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In order to describe the pore scale fractal distribution, we present a 3D network model for fractal porous medium in this paper. According to the proposed model we simulate the immiscible two-phase flow displacement in a medium and study the viscous fingering pattern of displacement front influenced by the fractal dimension Df for pore size distribution and viscosity ratio M. The simulation results show that the capacity dimension Dh of the viscous fingering pattern decreases with Df and M increasing, and their quantitative relationship is derived by fitting the obtained data.
[1] Bensimon D, Kadanoff L P, Liang S 1996 Rev. Mod. Phys. 58 977
[2] Scheidegger A E 1974 The Physics of Flow through Porous Media (Toronto: Univ.of Toronto Press) p236
[3] King P R 1987 Phys. A: Math. Gen. 20 529
[4] Tian J P,Yao K L 2001 Chin. Phys. 10 128
[5] Luo Y Y, Zhan J M, Li M X. 2008 Acta Phys. Sin. 57 2306 (in Chinese) [罗莹莹、 詹杰民、 李毓湘 2008 57 2306]
[6] Ferer M, Bromhal G S, Simth D H 2009 Phys. Rev. E 80 011602
[7] Xu Y S 2003 Acta Phys. Sin. 52 626 (in chinese)[许友生 2003 52 626]
[8] Huang G-X, Liu Y, Wu B-Z, Xu Y-S 2005 Chin. Phys. 14 2046
[9] Zhang T, Li D L, Lu D T 2009 Sci. China G 39 1348 (in Chinese) [张 挺、 李道伦、 卢德唐 2009 中国科学G 39 1348]
[10] Katz A J, Thompson A H 1985 Phys. Rev. Lett. 54 1325
[11] Wong P Z 1988 Physics Today 41 24
[12] Yu B M, Li J H 2001 Fractals 9 365
[13] Yu B M, Chen P 2002 Int. J. Heat Mass Transfer 45 2983
[14] Yu B M 2008 Appl. Mech. Rev. 61 050801
[15] Yu B M 2009 Chinese Mechanics Digest. 23 1(in Chinese)[郁伯铭 2009 中国力学文摘 23 1]
[16] Valvatne P, Piri M, Lopez X 2005 Transport in Porous Media 58 23
[17] Chen J D, Wilkinson D 1985 Phys. Rev. Lett. 55 1892
[18] Peyret R 1996 Handbook of computational fluid mechanics (New York: Academic Press Limited) p198
[19] Xu S L 1995 Common Algorithms for Computers (Beijing: Tsinghua Press) p95(in Chinese)[徐士良1995 计算机常用算法 (北京: 清华大学出版社) 第95页]
[20] Yu B M, Zou M Q Feng Y J 2005 International Journal of Heat and Mass Transfer 48 2787
[21] Zou M Q, Yu B M, Feng Y J, Xu P 2007 Physica A 386 176
[22] Feng Y J, Yu B M, Xu P Zou M Q, 2008 J. Nanoparticle Research 10 1319
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[1] Bensimon D, Kadanoff L P, Liang S 1996 Rev. Mod. Phys. 58 977
[2] Scheidegger A E 1974 The Physics of Flow through Porous Media (Toronto: Univ.of Toronto Press) p236
[3] King P R 1987 Phys. A: Math. Gen. 20 529
[4] Tian J P,Yao K L 2001 Chin. Phys. 10 128
[5] Luo Y Y, Zhan J M, Li M X. 2008 Acta Phys. Sin. 57 2306 (in Chinese) [罗莹莹、 詹杰民、 李毓湘 2008 57 2306]
[6] Ferer M, Bromhal G S, Simth D H 2009 Phys. Rev. E 80 011602
[7] Xu Y S 2003 Acta Phys. Sin. 52 626 (in chinese)[许友生 2003 52 626]
[8] Huang G-X, Liu Y, Wu B-Z, Xu Y-S 2005 Chin. Phys. 14 2046
[9] Zhang T, Li D L, Lu D T 2009 Sci. China G 39 1348 (in Chinese) [张 挺、 李道伦、 卢德唐 2009 中国科学G 39 1348]
[10] Katz A J, Thompson A H 1985 Phys. Rev. Lett. 54 1325
[11] Wong P Z 1988 Physics Today 41 24
[12] Yu B M, Li J H 2001 Fractals 9 365
[13] Yu B M, Chen P 2002 Int. J. Heat Mass Transfer 45 2983
[14] Yu B M 2008 Appl. Mech. Rev. 61 050801
[15] Yu B M 2009 Chinese Mechanics Digest. 23 1(in Chinese)[郁伯铭 2009 中国力学文摘 23 1]
[16] Valvatne P, Piri M, Lopez X 2005 Transport in Porous Media 58 23
[17] Chen J D, Wilkinson D 1985 Phys. Rev. Lett. 55 1892
[18] Peyret R 1996 Handbook of computational fluid mechanics (New York: Academic Press Limited) p198
[19] Xu S L 1995 Common Algorithms for Computers (Beijing: Tsinghua Press) p95(in Chinese)[徐士良1995 计算机常用算法 (北京: 清华大学出版社) 第95页]
[20] Yu B M, Zou M Q Feng Y J 2005 International Journal of Heat and Mass Transfer 48 2787
[21] Zou M Q, Yu B M, Feng Y J, Xu P 2007 Physica A 386 176
[22] Feng Y J, Yu B M, Xu P Zou M Q, 2008 J. Nanoparticle Research 10 1319
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