A Study of Mathematical Model for Pollutant Concentration and Dissolved Oxygen Concentration in the Kshipra River (India)

A. Jain¹ , V. H. Badshah² , V. Gupta³

Section:Research Paper, Product Type: Isroset-Journal
Vol.6 , Issue.2 , pp.56-60, Apr-2019

CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i2.5660

Online published on Apr 30, 2019

Copyright © A. Jain, V. H. Badshah, V. Gupta . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

View this paper at   Google Scholar | DPI Digital Library

XML View     PDF Download

How to Cite this Paper

906 Views    947 Downloads    295 Downloads

Abstract :
This paper addresses a mathematical model for pollutant and dissolved oxygen concentrations in a river. The physical and mass conservation laws governing the interaction of pollutant and dissolved oxygen are expressed as non-linear one-dimensional, time-dependent, coupled partial differential equations and are solved numerically, for zero-diffusion case, using fourth-order Runge-Kutta method. Time required for the pollutant to decay completely and dissolved oxygen to reach its saturation level is obtained graphically through simulation study. A particular case of the River Kshipra (Madhya Pradesh, India) is studied in detail. The result indicates the self-purification ability of the river at four different monitoring stations along its stretch in Ujjain city, using some standard parameters of water quality. The study is motivated by the pathetic condition of the river, as it receives large amount of untreated sewage daily. This study provides a better understanding of the complex phenomena of pollution transportation in the River Kshipra.

Key-Words / Index Term :
Dissolved Oxygen, Biochemical Oxygen Demand, Diffusion, Advection, Runge-Kutta Method

References :
[1]. B. Pimpunchat, W.L. Sweatman, G.C. Wake, W. Triampo, A. Parshotam, “A Mathematical Model for Pollution in a River and its Remediation by Aeration”, Applied Mathematics Letters 22, Elsevier, pp.304-308, 2009.
[2]. H.W. Streeter, E.B. Phelps, “A Study of the Pollution and Natural Purification of the Ohio river”, US Public Health Service, Public Health Bulletin, 146, pp.1-65, 1925.
[3]. S.C. Chapra, “Surface Water Quality Modeling”, McGraw Hill, New York, pp.235-257, 1997.
[4]. B. Pimpunchat, W.L. Sweatman, W. Triampo, G.C. Wake, A. Parshotam, “Modelling River Pollution and Removal by Aeration”, in: L. Oxley. D. Kulasiri (Eds.) MODSIM 2007 International Congress on Modelling and Simulation. Land, Water and Environmental Management: Integrated Systems for Sustainability. Modelling and Simulation Society of Australia and New Zealand, December 2007, pp.2431-2437, 2007.
[5]. S. Hasadsri, M. Maleewong, “Finite Element Method for Dissolved Oxygen and Biochemical Oxygen Demand in an Open Channel”, Procedia Environmental Sciences, 13, pp.1019-1029, 2012.
[6]. T. Simon, P. R. Koya, “Studying the Effects of Reaction, Diffusion and Reaeration on River Pollution Using Numerical Simulation of Diffusion-Reaction Equations”, IOSR Journal of Mathematics, Vol.13, Issue 3(11), pp.30-36, 2017.
[7]. M. Benedini, G. Tsakiris, “Water Quatity Modelling for Rivers and Streams”, Springer Science + Business Media Dordrecht, pp.27-53, 2013.
[8]. S.A. Hussain, W.G. Atshan, Z.M. Najam, “Mathematical Model for the Concentration of Pollution and Dissolved Oxygen in the Diwaniya River (Iraq)”. American Journal of Scientific Research, Issue 78, pp.33-37, 2012.
[9]. T. Simon, P. R. Koya, “Modeling and Numerical Simulation of River Pollution using Diffusion-Reaction Equation”. American Journal of Applied Mathematics, Vol. 3, Issue 6, pp.335-340, 2015.
[10]. A.S. Wadi, M.F. Dimian, F.N. Ibrahim, “Analytical solutions for one-dimensional advection-dispersion equation of the pollutant concentration”, Journal of Earth System Science. Vol.123, No.6, pp.1317-1324, 2014.
[11]. K.S. Kumar, H.L. Tiwari, R.V. Galkate, “Water Availability Assessment in Shipra River”, International Journal of Research in Engineering and Technology, Vol.4, Issue 11, pp.126-130, 2015.
[12]. R.C. Gupta, A.K. Gupta, R.K. Shrivastava, “Water quality management of river Kshipra (India)”, International Journal of Environmental Sciences, Vol.5, No.2, pp.438-446. 2014.