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.
[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.
[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.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:59144", author = "Anton Purnama", title = "Analytical Model for Brine Discharges from a Sea Outfall with Multiport Diffusers", abstract = "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.", keywords = "Desalination brine discharge, mathematical model,multiport diffuser, two sea outfalls.", volume = "5", number = "8", pages = "1345-5", }