Heat exchanger network synthesis based on minimum rule variations

A minimum rule (MR) is developed for use as a tool in the synthesis of a process-to-process (PTP) heat exchanger network (HEN) to achieve optimal heat exchange. The rule uses the minimum of four simple algebraic expressions determined at each countercurrent heat exchanger (HEX) of the HEN as the optimal HEX heat load. Two expressions are related to the hot–cold temperature differentials at the input and output of each HEX, and the other two are related to the heat load balances along the hot and cold streams associated with each HEX. It should be noted that if any of the two algebraic expressions associated with HEX temperature differentials becomes negative, the rule sets it to zero, however, if the HEX heat load equals one or two of the algebraic expressions associated with HEX temperature differentials indicates a pinch temperature at the HEX input and/or output. An MR-based technique is developed to determine the optimal HEN heat loads in sequence, which optimizes the PTP heat exchange starting from a specific HEX. The underlying principle of the technique is to capture as much HEX heat load as possible during the scan of the HEN. During the search for optimal solutions, setting the heat duty of a HEX to zero eliminates the HEX from the resulting HEN synthesis. Furthermore, the MR is satisfied at all HEN HEXs. It should be emphasized that the calculations in the MR-based technique are algebraic and numerical optimization techniques are not required. PTP heat exchange in general HENs is handled using an optimization scheme based on a modification of the MR-based technique. The two algebraic expressions in the MR, which are related to the temperature differentials around each HEX, are retained. Furthermore, the MR condition, if any of the expressions becomes negative the technique sets it to zero (i.e., no realizable HEX), is also retained. The other two algebraic expressions of the hot and cold stream heat load balances are restructured to inclu