The process synthesis problem referred to as work and heat exchange networks (WHENs) is an extension of the classical heat exchanger networks problem considering only temperature and heat. In WHENs, additional properties are pressure and work, and strong interactions exist between temperature, pressure, work, and heat. The actual sequence of heating, cooling, compression, and expansion for pressure changing streams (PCs) will affect the shape of the composite and grand composite curves, the Pinch point, and the thermal utility demands. Even stream identities (hot or cold) will sometimes change. The identification of the optimal thermodynamic path from supply to target state for PCs becomes a primary and fundamental task in WHENs. An MINLP model has been developed based on an extension of the Duran-Grossmann model (that can handle variable temperatures) to also consider changing stream identities. Three reformulations of the extended Duran-Grossmann model have been developed and tested for two examples. (c) 2018 American Institute of Chemical Engineers AIChE J, 65: 549-561, 2019