Effects of Domain Shapes and Mesh Discretization Error on the Morphological Evolution of Nonaqueous-Phase-Liquid Dissolution Fronts in Fluid-Saturated Porous Media

  • Chongbin ZhaoEmail author
Part of the Lecture Notes in Earth System Sciences book series (LNESS)


In the field of contaminant hydrology, both land contamination and land remediation problems are often encountered. Land contamination is known as the distribution of chemical and pollutants on land sites, while land remediation is known as the cleanup of chemical and pollutants on land sites that causes health concerns to the humans and the environment. When nonaqueous phase liquids (NAPLs), such as trichloroethylene, ethylene dibromide, benzene, toluene and so forth (Miller et al. 1990), are released to groundwater, they can reside in the form of disconnected ganglia or blobs as residual saturations within the pores of porous media. This process belongs to the land contamination problem


  1. Alt-Epping P, Smith L (2001) Computing geochemical mass transfer and water/rock ratios in submarine hydrothermal systems: implications for estimating the vigour of convection. Geofluids 1:163–181CrossRefGoogle Scholar
  2. Bear J (1972) Dynamics of fluids in porous media. American Elsevier Publishing Company, New YorkGoogle Scholar
  3. Chadam J, Hoff D, Merino E, Ortoleva P, Sen A (1986) Reactive infiltration instabilities. IMA J Appl Math 36:207–221CrossRefGoogle Scholar
  4. Chadam J, Ortoleva P, Sen A (1988) A weekly nonlinear stability analysis of the reactive infiltration interface. IMA J Appl Math 48:1362–1378Google Scholar
  5. Chen X, Jawitz JW (2008) Reactive tracer tests to predict nonaqueous phase liquid dissolution dynamics in laboratory flow chambers. Environ Sci Technol 42:5285–5291CrossRefGoogle Scholar
  6. Chen JS, Liu CW (2002) Numerical simulation of the evolution of aquifer porosity and species concentrations during reactive transport. Comput Geosci 28:485–499CrossRefGoogle Scholar
  7. Chen JS, Liu CW (2004) Interaction of reactive fronts during transport in a homogeneous porous medium with initial small non-uniformity. J Contam Hydrol 72:47–66CrossRefGoogle Scholar
  8. Chen JS, Liu CW, Lai GX, Ni CF (2009) Effects of mechanical dispersion on the morphological evolution of a chemical dissolution front in a fluid-saturated porous medium. J Hydrol 373:96–102CrossRefGoogle Scholar
  9. Christ JA, Ramsburg CA, Pennell KD, Abriola LM (2006) Estimating mass discharge from dense nonaqueous phase liquid source zones using upscaled mass transfer coefficients: an evaluation using multiphase numerical simulations. Water Resour Res 42:W11420. doi: 10.1029/2006WR004886 CrossRefGoogle Scholar
  10. Christ JA, Lemke LD, Abriola LM (2009) The influence of dimensionality on simulations of mass recovery from nonuniform dense non-aqueous phase liquid (DNAPL) source zones. Adv Water Resour 32:401–412CrossRefGoogle Scholar
  11. Daus AD, Frid EO, Sudicky EA (1985) Comparative error analysis in finite element formulations of the advection-dispersion equation. Adv Water Resour 8:86–95CrossRefGoogle Scholar
  12. DiFilippo EL, Carroll KC, Brusseau ML (2010) Impact of organic-liquid distribution and flow field heterogeneity on reduction in mass flux. J Contam Hydrol 115:14–25CrossRefGoogle Scholar
  13. Geller JT, Hunt JR (1993) Mass transfer from nonaqueous phase organic liquids in water-saturated porous media. Water Resour Res 29:833–845CrossRefGoogle Scholar
  14. Gerhard JI, Pang T, Kueper BH (2007) Time scales of DNAPL migration in sandy aquifers examined via numerical simulation. Ground Water 45:147–157CrossRefGoogle Scholar
  15. Grant GP, Gerhard JI (2007) Simulating the dissolution of a complex dense nonaqueous phase liquid zone: 1. Model to predict interfacial area. Water Resour Res 43:W12410. doi: 10.1029/2007WR006038
  16. Holzbecher EO (1998) Modeling density-driven flow in porous media. Springer, BerlinCrossRefGoogle Scholar
  17. Hong J, Hecker WC, Fletcher TH (1999) Predicting effectiveness factor for m-th order and langmuir rate equations in spherical coordinates. ACS Div Fuel Chem 44:1011–1015Google Scholar
  18. Imhoff PT, Miller CT (1996) Dissolution fingering during the solubilization of nonaqueous phase liquids in saturated porous media: 1 Model predictions. Water Resour Res 32:1919–1928CrossRefGoogle Scholar
  19. Imhoff PT, Jaffe PR, Pinder GF (1994) An experimental study of complete dissolution of a nonaqueous phase liquid in saturated porous media. Water Resour Res 30:307–320CrossRefGoogle Scholar
  20. Imhoff PT, Thyrum GP, Miller CT (1996) Dissolution fingering during the solubilization of nonaqueous phase liquids in saturated porous media: 2 Experimental observations. Water Resour Res 32:1929–1942CrossRefGoogle Scholar
  21. Imhoff PT, Farthing MW, Gleyzer SN, Miller CT (2002) Evolving interface between clean and nonaqueous phase liquid (NAPL)-contaminated regions in two-dimensional porous media. Water Resour Res 38:1093–1106CrossRefGoogle Scholar
  22. Imhoff PT, Farthing MW, Miller CT (2003a) Modeling NAPL dissolution fingering with upscaled mass transfer rate coefficients. Adv Water Resour 26:1097–1111CrossRefGoogle Scholar
  23. Imhoff PT, Mann AS, Mercer M, Fitzpatrick M (2003b) Scaling DNAPL migration from the laboratory to the field. J Contam Hydrol 64:73–92CrossRefGoogle Scholar
  24. Kalia N, Balakotaiah V (2009) Effect of medium heterogeneities on reactive dissolution of carbonates. Chem Eng Sci 64:376–390CrossRefGoogle Scholar
  25. Maji R, Sudicky EA (2008) Influence of mass transfer characteristics for DNAPL source depletion and contaminant flux in a highly characterized glaciofluvial aquifer. J Contam Hydrol 102:105–119CrossRefGoogle Scholar
  26. Miller CT, Poirier-McNeil MM, Mayer AS (1990) Dissolution of trapped nonaqueous phase liquids: mass transfer characteristics. Water Resour Res 26:2783–2796CrossRefGoogle Scholar
  27. Miller CT, Christakos TG, Imhoff PT, McBride JF, Pedit JA, Trangenstein JA (1998) Multiphase flow and transport modeling in heterogeneous porous media: challenges and approaches. Adv Water Resour 21:77–120CrossRefGoogle Scholar
  28. Morris MI, Ball RC (1990) Renormalization of miscible flow functions. J Phys A: Math Gen 23:4199–4209CrossRefGoogle Scholar
  29. Ormond A, Ortoleva P (2000) Numerical modeling of reaction-induced cavities in a porous rock. J Geophys Res 105:16737–16747CrossRefGoogle Scholar
  30. Ortoleva P, Chadam J, Merino E, Sen A (1987) Geochemical self-organization II: The reactive-infiltration instability. Am J Sci 287:1008–1040CrossRefGoogle Scholar
  31. Parker JC, Park E (2004) Modeling field-scale dense nonaqueous phase liquid dissolution kinetics in heterogeneous aquifers. Water Resour Res 40:W05109. doi: 10.1029/2003WR002807 CrossRefGoogle Scholar
  32. Powers SE, Abriola LM, Weber WJ Jr (1994) An experimental investigation of nonaqueous phase liquid dissolution in saturated subsurface systems: transient mass transfer rates. Water Resour Res 30:321–332CrossRefGoogle Scholar
  33. Raffensperger JP, Garven G (1995) The formation of unconformity-type uranium ore deposits: coupled hydrochemical modelling. Am J Sci 295:639–696CrossRefGoogle Scholar
  34. Renard F, Gratier JP, Ortoleva P, Brosse E, Bazin B (1998) Self-organization during reactive fluid flow in a porous medium. Geophys Res Lett 25:385–388CrossRefGoogle Scholar
  35. Scheidegger AE (1961) General theory of dispersion in porous media. J Geophys Res 66:3273–3278CrossRefGoogle Scholar
  36. Seyedabbasi MA, Farthing MW, Imhoff PT, Miller CT (2008) The influence of wettability on NAPL dissolution fingering. Adv Water Resour 31:1687–1696CrossRefGoogle Scholar
  37. Soerens TS, Sabatini DA, Harwell JH (1998) Effects of flow bypassing and nonuniform NAPL distribution on the mass transfer characteristics of NAPL dissolution. Water Resour Res 34:1657–1673CrossRefGoogle Scholar
  38. Steefel CI, Lasaga AC (1990) Evolution of dissolution patterns: permeability change due to coupled flow and reaction. In: Melchior DC, Basset RL (eds) Chemical modeling in aqueous systems II, American Chemistry Society Symposium Series, vol 416, pp 213–225Google Scholar
  39. Steefel CI, Lasaga AC (1994) A coupled model for transport of multiple chemical species and kinetic precipitation/dissolution reactions with application to reactive flow in single phase hydrothermal systems. Am J Sci 294:529–592CrossRefGoogle Scholar
  40. Tan CT, Homsy GM (1987) Stability of miscible displacements in porous media: radial source flow. Phys Fluids 30(5):1239–1245CrossRefGoogle Scholar
  41. Willson CS, Hall JL, Miller CT, Imhoff PT (1999) Factors affecting bank formation during surfactant-enhanced mobilization of residual NAPL. Environ Sci Technol 33:2440–2446CrossRefGoogle Scholar
  42. Yang Z, Yortsos YC (1998) Effect of no-flow boundaries on viscous fingering in porous media of large aspect ratio. Soc Petrol Eng J 3:285–292Google Scholar
  43. Yeh GT, Tripathi VS (1991) A model for simulating transport of reactive multispecies components: model development and demonstration. Water Resour Res 27:3075–3094CrossRefGoogle Scholar
  44. Zhang C, Werth CJ, Webb AG (2007) Characterization of NAPL source zone architecture and dissolution kinetics in heterogeneous porous media using magnetic resonance imaging. Environ Sci Technol 41:3672–3678CrossRefGoogle Scholar
  45. Zhao C, Steven GP (1996a) A posteriori error estimator/corrector for natural frequencies of thin plate vibration problems. Comput Struct 59:949–963CrossRefGoogle Scholar
  46. Zhao C, Steven GP (1996b) An asymptotic formula for correcting finite element predicted natural frequencies of membrane vibration problems. Commun Numer Methods Eng 11:63–73CrossRefGoogle Scholar
  47. Zhao C, Steven GP (1996c) A practical error estimator for predicted natural frequencies of two-dimensional elastodynamic problems. Eng Comput 13:19–37CrossRefGoogle Scholar
  48. Zhao C, Hobbs BE, Hornby P, Ord A, Peng S, Liu L (2008a) Theoretical and numerical analyses of chemical-dissolution front instability in fluid-saturated porous rocks. Int J Numer Anal Meth Geomech 32:1107–1130Google Scholar
  49. Zhao C, Hobbs BE, Ord A, Hornby P, Peng S (2008b) Effect of reactive surface areas associated with different particle shapes on chemical-dissolution front instability in fluid-saturated porous rocks. Transp Porous Media 73:75–94Google Scholar
  50. Zhao C, Hobbs BE, Ord A, Hornby P, Peng S (2008c) Morphological evolution of three-dimensional chemical dissolution front in fluid-saturated porous media: a numerical simulation approach. Geofluids 8:113–127Google Scholar
  51. Zhao C, Hobbs BE, Ord A (2009) Fundamentals of computational geoscience: numerical methods and algorithms. Springer, BerlinGoogle Scholar
  52. Zhao C, Hobbs BE, Ord A, Peng S (2010a) Effects of mineral dissolution ratios on chemical-dissolution front instability in fluid-saturated porous media. Transp Porous Media 82:317–335Google Scholar
  53. Zhao C, Hobbs BE, Ord A (2010b) Theoretical analyses of the effects of solute dispersion on chemical-dissolution front instability in fluid-saturated porous rocks. Transp Porous Media 84:629–653Google Scholar
  54. Zhao C, Hobbs BE, Ord A (2010c) Theoretical analyses of nonaqueous-phase-liquid dissolution induced instability in two-dimensional fluid-saturated porous media. Int J Numer Anal Meth Geomech 34:1767–1796Google Scholar
  55. Zhao C, Hobbs BE, Regenauer-Lieb K, Ord A (2011) Computational simulation for the morphological evolution of nonaqueous-phase-liquid dissolution fronts in two-dimensional fluid-saturated porous media. Comput Geosci 15:167–183CrossRefGoogle Scholar
  56. Zhao C, Hobbs BE, Ord A (2012) Effects of domain shapes on the morphological evolution of nonaqueous-phase-liquid dissolution fronts in fluid-saturated porous media. J Contam Hydrol 138–139:123–140CrossRefGoogle Scholar
  57. Zienkiewicz OC (1977) The finite element method. McGraw-Hill, LondonGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Computational Geosciences Research CentreCentral South UniversityChangshaChina

Personalised recommendations