Extraction of Model Parameters for Reactive Solute Transport

Document Type: Regular Paper


1 Civil engineering department, Faculty of engineering

2 Head of river engineering department, East Azarbayjan regional water authority


Rock material is common in the construction of hydraulic structures. In the present study, to the aim is to examine the reactive solute relationships for transport and degradation processes through the rockfill media. By applying the analytical solution of reactive transport, the 1st to 3rd theoretical temporal moments have been extracted, consequently by applying two methods of curve fitting and temporal moment matching, the coefficients of dispersion and degradation have been exploited. Two rock diameter, two operating discharges and five instantly injection mass have been used as the variables of experiments. The EC sensors with operation software were installed inside the rockfill media and then the experimental breakthrough curves with intervals of 4 seconds have been extracted. It is concluded that both methods are suitable for application of transport and degradation processes inside the media. It was found that by increasing inflow discharges, pore velocity, and media diameters the dispersion coefficient decreases and with a decrease in media diameter or with increase in injection mass the decay rate decreases. The sensitivity analysis on the derived moment equation and also skewness coefficient equation indicated that the velocity and degradation are the most and less effective parameters on the moment equations respectively.


Main Subjects

[1] Taylor, G. I. (1954). ‘‘The dispersion of matter in turbulent flow through a pipe.’’ Proc., Royal Soc., London, 223A, 446–468.

[2] Fisher, H.B., List, E.J., Koh, R.C., Imberger, J. and Brooks, N.H. (1979). “Mixing in Inland and Coastal Waters.” Academic. New York.

[3] Chanson, H. (2004). “Environmental hydraulics of open channel flows.” Frist Edition. Elsevier Butterworth-Heinemann Linacre House. Jordan Hill. Oxford.

[4] Thackston, E.L. and Schnelle, K.B.J. (1970). “Predicting effects of dead zones on stream mixing.” Journal of the Sanitary Engineering Division, 96: 319–331.

[5] Pedersen, F. B. (1977). ‘‘Prediction of longitudinal dispersion in natural streams.’’ Hydrodynamics and Hydr. Engrg. Ser. Paper No. 14, Technical University of Denmark, Lyngby, Denmark.

[6] Nordin, C.F. and Troutman, B.M. (1980). “Longitudinal dispersion in rivers: the persistence of skewness in observed data.” Water resources research, 16(1):123–8.

[7] Seo, I. W., and Maxwell, W. H. C. (1992). ‘‘Modeling low-flow mixing through pools and riffles.’’ J. Hydr. Engrg., ASCE, 118(10), 1406–1423.

[8] Czernuszenko, W., and Rowinski, P. M. (1997). “Properties of the dead-zone model of longitudinal dispersion in rivers.” Journal of Hydraulic Research, 35(4), 491–504.

[9] Hays, J. R., Krenkel, P. A., Karl, B., and Schnelle, J. (1966). ‘‘Mass transport mechanisms in open-channel flow.’’ Tech. Rep. 8, Dept. of
Civ. Engrg., Vanderbilt University, Nashville, Tenn.

[10] Schmid, B. H. (1995). ‘‘On the transient storage equations for longitudinal solute transport in open channels: Temporal moments accounting for the effects of first-order decay.’’ J. Hydr. Res., Delft, the Netherlands, 33(5), 595–610.

[11] Seo, I.W. and Cheong, T.S. (2001). “Moment-based calculation of parameters for the storage zone model for river dispersion.” Journal of hydraulic engineering, 127(6):453–65.

[12] Harvey, C. F., and S. M. Gorelick (1995). “Temporal moment-generating equations: Modeling transport and mass transfer in heterogeneous aquifers.” Water Resour. Res., 31(8), 1895–1911.

[13] Luo, J., O. A. Cirpka, M. Dentz, and J. Carrera (2008). “Temporal moments for transport with mass transfer described by an arbitrary memory function in heterogeneous media.” Water Resour. Res., 44, W01502.

[14] Schmid, B. H. (2003). “Temporal moments routing in streams and rivers with transient storage.” Advances in Water Resources, 26, 1021–1027.

[15] Goltz, M. N., and P. V. Roberts (1987). “Using the method of moments to analyze three-dimensional diffusion-limited solute transport from temporal and spatial perspectives.“ Water Resour. Res., 23(8), 1575–1585.

[16] Cunningham, J. A., and P. V. Roberts (1998). “Use of temporal moments to investigate the effects of nonuniform grain-size distribution on the transport of sorbing solutes.” Water Resour. Res., 34(6), 1415–1425.

[17] Lees, M. J., L. A. Camacho, and S. Chapra (2000). “On the relationship of transient storage and aggregated dead zone models of longitudinal solute transport in streams.” Water Resour. Res., 36(1), 213–224.

[18] Argerich, A., R. Haggerty, E. Martı, F. Sabater, and J. Zarnetske (2011). “Quantification of metabolically active transient storage (MATS) in two reaches with contrasting transient storage and ecosystem respiration.” J. Geophys. Res., 116, G03034.

[19] Majedi Asl, M., Jafari, R. (2012). “The Mathematical Modeling of Self-Purification of the Zarjoob River for Justification of Emission.” Journal of Environmental Science and Engineering, A1:1-10.

[20] Gonzalez-Pinz, R., Haggerty, R., Dentz, M. (2013). “Scaling and predicting solute transport processes in streams.” Wyoming. Water Resources Research, 49: 4071-4088.