Non-Fickian Transport in Transparent Replicas of Rough-Walled Rock Fractures

Transport in Porous Media

Volumn 98, Issue 3, 2013, Pages 651-682

  Nowamooz, Ali ^a,b   Radilla, Giovanni ^a,b   Fourar, Mostafa ^a   Berkowitz, Brian ^c  

^a NANCY UNIVERSITÉ   (France)

^b ARTS ET MÉTIERS PARISTECH   (France)

^c WEIZMANN INSTITUTE OF SCIENCE   (Israel)

Author keywords

Anomalous transport; Breakthrough curves; Continuous time random walk; Equivalent stratified porous medium; Heterogeneous media; Rough fractures

Indexed keywords

ADVECTION; AROMATIC COMPOUNDS; CONTINUOUS TIME SYSTEMS; GRANITE; IMAGE PROCESSING; POROUS MATERIALS; RANDOM PROCESSES; SANDSTONE;

ANOMALOUS TRANSPORT; BREAK THROUGH CURVE; CONTINUOUS TIME RANDOM WALKS; HETEROGENEOUS MEDIA; POROUS MEDIUM; ROUGH FRACTURES;

FRACTURE;

ADVECTION-DIFFUSION EQUATION; BREAKTHROUGH CURVE; FRACTURE; GRANITE; HETEROGENEOUS MEDIUM; POROUS MEDIUM; RANDOM WALK METHOD; SANDSTONE; STRATIFIED FLOW; TRACER; TRANSPORT PROCESS; WALL ROCK;

EID: 84878810731     PISSN: 01693913     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11242-013-0165-7     Document Type: Article

References (47)

1. Aris, R.: On the dispersion of a solute particle in a fluid moving through a tube. Proc. R. Soc. London. Ser. A. 235, 67-77 (1956).
2. Bauget, F., Fourar, M.: Non-Fickian dispersion in a single fracture. J. Contam. Hydrol. 100(3-4), 137-148 (2008). doi: 10. 1016/j. jconhyd. 2008. 06. 005.
3. Becker, M. W., Shapiro, A. M.: Tracer transport in fractured crystalline rock: evidence of nondiffusive breakthrough tailing. Water Resour. Res. 36(7), 1677-1686 (2000). doi: 10. 1029/2000WR900080.
4. Berkowitz, B., Cortis, A., Dentz, M., Scher, H.: Modeling non-Fickian transport in geological formations as a continuous time random walk. Rev. Geophys. 44, RG2003 (2006). doi: 10. 1029/2005RG000178.
5. Berkowitz, B., Kosakowski, G., Margolin, G., Scher, H.: Application of continuous time random walk theory to tracer test measurements in fractured and heterogeneous porous media. Ground Water 39(4), 593-604 (2001). doi: 10. 1111/j. 1745-6584. 2001. tb02347. x.
6. Berkowitz, B., Scher, H.: Anomalous transport in random fracture networks. Phys. Rev. Lett. 79(20), 4038-4041 (1997). doi: 10. 1103/PhysRevLett. 79. 4038.
7. Berkowitz, B., Scher, H.: Exploring the nature of non-Fickian transport in laboratory experiments. Adv. Water Res. 32(5), 750-755 (2008). doi: 10. 1016/j. advwatres. 2008. 05. 004.
8. Berkowitz, B., Scher, H., Silliman, S. E.: Anomalous transport in laboratory scale, heterogeneous porous media. Water Resour. Res. 36(1), 149-158 (2000). doi: 10. 1029/1999WR900295.
9. Bolster, D., Valdés-Parada, F. J., LeBorgne, T., Dentz, M., Carrera, J.: Mixing in confined stratified aquifers. J. Contam. Hydrol. 120-120, 198-212 (2010). doi: 10. 1016/j. jconhyd. 2010. 02. 003.
10. Brown, S. R., Caprihan, A., Hardy, R.: Experimental observation of fluid flow channels in a single fracture. J. Geophys. Res. 103(B3), 5125-5132 (1998). doi: 10. 1029/97JB03542.
11. Christakos, G., Bogaert, P., Serre, M. L.: Temporal GIS: Advanced Functions for Field-Based Applications. Springer, New York (2002).
12. Communar, G. M.: A solute transport in stratified media. Transp. Porous Media 31(2), 133-134 (1998). doi: 10. 1023/A: 1006557032656.
13. Dentz, M., Cortis, A., Scher, H., Berkowitz, B.: Time behavior of solute transport in heterogeneous media: transition from anomalous to normal transport. Adv. Water Resour. 27(2), 155-173 (2003). doi: 10. 1016/j. advwatres. 2003. 11. 002.
14. Detwiler, R. L., Pringle, S. E., Glass, R. J.: Measurement of fracture aperture fields using transmitted light: an evaluation of measurement errors and their influence on simulations of flow and transport through a single fracture. Water Resour. Res. 35(9), 2605-2617 (1999). doi: 10. 1029/1999WR900164.
15. Detwiler, R., Rajaram, H., Glass, R. J.: Solute transport in variable aperture fractures: An investigation of the relative importance of Taylor dispersion and macrodispersion. Water Resour. Res. 36(7), 1611-1625 (2000). doi: 10. 1029/2000WR900036.
16. Didierjean, S., Amaral Souto, H. P., Christian, Moyne C.: Dispersion in periodic porous media. Experience versus theory for two-dimensional systems. Chem. Eng. Sci. 52(12), 1861-1874 (1997). doi: 10. 1016/S0009-2509(96)00518-0.
17. Dronfield, D. G., Silliman, S. E.: Velocity dependence of dispersion for transport through a single fracture of variable roughness. Water Resour. Res. 29(10), 3477-3483 (1993). doi: 10. 1029/93WR01407.
18. Fourar, M.: Characterization of heterogeneities at the core-scale using the equivalent stratified porous medium approach. In: Proceedings of the International Symposium of the Society of Core Analysts, Trondheim, 12-16 Sept 2006.
19. Fourar M., Radilla G. (2009) Non-Fickian description of tracer transport through heterogeneous porous media. Transp. Porous Media (80)3: 561-579. doi: 10. 1007/s11242-009-9380-7.
20. Gao, G., Zhan, H., Feng, S., Huang, G., Mao, X.: Comparison of alternative models for simulating anomalous solute transport in a large heterogeneous soil column. J. Hydrol. 377(3-4), 391-404 (2009). doi: 10. 1016/j. jhydrol. 2009. 08. 036.
21. Güven, O., Molz, F. J., Melville, J. G.: An analysis of macrodispersion in a stratified aquifer. Water Resour. Res. 20(10), 1337-1354 (1984). doi: 10. 1029/WR020i010p01337.
22. Hakami, E., Larsson, E.: Aperture measurements and flow experiments on a single natural fracture. Int. J. Rock Mech. Min. Sci. Geomech. Abstr 33(4), 395-404 (1996). doi: 10. 1016/0148-9062(95)00070-4.
23. Ippolito, I., Hinch, E. J., Daccord, G., Hulin, J. P.: Tracer dispersion in 2-D fractures with flat and rough walls in a radial flow geometry. Phys. Fluids A 5(8), 1952-1962 (1993). doi: 10. 1063/1. 858822.
24. Isakov, E., Ogilvie, S. R., Taylor, C. W., Glover, P. W. J.: Fluid flow through rough fractures in rocks I: high resolution aperture determinations. Earth Planet. Sci. Lett. 191(3-4), 267-282 (2001). doi: 10. 1016/S0012-821X(01)00424-1.
25. Iwano, M., Einstein, H. H.: Stochastic analysis of surface roughness, aperture and flow in a single fracture. In: Proceedings of the International Symposium EUROCK '93, pp. 135-141, Lisbon (1993).
26. Jiménez-Hornero, F. J., Giráldez, J. V., Laguna, A., Pachepsky, Y.: Continuous time random walks for analyzing the transport of a passive tracer in a single fissure. Water Resour. Res. 41, W04009 (2005). doi: 10. 1029/2004WR003852.
27. Johns, R. A., Steude, J. S., Castanier, L. M., Roberts, P. V.: Nondestructive measurements of fracture aperture in crystalline rock cores using X-ray computed tomography. J. Geophys. Res. 98(B2), 1889-1900 (1993). doi: 10. 1029/92JB02298.
28. Kosakowski, G., Berkowitz, B., Scher, H.: Analysis of field observations of tracer transport in a fractured till. J. Contam. Hydrol. 47(1), 29-51 (2001). doi: 10. 1016/S0169-7722(00)00140-6.
29. Kuntz, B. W., Rubin, S., Berkowitz, B., Singha, K.: Quantifying solute transport at the Shale Hills Critical Zone Observatory. Vadose Zone J. 10(3), 843-857 (2011). doi: 10. 2136/vzj2010. 0130.
30. Levy, M., Berkowitz, B.: Measurement and analysis of non-Fickian dispersion in heterogeneous porous media. J. Contam. Hydrol. 64(3-4), 203-226 (2003). doi: 10. 1016/S0169-7722(02)00204-8.
31. Margolin, G., Berkowitz, B.: Application of continuous time random walks to transport in porous media. J. Phys. Chem. B104(16), 3942-3947 (2000). doi: 10. 1021/jp993721x.
32. Moreno, L., Neretnieks, I., Eriksen, T.: Analysis of some laboratory tracer runs in natural fissures. Water Resour. Res. 21(7), 951-958 (1985). doi: 10. 1029/WR021i007p00951.
33. Moreno, L., Tsang, Y. W., Tsang, C. F., Hale, F. V., Neretnieks, I.: Flow and tracer transport in a single fracture: a stochastic model and its relation to some field observations. Water Resour. Res. 24(12), 2033-2048 (1988). doi: 10. 1029/WR024i012p02033.
34. Neretnieks, I., Eriksen, T., Tahtinen, P.: Tracer movement in a single fissure in granitic rock: some experimental results and their interpretation. Water Resour. Res. 18(4), 849-858 (1982). doi: 10. 1029/WR018i004p00849.
35. Nordqvist, A. W., Tsang, Y. W., Tsang, C. F., Dverstorp, B., Andersson, J.: Effects of high variance of fracture transmissivity on transport and sorption at different scales in a discrete model for fractured rocks. J. Contam. Hydrol. 22(1-2), 39-66 (1996). doi: 10. 1016/0169-7722(95)00064-X.
36. Ogata, A., Banks, R. B.: A solution of the differential equation of longitudinal dispersion in porous media. U. S. Geol. Survey, Professional Papers, 411-A, pp. A1-A7 (1961).
37. Oron, A. P., Berkowitz, B.: Flow in rock fractures: The local cubic law assumption re-examined. Water Resour. Res. 34(11), 2811-2825 (1998). doi: 10. 1029/98WR02285.
38. Pyrak-Nolte, L. J., Montemagno, C. D., Nolte, D. D.: Volumetric imaging of aperture distributions in connected fracture networks. Geophy. Res. Lett. 24(18), 2343-2346 (1997). doi: 10. 1029/97GL02057.
39. Radilla, G., Sausse, J., Sanjuan, B., Fourar, M.: Interpreting tracer tests in the enhanced geothermal system (EGS) of Soultz-sous-Forêts using the equivalent stratified medium approach. Geothermics (2012). doi: 10. 1016/j. geothermics. 2012. 07. 001.
40. Sharifzadeh, M., Mitani, Y., Esaki, T., Urakawa, F.: An investigation of joint aperture distribution using precise surface asperities measurement and GIS data processing. In: Ohnishi Y., Aoki K. (eds.) Proceedings of the 3rd International Asian Rock Mechanics Symposium, pp. 165-171, Kyoto (2004).
41. Taylor, G. I.: Dispersion of soluble matter in solvent flowing slowly through a tube. Proc. R. Soc. London. Ser. A. 219, 186-203 (1953).
42. Tsang, C. F., Tsang, Y. W., Hale, F. V.: Tracer transport in fractures: analysis of field data based on a variable-aperture channel model. Water Resour. Res. 27(12), 3095-310 (1991). doi: 10. 1029/91WR02270.
43. Wan, J., Tokunaga, T. K., Orr, T. R., O'Neill, J., Connors, R. W.: Glass casts of rock fracture surfaces: a new tool for studying flow and transport. Water Resour. Res. 36(1), 355-360 (2000). doi: 10. 1029/1999WR900289.
44. Xiong, Y., Huang, G., Huang, Q.: Modeling solute transport in one-dimensional homogeneous and heterogeneous soil columns with continuous time random walk. J. Contam. Hydrol. 86(3-4), 163-175 (2006). doi: 10. 1016/j. jconhyd. 2006. 03. 001.
45. Yeo, I. W.: Effect of fracture roughness on solute transport. Geosciences J. 5(2), 145-151 (2001). doi: 10. 1007/BF02910419.
46. Zavala-Sanchez, V., Dentz, M., Sanchez-Vila, X.: Characterization of mixing and spreading in a bounded stratified medium. Adv. Water Resour. 32(5), 635-648 (2009). doi: 10. 1016/j. advwatres. 2008. 05. 003.
47. Zimmerman, R. W., Bodvarsson, G. S.: Hydraulic conductivity of rock fractures. Transp. Porous Media 23(1), 1-30 (1996). doi: 10. 1007/BF00145263.