A seawater desalination plant's reliability and service availability are essential to sustain and allow the continuing development in the and climate countries. As desalinated seawater is indispensably required at any cost, the conventional disposal method used for a large size desalination plant is to continuously discharge brine waste stream back into the sea via an outfall at some distance from the beach. One major factor in assessing the potential environmental impact of brine discharges from desalination plants is the oscillatory nature of the coastal currents. A model simulation of the long-time brine plumes steadily discharged into the seawaters is presented using a two-dimensional advection-diffusion equation. The model parameters that minimize the impact of brine discharges are discussed.