Abstract
The influence of fracture roughness on solute transport is an important research direction of hydrogeology. It provides guidance for fluid transport in rough fractures. In this paper, the common self-affine method is used to construct a single fracture with different roughness. The solute transport in three-dimensional fractures with different roughness is numerically simulated by LBM, and the flow field and concentration field are analyzed. The non-Fickian transport characteristics of solute are described through the spatial evolution of solute, and the non-Fickian degree of solute is described and explained. The penetration curve (BTC) and residence time distribution (RTD) are calculated, and the degree of non-Fickian phenomenon is quantified according to the continuous time random walk (CTRW TPL) inversion model. The results show that under the same Reynolds number, the coarser the fracture surface is, the more obvious the non-Fickian fracture is. The velocity and streamline are evenly distributed on the fracture surface with the smallest roughness. With the increase of roughness, the velocity and streamline become more and more uneven. These results are due to the preference channel, which allows part of the solution to reach the outlet early at a higher speed, resulting in “early arrival.” In addition to the inferior channel, the blocked area shall also be mainly responsible for the “long tail.” In this paper, a new interpretation of non-Fickian solute transport in three-dimensional rough fractures is proposed, which provides theoretical support and scheme suggestions for engineering applications such as groundwater resources development and pollution prevention.
Similar content being viewed by others
References
Albarran N, Missana T et al (2013) Analysis of latex, gold and smectite colloid transport and retention in artificial fractures in crystalline rock. Colloids Surf, A 435:115–126. https://doi.org/10.1016/j.colsurfa.2013.02.002
Barkai E (2002) CTRW pathways to the fractional diffusion equation. Chem Phys 284(1):13–27. https://doi.org/10.1016/S0301-0104(02)00533-5
Bauget F, Fourar M (2008) Non-Fickian dispersion in a single fracture. J Contam Hydrol 100(3):137–148. https://doi.org/10.1016/j.jconhyd.2008.06.005
Bear J (1988) Dynamics of Fluids in Porous Media. New York, Dover Publications. https://doi.org/10.1016/0013-7952(73)90047-1
Becker MW, Shapiro AM (2000) Tracer transport in fractured crystalline rock: Evidence of nondiffusive breakthrough tailing. Water Resour Res 36(7):1677–1686. https://doi.org/10.1029/2000wr900080
Cai J, Zhou Z et al (2011) Laboratory experiments on solute transport in a partial transfixion single fracture. J Hydrodyn Ser B 23(5):570–579. https://doi.org/10.1016/S1001-6058(10)60151-5
Cardenas M, Slottke D et al (2009) Effects of inertia and directionality on flow and transport in a rough asymmetric fracture. J Geophys Res 114(B06204):1–11. https://doi.org/10.1029/2009JB006336
Chaaban M, Heider Y, Markert B (2020) Upscaling LBM-TPM simulation approach of Darcy and non-Darcy fluid flow in deformable, heterogeneous porous media. Int J Heat Fluid Flow 83:108566. https://doi.org/10.1016/j.ijheatfluidflow.2020.108566
Cortis A, Berkowitz B (2005) Computing Anomalous contaminant transport in porous media: The CTRW MATLAB toolbox. Ground water 43:947–50. https://doi.org/10.1111/j.1745-6584.2005.00045.x
Cortis A, Berkowitz B (2010) Computing Anomalous Contaminant Transport in Porous Media: The CTRW MATLAB Toolbox. Ground Water 43(6):947–950. https://doi.org/10.1111/j.1745-6584.2005.00045.x
de Dreuzy J, Ramírez J (2015) On the validity of effective formulations for transport through heterogeneous porous media. Hydrol Earth Syst Sci Discuss 12:12281–12310. https://doi.org/10.5194/hessd-12-12281-2015
Dentz M, Le Borgne T et al (2011) Mixing, spreading and reaction in heterogeneous media: A brief review. J Contam Hydrol 120–121:1–17. https://doi.org/10.1016/j.jconhyd.2010.05.002
Dou Z, Zhou ZF (2014) Lattice Boltzmann simulation of solute transport in a single rough fracture. Water Sci Eng 7(3):277–287. https://doi.org/10.3882/j.issn.1674-2370.2014.03.004
Dou Z, Zhou ZF et al (2016) Three-dimensional analysis of spreading and mixing of miscible compound in heterogeneous variable-aperture fracture. Water Sci Eng 9(4):293–299. https://doi.org/10.1016/j.wse.2017.01.007
Dou Z, Chen Z et al (2018) Influence of eddies on conservative solute transport through a 2D single self-affine fracture. Int J Heat Mass Transf 121:597–606. https://doi.org/10.1016/j.ijheatmasstransfer.2018.01.037
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 Transfer 133:606–618. https://doi.org/10.1016/j.ijheatmasstransfer.2018.12.141
Drazer G, Koplik J (2002) Transport in rough self-affine fractures. Phys Rev E Stat Nonlin Soft Matter Phys 66(2 Pt 2):026303. https://doi.org/10.1103/physreve.66.026303
Dullien F (1992) Porous media: fluid transport and pore structure, 2nd edn. Academic Press, San Diego. J Geochem Explor 48(3):372. https://doi.org/10.1016/0375-6742(93)90016-F
Ekeleme AC, Ekwueme BN, Agunwamba JC (2021) Modeling contaminant transport of nitrate in soil column. Emerging Sci J 5(4):471–485. https://doi.org/10.28991/esj-2021-01290
Golian et al (2020) Prediction of tunnelling impact on flow rates of adjacent extraction water wells. Q J Eng Geol Hydrogeol 53(2):236. https://doi.org/10.1144/qjegh2019-055
Gudmundsson A, Berg SS, Lyslo KB, Skurtveit E (2001) Fracture network and fluid transport in active fault zones. J Struct Geol 23(2):343–353. https://doi.org/10.1016/S0191-8141(00)00100-0
Guo Z, Chang S (2013) Lattice Boltzmann method and its applications in engineering. Word Sci. https://doi.org/10.1142/9789814508308_0001
Guo Z, Zheng C, Shi B (2002) An extrapolation method for boundary conditions in lattice boltzmann method. Phys Fluids 14(6):2007–2010. https://doi.org/10.1063/1.1471914
He X, Luo L (1997) Lattice Boltzmann Model for the Incompressible Navier-Stokes Equation. J Stat Phys 88(3):927–944. https://doi.org/10.1023/B:JOSS.0000015179.12689.e4
Hosseini N, Bajalan Z, Khoei AR (2020) Numerical modeling of density-driven solute transport in fractured porous media with the extended finite element method. Adv Water Resour 136:103453. https://doi.org/10.1016/j.advwatres.2019.103453
Houseworth JE (2006) An analytical model for solute transport in unsaturated flow through a single fracture and porous rock matrix. Water Resour Res 42:W01416. https://doi.org/10.1029/2004WR003770
Hu Y, Xu W, Zhan L, Ye Z, Chen Y (2020) Non-fickian solute transport in rough-walled fractures: the effect of contact area. Water 12(7):2049. https://doi.org/10.3390/w12072049
Huang N, Liu R et al (2017) Numerical study of the geometrical and hydraulic characteristics of 3D self-affine rough fractures during shear. J Natural Gas Sci Eng 45:127–142. https://doi.org/10.1016/j.jngse.2017.05.018
Kang PK, Dentz M, Le Borgne T et al (2015) (2015) Anomalous transport on regular fracture networks: Impact of conductivity heterogeneity and mixing at fracture intersections[J]. Phys Rev E 92(2):022148. https://doi.org/10.1103/PhysRevE.92.022148
Krüger T (2011) Unit conversion in LBM. Talk presented at LBM Workshop 2011. Edmonton, Canada. 2011-08-22 - 2011-08-26. http://hdl.handle.net/11858/00-001M-0000-0019-3070-F
Land LF (1978) Unsteady solute-transport simulation in streamflow using a finite-difference model. Water Resources Investigations Report. 78-18 Reston, VA. https://doi.org/10.3133/wri7818
Lapcevic PA, Novakowski KS, Sudicky EA (1999) The interpretation of a tracer experiment conducted in a single fracture under conditions of natural groundwater flow. Water Resour Res 35(8):2301–2312. https://doi.org/10.1029/1999wr900143
Lee SH, Yeo IW, Lee KK, Lee WS (2017) The role of eddies in solute transport and recovery in rock fractures: implication for groundwater remediation. Hydrol Process 31(20):3580–3587. https://doi.org/10.1002/2015GL065116
Li B, Mo Y, Zou L, Liu R, Cvetkovic V (2020) Influence of surface roughness on fluid flow and solute transport through 3D crossed rock fractures. J Hydrol 582:124284. https://doi.org/10.1016/j.jhydrol.2019.124284
Liu HH, Bodvarsson GS et al (2004) A corrected and generalized successive random additions algorithm for simulating fractional levy motions. Math Geol 36(3):361–378. https://doi.org/10.1023/B:MATG.0000028442.71929.26
Liu R, Huang N, Jiang Y, Jing H, Yu L (2020) A numerical study of shear-induced evolutions of geometric and hydraulic properties of self-affine rough-walled rock fractures. Int J Rock Mech Min Sci 127:104211. https://doi.org/10.1016/j.ijrmms.2020.104211
Mittal R, Iaccarino G (2005) IMMERSED BOUNDARY METHODS. Annu Rev Fluid Mech 37(1):239–261. https://doi.org/10.1146/annurev.fluid.37.061903.175743
Molz F, Liu H et al (1997) Fractional Brownian Motion and Fractional Gaussian Noise in Subsurface Hydrology: A Review, Presentation of Fundamental Properties, and Extensions. Water Resources Research - WATER RESOUR RES 33:2273–2286. https://doi.org/10.1029/97wr01982
Moukalled F, Mangani L, Darwish M (2016) The finite volume method in computational fluid dynamics: an advanced introduction with OpenFOAM® and Matlab. https://doi.org/10.1007/978-3-319-16874-6
Murdoch LC, Richardson JR et al (2006) Forms and sand transport in shallow hydraulic fractures in residual soil. Can Geotech J 43(10):1061–1073. https://doi.org/10.1139/t06-063
Ostad-Ali-Askari K, Shayannejad M (2021) Quantity and quality modelling of groundwater to manage water resources in Isfahan-Borkhar Aquifer. Environ Dev Sustain 23:15943–15959. https://doi.org/10.1007/s10668-021-01323-1
Ostad-Ali-Askari and Hossein Ghorbanizadeh Kharazi,te al. (2019), Effect of Management Strategies on Reducing Negative Impacts of Climate Change on Water Resources of the Isfahan-Borkhar Aquifer Using MODFLOW. River Research and Applications, John Wiley & Sons Ltd. 35(6):611-631.https://doi.org/10.1002/rra.3463
Ouzaid I, Benmebarek N, Benmebarek S (2020) FEM Optimisation of Seepage Control System Used for Base Stability of Excavation. Civil Eng J 6(9):1739–1751. https://doi.org/10.28991/cej-2020-03091579
Qian YH, D’Humières D et al (1992) Lattice BGK Models for Navier-Stokes Equation. Europhysics Letters (EPL) 17(6):479–484. https://doi.org/10.1209/0295-5075/17/6/001
Qian JZ, Chen Z et al (2011) Solute transport in a filled single fracture under non-Darcian flow. Int J Rock Mech Min Sci 48(1):132–140. https://doi.org/10.1016/j.ijrmms.2010.09.009
Schmid C, Risken H (1966) The Fokker-Planck equation for quantum noise of theN-level system. Z Phys 189(4):365–384. https://doi.org/10.1007/bf01375491
Voss RF (1988) Fractals in nature: from characterization to simulation. In: Peitgen HO, Saupe D (eds) The science of fractal images. Springer, New York. https://doi.org/10.1007/978-1-4612-3784-6_1
Wang L, Bayani Cardenas M (2017) Transition from non-Fickian to Fickian longitudinal transport through 3-D rough fractures: Scale-(in)sensitivity and roughness dependence. J Contam Hydrol 198:1–10. https://doi.org/10.1016/j.jconhyd.2017.02.002
Wang Y-P, Xiong L-X (2020) Numerical Analysis of the Influence of Bolt Set on the Shear Resistance of Jointed Rock Masses. Civil Eng J 6:1039–1055. https://doi.org/10.28991/cej-2020-03091527
Wang M, Chen YF, Ma GW et al (2016) Influence of surface roughness on nonlinear flow behaviors in 3D self-affine rough fractures: Lattice Boltzmann simulations[J]. Adv Water Resour 96:373–388. https://doi.org/10.1016/j.advwatres.2016.08.006
Wang H, Cater J et al (2017) A lattice boltzmann model for solute transport in open channel flow. J Hydrol 556:419–426. https://doi.org/10.1016/j.jhydrol.2017.11.034
Wang, Min; Chen, Yi-Feng; Ma, Guo-Wei; Zhou, Jia-Qing; Zhou, Chuang-Bing (2016b). Influence of surface roughness on nonlinear flow behaviors in 3D self-affine rough fractures: Lattice Boltzmann simulations. Advances in Water Resources, 96(), 373–388. https://doi.org/10.1016/j.advwatres.2016.08.006
Xu, K. and D. Bushnell (2002) Regularization of the Chapman-Enskog Expansion and Its Description of Shock Structure. Physics of Fluids,14https://doi.org/10.1063/1.1453467
Yeo W (2001) Effect of fracture roughness on solute transport. J Geosci 5(2):145–151. https://doi.org/10.1007/bf02910419
Zhang, Y. , Zhou, D, et al. (2020). Nonlocal‐transport models for capturing solute transport in one‐dimensional sand columns: model review, applicability, limitations, and improvement. Hydrological Processeshttps://doi.org/10.1002/hyp.13930
Zhou Q, Liu H et al (2006) Evidence of Multi-Process Matrix Diffusion in a Single Fracture from a Field Tracer Test. Transp Porous Media 63(3):473–487. https://doi.org/10.1007/s11242-005-1123-9
Funding
This work was financially supported by the National Key Research and Development Program (2019YFC1805801) and the National Natural Science Foundation of China (nos. 41172277, 40572163, and 40202036).
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare no competing interests.
Additional information
Responsible Editor: François Roure
Rights and permissions
About this article
Cite this article
Deng, Y., Tian, X., Li, P. et al. Research on the influence of roughness on solute transport through 3D self-affine fractures by lattice Boltzmann simulation. Arab J Geosci 15, 393 (2022). https://doi.org/10.1007/s12517-022-09651-w
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s12517-022-09651-w