Oil and gas industries produce a huge amount of wastewater known as produced water which contains diverse contaminants including salts, dissolved organics, dispersed oils, and solids making separation and purification challenging. The chemical and thermal stability of graphene oxide (GO) membranes make them promising for use in membrane pervaporation, which may provide a more economical route to purifying this water for disposal or re-use compared to other membrane-based separation techniques. In this study, we investigate the performance and stability of GO membranes cast onto polyethersulfone (PES) supports in the separation of simulated produced water containing high salinity brackish water (30 g/L NaCl) contaminated with phenol, cresol, naphthenic acid, and an oil-in-water emulsion. The GO/PES membranes achieve water flux as high as 47.8 L m−2 h−1 for NaCl solutions for membranes operated at 60 °C, while being able to reject 99.9% of the salt and upwards of 56% of the soluble organic components. The flux for membranes tested in pure water, salt, and simulated produced water was found to decrease over 72 h of testing but only to 50–60% of the initial flux in the worst-case scenario. This drop was concurrent with an increase in contact angle and C/O ratio indicating that the GO may become partially reduced during the separation process. Additionally, a closer look at the membrane crosslinker (Zn2+) was investigated and found to hydrolyze over time to Zn(OH)2 with much of it being washed away during the long-term pervaporation.