A new method for analyzing an industrial energy system has been introduced in this paper. This method is based on the development and modifications of the R-curve concept. It consists of three graphical tools, namely, "R-curve": "R-ratio vs. Total Annual Cost (TAC) curve" and "R-ratio vs. Emissions (EM) curve". This new method can be applied to different scenarios which may include: retrofitting the utility system of a total site; and choosing the cleanest and most efficient and economical fuel for the boiler(s) of the utility system. Originally, "R-curve" indicates how the existing operation of utility system of the total site may be improved without any capital investments. "R-ratio vs. TAC curve" has been introduced to determine total annual cost of the utility system of a total site in each R-ratio value. "R-ratio vs. EM curve", demonstrates the emission values of each pollutant in each R-ratio value. Therefore; these curves give a good sense for improving the operation, cost and emission values of any operating or under design total site. These curves are easy to be constructed and simple to be understood, they are also too powerful in providing insights for improving existing energy systems. (C) 2012 Elsevier Ltd. All rights reserved.