The need for high efficiency energy systems is of vital importance, due to depleting reserves of fossil fuels and increasing environmental problems. Industrial operations commonly feature the problem of rejecting large quantities of low-grade waste heat to the environment. The aim of this work is to develop methods for the conceptual screening and incorporation of low-temperature heat upgrading technologies in process sites. The screening process involves determination of the best technology to upgrade waste heat in process sites, and the combination of waste heat source and sink temperatures for a technology. Novel simplified models of mechanical heat pumps, absorption heat pumps and absorption heat transformers are proposed to support this analysis. These models predict the ratio of the real performance to the ideal performance in a more accurate way, than previous simplified models, taking into account the effect of changing operating temperatures, working fluids non-ideal behaviour and the system component inefficiencies. A novel, systems-oriented criterion is also proposed for conceptual screening and selection of heat pumps in process sites. The criterion (i.e. the primary fuel recovery ratio) measures the savings in primary fuel from heat upgraded, taking into account power required to drive mechanical heat pumps and missed opportunities for steam generation when absorption systems are used. A graphical based methodology is also developed for applying the PRR in process sites and applied to a medium scale petroleum refinery. Results show that applying the PRR yields 9.2% additional savings in primary fuel compared to using the coefficient of performance to screen and incorporate heat pumps. (C) 2016 Elsevier Ltd. All rights reserved.