Simulation of density-driven flow in fractured porous media

Advances in Water Resources

Volumn 33, Issue 12, 2010, Pages 1494-1507

  Grillo, A ^a   Logashenko, D ^b   Stichel, S ^a   Wittum, G ^a  

^a GOETHE UNIVERSITY   (Germany)

^b Steinbeis Research Center 936   (Germany)

Author keywords

Density driven flow; Finite volume discretization; Fracture; Porous medium

Indexed keywords

DENSITY DRIVEN FLOWS; EQUATIONS OF DENSITY; FINITE VOLUME DISCRETIZATIONS; FINITE-VOLUME; FRACTURE WIDTH; FRACTURED POROUS MEDIA; NUMERICAL EXPERIMENTS; POROUS MEDIUM; REDUCED DIMENSIONALITY;

FINITE VOLUME METHOD; POROUS MATERIALS; VOLUME MEASUREMENT;

FRACTURE;

COMPUTER SIMULATION; DENSITY; FINITE VOLUME METHOD; FLUID FLOW; FRACTURED MEDIUM; POROUS MEDIUM;

EID: 78649634086     PISSN: 03091708     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.advwatres.2010.08.004     Document Type: Article

References (50)

1. Angot P., Boyer F., Hubert F. Asymptotic and numerical modelling of flow in fractured porous media. ESAIM: M2AN. Math Model Numer Anal 2009, 43:239-275.
2. Attinger S., Eberhardt J., Neuss N. Filtering procedures for flow in heterogeneous porous media: numerical results. Comput Vision Sci 2002, 5(2):67-72.
3. Barrett R., Berry M., Chan T.F., Demmel J., Donato J., Dongarra J., et al. Templates for the solution of linear systems: building blocks for iterative methods 1993, SIAM, Philadelphia, PA.
4. Bastian P., Birken K., Johannsen K., Lang S., Reichenberger V., Wieners C., et al. Parallel solution of partial differential equations with adaptive multigrid methods on unstructured grids. High performance computing in science and engineering 2000, 506-519. Springer, Berlin. W. Jäger, E. Krause (Eds.).
5. Bastian P., Chen Z., Ewing R.E., Helmig R., Jakobs H., Reichenberger V. Numerical simulation of multiphase flow in fractured porous media. Lecture notes physics 2000, vol. 552:50-68. Springer, Berlin. Z. Chen (Ed.).
6. Bear J. Dynamics of fluid in porous media 1972, Dover Publications, Inc., New York.
7. Bear J. On the aquifer's integrated balance equations. Adv Water Resources 1977, 1(1):15-23.
8. Bear J. Hydraulics of groundwater 1979, Dover Publications, Inc., Mineola.
9. Bear J., Bachmat Y. Introduction to modeling of transport phenomena in porous media 1990, Kluwer Academic Publishers, Dordrecht, Boston, London.
10. Bear J., Tsang C.-F., deMarsily G. Flow and contaminant transport in fractured rocks 1993, Academic Press Inc., New York.
11. Bennethum L.S., Murad M.A., Cushman J.H. Macroscale thermodynamics and the chemical potential for swelling porous media. Transp Porous Media 2000, 39:187-225.
12. Bensoussan A., Lions J.L., Papanicolau G. Asymptotic analysis for periodic structures 1978, North-Holland, Amsterdam.
13. Brenner H. The diffusion model of longitudianl mixing in beds of finite length: numerical values. Chem Eng Sci 1962, 17:229-243.
14. Cai Z. On the finite volume element method. Numer Math 1990, 58(1):713-735.
15. Cermelli P., Fried E., Gurtin M.E. Transport relations for surface integrals arising in the formulation of balance laws for evolving fluid interfaces. J Fluid Mech 2005, 544:339-351.
16. De Groot S., Mazur P. Non-equilibrium thermodynamics 1954, North-Holland Publishing Company. 2nd reprint.
17. Diersch H.-J.-G., Kolditz O. Variable-density flow and transport in porous media: approaches and challenges. Wasy Software FEFLOW©- finite element subsurface flow and transport simulation system 2005, vol. 2. Wasy GmbH.
18. Fein E. Ein programmpaket zur modellierung von dichteströmungen. Braunschweig 139: GRS; 1999 [in German].
19. Frolkovič P. Consistent velocity approximation for density driven flow and transport. Advanced computational methods in engineering. Part 2: Contributed papers 1998, 603-611. Shaker Publishing, Maastricht. R. Van Keer (Ed.).
20. Frolkovič P. Maximum principle and local mass balance for numerical solutions of transport equation coupled with variable density flow. Acta Math Universitatis Comenianae 1998, 1(68):137-157.
21. Frolkovič P., Knabner P. Consistent velocity approximations in finite element or volume discretizations of density driven flow. Computational methods in water resources XI 1996, 93-100. Computational Mechanics Publication, Southhampten. A.A. Aldama (Ed.).
22. Graf T., Therrien R. Variable-density groundwater flow and solute transport in porous media containing nonuniform discrete fractures. Adv Water Resources 2005, 28:1351-1367.
23. Graf T., Therrien R. Variable-density groundwater flow and solute transport in irregular 2D fracture networks. Adv Water Resources 2007, 30:455-468.
24. Graf T., Therrien R. Stable-unstable flow of geothermal fluids in fractured rock. Geofluids 2009, 9:138-152.
25. Gray W.G. Derivation of vertically averaged equations describing multiphase flow in porous media. Water Resources Res 1982, 18:1705-1712.
26. Gray W.G. Constitutive theory for vertically averaged equations describing steam-water flow in porous media. Water Resources Res 1983, 19:1501-1510.
27. Hassanizadeh S.M. Derivation of basic equations of mass transport in porous media. Part 1: Generalized Darcy's and Fick's laws. Adv Water Resources 1986, 9:196-206.
28. Hassanizadeh S.M., Gray W.G. Boundary and interface conditions in porous media. Water Resources Res 1989, 25(7):1705-1715.
29. Hassanizadeh S.M., Gray W.G. Derivation of conditions describing transport across zones of reduced dynamics within multiphase systems. Water Resources Res 1989, 25:529-539.
30. Hassanizadeh S.M., Gray W.G. Mechanics and thermodynamics of multiphase flow in porous media including interphase boundaries. Adv Water Resources 1990, 13:169-186.
31. Henry HR. Effects of dispersion on salt encroachment in coastal aquifers. In: Sea water in coastal aquifers. USGS Water Supply Paper 1613-c; 1964. p. 70-84.
32. Holzbecher N. Modeling density-driven flow in porous media 1998, Springer-Verlag, Heidelberg. 1st ed.
33. Johannsen K., Kinzelbach W., Oswald S., Wittum G. The saltpool benchmark problem - numerical simulation of saltwater upconing in a porous medium. Adv Water Res 2002, 25(3):335-348.
34. Johannsen K., Oswald S., Held R., Kinzelbach W. Numerical simulation of three-dimensional saltwater-freshwater fingering instabilities observed in a porous medium. Adv Water Resources 2006, 29(11):1690-1704.
35. Karimian S.M., Schneider G.E. Pressure-based control-volume finite element method for flow at all speeds. AIAA J 1995, 33(9):1611-1618.
36. Lang S., Wittum G. Large-scale density-driven flow simulations using parallel unstructured Grid adaptation and local multigrid methods. Concurr Computat: Pract Exper 2005, 17:1415-1440.
37. Malkovsky V.I., Pek A.A. Conditions for the onset of thermal convection of a homogeneous fluid in a vertical fault. Petrology 1997, 5:381-387.
38. Martinez-Landa L., Carrera J. A methodology to interpret cross-hole tests in a granite block. J Hydrogeol 2006, 325(1-4):222-240.
39. Murdoch A.I. Some fundamental aspects of surface modelling. J Elast 2005, 80:33-52.
40. Murdoch A.I., Soliman A. On the slip-boundary condition for liquid flow over planar porous boundaries. Proc Roy Soc Lond A 1999, 455:1315-1340.
41. Murphy H.D. Convective instabilities in vertical fractures and faults. J Geophys Res 1979, 84:6121-6130.
42. Neumann S. Trends, prospects and challenges in quantifying flow and transport through fractured rocks. Hydrogeol J 2005, 13:124-147.
43. Oldenburg C.M., Pruess K. Layered thermohaline convection in hypersaline geothermal systems. Transp Porous Media 1998, 33:29-63.
44. Scheidegger A.E. The physics of flow through porous media 1974, University of Toronto Press, Toronto. 3rd ed.
45. Sharp J.M.J., Shi M. Heterogeneity effects on possible salinity-driven free convection in low-permeability strata. Geofluids 2009, 34:263-274.
46. Shikaze S.G., Sudicky E.A., Schwartz F.W. Density-dependent solute transport in discretely-fractured geologic media: is prediction possible?. J Contam Hydrogeol 1998, 34:273-291.
47. Simmons C.T., Fenstemaker T.R., Sharp J.M.J. Variable-density groundwater flow and solute transport in heterogeneous porous media: approaches, resolutions and future challenges. J Contam Hydrogeol 2001, 52:245-275.
48. Simpson M., Clement T. Improving the worthiness of the Henry problem as a benchmark for density-dependent groundwater flow models. Water Resources Res 2004, 40.
49. Sorek S., Borisov V., Yakirevich A. A two-dimensional areal model for density dependent flow regime. Transp Porous Media 2001, 43:87-105.
50. Whitaker S. The method of volume averaging - theory and applications of transport in porous media 1999, Kluwer Academic Publishers, Dordrecht, The Netherlands. 1st ed.