بررسی عدد رینولدز بحرانی برای جریان غیرخطی نفت درون شکستگی های سنگی دارای زبری

نوع مقاله : یادداشت فنی

نویسنده

گروه استخراج دانشکده مهندسی معدن، نقت و ژئوفیریک، دانشگاه صنعتی شاهرود

چکیده

در این مقاله جریان غیرخطی نفت درون شکستگی‌های سنگی و با تاکید بر روی عدد رینولدز بحرانی مورد مطالعه قرار گرفته است. بدین منظور، شبیه‌سازی جریان نفت در داخل شش شکستگی سه‌بعدی با هندسه‌های متفاوت با روش حجم محدود انجام و برای دامنه وسیعی از عدد رینولدز انجام شد. نتایج حاصل از شبیه‌سازی جریان از دیدگاه  قانون فورچی میر مورد ارزیابی قرار گرفت و ضرایب افت انرژی با مکانیسم‌های ویسکوز و اینرسی (ضرایب A و B فورچی میر) محاسبه شد. سپس، تاثیر ترم‌های خطی و غیرخطی از کل افت انرژی و وابستگی بین عدد بی‌بعد فورچی میر به عدد بی‌بعد رینولدز مورد بررسی قرار گرفت. درنهایت بر اساس جمع‌بندی نتایج مراحل پیش، مقدار بحرانی عدد بی‌بعد رینولدز برای شروع جریان غیرخطی در هر یک از شکستگی‌ها تعیین شده است. نتایج حاصل از این مطالعه نشان می‌دهد، قانون فورچی میر با دقت بسیار زیادی با نتایج شبیه‌سازی انطباق دارد. با افزایش عدد رینولدز، سهم ترم خطی از کل افت فشار استاتیک (هدررفت انرژی) کاهش یافته و بطور همزمان، سهم ترم غیرخطی افزایش می‌یابد. برای شکستگی‌های مورد بررسی در این مقاله (شکستگی‌های کاملا باز)، مقدار عدد رینولدز بحرانی در بازه 30 الی 46 قرار دارد. بیشترین و کمترین مقدار عدد رینولدز بحرانی مربوط به شکستگی‌هایی است که به ترتیب دارای کمترین و بیشترین شیب نمودار عدد رینولدز-عدد فورچی میر بوده و دارای کمترین و بیشترین ضریب هدررفت انرژی با مکانیسم اینرسی هستند.

کلیدواژه‌ها


عنوان مقاله [English]

Evaluation of Critical Reynolds Number for Non-linear Crude Oil Flow through Rough-walled Fractures

نویسنده [English]

  • Morteza Javadi
Mining, Petroleum and geophysics Shahrood University of Technology
چکیده [English]

One of the most important aspects of governing physical processes through rough-walled fractures is the non-linear behavior of flow. The onset of non-linear flow in rock fractures is characterized by critical Reynolds number, which is the main object of this paper. In this paper, the technical aspects of non-linear flow of crude oil through open rock fractures and critical Reynolds number were studied. These issues were studied based on the results of three-dimensional numerical simulation of the Navier-Stokes equations for crude oil flow through rough-walled fractures. The finite volume simulation of crude oil flow through three-dimensional space of rough-walled fractures was performed for a wide range of Reynolds numbers or flow rates. The results of crude oil flow simulations were analyzed based on the Forchheimer’s law. The coefficients of energy losses due to viscous and inertial dissipation mechanisms were derived from the Forchheimer’s law regression on the results. Then, the role of linear and nonlinear energy losses with viscous and inertial dissipation mechanisms was evaluated based on the relation between Reynolds and Forchheimer non-dimension numbers. Finally, the critical Reynolds number was determined for onset of non-linear flow through rough-walled fractures. The results of this study indicate that the Forchheimer’s law appropriately describes the non-linear crude oil flow through rough-walled fractures. By increasing the Reynolds number (or flow rate), the ratio of viscous energy lose from total energy losses decreases non-linearly and simultaneously, the inertial dissipation becomes the dominant mechanism of energy lose. The critical Reynolds number for crude oil is in the range of 30 to 46 for the open fractures of this study. The maximum and minimum of critical Reynolds number follow the minimum and maximum of inertial dissipation coefficient and also the gradient of Reynolds- Forchheimer curve, respectively.

کلیدواژه‌ها [English]

  • Critical Reynolds
  • Forchheimer Number
  • Rough-walled Fractures
  • Non-linear Flow
  • Crude Oil
  • Rough Fracture
[1] Nelson, R. (2001). Geologic Analysis of Naturally Fractured Reservoirs. United States of America: Gulf Professional Publishing.
[2] Bear, J., Tsang, C.-F., & de Marsily, G. (1993). Flow and Contaminant Transport in Fractured Rock. San Diego: Academic Press, Inc.
[3] Javadi, M., Sharifzadeh, M., Shahriar, K., & Mehrjooii, M. (2012). Roughness effect on velocity domain through rock fractures. Sharif Journal of Science and Technology, Civil Engineering, 21-28.
[4] Witherspoon, P., Wang, J., Iwai, K., & Gale, J. (1980). Validity of cubic law for fluid flow in a deformable rock fracture. Water Resour. Res., 1016–1024.
[5] Sarkar, S., Toksöz, M., & Burns, D. (2002). Fluid Flow Simulation in Fractured Reservoirs. MIT Earth Resources Laboratory.
[6] Zimmerman, R., & Bodvarsson, G. (1996). Hydraulic conductivity of rock fractures. Transport in Porous Media, 1−30.
[7] Neuzil, C., & Tracy, J. (1981). Flow through fractures. Water Resource. Res., 191–199.
[8] Javadi, M., Sharifzadeh, M., Shahriar, K., & Mitani, Y. (2014). Critical Reynolds Number For Non-linear Flow Through Rough-walled Fractures: The Role of Shear Processes. Water Resources Research, 1789–1804.
[9] Wilson, C. R., & Witherspoon, P. A. (1974). Steady state flow in rigid networks of fractures. Water Res. Res., 328–335.
[10] Elsworth, D., & Goodman, R. (1986). Characterization of Rock Fissure Hydraulic Conductivity Using Idealized Wall Roughness Profiles. Int. J. Rock Mech. Min. Sci., 233-243.
[11] Tsang, Y. W., & Tsang, C. F. (1987). Channel Model of Flow through Fractured Media. Water Resour. Res., 467–479.
[12] Tsang, Y., & Witherspoon, P. (1981). Hydromechanical Behavior of a Deformable Rock Fracture Subject to Normal Stress. J. Geophys. Res., 9287-9298.
[13] Renshaw, C. E. (1995). On the relationship between mechanical and hydraulic apertures in rough-walled fractures. Journal of Geophysical Research, 629-636.
[14] Thompson, M. E., & Brown, S. R. (1991). The effect of anisotropic surface roughness on flow and transport in fracture. Journal of Geophysical Research , 923–932.
[15] Koyama, T., Fardin, N., Jing, L., & Stephansson, O. (2006). Numerical simulation of shear-induced flow anisotropy and scale-dependent aperture and transmissivity evolution of rock fracture replicas. International Journal of Rock Mechanics & Mining Sciences, 89–106.
[16] Brown, S., Stockman, H., & Reeves, S. (1995). Applicability of the Reynolds equation for modeling fluid flow between rough surfaces. Geophys. Res. Lett., 2537–2540.
[17] Nicholl, M., Rajaram, J. H., Glass, R., & Detwiler, R. (1999). Saturated flow in a single fracture: Evaluation of the Reynolds equation in measured aperture field. Water Res., Res., 3361-3373.
[18] Oron, A. P., & Berkowitz, B. (1998). Flow in rock fractures: the local cubic law assumption reexamined. Water Resources Research, 2811-2824.
[19] Ge, S. (1997). A governing equation for fluid flow in rough fractures. Water Resour. Res., 53–61.
[20] Yeo, I. W., & Ge, S. (2005). Applicable range of the Reynolds equation for fluid flow in a rock Fracture. Geosciences Journal, 347-352.
[21] Brown, S. R. (1987). Fluid flow through rock joints: the effect of surface roughness. Journal of Geophysical Research , 1337-1347.
[22] Moreno, L., Tsang, Y. W., Tsang, C. F., Hale, F. V., & Neretnieks, I. (1988). Flow and tracer transport in a single fracture: A stochastic model and its relation to some field observations. Water Resources Research, 2033-2048.
[23] Saedi, B., Ayatollahi, S., & Masihi, M. (2015). Free fall and controlled gravity drainage processes in fractured porous media: Laboratory and modelling investigation. Can. J. Chem. Eng., 2286-2297.
[24] Harimi, B., Ghazanfari, M. H., & Masihi, M. (2020). Modeling of capillary pressure in horizontal rough-walled fractures in the presence of liquid bridges. Journal of Petroleum Science and Engineering, 106642.
[25] Koyama, T., Neretnieks, I., & Jing, L. (2008). A numerical study on differences in using Navier–Stokes and Reynolds equations for modeling the fluid flow and particle transport in single rock fractures with shear. International Journal of Rock Mechanics and Mining Science, 1082–1101.
[26] Brush, D., & Thomson, N. R. (2003). Fluid flow in synthetic rough-walled fractures: Navier-Stokes, Stokes, and local cubic law simulations. Water Res. Res., 1085-1099.
[27] Zimmerman, R. W., Al-Yaarubi, A. H., Pain, C. C., & Grattoni, C. A. (2004). Non-linear regimes of fluid flow in rock fractures. International Journal of Rock Mechanics and Mining Science, 163-169.
[28] Nazridoust, K., Ahmadi, G., & Smith, D. H. (2006). A new friction factor correlation for laminar, single-phase flows through rock fractures. Journal of Hydrology, 315– 328.
[29] Sharifzadeh, M., Javadi, M., & Shahriar, K. (2010). Evaluation of Non-linear fluid flow through rough-walled fractures. Amirkabir Journal of Science and Technology, Civil Engineering, 21-28.
[30] Zhou, J.-Q., Hu, S.-H., Chen, Y.-F., Wang, M., & Zhou, C.-B. (2016). The Friction Factor in the Forchheimer Equation for Rock. Rock Mech Rock Eng, DOI 10.1007/s00603-016-0960-x.
[31] Zhou, J.-Q., Hu, S.-H., Fang, S., Chen, Y.-F., & Zhou, C.-B. (2015). Nonlinear flow behavior at low Reynolds numbers through rough-walled fractures subjected to normal compressive loading . International Journal of Rock Mechanics & Mining Sciences, 202–218.
[32] Rong, G., Tan, J., Zhan, H., He, R., & Zhang, Z. (2020). Quantitative evaluation of fracture geometry influence on nonlinear flow in a single rock fracture. Journal of Hydrology, 125162.
[33] Konzuk, J., & Kueper, B. (2004). Evaluation of cubic law based models describing single-phase flow through a rough-walled fracture. WATER RESOURCES RESEARCH, W02402,.
[34] Javadi, M., Sharifzadeh, M., & Shahriar, K. (2010). A New Geometrical Model for Non-Linear Fluid Flow through Rough Fractures. J. Hydrol., 18–30.
[35] Zou, L., Jing, L., & Cvetkovic, V. (2015). Roughness decomposition and nonlinear fluid flow in a single rock fracture. International Journal of Rock Mechanics & Mining Sciences, 102–118.
[36] Liu, R., Li, B., & Jiang, Y. (2016). Critical hydraulic gradient for nonlinear flow through rock fracture networks: The roles of aperture, surface roughness, and number of intersections. Advances in Water Resources, 53–65.
[37] Javadi, M. (2018). Tree-dimensional Crude Oil Flow Simulation through Rough-walled Fractures for Evaluating the Classic Geometrical Equations. Journal of Petroleum Geomechanics, 1-17.
[38] Javadi, M. (2019). Non-linear Behavior of Crude Oil Flow through Rough-walled Fractures by Three-Dimensional Nevier-Stokes Numerical Simulation . Journal of Petroleum Geomechanics, 44-59.
[39] Sharifzadeh, M., & Javadi, M. (2017). Groundwater and underground excavations: From theory to practice. In X.-T. Feng, Rock Mechanics and Engineering, Volume 3: Analysis, Modelling and Design; Editor (pp. 299-330).
[40] Kitandis, P., & Dykaar, B. (1997). Stokes Flow in a Slowly Varying Two-Dimensional Periodic Pore. Transport in Porous Media, 89–98.
[41] Bear, J. (1972). Dynamics of Fluids in Porous Media. New York: Elsevier.