Process optimization for zero-liquid discharge desalination of shale gas flowback water under uncertainty

Sustainable and efficient desalination is required to treat the large amounts of high-salinity flowback water from shale gas extraction. Nevertheless, uncertainty associated with well data (including water flowrates and salinities) strongly hampers the process design task. In this work, we introduce a new optimization model for the synthesis of zero-liquid discharge (ZLD) desalination systems under uncertainty. The desalination system is based on multiple-effect evaporation with mechanical vapor recompression (MEE-MVR). Our main objective is energy efficiency intensification through brine discharge reduction, while accounting for distinct water feeding scenarios. For this purpose, we consider the outflow brine salinity near to salt saturation condition as a design constraint to achieve ZLD operation. In this innovative approach, uncertain parameters are mathematically modelled as a set of correlated scenarios with known probability of occurrence. The scenarios set is described by a multivariate normal distribution generated via a sampling technique with symmetric correlation matrix. The stochastic multiscenario non-linear programming (NLP) model is implemented in GAMS, and optimized by the minimization of the expected total annualized cost. An illustrative case study is carried out to evaluate the capabilities of the proposed new approach. Cumulative probability curves are constructed to assess the financial risk related to uncertain space for different standard deviations of expected mean values. Sensitivity analysis is performed to appraise optimal system performance for distinct brine salinity conditions. This methodology represents a useful tool to support decision-makers towards the selection of more robust and reliable ZLD desalination systems for the treatment of shale gas flowback water.