Model studies for the mixing and spreading of brine effluents continuously being discharged from a coastal desalination plant through outfall pipes into the sea are presented in two parts: i. in the far field region, where the brine effluent plumes are eventually dispersed in the ambient environment, we used an analytical solution of a two-dimensional advection diffusion equation with multiple point sources on a sloping beach, and ii. in the near field region, where the initial momentum of discharge and brine effluent buoyancy dominated, we used commercial PC-based software packages CORMIX and VISJET to simulate and graphically visualize the three-dimensional effluents plume released from a single port and the merging of multiple plumes released from a multiport diffuser. Since the unwanted brine product is primarily seawater but at a more concentrated level, in Chapter 2, we first ignore the effect of brine effluents density, and solve analytically a two-dimensional advection diffusion equation with multiple point sources on a sloping beach. The solutions are illustrated graphically by plotting contours of concentration to replicate and capture the merging and overlapping process of brine plumes discharged in shallow coastal waters. As the water depth is gradually decreasing towards the beach, it is expected that, on a sloping beach, the build-up of concentration will occur close to the beach. Asymptotic approximation will then be made to the concentration at the beach to measure how well the brine plumes are diluted in the far field. Formula is also given for calculating the maximum concentration value at the beach. To investigate the effect of effluents discharged density, we first run CORMIX model in Chapter 3 to simulate two scenarios: heated brine discharges to represent a positively buoyant plume that will eventually rise to the surface, and dense brine discharges to represent a negatively buoyant plume that will sink to the seabed. Beyond the near field region, CORMIX is also designed to analyze water quality criteria within regulatory mixing zones and is widely used to demonstrate the compliance of a marine outfall system with the regulations for discharging brine effluents in marine environment. Finally, in Chapter 4, we run VISJET model to simulate the details of brine discharged plumes in the near field region. Unlike CORMIX model, VISJET can visually display the evolution of a group of brine discharged plumes from a multiport diffuser at different angles to the ambient current.