A mixed integer nonlinear formulation for improving membrane filtration water treatment plant design
Klampfl, Erica Zimmer
Dennis, John E., Jr.
Doctor of Philosophy
This thesis provides several contributions to the problem of building large-scale membrane filtration water treatment plants needed to meet increasingly stringent drinking water standards. The first contribution is an extension of a small-scale model of membrane filtration water treatment plants to a model that determines building specifications for the needed large-scale plants at a minimum cost. The large-scale model allows choosing a mix of feed and backflush pumps and partitioning the membrane area into more than one array in order to capture design decisions that can greatly reduce the cost. However, these additions to the model change the mathematical formulation from a small nonconvex nonlinear programming problem (NLP) to a large nonconvex mixed integer nonlinear programming problem (MINLP), which is much more difficult to solve. To address the difficulties associated with solving general nonconvex MINLPs, the second contribution is the development of an algorithm that exploits the structure of the nonconvex MINLP problem and the code written to implement the algorithm. The special structure of our nonconvex MINLP allows the development of a specific algorithm that exploits the structure and allows many benefits over existing methods. The algorithm guarantees termination to local optimizer for the MINLP, requires the solution of a small NLP and a relatively small IP compared to most algorithms that require the solution of a large NLP and a large MILP, requires the solution of an IP instead of an MILP, and requires very few iterations for termination. The MINLP is reformulated so that the algorithm needs only to iteratively solve alternations of an NLP and an integer programming problem (IP). Finally, we establish design guidelines for building large-scale membrane filtration water treatment plants. These guidelines include suggestions on how to choose an appropriate mix of feed and backflush pumps, how to partition the membrane area for different size plants, and how to estimate costs. Specifically, we show that larger plants can be operated more cost efficiently than smaller plants at higher recoveries and that a more flexible consideration of facility configuration and pump selection may reduce costs for larger plants by approximately 20% per year.
Mathematics; Environmental science