Experimental and Mathematical Investigation of Time-Dependence of Contaminant Dispersivity in Soil

Document Type : Research Paper


Department of Water Engineering, Faculty of Agriculture, University of Tabriz, Tabriz, Iran


Laboratory and field experiments have shown that dispersivity is one of the key parameters in contaminant transport in porous media and varies with elapsed time. This time-dependence can be shown using a time-variable dispersivity function. The advantage of this function as opposed to constant dispersivity is that it has at least two coefficients that increase the accuracy of the dispersivity prediction. In this study, longitudinal dispersivity values were obtained for the conservative NaCl solute transport in a laboratory porous medium saturated with tap water. The results showed that the longitudinal dispersivity initially increased with time (pre-asymptotic stage) and eventually reached a constant value (asymptotic stage). Four functions were used to investigate the time variations of dispersivity: linear, power, exponential and logarithmic. In general, because of the linear increase of dispersivity during a long time of transport, the linear function with R2=0.97 showed better time variations than the other three functions; the logarithmic function, having an asymptotic nature, predicted the asymptotic stage successfully (R2=0.95). The ratio of the longitudinal dispersivity to the medium length was not constant during the transport process and varied from 0.01 to 0.05 cm with elapsed time.


Main Subjects

[1] Bear, J. (1979). Analysis of flow against dispersion in porous media—Comments. Journal of hydrology, 40(3-4), 381-385.
[2] Zhang, X., Qi, X., Zhou, X., Pang, H. (2006). An in situ method to measure the longitudinal and transverse dispersion coefficients of solute transport in soil. Journal of hydrology, 328(3-4), 614-619.
[3] Su, N., Sander, G. C., Liu, F., Anh, V., Barry, D. A. (2005). Similarity solutions for solute transport in fractal porous media using a time-and scale-dependent dispersivity. Applied mathematical modelling, 29(9), 852-870.
[4] Gelhar, L. W. (1993). Stochastic subsurface hydrology. Prentice-Hall.
[5] Kumar, G. S., Sekhar, M., Misra, D. (2006). Time dependent dispersivity behavior of non-reactive solutes in a system of parallel fractures. Hydrology and earth system sciences discussions, 3(3), 895-923.
[6] Glimm, J., Lindquist, W. B., Pereira, F., Zhang, Q. (1993). A theory of macrodispersion for the scale-up problem. Transport in Porous Media, 13(1), 97-122.
[7] Levy, M., Berkowitz, B. (2003). Measurement and analysis of non-Fickian dispersion in heterogeneous porous media. Journal of contaminant hydrology, 64(3-4), 203-226.
[8] Cortis, A., Berkowitz, B. (2004). Anomalous transport in “classical” soil and sand columns. Soil science society of America journal, 68(5), 1539-1548.
[9] Zhou, L. (2002). Solute transport in layered and heterogeneous soils. Dissertation of Doctor of Philosophy, Department of Agronomy, Tsinghua University of Chinese.
[10] Neretnieks, I., Eriksen, T., Tähtinen, P. (1982). Tracer movement in a single fissure in granitic rock: Some experimental results and their interpretation. Water resources research, 18(4), 849-858.
[11] Moreno, L., Neretnieks, I., Eriksen, T. (1985). Analysis of some laboratory tracer runs in natural fissures. Water resources research, 21(7), 951-958.
[12] Dagan, G. (1988). Time‐dependent macrodispersion for solute transport in anisotropic heterogeneous aquifers. Water resources research, 24(9), 1491-1500.
[13] Basha, H. A., El‐Habel, F. S. (1993). Analytical solution of the one‐dimensional time‐dependent transport equation. Water resources research, 29(9), 3209-3214.
[14] Aral, M. M., Liao, B. (1996). Analytical solutions for two-dimensional transport equation with time-dependent dispersion coefficients. Journal of hydrologic engineering, 1(1), 20-32.
[15] Srivastava, R., Sharma, P. K., Brusseau, M. L. (2002). Spatial moments for reactive transport in heterogeneous porous media. Journal of hydrologic engineering, 7(4), 336-341.
[16] Sharma, P. K., Srivastava, R. (2011). Concentration profiles and spatial moments for reactive transport through porous media. Journal of hazardous, toxic, and radioactive waste, 16(2), 125-133.
[17] Sharma, P. K., Ojha, C. S. P., Joshi, N. (2014). Finite volume model for reactive transport in fractured porous media with distance-and time-dependent dispersion. Hydrological sciences journal, 59(8), 1582-1592.
[18] Natarajan, N. (2016). Effect of distance-dependent and time-dependent dispersion on non-linearly sorbed multispecies contaminants in porous media. ISH Journal of hydraulic engineering, 22(1), 16-29.
[19] Toride, N., Leij, F. J., Van Genuchten, M. T. (1995).The CXTFIT code for estimating transport parameters from laboratory or field tracer experiments, research report, U. S. Department of agriculture.
[20] Pang, L., Hunt, B. (2001). Solutions and verification of a scale-dependent dispersion model. Journal of contaminant hydrology, 53(1-2), 21-39.
[21] Jacques, D., Šimůnek, J., Timmerman, A., Feyen, J. (2002). Calibration of Richards' and convection–dispersion equations to field-scale water flow and solute transport under rainfall conditions. Journal of hydrology, 259(1-4), 15-31.
[22] Suresh Kumar, G., Sekhar, M., Misra, D. (2008). Time-dependent dispersivity of linearly sorbing solutes in a single fracture with matrix diffusion. Journal of hydrologic engineering, 13(4), 250-257.
[23] Legates, D. R., McCabe Jr, G. J. (1999). Evaluating the use of “goodness‐of‐fit” measures in hydrologic and hydroclimatic model validation. Water resources research, 35(1), 233-241.
[24] Gelhar, L. W., Welty, C., Rehfeldt, K. R. (1992). A critical review of data on field‐scale dispersion in aquifers. Water resources research, 28(7), 1955-1974.
[25] Beven, K. J., Henderson, D. E., Reeves, A. D. (1993). Dispersion parameters for undisturbed partially saturated soil. Journal of hydrology, 143(1-2), 19-43.
[26] Phogat, V., Mahadevan, M., Skewes, M., Cox, J. W. (2012). Modelling soil water and salt dynamics under pulsed and continuous surface drip irrigation of almond and implications of system design. Irrigation science, 30(4), 315-333.