Non-Fourier thermal transport in fractured geological media

Water Resources Research

Volumn 46, Issue 7, 2010, Pages

  Geiger, Sebastian ^a   Emmanuel, Simon ^b  

^a HERIOT WATT UNIVERSITY   (United Kingdom)

^b HEBREW UNIVERSITY OF JERUSALEM   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

ADVECTION; CONTINUOUS TIME SYSTEMS; DIFFUSION IN LIQUIDS; ENHANCED RECOVERY; FOURIER TRANSFORMS; FRACTURE; GEOTHERMAL FIELDS; HEAT TRANSFER; OIL WELL FLOODING; PARTIAL DIFFERENTIAL EQUATIONS; PETROLEUM RESERVOIRS; SOLUTE TRANSPORT;

ADVECTION PROCESS; ADVECTION-DIFFUSION EQUATION; CONTINUOUS TIME RANDOM WALKS; DISPERSION PROCESS; GEOLOGICAL MEDIUM; HEAT TRANSPORT; NON-FICKIAN; NON-FOURIER; POROUS MEDIUM; THERMAL TRANSPORT;

POROUS MATERIALS;

EID: 85121867201     PISSN: 00431397     EISSN: 19447973     Source Type: Journal    
DOI: 10.1029/2009WR008671     Document Type: Article

References (62)

1. Abramowitz, M., and I. Stegun (1970), Handbook of Mathematical Functions, Dover, New York.
2. Alajmi, A. F., R. Gharbi, and M. Algharaib (2009), Investigating the performance of hot water injection in geostatistically generated permeable media, J. Petrol. Sci. Eng., 66(3–4), 143–155.
3. Andre, L., V. Rabemanana, and F. D. Vuataz (2006), Influence of water-rock interactions on fracture permeability of the deep reservoir at Soultz-sous-Forets, France, Geothermics, 35, 507–531.
4. Bächler, D., and T. Kohl (2005), Coupled thermal-hydraulic-chemical modelling of enhanced geothermal systems, Geophys. J. Int., 161(2), 533–548.
5. Barenblatt, G. E., I. P. Zheltov, and I. N. Kochina (1960), Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks, J. Appl. Math., 24, 1286–1303.
6. Belayneh, M. (2004), Paleostress orientation inferred from surface morphology of joints on the southern margin of the Bristol Channel Basin, UK, in The Initiation, Propagation, and Arrest of Joints and Other Fractures, edited by J. W. Cosgrove, and T. Engelder, Geol. Soc. Spec. Publ., 231, 243–255.
7. Belayneh, M., S. Geiger, and S. K. Matthäi (2006), Numerical simulation of water injection into layered fractured carbonate reservoir analogs, AAPG Bull., 90, 1473–1493.
8. Berkowitz, B. (2002), Characterizing flow and transport in fractured geological media: A review, Adv. Water Resour., 25, 861–884.
9. Berkowitz, B., and H. Scher (1998), Theory of anomalous chemical transport in fracture networks, Phys. Rev. E, 57(5), 5858–5869.
10. Berkowitz, B., O. Bour, P. Davy, and N. Odling (2000a), Scaling of fracture connectivity in geological formations, Geophys. Res. Lett., 27(14), 2061–2064.
11. Berkowitz, B., H. Scher, and S. E. Silliman (2000b), Anomalous transport in laboratory-scale, heterogeneous porous media, Water Resour. Res., 36(1), 149–158.
12. Berkowitz, B., G. Kosakowski, G. Margolin, and H. Scher (2001), Application of continuous time random walk theory to tracer test measurements in fractured and heterogeneous porous media, Ground Water, 39, 593–604.
13. Berkowitz, B., J. Klafter, R. Metzler, and H. Scher (2002), Physical pictures of transport in heterogeneous media: Advection-dispersion, random walk and fractional derivative formulations, Water Resour. Res., 38(10), 1191, doi:10.1029/2001WR001030.
14. 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, RG2003, doi:10.1029/2005RG000178.
15. Berkowitz, B., S. Emmanuel, and H. Scher (2008), Non-Fickian transport and multiple-rate mass transfer in porous media, Water Resour. Res., 44, W03402, doi:10.1029/2007WR005906.
16. Bonnet, E., O. Bour, N. E. Odling, P. Davy, I. Main, P. Cowie, and B. Berkowitz (2001), Scaling of fracture systems in geological media, Rev. Geophys., 39, 347–383.
17. Bour, O., P. Davy, C. Darcel, and N. Odling (2002), A statistical scaling model for fracture network geometry, with validation on a multiscale mapping of a joint network (Hornelen Basin, Norway), J. Geophys. Res., 107(B6), 2113, doi:10.1029/2001JB000176.
18. Cortis, A. (2007), Peclet-dependent memory kernels for transport in heterogeneous media, Phys. Rev. E, 76, 030102(R), doi:10.1103/PhysRevE.76.030102.
19. Cortis, A., and B. Berkowitz (2004), Anomalous transport in “classical” soil and sand columns, Soil Sci. Soc. Am. J., 68, 1539–1548.
20. Cortis, A., and B. Berkowitz (2005), Computing ‘anomalous’ contaminant transport in porous media: The CTRW MATLAB toolbox, Ground Water, 43, 947–950.
21. Cortis, A., and J. Birkholzer (2008), Continuous time random walk analysis of solute transport in fractured porous media, Water Resour. Res., 44, W06414, doi:10.1029/2007WR006596.
22. Cortis, A., C. Gallo, H. Scher, and B. Berkowitz (2004), Numerical simulation of non-Fickian transport in geological formations with multiple-scale heterogeneities, Water Resour. Res., 40, W04209, doi:10.1029/2003WR002750.
23. de Hoog, F. R., J. H. Knight, and A. N. Stokes (1982), An improved method for numerical inversion of Laplace transforms, SIAM J. Sci. Stat. Comput., 3, 357–366.
24. Dentz, M., and B. Berkowitz (2003), Transport behavior of a passive solute in continuous time random walks and multirate mass transfer, Water Resour. Res., 39(5), 1111, doi:10.1029/2001WR001163.
25. Dentz, M., A. Cortis, H. Scher, and B. Berkowitz (2004), Time behavior of solute transport in heterogeneous media: Transition from anomalous to normal transport, Adv. Water Resour., 27, 155–173, doi:10.1016/j.advwatres.2003.11.002.
26. Emmanuel, S., and B. Berkowitz (2007), Continuous time random walks and heat transfer in porous media, Transp. Porous Media, 67, 413–430.
27. Fisher, A. T. (1998), Permeability within basaltic oceanic crust, Rev. Geophys., 36, 143–182.
28. Geiger, S., S. G. Roberts, S. K. Matthäi, C. Zoppou, and A. Burri (2004), Combining finite element and finite volume methods for efficient multiphase flow simulations in highly heterogeneous and structurally complex geologic media, Geofluids, 4(4), 284–299.
29. Geiger, S., T. Driesner, C. A. Heinrich, and S. K. Matthäi (2006a), Multiphase thermohaline convection in the Earth's crust: I. A new finite element–finite volume solution technique combined with a new equation of state for NaCl-H2O, Transp. Porous Media, 63, 399–434.
30. Geiger, S., T. Driesner, C. A. Heinrich, and S. K. Matthäi (2006b), Multiphase thermohaline convection in the Earth's crust: II. Benchmarking and application of a finite element–finite volume solution technique with a NaCl-H2O equation of state, Transp. Porous Med., 63, 435–461.
31. Geiger, S., S. K. Matthäi, J. Niessner, and R. Helmig (2009), Black-oil simulations for three-phase – three-component flow in fractured porous media, SPEJ Soc. Pet. Eng. J., 14(2), 338–354.
32. Haar, J. S., L. Gallagher, and G. S. Kell (1984), NBS/NRC Steam Tables, Hemisphere, Washington, D. C.
33. Haggerty, R., and S. M. Gorelick (1995), Multiple-rate mass transfer for modelling diffusion and surface reactions in media with pore-scale heterogeneities, Water Resour. Res., 31(10), 2383–2400.
34. Haggerty, R., S. A. McKenna, and L. C. Meigs (2000), On the late-time behavior of tracer test breakthrough curves, Water Resour. Res., 36(12), 3467–3479.
35. Haggerty, R., S. W. Fleming, L. C. Meigs, and S. A. McKenna (2001), Tracer tests in a fractured dolomite: 2. Analysis of mass transfer in single-well injection withdrawal test, Water Resour. Res., 37(5), 1129–1142.
36. Ingebritsen, S., W. Sanford, and C. Neuzil (2006), Groundwater in Geologic Processes, 2nd ed., 536 pp., Cambridge Univ. Press, Cambridge, U. K.
37. Kim, J., Y. Park, and T. C. Harmon (2005), Real-time model parameter estimation for analyzing transport in porous media, Ground Water Monit. Rem., 25, 78–86.
38. Kosakowski, G., B. Berkowitz, and H. Scher (2001), Analysis of field observations of tracer transport in a fractured till, J. Contam. Hydrol., 47, 29–51.
39. Levec, J., and R. G. Carbonell (1985), Longitudinal and lateral thermal dispersion in packed beds, part II: Comparison between theory and experiment, AIChE J., 31, 591–602.
40. Manning, C. E., and S. E. Ingebritsen (1999), Permeability of the continental crust: Implications of geothermal data and metamorphic systems, Rev. Geophys., 37, 127–150.
41. Matthäi, S. K., and M. Belayneh (2004), Fluid flow partitioning between fractures and a permeable rock matrix, Geophys. Res. Lett., 31, L07602, doi:10.1029/2003GL019027.
42. Matthäi, S. K., et al. (2007), Numerical simulations of multiphase fluid flow in structurally complex reservoirs, in Structurally Complex Reservoirs, edited by S. J. Jolley et al., Geol. Soc. Spec. Publ., 292, 405–429.
43. Matthäi, S. K., H. M. Nick, C. Pain, and I. Neuweiler (2010), Simulation of solute transport through fractured rock: A higher-order accurate finite-element finite-volume method permitting large time steps, Transp. Porous Media, 83, 289–318, doi:10.1007/s11242-009-9440-z.
44. McDermott, C. I., A. R. L. Randriamanjatosoa, H. Tenzer, and O. Kolditz (2006), Simulation of heat extraction from crystalline rocks: The influence of coupled processes on differential reservoir cooling, Geothermics, 35, 321–344.
45. McDermott, C. I., R. Walsh, R. Mettier, G. Kosakowski, and O. Kolditz (2009), Hybrid analytical and finite element numerical modeling of mass and heat transport in fractured rocks with matrix diffusion, Comput. Geosci., 13, 349–361.
46. McKenna, S. A., L. C. Meigs, and R. Haggerty (2001), Tracer tests in a fractured dolomite: 3. Double-porosity, multi-rate mass transfer processes in convergent flow tracer tests, Water Resour. Res., 37(5), 1143–1154.
47. Montroll, E. W., and H. Scher (1973), Random walks on lattices. IV. Continuous time random walks and influence of absorbing boundaries, J. Stat. Phys., 9(2), 101–135.
48. Nield, D. A., and A. Bejan (Eds.) (1992), Convection in Porous Media, Springer, New York.
49. Ochsner, T. E., R. Horton, G. J. Kluitenberg, and Q. J. Wang (2005), Evaluation of the heat pulse ratio method for measuring soil water flux, Soil Sci. Soc. Am. J., 69, 757–769.
50. Odling, N. E. (1997), Scaling and conenctivity of joint systems in sandstones from western Norway, J. Struct. Geol., 19(10), 1257–1271.
51. Paek, J. W., B. H. Kang, and J. M. Hyun (1999), Transient cool-down of a porous medium in pulsating flow, Int. J. Heat Mass Transfer, 42, 3523–3527.
52. Paek, J. W., B. H. Kang, and J. M. Hyun (2001), An experimental study on cool-down of a heterogeneous porous body in throughflow, Int. J. Heat Mass Transfer, 44, 683–687.
53. Paluszny, A., S. K. Matthäi, and M. Hohmeyer (2007), Hybrid finite element-finite volume discretization of complex geologic structures and a new simulation workflow demonstrated on fractured rocks, Geofluids, 7(2), 186–208.
54. Rhodes, M. E., B. Bijeljic, and M. J. Blunt (2008), Pore-to-field simulation of single-phase transport using continuous time random walks, Adv. Water Resour., 31, 1527–1539.
55. Rutqvist, J., Y. S. Wu, C. Tsang, and G. Bodvarsson (2002), A modeling approach for analysis of coupled multiphase fluid flow, heat transfer, and deformation in fractured porous rock, Int. J. Rock Mech. Min. Sci., 429–442.
56. Saar, M. O., and M. Manga (2004), Depth dependence of permeability in the oregon cascades inferred from hydrogeologic, thermal, seismic, and magmatic modeling constraints, J. Geophys. Res., 109, B04204, doi:10.1029/2003JB002855.
57. Scher, H., and E. W. Montroll (1975), Anomalous transit time dispersion in amorphous solids, Phys. Rev. B, 12(6), 2455–2477.
58. Stüben, K. (2001), A review of algebraic multigrid, J. Comput. Appl. Math., 128, 281–309.
59. Tsang, Y., J. T. Birkholzer, and S. Mukhopadhyay (2009), Modeling of thermally driven hydrological processes in partially saturated fractured rock, Rev. Geophys., 47, RG3004, doi:10.1029/2008RG000265.
60. Warren, J. E., and P. J. Root (1963), The behavior of naturally fractured reservoirs, Soc. Pet. Eng. J., 3(3), 244–255.
61. Xu, T. F., Y. Ontoy, P. Molling, N. Spycher, M. Parini, and K. Pruess (2004), Reactive transport modeling of injection well scaling and acidizing at Tiwi Field, Philippines, Geothermics, 33, 477–491.
62. Zhang, X., N. C. Koutsabeloulis, and K. Heffer (2007), Hydromechanical modelling of critically stressed and faulted reservoirs, AAPG Bull., 91, 31–50.