The oil and gas energy sector uses billions of gallons of water for hydraulic fracturing each year to extract oil and gas. The water injected into the ground for fracturing along with naturally occurring formation water from the oil wells surfaces back in the form of produced water. Produced water can contain high concentrations of total dissolved solids and is unfit for reuse outside the oil and gas industry without desalination. In semi-arid shale plays, produced water desalination for beneficial reuse could play a crucial role in alleviating water shortages and addressing extreme drought conditions. In this paper we co-optimize the design and operation of desalination technologies along with operational decisions across produced water networks. A multi-period produced water network model with simplified split-fraction-based desalination nodes is developed. Rigorous steady-state desalination mathematical models based on mechanical vapor recompression are developed and embedded at the desalination sites in the network model. An optimal common design is ensured across all periods using global capacity constraints. The solution approach is demonstrated for multi-period planning problems on networks from the PARETO open-source library. Model formulation and challenges associated with scalability are discussed.