高含水开发期基于微观渗流机理的宏观油藏数值模拟研究
|
摘要
在分析不同尺度油藏动态研究方法的特点基础上，指出处于高含水开发期间的油藏需要将微观研究与宏观研究相结合来得到此时地下流体的分布规律。通过分析微观油水运动机理，指出稳定法和不稳定方法测量的油水相对渗透率曲线是一种宏观上的统计规律，没有考虑岩石微观特征对油水运动分布规律的影响，不适用于油藏高含水开发期间描述地下油水分布规律。同时指出了经典数值模拟计算中出现的各种问题，并分析了造成这些问题出现的原因。
指出利用孔隙网络模型可以计算出基于微观孔喉特征的相对渗透率曲线，再和经典油藏数值模拟技术相结合，可以得到基于微观渗流机理的宏观油藏数值模拟方法。采用逾渗理论和孔隙水平网络模型，导出了不同润湿体系和饱和历史下的逾渗可进入度、逾渗临界值、有效分数和相导流能力的具体表达形式。利用截面为等边三角形的棱柱管代替以往网络模型中采用的圆管，更细致地描述了岩石的润湿性影响和微观油水分布特征。采用Bethe网络计算了油水相对渗透率规律，并分析了微观特征参数对相对渗透率的影响，计算结果分析表明该方法可行。
对考虑启动压力下的一维油水动态进行了推导，扩展了该方法的适用范围，可以用于低渗透油藏动态的计算，分析了重力、毛管压力和启动压力的存在对油藏动态参数的影响规律。建立了考虑微观渗流特征的油气水三维三相渗流的数学模型，采用差分离散方法形成数值模型；讨论了由于网格加密和死节点消除给系数矩阵造成的影响；给出利用数值模拟结果计算油藏开发指标的方法；利用预处理共轭梯度正交极小化方法求解方程组，并编制了相应地计算软件。
与经典的数值模拟方法相比，基于微观渗流机理的宏观数值模拟计算方法主要的优点是考虑了油藏不同部位由于微观孔喉结构分布不同导致地油水渗流规律的改变，并可以得到剩余油在不同孔喉空间中的分布形式和规律，实现了利用黑油模型即可以为调剖堵水、化学驱等提高采收率措施提供决策依据。此外该模型
中还可以考虑的问题有:不同孔喉分布采用不同的油水渗流关系;网格加密和死
节点消除的新方法;原油粘度和地层的渗透率随开发过程的变化;波及系数;计
算剩余油储量丰度、可采储量丰度、单井控制储量、单井控制可采储量;水淹状
况等参数。最后利用该模型对胜利油区的某油藏区块进行了计算，利用取心资料
分析计算不同部位的相对渗透率曲线，讨论了运用过程中的处理方法。对区块计
算结果进行了分析，对涉及到的问题进行了验证，结果表明计算过程稳定，考虑
问题全面，可以为现场决策提供丰富的结果信息。
关键词:
高含水开发期;网络模型;逾渗理论;微观渗流机理;
宏观油藏数值模拟;剩余油分布形式
After analyzing different scale reservoir development methods, the paper indicates that study based on micro seepage mechanism and macro reservoir simulation should be used to calculate liquid distributing features during high water-cut development period. By studying micro seepage mechanism of water and oil, the paper shows that the relative permeability curve measured in reservoir physics lab by steady or unsteady method is a macro statistical regularity, which doesn't allow for the influence of micro rock features on liquid flow rules, so the relative permeability curve measured in reservoir physics lab is not applicable to describing water and oil distribution in reservoir during high water-cut development period. At the same time, the paper indicates some questions of classical reservoir simulation, finds out reasons that result in those questions.Pore-level network model can be used to calculate the relative permeability curve based on micro throat and hole features and if it could be combined with classical reservoir simulation technique, the macro reservoir numerical simulation method based on micro seepage mechanism will be accessible. According to percolation theory and pore-level network model, the calculating formulae of accessible fraction, critical percolation value, effective fraction and phase equivalent conductivity in different wet systems and displacement processes are derived in dissertation. Substituting prismatic tube with equilateral triangle section for ancient tube with circular section is favorable for describing rock wetting characteristics and calculating micro liquid distributing features. The relative permeability curves are worked out by Bethe network model, at the same time the influence of micro characteristics on curves are analyzed. The analyzing results prove the method feasible.The 1D reservoir developing method with starting pressure is put forward, which enlarges applicable range and which analyzes the influence of gravity, capillary, starting pressure on reservoir performance parameters. . The three -dimension and three -phase
mathematical model of water, oil and gas are established, which takes micro seepage mechanism into account. The difference method is used to get numerical equations, the equations are solved by conjugating pretreatment grads orthomin method, at the same time the influences of grid refinement and dead node elimination on coefficient matrix are discussed, the methods to calculating development indexes are put forward. According to the solving method, the computer program is compiled and completed.Compared with classical reservoir simulation, the most important advantage of macro reservoir simulation based on micro seepage mechanism is that the oil and water relative permeability changes because of different micro throat and hole distribution features in reservoir are taken into account. By this improvement, the distributing rules and form of remaining oil in reservoir pore can be described clearly. It become a reality that black oil mathematical model could provide decision making explanations for profile controlling, water plugging, chemical flooding and other enhanced oil recovery(EOR) methods. In addition, the model has other merits, for example, adopting different relative permeability curves in different formation, the new way to refine grid and to eliminate dead node, dealing with the changes of permeability and oil viscosity in different development period. The following parameters can be gained through analyzing simulation result: sweep efficiency, remaining oil reserves abundance, recoverable reserves abundance, controlling reserves by single well, recoverable controlling reserves by single well, water-flooded area, and so on. At last, the model is tested by one reservoir block in Sheng-Li petroliferous area, the different relative permeability curves in different parts of reservoir are worked out by network model and the method to deal with permeability is discussed. The results are analyzed, the merits mentioned are also tested. The analyzing resu
指出利用孔隙网络模型可以计算出基于微观孔喉特征的相对渗透率曲线，再和经典油藏数值模拟技术相结合，可以得到基于微观渗流机理的宏观油藏数值模拟方法。采用逾渗理论和孔隙水平网络模型，导出了不同润湿体系和饱和历史下的逾渗可进入度、逾渗临界值、有效分数和相导流能力的具体表达形式。利用截面为等边三角形的棱柱管代替以往网络模型中采用的圆管，更细致地描述了岩石的润湿性影响和微观油水分布特征。采用Bethe网络计算了油水相对渗透率规律，并分析了微观特征参数对相对渗透率的影响，计算结果分析表明该方法可行。
对考虑启动压力下的一维油水动态进行了推导，扩展了该方法的适用范围，可以用于低渗透油藏动态的计算，分析了重力、毛管压力和启动压力的存在对油藏动态参数的影响规律。建立了考虑微观渗流特征的油气水三维三相渗流的数学模型，采用差分离散方法形成数值模型；讨论了由于网格加密和死节点消除给系数矩阵造成的影响；给出利用数值模拟结果计算油藏开发指标的方法；利用预处理共轭梯度正交极小化方法求解方程组，并编制了相应地计算软件。
与经典的数值模拟方法相比，基于微观渗流机理的宏观数值模拟计算方法主要的优点是考虑了油藏不同部位由于微观孔喉结构分布不同导致地油水渗流规律的改变，并可以得到剩余油在不同孔喉空间中的分布形式和规律，实现了利用黑油模型即可以为调剖堵水、化学驱等提高采收率措施提供决策依据。此外该模型
中还可以考虑的问题有:不同孔喉分布采用不同的油水渗流关系;网格加密和死
节点消除的新方法;原油粘度和地层的渗透率随开发过程的变化;波及系数;计
算剩余油储量丰度、可采储量丰度、单井控制储量、单井控制可采储量;水淹状
况等参数。最后利用该模型对胜利油区的某油藏区块进行了计算，利用取心资料
分析计算不同部位的相对渗透率曲线，讨论了运用过程中的处理方法。对区块计
算结果进行了分析，对涉及到的问题进行了验证，结果表明计算过程稳定，考虑
问题全面，可以为现场决策提供丰富的结果信息。
关键词:
高含水开发期;网络模型;逾渗理论;微观渗流机理;
宏观油藏数值模拟;剩余油分布形式
After analyzing different scale reservoir development methods, the paper indicates that study based on micro seepage mechanism and macro reservoir simulation should be used to calculate liquid distributing features during high water-cut development period. By studying micro seepage mechanism of water and oil, the paper shows that the relative permeability curve measured in reservoir physics lab by steady or unsteady method is a macro statistical regularity, which doesn't allow for the influence of micro rock features on liquid flow rules, so the relative permeability curve measured in reservoir physics lab is not applicable to describing water and oil distribution in reservoir during high water-cut development period. At the same time, the paper indicates some questions of classical reservoir simulation, finds out reasons that result in those questions.Pore-level network model can be used to calculate the relative permeability curve based on micro throat and hole features and if it could be combined with classical reservoir simulation technique, the macro reservoir numerical simulation method based on micro seepage mechanism will be accessible. According to percolation theory and pore-level network model, the calculating formulae of accessible fraction, critical percolation value, effective fraction and phase equivalent conductivity in different wet systems and displacement processes are derived in dissertation. Substituting prismatic tube with equilateral triangle section for ancient tube with circular section is favorable for describing rock wetting characteristics and calculating micro liquid distributing features. The relative permeability curves are worked out by Bethe network model, at the same time the influence of micro characteristics on curves are analyzed. The analyzing results prove the method feasible.The 1D reservoir developing method with starting pressure is put forward, which enlarges applicable range and which analyzes the influence of gravity, capillary, starting pressure on reservoir performance parameters. . The three -dimension and three -phase
mathematical model of water, oil and gas are established, which takes micro seepage mechanism into account. The difference method is used to get numerical equations, the equations are solved by conjugating pretreatment grads orthomin method, at the same time the influences of grid refinement and dead node elimination on coefficient matrix are discussed, the methods to calculating development indexes are put forward. According to the solving method, the computer program is compiled and completed.Compared with classical reservoir simulation, the most important advantage of macro reservoir simulation based on micro seepage mechanism is that the oil and water relative permeability changes because of different micro throat and hole distribution features in reservoir are taken into account. By this improvement, the distributing rules and form of remaining oil in reservoir pore can be described clearly. It become a reality that black oil mathematical model could provide decision making explanations for profile controlling, water plugging, chemical flooding and other enhanced oil recovery(EOR) methods. In addition, the model has other merits, for example, adopting different relative permeability curves in different formation, the new way to refine grid and to eliminate dead node, dealing with the changes of permeability and oil viscosity in different development period. The following parameters can be gained through analyzing simulation result: sweep efficiency, remaining oil reserves abundance, recoverable reserves abundance, controlling reserves by single well, recoverable controlling reserves by single well, water-flooded area, and so on. At last, the model is tested by one reservoir block in Sheng-Li petroliferous area, the different relative permeability curves in different parts of reservoir are worked out by network model and the method to deal with permeability is discussed. The results are analyzed, the merits mentioned are also tested. The analyzing resu
引文
1．陈月明．油藏数值模拟原理[M]．山东东营：石油大学出版社，1988
2．谷建伟．复杂条件下低渗透油田生产特征[J]．石油大学学报(自然科学版)，2003，27(2)：55-57
3．谷建伟．微生物在多孔介质中的渗流的数学模型[J]．生物数学学报，2003，18(4)：423-426
4．谷建伟．利用数值模拟结果计算油藏水驱波及系数[J]．河南石油，2004，18(4)：35-36
5．郭尚平，黄延章，周娟．物理化学渗流微观机理[M]．北京：科学出版社，1990
6．韩大匡，陈钦雷，闫存章．油藏数值模拟基础[M]．北京：石油工业出版社，1993
7．胡雪涛，李允．随机网络模拟研究微观剩余油分布[J]．石油学报，2000，21(4)：46-51
8．姜汉桥，谷建伟，陈月明．剩余油分布规律的精细数值模拟[J]．石油大学学报(自然科学版)，1999，23(5)：31-34
9．姜汉桥，姚军，姜瑞忠．油藏工程原理与基础[M]．山东东营：石油大学出版社，2000
10．刘建民，李阳，毕研鹏，何秋轩．应用驱油微观模拟实验技术研究储层剩余油微观分布特征[J]．中国海上油气(地质)，2000，14(1)：51-54
11．秦积舜，李爱芬，孙仁远．油层物理学[M]．山东东营：石油大学出版社，2001
12．沈平平．油水在多孔介质中的运动理论和实践[M]．北京：石油工业出版社，2000：1-13
13．王金勋，吴晓东，杨普华．孔隙网络模型法计算气液体系吸吮过程相对渗透率(J)．天然气工业，2003，23(3)：8-11
14．王金勋，刘庆杰，杨普华，沈平平．应用逾渗理论计算非稳态法油水相渗曲线[J]．石油勘探与开发，2001，28(2)：79-82
15．翟世奎，陈丽蓉，王镇，干晓群．冲绳海槽浮岩岩浆活动模式浅析[J]．海洋地质与第四纪地质，1997，17(1)：59-66
16．翟世奎，许淑梅，于增慧，秦蕴珊，赵一阳．冲绳海槽北部两个可能的现代海底热液喷溢点[J]．科学通报，2001，48(6)：490～492
17．张永祥，陈鸿汉．多孔介质溶质运移动力学[M]．北京：地震出版社，2000．6-9
18．朱九成，郎兆新，张丽华．多尺度油藏数值模拟的渗虑方法[J]．石油学报，1998，19(2)：49-53
19. Acuna, J.A., Yortsos, Y.C.. Numerical construction and flow simulation in networks of fractures using fractal geometry. SPE 22703, 66th Annual technical conference of SPE ,in Dallas. 1991
20. Aker E., Maloy K.J.. A two dimensional network simulator for two phase flow in porous media. Transport in Porous Media, 1998, 32: 163-186
21. Aziz K., Settari A.. Petroleum Reservoir Simulation. Applied Science Publishers, 1979
22. Bakke S., Oren P.E.. 3D pore scale modeling of heterogeneous sandstone reservoir rocks and quantitative analysis of the architecture, geometry and spatial continuity of the pore network. SPE 35479, European 3D reservoir modeling conference, in Stavanger, Norway, April, 1996
23. Bear J., Braester C.. Effective and relative permeability of anisotropic porous media. Transport in Porous Media, 1987, 2: 301-316
24. Berkowitz B., Balberg I.. Percolation approach to the problem of hydraulic conductivity in porous media. Transport in Porous Media, 1992,9:275-286
25. Berkowitz B., Balberg I.. Percolation theory and its application to groundwater hydrology. Water Resource Research, 1993, 29(4) :775-794
26. Bernadiner M.. A capillary microstructure of the wetting front. Transport in Porous Media, 1998,30:251-265
27. Bhat S. K.. Network modeling of permeability evolution of diatomite. SPE International Student Paper Contest. 1998
28. Bidner M. S., Porcell C.. Influence of phase behavior on chemical flood transport phenomena. Transport in Porous Media, 1996,24:247-273
29. Blunt M. J.. An empirical model for three phase relative permeability. SPE 56474, SPE annual technical conference in Houston, Texas, 1999
30. Blunt M. J, Richard G. H.. Pore scale modeling of multiphase flow in fractures and matrix/fracture transfer. SPE 56411, SPE annual technical conference, in Houston, Texas, Oct, 1999
31. Blunt M. J.. Pore-level network modeling of the effects of wettability. Journal of Petroleum Science and Engineering, 1997,2:494-510
32. Blunt M. J.. Physically based network modeling of multiphase flow in intermediate wet porous media. Journal of Petroleum Science and Engineering, 1998, 2:117-125
33. Blunt M. J.. Effects of heterogeneity and wetting on relative permeability using pore level modeling. SPEJ 36762, Nov 1997
34. Blunt M. J., King P. R., Goshawk A.. Relative permeability for two and three dimensional pore scale network modeling. Trans Porous Media. 1991,6:407-433
35. Braun E. M., Holland R. F.. Relative permeability hysteresis laboratory measurements and a conceptual model. SPE 28615, SPE 69th annual technical conference, in New Orleans, Sep 1994
36. Broadbent S. R., Hammersley J. M.. Percolation process crystals and mazes. Proo. Camb. Phil. Soc. 1957(53): 629-641
37. Caruana A., Dawe R. A.. Flow behavior in the presence of wettability heterogeneities. Transport I Porous media, 1996,25:217-233
38. Chandler R., Koplik J.. Capillary displacement and percolation in porous media. J. Fluid Mech, 1982,119:269-267
39. Chang Jincai, Yortsos, Yanis C.. Effect of capillary heterogeneity on Buckly-Leverett displacement. SPERE 18798,1992
40. Chatenever A, Calhoun J. C.. Visual examination of fluid benhavior in porous media- part I. Trans, AIME, 1952,195:149-156
41. Chatzis I., Dullien F. A. L.. Modeling of pore structure by 2-D and 3-D network with application to sandstone. J. Can. Pet. Technol, 1977,16:97-108
42. Chatzis I., Dullien F. A. L.. Dynamic immiscible displacement mechanisms in porous doublets: theory and experiment. J. Colloid Interface Science, 1983,91(1)
43. Cheng Yuanlin.. Three-dimensional randomized, network model for two-phase flow through porous media. SPE/DOE 9803, second Joint symposium on EOR in Tulsa, Oklahoma, April, 1981
44. Chou S.I.. Percolation theory of poam in porous media. SPE/DOE 20239, 1990
45. Collins, R. E. Flow of Fluids Through Porous Materials. Petroleum publishing CO., Tulsa, 1972
46. Colonna J., Brissaud F., Millet J.L.. Evolution of capillary and relative permeability hysteresis. SPEJ 2941,1972
47. David Wilkinson, Jorge F. W.. Invasion percolation: a new form of percolation theory. J.Phys, A:Math. 1983,16:3365-3376
48. Davis J. A., Jones S. C.. Displacement mechanisms of micellar solutions. JPT. 1968,20:7-20
49. Dias M. M., Payatakes A. C.. Network models for two Phase flow in porous media: I. Immiscible micro displacement of non-wetting fluid, II: Motion of oil ganglia. J. Fluid Mech, 1986,164:305-306; 337-358
50. Diaz C. E., Chatzis I., Dullien F. A. L.. Simulation of capillary pressure curves using bond correlated site percolation on a simple cubic network. Transport in Porous Media, 1987,2:215-240
51. Dixit A. B., Mcdougall, S. R., Sorbie, K. S.. A pore level investigation of relative permeability hysteresis in water wetting system. SPE 37233, SPE international symposium, in Houston, Texas, Feb 1997
52. Dixit A. B., Mcdougall, S. R., Sorbie, K. S., Buckley J. S.. pore scale modeling of wettability and influences on oil recovery. Proceedings of SPE/DOE Symposium on Improved Oil Recovery, in Tulsa, SPE/DOE35451, 1996
53. Dixit A. B., Mcdougall, S. R., Sorbie, K.S., Buckley J. S.. Pore scale modeling of wettability effects and their influences on oil recovery. SPE Reservoir Eval. And Eng, 1999, 2(1): 25-36
54. Dodds C. G., Kiel 0. G. Evaluation of monte-Carlo methods in studying fluid-fluid displacement and wettability in porous rock. J. Phys. Chem. 1959,63:1646-1632
55. Dong Mingzhe, Dullien F. A. L.. Characterization of water-flood saturation profile history by the complete capillary number. Transport in Porous Media, 1998,31: 213-237
56. Du C., Yortsos Y. C.. A numerical study of the critical gas saturation in porous media. Transport in Porous Media, 1999,35: 205-225
57. Dullien, F. A. L., Dhawan, G. K.. Bivariate pore size distribution of some sandstone. Journal of Colloid and Interface Science, 1957, 52(1): 129-135
58. Ewing R., Gupta S. C.. Modeling percolation properties of random media using a domain network. Water Resource Research, 1993,29(9):3169-3178
59. Fang Yisheng, Li Baozhu, Hu Yonghe, Sun Zhidao, Zhu Yuxin.. Condensate gas phase behavior and development.. SPE 50925, SPE international Oil & Gas conference, Beijing, 1998
60. Fatt I.. The network model of porous media, I: Capillary pressure characteristics. Trans. SPE AIMM, 1956,207:144-159
61. Fatt I.. The network model of porous media, II: Dynamic properties of a single size tube network. Trans. AIMM, 1956,207:160-163
62. Fatt I.. The network model of porous media, III: Dynamic properties of networks with tube radius distributions. Trans. AIMM, 1956,207:164-177
63. Fleming P. D.. An interpretation of the petrophysical properties of reservoir rocks based on percolation theory. SPE 12515,1967
64. Goslinga J.. The use of adaptive grids in numerical simulation. SPE symposium on reservoir simulation, San Francisco, Nov, 1983
65. Hardy H. H.. Mathematical model of microscopic fluid flow in porous Media. Transport in Porous Media, 1990,4:24-27
66. Heiba A. A., Davis H. T., Scriven L. E.. Effects of wettability on two phase relative permeability and capillary pressures. SPE 12172, SPE 58th technical conference, in San Fran. , Oct, 1983
67. Heiba A. A., Davis H. T., Scriven L. E.. Statistical network theory of three phase relative permeability. SPE 12690, SPE AIME 4th symposium on EOR, in Tulsa OK, April, 1984
68. Heiba A. A.. Sahimi, Muhammad, Scriven L. E.. Percolation theory of Two Phase relative permeability. SPE 11015,1983
69. Huang Yanzhang, Zhou juan, Tian genlin, Zhang jian. The phase behavior and displacement mechanism of microemulsion systems. 4th European symposium on EOR, Humberg, 1987
70. Jerauld G. R., Scriven L. E., Davis H. T.. Percolation and conduction on the 3D regular networks: A second case study in Topological disorder. J. Phys. Chem. 1984,17:3429-3439
71. Johnson E. F., Bcssler D. P., Naumann V. 0.. Calculation of relative permeability from displacement experiments. JPT. 1959(Jan):61-68
72. Kalaydjian F.. Origin and quantification of coupling between relative permeability for two-phase flow in porous media. Transport in Porous media. 1990, 5:215-229,
73. Kamath J., Xu B., Yortsos Y. C., Lee S.H.. Pore network modeling of laboratory experiment on heterogeneous carbonate. SPE 36681, SPE annual technical conference in Denver, Colorado, Oct, 1996
74. Katz A. J., Thompson A. H.. Fractal sandstone pores: implications for conductivity and pore formation. Phys. Rev. Lett, 1985, 54(12):1325-1328
75. Kharabaf H., Yortsos Y. C.. A pore network modeling for foam formation and propagation in porous media. SPE 36663, SPE annual technical conference in Denver, Colorado, Oct, 1996
76. Khatib Z. I., Vitthal S.. The use of effective medium theory and 3-D network model to predict matrix damage in sandstone formation. SPE 19649, 1989
77. King P. R.. The use of renormalization for calculating effective permeability. TIPm. 1989,4:37-58
78. Kishore K. M., Stephen J. S.. Multiphase flow in porous media: II pore-level modeling. SPE 11018, SPE AIME 57th annual fall technical conference in New Orleans, Sep, 1982
79. Koplik J., lasseter T. J.. Two-phase flow in random network models of porous media. SPEJ 11014, 1985
80. Kovscek A. R., Wong H., Radke C. J. A pore level scenario for the development of mixed wettability in oil reservoirs. AICHE J. 1993, 39(6):1072-1085
81. Laidlaw W. G., Wilson W. G., Coombe D.A.. A lattice model of foam flow in porous media: A percolation approach. Trans in Porous Media. 1993,11:139-159
82. Larson R. G., Davis, H. T., Scriven, L. E.. Elementary mechanisms of oil recovery by chemical methods. JPT, 1982, 34:243-258
83. Larson R. G., Scriven L. E., Davis H.T.. Percolation theory of two-phase flow in porous media. Chemical Engineering Science, 1980, 36:57-73
84. Laroche C., Vizika 0.. Network modeling to predict the effect of wettability heterogeneities on multiphase flow. SPE 56674, SPE annual technical conference in Houston Texas, Oct, 1999
85. Lemaitre R., Adler P.M.. Fractal porous media IV: three dimensional stick flow through random media and regular fractal. Transport in Porous media. 1990,5:325-340
86. Lendhard R. J., Ostrom M.. A parametric model for predicting relative permeability saturation-capillary pressure relationships of oil-water systems in porous media with mixwd wettability. Transport in Porous Media, 1998, 31:109-131
87. Lenormand R., Touboul E., Zarcone C.. Numerical models and experiments on immiscible displacement in porous media. J. Fluid Mech, 1988,189:165-187
88. Lenormand R.. Transport equations for fluid displacement in stratified porous media: the MHD model. SPE 30797, SPE annual technical conference in Dallas, TX , Oct, 1995
89. Lenormand R., Zaucone, C.. Role of roughness and edges during imbibition in square capillary. SPE 13264, AIME SPE 59th technical conference in Houston, TX Sep, 1984
90. Lenormand R., Zaucone, C.. Physics of blob displacement in a two dimensional porous medium. SPEFE 14882,1988
91. Maier R., Ladilaw W. G.. Fluid topology for invasion percolation in 3-D Lattices. Transport in Porous Media. 1990,5:421-428
92. Mani, V., Mohanty, K. K.. Pore-level network modeling of three phase capillary pressure and relative permeability curves. SPE 38883, 1997
93. Masson, G., Morrow, N. R.. Capillary behavior of a Perfectly wetting liquid irregular triangular tubes. Journal of Colloid and Interface Science. 1991,141(1):262-274
94. Mcdougall, S. R., Sorbie, K. S.. The combined effect of capillary and viscous on water-flood displacement efficiency in finely laminated porous media. SPE 26659, SPE 68th annual technical conference in Houston, TX, Oct, 1993
95. Mei wenrong, Shu shihong, Lai tianhua.. Pore and throat network model and application to the optimal selection of temporary plugging particles. SPE 31099,1996
96. Miller J. M., Fogler H. S.. Prediction of fluid distribution in porous media treated with foamed gel. Chem. Eng. Sci. 1995,50:3261-3274
97. Mogensen K., Stenby E.. A dynamic Two Phase pore-scale model of imbibition. Transport in Porous Media, 1998,32:299-327
98. Mohammadi S.,Sorbie K.S. .Danesh A. ,PedenJ.M. ,Heriot-watt U.. Pore-level modeling of gas-condensate flow through horizontal porous media. SPE 20479, 65th annual technical conference of SPE, New Orleans, 1990
99. Morrow R., Norman, Harris C. C.. Capillary equilibrium in porous materials. SPEJ, 1965,3:15-24
100. Mohanty K. K., Davis H. T., Scriven L. E.. Physics of oil entrapment in water wet rock. SPERE. 1987(FEB):113-128
101. Mu Honghui, Martin J. B.. Pore-scale modeling of three phase flow and the effects of wettability. SPE 59309, SPE/DOE IOR symposium in Tulsa, Oklahoma, April, 2000
102. Oren P. E., Bakke S.. Extending predictive capabilities to network models. SPE 38880, SPE annual technical conference in San Antonio, TX, Oct, 1997
103. Oren P. E.. Pore-scale network modeling of water-flood residual oil recovery by immiscible gas flooding. SPE 27814, 1994
104. Parlar M., Yortsos Y. C.. Percolation theory of steam/water relative permeability. SPE 16969, SPE 62nd annual technical conference in Dallas, TX, Sep, 1987
105. Pavone D. R.. A Darcy law extension and a new capillary pressure equation for two phase flow in porous media. SPE 20474, SPE 65th annual technical conference in New Orleans, Sep, 1990
106. Peaceman D. W.. Interpretation of well block in numerical reservoir simulation with nonsqure grid block and anisotropic permeability. SPEJ, June, 1983
107.Ransohoff T. C., Radke C. J.. Laminar flow of a wetting liquid along the corners of a predominantly gas-occupied noncircular pore. Journal of Colloid and interface Science. 1987,121(2):392-401
108. Rose W., Witherspoon P. A.. Trapping of oil in a pore doublet. Prod. Monthly. 1956,21(2): 32-37
109. Rossen W. R., Gauglitz P. A.. Percolation theory of creation and mobilization of foam in porous media. AICHEJ. 1990,36:1176-1188
110. Rossen W. R., Mamum C. K.. Minimal Path for transport in network. Phys. REV. 1993, 47B:11815-11825
111. Rosenberg D. U.. Local mesh refinement for finte difference methods. SPE 57th annual fall technical conference and exhibition of AIME, New Orleans, Sep, 1982, SPE 10974
112. Sahimi Muhammad, Yortsos Y. C.. application of fractal geometry to porous media: a review. SPE20746, SPE 65th annual technical conference in New Orleans, Sep, 1990
113. Salathiel R. A.. Oil recovery by surface film drainage in mixed wettability rocks. JPT, 1973 (OCT):1216-1224
114.Salomao M. C.. Analysis of flow in spatially correlated systems by applying the percolation theory. SPE 39039, SPE 5th Latin American and Caribbean PE conference in Rio de Janeiro, Sep 1997
115.Saraf D. N., Fatt I.. Three relative permeability measurements by unsteady-state method. SPEJ, 1966, 6:199-205
116.Singhal A. K., Somertron W. H.. Network model for the study of multiphase flow behavior in porous media. SPE 2906, AIME SPE regional meeting, in Casper Wyo, June, 1967
117.Stinchcombe R.B.. Conductivity and spin-wave stiffness in disorder system: An exactly soluble model. J. Physic: C Solid State Phy. 1974,7:179-203
118.Suchomel B., Chen B. M.. Network model of flow, transport and biofilm effects in porous media. Transport in Porous Media. 1998,30: 1-23
119. Thomas G. W.. Principles of Hydrocarbon Reservoir Simulation. 1953
120.Toledo P.G.. Capillary pressure , water relative permeability and electrical conductivity of porous media at low wetting phase saturation. SPE 23675,1992
121. Van Di jke M. I. J., Sorbie K. S., Mcdougall, S. R.. A process based approach for three phase capillary pressure and relative permeability relationships in mixed wet systems. SPE 59310, SPE/DOE symposium on IOR in Tulsa Oklahoma, April, 2000
122. Van Dijke M. I. J., Sorbie K. S., Mcdougall, S. R. Saturation dependencies of three phase relative permeability in mixed-wet and fractionally-wet systems. Adv. Water Resour. 2001,24:365-384
123. Van Dijke M. I. J., Sorbie K. S., Sohrabi D.. Three phase flow in WAG processes in mixed-wet porous media: porous-scale network simulations and comparison with micromodel experiments. SPE 75192, SPE/DOE 3th IOR symposium in Tulsa, Oklahoma, April, 2002
124. Wang X., Mohanty K. K.. Multiphase Non-darcy flow in gas-condensate reservoir. SPE 56486, SPE annual technical conference, in Houston, 1999
125.Wilkinson D. ,Willemsen J. F.. Invasion percolation: a new form of percolation theory. J.Phys.A. 1983,16: 3365-3376
126. Wu yushu, Pruess K.. Gas flow in porous media with klingbenberg effects. Transport in Porous Media. 1998,32: 117-137
127. Xu B., Kamath J., Yortsos Y. C., Lee S. H.. use of pore network model to simulate laboratory corefloods in a heterogeneous carbonate sample. SPE 38879, SPE annual conference in San Antonio, TX, Oct, 1997
128.Yortsos Y. C., Satik C.. Large scale percolation theory of drainage. Transport in Porous Media, 1993,10: 171-195
129. Zhou Dengen, Martib Blunt.. Wettability effects in three phase gravity drainage. J.Petr.Science and Engineering, 1998,20:203-211
2．谷建伟．复杂条件下低渗透油田生产特征[J]．石油大学学报(自然科学版)，2003，27(2)：55-57
3．谷建伟．微生物在多孔介质中的渗流的数学模型[J]．生物数学学报，2003，18(4)：423-426
4．谷建伟．利用数值模拟结果计算油藏水驱波及系数[J]．河南石油，2004，18(4)：35-36
5．郭尚平，黄延章，周娟．物理化学渗流微观机理[M]．北京：科学出版社，1990
6．韩大匡，陈钦雷，闫存章．油藏数值模拟基础[M]．北京：石油工业出版社，1993
7．胡雪涛，李允．随机网络模拟研究微观剩余油分布[J]．石油学报，2000，21(4)：46-51
8．姜汉桥，谷建伟，陈月明．剩余油分布规律的精细数值模拟[J]．石油大学学报(自然科学版)，1999，23(5)：31-34
9．姜汉桥，姚军，姜瑞忠．油藏工程原理与基础[M]．山东东营：石油大学出版社，2000
10．刘建民，李阳，毕研鹏，何秋轩．应用驱油微观模拟实验技术研究储层剩余油微观分布特征[J]．中国海上油气(地质)，2000，14(1)：51-54
11．秦积舜，李爱芬，孙仁远．油层物理学[M]．山东东营：石油大学出版社，2001
12．沈平平．油水在多孔介质中的运动理论和实践[M]．北京：石油工业出版社，2000：1-13
13．王金勋，吴晓东，杨普华．孔隙网络模型法计算气液体系吸吮过程相对渗透率(J)．天然气工业，2003，23(3)：8-11
14．王金勋，刘庆杰，杨普华，沈平平．应用逾渗理论计算非稳态法油水相渗曲线[J]．石油勘探与开发，2001，28(2)：79-82
15．翟世奎，陈丽蓉，王镇，干晓群．冲绳海槽浮岩岩浆活动模式浅析[J]．海洋地质与第四纪地质，1997，17(1)：59-66
16．翟世奎，许淑梅，于增慧，秦蕴珊，赵一阳．冲绳海槽北部两个可能的现代海底热液喷溢点[J]．科学通报，2001，48(6)：490～492
17．张永祥，陈鸿汉．多孔介质溶质运移动力学[M]．北京：地震出版社，2000．6-9
18．朱九成，郎兆新，张丽华．多尺度油藏数值模拟的渗虑方法[J]．石油学报，1998，19(2)：49-53
19. Acuna, J.A., Yortsos, Y.C.. Numerical construction and flow simulation in networks of fractures using fractal geometry. SPE 22703, 66th Annual technical conference of SPE ,in Dallas. 1991
20. Aker E., Maloy K.J.. A two dimensional network simulator for two phase flow in porous media. Transport in Porous Media, 1998, 32: 163-186
21. Aziz K., Settari A.. Petroleum Reservoir Simulation. Applied Science Publishers, 1979
22. Bakke S., Oren P.E.. 3D pore scale modeling of heterogeneous sandstone reservoir rocks and quantitative analysis of the architecture, geometry and spatial continuity of the pore network. SPE 35479, European 3D reservoir modeling conference, in Stavanger, Norway, April, 1996
23. Bear J., Braester C.. Effective and relative permeability of anisotropic porous media. Transport in Porous Media, 1987, 2: 301-316
24. Berkowitz B., Balberg I.. Percolation approach to the problem of hydraulic conductivity in porous media. Transport in Porous Media, 1992,9:275-286
25. Berkowitz B., Balberg I.. Percolation theory and its application to groundwater hydrology. Water Resource Research, 1993, 29(4) :775-794
26. Bernadiner M.. A capillary microstructure of the wetting front. Transport in Porous Media, 1998,30:251-265
27. Bhat S. K.. Network modeling of permeability evolution of diatomite. SPE International Student Paper Contest. 1998
28. Bidner M. S., Porcell C.. Influence of phase behavior on chemical flood transport phenomena. Transport in Porous Media, 1996,24:247-273
29. Blunt M. J.. An empirical model for three phase relative permeability. SPE 56474, SPE annual technical conference in Houston, Texas, 1999
30. Blunt M. J, Richard G. H.. Pore scale modeling of multiphase flow in fractures and matrix/fracture transfer. SPE 56411, SPE annual technical conference, in Houston, Texas, Oct, 1999
31. Blunt M. J.. Pore-level network modeling of the effects of wettability. Journal of Petroleum Science and Engineering, 1997,2:494-510
32. Blunt M. J.. Physically based network modeling of multiphase flow in intermediate wet porous media. Journal of Petroleum Science and Engineering, 1998, 2:117-125
33. Blunt M. J.. Effects of heterogeneity and wetting on relative permeability using pore level modeling. SPEJ 36762, Nov 1997
34. Blunt M. J., King P. R., Goshawk A.. Relative permeability for two and three dimensional pore scale network modeling. Trans Porous Media. 1991,6:407-433
35. Braun E. M., Holland R. F.. Relative permeability hysteresis laboratory measurements and a conceptual model. SPE 28615, SPE 69th annual technical conference, in New Orleans, Sep 1994
36. Broadbent S. R., Hammersley J. M.. Percolation process crystals and mazes. Proo. Camb. Phil. Soc. 1957(53): 629-641
37. Caruana A., Dawe R. A.. Flow behavior in the presence of wettability heterogeneities. Transport I Porous media, 1996,25:217-233
38. Chandler R., Koplik J.. Capillary displacement and percolation in porous media. J. Fluid Mech, 1982,119:269-267
39. Chang Jincai, Yortsos, Yanis C.. Effect of capillary heterogeneity on Buckly-Leverett displacement. SPERE 18798,1992
40. Chatenever A, Calhoun J. C.. Visual examination of fluid benhavior in porous media- part I. Trans, AIME, 1952,195:149-156
41. Chatzis I., Dullien F. A. L.. Modeling of pore structure by 2-D and 3-D network with application to sandstone. J. Can. Pet. Technol, 1977,16:97-108
42. Chatzis I., Dullien F. A. L.. Dynamic immiscible displacement mechanisms in porous doublets: theory and experiment. J. Colloid Interface Science, 1983,91(1)
43. Cheng Yuanlin.. Three-dimensional randomized, network model for two-phase flow through porous media. SPE/DOE 9803, second Joint symposium on EOR in Tulsa, Oklahoma, April, 1981
44. Chou S.I.. Percolation theory of poam in porous media. SPE/DOE 20239, 1990
45. Collins, R. E. Flow of Fluids Through Porous Materials. Petroleum publishing CO., Tulsa, 1972
46. Colonna J., Brissaud F., Millet J.L.. Evolution of capillary and relative permeability hysteresis. SPEJ 2941,1972
47. David Wilkinson, Jorge F. W.. Invasion percolation: a new form of percolation theory. J.Phys, A:Math. 1983,16:3365-3376
48. Davis J. A., Jones S. C.. Displacement mechanisms of micellar solutions. JPT. 1968,20:7-20
49. Dias M. M., Payatakes A. C.. Network models for two Phase flow in porous media: I. Immiscible micro displacement of non-wetting fluid, II: Motion of oil ganglia. J. Fluid Mech, 1986,164:305-306; 337-358
50. Diaz C. E., Chatzis I., Dullien F. A. L.. Simulation of capillary pressure curves using bond correlated site percolation on a simple cubic network. Transport in Porous Media, 1987,2:215-240
51. Dixit A. B., Mcdougall, S. R., Sorbie, K. S.. A pore level investigation of relative permeability hysteresis in water wetting system. SPE 37233, SPE international symposium, in Houston, Texas, Feb 1997
52. Dixit A. B., Mcdougall, S. R., Sorbie, K. S., Buckley J. S.. pore scale modeling of wettability and influences on oil recovery. Proceedings of SPE/DOE Symposium on Improved Oil Recovery, in Tulsa, SPE/DOE35451, 1996
53. Dixit A. B., Mcdougall, S. R., Sorbie, K.S., Buckley J. S.. Pore scale modeling of wettability effects and their influences on oil recovery. SPE Reservoir Eval. And Eng, 1999, 2(1): 25-36
54. Dodds C. G., Kiel 0. G. Evaluation of monte-Carlo methods in studying fluid-fluid displacement and wettability in porous rock. J. Phys. Chem. 1959,63:1646-1632
55. Dong Mingzhe, Dullien F. A. L.. Characterization of water-flood saturation profile history by the complete capillary number. Transport in Porous Media, 1998,31: 213-237
56. Du C., Yortsos Y. C.. A numerical study of the critical gas saturation in porous media. Transport in Porous Media, 1999,35: 205-225
57. Dullien, F. A. L., Dhawan, G. K.. Bivariate pore size distribution of some sandstone. Journal of Colloid and Interface Science, 1957, 52(1): 129-135
58. Ewing R., Gupta S. C.. Modeling percolation properties of random media using a domain network. Water Resource Research, 1993,29(9):3169-3178
59. Fang Yisheng, Li Baozhu, Hu Yonghe, Sun Zhidao, Zhu Yuxin.. Condensate gas phase behavior and development.. SPE 50925, SPE international Oil & Gas conference, Beijing, 1998
60. Fatt I.. The network model of porous media, I: Capillary pressure characteristics. Trans. SPE AIMM, 1956,207:144-159
61. Fatt I.. The network model of porous media, II: Dynamic properties of a single size tube network. Trans. AIMM, 1956,207:160-163
62. Fatt I.. The network model of porous media, III: Dynamic properties of networks with tube radius distributions. Trans. AIMM, 1956,207:164-177
63. Fleming P. D.. An interpretation of the petrophysical properties of reservoir rocks based on percolation theory. SPE 12515,1967
64. Goslinga J.. The use of adaptive grids in numerical simulation. SPE symposium on reservoir simulation, San Francisco, Nov, 1983
65. Hardy H. H.. Mathematical model of microscopic fluid flow in porous Media. Transport in Porous Media, 1990,4:24-27
66. Heiba A. A., Davis H. T., Scriven L. E.. Effects of wettability on two phase relative permeability and capillary pressures. SPE 12172, SPE 58th technical conference, in San Fran. , Oct, 1983
67. Heiba A. A., Davis H. T., Scriven L. E.. Statistical network theory of three phase relative permeability. SPE 12690, SPE AIME 4th symposium on EOR, in Tulsa OK, April, 1984
68. Heiba A. A.. Sahimi, Muhammad, Scriven L. E.. Percolation theory of Two Phase relative permeability. SPE 11015,1983
69. Huang Yanzhang, Zhou juan, Tian genlin, Zhang jian. The phase behavior and displacement mechanism of microemulsion systems. 4th European symposium on EOR, Humberg, 1987
70. Jerauld G. R., Scriven L. E., Davis H. T.. Percolation and conduction on the 3D regular networks: A second case study in Topological disorder. J. Phys. Chem. 1984,17:3429-3439
71. Johnson E. F., Bcssler D. P., Naumann V. 0.. Calculation of relative permeability from displacement experiments. JPT. 1959(Jan):61-68
72. Kalaydjian F.. Origin and quantification of coupling between relative permeability for two-phase flow in porous media. Transport in Porous media. 1990, 5:215-229,
73. Kamath J., Xu B., Yortsos Y. C., Lee S.H.. Pore network modeling of laboratory experiment on heterogeneous carbonate. SPE 36681, SPE annual technical conference in Denver, Colorado, Oct, 1996
74. Katz A. J., Thompson A. H.. Fractal sandstone pores: implications for conductivity and pore formation. Phys. Rev. Lett, 1985, 54(12):1325-1328
75. Kharabaf H., Yortsos Y. C.. A pore network modeling for foam formation and propagation in porous media. SPE 36663, SPE annual technical conference in Denver, Colorado, Oct, 1996
76. Khatib Z. I., Vitthal S.. The use of effective medium theory and 3-D network model to predict matrix damage in sandstone formation. SPE 19649, 1989
77. King P. R.. The use of renormalization for calculating effective permeability. TIPm. 1989,4:37-58
78. Kishore K. M., Stephen J. S.. Multiphase flow in porous media: II pore-level modeling. SPE 11018, SPE AIME 57th annual fall technical conference in New Orleans, Sep, 1982
79. Koplik J., lasseter T. J.. Two-phase flow in random network models of porous media. SPEJ 11014, 1985
80. Kovscek A. R., Wong H., Radke C. J. A pore level scenario for the development of mixed wettability in oil reservoirs. AICHE J. 1993, 39(6):1072-1085
81. Laidlaw W. G., Wilson W. G., Coombe D.A.. A lattice model of foam flow in porous media: A percolation approach. Trans in Porous Media. 1993,11:139-159
82. Larson R. G., Davis, H. T., Scriven, L. E.. Elementary mechanisms of oil recovery by chemical methods. JPT, 1982, 34:243-258
83. Larson R. G., Scriven L. E., Davis H.T.. Percolation theory of two-phase flow in porous media. Chemical Engineering Science, 1980, 36:57-73
84. Laroche C., Vizika 0.. Network modeling to predict the effect of wettability heterogeneities on multiphase flow. SPE 56674, SPE annual technical conference in Houston Texas, Oct, 1999
85. Lemaitre R., Adler P.M.. Fractal porous media IV: three dimensional stick flow through random media and regular fractal. Transport in Porous media. 1990,5:325-340
86. Lendhard R. J., Ostrom M.. A parametric model for predicting relative permeability saturation-capillary pressure relationships of oil-water systems in porous media with mixwd wettability. Transport in Porous Media, 1998, 31:109-131
87. Lenormand R., Touboul E., Zarcone C.. Numerical models and experiments on immiscible displacement in porous media. J. Fluid Mech, 1988,189:165-187
88. Lenormand R.. Transport equations for fluid displacement in stratified porous media: the MHD model. SPE 30797, SPE annual technical conference in Dallas, TX , Oct, 1995
89. Lenormand R., Zaucone, C.. Role of roughness and edges during imbibition in square capillary. SPE 13264, AIME SPE 59th technical conference in Houston, TX Sep, 1984
90. Lenormand R., Zaucone, C.. Physics of blob displacement in a two dimensional porous medium. SPEFE 14882,1988
91. Maier R., Ladilaw W. G.. Fluid topology for invasion percolation in 3-D Lattices. Transport in Porous Media. 1990,5:421-428
92. Mani, V., Mohanty, K. K.. Pore-level network modeling of three phase capillary pressure and relative permeability curves. SPE 38883, 1997
93. Masson, G., Morrow, N. R.. Capillary behavior of a Perfectly wetting liquid irregular triangular tubes. Journal of Colloid and Interface Science. 1991,141(1):262-274
94. Mcdougall, S. R., Sorbie, K. S.. The combined effect of capillary and viscous on water-flood displacement efficiency in finely laminated porous media. SPE 26659, SPE 68th annual technical conference in Houston, TX, Oct, 1993
95. Mei wenrong, Shu shihong, Lai tianhua.. Pore and throat network model and application to the optimal selection of temporary plugging particles. SPE 31099,1996
96. Miller J. M., Fogler H. S.. Prediction of fluid distribution in porous media treated with foamed gel. Chem. Eng. Sci. 1995,50:3261-3274
97. Mogensen K., Stenby E.. A dynamic Two Phase pore-scale model of imbibition. Transport in Porous Media, 1998,32:299-327
98. Mohammadi S.,Sorbie K.S. .Danesh A. ,PedenJ.M. ,Heriot-watt U.. Pore-level modeling of gas-condensate flow through horizontal porous media. SPE 20479, 65th annual technical conference of SPE, New Orleans, 1990
99. Morrow R., Norman, Harris C. C.. Capillary equilibrium in porous materials. SPEJ, 1965,3:15-24
100. Mohanty K. K., Davis H. T., Scriven L. E.. Physics of oil entrapment in water wet rock. SPERE. 1987(FEB):113-128
101. Mu Honghui, Martin J. B.. Pore-scale modeling of three phase flow and the effects of wettability. SPE 59309, SPE/DOE IOR symposium in Tulsa, Oklahoma, April, 2000
102. Oren P. E., Bakke S.. Extending predictive capabilities to network models. SPE 38880, SPE annual technical conference in San Antonio, TX, Oct, 1997
103. Oren P. E.. Pore-scale network modeling of water-flood residual oil recovery by immiscible gas flooding. SPE 27814, 1994
104. Parlar M., Yortsos Y. C.. Percolation theory of steam/water relative permeability. SPE 16969, SPE 62nd annual technical conference in Dallas, TX, Sep, 1987
105. Pavone D. R.. A Darcy law extension and a new capillary pressure equation for two phase flow in porous media. SPE 20474, SPE 65th annual technical conference in New Orleans, Sep, 1990
106. Peaceman D. W.. Interpretation of well block in numerical reservoir simulation with nonsqure grid block and anisotropic permeability. SPEJ, June, 1983
107.Ransohoff T. C., Radke C. J.. Laminar flow of a wetting liquid along the corners of a predominantly gas-occupied noncircular pore. Journal of Colloid and interface Science. 1987,121(2):392-401
108. Rose W., Witherspoon P. A.. Trapping of oil in a pore doublet. Prod. Monthly. 1956,21(2): 32-37
109. Rossen W. R., Gauglitz P. A.. Percolation theory of creation and mobilization of foam in porous media. AICHEJ. 1990,36:1176-1188
110. Rossen W. R., Mamum C. K.. Minimal Path for transport in network. Phys. REV. 1993, 47B:11815-11825
111. Rosenberg D. U.. Local mesh refinement for finte difference methods. SPE 57th annual fall technical conference and exhibition of AIME, New Orleans, Sep, 1982, SPE 10974
112. Sahimi Muhammad, Yortsos Y. C.. application of fractal geometry to porous media: a review. SPE20746, SPE 65th annual technical conference in New Orleans, Sep, 1990
113. Salathiel R. A.. Oil recovery by surface film drainage in mixed wettability rocks. JPT, 1973 (OCT):1216-1224
114.Salomao M. C.. Analysis of flow in spatially correlated systems by applying the percolation theory. SPE 39039, SPE 5th Latin American and Caribbean PE conference in Rio de Janeiro, Sep 1997
115.Saraf D. N., Fatt I.. Three relative permeability measurements by unsteady-state method. SPEJ, 1966, 6:199-205
116.Singhal A. K., Somertron W. H.. Network model for the study of multiphase flow behavior in porous media. SPE 2906, AIME SPE regional meeting, in Casper Wyo, June, 1967
117.Stinchcombe R.B.. Conductivity and spin-wave stiffness in disorder system: An exactly soluble model. J. Physic: C Solid State Phy. 1974,7:179-203
118.Suchomel B., Chen B. M.. Network model of flow, transport and biofilm effects in porous media. Transport in Porous Media. 1998,30: 1-23
119. Thomas G. W.. Principles of Hydrocarbon Reservoir Simulation. 1953
120.Toledo P.G.. Capillary pressure , water relative permeability and electrical conductivity of porous media at low wetting phase saturation. SPE 23675,1992
121. Van Di jke M. I. J., Sorbie K. S., Mcdougall, S. R.. A process based approach for three phase capillary pressure and relative permeability relationships in mixed wet systems. SPE 59310, SPE/DOE symposium on IOR in Tulsa Oklahoma, April, 2000
122. Van Dijke M. I. J., Sorbie K. S., Mcdougall, S. R. Saturation dependencies of three phase relative permeability in mixed-wet and fractionally-wet systems. Adv. Water Resour. 2001,24:365-384
123. Van Dijke M. I. J., Sorbie K. S., Sohrabi D.. Three phase flow in WAG processes in mixed-wet porous media: porous-scale network simulations and comparison with micromodel experiments. SPE 75192, SPE/DOE 3th IOR symposium in Tulsa, Oklahoma, April, 2002
124. Wang X., Mohanty K. K.. Multiphase Non-darcy flow in gas-condensate reservoir. SPE 56486, SPE annual technical conference, in Houston, 1999
125.Wilkinson D. ,Willemsen J. F.. Invasion percolation: a new form of percolation theory. J.Phys.A. 1983,16: 3365-3376
126. Wu yushu, Pruess K.. Gas flow in porous media with klingbenberg effects. Transport in Porous Media. 1998,32: 117-137
127. Xu B., Kamath J., Yortsos Y. C., Lee S. H.. use of pore network model to simulate laboratory corefloods in a heterogeneous carbonate sample. SPE 38879, SPE annual conference in San Antonio, TX, Oct, 1997
128.Yortsos Y. C., Satik C.. Large scale percolation theory of drainage. Transport in Porous Media, 1993,10: 171-195
129. Zhou Dengen, Martib Blunt.. Wettability effects in three phase gravity drainage. J.Petr.Science and Engineering, 1998,20:203-211