Lattice Boltzmann modeling for tracer test analysis in a fractured Gneiss aquifer

Ramadan Abdelaziz, Andrew J. Pearson, Broder J. Merkel

Florida International University, University Park, USA.
TU Bergakademie Freiberg, Instuite for Geology, Freiberg, Germany.
TU Bergakafemie Freiberg, Instuite for Geology, Freiberg, Germany.

DOI: 10.4236/ns.2013.53050                

Abstract

Fractured Gneiss aquifers present a challenge to hydrogeologists because of their geological complexity. Interpretation methods which can be applied to porous media cannot be applied to fractured Gneiss aquifers because flow and transport occur in fractures, joints, and conduits. In contrast, the rock matrix contribution to groundwater flow is not very important in Gneiss aquifers. Sodium chloride was injected into groundwater flow under steady state condition as tracer to determine transport parameters which are needed for transport modeling. QTRACER2 was used to evaluate the tracer test data. Lattice Boltzmann method was applied to simulate flow and tracer transport through a fracture zone in Gneiss. Experimental tracer data and the numerical solution by lattice Boltzmann method are compared. In general, the results indicate that a 2D Lattice Boltzmann model is able to simulate solute transport in fractured gneiss aquifer at field scale level.

Keywords

LBM; QTRACER2

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	K?ss, W., Behrens, H., Himmelsbach, T. and H?tzl, H. (1998) Tracing technique in geohydrology. Balkema, Rotterdam, 581.
[2]	Bodin, J., Delay, F. and De Marsily, G. (2003) Solute transport in a single fracture with negligible matrix permeability: 1. Fundamental mechanisms. Hydrogeology Journal, 11, 418-433. doi:10.1007/s10040-003-0268-2
[3]	Leibundgut, C., Maloszewski, P. and Külls, C. (2011) Tracers in hydrology. John Wiley and Sons, Ltd., Hoboken.
[4]	Schwartz, F.W. and Zhang, H. (2003) Fundamentals of ground water. John Wiley and Sons, Ltd., Hoboken.
[5]	Singhal, B.B.S. and Gupta, R.P. (2010) Applied hydrogeology of fractured rocks. 2nd Edition, Springer, Berlin. doi:10.1007/978-90-481-8799-7
[6]	Garabedian, S.P., LeBlanc, D.R., Gelhar, L.W. and Celia, M.A. (1991) Large-scale natural gradient tracer test in sand and gravel, Cape Cod, Massachusetts: 2. Analysis of spatial moments for a nonreactive tracer. Water Resources Research, 27, 911-924. doi:10.1029/91WR00242
[7]	LeBlanc, D.R., Garabedian, S.P., Hess, K.M., Gelhar, L. W., Quadri, R.D., Stollenwerk, K.G. and Wood, W.W. (1991) Large-scale natural-gradient tracer test in sand and gravel. Cape Cod, Massachusetts: 1. Experimental design and observed tracer movement. Water Resources Research, 27, 895-910. doi:10.1029/91WR00241
[8]	Adams, E.E. and Gelhar, L.W. (1992) Field study of dispersion in a heterogeneous aquifer: 2. Spatial moments analysis. Water Resources Research, 28, 3293-3307. doi:10.1029/92WR01757
[9]	Rehfeldt, K.R., Boggs, J.M. and Gelhar, L.W. (1992) Field study of dispersion in a heterogeneous aquifer: 3. Geostatistical analysis of hydraulic conductivity. Water Resources Research, 28, 3309-3324. doi:10.1029/92WR01758
[10]	Hess, K.M., Wolf, S.H. and Celia, M.A. (1992) Largescale natural gradient tracer test in sand and gravel, Cape Cod, Massachusetts: 3. Hydraulic conductivity variability and calculated macrodispersivities. Water Resources Research, 28, 2011-2027. doi:10.1029/92WR00668
[11]	Sudicky, E.A. (1986) A natural gradient experiment on solute transport in a sand aquifer: Spatial variability of hydraulic conductivity and its role in the dispersion process. Water Resources Research, 22, 2069-2082. doi:10.1029/WR022i013p02069
[12]	Abdelaziz, R. and Merkel, B.J. (2012) Analytical and numerical modeling of flow in a fractured gneiss aquifer. Journal of Water Resource and Protection, 4, 657-662. doi:10.4236/jwarp.2012.48076
[13]	Slichter, C.S. (1905) Field measurements of the rate of movement of underground waters. United States Geological Survey Water-Supply and Irrigation Paper, 140, 711218.
[14]	Bear, J., Tsang, C.F. and Marsily, G.D. (1993) Flow and contaminant transport in fractured rocks. Academic Press, San Diego.
[15]	Gerke, H.H. and Van Genuchten, M.T. (1993) A dualporosity model for simulating the preferential movement of water and solutes in structured porous media. Water Resources Research, 29, 305-319. doi:10.1029/92WR02339
[16]	Gerke, H.H. and Van Genuchten, M.T. (1993) Evaluation of a first-order water transfer term for variably saturated dual-porosity flow models. Water Resources Research, 29, 1225-1238. doi:10.1029/92WR02467
[17]	Zhang, D. and Sun, A.Y. (2000) Stochastic analysis of transient saturated flow through heterogeneous fractured porous media: A double-permeability approach. Water Resources Research, 36, 865-874. doi:10.1029/2000WR900003
[18]	Hu, B.X., Huang, H. and Zhang, D. (2002) Stochastic analysis of solute transport in heterogeneous, dual-permeability media. Water Resources Research, 38, 14-1- 14-16. doi:10.1029/2001WR000442
[19]	Qian, Y.H., d’Humieres, D. and Lallemand, P. (2007) Lattice BGK models for Navier-Stokes equation. EPL (Europhysics Letters), 17, 479. doi:10.1209/0295-5075/17/6/001
[20]	Chen, H., Chen, S. and Matthaeus, W.H. (1992) Recovery of the Navier-Stokes equations using a lattice-gas Boltzmann method. Physical Review A, 45, R5339-R5342. doi:10.1103/PhysRevA.45.R5339
[21]	Chen, S., Martinez, D. and Mei, R. (1996) On boundary conditions in lattice Boltzmann methods. Physics of Fluids, 8, 2527. doi:10.1063/1.869035
[22]	Flekk?y, E.G. (1993) Lattice Bhatnagar-Gross-Krook models for miscible fluids. Physical Review E, 47, 4247- 4257. doi:10.1103/PhysRevE.47.4247
[23]	Gutfraind, R. and Hansen, A. (1995) Study of fracture permeability using lattice gas automata. Transport in Porous Media, 18, 131-149. doi:10.1007/BF01064675
[24]	Yeo, W. (2001) Effect of fracture roughness on solute transport. Geosciences Journal, 5, 145-151. doi:10.1007/BF02910419
[25]	He, X., Doolen, G.D. and Clark, T. (2002) Comparison of the lattice Boltzmann method and the artificial compressibility method for Navier-Stokes equations. Journal of Computational Physics, 179, 439-451. doi:10.1006/jcph.2002.7064
[26]	Yoshino, M. and Inamuro, T. (2003) Lattice Boltzmann simulations for flow and heat/mass transfer problems in a three-dimensional porous structure. International Journal for Numerical Methods in Fluids, 43, 183-198. doi:10.1002/fld.607
[27]	Zhang, X. and Ren, L. (2003) Lattice Boltzmann model for agrochemical transport in soils. Journal of Contaminant Hydrology, 67, 27-42. doi:10.1016/S0169-7722(03)00086-X
[28]	Succi, S. (2001) The Lattice Boltzmann equation for fluid dynamics and beyond. Oxford University Press, New York.
[29]	Sukop, M.C. and Thorne, D.T. (2006) Lattice Boltzmann modeling. Springer, Berlin.
[30]	Field, M.S. (2002) The QTRACER2 program for tracerbreakthrough curve analysis for tracer tests in karstic aquifers and other hydrologic systems. National Center for Environmental Assessment—Washington Office, Office of Research and Development, US Environmental Protection Agency, Washington DC.
[31]	Tam, V.T., Vu, T.M.N. and Batelaan, O. (2001) Hydrogeological characteristics of a cast mountainous catchment in the northwest of Vietnam. Acta Geologica Sinica— English Edition, 75, 260-268. doi:10.1111/j.1755-6724.2001.tb00529.x
[32]	Birk, S., Geyer, T., Liedl, R. and Sauter, M. (2005) Processbased interpretation of tracer tests in carbonate aquifers. Groundwater, 43, 381-388. doi:10.1111/j.1745-6584.2005.0033.x
[33]	Massei, N., Wang, H.Q., Field, M.S., Dupont, J.P., Bakalowicz, M. and Rodet, J. (2006). Interpreting tracer breakthrough tailing in a conduit-dominated karstic aquifer. Hydrogeology Journal, 14, 849-858. doi:10.1007/s10040-005-0010-3
[34]	Gabrov?ek, F., Kogov?ek, J., Kova?i?, G., Petri?, M., Ravbar, N. and Turk, J. (2010) Recent results of tracer tests in the catchment of the Unica river (sw slovenia). Acta Carsologica, 1, 39.
[35]	Bear, J. (1979) Hydraulics of groundwater, McGraw-Hill series in water resources and environmental engineering. McGraw-Hill, New York.
[36]	He, X. and Luo, L.S. (1997) A priori derivation of the lattice Boltzmann equation. Physical Review E, 55, 6333- 6336. doi:10.1103/PhysRevE.55.R6333
[37]	Sukop, M.C., Anwar, S., Lee, J.S., Cunningham, K.J. and Langevin, C.D. (2008) Modeling ground-water flow and solute transport in karst with lattice Boltzmann methods. In Proceedings of the US Geological Survey Karst Interest Group Workshop, Bowling Green, 27-29 May 2008, 77-86.
[38]	Lee, J.Y. and Lee, K.K. (2000) Use of hydrologic time series data for identification of recharge mechanism in a fractured bedrock aquifer system. Journal of Hydrology, 229, 190-201. doi:10.1016/S0022-1694(00)00158-X
[39]	Shook, G.M., Ansley, S.L. and Wylie, A. (2004) Tracers and tracer testing: Design, implementation, and interpretation methods. Idaho National Engineering and Environmental Laboratory, Idaho Falls. www.inl.gov/technicalpublications/Documents/2603379.pdf doi:10.2172/910642
[40]	Field, M.S. (1999) The QTRACER program for tracerbreakthrough curve analysis for karst and fractured-rock aquifers. National Center for Environmental Assessment— Washington Office, Office of Research and Development, US Environmental Protection Agency, Washington DC.
[41]	Field, M.S. and Pinsky, P.F. (2000) A two-region nonequilibrium model for solute transport in solution conduits in karstic aquifers. Journal of Contaminant Hydrology, 44, 329-351. doi:10.1016/S0169-7722(00)00099-1
[42]	Anwar, S. (2008) Lattice Boltzmann modeling of fluid flow and solute transport in karst aquifers. FIU Electronic Theses and Dissertations, Florida International University, University Park.
[43]	Anwar, S. and Sukop, M.C. (2009) Lattice Boltzmann models for flow and transport in saturated karst. Groundwater, 47, 401-413. doi:10.1111/j.1745-6584.2008.00514.x
[44]	Komori, F.S., Mielli, M.Z. and Carre?o, M.N. (2011) Simulator for microfluidics based on the lattice Boltzmann method. ECS Transactions, 39, 461-468. doi:10.1149/1.3615227
[45]	Komori, F.S. (2012) Development of a simulator computational fluid dynamics using the lattice Boltzmann method. M.Sc. Theses, University of S?o Paulo, S?o Paulo.
[46]	Fetter, C.W. (2008) Contaminant hydrogeology. 2nd Edition, Waveland Press, Inc., Long Grove.