complex Conductivity and Induced Polarization Responses of Berea Sandstone. J. Geophys. Res.-Sol. Ea. 106 (B3): 4079–4090. https://doi.org/10.1029/2000JB900392.
Liang, Z., Ioannidis, M. A. and Chatzis, I. 2000. Permeability and Electrical Conductivity of Porous Media from 3D Stochastic Replicas of the Microstructure. Chem. Eng. Sci. 55 (22): 5247–5262. https://doi.org/10.1016/S0009-2509(00)00142-1.
Manwart, C., Torquato, S. and Hilfer, R. 2000. Stochastic Reconstruction of Sandstones. Phys. Rev. E 62 (1): 893. https://doi.org/10.1103/PhysRevE.62.893.
Mariethoz, G., Renard, P. and Straubhaar, J. 2010. The Direct Sampling Method to Perform Multiple-Point Geostatistical Simulations. Water Resour. Res. 46 (11). https://doi.org/10.1029/2008WR007621.
Moulinec, H. and Suquet, P. 1998. A Numerical Method for Computing the Overall Response of Nonlinear Composites with Complex Microstructure. Comput. Method Appl. M. 157 (1): 69–94. https://doi.org/10.1016/S0045-7825(97)00218-1.
Okabe, H. and Blunt, M. J. 2004. Prediction of Permeability for Porous Media Reconstructed Using Multiple-Point Statistics. Phys. Rev. E 70 (6): 066135. https://doi.org/10.1103/PhysRevE.70.066135.
Quiblier, J. A. 1984. A New Three-Dimensional Modeling Technique for Studying Porous Media. J. Colloid Interf. Sci. 98 (1): 84–102. https://doi.org/10.1016/0021-9797(84)90481-8.
Rezaee, H., Mariethoz, G., Koneshloo, M. et al. 2013. Multiple-Point Geostatistical Simulation Using the Bunch-Pasting Direct Sampling Method. Comput. Geosci. 54 (April): 293–308. https://doi.org/10.1016/j.cageo.2013.01.020.
Silin, D. and Patzek, T. 2006. Pore Space Morphology Analysis Using Maximal Inscribed Spheres. Physica A 371 (2): 336–360. https://doi.org/10.1016/j.physa.2006.04.048.
Strebelle, S. 2002. Conditional Simulation of Complex Geological Structures Using Multiple-Point Statistics. Math. Geol. 34 (1): 1–22. https://doi.org/10.1023/A:1014009426274.
Tahmasebi, P. and Sahimi, M. 2012. Reconstruction of Three-Dimensional Porous Media Using a Single Thin Section. Phys. Rev. E 85 (6): 066709. https://doi.org/10.1103/PhysRevE.85.066709.
Tahmasebi, P. and Sahimi, M. 2015. Geostatistical Simulation and Reconstruction of Porous Media by a Cross-Correlation Function and Integration of Hard and Soft Data. Transport Porous Med. 107 (3): 871–905. https://doi.org/10.1007/s11242-015-0471-3.
Tahmasebi, P., Hezarkhani, A. and Sahimi, M. 2012. Multiple-Point Geostatistical Modeling Based on the Cross-Correlation Functions. Computat. Geosci. 16 (3): 779–797. https://doi.org/10.1007/s10596-012-9287-1.
Tahmasebi, P., Javadpour, F. and Sahimi, M. 2015a. Three-Dimensional Stochastic Characterization of Shale SEM Images. Transport Porous Med. 110 (3): 521–531. https://doi.org/10.1007/s11242-015-0570-1.
Tahmasebi, P., Javadpour, F. and Sahimi, M. 2015b. Multiscale and Multiresolution Modeling of Shales and Their Flow and Morphological Properties. Sci. Rep. 5: 16373. https://doi.org/10.1038%2Fsrep16373.
Tahmasebi, P., Javadpour, F., Sahimi, M. et al. 2016. Multiscale Study for Stochastic Characterization of Shale Samples. Adv. Water Resour. 89 (March): 91–103. https://doi.org/10.1016/j.advwatres.2016.01.008.
Zhang, T., Switzer, P. and Journel, A. 2006. Filter-Based Classification of Training Image Patterns for Spatial Simulation. Math. Geol. 38 (1): 63–80. https://doi.org/10.1007/s11004-005-9004-x.