THE USE OF NONLINEAR PROGRAMMING TO OPTIMAL WATER ALLOCATION

Abstract

Environmental protection, shortage of fresh-water and rising costs for wastewater treatment are all convincing motives for reducing fresh-water consumption and wastewater discharge of the chemical, petrochemical, petroleum refining and other process industries. Maximizing water reuse, regeneration re-use, and regeneration recycling within the chemical plant, as well as optimal distribution of waste streams for end-of-pipe treatment can reduce fresh-water usage and wastewater discharge, while they are also significant in shrinking capital investment in wastewater treatment systems. Optimal assignment and design of water consuming, regenerating, and treatment systems is a complicated task that can be mathematically formulated as mixed integer non-linear programming (MINLP). In the present article the superstructure based ‘Cover and Eliminate’ approach with NLP is applied with the tools of the GAMS/M1NOS/CONOPT package and compared to previous results. After introducing the problem in the context of chemical process synthesis, a mathematical model is described and the use of the methodology is explained. Experience with the use of GAMS is discussed. Several case studies are solved including basic examples from the literature and their variants. The main conclusion is that the application of the mathematical programming for the optimal water allocation problem is essential owing to the broad variety of the specification opportunities. The complex nature of re-use, regeneration re-use, and recycling with multiple pollutants and multiple treatment processes cannot be simultaneously taken into account by conceptual approaches. It is also shown that the assumption on the independency of contamination rates, generally applied in earlier works, are not necessarily valid; and the NLP approach can deal with the more reliable specifications.