The exergy topological method is used to present a quantitative estimation of the exergy destroyed in an organic Rankine cycles (ORC) operating on R113. A detailed roadmap of exergy flow is presented using an exergy wheel, and this visual representation clearly depicts the exergy accounting associated with each thermodynamic process responsible for this is the heat transfer across a finite temperature difference. In addition, the results confirm the thermodynamic superiority of the regenerative ORC over the basis ORC since regenerative heating helps offset a significant amount of exergy destroyed in the evaporator, thereby resulting in a thermodynamically more efficient process. Parameters such as thermodynamic influence coefficient and degree of thermodynamic perfection are identified as useful design metrics to assist exergy-based design of devices. This paper also examines the impact of operating parameters such as evaporator destruction decreases with increasing evaporator pressure and decreasing turbine inlet temperatures. Finally, the analysis reveals the potential of the exergy topological methodology as a robust technique to identify the magnitude of irreversibilities associated with real thermodynamic processes in practical thermal systems. Copyright (C) 2008 John Wiley & Sons, Ltd.