Presentation of a New Method in Mathematical Modeling of Pollutant Transport in Rivers with Storage Zones

Document Type : Research Article

Authors

1 Msc. Graduate of Water Structures, Faculty of Agriculture, Tarbiat Modares University, Tehran, Iran,

2 Professor, Department of Water Structures, Faculty of Agriculture, Tarbiat Modares University,Tehran, Iran

Abstract

Prediction of pollutants transport in water resources is of particular importance in the management and prevention of their pollution. The heterogeneity and non-uniformity in the morphology throughout rivers which is known as the storage area, will make changes in the uniform transport of pollutants to downstream. Storage areas along rivers are actually places around the river where flow velocity in these places is significantly slower than the river’s flow velocity and are also known as dead zones. The presence of these places in rivers makes it difficult to apply the classic pollutant transport equation for them. For a more accurate simulation of the pollutant transport in natural rivers containing storage zones, some improvements should be made to the classic advection-dispersion equation. In this study, a new approach is presented by considering nonlinear flux dispersion and applying storage zones. In order for verification and validation of the proposed model, two series of hypothetical and real data examples have been used. Based on the measured results, the model outputs have acceptable adaptation with observational data and show that the proposed model is an accurate and acceptable model in the simulation of dissolved pollutant transport in rivers with storage zones. According to the obtained concentration-time curves, it can be concluded that the proposed model can model any type of storage area with any amount of area. Also, this model is applicable for all rivers with and without storage area and it is more superior in comparison with other similar models in terms of the number of parameters (considering merely one parameter) and simplicity in physical interpretation; and can be an appropriate alternative instead of the classic pollutant transport model in these type of rivers.

Keywords

Main Subjects

References

[1] V. Batu, Applied flow and solute transport modeling in aquifers: fundamental principles and analytical and numerical methods, CRC Press, 2005.
[2] A.P. Jackman, R.A. Walters, V.C. Kennedy, Low-flow Transport Models for Conservative and Sorbed Solutes, Uvas Creek, Near Morgan Hill, California, US Department of the Interior, Geological Survey, 1984.
[3] E.M. Valentine, I.R. Wood, Longitudinal dispersion with dead zones, Journal of the Hydraulics Division, 103(9) (1977) 975-990.
[4] E.M. Valentine, I.R. Wood, Experiments in longitudinal dispersion with dead zones, Journal of the Hydraulics Division, 105(8) (1979) 999-1016.
[5] E.M. Valentine, I.R. Wood, Dispersion in rough rectangular channels, Journal of the Hydraulics Division, 105(12) (1979) 1537-1553.
[6] T.J. Day, Longitudinal dispersion in natural channels, Water Resources Research, 11(6) (1975) 909-918.
[7] R.L. Runkel, K.E. Bencala, Transport of reacting solutes in rivers and streams, in: Environmental hydrology, Springer, 1995, pp. 137-164.
[8] A. Parsaie, A.H. Haghiabi, Calculation of Longitudinal Dispersion Coefficient and Modeling of Pollution transport in Rivers (Case Study: Severn and Narew Rivers), Water and Soil, 29 (5) (2015) 1070-1085. [in Persian]
[9] A. Parsaie, A.H. Haghiabi, Computational modeling of pollution transmission in rivers, Applied water science, 7(3) (2017) 1213-1222.
[10] K.E. Bencala, Simulation of solute transport in a mountain pool‐and‐riffle stream with a kinetic mass transfer model for sorption, Water Resources Research, 19(3) (1983) 732-738.
[11] K. Bencala, R. Walters, Simulation of solute transport in a mountain pool-and-riffle stream: A transient storage zone model, Water Resources Research, 19 (1983) 718-724.
[12] R.L. Runkel, One-dimensional transport with inflow and storage (OTIS): A solute transport model for streams and rivers, US Department of the Interior, US Geological Survey, 1998.
[13] S.K. Singh, Treatment of stagnant zones in riverine advection-dispersion, Journal of Hydraulic Engineering, 129(6) (2003) 470-473.
[14] M. Barati Moghaddam, M. Mazaheri, J. MohammadVali Samani, A comprehensive one-dimensional numerical model for solute transport in rivers, Hydrology and Earth System Sciences, 21(1) (2017) 99-116.
[15] Barati Moghaddam M, Mazaheri M, MohammadVali Samani J. Numerical Solution of Advection-Dispersion Equation with Temporal Conservation Zones in Case of Unsteady Flow in Irregular Sections. Journal of Science And Irrigation Engineering.2015;40(1): 99-117.[in Persian]
[16] S. Wallis, R. Manson, Sensitivity of optimized transient storage model parameters to spatial and temporal resolution, Acta Geophysica, 67(3) (2019) 951-960.
[17] Z.-Q. Deng, V.P. Singh, L. Bengtsson, Numerical solution of fractional advection-dispersion equation, Journal of Hydraulic Engineering, 130(5) (2004) 422-431.
[18] S. Kim, M.L. Kavvas, Generalized Fick’s law and fractional ADE for pollution transport in a river: Detailed derivation, Journal of Hydrologic Engineering, 11(1) (2006) 80-83.
[19] S.K. Singh, Comparing three models for treatment of stagnant zones in riverine transport, Journal of irrigation and drainage engineering, 134(6) (2008) 853-856.
[20] A. Marion, M. Zaramella, A. Bottacin‐Busolin, Solute transport in rivers with multiple storage zones: The STIR model, Water resources research, 44(10) (2008).
[21] A. Parsaie, A.H. Haghiabi, Numerical routing of tracer concentrations in rivers with stagnant zones, Water Science and Technology: Water Supply, 17(3) (2017) 825-834.
[22] Jafari H, Mazaheri M, MohammadVali Samani J. Numerical Modeling of Pollutant Transport in Sediments and Non-Uniform Flow Waterways Using Fractional Advection-Dispersion Equation. water and soil. 2017 Dec 4; 31 (3): 689-700.[in Persian]
[23] H. Jung, Modeling of solute transport and retention in Upper Amite River,  (2008).
[24] Z.-Q. Deng, H.-S. Jung, B. Ghimire, Effect of channel size on solute residence time distributions in rivers, Advances in Water Resources, 33(9) (2010) 1118-1127.
[25] Z.Q. Deng, H.S. Jung, Variable residence time–based model for solute transport in streams, Water resources research, 45(3) (2009).
[26] S.C. Chapra, Surface water-quality modeling, Waveland press, 2008.
[27] H. Fischer, E. List, R. Koh, J. Imberger, N. Brooks, Mixing in inland and coastal waters Academic Press, New York,  (1979) 229-242.
[28] D. Zwillinger, Handbook of differential equations, Gulf Professional Publishing, 1998.
[29] R.J. Avanzino, G.W. Zellweger, V.C. Kennedy, S.M. Zand, K.E. Bencala, Results of a solute transport experiment at Uvas Creek, September 1972, 2331-1258, US Geological Survey, 1984.
Amirkabir Journal of Civil Engineering
Volume 53, Issue 9
December 2021
Pages 3933-3946

Files

Share

How to cite

Statistics