Search for Articles:
Journal:
Subject:
MOSP / Journal / Advanced Energy Systems and Intelligent Geoscience

Journal Menu

Home
Journal Info
Editorial Board
For Authors
For Reviewers
Ethics & Policies
Article Processing Charges

Journal Browser

Vol.2 (2026) Iss. 1
Vol.1 (2025) Iss. 1

Table of Contents

Abstract
Full Text
Funding
References
Review

A Review of Numerical Simulation and Connectivity Analysis in Complex Media Reservoirs

Wentao Zhan1,2,*, Yixin Zhang3, Liang Pu4, Zhaolin Pu3

1 Western Research Institute, Yangtze University, Karamay 834000, China.
2 Key Laboratory of Exploration Technologies for Oil and Gas Resources, Ministry of Education, Yangtze University, Wuhan 430100, China.
3 College of Petroleum Engineering, Yangtze University, Wuhan 430100, China.
4 Engineering Technology Supervision Center, Changqing Oilfield Company, Petro China, xian, shanxi, 710000, China.
* Correspondence: Wentao Zhan, E-mail: zhanwt1996@163.com
 
AESIG, 2026, 2(1), 4-31; https://doi.org/10.58244/aesig.253469
Received : 29 Dec 2025 / Accepted : 06 Jan 2026 / Published : 28 Feb 2026

Funding

This research was no funding provided.

Download
Cite
Abstract
 
This paper reviews the key technologies and challenges in numerical reservoir simulation and inter-well connectivity analysis for complex media. Addressing the issues of complex fluid flow patterns and strong heterogeneity in deep-layer, deep-water, and unconventional reservoirs, this study systematically summarizes the advantages and disadvantages of three mainstream approaches: reservoir engineering, numerical simulation, and machine learning. Four core components of numerical reservoir simulation are analyzed, with a detailed comparison of various computational domain discretization techniques, including Cartesian, corner-point, PEBI grids, and meshless methods. Furthermore, the principles and applicability of six major numerical models (e.g., equivalent continuum, dual-porosity, and discrete fracture models) used to characterize complex media such as fractures and vugs are discussed in depth. Regarding inter-well connectivity analysis, the progress of traditional reservoir engineering methods—such as logging, well testing, and chemical analysis—as well as numerical methods like streamline models and physical connectivity network models are summarized. Finally, the paper identifies current technical deficiencies in handling anisotropy, characterization efficiency of complex geometries, and quantitative characterization of dynamic connectivity, providing directions for future research.
 
Keywords: Complex media reservoirs; Computational domain discretization; Numerical simulation; Inter-well connectivity

Full Text

Download the full text PDF for viewing and using it according to the license of this paper.

Funding

This research was no funding provided.

References

  1. Jia Chengzao, Wang Zugang, Jiang Lin, et al. Progress and scientific and technological issues of shale oil exploration and development in China [J]. World Petroleum Industry, 2024, 31(04): 1-11+13.
  2. Luo Pingya, Zhu Suyang. Theoretical and technical foundation for establishing a large-scale coalbed methane industry with 100 billion cubic meters in China [J]. Acta Petrolei Sinica, 2023, 44(11): 1755-1763.
  3. Liu He. Application of artificial intelligence in digital transformation of oil and gas exploration and development is the trend of the times [J]. Oil Forum, 2023, 42(03): 1-9+47.
  4. Peng Kai, Fang Duo, Wu Chigong. Generation of orthogonal numerical grid and calculation of two-dimensional flow field [J]. Journal of Hydraulic Engineering, 1990(4): 9.
  5. Xiao Hanshan, Chen Zuobin, Luo Gang, et al. Application of adaptive Cartesian grid in numerical simulation of flow field around 3D complex shapes [C]// Proceedings of the 4th Cross-Strait Symposium on Computational Fluid Dynamics. 2003: 9.
  6. Hou Xiaolin, Yang Bo. Surface model extraction algorithm of 3D geological bodies based on pillar grid [J]. Computer Engineering and Applications, 2017, 53(11): 1-6.
  7. Wang Daigang, Hou Jian, Xing Xuejun, et al. An improved PEBI grid generation method based on front-advancing [J]. Chinese Journal of Computational Physics, 2012, 29(5): 9.
  8. Xie Haibing, Huan Guanren, Guo Shangping, et al. Two-dimensional two-phase flow numerical simulation with PEBI grid [J]. Acta Petrolei Sinica, 1999, (02): 65-69+6.
  9. Tian Junwei, Cheng Gang. Improved Delaunay triangulation algorithm [J]. Journal of Xi’an Technological University, 2011, 31(4): 6.
  10. Shi Yijing, Shao Guojian, Ding Shengyong. Generation method of polygonal element grid based on Voronoi structure [J]. Journal of Henan University of Science and Technology (Natural Science), 2016, 37(05): 51-55+6-7.
  11. He J. Numerical Simulation of a Class I Gas Hydrate Reservoir Depressurized by a Fishbone Well[J]. Processes 2023, 11, 771.
  12. Lei Q, Doonechaly N G, Tsang C F. Modelling fluid injection-induced fracture activation, damage growth, seismicity occurrence and connectivity change in naturally fractured rocks[J]. International Journal of Rock Mechanics and Mining Sciences, 2021, 138: 104598.
  13. Russell D, Wang Z J. A Cartesian grid method for modeling multiple moving objects in 2D incompressible viscous flow[J]. Journal of Computational Physics, 2003, 191(1): 177-205.
  14. Eldredge J D. A method of immersed layers on Cartesian grids, with application to incompressible flows[J]. Journal of Computational Physics, 2022, 448: 110716.
  15. Zhao P, Xu J, Liu X, et al. A computational fluid dynamics-discrete element-immersed boundary method for Cartesian grid simulation of heat transfer in compressible gas–solid flow with complex geometries[J]. Physics of Fluids, 2020, 32(10).
  16. Ponting D K. Corner point geometry in reservoir simulation[C]//ECMOR I-1st European conference on the mathematics of oil recovery. European Association of Geoscientists & Engineers, 1989: cp-234-00003.
  17. Andersen O, Nilsen H M I I, Raynaud X. Coupled geomechanics and flow simulation on corner-point and polyhedral grids[C]//SPE Reservoir Simulation Conference[J]. SPE, 2017: D031S010R004.
  18. Xu Y, Fernandes B R B, Marcondes F, et al. Embedded discrete fracture modeling for compositional reservoir simulation using corner-point grids[J]. Journal of Petroleum Science and Engineering, 2019, 177: 41-52.
  19. Mao Xiaoping, Zhang Zhiting, Qian Zhen. Analysis of geological models expressed by corner-point grid and its application in the simulation of hydrocarbon accumulation process [J]. Journal of Geology, 2012(03): 45-53.
  20. Li Muzhe, Hou Xiaolin, Yang Bo, et al. Surface extraction algorithm of complex geological models based on corner-point grid [J]. Computer Engineering and Applications, 2016, 52(9): 6.
  21. Lin Chunyang. Research, development and application of reservoir numerical simulator based on PEBI grid [D]. University of Science and Technology of China, 2010.
  22. Heinemann Z E. Interactive generation of irregular simulation grids and its practical applications[C] SPE University of Tulsa Centennial Petroleum Engineering Symposium. SPE, 1994: SPE-27998-MS.
  23. Liu G R, Gu Y T. An introduction to meshfree methods and their programming[M]. Springer Science & Business Media, 2005.
  24. Zhao Hui, Liu Wei, Rao Xiang, et al. Connection element method for reservoir numerical simulation [J]. Scientia Sinica Technologica, 2022, 52(12): 1869-1886.
  25. Zhao H, Zhan W, Yuhui Z, et al. A connection element method: Both a new computational method and a physical data-driven framework—-Take subsurface two-phase flow as an example[J]. Engineering Analysis with Boundary Elements, 2023, 151: 473-489.
  26. Snow D T. Rock fracture spacings, openings and porosities[J]. Journal of the Soil Mechanics & Foundations Division, 1968, 94(1):73-92.
  27. Oda, Mc. “Permeability tensor for discontinuous rock masses[J].” Geotechnique 35. 4 (1985): 483-495.
  28. Lough M F, S H Lee, and J Kamath. An efficient boundary integral formulation for flow through fractured porous media[J]. Journal of Computational Physics 143. 2 (1998): 462-483.
  29. Lee S H, C L Jensen, and M F Lough. An efficient finite difference model for flow in a reservoir with multiple length-scale fractures[J]. SPE Annual Technical Conference and Exhibition. Society of Petroleum Engineers, 1999.
  30. Fang Sidong. Research on numerical simulation of fractured horizontal wells using hybrid boundary element method [D]. China University of Petroleum (Beijing), 2017.
  31. Muskat M, Meres M W. The flow of heterogeneous fluids through porous media[J]. Physics, 1936, 7(9): 346-363.
  32. An Yongsheng. Analysis of the impact of reservoir anisotropy on the productivity of fishbone multilateral wells [J]. Journal of Southwest Petroleum University (Science & Technology Edition), 2011, 33(03): 145-148+201.
  33. Møyner O, Lie K A. A multiscale two-point flux-approximation method[J]. Journal of Computational Physics, 2014, 275: 273-293.
  34. Rao X, He X, Du K, et al. A novel projection-based embedded discrete fracture model (pEDFM) for anisotropic two-phase flow simulation using hybrid of two-point flux approximation and mimetic finite difference (TPFA-MFD) methods[J]. Journal of Computational Physics, 2024, 499: 112736.
  35. Sandve T H, Berre I, Nordbotten J M. An efficient multi-point flux approximation method for discrete fracture–matrix simulations[J]. Journal of Computational Physics, 2012, 231(9): 3784-3800.
  36. Chen Q Y, Wan J, Yang Y, et al. A new multipoint flux approximation for reservoir simulation[C]//SPE Reservoir Simulation Conference. SPE, 2007: SPE-106464-MS.
  37. Aavatsmark I. An introduction to multipoint flux approximations for quadrilateral grids[J]. Computational Geosciences, 2002, 6: 405-432.
  38. Contreras F R L, Lyra P R M, Souza M R A, et al. A cell-centered multipoint flux approximation method with a diamond stencil coupled with a higher order finite volume method for the simulation of oil–water displacements in heterogeneous and anisotropic petroleum reservoirs[J]. Computers & Fluids, 2016, 127: 1-16.
  39. Chen Q Y, Wan J, Yang Y, et al. Enriched multi-point flux approximation for general grids[J]. Journal of Computational Physics, 2008, 227(3): 1701-1721.
  40. Barenblatt G I, Zheltov I P, Kochina I N. Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks[J]. Journal of Applied Mathematics & Mechanics, 1960, 24(5):1286-1303.
  41. Warren J E, Root P J. The Behavior of Naturally Fractured Reservoirs[J]. Society of Petroleum Engineers Journal, 1963, 3(3):245-255.
  42. Coats K H. Implicit compositional simulation of single-porosity and dual-porosity reservoirs[J]. SPE 18427, SPE Reservoir Simulation Symposium, Houston, TX, 1989, 6-8.
  43. Lim K T, Aziz K. Matrix-fracture transfer shape factors for dual porosity simulators[J]. Journal of Petroleum Science and Engineering, 1995, Vol. 13, 169-178.
  44. Kazemi H. Seth M S, Thomas G W. Pressure Transient Analysis of Naturally Fractured Reservoirs with Uniform Fracture Distribution[J]. Society of Petroleum Engineers Journal, 1969, 9(4):451-462.
  45. James R Glman, Hossein Kazemi. Improvements in simulation of naturally fractured Reservoirs[C]// SPE 10511. 1982.
  46. Deswaan O A. Analytic solutions for determining naturally fractured reservoir properties by well testing[C]// SPE 5346. 1976.
  47. Cigun L. The unsteady radial flow of compressible liquids through a medium with multiple porosity[C]//SPE International Oil and Gas Conference and Exhibition in China. SPE, 1982: SPE-10580-MS.
  48. Abdassah D, Ershaghi I. Triple- porosity systems for representing naturally fractured reservoirs[J]. SPE 13409. 1986.
  49. Wu Y S, Moridis G, Berkeley L, et al. A multicontinuum model for gas production in tight fractured reservoirs[C]//SPE 118944. SPE Hydraulic Fracturing Technology Conference. Society of Petroleum Engineers. 2009.
  50. Pruess K. GMINC- A mesh generator for flow simulations in fractured reservoirs[J]. Lawrence Berkeley Laboratory. 2008.
  51. Gilman J R, Kazemi H. Improvements in simulation of naturally fractured reservoirs[J]. Society of Petroleum Engineers Journal, 1982, 23:4(4):695-707.
  52. Wu Y S, Pruess K. A Multiple-Porosity Method for Simulation of Naturally Fractured Petroleum Reservoirs[J]. Spe Reservoir Engineering, 1988, 3(1):327-336.
  53. Pruess K. TOUGH2: A general-purpose numerical simulator for multiphase fluid and heat flow[J]. Nasa Sti/recon Technical Report N, 1991, 92.
  54. Noorishad J, Mehran M. An upstream finite element method for solution of transient transport equation in fractured porous media[J]. Water Resources Research, 1982, 18(3):588-596.
  55. Karimi-Fard M, Firoozabadi A. Numerical Simulation of Water Injection in 2D Fractured Media Using Discrete-Fracture Model[J]. SPE Reservoir Evaluation & Engineering, 2001, 4.
  56. Karimi-Fard M, Durlofsky L J, Aziz K. An Efficient Discrete-Fracture Model Applicable for General-Purpose Reservoir Simulators[J]. SPE Journal, 2004, 9(2): 227-236.
  57. Monteagudo J E P, Firoozabadi A. Control‐volume method for numerical simulation of two‐phase immiscible flow in two and three dimensional discrete‐fractured media[J]. Water Resources Research, 2004, 40(7):7405.
  58. Matthi S K, Mezentsev A, Belayneh M. Control-Volume Finite-Element Two-Phase Flow Experiments with Fractured Rock Represented by Unstructured 3D Hybrid Meshes[C]// SPE Reservoir Simulation Symposium. Society of Petroleum Engineers, 2005.
  59. Chavent G, Roberts J. A unified physical presentation of mixed, mixed-hybrid finite element method and standard finite difference approximations for the determination of velocities in water flow problems[J]. Advances in Water Resources, 1991, 14(6): 329–33.
  60. Fang S, Cheng L, Ayala L F. A coupled boundary element and finite element method for the analysis of flow through fractured porous media[J]. Journal of Petroleum Science and Engineering, 2017, 152: 375-390.
  61. Lee S H, Jensen C L, Lough M F. Efficient finite-difference model for flow in a reservoir with multiple length-scale fractures[J]. SPE Journal, 2000, 5(03): 268-275.
  62. Moinfar A, Varavei A, Sepehrnoori K, et al. Development of an efficient embedded discrete fracture model for 3D compositional reservoir simulation in fractured reservoirs[J]. SPE Journal, 2014, 19(02): 289-303.
  63. Wu Y, Cheng L, Fang S, et al. A Green element method-based discrete fracture model for simulation of the transient flow in heterogeneous fractured porous media[J]. Advances in Water Resources, 2020, 136:103489.
  64. Rao X, Cheng L, Cao R, et al. An efficient three-dimensional embedded discrete fracture model for production simulation of multi-stage fractured horizontal well[J]. Engineering Analysis with Boundary Elements, 2019, 106: 473-492.
  65. Ţene M, Bosma S B M, Al Kobaisi M S, et al. Projection-based embedded discrete fracture model (pEDFM)[J]. Advances in Water Resources, 2017, 105: 205-216.
  66. Jiang J, Younis R M. An improved projection-based embedded discrete fracture model (pEDFM) for multiphase flow in fractured reservoirs[J]. Advances in water resources, 2017, 109: 267-289. 
  67. Rao X, Cheng L, Cao R, et al. A modified projection-based embedded discrete fracture model (pEDFM) for practical and accurate numerical simulation of fractured reservoir[J]. Journal of Petroleum Science and Engineering, 2020, 187: 106852.
  68. Li J, Yu W, Guerra D, et al. Modeling wettability alteration effect on well performance in Permian basin with complex fracture networks[J]. Fuel, 2018, 224: 740-751.
  69. Dachanuwattana S, Jin J, Zuloaga-Molero P, et al. Application of proxy-based MCMC and EDFM to history match a Vaca Muerta shale oil well[J]. Fuel, 2018, 220: 490-502.
  70. Wang Y, Shahvali M. Discrete fracture modeling using Centroidal Voronoi grid for simulation of shale gas plays with coupled nonlinear physics[J]. Fuel, 2016, 163: 65-73.
  71. Shakiba M, de Araujo Cavalcante Filho J S, Sepehrnoori K. Using Embedded Discrete Fracture Model (EDFM) in numerical simulation of complex hydraulic fracture networks calibrated by microseismic monitoring data[J]. Journal of Natural Gas Science and Engineering, 2018, 55: 495-507.
  72. Rao X, Cheng L, Cao R, et al. A modified embedded discrete fracture model to study the water blockage effect on water huff-n-puff process of tight oil reservoirs[J]. Journal of Petroleum Science and Engineering, 2019, 181: 106232.
  73. Ren G, Jiang J, Younis R M. A Model for Coupled Geomechanics and Multiphase Flow in Fractured Porous Media Using Embedded Meshes[J]. Advances in Water Resources, 2018, 122: 113-130.
  74. Ren G, Rami Y. An integrated numerical model for coupled poro-hydro-mechanics and fracture propagation using embedded meshes[J]. Computer Methods in Applied Mechanics and Engineering, 2021, 376(1): 113606.
  75. Yan X, Huang Z Q, Yao J, et al. An efficient numerical hybrid model for multiphase flow in deformable fractured-shale reservoirs[J]. SPE Journal, 2018, 23(04): 1412-1437.
  76. Hou T Y, Wu X H. A multiscale finite element method for elliptic problems in composite materials and porous media[J]. Journal of computational physics, 1997, 134(1): 169-189.
  77. Efendiev Y R, Hou T Y, Wu X H. Convergence of a nonconforming multiscale finite element method[J], SIAM Journal on Numerical Analysis. 2000, 37(3): 888–910.
  78. Zhang N, Yan B, Sun Q, et al. Improving multiscale mixed finite element method for flow simulation in highly heterogeneous reservoir using adaptivity[J]. Journal of Petroleum Science and Engineering, 2017, 154: 382-388.
  79. Aarnes J E , Krogstad S, Lie K A. A hierarchical multiscale method for two-phase flow based upon mixed finite elements and nonuniform coarse grids, Multiscale Model[J]. Multiscale Modeling & Simulation, 2006, 5(2): 337–363.
  80. Zhang Q, Huang Z, Yao J. et al. Multiscale Mimetic Method for Two-Phase Flow in Fractured Media Using Embedded Discrete Fracture Model[J]. Advances in Water Resources, 2017, 107: 180–190.
  81. Hughes T J, Feijóo G R, Mazzei L, et al. The variational multiscale method—a paradigm for computational mechanics[J]. Computer methods in applied mechanics and engineering, 1998 166 (1) : 3–24.
  82. Jenny P, Lee S, Tchelepi H. Multi-scale finite-volume method for elliptic problems in subsurface flow simulation[J], Journal of Computational Physics, 2003, 187 (1): 47–67.
  83. Zhang Q, Huang Z, Yao J. et al. A Multiscale Mixed Finite Element Method with Oversampling for Modeling Flow in Fractured Reservoirs Using Discrete Fracture Model[J]. Journal of Computational and Applied Mathematics, 2017, 323: 95–110.
  84. Zhang N, Sun Q, Wang Y T, et al. A Locally Conservative Multiscale Finite Element Method for Multiphase Flow Simulation through Heterogeneous and Fractured Porous Media[J]. Journal of Computational and Applied Mathematics. 343 (2018): 501-519.
  85. Hajibeygi H, Karvounis D, Jenny P. A hierarchical fracture model for the iterative multiscale finite volume method[J]. Journal of Computational Physics, 2011, 230(24): 8729-8743.
  86. Ţene M, Al Kobaisi M S, Hajibeygi H. Algebraic multiscale method for flow in heterogeneous porous media with embedded discrete fractures (F-AMS) [J]. Journal of Computational Physics, 2016, 321: 819-845.
  87. Kang Zhijiang, Di Yuan, Zhao Yanyan, et al. Characteristics of fluid flow in vugs for fractured-vuggy reservoirs [J]. Petroleum Geology and Oilfield Development in Daqing, 2014, 33(03): 82-85.
  88. Cui Shuyue, Di Yuan. Numerical simulation of fractured-vuggy reservoirs based on gravity segregation assumption [J]. Journal of Basic Science and Engineering, 2020, 28(02): 331-341.
  89. Cheng Qian. Study on flow laws of fractured-vuggy carbonate reservoirs in Tahe Oilfield [D]. Graduate University of Chinese Academy of Sciences (Institute of Porous Flow Fluid Mechanics), 2009.
  90. Li Yang. Theory and method of development for carbonate fractured-vuggy reservoirs in Tahe Oilfield [J]. Acta Petrolei Sinica, 2013, 34(01): 115-121.
  91. Wang Yong. Study on oil-water and oil-gas two-phase flow laws in fractured-vuggy carbonate reservoirs [D]. China University of Petroleum (Beijing), 2018.
  92. Yao Jun, Huang Zhaoqin, Wang Zisheng, et al. Discrete fracture-vug network model for flow in fractured-vuggy reservoirs [J]. Acta Petrolei Sinica, 2010, 31(05): 815-819+824.
  93. Huang Zhaoqin, Yao Jun, Li Yajun, et al. Permeability analysis of fractured-vuggy media based on homogenization theory [J]. Scientia Sinica Technologica, 2010, 40(09): 1095-1103.
  94. Zhang Hongfang. Research on discrete numerical simulation method for fracture-vug units in carbonate reservoirs [J]. Petroleum Drilling Techniques, 2015, 43(02): 71-77.
  95. Zhang Dongli, Cui Shuyue, Zhang Yun. Multi-scale fracture simulation method for fractured-vuggy reservoirs [J]. Chinese Journal of Hydrodynamics (Series A), 2019, 34(01): 13-20.
  96. Yao Jun, Zhang Xu, Huang Zhaoqin, et al. Coupled numerical simulation of fluid flow and heat transfer in fractured-vuggy karstic geothermal reservoirs [J]. Natural Gas Industry, 2022, 42(04): 107-116.
  97. Yan Xia, Huang Zhaoqin, Li Yang, et al. A hybrid model for fractured-vuggy reservoirs based on discrete fracture-vug network model [J]. Journal of Central South University (Science and Technology), 2017, 48(9): 2474-2483.
  98. Liu L, Fan W, Sun X, et al. Gas condensate well productivity in fractured vuggy carbonate reservoirs: A numerical modeling study[J]. Geoenergy Science and Engineering, (2023), 225, 211694.
  99. Kou J, Sun S, Wu Y. Mixed finite element-based fully conservative methods for simulating wormhole propagation[J]. Computer Methods in Applied Mechanics & Engineering, 2016, 298: 279-302.
  100. Yuan T, Ning Y, Qin G. Numerical Modeling and Simulation of Coupled Processes of Mineral Dissolution and Fluid Flow in Fractured Carbonate Formations[J]. Transport in Porous Media, 2016, 114(3): 747-775.
  101. Zhao Lei. Numerical simulation of discrete medium network model for fractured-vuggy reservoirs [D]. Southwest Petroleum University, 2013.
  102.  Huang Zhaoqin. Theoretical research on multi-scale two-phase flow simulation based on discrete fracture-vug network model [D]. China University of Petroleum (East China), 2012.
  103.  Li Longxin. Research on numerical simulation method of multi-scale carbonate fractured-vuggy reservoirs [D]. Southwest Petroleum University, 2013.
  104. Chorin A J, Numerical study of slightly viscous flow[J]. J. of Fluid Mechanics, 1973, 57, 785-796.
  105. Bernard P S. A deterministic vortex sheet method for boundary layer flow[J]. J. of Computational Physics, 1995, 117, 132-145.
  106. Girault V. Theory of a GDM on irregular networks[J]. SIAM journal on numerical analysis, 1974, 11: 260-282.
  107. Pavlin V and Perrone N, Finite difference energy rechniques for arbitrary meshes[J]. Comput Struct. 1975, 5: 45-58.
  108. Krok J, Orkisz J. A unified approach to the FE generalized variational FD method for nonlinear mechanics[J]. Concept and numerical approach. 1989, 353-362. Springer-Verlag.
  109. Lucy L. A Numerical Approach to Testing the Fission Hypothesis[J], Astron. J.1977, 82, 1013 - 1024.
  110. Gingold R A, Moraghan J J. Smooth particle hydrodynamics:theory and applications to non spherical stars[J]. Monthly notices of the royal astronomical society, 1977, 181, 375-389.
  111. Nayroles B, Touzot G, Villon P. Generalizing the finite element method: diffuse approximation and diffuse elements[J]. Computational mechanics, 1992, 10(5): 307-318.
  112. Belytschko T, Lu Y Y, Gu L. Element‐free Galerkin methods[J]. International journal for numerical methods in engineering, 1994, 37(2): 229-256.
  113. Onate E, Idelsohn S, Zienkiewicz O C. et al. A finite point method in computational mechanics: Applications to convective transport and fluid flow[J]. International journal for numerical methods in engineering, 1996, 39: 3839~3866.
  114. Zhu T, Zhang J, Atluri S N. A local boundary integral equation(LBIE) method in computational mechanics, and a meshless discretization approach[J]. Computational mechanics, 1998, 21: 223~235.
  115. Zhu T, Zhang J, Atluri S N. A meshless local boundary integral equation (LBIE) method for solving nonlinear problems[J]. Computational mechanics, 1998, 22 : 174-186.
  116. Atluri S N, Sladek J, Sladek V et al. The Loacl boundary integral equation(LBIE) and it’s meshless implementation for linear elasticity[J]. Computational mechanics, 2000, 25 :180~198.
  117. Atluri S N, Zhu T. A new meshless local Petrov-Galerkin(MLPG) approach in computational mechanics[J]. Computational mechanics, 1998, 22:117~127.
  118. Atluri S N, Zhu T. The meshless local Petrov-CGalerkin (MLPG) approach for solving problems in elasto-statics[J]. Computational mechanics, 2000, 25:169~179.
  119. Atluri S N, Cho J Y, Kim H G. Analysis of thin beams, using the meshless local Petrov- Galerkin method, with generalized moving least squares interpolations[J]. Computational mechanics. 1999, 24 : 334~347.
  120. Atluri S N, Kim H G, Cho J Y. A critical assessment of the truly Meshless Local Petrov-Galerkin (MLPG), and Local Boundary Integral Equation (LBIE) methods[J]. Computational mechanics, 1999, 24 : 348~372.
  121. Zhang X, Xiao‐Hu Liu, Kang‐Zu Song, et al. Least-squares collocation meshless method[J]. International Journal for Numerical Methods in Engineering, 2010, 51(9):1089-1100.
  122. Zhang Xiong, Hu Wei, Pan Xiaofei. Weighted least-squares meshless method [J]. Acta Mechanica Sinica, 2003, 35(4): 425-431.
  123. Yan L , Xiong Z , Mingwan L U . Meshless Least-Squares Method for Solving the Steady-State Heat Conduction Equation[J]. Tsinghua Science & Technology, 2005, 10(001):61-66.
  124. Li Yu-kun. Meshless Numerical Well-Test on Complex Fault-Block Reservoir[D]. China University of petroleum, 2007.
  125. Benito J J, Ureña F, Gavete L. Influence of several factors in the generalized finite difference method[J]. Applied Mathematical Modelling, 2001, 25(12): 1039–53.
  126. Benito J J, Ureña F, Gavete L, et al. An h-adaptive method in the generalized finite differences[J]. Computer methods in applied mechanics and engineering, 2003, 192(5–6): 735–59.
  127. Ureña F, Salete E, Benito J J, et al. Solving third- and fourth-order partial differential equations using GFDM: application to solve problems of plates[J]. International Journal of Computer Mathematics, 2012, 89(3): 366-376.
  128. Wang Y, Gu Y, Fan C M, et al. Domain-decomposition generalized finite difference method for stress analysis in multi-layered elastic materials[J], Engineering Analysis with Boundary Elements. 2018, 94:94–102.
  129. Li P W, Fan C M. Generalized finite difference method for two-dimensional shallow water equations[J], Engineering Analysis with Boundary Elements. 2017, 80: 58–71.
  130. Fu Z J, Xie Z Y, Ji S Y, et al. Meshless generalized finite difference method for water wave interactions with multiple-bottom-seated-cylinder-array structures[J], Ocean Engineering, 2020, 195:106736.
  131. Rao X. An upwind generalized finite difference method (GFDM) for meshless analysis of heat and mass transfer in porous media[J]. Computational Particle Mechanics, 2023, 10: 533–554.
  132. Benito J J, Ure˜na F, Gavete L, et al. Implementations with generalized finite differences of the displacements and velocity-stress formulations of seismic wave propagation problem[J], Applied Mathematical Modelling, 2017, 52: 1–14.
  133. Liu Y, Rao X, Zhao H, et al. Generalized finite difference method based meshless analysis for coupled two-phase porous flow and geomechanics[J]. Engineering Analysis with Boundary Elements, 2023, 146: 184-203.
  134. Xia H, Gu Y, Short communication: The generalized finite difference method for electroelastic analysis of 2D piezoelectric structures[J], Engineering Analysis with Boundary Elements. 2021, 124: 82–86.
  135. Gu Y, Qu W, Chen W, et al. The generalized finite difference method for long-time dynamic modeling of three-dimensional coupled thermoelasticity problems[J], Journal of Computational Physics, 2019, 384: 42–59.
  136. Rao X, Liu Y, Zhao H. An upwind generalized finite difference method for meshless solution of two-phase porous flow equations[J]. Engineering Analysis with Boundary Elements, 2022, 137: 105-118.
  137. Gu Y, Wang L, Chen W, et al. Application of the meshless generalized finite difference method to inverse heat source problems[J]. International Journal of Heat and Mass Transfer, 2017, 108(A): 721-729.
  138. Qu W, He H, A spatial–temporal GFDM with an additional condition for transient heat conduction analysis of FGMs[J], Applied Mathematics Letters, 110 (2020) 106579.
  139. Zhan W, Rao X, Zhao H, et al. Generalized finite difference method (GFDM) based analysis for subsurface flow problems in anisotropic formation[J]. Engineering Analysis with Boundary Elements, 2022, 140: 48-58.
  140. Fan C M, Li P W. Generalized finite difference method for solving two-dimensional Burgers’ equations[J], Procedia Engineering, 2014, 79 :55–60.
  141. Fu Z J, Tang Z C, Zhao H T, et al. Numerical solutions of the coupled unsteady nonlinear convection–diffusion equations based on generalized finite difference method[J], Eur. Phys. J. Plus 2019, 134 (6): 272.
  142. Gu Y, Sun HG. A meshless method for solving three-dimensional time fractional diffusion equation with variable-order derivatives[J]. Applied Mathematical Modelling, 2020, 78: 539-549.
  143. Chan H F, Fan C M, Kuo C W. Generalized finite difference method for solving two-dimensional non-linear obstacle problems[J]. Engineering Analysis with Boundary Elements, 2013, 37(9): 1189-1196.
  144. Rao X. An upwind generalized finite difference method (GFDM) for meshless analysis of heat and mass transfer in porous media[J]. Computational Particle Mechanics, 2023, 10(3): 533-554.
  145. Rao X, Zhao H, Liu Y. A novel meshless method based on the virtual construction of node control domains for porous flow problems[J]. Engineering with Computers, 2024, 40(1): 171-211.
  146. Rao X, Zhao H, Liu Y. A meshless numerical modeling method for fractured reservoirs based on extended finite volume method[J]. SPE Journal, 2022, 27(06): 3525-3564.
  147. Qian Zhi, Hu Xinhong, Yang Hongwei, et al. Comprehensive utilization of multiple logging curves for formation division and correlation [J]. Petroleum Instruments, 2008(05): 46-47+52+25.
  148. Wu Hao. Optimized inversion of interwell connectivity based on production logging data [D]. Yangtze University, 2021.
  149. Wang Xiang, Xia Zhujun, Zhang Hongwei, et al. Research on the method of identifying large-scale channels using water injection profile logging data [J]. Well Logging Technology, 2002, 26(2): 162-164.
  150. Meng Fanshun, Sun Tiejun, Zhu Yan, et al. Identification of large-scale channels in sandstone reservoirs using conventional logging data [J]. Periodical of Ocean University of China (Natural Science Edition), 2007, 37(3): 463-468.
  151. Hong Jinxiu, Xu Wei, Tu Guoping. Formation mechanism of large-scale channels in fluvial-deltaic depositional reservoirs and identification method using DLS logging curves [J]. Petroleum Geology and Oilfield Development in Daqing, 2006, 10(4): 51-53+122.
  152. Zhao Xiaoqing, Pan Baozhi, Zhu Daoping, et al. Evaluation of large-scale channels in reservoirs using carbon-oxygen ratio (C/O) spectral logging data [J]. Well Logging Technology, 2009, 33(2): 4.
  153. Shang Hailan, Wei Yanmei, Li Zhigang, et al. Application of pulsed neutron oxygen activation technology to guide the treatment of large-scale channels in Jing-11 fault block [J]. Well Testing, 2009, 3(5): 66-67+78.
  154. Kaufman R L, Ahmed A S, Hempkins W B. A new technique for the analysis of comingled oils and its application to production allocation calculations[J]. indonesian petroleum association, 1987.
  155. Wen Zhigang, Zhu Dan, Li Yuquan, et al. Application of chromatography fingerprinting technology in the study of reservoir connectivity in Block 6 of Gudong Oilfield [J]. Petroleum Exploration and Development, 2004, 31(1): 82-83.
  156. Li Ning. Research on the interpretation and application model of multi-well reservoir dynamic testing data [D]. Xi’an Shiyou University, 2012.
  157. Ding Yao. Application research on interwell dynamic connectivity inversion method for high water-cut reservoirs [D]. China University of Petroleum (Beijing), 2017.
  158. Li Yuegang, Xu Wen, Xiao Feng, et al. Optimization of development well patterns based on dynamic characteristics [J]. Natural Gas Industry, 2014, 34(11): 56-61.
  159. Wan Xinde, Wu Yi. Application of pulse testing in oilfield development [J]. Special Oil & Gas Reservoirs, 2006, 13(3): 66-69.
  160. Su Qunying, XiongNian, Zhang Jing. Application of pulse testing to analyze interwell connectivity in polymer-flooded reservoirs [J]. Liaoning Chemical Industry, 2012, 41(09): 951-952.
  161. Liu Zhenyu, Zeng Zhaoying, Zhai Yunfang, et al. Study on connectivity of low permeability reservoirs using pulse testing method [J]. Acta Petrolei Sinica, 2003, 24(1): 73-77.
  162. Tiab D, Dinh A V. Inferring interwell connectivity from well bottomhole-pressure fluctuations in waterfloods[J]. SPE Reservoir Evaluation & Engineering, 2008, 11(05):874-881.
  163. Liao Hongwei, Wang Chen, Zuo Dairong. Determination of interwell connectivity using unsteady-state well testing [J]. Petroleum Exploration and Development, 2002, 29(4): 87-89.
  164. Lin Jia’en, Wang Yaozu, Yang Jinghai. Qualitative analysis of injection-production balance and interwell connectivity using unsteady-state pressure testing data [J]. Well Testing, 1997, 6(2): 4-9.
  165. Shi Yougang, Zeng Qinghui, Zhou Xiaojun. Theoretical interpretation model of well testing for large-scale channels [J]. Oil Drilling & Production Technology, 2003, 15(3): 48-50+84.
  166. Muskat M. A note on a problem in potential theory[J]. Journal of Applied Physics, 1937, 8(6): 434-440.
  167. Fay J A, & Pratts S A. The Flow of Permeable Media[J]. In Journal of Applied Physics, 1951, 22(5), 655-658.
  168. Martin J C, Woo P T, Wegner R E. Failure of Stream Tube Methods to Predict Waterflood Performance of an Isolated Inverted Five-Spot at Favorable Mobility Ratios[J]. JPT, 1973, 25: 151-153.
  169. Higgins R V, Leighton A J. Computer Prediction of Water Drive of Oil and Gas Mixtures Through Irregularly Bounded Porous Media-Three-Phase Flow[J]. JPT, 1962, 14: 1048-1054.
  170. Martin J C, Wegner R T. Numerical Solution of Multiphase, Two-Dimensional Incompressible Flow Using Streamtube Relationships[J]. Society of Petroleum Engineers Journal, 1979, 19: 313-323.
  171. Lake L W, Johnston J R, Stegemeier G L. Simulation and Performance Prediction of a Large-Surfactant/Polymer Project[J]. Society of Petroleum Engineers Journal, 1981, 21: 731-739.
  172. Pollock D W. Semianalytical Computation of Path Lines for Finite-Difference Models[J]. Ground Water, 1988, 26(6): 743-750.
  173. Datta-Gupta A, King M J. A Semianalytic Approach to Tracer Flow Modeling in Heterogeneous Permeable Media[J]. SPE Formation Evaluation, 1995, 10: 40-48.
  174. Peddibhotla S, Cubillos H, Datta-Gupta A, et al. Rapid simulation of multiphase flow through fine-scale geostatistical realizations using a new, 3-D, streamline model: a field example[C]//SPE Petroleum Computer Conference. SPE, 1996: SPE-36008-MS.
  175. Zhao Hui, Kang Zhijiang, Zhang Yun, et al. A connectivity method for characterizing interwell formation parameters and oil-water performance [J]. Acta Petrolei Sinica, 2014, 35(5): 922-927.
  176. Zhao H, Kang Z, Zhang X, et al. INSIM: A data-driven model for history matching and prediction for waterflooding monitoring and management with a field application[C] SPE reservoir simulation symposium, 2015, SPE-173213-MS.
  177. Zhao H, Kang Z, Zhang X, et al. A physics-based data-driven numerical model for reservoir history matching and prediction with a field application[J]. SPE Journal, 2016, 21(06): 2175-2194.
  178. Zhao H, Li Y, Cui S, et al. History matching and production optimization of water flooding based on a data-driven interwell numerical simulation model[J]. Journal of Natural Gas Science and Engineering, 2016, 31: 48-66.
  179. Zhao H, Kang Z, Sun H, et al. An interwell connectivity inversion model for waterflooded multilayer reservoirs[J]. Petroleum Exploration and Development, 2016, 43(1): 106-114.
  180. Xie X, Zhao H, Kang X, et al. Prediction method of produced polymer concentration based on interwell connectivity[J]. Petroleum Exploration and Development, 2017, 44(2): 286-293.
  181. Guo Z, Reynolds A C, Zhao H. A physics-based data-driven model for history matching, prediction, and characterization of waterflooding performance[J]. SPE Journal, 2018, 23(02): 367-395.
  182. Guo Z, Reynolds A C, Zhao H. Waterflooding optimization with the INSIM-FT data-driven model[J]. Computational Geosciences, 2018, 22: 745-761.
  183. Zhao H, Xu L, Guo Z, et al. A new and fast waterflooding optimization workflow based on INSIM-derived injection efficiency with a field application[J]. Journal of Petroleum Science and Engineering, 2019, 179: 1186-1200.
  184. Guo Z, Reynolds A C. INSIM-FT in three-dimensions with gravity[J]. Journal of Computational Physics, 2019, 380: 143-169.
  185. Zhao H, Xu L, Guo Z, et al. Flow-path tracking strategy in a data-driven interwell numerical simulation model for waterflooding history matching and performance prediction with infill wells[J]. SPE Journal, 2020, 25(02): 1007-1025.
  186. Liu W, Zhao H, Sheng G, et al. A rapid waterflooding optimization method based on INSIM-FPT data-driven model and its application to three-dimensional reservoirs[J]. Fuel, 2021, 292: 120219.
  187. Zhao H, Liu W, Rao X, et al. INSIM-FPT-3D: A Data-driven Model for History Matching, Water-breakthrough Prediction and Well-connectivity Characterization in Three-dimensional Reservoirs[C]. SPE Reservoir Simulation Conference, Galveston, Texas, USA, 4–6 October 2021, SPE-203931-MS.
  188. Liu W, Zhao H, Zhong X, et al. A Novel Data-Driven Model for Dynamic Prediction and Optimization of Profile Control in Multilayer Reservoirs[J]. Geofluids, 2021, 3272860.
Subscribe Your Manuscript
Branches
HanLin Group
澳科中文官网
Book Center
Patent Center
Services
For Authors
Book Builder
Projects
Young Mind
Beyond Expo.
About us
MOSP Team
MOAJ Team
Blog & News
Partnership
Careers
Contact
© 2021-2023 Macao Scientific Publishers ( Macao, P.R. China )
www.mospbs.com