Applications of digital core analysis and hydraulic flow units in petrophysical characterization
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Abstract
Conventional petrophysical characterizations are often based on direct laboratory measurements. Although they provide accurate results, such measurements are time-consuming and limited by instrument and environment. What’s more, in the geo- resource energy industry, availability and cuttings of core plugs are difficult. Because of these reasons, virtual digital core technology is of increasing interest due to its capability of characterizing rock samples without physical cores and experiments. Virtual digital core technology, also known as digital rock physics, is used to discover, understand and model relationships between material, fluid composition, rock microstructure and macro equivalent physical properties. Based on actual geological conditions, modern mathematical methods and imaging technology, the digital model of the core or porous media is created to carry out physical field numerical simulation. In this review, the methods for constructing digital porous media are introduced first, then the characterization of thin rock cross section and the capillary pressure curve using scanning electron microscope image under mixed wetting are presented. Finally, we summarize the hydraulic flow unit methods in petrophysical classification.
Cited as: Chen, X., Zhou, Y. Applications of digital core analysis and hydraulic flow units in petrophysical characterization. Advances in Geo-Energy Research, 2017, 1(1): 18-30, doi: 10.26804/ager.2017.01.02
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Aguilera, R. A method for estimating hydrocarbon cumulative production distribution of individual wells in naturally fractured carbonates, sandstones, shale gas, coalbed methane and tight gas formations. J. Can. Pet. Technol. 2010, 49(8): 53-58.
Aguilera, R. Flow units: from conventional to tight-gas to shale-gas to tight-oil to shale-oil reservoirs. SPE Reserv. Eval. Eng. 2014, 17(2): 190-208.
Ahrenholz, B., Tlke, J., Lehmann, P., et al. Prediction of capillary hysteresis in a porous material using lattice-Boltzmann methods and comparison to experimental data and a morphological pore network model. Adv. Water Resour. 2008, 31(9): 1151-1173.
Aliyev, E., Saidian, M., Prasad, M., et al. Rock typing of tight gas sands: A case study in Lance and Mesaverde formations from Jonah field. J. Nat. Gas Sci. Eng. 2016, 33: 1260-1270.
Amaefule, J.O., Altunbay, M., Tiab, D., et al. Enhanced reservoir description: Using core and log data to identify hydraulic (flow) units and predict permeability in uncored intervals/wells. Paper SPE 26436 Presented at SPE Annual Technical Conference and Exhibition, Houston, Texas, 3-6 October, 1993.
Andr, H., Combaret, N., Dvorkin, J., et al. Digital rock physics benchmarkspart II: Computing effective properties. Comput. Geosci. 2013, 50: 33-43.
Archie, G.E. Introduction to petrophysics of reservoir rocks. AAPG Bull. 1950, 34(5): 943-961.
Arns, J.Y., Sheppard, A., Arns, C., et al. Pore-level validation of representative pore networks obtained from micro-CT images. Paper SCA2007-15 Presented at the International Symposium of the Society of Core Analysts held in Calgary, Canada, 10-12 September, 2007.
Asmussen, P., Conrad, O., Gnther, A., et al. Semi-automatic segmentation of petrographic thin section images using a “seeded-region growing algorithm”with an application to characterize wheathered subarkose sandstone. Comput. Geosci. 2015, 83: 89-99.
Baker, L.E. Three-phase relative permeability correlations. Paper SPE 17369 Presented at SPE Enhanced Oil Recovery Symposium, Tulsa, Oklahoma, 16-21 April, 1988.
Balhoff, M.T., Wheeler, M.F. A predictive pore-scale model for non-darcy flow in porous media. SPE J. 2009, 14(4): 579-587.
Baveye, P.C., Laba, M., Otten, W., et al. Observer-dependent variability of the thresholding step in the quantitative analysis of soil images and X-ray microtomography data. Geoderma 2010, 157(1-2): 51-63.
Behrang, A., Kantzas, A. A hybrid methodology to predict gas permeability in nanoscale organic materials; a combination of fractal theory, kinetic theory of gases and Boltzmann transport equation. Fuel 2017, 188: 239-245.
Blunt, M.J. An empirical model for three-phase relative permeability. SPE J. 1999, 5(4): 435-445.
Blunt, M.J., Bijeljic, B., Dong, H., et al. Pore-scale imaging and modelling. Adv. Water Resour. 2013, 51: 197-216.
Blunt, M.J., Jackson, M.D., Piri, M., et al. Detailed physics, predictive capabilities and macroscopic consequences for pore-network models of multiphase flow. Adv. Water Resour. 2002, 25(8): 1069-1089.
Borazjani, O., Ghiasi-Freez, J., Hatampour, A. Two intelligent pattern recognition models for automatic identification of textural and pore space characteristics of the carbonate reservoir rocks using thin section images. J. Nat. Gas Sci. Eng. 2016, 35: 944-955.
Byon, C., Kim, S.J. The effect of the particle size distribution and packing structure on the permeability of sintered porous wicks. Int. J. Heat Mass Transf. 2013, 61: 499-504.
Cai, J., Perfect, E., Cheng, C.L., et al. Generalized modeling of spontaneous imbibition based on Hagen-Poiseuille flow in tortuous capillaries with variably shaped apertures. Langmuir 2014a, 30(18): 5142-5151.
Cai, J., San Jos ´e Mart´ınez, F., Mart´ın, M.A., et al. An introduction to flow and transport in fractal models of porous media: Part II. Fractals 2015, 23(1): 1502001.
Cai, J., San Jos ´e Marti´ınez, F., Mart´ın, M. A., et al. An introduction to flow and transport in fractal models of porous media: Part I. Fractals 2014b, 22(3): 1402001.
Cai, J., Yu, B. A discussion of the effect of tortuosity on the capillary imbibition in porous media. Transp. Porous Media 2011, 89(2): 251-263.
Cai, J., Yu, B., Zou, M., et al. Fractal analysis of invasion depth of extraneous fluids in porous media. Chem. Eng. Sci. 2010, 65(18): 5178-5186.
Chalmers, G.R., Bustin, R.M., Power, I.M. Characterization of gas shale pore systems by porosimetry, pycnometry, surface area, and field emission scanning electron microscopy/transmission electron microscopy image analyses: Examples from the barnett, woodford, hay-nesville, marcellus, and doig units. AAPG Bull. 2012, 96(6): 1099-1119.
Chen, S., Doolen, G.D. Lattice Boltzmann method for fluid flows. Annu. Rev. Fluid Mech. 1998, 30(1): 329-364.
Chen, X., Yao, G., Cai, J., et al. Fractal and multifractal analysis of different hydraulic flow units based on micro-CT images. J. Nat. Gas Sci. Eng. 2017, 48: 145-156.
Clarkson, C.R., Haghshenas, B., Ghanizadeh, A., et al. Nanopores to megafractures: Current challenges and methods for shale gas reservoir and hydraulic fracture characterization. J. Nat. Gas Sci. Eng. 2016, 31: 612-657.
Clarkson, C.R., Solano, N., Bustin, R.M., et al. Pore structure characterization of North American shale gas reservoirs using USANS/SANS, gas adsorption, and mercury intrusion. Fuel 2013, 103: 606-616.
Comunian, A., Renard, P., Straubhaar, J. 3D multiple-point statistics simulation using 2D training images. Comput. Geosci. 2012, 40: 49-65.
Deng, H., Hu, X., Li, H.A., et al. Improved pore-structure characterization in shale formations with FESEM technique. J. Nat. Gas Sci. Eng. 2016, 35: 309-319.
Desbois, G., Urai, J.L., Kukla, P.A., et al. High-resolution 3D fabric and porosity model in a tight gas sandstone reservoir: A new approach to investigate microstructures from mm-to nm-scale combining argon beam cross-sectioning and SEM imaging. J. Pet. Sci. Eng. 2011, 78(2): 243-257.
Dijke, M.I.J.V., Piri, M., Helland, J.O., et al. Criteria for three-fluid configurations including layers in a pore with nonuniform wettability. Water Resour. Res. 2007, 43(12): 55-60.
Dong, H., Blunt, M.J. Pore-network extraction from micro-computerized-tomography images. Phys. Rev. E 2009, 80(3): 036307.
Dvorkin, J., Derzhi, N., Diaz, E., et al. Relevance of computational rock physics. Geophysics 2011, 76(5): E141-E153.
Egermann, P., Mejdoub, K., Lombard, J.M., et al. Drainage three-phase flow relative permeability on oil-wet car-bonate reservoir rock types: Experiments, interpretation and comparison with standard correlations. Petrophysics 2014, 55(4): 287-293.
Fu, H., Tang, D., Xu, T., et al. Characteristics of pore structure and fractal dimension of low-rank coal: A case study of Lower Jurassic Xishanyao coal in the southern Junggar Basin, NW China. Fuel 2017, 193: 254-264.
Ge, X., Fan, Y., Li, J., et al. Pore structure characterization and classification using multifractal theory−An application in Santanghu basin of western China. J. Pet. Sci. Eng. 2015, 127: 297-304.
Gundogar, A.S., Ross, C.M., Akin, S., et al. Multiscale pore structure characterization of middle east carbonates. J. Pet. Sci. Eng. 2016, 146: 570-583.
Hajizadeh, A., Safekordi, A., Farhadpour, F.A. A multiple-point statistics algorithm for 3D pore space reconstruction from 2D images. Adv. Water Resour. 2011, 34(10): 1256-1267.
Hamon, G. Field-wide variations of wettability. Paper SPE 63144 Presented at SPE Annual Technical Conference and Exhibition, Texas, 1-4 October, 2000.
Hamon, G., Pellerin, F. Evidencing capillary pressure and relative permeability trends for reservoir simulation. Paper SPE 38898 Presented at SPE Annual Technical Conference and Exhibition, San Antonio, Texas, 5-8 October, 1997.
Helland, J.O., Zhou, Y., Hatzignatiou, D.G. Dynamic capillary pressure curves from pore-scale modeling in mixed-wet-rock images. SPE J. 2013, 18(4): 634-645.
Hikosaka, R., Nagata, F., Tomita, M., et al. Optimization of pore structure and particle morphology of mesoporous silica for antibody adsorption for use in affinity chro-matography. Appl. Surf. Sci. 2016, 384: 27-35.
Hildebrand, T., Ruegsegger, P. A new method for the model-independent assessment of thickness in three-dimensional images. J. Microsc. 1997, 185: 67-75.
Hinai, A.A., Rezaee, R., Esteban, L., et al. Comparisons of pore size distribution: A case from the Western Australian gas shale formations. J. Unconv. Oil Gas Resour. 2014, 8: 1-13.
Hofmann, P., Marschallinger, R., Unterwurzacher, M., et al. Marble provenance designation with object based image analysis: State-of-the-art rock fabric characterization from petrographic micrographs. Austrian J. Earth Sci. 2013, 106(2): 73-82.
Houston, A.N., Otten, W., Baveye, P.C., et al. Adaptive-window indicator kriging: A thresholding method for computed tomography images of porous media. Comput. Geosci. 2013a, 542: 39-48.
Houston, A.N., Schmidt, S., Tarquis, A.M., et al. Effect of scanning and image reconstruction settings in X-ray computed microtomography on quality and segmentation of 3D soil images. Geoderma 2013b, 208: 154-165.
Iassonov, P., Gebrenegus, T., Tuller, M. Segmentation of X-ray computed tomography images of porous materials: A crucial step for characterization and quantitative analysis of pore structures. Water Resour. Res. 2009, 45(9): W09415.
Ismail, I., Gamio, J.C., Bukhari, S.F.A., et al. Tomography for multi-phase flow measurement in the oil industry. Flow Meas. Instrum. 2005, 16(2-3): 145-155.
Izadi, H., Baniassadi, M., Hasanabadi, A., et al. Application of full set of two point correlation functions from a pair of 2D cut sections for 3D porous media reconstruction. J. Pet. Sci. Eng. 2017a, 149: 789-800.
Izadi, H., Sadri, J., Bayati, M. An intelligent system for mineral identification in thin sections based on a cascade approach. Comput. Geosci. 2017b, 99: 37-49.
Izadi, H., Sadri, J., Mehran, N.A. A new intelligent method for minerals segmentation in thin sections based on a novel incremental color clustering. Comput. Geosci. 2015, 81: 38-52.
Kareem, R., Cubillas, P., Gluyas, J., et al. Multi-technique approach to the petrophysical characterization of Berea sandstone core plugs (Cleveland Quarries, USA). J. Pet. Sci. Eng. 2017, 149: 436-455.
Keehm, Y., Mukerji, T., Nur, A. Permeability prediction from thin sections: 3D reconstruction and Lattice−Boltzmann flow simulation. Geophys. Res. Lett. 2004, 31: L04606.
Khoei, A., Hosseini, N., Mohammadnejad, T. Numerical modeling of two-phase fluid flow in deformable fractured porous media using the extended finite element method and an equivalent continuum model. Adv. Water Resour. 2016, 94: 510-528.
Landry, C.J., Karpyn, Z.T., Ayala, O. Relative permeability of homogenous-wet and mixed-wet porous media as determined by pore-scale lattice Boltzmann modeling. Water Resour. Res. 2014, 50(5): 3672-3689.
Lemmens, H., Butcher, A., Botha, P.W. FIB/SEM and automated mineralogy for core and cuttings analysis. Paper SPE 136327 Presented at the SPE Russian oil and gas conference and exhibition, Moscow, Russia 26-28 October, 2010.
Li, Z., Favier, J., D’Ortona, U., et al. An immersed boundary-lattice Boltzmann method for single-and multi-component fluid flows. J. Comput. Phys. 2016, 304(C): 424-440.
Liang, Z., Ioannidis, M., Chatzis, I. Permeability and electrical conductivity of porous media from 3D stochastic replicas of the microstructure. Chem. Eng. Sci. 2000, 55(22): 5247-5262.
Liu, J., Pereira, G.G., Liu, Q., et al. Computational challenges in the analyses of petrophysics using microtomography and upscaling: A review. Comput. Geosci. 2016a, 89: 107-117.
Liu, R., Jiang, Y., Li, B., et al. A fractal model for characterizing fluid flow in fractured rock masses based on randomly distributed rock fracture networks. Comput. Geotech. 2015, 65: 45-55.
Liu, R., Jiang, Y., Li, B., et al. Estimating permeability of porous media based on modified Hagen-Poiseuille flow in tortuous capillaries with variable lengths. Microfluid. Nanofluid. 2016b, 20(8): 120.
Lopez, X., Valvatne, P.H., Blunt, M.J. Predictive network modeling of single-phase non-Newtonian flow in porous media. J. Colloid Interface Sci. 2003, 264(1): 256-265.
Madonna, C., Almqvist, B.S., Saenger, E.H. Digital rock physics: numerical prediction of pressure-dependent ultrasonic velocities using micro-CT imaging. Geophys. J. Int. 2012, 189(3): 1475-1482.
Malpica, N., Ortiz de Solorzano, C., Vaquero, J.J., et al. Applying watershed algorithms to the segmentation of clustered nuclei. Cytometry 1997, 28(4): 289-297.
Marmo, R., Amodio, S., Tagliaferri, R., et al. Textural identification of carbonate rocks by image processing and neural network: Methodology proposal and examples. Comput. Geosci. 2005, 31(5): 649-659.
Martys, N.S., Chen, H.D. Simulation of multicomponent fluids in complex three-dimensional geometries by the lattice Boltzmann method. Phys. Rev. E 1996, 53(1): 743-750.
Meakin, P. Fractals, scaling and growth far from equilibrium. Cambridge, USA, Cambridge University Press, 1998.
Mirzaei-Paiaman, A., Saboorian-Jooybari, H. A method based on spontaneous imbibition for characterization of pore structure: Application in pre-SCAL sample selection and rock typing. J. Nat. Gas Sci. Eng. 2016, 35A: 814-825.
Mynarczuk, M. Description and classification of rock surfaces by means of laser profilometry and mathematical morphology. Int. J. Rock Mech. Min. 2010, 47(1): 138-149.
Mynarczuk, M., Grszczyk, A., lipek, B. The application of pattern recognition in the automatic classification of microscopic rock images. Comput. Geosci. 2013, 60: 126-133.
Mollajan, A., Ghiasi-Freez, J., Memarian, H. Improving pore type identification from thin section images using an integrated fuzzy fusion of multiple classifiers. J. Nat. Gas Sci. Eng. 2016, 31: 396-404.
Naraghi, M.E., Javadpour, F. A stochastic permeability model for the shale-gas systems. Int. J. Coal Geol. 2015, 140: 111-124.
Nie, B., Liu, X., Yang, L., et al. Pore structure characterization of different rank coals using gas adsorption and scanning electron microscopy. Fuel 2015, 158: 908-917.
Oh, W., Lindquist, B. Image thresholding by indicator kriging. IEEE Trans. Pattern Anal. Mach. Intell. 1999, 21(7): 590-602.
Okabe, H., Blunt, M.J. Pore space reconstruction using multiple-point statistics. J. Pet. Sci. Eng. 2005, 46(1-2): 121-137.
Oren, P.E., Bakke, S., Arntzen, O.J. Extending predictive capabilities to network models. SPE J. 1998, 3(4): 324-336.
Otsu, N. A threshold selection method from gray-level histograms. Automatica 1975, 11(285-296): 23-27.
Ougier-Simonin, A., Renard, F., Boehm, C., et al. Microfrac-turing and microporosity in shales. Earth-Sci. Rev. 2016, 162: 198-226.
Pan, N. Analytical characterization of the anisotropy and local heterogeneity of short fiber composites: Fiber fraction as a variable. J. Compos. Mater. 1994, 28(16): 1500-1531.
Peng, S., Hassan, A., Loucks, R.G. Permeability estimation based on thin-section image analysis and 2D flow modeling in grain-dominated carbonates. Mar. Pet. Geol. 2016, 77: 763-775.
Peng, S., Yang, J., Xiao, X., et al. An integrated method for upscaling pore-network characterization and permeability estimation: Example from the mississippian barnett shale. Transp. Porous Media 2015, 109(2): 359-376.
Raabe, D. Overview of the lattice Boltzmann method for nano-and microscale fluid dynamics in materials science and engineering. Model. Simul. Mat. Sci. Eng. 2004, 12(6): R13. Rabbani, A., Ayatollahi, S., Kharrat, R., et al. Estimation of 3-D pore network coordination number of rocks from watershed segmentation of a single 2-D image. Adv. Water Resour. 2016, 94: 264-277.
Rabbani, A., Jamshidi, S. Specific surface and porosity relationship for sandstones for prediction of permeability. Int. J. Rock Mech. Min. 2014, 71: 25-32.
Rabbani, A., Jamshidi, S., Salehi, S. An automated simple algorithm for realistic pore network extraction from micro-tomography images. J. Pet. Sci. Eng. 2014a, 123: 164-171.
Rabbani, A., Jamshidi, S., Salehi, S. Determination of specific surface of rock grains by 2D imaging. J. Geol. Res. 2014b, 20: 141-147.
Ramstad, T., Oren, P.E., Bakke, S. Simulation of two phase flow in reservoir rocks using a lattice Boltzmann method. SPE J. 2009, 15(4): 917-927.
Ross, B., Fueten, F., Yashkir, D. Automatic mineral identifi-cation using genetic programming. Mach. Vision Appl. 2001, 13: 61-69.
Ryazanov, A.V., Dijke, M.I.J.V., Sorbie, K.S. Two-phase pore-network modelling: Existence of oil layers during water invasion. Transp. Porous Media 2009, 80(1): 79-99.
Sachsenhofer, R.F., Koltun, Y.V. Black shales in Ukraine-A review. Mar. Pet. Geol. 2012, 31(1): 125-136.
Sander, R., Pan, Z., Connell, L.D. Laboratory measurement of low permeability unconventional gas reservoir rocks: A review of experimental methods. J. Nat. Gas Sci. Eng. 2017, 37: 248-279.
Saxena, N., Mavko, G. Estimating elastic moduli of rocks from thin sections: Digital rock study of 3D properties from 2D images. Comput. Geosci. 2016, 889-921.
Saxena, N., Mavko, G., Hofmann, R., et al. Estimating permeability from thin sections without reconstruction: Digital rock study of 3D properties from 2D images. Comput. Geosci. 2017, 10: 279-299.
Sezgin, M. Survey over image thresholding techniques and quantitative performance evaluation. J. Electron. Imaging 2004, 13(1): 146-168.
Shan, X., Chen, H. Lattice Boltzmann model for simulating flows with multiple phases and components. Phys. Rev. E 1993, 47(3): 18-15.
Silin, D., Patzek, T. Pore space morphology analysis using maximal inscribed spheres. Phys. A 2006, 371(2): 336-360.
Silin, D., Tomutsa, L., Benson, S.M., et al. Microtomography and pore-scale modeling of two-phase fluid distribution. Transp. Porous Media 2011, 86(2): 495-515.
Singh, N., Singh, T., Tiwary, A., et al. Textural identification of basaltic rock mass using image processing and neural network. Comput. Geosci. 2010, 14(2): 301-310.
Song, W., Yao, J., Li, Y., et al. New pore size distribution calculation model based on chord length and digital image. J. Nat. Gas Sci. Eng. 2016.
Thompson, S., Fueten, F., Bockus, D. Mineral identification using artificial neural networks and the rotating polarizer stage. Comput. Geosci. 2001, 27(9): 1081-1089.
Tomutsa, L., Silin, D.B., Radmilovic, V. Analysis of chalk petrophysical properties by means of submicron-scale pore imaging and modeling. SPE Reserv. Eval. Eng. 2007, 10(3): 285-293.
Van den Berg, E., Meesters, A., Kenter, J., et al. Automated separation of touching grains in digital images of thin sections. Comput. Geosci. 2002, 28(2): 179-190.
Verma, A., Pitchumani, R. Fractal description of microstruc-tures and properties of dynamically evolving porous media. Int. Commun. Heat Mass Transf. 2017, 81: 51-55.
Vidal, D., Ridgway, C., Pianet, G., et al. Effect of particle size distribution and packing compression on fluid per-meability as predicted by lattice-Boltzmann simulations. Comput. Chem. Eng. 2009, 33(1): 256-266.
Virnovsky, G., Vatne, K., Iversen, J., et al. Three-phase capillary pressure measurements in centrifuge at reservoir conditions. Paper SCA2004-19 Presented at the Interna-tional Symposium of the Society of Core Analysts, Abu Dhabi, 2004.
Wang, J., Dong, M. Trapping of the non-wetting phase in an interacting triangular tube bundle model. Chem. Eng. Sci. 2011, 66(3): 250-259.
Wang, J., Li, C., Kang, Q., et al. The lattice Boltzmann method for isothermal micro-gaseous flow and its application in shale gas flow: A review. Int. J. Heat Mass Transf. 2016a, 95: 94-108.
Wang, J., Zhao, J., Zhang, Y., et al. Analysis of the effect of particle size on permeability in hydrate-bearing porous media using pore network models combined with CT. Fuel 2016b, 163: 34-40.
Wang, M., Pan, N. Predictions of effective physical properties of complex multiphase materials. Mat. Sci. Eng. R Rep. 2008, 63(1): 1-30.
Wang, M., Wang, J., Pan, N., et al. Mesoscopic predictions of the effective thermal conductivity for microscale random porous media. Phys. Rev. E 2007, 75(3): 036702.
Wang, W., Kravchenko, A.N., Smucker, A.J.M., et al. Comparison of image segmentation methods in simulated 2D and 3D microtomographic images of soil aggregates. Geoderma 2011, 162(3-4): 231-241.
Wargo, E.A., Kotaka, T., Tabuchi, Y., et al. Comparison of focused ion beam versus nano-scale X-ray computed tomography for resolving 3-D microstructures of porous fuel cell materials. J. Power Sources 2013, 241: 608-618.
Wiegmann, A. Computation of the permeability of porous materials from their microstructure by FFF-Stokes. Fraunhofer-Institut fur Techno-und Wirtschaftsmathe-matik, Fraunhofer (ITWM), 2007.
Wiegmann, A., Bube, K.P. The explicit-jump immersed interface method: Finite difference methods for DEs with piecewise smooth aolutions. SIAM J. Numer. Anal. 2000, 37(3): 827-862.
Wilson, M.J., Wilson, L., Shaldybin, M.V. Clay mineralogy and unconventional hydrocarbon shale reservoirs in the USA. II. Implications of predominantly illitic clays on the physico-chemical properties of shales. Earth-Sci. Rev. 2016, 15: 81-88.
Wolfram, S. A New Kind of Science. Champaign, Wolfram media, 2002.
Xiao, D., Lu, S., Lu, Z., et al. Combining nuclear magnetic resonance and rate-controlled porosimetry to probe the pore-throat structure of tight sandstones. Pet. Exprol. Dev. 2016, 43(6): 1049-1059.
Xie, S., Cheng, Q., Ling, Q., et al. Fractal and multifractal analysis of carbonate pore-scale digital images of petroleum reservoirs. Mar. Pet. Geol. 2010, 27(2): 476-485.
Xu, P., Yu, B. Developing a new form of permeability and Kozeny−Carman constant for homogeneous porous media by means of fractal geometry. Adv. Water Resour. 2008, 31(1): 74-81.
Xu, Z., Teng, Q., He, X., et al. Multiple-point statistics method based on array structure for 3D reconstruction of Fontainebleau sandstone. J. Pet. Sci. Eng. 2012, 100: 71-80.
Yan, Y.Y., Zu, Y.Q., Dong, B. LBM, a useful tool for mesoscale modelling of single-phase and multiphase flow. Appl. Therm. Eng. 2011, 31(5): 649-655.
Yang, C., Zhang, J., Tang, X., et al. Comparative study on micro-pore structure of marine, terrestrial, and transitional shales in key areas, China. Int. J. Coal Geol. 2017, 171: 76-92.
Yiotis, A.G., Tsimpanogiannis, I.N., Stubos, A.K., et al. Pore-network study of the characteristic periods in the drying of porous materials. J. Colloid Interface Sci. 2006, 297(2): 738-748.
Young, I., Crawford, J., Rappoldt, C. New methods and models for characterising structural heterogeneity of soil. Soil Tillage Res. 2001, 61(1): 33-45.
Yu, B., Cheng, P. A fractal permeability model for bi-dispersed porous media. Int. J. Heat Mass Transf. 2002, 45(14): 2983-2993.
Yu, B., Cheng, P., Zhan, X., et al. Pore-scale modeling of electrical and fluid transport in Berea sandstone. Geophyscics 2010, 75(75): F135-F142. Zhao, Y., Sun, Y., Liu, S., et al. Pore structure characterization of coal by NMR cryoporometry. Fuel 2017, 190: 359-369.
Zhou, Y., Helland, J., Hatzignatiou, D.G. Pore-scale modeling of waterflooding in mixed-wet-rock images: Effects of initial saturation and wettability. SPE J. 2014, 19(1): 88-100.
Zhou, Y., Helland, J.O., Hatzignatiou, D.A. Dimensionless capillary pressure function for imbibition derived from pore-scale modelling in mixed-wet rock images. SPE J. 2012, 18(2): 296-308.
Zhou, Y., Helland, J.O., Hatzignatiou, D.G. Computation of three-phase capillary pressure curves and fluid configurations at mixed-wet conditions in 2D rock images. SPE J. 2016, 21(1): 152-169.
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