Conceptual Modeling of Contaminated Solute Transport Based on Stream Tube Model

Seung-Gun Chung, Soon-Jae Lee, Dong-Ju Kim, Sang-Hyup Lee, Jae-Woo Choi

Center for Water Resource Cycle Research, Korea Institute of Science and Technology, Seoul, Republic of Korea.
Department of Earth and Environmental Sciences, College of Science, Korea University, Seoul, Republic of Korea.

DOI: 10.4236/aces.2012.24059                

Abstract

In this study, we performed a conceptual modeling on solute transport based on theoretical stream tube model (STM) with various travel time distributions assuming a pure convective flow through each tube in order to investigate how the lengths and distributions of solute travel time through STM affect the breakthrough curves at the end mixing surface. The conceptual modeling revealed that 1) the shape of breakthrough curve (BTC) at the mixing surface was determined by not only input travel time distributions but also solute injection mode such as sampling time and pulse lengths; 2) the increase of pulse length resulted in the linear increase of the first time moment (mean travel time) and quadratic increase of the second time moment (variance of travel time) leading to more spreading of solute, however, the second time moment was not affected by travel time distributions and 3) for a given input distributions the increase in travel distance resulted in more dispersion with the quadratic increase of travel time variance. This indicates that stream tube model obeying strictly pure convective flow follows the concept of convective-lognormal transport (CLT) model regardless the input travel time distributions.

Keywords

Conceptual Modeling; Solute Transport; Pure Convective Flow; Stream Tube Model; Travel Time Distribution

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	J. Bear, “Dynamics of Fluids in Porous Media,” Elsevier, Amsterdam, 1972.
[2]	W. A. Jury, “Simulation of Solute Transport Using a Transfer Function Model,” Water Resources Research, Vol. 18, No. 2, 1982, pp. 363-368. doi:10.1029/WR018i002p00363
[3]	W. E. Bardsley, “Temporal Moments of a Tracer Pulse in a Perfectly Parallel Flow System,” Advances in Water Resources, Vol. 26, No. 6, 2003, pp. 599-607. doi:10.1016/S0309-1708(03)00047-2
[4]	L. W. Gelhar, A. L. Gutjahr and R. L. Naff, “Stochastic Aquifer Analysis of Macrodispersion in a Stratified Aquifer,” Water Resources Research, Vol. 15, No. 6, 1979, pp. 1387-1397. doi:10.1029/WR015i006p01387
[5]	O. Güven, F. J. Molz and J. G. Melville, “An Analysis of Dispersion in a Stratified Aquifer,” Water Resources Research, Vol. 20, No. 10, 1984, pp. 1337-1354. doi:10.1029/WR020i010p01337
[6]	G. Matheron and G. de Marsily, “Is Transport in Porous Media Always Diffusive? A Counter Example,” Water Resources Research, Vol. 16, No. 5, 1980, pp. 901-917. doi:10.1029/WR016i005p00901
[7]	J. F. Pickens and G. E. Grisak, “Scale-Dependent Dispersion in a Stratified Granular Aquifer,” Water Resources Research, Vol. 17, No. 4, 1981, pp. 1191-1211. doi:10.1029/WR017i004p01191
[8]	K. W. Thorbjarnarson and D. M. Mackay, “A Field-Test of Tracer Transport and Organic Contaminant Elution in a Stratified Aquifer at the Rocky-Mountain Arsenal (Denver, Colorado, USA),” Journal of Contaminant Hydrology, Vol. 24, No. 3-4, 1997, pp. 287-312. doi:10.1016/S0169-7722(96)00015-0
[9]	W. A. Jury and K. Roth, “Transfer Functions and Solute Movement Through Soil,” Birkhauser, Boston, 1990.
[10]	C. S. Simmons, “A Stochastic-Convective Transport Representation of Dispersion in One-Dimensional Porous Media Systems,” Water Resources Research, Vol. 18, No. 4, 1982, pp. 1193-1214. doi:10.1029/WR018i004p01193
[11]	A. Mercado, “The Spreading Pattern of Injected Water in a Permeability Stratified Aquifer,” In: Artificial Recharge and Management of Aquifers. Symposium of Haifa, March 1967, Organized in the Framework of the IHD, IASH Publication, Gentbrugge, 1967, pp. 23-26.
[12]	D. Grecov and J. R. Clermont, “Numerical Simulations of Non-Newtonian Flows between Eccentric Cylinders by Domain Decomposition and Stream-Tube Method,” Journal of Non-Newtonian Fluid Mechanics, Vol. 126, No. 2-3, 2005, pp. 175-185. doi:10.1016/j.jnnfm.2004.10.004
[13]	G. Demmy, S. Berglund and W. Graham, “Injection Mode Implications for Solute Transport in Porous-Media-Analysis in a Stochastic Lagrangian Framework,” Water Resources Research, Vol. 35, No. 7, 1999, pp. 1965-1973. doi:10.1029/1999WR900027
[14]	J. M. K?hne, S. K?hne and J. ?im?nek, “A Review of Model Applications for Structured Soils: a) Water Flow and Tracer Transport,” Journal of Contaminant Hydrology, Vol. 104, No. 1-4, 2009, pp. 4-35. doi:10.1016/j.jconhyd.2008.10.002