Energy integration is a key solution in chemical process and crude refining industries to minimise external fuel consumption and to face the impact of growing energy crises. Typical energy integration projects can reach a reduction of heating fuels and cold utilities by up to 40% compared with original designs or existing installations. Pinch Analysis is a leading tool and regarded as an efficient method to increase energy efficiency and minimise fuel flow consumptions. It is valid for both natures of design, grassroots and retrofit situations. It can practically be applied to synthesise a HEN (heat exchanger network) or modify an existing preheat train for minimum energy consumption. Heat recovery systems or HENs are networks for exchanging heat between hot and cold process sources. All heat transferred from hot process sources into cold process sinks represent the scope for energy integration. On the other hand, energies required beyond this integrated amount are to be satisfied by external utilities. Graphical representations of Pinch Analysis, such as Composite and Grand Composite Curves are very useful for grassroots designs. Nevertheless, in retrofit situation the analysis is not adequate and besides it is graphically tedious to represent existing exchangers on such graphs. This research proposes a new graphical method for the analysis of heat recovery systems, applicable to HEN retrofit. The new graphical method is based on plotting temperatures of process hot streams versus temperatures of process cold streams. A new graph is constructed for representing existing HENs. For a given network, each existing exchanger is represented by a straight line, whose slope is proportional to the ratio of heat capacities and flows. Further, the length of each exchanger line is related to the heat flow transferred across this exchanger. This new graphical representation can easily identify exchangers across the pinch, Network Pinch, pinching matches and improper placement of fuel consumption. Furthermore, such a graph can recognise promising modifications to improve the energy performance and hence less fuel and cooling water requirement. Graphs developed in this work can be used to analyse the energy performance of existing networks with respect to energy targets. They can also be used in junction with the background process to modify basic designs or existing network for better energy integration opportunities and minimum fuel demands. The application of the new graphical method to a case study showed savings of approximately 17% in energy demands and fuel consumption. (C) 2014 Elsevier Ltd. All rights reserved.