Multistage membrane distillation for the treatment of shale gas flowback water: multiobjective optimization under uncertainty

Abstract

In this work, we analyze the effect of shale gas well data uncertainty on the multiobjective optimization of a multistage direct contact membrane distillation (DCMD) model. The uncertain parameters, flowrate and salt concentration of the flowback water, are modelled by a set of correlated scenarios. A bi-criterion stochastic MINLP was formulated to minimize the expected total annual cost (TAC) and its variability, controlled by the worst case (WC) risk management metric. The model was solved using a modified version of the sample average approximation (SAA) algorithm, which decomposes the original problem into two: a deterministic MINLP model and a stochastic NLP model. The solution is a set of Pareto curves, where the two global extreme solutions provide the DCMD designs that achieve the minimum expected TAC and the minimum WC, respectively. Furthermore, both designs are able to satisfy the zero liquid discharge (ZLD) requirement imposed in the outflow stream.