The purpose of this paper is to carry out the optimal design of a non-dispersive solvent extraction (NDSX) process for the removal and recovery of chromium from waste waters of surface treatment industries. The objective is to design a process that can separate the waste stream into an environmentally acceptable stream with a low chromium concentration and a stream in which chromium is concentrated for further processing. A superstructure of the problem which is rich enough to account for all potential configurations and connectivity of the system is proposed. The problem is formulated as a MINLP optimisation problem to minimise the total cost of the process subject to design specifications and is solved using an Outer Approximation algorithm. The nonconvexivity of the problem due to bilinear terms in the model equations makes necessary the reformulation of the nonconvex equations into linear inequalities. Three different approaches are tried for this reformulation. A bound tightening strategy based on the application of branch and bound methods to the Outer Approximation algorithm is shown to be the most effective approach.