Experimental study on the velocity-dependent dispersion of the solute transport in different porous media
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摘要
The hydrodynamic dispersion is an important factor influencing the reactive solute transport in the porous media, and many previous studies assumed that it linearly varied with the average velocity of the groundwater flow. Actually, such linear relationship has been challenged by more and more experimental observations, even in homogeneous media. In this study, we aim to investigate the relationship between hydrodynamics dispersion and the flow velocity in different types of porous media through a laboratory-controlled experiment. The results indicate that(1) the dispersion coefficient should not be a linear function of the flow velocity when the relationship between the flow velocity and the hydraulic gradient can be described by Darcy's law satisfactorily;(2) Power function works well in describing the dispersion coefficient changing with the flow velocity for different types of porous media, and the power value is between 1.0-2.0 for different particle sizes.
The hydrodynamic dispersion is an important factor influencing the reactive solute transport in the porous media, and many previous studies assumed that it linearly varied with the average velocity of the groundwater flow. Actually, such linear relationship has been challenged by more and more experimental observations, even in homogeneous media. In this study, we aim to investigate the relationship between hydrodynamics dispersion and the flow velocity in different types of porous media through a laboratory-controlled experiment. The results indicate that(1) the dispersion coefficient should not be a linear function of the flow velocity when the relationship between the flow velocity and the hydraulic gradient can be described by Darcy's law satisfactorily;(2) Power function works well in describing the dispersion coefficient changing with the flow velocity for different types of porous media, and the power value is between 1.0-2.0 for different particle sizes.
The hydrodynamic dispersion is an important factor influencing the reactive solute transport in the porous media, and many previous studies assumed that it linearly varied with the average velocity of the groundwater flow. Actually, such linear relationship has been challenged by more and more experimental observations, even in homogeneous media. In this study, we aim to investigate the relationship between hydrodynamics dispersion and the flow velocity in different types of porous media through a laboratory-controlled experiment. The results indicate that(1) the dispersion coefficient should not be a linear function of the flow velocity when the relationship between the flow velocity and the hydraulic gradient can be described by Darcy's law satisfactorily;(2) Power function works well in describing the dispersion coefficient changing with the flow velocity for different types of porous media, and the power value is between 1.0-2.0 for different particle sizes.
引文
Arriaza J L,Ghezzehei T A.2013.Explaining longitudinal hydrodynamic dispersion using variance of pore size distribution.Journal of Porous Media,16(1):11-19.
Bear J.1972.Dynamics of fluid in porous media.New York:The American Elsevier Publishing Company,Inc.
Bijeljic B,Blunt M J.2007.Pore-scale modeling of transverse dispersion in porous media.Water Resources Research,43(12):12-11.
Bond W J.1986.Velocity-dependent hydrodynamic dispersion during unsteady,unsaturated soil water flow:Experiments.Water Resources Research,22(13):1881-1889.
Connolly M,Johns R T.2016.Scale-dependent mixing for adverse mobility ratio flows in heterogeneous porous media.Transport in Porous Media,113(1):29-50.
De Smedt F,Wierenga P J.1984.Solute transfer through columns of glass beads.Water Resources Research,20(2):225-232.
Dronfield D G,Silliman S E.1993.Velocity dependence of dispersion for transport through a single fracture of variable roughness.Water Resources Research,29(10):3477-3483.
Eidsath A,Carbonell R G,et al.1983.Dispersion in pulsed systems-III comparison between theory and experiments for packed beds.Chemical Engineering Science,38(11):1803-1816.
Fahs M,Ataie-Ashtiani B,et al.2016.The Henry problem:New semi-analytical solution for velocity-dependent dispersion.Water Resources Research,52:7382-7407.
Fried J J,Combarnous M A.1971.Dispersion in porous media.Advances in Hydroscience,7:169-282.
Ghesmat K,Azaiez J.2008.Viscous fingering instability in porous media:Effect of anisotropic velocity-dependent dispersion tensors.Transport in Porous Media,73(3):297-318.
Graf T,Therrien R.2005.Variable-density groundwater flow and solute transport in porous media containing nonuniform discrete fractures.Advances in Water Resources,28(12):1351-1367.
Koch D L,Brady J F.1985.Dispersion in fixed beds.Journal of Fluid Mechanics,154(1):399-427.
LI Xiao-ping,ZHU Wei,University Hohai.2014.Effect of distribution of soil pore size on dispersion coefficient in migration process of pollutant.Journal of Water Resources and Water Engineering,25(2):172-175.
LI Yuan-hui,Gregory S.1974.Diffusion of ions in sea water and in deep-sea sediments.Geochimica et Cosmochimica Acta,38(5):703-714.
Pugliese L,Poulsen T G.2014.Estimating solute dispersion coefficients in porous media at low pore water velocities.Soil Science,179(4):175-181.
QIAN Jia-zhong,ZHAN Hong-bin,et al.2015.Numerical simulation and experimental study of bimolecular reactive transport in porous media.Transport in Porous Media,109(3):727-746.
Sahimi M,Hughes B D,et al.1986.Dispersion in flow through porous media-I.One-phase flow.Chemical Engineering Science,41(8):2103-2122.
Salama A,Geel P J V.2008.Flow and solute transport in saturated porous media:2.Violating the continuum hypothesis.Journal of Porous Media,11(5):421-441.
Simmons C T,Fenstemaker T R,Sharp J M.2001.Variable-density groundwater flow and solute transport in heterogeneous porous media:Approaches,resolutions and future challenges.Journal of Contaminant Hydrology,52(1-4):245-275.
Simmons C T,Pierini M L,Hutson J L.2002.Laboratory investigation of variable-density flow and solute transport in unsaturatedsaturated porous media.Transport in Porous Media,47(2):215-244.
Taylor G.1953.Dispersion of soluble matter in solvent flowing slowly through a tube.Proceedings of the Royal Society of London,219(1137):186-203.
WANG Kang,ZHANG Ren-duo,JIAO Xi-yun.2007.Characterizing heterogeneity of water flow and solute transport in the porous media using dye tracer.Advances in Water Science,18(5):662-667.
WANG Li-chun,Cardenas M B,et al.2012.Theory for dynamic longitudinal dispersion in fractures and rivers with Poiseuille flow.Geophysical Research Letters,39(5):131-138.
Zaheer M,WEN Zhang,et al.2017.An experimental study on solute transport in onedimensional clay soil columns.Geofluids,DOI:10.1155/2017/6390607.
Bear J.1972.Dynamics of fluid in porous media.New York:The American Elsevier Publishing Company,Inc.
Bijeljic B,Blunt M J.2007.Pore-scale modeling of transverse dispersion in porous media.Water Resources Research,43(12):12-11.
Bond W J.1986.Velocity-dependent hydrodynamic dispersion during unsteady,unsaturated soil water flow:Experiments.Water Resources Research,22(13):1881-1889.
Connolly M,Johns R T.2016.Scale-dependent mixing for adverse mobility ratio flows in heterogeneous porous media.Transport in Porous Media,113(1):29-50.
De Smedt F,Wierenga P J.1984.Solute transfer through columns of glass beads.Water Resources Research,20(2):225-232.
Dronfield D G,Silliman S E.1993.Velocity dependence of dispersion for transport through a single fracture of variable roughness.Water Resources Research,29(10):3477-3483.
Eidsath A,Carbonell R G,et al.1983.Dispersion in pulsed systems-III comparison between theory and experiments for packed beds.Chemical Engineering Science,38(11):1803-1816.
Fahs M,Ataie-Ashtiani B,et al.2016.The Henry problem:New semi-analytical solution for velocity-dependent dispersion.Water Resources Research,52:7382-7407.
Fried J J,Combarnous M A.1971.Dispersion in porous media.Advances in Hydroscience,7:169-282.
Ghesmat K,Azaiez J.2008.Viscous fingering instability in porous media:Effect of anisotropic velocity-dependent dispersion tensors.Transport in Porous Media,73(3):297-318.
Graf T,Therrien R.2005.Variable-density groundwater flow and solute transport in porous media containing nonuniform discrete fractures.Advances in Water Resources,28(12):1351-1367.
Koch D L,Brady J F.1985.Dispersion in fixed beds.Journal of Fluid Mechanics,154(1):399-427.
LI Xiao-ping,ZHU Wei,University Hohai.2014.Effect of distribution of soil pore size on dispersion coefficient in migration process of pollutant.Journal of Water Resources and Water Engineering,25(2):172-175.
LI Yuan-hui,Gregory S.1974.Diffusion of ions in sea water and in deep-sea sediments.Geochimica et Cosmochimica Acta,38(5):703-714.
Pugliese L,Poulsen T G.2014.Estimating solute dispersion coefficients in porous media at low pore water velocities.Soil Science,179(4):175-181.
QIAN Jia-zhong,ZHAN Hong-bin,et al.2015.Numerical simulation and experimental study of bimolecular reactive transport in porous media.Transport in Porous Media,109(3):727-746.
Sahimi M,Hughes B D,et al.1986.Dispersion in flow through porous media-I.One-phase flow.Chemical Engineering Science,41(8):2103-2122.
Salama A,Geel P J V.2008.Flow and solute transport in saturated porous media:2.Violating the continuum hypothesis.Journal of Porous Media,11(5):421-441.
Simmons C T,Fenstemaker T R,Sharp J M.2001.Variable-density groundwater flow and solute transport in heterogeneous porous media:Approaches,resolutions and future challenges.Journal of Contaminant Hydrology,52(1-4):245-275.
Simmons C T,Pierini M L,Hutson J L.2002.Laboratory investigation of variable-density flow and solute transport in unsaturatedsaturated porous media.Transport in Porous Media,47(2):215-244.
Taylor G.1953.Dispersion of soluble matter in solvent flowing slowly through a tube.Proceedings of the Royal Society of London,219(1137):186-203.
WANG Kang,ZHANG Ren-duo,JIAO Xi-yun.2007.Characterizing heterogeneity of water flow and solute transport in the porous media using dye tracer.Advances in Water Science,18(5):662-667.
WANG Li-chun,Cardenas M B,et al.2012.Theory for dynamic longitudinal dispersion in fractures and rivers with Poiseuille flow.Geophysical Research Letters,39(5):131-138.
Zaheer M,WEN Zhang,et al.2017.An experimental study on solute transport in onedimensional clay soil columns.Geofluids,DOI:10.1155/2017/6390607.