Effluent Discharges from Two Outfalls on a Sloping Beach
Author(s)
Anton Purnama
Affiliation(s)
Department of Mathematics and Statistics, College of Science, Sultan Qaboos University, Muscat, Sultanate of Oman.
Department of Mathematics and Statistics, College of Science, Sultan Qaboos University, Muscat, Sultanate of Oman.
ABSTRACT
A marine outfall is a long pipeline that continuously discharges large amounts of effluent streams into the sea. As the number of marine outfalls along the coastal areas is growing, a far field mathematical model with two point sources on a sloping beach is used to assess the coastal water quality following discharges from two outfalls. Asymptotic approximation will be made to the concentration at the beach to measure how well the effluent plumes are mixed and diluted in the coastal waters. The result found agrees with the engineering practice of installing a two-port diffuser at the end of a single outfall to minimize its potential environment impacts.
A marine outfall is a long pipeline that continuously discharges large amounts of effluent streams into the sea. As the number of marine outfalls along the coastal areas is growing, a far field mathematical model with two point sources on a sloping beach is used to assess the coastal water quality following discharges from two outfalls. Asymptotic approximation will be made to the concentration at the beach to measure how well the effluent plumes are mixed and diluted in the coastal waters. The result found agrees with the engineering practice of installing a two-port diffuser at the end of a single outfall to minimize its potential environment impacts.
Cite this paper
Purnama, A. (2014) Effluent Discharges from Two Outfalls on a Sloping Beach. Applied Mathematics, 5, 3117-3126. doi: 10.4236/am.2014.519295.
Purnama, A. (2014) Effluent Discharges from Two Outfalls on a Sloping Beach. Applied Mathematics, 5, 3117-3126. doi: 10.4236/am.2014.519295.
References
[1] Institution of Civil Engineers (2001) Long Sea Outfalls. Thomas Telford Ltd., London. [2] Signell, R.P.,Jenter, H.L. and Blumberg A.F. (2000)Predicting the Physical Effects of Relocating Boston’s Sewage Outfall. Estuarine, Coastal and Shelf Sciences, 50, 59-71.
http://dx.doi.org/10.1006/ecss.1999.0532 [3] Macqueen, J.F. and Preston, R.W. (1983) Cooling Water Discharges into a Sea with a Sloping Bed. Water Research, 17, 389-395.
http://dx.doi.org/10.1016/0043-1354(83)90134-3 [4] Lattemann, S. and Hopner, T. (2008) Environmental Impact and Impact Assessment of Seawater Desalination. Desalination, 220, 1-15.
http://dx.doi.org/10.1016/j.desal.2007.03.009 [5] Bleninger, T. and Jirka, G.H. (2008) Modelling and Environmentally Sound Management of Brine Discharges from Desalination Plants. Desalination, 221, 585-597.
http://dx.doi.org/10.1016/j.desal.2007.02.059 [6] Purnama, A., Al-Barwani, H.H., Bleninger, T. and Doneker, R.L. (2011) CORMIX Simulations of Brine Discharges from Barka Plants, Oman. Desalination and Water Treatment, 32, 329-338.
http://dx.doi.org/10.5004/dwt.2011.2718 [7] Roberts, D.A., Johnston, E.L. and Knott, N.A. (2010) Impacts of Desalination Plant Discharges on the Marine Environment: A Critical Review of Published Studies. Water Research, 44, 5117-5128.
http://dx.doi.org/10.1016/j.watres.2010.04.036 [8] Palomar, P. and Losada, I.J. (2011) Impacts of Brine Discharge on the Marine Environment. Modelling as a Predictive Tool. In: Schorr, M., Ed., Desalination, Trends and Technologies, InTech Open Access Publisher, Rijeka, Croatia, 279-310. [9] Al-Barwani, H.H. and Purnama, A. (2009) Analytical Solutions for Brine Discharge Plumes on a Sloping Beach. Desalination and Water Treatment, 11, 2-6.
http://dx.doi.org/10.5004/dwt.2009.835 [10] Kay, A. (1987) The Effect of Cross-Stream Depth Variations upon Contaminant Dispersion in a Vertically Well-Mixed Current. Estuarine and Coastal Shelf Science, 24, 177-204.
http://dx.doi.org/10.1016/0272-7714(87)90064-3 [11] Purnama, A. (2012) Merging Effluent Discharge Plumes from Multiport Diffusers on a Sloping Beach. Applied Mathematics, 3, 24-29.
http://dx.doi.org/10.4236/am.2012.31004 [12] Smith, R. and Purnama, A. (1999) Two Outfalls in an Estuary: Optimal Wasteload Allocation. Journal of Engineering Mathematics, 35, 273-283.
http://dx.doi.org/10.1023/A:1004332007489 [13] Bikangaga, J.H. and Nassehi, V. (1995) Application of Computer Modeling Techniques to the Determination of Optimum Effluent Discharge Policies in Tidal Water Systems. Water Research, 29, 2367-2375.
http://dx.doi.org/10.1016/0043-1354(95)00045-M [14] Smith, R. (1976) Longitudinal Dispersion of Buoyant Contaminant in a Shallow Channel. Journal of Fluid Mechanics, 78, 677-688.
http://dx.doi.org/10.1017/S0022112076002681 [15] Murphy, G.M. (1960) Ordinary Differential Equations and Their Solutions. D. Van Nostrand, London. [16] Gradshteyn, I.S. and Ryzhik, I. (1980) Tables of Integrals, Series and Products. Academic Press, London.
[1] Institution of Civil Engineers (2001) Long Sea Outfalls. Thomas Telford Ltd., London. [2] Signell, R.P.,Jenter, H.L. and Blumberg A.F. (2000)Predicting the Physical Effects of Relocating Boston’s Sewage Outfall. Estuarine, Coastal and Shelf Sciences, 50, 59-71.
http://dx.doi.org/10.1006/ecss.1999.0532 [3] Macqueen, J.F. and Preston, R.W. (1983) Cooling Water Discharges into a Sea with a Sloping Bed. Water Research, 17, 389-395.
http://dx.doi.org/10.1016/0043-1354(83)90134-3 [4] Lattemann, S. and Hopner, T. (2008) Environmental Impact and Impact Assessment of Seawater Desalination. Desalination, 220, 1-15.
http://dx.doi.org/10.1016/j.desal.2007.03.009 [5] Bleninger, T. and Jirka, G.H. (2008) Modelling and Environmentally Sound Management of Brine Discharges from Desalination Plants. Desalination, 221, 585-597.
http://dx.doi.org/10.1016/j.desal.2007.02.059 [6] Purnama, A., Al-Barwani, H.H., Bleninger, T. and Doneker, R.L. (2011) CORMIX Simulations of Brine Discharges from Barka Plants, Oman. Desalination and Water Treatment, 32, 329-338.
http://dx.doi.org/10.5004/dwt.2011.2718 [7] Roberts, D.A., Johnston, E.L. and Knott, N.A. (2010) Impacts of Desalination Plant Discharges on the Marine Environment: A Critical Review of Published Studies. Water Research, 44, 5117-5128.
http://dx.doi.org/10.1016/j.watres.2010.04.036 [8] Palomar, P. and Losada, I.J. (2011) Impacts of Brine Discharge on the Marine Environment. Modelling as a Predictive Tool. In: Schorr, M., Ed., Desalination, Trends and Technologies, InTech Open Access Publisher, Rijeka, Croatia, 279-310. [9] Al-Barwani, H.H. and Purnama, A. (2009) Analytical Solutions for Brine Discharge Plumes on a Sloping Beach. Desalination and Water Treatment, 11, 2-6.
http://dx.doi.org/10.5004/dwt.2009.835 [10] Kay, A. (1987) The Effect of Cross-Stream Depth Variations upon Contaminant Dispersion in a Vertically Well-Mixed Current. Estuarine and Coastal Shelf Science, 24, 177-204.
http://dx.doi.org/10.1016/0272-7714(87)90064-3 [11] Purnama, A. (2012) Merging Effluent Discharge Plumes from Multiport Diffusers on a Sloping Beach. Applied Mathematics, 3, 24-29.
http://dx.doi.org/10.4236/am.2012.31004 [12] Smith, R. and Purnama, A. (1999) Two Outfalls in an Estuary: Optimal Wasteload Allocation. Journal of Engineering Mathematics, 35, 273-283.
http://dx.doi.org/10.1023/A:1004332007489 [13] Bikangaga, J.H. and Nassehi, V. (1995) Application of Computer Modeling Techniques to the Determination of Optimum Effluent Discharge Policies in Tidal Water Systems. Water Research, 29, 2367-2375.
http://dx.doi.org/10.1016/0043-1354(95)00045-M [14] Smith, R. (1976) Longitudinal Dispersion of Buoyant Contaminant in a Shallow Channel. Journal of Fluid Mechanics, 78, 677-688.
http://dx.doi.org/10.1017/S0022112076002681 [15] Murphy, G.M. (1960) Ordinary Differential Equations and Their Solutions. D. Van Nostrand, London. [16] Gradshteyn, I.S. and Ryzhik, I. (1980) Tables of Integrals, Series and Products. Academic Press, London.