Transport of conservative solutes in simulated fracture networks: 2. Ensemble solute transport and the correspondence to operator-stable limit distributions

Water Resources Research

Volumn 44, Issue 5, 2008, Pages

  Reeves, Donald M ^a   Benson, David A ^b   Meerschaert, Mark M ^c   Scheffler, Hans Peter ^d  

^a DESERT RESEARCH INSTITUTE   (United States)

^b Department of Geology and Geological Engineering   (United States)

^c MICHIGAN STATE UNIVERSITY   (United States)

^d UNIVERSITY OF SIEGEN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ADVECTION; CONCENTRATION (PROCESS); DIFFERENCE EQUATIONS; DIFFERENTIATION (CALCULUS); DISPERSION (WAVES); DISPERSIONS; EQUATIONS OF MOTION; FRACTURE FIXATION; IMAGE SEGMENTATION; LAWS AND LEGISLATION; MATHEMATICAL OPERATORS; PETROLEUM DEPOSITS; PETROLEUM RESERVOIRS; SOLUTE TRANSPORT; TRELLIS CODES; TURBULENT FLOW;

ADVECTION-DISPERSION EQUATION; ADVECTION-DISPERSION EQUATIONS; ARRIVAL TIMES; CONTINUOUS-TIME RANDOM WALK; EIGENVALUES; EIGENVECTORS; FINITE VARIANCE; FRACTAL DISTRIBUTIONS; FRACTURE GROUP; FRACTURE LENGTH; FRACTURE NETWORKS; FRACTURE-LENGTH DISTRIBUTION; GAUSSIAN; GAUSSIAN PLUMES; GOVERNING EQUATIONS; GROWTH DIRECTIONS; GROWTH PROCESSES; GROWTH RATES; LEADING EDGES; LIMIT DISTRIBUTIONS; LOW VELOCITIES; MODEL SELECTIONS; MULTI-RATE; MULTI-SCALING; PARAMETERIZED; PARTICLE CLOUDS; PARTICLE MOTIONS; PARTICLE RETENTION; POWER LAWS; POWER-LAW EXPONENTS; RETENTION MODELLING; SCALING MATRIX; SCALING RATES; SIMULATED FRACTURE; SOLUTE PLUMES; SPATIAL DENSITIES; TRANSMISSIVITY;

FRACTURE;

ADVECTION; EIGENVALUE; FRACTURE NETWORK; PLUME; POWER LAW; SOLUTE TRANSPORT; TRANSMISSIVITY;

EID: 46049098771     PISSN: 00431397     EISSN: None     Source Type: Journal    
DOI: 10.1029/2008WR006858     Document Type: Article

References (52)

1. Aban, I. B., M. M. Meerschaert, and A. K. Panorska (2006), Parameter estimation methods for the truncated Pareto distribution, J. Am. Stat Assoc., 101, 270-277.
2. Baeumer, B., D. A. Benson, and M. M. Meerschaert (2005), Advection and dispersion in time and space, Physica A, 350(2/4), 245-262.
3. Barton, C. C. (1995), Fractal analysis of scaling and spatial clustering of fractures, in Fractals in the Earth Sciences, edited by C. C. Barton and P. R. LaPointe, pp. 141-178, Plenum, New York.
4. Becker, M. W., and A. M. Shapiro (2000), Tracer transport in fractured crystalline rock: Evidence of non-diffusive breakthrough tailing, Water Resour. Res., 36(7), 1677-1686.
5. Benson, D. A. (1998), The fractional advection-dispersion equation: Development and application, Ph.D. thesis, Univ. of Nev., Reno.
6. Benson, D. A., S. W. Wheatcraft, and M. M. Meerschaert (2000), Application of a fractional advection-dispersion equation, Water Resour. Res., 36(6), 1403-1412.
7. Berkowitz, B., and H. Scher (1995), On the characterization of anomalous dispersion in porous and fractured media, Water Resour. Res., 31(6), 1461-1466.
8. Berkowitz, B., and H. Scher (1997), Anomalous transport in random fracture networks, Phys. Rev. Lett., 79(20), 4038-4041.
9. Bijeljic, B., and M. J. Blunt (2006), Pore-scale modeling and continuous time random walk analysis of dispersion in porous media, Water Resour. Res., 42, W01202, doi:10.1029/2005WR004578.
10. Billaux, D. M., J. P. Chiles, and C. Hestir (1989), Three-dimensional statistical modelling of a fractured rock mass - An example from the Fanay-Augères Mine, Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 36(3-4), 281-299.
11. Bingham, C. (1964), Distributions on the sphere and on the projective plane, Ph.D, dissertation, Yale Univ., New Haven, Conn.
12. Bonnet, E., O. Bour, N. E. Odling, P. Davy, I. Main, P. Cowie, and B. Berkowitz (2001), Scaling of fracture systems in geologic media, Rev. Geophys., 39(3), 347-383.
13. Bour, O., and P. Davy (1997), Connectivity of random fault networks following a power law fault length distribution, Water Resour. Res., 33(7), 1567-1583.
14. Butler, R. F. (1992), Paleomagnetism: Magnetic Domains to Geologic Terranes, Blackwell Sci., Oxford, U. K.
15. Carr, J. R. (2002), Data Visualization in the Geosciences, Prentice-Hill, Upper Saddle River, N. J.
16. de Dreuzy, J.-R., P. Davy, and O. Bour (2001), Hydraulic properties of two-dimensional random fracture networks follwing a power law length distribution: 1. Effective connectivity, Water Resour. Res., 37(8), 2065-2078.
17. 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.
18. Ehlen, J. (2000), Fractal analysis of joint patterns in granite, Int. J. Rock Mech. Min. Sci., 37, 909-922.
19. Fisher, R. (1953), Dispersion on a sphere, Proc. R. Soc. London, Ser. A, 217, 295-305.
20. Follin, S., and R. Thunvik (1994), On the use of continuum approximations for regional modeling of groundwater flow through crystalline rocks, Adv. Water Resour., 17, 133-145.
21. Gillespie, P. A., C. B. Howard, J. J. Walsh, and J. Watterson (1993), Measurement and characterization of spatial distributions of fractures, Tectonophysics, 226, 113-141.
22. Gustafson, G., and A. Fransson (2005), The use of the Pareto distribution for fracture transmissivity assessment, Hydrogeol. J., 14, 15-20, doi:10.1007/s10040-005-0440-y.
23. Haggerty, R., and S. M. Gorelick (1995), Multiple-rate mass transfer for modeling diffusion and surface reactions in media with pore-scale heterogeneity, Water Resour. Res., 31(10), 2383-2400.
24. 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.
25. Jiménez-Hornero, J., V. Giráldez, A. Laguna, and Y. Pachepsky (2005), Continuous time random walks for analyzing the transport of a passive tracer in a single fissure, Water Resour. Res., 41, W04009, doi:10.1029/2004WR003852.
26. Jurek, Z. J. (1984), Polar coordinates in Banach spaces, Bull. Acad. Pol. Math., 32, 61-66.
27. Kemeny, J., and R. Post (2003), Estimating three-dimensional rock discontinuity orientation from digital images of fracture traces, Comput. Geosci., 29, 65-77.
28. Kosakowski, G. (2004), Anomalous transport of colloids and solutes in a shear zone, J. Contam. Hydrol., 72, 23-46.
29. LaPointe, P. R., and J. A. Hudson (1985), Characterization and interpretation of rock mass joint patterns, Geol. Soc. Am. Spec. Pap., 199.
30. Long, J. C. S., J. S. Remer, C. R. Wilson, and P. A. Witherspoon (1982), Porous media equivalent for networks of discontinuous fractures, Water Resour. Res., 18(3), 645-658.
31. Meerschaert, M. M., and H. P. Scheffler (2001), Limit Distributions for Sums of Independent Random Vectors: Heavy Tails in Theory and Practice, John Wiley, New York.
32. Meerschaert, M. M., and H. P. Scheffler (2003), Nonparametric methods for heavy tailed vector data: A survey with applicatons from finance to hydrology, in Recent Advances and Trends in Nonparametric Statistics, edited by M. G. Akritas and D. N. Politis, pp. 256-279, Elsevier Sci., Amsterdam.
33. Meerschaert, M. M., D. A. Benson, and B. Baeumer (1999), Multidimensional advection and fractional dispersion, Phys. Rev. E, 59, 5026-5028.
34. Meerschaert, M. M., D. A. Benson, and B. Baeumer (2001), Operator Levy motion and multiscaling anomalous diffusion, Phys. Rev. E, 63, 021112.
35. Mercado, A. (1967), The spreading pattern of injected water in a permeability-statified aquifer, IAHS AISH Publ., 72, 23-36.
36. Munier, R. (2004), Statistical analysis of fracture data adapted for modelling discrete fracture networks version 2, Rep. R 04-66, Swed. Nucl. Fuel and Waste Manage., Stockholm.
37. Odling, N. (1997), Scaling and connectivity of joint systems in sandstones from western Norway, J. Struct. Geol., 19, 1257-1271.
38. Painter, S., V. Cvetkovic, and J. Selroos (2002), Power-law velocity distributions in fracture networks: Numerical evidence and implications for tracer transport, Geophys. Res. Lett., 29(14), 1676, doi:10.1029/ 2002GL014960.
39. Reeves, D. M., D. A. Benson, and M. M. Meerschaert (2008), Transport of conservative solutes in simulated fracture networks: 1. Synthetic data generation, Water Resour. Res., doi:10.1029/2007WR006069, in press.
40. Renshaw, C. E. (1997), Mechanical controls on the spatial density of opening-mode networks, Geology, 25(10), 923-926.
41. Renshaw, C. E. (1999), Connectivity of joint networks with power law length distributions, Water Resour. Res., 35(9), 2661-2670.
42. Ross, S. M. (1985), Introduction to Probability Models, 3rd ed., Academic, Orlando, Fla.
43. Scheffler, H.-P. (1999), On estimation of the spectral measure of certain nonnormal operator stable laws, Stat. Probab. Lett., 43, 385-392.
44. Scher, H., G. Margolin, and B. Berkowitz (2002), Towards a unified framework for anomalous transport in heterogeneous media, Chem. Phys., 284, 349-359.
45. Schumer, R., D. A. Benson, M. M. Meerschaert, and B. Baeumer (2003a), Multiscaling fractional advection-dispersion equations and their solutions, Water Resour. Res., 39(1), 1022, doi:10.1029/2001WR001229.
46. Schumer, R., D. A. Benson, M. M. Meerschaert, and B. Baeumer (2003b), Fractal mobile/immobile solute transport, Water Resour. Res., 39(10), 1296, doi:10.1029/2003WR002141.
47. Schwartz, F. W., L. Smith, and A. S. Crowe (1983), A stochastic analysis of macroscopic dispersion in fractured media, Water Resour. Res., 19(5), 1253-1265.
48. Smith, L., and F. W. Schwartz (1984), An analysis on the influence of fracture geometry on mass transport in fractured media, Water Resour. Res., 20(9), 1241-1252.
49. Stigsson, M., N. Outters, and J. Hermanson (2001), Äspö Hard Rock Laboratory, prototype repository hydraulic DFN model 2, Int. Prog. Rep. IPR 01-39, Swed. Nucl. Fuel and Waste Manage., Stockholm.
50. Strang, G. (1988), Linear Algebra and its Applications, 3rd ed., Harcourt, New York.
51. Zhang, D., and Q. Kang (2004), Pore scale simulation of solute transport in fractured porous media, Geophys. Res. Lett., 31, L12504, doi:10.1029/2004GL019886.
52. Zimmermann, G., H. Burkhardt, and L. Engelhard (2003), Scale dependence of hydraulic and structural parameters in the crystalline rock of the KTB, Pure Appl. Geophys., 160, 1067-1085.