Scale Dependence of Dispersion Coefficient for Solute Transport in Porous Media Using Image Analysis
Publication: Journal of Hydrologic Engineering
Volume 28, Issue 6
Abstract
Scale dependence of dispersion coefficient () in the advection-dispersion equation (ADE) for solute transport in porous media was investigated by a series of experiments using image analysis. A hexahedral plexiglass box sized () was set and packed with glass beads as porous media. The solute transport under different conditions was simulated by changing the particle size of glass beads, flow rate, and detection scale using Bright Blue as tracer. The image analysis method was used to dynamically monitor and identify the spatiotemporal variation of solute concentration distribution. The results showed that image analysis can effectively monitor and identify the solute concentration in porous media, as indicated by an value of 0.9890. There is an obvious linear relationship between hydraulic gradient () and velocity () in porous media under different experimental conditions. The ADE model is suitable for solute breakthrough curve (BTC) with good fitting accuracy, and can effectively reflect the concentration variation during solute transport. The key parameters controlling the solute transport were analyzed. has abnormal diffusion (i.e., non-Fickian phenomenon) and scale dependence, and BTCs had a long tail, which becomes more obvious with the increase of flow rate, medium particle size, and transport scale.
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Data Availability Statement
Some or all experimental and simulated data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
This work was supported by National Natural Science Foundation of China (Nos. 41877191 and 41831289).
References
Aeby, P., U. Schultze, D. Braichotte, M. Bundt, F. Moser-Boroumand, H. Wydler, and H. Flühler. 2001. “Fluorescence imaging of tracer distributions in soil profiles.” Environ. Sci. Technol. 35 (4): 753–760. https://doi.org/10.1021/es000096x.
Akara, M. E. M., D. M. Reeves, and R. Parashar. 2021. “Impact of horizontal spatial clustering in two-dimensional fracture networks on solute transport.” J. Hydrol. 603 (Part C): 127055. https://doi.org/10.1016/j.jhydrol.2021.127055.
Aubert, A. H., et al. 2013. “Solute transport dynamics in small, shallow groundwater-dominated agricultural catchments: Insights from a high-frequency, multisolute 10 yr-long monitoring study.” Hydrol. Earth Syst. Sci. 17 (4): 1379–1391. https://doi.org/10.5194/hess-17-1379-2013.
Babadagli, T., X. Ren, and K. Develi. 2015. “Effects of fractal surface roughness and lithology on single and multiphase flow in a single fracture: An experimental investigation.” Int. J. Multiphase Flow 68 (Jan): 40–58. https://doi.org/10.1016/j.ijmultiphaseflow.2014.10.004.
Basha, H. A., and F. S. El-Habel. 1993. “Analytical solution of the one-dimensional time-dependent transport equation.” Water Resour. Res. 29 (9): 3209–3214. https://doi.org/10.1029/93WR01038.
Bauget, F., and M. Fourar. 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. 1972. Dynamics of fluids in porous media [M]. Amsterdam, Netherlands: Elsevier.
Berkowitz, B., A. Cortis, M. Dentz, and H. Scher. 2006. “Modeling non-Fickian transport in geological formations as a continuous time random walk.” Rev. Geophys. 44 (2): 1–49. https://doi.org/10.1029/2005RG000178.
Bromly, M., and C. Hinz. 2004. “Non-Fickian transport in homogeneous unsaturated repacked sand.” Water Resour. Res. 40 (7): W07402. https://doi.org/10.1029/2003WR002579.
Chaaban, M., Y. Heider, and B. Markert. 2020. “Upscaling LBM-TPM simulation approach of Darcy and non-Darcy fluid flow in deformable, heterogeneous porous media.” Int. J. Heat Fluid Flow 83 (1): 108566. https://doi.org/10.1016/j.ijheatfluidflow.2020.108566.
Chen, J. S., C.-F. Na, C.-P. Liang, and C.-C. Chiang. 2008. “Analytical power series solution for contaminant transport with hyperbolic asymptotic distance-dependent dispersivity.” J. Hydrol. 362 (1): 142–149. https://doi.org/10.1016/j.jhydrol.2008.08.020.
de Barros, F. P. J., and M. Dentz. 2016. “Pictures of blockscale transport: Effective versus ensemble dispersion and its uncertainty.” Adv. Water Resour. 91 (May): 11–22. https://doi.org/10.1016/j.advwatres.2016.03.004.
Dejam, M. 2019. “Hydrodynamic dispersion due to a variety of flow velocity profiles in a porous-walled microfluidic channel.” Int. J. Heat Mass Transf. 136 (1): 87–98. https://doi.org/10.1016/j.ijheatmasstransfer.2019.02.081.
Dong, S., B. Gao, Y. Sun, H. Guo, J. Wu, S. Cao, and J. Wu. 2019. “Visualization of graphene oxide transport in two-dimensional homogeneous and heterogeneous porous media.” J. Hazard. Mater. 369 (1): 334–341. https://doi.org/10.1016/j.jhazmat.2019.02.042.
Dou, Z., Z. Chen, Z. Zhou, J. Wang, and Y. Huang. 2018. “Influence of eddies on conservative solute transport through a 2D single self-affine fracture.” Int. J. Heat Mass Transfer 121 (Jun): 597–606. https://doi.org/10.1016/j.ijheatmasstransfer.2018.01.037.
Dou, Z., B. Sleep, H. Zhan, Z. Zhou, and J. Wang. 2019. “Multiscale roughness influence on conservative solute transport in self-affine fractures.” Int. J. Heat Mass Transfer 133 (Apr): 606–618. https://doi.org/10.1016/j.ijheatmasstransfer.2018.12.141.
Dronfield, D. G., and S. E. Silliman. 1993. “Velocity dependence of dispersion for transport through a single fracture of variable roughness.” Water Resour. Res. 29 (10): 3477–3483. https://doi.org/10.1029/93WR01407.
Gao, G., H. Zhan, S. Feng, B. Fu, Y. Ma, and G. Huang. 2010. “A new mobile-immobile model for reactive solute transport with scale-dependent dispersion.” Water Resour. Res. 46 (8): W08533. https://doi.org/10.1029/2009WR008707.
Gelhar, L. W., C. Welty, and K. R. Rehfeldt. 1992. “A critical review of data on field-scale dispersion in aquifers.” Water Resour. Res. 28 (7): 1955–1974. https://doi.org/10.1029/92WR00607.
Godoy, V. A., L. V. Zuquette, and J. Jaime Gómez-Hernández. 2018. “Scale effect on hydraulic conductivity and solute transport: Small and large-scale laboratory experiments and field experiments.” Eng. Geol. 243 (Sep): 196–205. https://doi.org/10.1016/j.enggeo.2018.06.020.
Guo, M., J. Wan, and K. Huang. 2022. “Solute transport characteristics and influencing factors in a coastal unconfined aquifer under tidal action identified by image monitoring in a laboratory experimental setup.” Hydrogeol. J. 30 (3): 989–1004. https://doi.org/10.1007/s10040-022-02476-7.
Guo, Z., R. Ma, Y. Zhang, and C. Zheng. 2021. “Contaminant transport in heterogeneous aquifers: A critical review of mechanisms and numerical methods of non-Fickian dispersion.” Sci. China Earth Sci. 64 (8): 1224–1241. https://doi.org/10.1007/s11430-020-9755-y.
Hasan, S. M., H. Ali Al-Jobouri, O. A. Jalal, J. Abduljabar Hasan, and L. A. Najam. 2020. “Determination the effect of gamma radiation on CR-39 detector by analysis of photoelasticity images using MATLAB software.” In Vol. 881 of Proc., IOP Conf. Series: Materials Science and Engineering, 012190. London: Institute of Physics. https://doi.org/10.1088/1757-899X/881/1/012190.
Hassanizadeh, S. M., and W. G. Gray. 1987. “High velocity flow in porous media.” Transp. Porous Media 2 (6): 521–531. https://doi.org/10.1007/BF00192152.
Huang, K., N. Toride, and M. T. Van Genuchten. 1995. “Experimental investigation of solute transport in large, homogeneous and heterogeneous, saturated soil columns.” Transp. Porous Media 18 (3): 283–302. https://doi.org/10.1007/BF00616936.
Ilankoon, I. M., K. E. Cole, and S. J. Neethling. 2013. “Measuring hydrodynamic dispersion coefficients in unsaturated packed beds: Comparison of PEPT with conventional tracer tests.” Chem. Eng. Sci. 89 (15): 152–157. https://doi.org/10.1016/j.ces.2012.11.013.
Kundu, P., V. Kumar, and I. M. Mishra. 2016. “Experimental and numerical investigation of fluid flow hydrodynamics in porous media: Characterization of pre-Darcy, Darcy and non-Darcy flow regimes.” Powder Technol. 303 (Dec): 278–291. https://doi.org/10.1016/j.powtec.2016.09.037.
Lee, J., M. Rolle, and P. K. Kitanidis. 2018. “Longitudinal dispersion coefficients for numerical modeling of groundwater solute transport in heterogeneous formations.” J. Contam. Hydrol. 212 (1): 41–54. https://doi.org/10.1016/j.jconhyd.2017.09.004.
Li, Y., J. Bian, Q. Wang, and T. Li. 2021. “Experiment and simulation of non-reactive solute transport in porous media.” Ground Water 60 (3): 330–343. https://doi.org/10.1111/gwat.13153.
Ma, Z., S. Dong, S. Yin, Z. Dai, L. Zhu, W. Jia, C. Wallace, and M. R. Soltanian. 2021. “Experimental investigations on scale-dependent dispersivity in three-dimensional heterogeneous porous media.” Environ. Sci. Pollut. Res. 28 (18): 23336–23348. https://doi.org/10.1007/s11356-020-12316-4.
Madie, C., F. K. Togue, and P. Woafo. 2022. “Analysis of the importance of the dispersion coefficient depending on the distance for the transport of solute in porous media.” Sādhanā 47 (2): 51. https://doi.org/10.1007/s12046-022-01810-9.
Neuman, S. P., and D. M. Tartakovsky. 2009. “Perspective on theories of non-Fickian transport in heterogeneous media.” Adv. Water Resour. 32 (5): 670–680. https://doi.org/10.1016/j.advwatres.2008.08.005.
Nowamooz, A., G. Radilla, and M. Fourar. 2009. “Non-Darcian two-phase flow in a transparent replica of a rough-walled rock fracture.” Water Resour. Res. 45 (7): W07406. https://doi.org/10.1029/2008WR007315.
Parker, J. C., and U. Kim. 2015. “An upscaled approach for transport in media with extended tailing due to back-diffusion using analytical and numerical solutions of the advection dispersion equation.” J. Contam. Hydrol. 182 (1): 157–172. https://doi.org/10.1016/j.jconhyd.2015.09.008.
Porta, G. M., S. Chaynikov, J. F. Thovert, M. Riva, A. Guadagnini, and P. M. Adler. 2013. “Numerical investigation of pore and continuum scale formulations of bimolecular reactive transport in porous media.” Adv. Water Resour. 62 (Part B): 243–253. https://doi.org/10.1016/j.advwatres.2013.09.007.
Pugliese, L., and T. G. Poulsen. 2014. “Estimating solute dispersion coefficients in porous media at low pore water velocities.” Soil Sci. 179 (4): 175–181. https://doi.org/10.1097/SS.0000000000000056.
Qian, J. Z., Z. Chen, H. B. Zhan, and S. H. Luo. 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.
Qian, J. Z., H. Zhan, W. Zhao, and F. Sun. 2005. “Experimental study of turbulent unconfined groundwater flow in a single fracture.” J. Hydrol. 311 (1–4): 134–142. https://doi.org/10.1016/j.jhydrol.2005.01.013.
Sanskrityayn, A., V. K. Bharati, and N. Kumar. 2018. “Solute transport due to spatio-temporally dependent dispersion coefficient and velocity: Analytical solutions.” J. Hydrol. Eng. 23 (4): 04018009. https://doi.org/10.1061/(ASCE)HE.1943-5584.0001615.
Saraceno, J. F., J. T. Kulongoski, and T. M. Mathany. 2018. “A novel high-frequency groundwater quality monitoring system.” Environ. Monit. Assess. 190 (Jul): 447. https://doi.org/10.1007/s10661-018-6853-6.
Shi, Z., Y. Deng, X. Tian, and X. Peng. 2020. “Influence of the grain structure on solute transport in constructed inhomogeneous media from pore-scale simulations.” Arabian J. Geosci. 13 (19): 1048. https://doi.org/10.1007/s12517-020-06025-y.
Silliman, S. E., and E. S. Simpson. 1987. “Laboratory evidence of the scale effect in dispersion of solutes in porous media.” Water Resour. Res. 23 (8): 1667–1673. https://doi.org/10.1029/WR023i008p01667.
Silliman, S. E., L. Zheng, and P. Conwell. 1998. “The use of laboratory experiments for the study of conservative solute transport in heterogeneous porous media.” Hydrogeol. J. 6 (1): 166–177. https://doi.org/10.1007/s100400050142.
Stoll, M., F. M. Huber, M. Trumm, F. Enzmann, D. Meinel, A. Wenka, E. Schill, and T. Schäfer. 2019. “Experimental and numerical investigations on the effect of fracture geometry and fracture aperture distribution on flow and solute transport in natural fractures.” J. Contam. Hydrol. 221 (1): 82–97. https://doi.org/10.1016/j.jconhyd.2018.11.008.
Sudicky, E. A., R. W. Gillham, and E. O. Frind. 1985. “Experimental investigation of solute transport in stratified porous media: 1. The nonreactive case.” Water Resour. Res. 21 (7): 1035–1041. https://doi.org/10.1029/WR021i007p01035.
Swain, R., B. Sahoo, and M. Perumal. 2018. “An embedded VPMM-AD model for riverine transient flow and non-reactive contaminant transports.” J. Hydrol. 563 (1): 711–725. https://doi.org/10.1016/j.jhydrol.2018.06.025.
Wang, H., N. Persaud, and X. Zhou. 2006. “Specifying scale-dependent dispersivity in numerical solutions of the convection–dispersion equation.” Soil Sci. Soc. Am. J. 70 (6): 1843–1850. https://doi.org/10.2136/sssaj2005.0166.
Wang, L., and M. B. Cardenas. 2017. “Transition from non-Fickian to Fickian longitudinal transport through 3-D rough fractures: Scale-(in) sensitivity and roughness dependence.” J. Contam. Hydrol. 198 (Mar): 1–10. https://doi.org/10.1016/j.jconhyd.2017.02.002.
Xiong, Y., J. Luo, X. Liu, Y. Liu, X. Xin, and S. Wang. 2022. “Machine learning-based optimal design of groundwater pollution monitoring network.” Environ. Res. 211 (Aug): 113022. https://doi.org/10.1016/j.envres.2022.113022.
Yan, X., J. Qian, L. Ma, M. Wang, and A. Hu. 2018. “Non-Fickian solute transport in a single fracture of marble parallel plate.” Geofluids 2018 (5). 7418140. https://doi.org/10.1155/2018/7418140.
Zhang, Y., and D. A. Benson. 2008. “Lagrangian simulation of multidimensional anomalous transport at the MADE site.” Geophys. Res. Lett. 35 (7): L07403. https://doi.org/10.1029/2008GL033222.
Zhuang, L., A. Raoof, M. G. Mahmoodlu, S. Biekart, R. de Witte, L. Badi, M. T. van Genuchten, and K. Lin. 2021. “Unsaturated flow effects on solute transport in porous media.” J. Hydrol. 598 (Jul): 126301. https://doi.org/10.1016/j.jhydrol.2021.126301.
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Received: Jul 11, 2022
Accepted: Feb 8, 2023
Published online: Apr 4, 2023
Published in print: Jun 1, 2023
Discussion open until: Sep 4, 2023
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