Research on the influence of geometry on nonlinear flow in constructed rough fractures by lattice Boltzmann simulation


The fluid flow behavior in widespread rough fractures has important impacts on the utilization and protection of groundwater resources, the development of oil and gas resources, and waste treatment. However, it is hard to describe and numerically construct the complex geometry of a real rough fracture. The influence of fracture geometry on the nonlinear flow within a fracture needs further illustration. This paper provides a new simple method for constructing a 2D single rough fracture. Fracture roughness is considered to consist of rough elements and large-scale waviness. The rough element size distribution was proven to be a Gaussian distribution through laser scanning and wavelet analysis. Circles whose radii satisfy the Gaussian distribution within an STD (standard deviation) were used to construct the rough elements, which are convexities when the radii are greater than 0 mm and concave pits when the radii are less than 0 mm. The circular rough elements are tangentially arranged, and their centers are located on the large-scale waviness. A sine function with random periods was adopted to control the large-scale waviness. To research the flow nonlinearity in rough fractures, 32 rough fractures with different STDs, apertures, and tortuosity values were constructed, and the LBM (lattice Boltzmann method) was adopted to simulate the water flow in the constructed fractures under different driving pressure gradients. Through 256 simulations, the pressure field, velocity field, streamlines, and vorticity field were qualitatively and comparatively analyzed. It was found that when the driving pressure gradient is constant, nonlinearity may increase first and then decrease as the element size distribution STD or aperture increases instead of always increasing. Nonlinearity is the combined result of the fracture aperture, element size distribution STD, driving pressure gradient, and fracture tortuosity, and the main influencing factor varies by situation. The results may enhance our understanding of nonlinear flow in rough fractures.

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  1. AssyTufim (2001) Solution for spillway flow by finite difference method. J Hydraul Res 39(3):241–247

  2. Bellos CV, Soulis JV, Sakkas JG (1988) Computing 2-D unsteady open-channel flow by finite-volume method. Dev Water Sci 35:357–362.

  3. Berkowitz B (2002) Characterizing flow and transport in fractured geological media: a review. Adv Water Resour 25(8):861–884.

  4. Bing K, Chen S (2018) Numerical simulation of fluid flow and sensitivity analysis in rough-wall fractures. J Pet Sci Eng 168:546–561.

  5. Chatzikyriakou D, Buongiorno J, Caviezel D, Lakehal D (2015) DNS and LES of turbulent flow in a closed channel featuring a pattern of hemispherical roughness elements. International Journal of Heat & Fluid Flow 53:29–43.

  6. Chen Z, Qian JZ, Luo SH, Zhan HB (2009) Experimental study of friction factor for groundwater flow in a single rough fracture. J Hydrodyn 21(6):820–825.

  7. Chen YF, Zhou JQ, Hu SH, Hu R, Zhou CB (2015) Evaluation of Forchheimer equation coefficients for non-Darcy flow in deformable rough-walled fractures. J Hydrol 529(3):993–1006.

  8. Childs EC (1972) Dynamics of fluids in porous media. Eng Geol 7(2):174–175.

  9. Chorin AJ (1994) Vortex equilibria in three-dimensional space. In: Vorticity and Turbulence. Applied Mathematical Sciences, vol 103. Springer, New York, pp 135–155

  10. Croce G, D’agaro P, Nonino C (2007) Three-dimensional roughness effect on microchannel heat transfer and pressure drop. International Journal of Heat & Mass Transfer 50(25–26):5249–5259.

  11. Deuell R, Kinnmark IPE, Silliman S (1988) Finite element model of fracture flow. Dev Water Sci 35:65–70.

  12. Dou Z, Sleep B, Zhan H, Zhou Z, Wang J (2019) Multiscale roughness influence on conservative solute transport in self-affine fractures. Int J Heat Mass Transf 133:606–618.

  13. Frisch U (1991) Relation between the lattice Boltzmann equation and the Navier-Stokes equations. Physica D Nonlinear Phenomena 47(1–2):231–232.

  14. Gadelmawla ES, Koura MM, Maksoud TMA, Elewa IM, Soliman HH (2002) Roughness parameters. J Mater Process Technol 123(1):133–145.

  15. Haiping F, Zuowei W, Zhifang L, Muren L (2002) Lattice Boltzmann method for simulating the viscous flow in large distensible blood vessels. Physical Review E Statistical Nonlinear & Soft Matter Physics 65(5):051925.

  16. Hasert M, Bernsdorf J, Roller S (2011) Lattice Boltzmann simulation of non-Darcy flow in porous media. Procedia Computer Science 4:1048–1057.

  17. Hashiguchi M, Kuwahara K (1993) Numerical computation of high Reynolds number flow by using multidirectional upwind finite difference method. In: Japan Society of Computational Fluid Dynamics, Proceedings of the 6th National Symposium on Computational Fluid Dynamics, pp 567–570 (SEE N94–34731 10–34)

  18. He X, Zou Q, Luo LS, Dembo M (1997) Analytic solutions of simple flows and analysis of nonslip boundary conditions for the lattice Boltzmann BGK model. J Stat Phys 87(1–2):115–136.

  19. Huo F, Hong Z (2013) MRT-LBM-based numerical simulation of seepage flow through fractal fracture networks. SCIENCE CHINA Technol Sci 56(12):3115–3122

  20. Iatan E, Iliescu M, Bode F, Nastase I, Damian RM, Sandu M (2016) Numerical study for open-channel flow over rows of hemispheres. Energy Procedia 85:260–265.

  21. ISRM (1978) International Society for Rock Mechanics commission on standardization of laboratory and field tests: Suggested methods for the quantitative description of discontinuities in rock masses. 15(6):319–368.

  22. Ivankovic A, Demirdzic I, Williams JG, Leevers PS (1994) Application of the finite volume method to the analysis of dynamic fracture problems. Int J Fract 66(4):357–371.

  23. Jeong WC, Cho YS, Song JW (2001) A numerical study of fluid flow and solute transport in a variable-aperture fracture using geostatistical method. KSCE J Civ Eng 5(4):357–369.

  24. Kim I, Lindquist WB, Durham WB (2003) Fracture flow simulation using a finite-difference lattice Boltzmann method. Physical Review E Statistical Nonlinear & Soft Matter Physics 67(4):046708.

  25. Konzuk JS, Kueper BH (2004) Evaluation of cubic law based models describing single-phase flow through a rough-walled fracture. Water Resour Res 40(2):389–391.

  26. Krüger T, Kusumaatmaja H, Kuzmin A, Shardt O, Silva G, Viggen EM (2017) The lattice Boltzmann method. Springer, New York

  27. Liu RC, Li B, Jiang YJ (2016a) Critical hydraulic gradient for nonlinear flow through rock fracture networks: the roles of aperture, surface roughness, and number of intersections. Adv Water Resour 88:53–65.

  28. Liu X, Hui Z, Luo K, Fan J (2016b) Direct numerical simulation of turbulent boundary layer over hemispherical rough walls. Int J Multiphase Flow 83:128–141.

  29. Mohammadipoor OR, Niazmand H, Mirbozorgi SA (2014) Alternative curved-boundary treatment for the lattice Boltzmann method and its application in simulation of flow and potential fields. Physical Review E Statistical Nonlinear & Soft Matter Physics 89(1):013309.

  30. Montemagno CD, Pyrak-Nolte LJ (1999) Fracture network versus single fractures: measurement of fracture geometry with X-ray tomography. Physics & Chemistry of the Earth Part A Solid Earth & Geodesy 24(7):575–579.

  31. Moreno L, Tsang CF, Tsang Y, Neretnieks I (1990) Some anomalous features of flow and solute transport arising from fracture aperture variability. Water Resour Res 26(10):2377–2391.

  32. Neuman SP (2005) Trends, prospects and challenges in quantifying flow and transport through fractured rocks. Hydrogeol J 13(1):124–147.

  33. Nukala PK, Barai P, Zapperi S, Alava MJ, Simunović S (2010) Fracture roughness in three-dimensional beam lattice systems. Physreve 82(2):026103.

  34. Pop I, Grosan T, Cornelia R (2010) Effect of heat generated by an exothermic reaction on the fully developed mixed convection flow in a vertical channel. Communications in Nonlinear Science and Numerical Simulation 15(3):471–474.

  35. Qian YH, Orszag SA (1993) Lattice BGK models for the Navier-sStokes equation: nonlinear deviation in compressible regimes. Europhysics Letters (EPL) 21(3):255–259.

  36. Qian J, Zhou C, Zhan H, Guan H (2011) Experimental study of the effect of roughness and Reynolds number on fluid flow in rough-walled single fractures: a check of local cubic law. Hydrol Process 25(4):614–622.

  37. Qiao X, Zhao C, Shao Q, Hassan M (2018) Structural characterization of corn Stover lignin after hydrogen peroxide presoaking prior to Ammonia Fiber expansion pretreatment. Energy Fuel 32.,

  38. Sharma KM, Roy DG, Singh PK, Sharma LK, Singh TN (2017) Parametric study of factors affecting fluid flow through a fracture. Arab J Geosci 10(16):362–318.

  39. Stéphane S et al (2007) Statistics of fracture surfaces. Physical Review E Statistical Nonlinear & Soft Matter Physics 75(1):016104.

  40. Stewart ML, Ward AL, Rector DR (2006) A study of pore geometry effects on anisotropy in hydraulic permeability using the lattice-Boltzmann method. Adv Water Resour 29(9):1328–1340.

  41. Succi S, Benzi R, Higuera F (1991) The lattice Boltzmann equation: a new tool for computational fluid-dynamics. Physica D: Nonlinear Phenomena 47(1–2):219–230.

  42. Sun JP, Zhao ZY (2011) Influences of fracture aperture and roughness on hydraulic conductivity in fractured rock. Mass Pesqvetbras 1376(1):1011–1023.

  43. Sun F, Yao Y, Li G, Li X (2018a) Geothermal energy development by circulating CO2 in a U-shaped closed loop geothermal system. Energy Convers Manag 174:971–982.

  44. Sun F, Yao Y, Li G, Li X (2018b) Geothermal energy extraction in CO2 rich basin using abandoned horizontal wells. Energy 158:760–773.

  45. Sun F, Yao Y, Li G, Li X (2018c) Performance of geothermal energy extraction in a horizontal well by using CO2 as the working fluid. Energy Convers Manag 171:1529–1539.

  46. Sun F, Yao Y, Li G, Dong M (2019a) Transport behaviors of real gas mixture through nanopores of shale reservoir. J Pet Sci Eng 177:1134–1141.

  47. Sun F, Yao Y, Li G, Li X (2019b) A slip-flow model for multi-component shale gas transport in organic nanopores. Arab J Geosci 12:1–11.

  48. Sun F, Yao Y, Li G, Li X (2019c) Transport zones of oil confined in lipophilic nanopores: a technical note. Arab J Geosci 12:136–134.

  49. Sun F, Yao Y, Li G, Liu W (2019d) Simulation of real gas mixture transport through aqueous nanopores during the depressurization process considering stress sensitivity. J Pet Sci Eng 178:829–837.

  50. Sun F, Yao Y, Li G, Zhang S, Xu Z, Shi Y, Li X (2019e) A slip-flow model for oil transport in organic nanopores. J Pet Sci Eng 172:139–148.

  51. Tan HF, Kang JT, Wang CG (2015) Study on grooved wall flow under rarefied condition using the lattice Boltzmann method. Int J Mech Sci 90:1–5.

  52. Wang M, Chen YF, Ma GW, Zhou JQ, Zhou CB (2016) Influence of surface roughness on nonlinear flow behaviors in 3D self-affine rough fractures: lattice Boltzmann simulations. Adv Water Resour 96:373–388.

  53. Witherspoon PA, Wang JSY, Iwai K, Gale JE (1980) Validity of cubic law for fluid flow in a deformable rock fracture. Water Resour Res 16:1016–1024.

  54. Wu Z, Fan L, Zhao S (2018) Effects of hydraulic gradient, intersecting angle, aperture, and fracture length on the nonlinearity of fluid flow in smooth intersecting fractures: an experimental investigation. Geofluids 2018:1–14

  55. Yan J, Yuan K, Chung JN (2006) Numerical simulation of wall roughness on gaseous flow and heat transfer in a microchannel. International Journal of Heat & Mass Transfer 49(7–8):1329–1339.

  56. Zeng Z, Grigg R (2006) A criterion for non-Darcy flow in porous media. Transp Porous Media 63(1):57–69.

  57. Zhang G, Feng C, Gong W, LI YJ (2017) Simulation and analysis of the effect of roughness elements on fluid flow through single fracture based on lattice Boltzmann method. SCIENTIA SINICA Physica, Mechanica & Astronomica 47(2):024701.

  58. Zhao C, Qiao X, YanCao QS (2017) Application of hydrogen peroxide presoaking prior to ammonia fiber expansion pretreatment of energy crops. Fuel 205:184–191.

  59. Zhi D, Zhou C, Zhou Z, Wang J, Yong H (2018) Influence of eddies on conservative solute transport through a 2D single self-affine fracture. International Journal of Heat & Mass Transfer 121:597–606.

  60. Zhou C, Qian J, Zhan H, Zhou Z, Wang J, Tan Y (2017) Effect of roughness on water flow through a synthetic single rough fracture. Environ Earth Sci 76(4):186–117.

  61. Zhu HG, Jiang YD, Yi C, Xie HP (2014) A new geometrical model of fluid flow in rock fractures for valid application of the cubic law. Applied Mechanics & Materials 580-583:841–846.

  62. Zimmerman RW, Al-Yaarubi A, Pain CC, Grattoni CA (2004) Non-linear regimes of fluid flow in rock fractures. International Journal of Rock Mechanics and Mining Sciences 41(supp-S1):163–169.

  63. 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 75:102–118.

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Correspondence to Yinger Deng.

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Tian, X., Deng, Y., Jing, D. et al. Research on the influence of geometry on nonlinear flow in constructed rough fractures by lattice Boltzmann simulation. Arab J Geosci 13, 69 (2020).

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  • Rough fracture construction
  • Surface rough elements
  • Geometry influence on nonlinear flow
  • Lattice Boltzmann method