Discharging brine effluents through long sea outfalls are an economic disposal strategy for coastal seawater desalination plants. The interactions of two or more brine discharge plumes are expected as many desalination outfalls often tend to be closely clustered together along open coastlines. A far field mathematical model using a two-dimensional advection diffusion equation in a highly simplified flat seabed is presented to study the dispersion and merging of brine discharge plumes in shallow coastal waters. The analytical solutions are illustrated graphically by plotting contours of concentration to replicate the overlapping plumes following discharges from multiple desalination outfalls. To assess the potential environmental impacts, the radius and the concentration at the end of the allocated mixing zone around the outfall are formulated. The compounded concentration at the edge of the regulatory mixing zone is then used as a measure for assessing the effectiveness of multiport diffusers over the single (port) outfall discharge. It is found that the modern engineering practice which installs a multiport diffuser at the end of the outfall pipe does minimize the impacts.