Transport in Porous Media

, Volume 110, Issue 2, pp 251–280

Free-Flow–Porous-Media Coupling for Evaporation-Driven Transport and Precipitation of Salt in Soil

  • V. A. Jambhekar
  • R. Helmig
  • N. Schröder
  • N. Shokri
Article

Abstract

Evaporative salinization of soil is a common issue observed in arid and coastal regions. This process is driven by mass, momentum and energy exchange between the porous medium and the free-flow region. To analyze such coupled systems, we present a representative elementary volume-scale model concept for coupling non-isothermal multi-phase compositional porous-media flow and single-phase compositional laminar free flow. Our numerical results illustrate evaporation behavior from a porous medium initially saturated with NaCl solution, manifesting its influence on dissolved salt distribution, salt precipitation and porous-media properties. We show that the new model is capable to capture the evaporation physics for different stages of evaporative salinization and compare the numerical results to two different experimental datasets: (1) cumulative mass loss of water and dissolved salt during stage-1 of saline water evaporation and (2) evaporation rate for different stages of evaporative salinization. In addition, influence of the initial salt concentration on the saline water saturation vapor pressure and transition to stage-2 evaporation are analyzed and discussed.

Keywords

Porous-media Free flow Coupling Evaporation  Salinization 

References

  1. Alazmi, B., Vafai, K.: Analysis of fluid flow and heat transfer interfacial conditions between a porous medium and a fluid layer. Int. J. Heat Mass Transf. 44(9), 1735–1749 (2001). doi:10.1016/S0017-9310(00)00217-9 CrossRefGoogle Scholar
  2. Baber, K., Mosthaf, K., Flemisch, B., Helmig, R., Mthing, S., Wohlmuth, B.: Numerical scheme for coupling two-phase compositional porous-media flow and one-phase compositional free flow. IMA J. Appl. Math. 77(6), 887–909 (2012). doi:10.1093/imamat/hxs048 CrossRefGoogle Scholar
  3. Bastian, P., Blatt, M., Dedner, A., Engwer, C., Klfkorn, R., Kornhuber, R., Ohlberger, M., Sander, O.: A generic grid interface for parallel and adaptive scientific computing. part ii: implementation and tests in dune. Computing 82(2–3), 121–138 (2008). doi:10.1007/s00607-008-0004-9 CrossRefGoogle Scholar
  4. Battistelli, A., Calore, C., Pruess, K.: The simulator tough2/ewasg for modelling geothermal reservoirs with brines and non-condensible gas. Geothermics 26(4), 437–464 (1997). doi:10.1016/S0375-6505(97)00007-2 CrossRefGoogle Scholar
  5. Batzle, M.L., Wang, Z.: Seismic properties of pore fluids. Geophysics 57, 1396–1408 (1992). doi:10.1190/1.1443207 CrossRefGoogle Scholar
  6. Beavers, G.S., Joseph, D.D.: Boundary conditions at a naturally permeable wall. J. Fluid Mech. 30, 197–207 (1967). doi:10.1017/S0022112067001375 CrossRefGoogle Scholar
  7. Bechtold, M., Haber-Pohlmeier, S., Vanderborght, J., Pohlmeier, A., Ferre, T.P.A., Vereecken, H.: Near-surface solute redistribution during evaporation. Geophys. Res. Lett. 38 (2011). doi:10.1029/2011GL048147
  8. Belleghem, M.V., Steeman, M., Janssen, H., Janssens, A., Paepe, M.D.: Validation of a coupled heat, vapour and liquid moisture transport model for porous materials implemented in cfd. Build. Environ. 81(0), 340–353 (2014). doi:10.1016/j.buildenv.2014.06.024 CrossRefGoogle Scholar
  9. Chandesris, M., Jamet, D.: Boundary conditions at a fluid–porous interface: an a priori estimation of the stress jump coefficients. Int. J. Heat Mass Transf. 50(1718), 3422–3436 (2007). doi:10.1016/j.ijheatmasstransfer.2007.01.053
  10. Chandesris, M., Jamet, D.: Boundary conditions at a planar fluid–porous interface for a Poiseuille flow. Int. J. Heat Mass Transf. 49(1314), 2137–2150 (2006). doi:10.1016/j.ijheatmasstransfer.2005.12.010
  11. Chandesris, M., Jamet, D.: Jump conditions and surface-excess quantities at a fluid/porous interface: a multi-scale approach. Transp. Porous Media 78(3), 419–438 (2009). doi:10.1007/s11242-008-9302-0 CrossRefGoogle Scholar
  12. Class, H., Helmig, R., Bastian, P.: Numerical simulation of non-isothermal multiphase multicomponent processes in porous media.: 1. An efficient solution technique. Adv. Water Resour. 25(5), 533–550 (2002). doi:10.1016/S0309-1708(02)00014-3 CrossRefGoogle Scholar
  13. Defraeye, T., Blocken, B., Derome, D., Nicolai, B., Carmeliet, J.: Convective heat and mass transfer modelling at air-porous material interfaces: overview of existing methods and relevance. Chem. Eng. Sci. 74, 49–58 (2012). doi:10.1016/j.ces.2012.02.032 CrossRefGoogle Scholar
  14. Derluyn, H., Moonen, P., Carmeliet, J.: Deformation and damage due to drying-induced salt crystallization in porous limestone. J. Mech. Phys. Solids 63(0), 242–255 (2014). doi:10.1016/j.jmps.2013.09.005 CrossRefGoogle Scholar
  15. Espinosa, R.M., Franke, L., Deckelmann, G., Gunstmann, C.: Gekoppelter wärme- und stofftransport einschlieälich der korrosionsprozesse in poräsen baustoffen mit dem simulationsprogramm astra. Bauphysik 29(3), 187–193 (2007). doi:10.1002/bapi.200710026 CrossRefGoogle Scholar
  16. Fisher, E.A.: Some factors affecting the evaporation of water from soil. J Agric. Sci. 13, 121–143 (1923). doi:10.1017/S0021859600003270 CrossRefGoogle Scholar
  17. Flemisch, B., Darcis, M., Erbertseder, K., Faigle, B., Lauser, A., Mosthaf, K., Müthing, S., Nuske, P., Tatomir, A., Wolff, M., Helmig, R.: DuMuX: DUNE for multi-phase, component, scale, physics, flow and transport in porous media. New computational methods and software tools. Adv. Water Resour. 34(9), 1102–1112 (2011). doi:10.1016/j.advwatres.2011.03.007 CrossRefGoogle Scholar
  18. Fujimaki, H., Shimano, T., M, I., Nakane, K.: Effect of a salt crust on evaporation from a bare saline soil. Vadose Zone J. 5(4), 1246–1256 (2006). doi:10.2136/vzj2005.0144 CrossRefGoogle Scholar
  19. Gamazo, P., Bea, S., Saaltink, M., Carrera, J., Ayora, C.: Modeling the interaction between evaporation and chemical composition in a natural saline system. J. Hydrol. 401(34), 154–164 (2011). doi:10.1016/j.jhydrol.2011.02.018 CrossRefGoogle Scholar
  20. Gamazo, P., Saaltink, M., Carrera, J., Slooten, L., Bea, S.: A consistent compositional formulation for multiphase reactive transport where chemistry affects hydrodynamics. Adv. Water Resour. 35, 83–93 (2012). doi:10.1016/j.advwatres.2011.09.006 CrossRefGoogle Scholar
  21. Gardner, W.R., Fireman, M.: Laboratory studies of evaporation from soil columns in the presence of a water table. Soil Sci. 85(5), 244–249 (1958)CrossRefGoogle Scholar
  22. Giorgis, T., Carpita, M., Battistelli, A.: 2d modeling of salt precipitation during the injection of dry co2 in a depleted gas reservoir. Geologic carbon sequestration and methane hydrates research from the TOUCH symposium 2006. Energy Convers. Manag. 48(6), 1816–1826 (2007). doi:10.1016/j.enconman.2007.01.012 CrossRefGoogle Scholar
  23. Hassanizadeh, S.M., Gray, W.G.: Derivation of conditions describing transport across zones of reduced dynamics within multiphase systems. Water Resour. Res. 25(3), 529–539 (1989). doi:10.1029/WR025i003p00529 CrossRefGoogle Scholar
  24. Helmig, R.: Multiphase Flow and Transport Processes in the Subsurfaces : A Contribution to the Modelling of Hydrosystems. Springer, Berlin (1997)CrossRefGoogle Scholar
  25. Jamet, D., Chandesris, M., Goyeau, B.: On the equivalence of the discontinuous one- and two-domain approaches for the modeling of transport phenomena at a fluid/porous interface. Transp. Porous Media 78(3), 403–418 (2009). doi:10.1007/s11242-008-9314-9 CrossRefGoogle Scholar
  26. Kelly, S.F., Selker, J.S.: Osmotically driven water vapor transport in unsaturated soils. Soil Sci. Soc. Am 65, 16341641 (2001)CrossRefGoogle Scholar
  27. Koniorczyk, M.: Heat and moisture transport in porous building materials containing salt. J. Build. Phys. 31(4), 279 (2008)CrossRefGoogle Scholar
  28. Koniorczyk, M.: Salt transport and crystallization in non-isothermal, partially saturated porous materials considering ions interaction model. Int. J. Heat Mass Transf. 55(4), 665–679 (2012). doi:10.1016/j.ijheatmasstransfer.2011.10.043 CrossRefGoogle Scholar
  29. Lehmann, P., Assouline, S., Or, D.: Characteristic lengths affecting evaporative drying of porous media. Phys. Rev. E 77, 056,309 (2008). doi:10.1103/PhysRevE.77.056309 CrossRefGoogle Scholar
  30. Lehmann, P., Or, D.: Evaporation and capillary coupling across vertical textural contrasts in porous media. Phys. Rev. E 80, 046,318 (2009). doi:10.1103/PhysRevE.80.046318 CrossRefGoogle Scholar
  31. Manthey, S.: Two-Phase Flow Processes with Dynamic Effects in Porous Media—Parameter Estimation and Simulation. Ph.D. thesis, Universitt Stuttgart, Holzgartenstr. 16, 70174 Stuttgart (2006)Google Scholar
  32. Michaelides, E.E.: Thermophysical properties of the geothermal fluids. Geotherm. Res. Counc. 5 (1981)Google Scholar
  33. Millington, R., Quirk, J.: Permeability of porous solids. Trans. Faraday Soc. 57, 1200–1207 (1961)CrossRefGoogle Scholar
  34. Mosthaf, K., Baber, K., Flemisch, B., Helmig, R., Leijnse, A., Rybak, I., Wohlmuth, B.: A coupling concept for two-phase compositional porous medium and single-phase compositional free flow. Water Resour. Res. 47 (2011). doi:10.1029/2011WR010685
  35. Mosthaf, K., Helmig, R., Or, D.: Modeling and analysis of evaporation processes from porous media on the rev scale. Water Resour. Res. 50(2), 1059–1079 (2014). doi:10.1002/2013WR014442 CrossRefGoogle Scholar
  36. Nachshon, U., Shahraeeni, E., Or, D., Dragila, M., Weisbrod, N.: Infrared thermography of evaporative fluxes and dynamics of salt deposition on heterogeneous porous surfaces. Water Resour. Res. 47 (2011). doi:10.1029/2011WR010776
  37. Nachshon, U., Weisbrod, N., Dragila, M.I., Grader, A.: Combined evaporation and salt precipitation in homogeneous and heterogeneous porous media. Water Resour. Res. 47 (2011). doi:10.1029/2010WR009677
  38. Nicolai, A., Grunewald, J., Zhang, J.S.: Salztransport und phasenumwandlung—modellierung und numerische lösung im simulationsprogramm delphin 5. Bauphysik 29(3), 231–239 (2007). doi:10.1002/bapi.200710032 CrossRefGoogle Scholar
  39. Norouzi Rad, M., Shokri, N., Sahimi, M.: Pore–scale dynamics of salt precipitation in drying porous media. Phys. Rev. E 88, 32404 (2013)CrossRefGoogle Scholar
  40. Nuske, P., Joekar-Niasar, V., Helmig, R.: Non-equilibrium in multiphase multicomponent flow in porous media: an evaporation example. Int. J. Heat Mass Transf. 74(0), 128–142 (2014). doi:10.1016/j.ijheatmasstransfer.2014.03.011 CrossRefGoogle Scholar
  41. Or, D., Lehmann, P., Sharaeeni, E., Shokri, N.: Advances in soil evaporation physics—a review. Vadose Zone J. (2013). doi:10.2136/vzj2012.0163
  42. Saffman, R.: On the boundary condition at the surface of the porous medium. Stud. Appl. Math. 50, 93–101 (1971)CrossRefGoogle Scholar
  43. Saneinejad, S., Moonen, P., Defraeye, T., Derome, D., Carmeliet, J.: Coupled cfd, radiation and porous media transport model for evaluating evaporative cooling in an urban environment. 13th international conference on wind engineering. J. Wind Eng. Ind. Aerodyn. 104–106, 455–463 (2012). doi:10.1016/j.jweia.2012.02.006 CrossRefGoogle Scholar
  44. Shahraeeni, E., Lehmann, P., Or, D.: Coupling of evaporative fluxes from drying porous surfaces with air boundary layer: characteristics of evaporation from discrete pores. Water Resour. Res. 48(9), n/a-n/a (2012). doi:10.1029/2012WR011857 Google Scholar
  45. Shahraeeni, E., Or, D.: Thermo-evaporative fluxes from heterogeneous porous surfaces resolved by infrared thermography. Water Resour. Res. 46(9), n/a-n/a (2010). doi:10.1029/2009WR008455 Google Scholar
  46. Sharma, D.R., Prihar, S.S.: Effect of depth and salinity of groundwater on evaporation and soil salinization. Ind. J. Agric. Sci. 43(6), 582–586 (1973)Google Scholar
  47. Shavit, U.: Transport phenomena at the interface between fluid and porous domains. Transp. Porous Media 78(3), 327–330 (2009). doi:10.1007/s11242-009-9414-1 CrossRefGoogle Scholar
  48. Shokri, N.: Pore–scale dynamics of salt transport and distribution in drying porous media. Phys. Fluids 26(1), 012106 (2014)CrossRefGoogle Scholar
  49. Shokri, N., Salvucci, G.: Evaporation from porous media in the presence of a water table. Vadose Zone J. 10(4), 1309–1318 (2011). doi:10.2136/vzj2011.0027 CrossRefGoogle Scholar
  50. Somerton, W.H., El-Shaarani, A.H., Mobarak, S.M.: High temperature Behavior of Rocks Associated with Geothermal Type Reservoirs. In: SPE California Regional Meeting. Society of Petroleum Engineers, San Francisco, California (1974). doi:10.2118/4897-MS
  51. Steiger, M., Kiekbusch, J., Nicolai, A.: An improved model incorporating pitzer’s equations for calculation of thermodynamic properties of pore solutions implemented into an efficient program code. Constr. Build. Mater. 22(8), 1841–1850 (2008). doi:10.1016/j.conbuildmat.2007.04.020 CrossRefGoogle Scholar
  52. van Duijn, C.J., Pop, I.S.: Crystal dissolution and precipitation in porous media: pore scale analysis. Journal fuer die reine und angewandte Mathematik 2004(577), 171–211 (2005). doi:10.1515/crll.2004.2004.577.171 Google Scholar
  53. Van Genuchten, M.T.: A closed-from equation for predicting the hydraulic conductivity of unstructured soil. Soil Sci. Soc. Am. J. 44, 892–898 (1980)CrossRefGoogle Scholar
  54. Verma, A., Pruess, K.: Thermohydrological conditions and silica redistribution near high-level nuclear wastes emplaced in saturated geological formations. J. Geophys. Res. Solid Earth 93(B2), 1159–1173 (1988). doi:10.1029/JB093iB02p01159 CrossRefGoogle Scholar
  55. Xu, T., Ontoy, Y., Molling, P., Spycher, N., Parini, M., Pruess, K.: Reactive transport modeling of injection well scaling and acidizing at tiwi field, Philippines. Selected papers from the TOUGH symposium 2003. Geothermics 33(4), 477–491 (2004). doi:10.1016/j.geothermics.2003.09.012 CrossRefGoogle Scholar
  56. Zeidouni, M., Pooladi-Darvish, M., Keith, D.: Analytical solution to evaluate salt precipitation during CO2 injection in saline aquifers. Int. J. Greenh. Gas Control 3(5), 600–611 (2009). doi:10.1016/j.ijggc.2009.04.004 CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  • V. A. Jambhekar
    • 1
  • R. Helmig
    • 1
  • N. Schröder
    • 1
  • N. Shokri
    • 2
  1. 1.Department of Hydromechanics and Modelling of HydrosystemsUniversity of StuttgartStuttgartGermany
  2. 2.School of Chemical Engineering and Analytical ScienceThe University of ManchesterManchesterUK

Personalised recommendations