بررسی رفتار غیرخطی جریان نفت درون شکستگی های سنگی دارای زبری با تکیه بر شبیه سازی سه بعدی معادلات ناویه-استوکس

نوع مقاله : مقاله پژوهشی

نویسنده

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

چکیده

در این مقاله، تاثیر جریان غیرخطی نفت درون شکستگی های سنگی بر پارامترهای هیدرولیکی و با هدف ارزیابی انحراف رفتار هیدرولیکی شکستگی ها از قانون دارسی مورد مطالعه قرار گرفته است. بدین منظور، جریان نفت در داخل شکستگی سه بعدی دارای دیواره های زبر برای دامنه وسیعی از دبی حجمی جریان عبوری و با استفاده از حل عددی همزمان معادلات ناویه-استوکس و پیوستگی به روش حجم محدود شبیه سازی شده است. نتایج حاصل از این مقاله نشان می دهد که جریان نفت درون شکستگی های سنگی دارای رفتار غیرخطی بوده و به همین دلیل، دهانه هیدرولیکی و نفوذپذیری شکستگی پارامترهای ثابت (مستقل) نبوده و کاملا به میزان دبی جریان عبوری از شکستگی وابسته هستند. در حقیقت، با افزایش سرعت جریان در داخل شکستگی ها، مقادیر دهانه هیدرولیکی شکستگی و نفوذپذیری بطور غیرخطی کاهش می یابند که مقدار کاهش نسبی این دو پارامتر برای شکستگی های مورد مطالعه در این مقاله بترتیب در بازه 10 و 20 درصد بوده است. همچنین، نتایج حاصل از برازش قوانین دارسی و فورچی میر به نتایچ حاصل از شبیه سازی نشان می دهد که رفتار جریان در شکستگی ها سنگی توسط قانون فورچی میر بخوبی توصیف می شود بگونه ای که دقت قانون فورچی میر برای توصیف رفتار جریان نفت در شکستگی مورد بررسی بیش از 98% بوده در حالی که خطای قانون دارسی به بیش از 27% نیز می رسد.

کلیدواژه‌ها


عنوان مقاله [English]

Non-linear Behavior of Crude Oil Flow through Rough-walled Fractures by Three-Dimensional Nevier-Stokes Numerical Simulation

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 main aim of this paper is to investigate the effect of non-linear flow on the hydraulic parameters and deviation from Darcy’s law. To reach this goal, the three-dimensional simulation of crude oil flow inside rough-walled fractures was performed by numerical solving the Navier-Stokes equations supplemented by the continuity equation through application of finite volume technique. The crude oil flow through three-dimensional space of rough-walled fractures was numerically simulated for a wide range of inlet velocity of flow rates. Then, the regime of flow, the deviation of crude oil flow through rough-walled open fractures from Darcy’s law, nonlinear relationship between hydraulic gradient and flow rate, and the effect of non-linear flow on the hydraulic aperture and permeability of fractures were investigated by analysis of crude oil flow simulation. The results of this study indicate that the crude oil flow through rough-walled fractures is non-linear; therefore the hydraulic parameters such as hydraulic aperture and permeability are not constant and highly depend on the flow rate of crude oil. In fact, hydraulic aperture and permeability of fractures decrease non-linearly by increment of flow rate, where these parameters show 10% and 20% of relative decrement, respectively. In addition, the results of regression analysis show that the Forchheimer’s law appropriately describes the behavior of crude oil flow through rough-walled fractures than Darcy’s law. Moreover, the accuracy of Forchheimer’s law is much more than 98%, but the relative error of Darcy’s law reaches to 27%.

کلیدواژه‌ها [English]

  • Fracture Hydraulic
  • Hydraulic Aperture
  • Rough-walled Fractures
  • Forchheimer’s law
  • Non-linear Flow
  • Darcy’s law Deviation
  • Crude Oil
Bear, J. (1972). Dynamics of Fluids in Porous Media. New York: Elsevier.
Bear, J., Tsang, C.-F., & de Marsily, G. (1993). Flow and Contaminant Transport in Fractured Rock. SanDiego: Academic Press, Inc.
Brown, S. R. (1987). Fluid flow through rock joints: the effect of surface roughness. Journal of Geophysical Research , 1337-1347.
Brown, S., Stockman, H., & Reeves, S. (1995). Applicability of the Reynolds equation for modeling fluid flow between rough surfaces. Geophys. Res. Lett., 2537–2540.
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.
David, C. (1993). Geometry of flow paths for fluid transport in rocks. Journal of Geophysical Research, 267-278.
Elsworth, D., & Goodman, R. (1986). Characterization of Rock Fissure Hydraulic Conductivity Using Idealized Wall Roughness Profiles. Int. J. Rock Mech. Min. Sci., 233-243. 
Ge, S. (1997). A governing equation for fluid flow in rough fractures. Water Resour. Res., 53–61.
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.
Javadi, M., Sharifzadeh, M., & Shahriar, K. (2010). A New Geometrical Model for Non-Linear Fluid Flow through Rough Fractures. J. Hydrol., 18–30.
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.
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.
Kitandis, P., & Dykaar, B. (1997). Stokes Flow in a Slowly Varying Two-Dimensional Periodic Pore. Transport in Porous Media, 89–98.
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.
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.
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.
Nelson, R. (2001). Geologic Analysis of Naturally Fractured Reservoirs. United States of America: Gulf Professional Publishing.
Neuzil, C., & Tracy, J. (1981). Flow through fractures. Water Resource. Res., 191–199.
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.
Oron, A. P., & Berkowitz, B. (1998). Flow in rock fractures: the local cubic law assumption reexamined. Water Resources Research, 2811-2824.
Piggott, A. R., & Elsworth, D. (1993). Laboratory assesment of the equivalent apertures of a rock fracture. Geophysical Research Letters, 1387-1390.
Renshaw, C. E. (1995). On the relationship between mechanical and hydraulic apertures in ro ugh-walled fractures. Journal of Geophysical Research, 629-636.
Rønningsen, H. P. (2012). Rheology of Petroleum Fluids. ANNUAL TRANSACTIONS OF THE NORDIC RHEOLOGY SOCIETY, 11-18.
Sarkar, S., Toksöz, M., & Burns, D. (2002). Fluid Flow Simulation in Fractured Reservoirs. MIT Earth Resources Laboratory.
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). CRC.
Sharifzadeh, M., Javadi, M., & Shahriar, K. (2010). Evaluation of Non-linear fluid flow through roughwalled fractures. Amirkabir Journal of Science and Technology, Civil Engineering, 21-28.
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.
Tsang, Y. W., & Tsang, C. F. (1987). Channel Model of Flow through Fractured Media. Water Resour. Res., 467–479.
Tsang, Y., & Witherspoon, P. (1981). Hydromechanical Behavior of a Deformable Rock Fracture Subject to Normal Stress. J. Geophys. Res., 9287-9298.
Wilson, C. R., & Witherspoon, P. A. (1974). Steady state flow in rigid networks of fractures. Water Res. Res., 328–335.
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.
Yeo, I. W., & Ge, S. (2005). Applicable range of the Reynolds equation for fluid flow in a rock Fracture. Geosciences Journal, 347-352.
Zimmerman, R. W., Al-Yaarubi, A. H., Pain, C. C., & Grattoni, C. A. (2004). Non-linear regimes of fluid flow in rock fractures. Int. J. Rock Mech. Min. Sci., 163–169.
Zimmerman, R., & Bodvarsson, G. (1996). Hydraulic conductivity of rock fractures. Transport in Porous Media, 1−30.