Analytical evaluation of temporal and spatial sensitivity of longitudinal dispersion coefficient in rivers for unsteady and nonuniform flows

Document Type : Research Paper

Authors

1 Master Student of Water Structures, Faculty of Agriculture, Tarbiat Modares University

2 Assistant Prof., Department of Water Structures, Faculty of Agriculture, Tarbiat Modares University

3 Professor, Department of Water Structures, Faculty of Agriculture, Tarbiat Modares University

Abstract

Longitudinal dispersion coefficient (LDC) is a key element in pollutant transport modeling in streams. The most important factor affecting dispersion coefficient is the hydrodynamic flow. Due to the variability of hydraulic and geometrical parameters of rivers, the dispersion coefficient is a function of time and place, therefore precise calculation in such conditions is difficult and almost impossible. Many researchers over the years have provided numerous relationships to estimate dispersion coefficients, which all of them are based on average hydraulic and geometric parameters, but none of them have acceptable accuracy. Therefore, according to the uncertainty in estimating the dispersion coefficient, this question is proposed, “can we -in some cases- neglect the accurate estimation of the longitudinal dispersion coefficient? “The aim of the present study is to investigate the importance of dispersion coefficient at different places and times in rivers in non-uniform and unsteady flow. To validate the proposed method, it is performed for a hypothetical river with two different input pollution time patterns as well as for a real river (Karun River) with a hypothetical and real input pollution intensity function. The results of this study show that accurate estimation of dispersion coefficient is necessary only in some time and place ranges of the river and in most cases precise calculation is not necessary throughout the river and under these conditions if the dispersion coefficient is estimated with high error, it will have little effect on concentration distribution calculations and cause little error.

Keywords

References

  1. براتی، م. و مظاهری، م. (1394). مدل یک­بعدی انتقال آلاینده در رودخانه­های طبیعی با تأکید بر نواحی نگهداشت. مدیریت آب و آبیاری. 5 (2): 169-190.
  2. فکوری دکاهی، ب.، محمد ولی سامانی، ج. و مظاهری، م. (1395). اثر سیلاب­ها و مدیریت منابع آلاینده بر تغییرات زمانی و مکانی شوری رودخانه کارون (ملاثانی تا فارسیاب). مدیریت آب و آبیاری. 6 (2): 295-314.
  3. Atkinson, T. C., & Davis, P. M. (2000). Longitudinal dispersion in natural channels: 1. Experimental results from the River Severn, UK. HYDROL EARTH SYST SC, 4(3), 345-353.
  4. Chapra, S. C., & Runkel, R. L. (1999). Modeling impact of storage zones on stream dissolved oxygen. Environmental Engineering, 125(5), 415-419.
  5. Deng, Z. Q., Bengtsson, L., Singh, V. P., & Adrian, D. D. (2002). Longitudinal dispersion coefficient in single-channel streams. Hydraulic Engineering, 128(10), 901-916.
  6. Disley, T., Gharabaghi, B., Mahboubi, A. A., & McBean, E. A. (2015). Predictive equation for longitudinal dispersion coefficient. Hydrological processes, 29(2), 161-172.
  7. Di Toro, D. M., Stream equations and methods of characteristics J,. Sanit. Eng. Div. Amer. Soc. Civil Eng., 95(SA4), 699-703, 1969.
  8. Dobbins, W. E. (1965). BOD and oxygen relationships in streams: Sanitary Engineering Division. In Proceedings of the American Society of Civil Engineers (Vol. 91, pp. 49-55).
  9. Fischer, H. B., List, J. E., Koh, C. R., Imberger, J., & Brooks, N. H. (2013). Mixing in inland and coastal waters. Elsevier.
  10. Gandolfi, C., Facchi, A., & Whelan, M. J. (2001). On the relative role of hydrodynamic dispersion for river water quality. Water Resources Research, 37(9), 2365-2375.
  11. Iwasa, Y., Aya, S. (1991). Predicting longitudinal dispersion coefficient in open channel flows. n: Proceedings of International Symposium on Environmental Hydraulics, Hong Kong, pp. 505– 10.
  12. Kashefipour, S. M., & Falconer, R. A. (2002). Longitudinal dispersion coefficients in natural channels. Water Research, 36(6), 1596-1608.
  13. Liu, H. (1977). Predicting dispersion coefficient of streams. Environmental Engineering Division, 103(1), 59-69.
  14. Li, W. H. (1972). Effects of dispersion on DO-Sag in uniform flow. Sanitary Engineering Division, 98(1), 169-182.
  15. Nezaratian, H., Zahiri, J., & Kashefipour, S. M. (2018). Sensitivity Analysis of Empirical and Data-Driven Models on Longitudinal Dispersion Coefficient in Streams. Environmental Processes, 5(4), 833-858.
  16. Polyanin, A. D. (2002). Linear partial differential equations for Engineers and Scientists.
  17. Rajeev, R.S., Dutta, S. (2009). Prediction of longitudinal dispersion coefficients in natural rivers using genetic algorithm. Hydraulic Engineering. 40 (6), 544–552.
  18. Ramezani, M., Noori, R., Hooshyaripor, F., Deng, Z., & Sarang, A. (2019). Numerical modelling-based comparison of longitudinal dispersion coefficient formulas for solute transport in rivers. Hydrological Sciences, 64(7), 808-819.
  19. Ruthven, D. M. (1971). The dispersion of a decaying effluent discharged continuously into a uniformly flowing stream, Water Resources Management., 5,343-352.
  20. Sahay, R. R. (2013). Predicting longitudinal dispersion coefficients in sinuous rivers by genetic algorithm.  Hydrology and Hydromechanics, 61(3), 214-221.
  21. Seo, I. W., & Cheong, T. S. (1998). Predicting longitudinal dispersion coefficient in natural streams.  hydraulic engineering, 124(1), 25-32.
  22. Soncini-Sessa, R, A. Nardini, and A. Kraszewski. (1994). Data gathering campaigns for the calibration of river quality models: [1] Considerations on design criteria, Internal Rep. 94.081, Dip. di Elettron., Politec. di Milano, Milan, Italy.
  23. Thomann, R. V. (1973). Effects of longitudinal dispersion on dynamic water quality response of streams and rivers, Water Resources., 9(2), 355-366
  24. Toprak, Z. F., & Cigizoglu, H. K. (2008). Predicting longitudinal dispersion coefficient in natural streams by artificial intelligence methods. Hydrological Processes: An International Journal, 22(20), 4106-4129.
  25. Zeng, Y., & Huai, W. (2014). Estimation of longitudinal dispersion coefficient in rivers. hydro-environment research, 8(1), 2-8.
Water and Irrigation Management
Volume 9, Issue 1
December 2019
Pages 155-169

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