AbstractThis article describes a novel approach to the systematic synthesis of heat exchanger networks. For a given synthesis problem, this approach leads to a complete listing of all solutions which exist, using a prescribed degree of energy recovery, the minimum number of exchangers, heaters and coolers, and no split streams. The approach is combinatorial, with a variety of thermodynamic criteria used to minimize the problem size by preventing infeasible solutions being generated. Two examples (5SPI and 6SPI) are discussed to illustrate complete solution by hand.