Analytical Model for Brine Discharges from a Sea Outfall with Multiport Diffusers

Multiport diffusers are the effective engineering devices installed at the modern marine outfalls for the steady discharge of effluent streams from the coastal plants, such as municipal sewage treatment, thermal power generation and seawater desalination. A mathematical model using a two-dimensional advection-diffusion equation based on a flat seabed and incorporating the effect of a coastal tidal current is developed to calculate the compounded concentration following discharges of desalination brine from a sea outfall with multiport diffusers. The analytical solutions are computed graphically to illustrate the merging of multiple brine plumes in shallow coastal waters, and further approximation will be made to the maximum shoreline's concentration to formulate dilution of a multiport diffuser discharge.

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References:
[1] S. Lattemann, and T. Hopner, "Environmental impact and impact
assessment of seawater desalination," Desalination, vol. 220, pp. 1-15,
2008.
[2] C. Sheppard, M. Al-Husiani, F. Al-Jamali, F. Al-Yamani, R. Baldwin, J.
Bishop, F. Benzoni, E. Dutrieux, N.K. Dulvy, S.R.V. Durvasula, D.A.
Jones, R. Loughland, D. Medio, M. Nithyanandan, G.M. Pilling, I.
Polykarpov, A.R.G. Price, S. Purkis, B Riegl, M. Saburova, K.S. Namin,
O. Taylor, S. Wilson, and K. Zainal, "The Gulf: A young sea in decline,
" Marine Pollution Bulletin, vol. 60, pp. 13-34, 2010.
[3] D.A. Roberts, E.L. Johnston, and N.A. Knott, "Impacts of desalination
plant discharges on the marine environment: A critical review of
published studies," Water Research, vol. 44, pp. 5117-5128, 2010.
[4] A. Purnama, H.H. Al-Barwani, T. Bleninger, and R.L. Doneker, "CORMIX
simulations of brine discharges from Barka plants, Oman," Desalination and
Water Treatment, vol. 31, pp. 1-10, 2011.
[5] T. Bleninger, and G.H. Jirka, "Modelling and environmentally sound
management of brine discharges from desalination plants," Desalination,
vol. 221, pp. 585-597, 2008.
[6] M. Barry and T. McAlister, "A comment on the application of numerical
hydrodynamic models to simulate brine discharges," Desalination and Water
Treatment, (to be published) 2010.
[7] G.H. Jirka, "Integral model for turbulent buoyant jets in unbounded stratified
flows. Part 2: Plane jet dynamics resulting from multiport diffuser jets,"
Environmental Fluid Dynamics, vol. 6, pp. 43-100, 2006.
[8] P.J.W. Roberts, and X. Tian, "New experimental techniques for
validation of marine discharge models," Environmental Modelling &
Software, vol. 19, pp. 691-699, 2004.
[9] H.H. Al-Barwani, and A. Purnama, "Analytical solutions for brine
discharge plumes on a sloping beach," Desalination and Water
Treatment, vol. 11, pp. 2-6, 2009.
[10] H.H. Al-Barwani, and A. Purnama, "Simulating brine plumes discharged
into the seawaters," Desalination, vol. 221, pp. 608-613, 2008.
[11] A. Kay, "Advection-diffusion in reversing and oscillating flows: 1. The
effect of a single reversal," IMA Journal of Applied Mathematics, vol.
45, pp. 115-137, 1990.
[12] A. Purnama, and A. Kay, "Effluent discharges into tidal waters: optimal
or economic strategy?," Environmetrics, vol. 10, pp. 601-624, 1999.
[13] W.E. Johns, G.A. Jacobs, J.C. Kindle, S.P. Murray, and M. Carron,
Arabian Marginal Seas and Gulfs, Technical Report 2000-01, RSMAS,
University of Miami, 2000,
(http://www.rsmas.miami.edu/personal/zantopp/AMSG-report.html).
[14] R. Smith, and C.F. Scott, "Mixing in the tidal environment," Journal of
Hydraulic Engineering, ASCE, vol. 123, pp. 332-340, 1997.
[15] I.S. Gradshteyn, and I. Ryzhik, "Tables of Integrals, Series and
Products," Academic Press, London, UK, 1980.