分形复合非牛顿幂律流体渗流模型解的研究
Research on the Solution of Fractal Composite Non-Newtonian Power-Law Fluid Seepage Model
DOI: 10.12677/aam.2026.154143, PDF,    科研立项经费支持
作者: 刘金凤：西华大学理学院，四川 成都
关键词: 分形复合非牛顿油藏；相似构造法；Fractured Composite Non-Newtonian Reservoir； Similarity Construction Method
摘要: 在实际油气田开发中，分形复合油藏由于储层孔隙结构复杂、非均质性较强，地层流体多表现为非牛顿幂律流体特性，针对此问题，本文建立了分形复合非牛顿幂律流体渗流模型，该模型结合了分形油藏的地质特征和非牛顿流体的流变特征，考虑了井筒储集与表皮因子的内边界情形，以便更精确地贴合实际油藏边界的弹性变形特性。在求解过程中，本文推广了相似构造法，结合无量纲化、Laplace变换及数值反演，获得了统一相似连分数结构的实空间解，从而简化了求解过程。
Abstract: In practical oil and gas field development, fractured composite reservoirs exhibit complex pore structures and strong heterogeneity, with formation fluids often displaying non-Newtonian power-law fluid characteristics. To address this problem, this paper establishes a seepage model for fractal composite non-Newtonian power-law fluids. This model combines the geological characteristics of fractal reservoirs and the rheological properties of non-Newtonian fluids, taking into account the inner boundary conditions of wellbore storage and skin factor, so as to more accurately reflect the elastic deformation characteristics of actual reservoir boundaries. In the solution process, this study extends the similarity construction method, combining dimensionless analysis, Laplace transform, and numerical inversion to obtain a unified similarity continued fraction structure for the real space solution, thus simplifying the solution process.
文章引用：刘金凤. 分形复合非牛顿幂律流体渗流模型解的研究[J]. 应用数学进展, 2026, 15(4): 130-141. https://doi.org/10.12677/aam.2026.154143

参考文献

[1] Mandelbrot, B.B. (1982) The Fractal Geometry of Nature. W. H. Freeman.
[2] Katz, A. and Lee, C. (1990) Fractal Model of Fluid Flow in Porous Media. Journal of Petroleum Science and Engineering, 3, 1-9.
[3] Flamenco-López, F. and Camacho-Velázquez, R. (2003) Determination of Fractal Parameters of Fracture Networks Using Pressure-Transient Data. SPE Reservoir Evaluation & Engineering, 6, 39-47. [Google Scholar] [CrossRef] 
[4] Jordan, C.L. and Mattar, L. (2002) Comparison of Pressure Transient Behaviour of Composite and Two-Layered Reservoirs. Journal of Canadian Petroleum Technology, 41, 47-54. [Google Scholar] [CrossRef] 
[5] 向开理, 李允, 李铁军. 不等厚分形复合油藏不稳定渗流问题的数学模型及压力特征[J]. 石油勘探与开发, 2001, 28(5): 49-52.
[6] 向开理, 涂晓青. 分形复合油藏非牛顿幂律流体不稳定渗流的数学模型[J]. 计算物理, 2004, 21(6): 558-564.
[7] 徐昌学, 李顺初, 朱维兵. 分形复合油藏试井分析解的相似结构[J]. 钻采工艺, 2006, 29(5): 39-42.
[8] 孔祥言, 李道伦, 卢德唐. 孔隙和裂缝分形油藏的瞬态压力分析[J]. 中国科学(E辑), 2008, 38(11): 1815-1826.
[9] Santos, A., Silva, M. and Costa, J. (2013) Relationship between Fractal Characteristics and Gas-Water Flooding Effects. Journal of Petroleum Science and Engineering, 108, 145-153.
[10] 李顺初, 王俊超, 许丽. 复合油藏球向渗流问题的解的相似结构[J]. 数学的实践与认识, 2014, 44(3): 122-127.
[11] Abbasi, M., Izadmehr, M., Karimi, M., Sharifi, M. and Kazemi, A. (2017) Analytical Study of Fluid Flow Modeling by Diffusivity Equation Including the Quadratic Pressure Gradient Term. Computers and Geotechnics, 89, 1-8. [Google Scholar] [CrossRef] 
[12] Abbasi, M., Kazemi, A. and Sharifi, M. (2019) Modeling of Transient Shape Factor in Fractured Reservoirs Considering the Effect of Heterogeneity, Pressure-Dependent Properties and Quadratic Pressure Gradient. Oil & Gas Science and Technology—Revue d’IFP Energies nouvelles, 74, Article No. 89. [Google Scholar] [CrossRef] 
[13] Su, H.B., Zhang, S.M., Sun, Y.H., et al. (2020) A Comprehensive Model for Oil-Water Relative Permeabilities in Low-Permeability Reservoirs by Fractal Theory. Fractals, 28, Article 2050055. [Google Scholar] [CrossRef] 
[14] 罗静. 弹性外边界条件下分形复合油藏渗流模型解的研究[D]: [硕士学位论文]. 成都: 西华大学, 2023.
[15] Dong, X.X., Peng, Y., Li, W.J., et al. (2025) Application of Polynomial Type Elastic Outer Boundary Conditions in Fractal Composite Reservoir Seepage Model. Computers & Geosciences, 194, Article 105764. [Google Scholar] [CrossRef] 
[16] Poollen, H.K. and Jargon, J.R. (1969) Steady-State and Unsteady-State Flow of Non-Newtonian Fluids through Porous Media. Society of Petroleum Engineers Journal, 1567, 1-8.
[17] Ikoku, C.U. and Ramey, H.J. (1978) Transient Flow of Non-Newtonian Power-Law Fluids in Porous Media. Stanford University.
[18] Ikoku, C.U. and Ramey, H.J. (1980) Wellbore Storage Effects on Transient Flow of Non-Newtonian Power-Law Fluids in Porous Media. Journal of Petroleum Technology, 9075, 1425-1434.
[19] Vongvuthipornchai, S. and Raghavan, R. (1987) Well Test Analysis of Data Dominated by Storage and Skin: Non-Newtonian Power-Law Fluids. SPE Formation Evaluation, 2, 618-628. [Google Scholar] [CrossRef] 
[20] 刘泽俊, 孙智, 宋考平. 有界地层非牛顿渗流试井解释模型[J]. 大庆石油地质与开发, 1996, 15(3): 63-66.
[21] 宋考平, 祝俊峰, 刘泽俊. 多区复合油藏非牛顿幂律流体试井解释[J]. 石油学报, 1997(2): 81-86.
[22] 向开理, 李顺初, 涂晓青. 分形复合油藏不稳定渗流模型及Laplace空间解析解[J]. 钻采工艺, 2004, 27(3): 48-51.
[23] 王雅茹, 王晓冬, 石在虹. 封闭地层中非牛顿幂律流体压降特征分析[J]. 水动力学研究与进展A辑, 2009, 24(1): 45-50.
[24] 龚伟, 李晓平. 非牛顿流体试井分析现状及展望[J]. 油气井测试, 2006, 15(1): 71-74.
[25] 刘文涛, 张德富, 程宏杰, 王晓光. 聚合物驱牛顿-非牛顿-牛顿三区复合试井模型[J]. 油气藏评价与开发, 2019, 9(4): 26-30.
[26] Oluogun, M.O. and Igbokoyi, A.O. (2022) A 2-D Analytical Solution to Infinite Conductivity Fracture Injection Pressure Transient Analysis in Non-Newtonian/Newtonian Composite Infinite Reservoirs. Journal of Petroleum Exploration and Production Technology, 12, 2453-2465. [Google Scholar] [CrossRef] 
[27] 刘式适, 刘式达. 特殊函数[M]. 第2版. 北京: 气象出版社, 2002.

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