Heat exchanger network synthesis based on minimum rule variations

Abstract

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 include the other HEX heat loads of the hot and cold streams associated with the HEX. These modifications allow for expansion of the optimal solution search domain. Furthermore, the two modified constraints on the heat load balance at each HEX are equivalent to the overall heat load balance of the network hot and cold streams and are replaced with HEN stream heat load balances. This equivalence reduces the number of constraints. The hot–cold temperature differential constraints at the input and output of each HEX and the stream heat load balances of the HEN hot and cold streams are used in an optimization problem with PTP heat exchange as an objective function. In this case the synthesis technique is referred to as the modified MR-based technique. It should be noted that in this technique, if 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. Furthermore, before the start of the computer search, the technique presented uses a characteristic quantity to identify the streams having non-feasible heat exchanges. The synthesis of general PTP HENs based on economic considerations can be handled using the modified MR-based technique again, except that the optimization objective function is expressed in terms of the annual cost of utilities and annualized HEX capital costs. Furthermore, besides being used as constraints, the two algebraic expressions related to HEX input and output temperature differentials in the modified MR-based technique are also used to determine the HEX input and output temperature differentials. These HEX temperature differentials are used to calculate the HEX areas which are used in calculations of the optimization objective function. The modified MR-based technique is extended to handle HENs having stream splitting by introducing extra optimization variables corresponding to split-stream heat capacity flow rates and split-stream HEX heat loads. The proposed optimization techniques are implemented in spreadsheet format utilizing Microsoft Excel™ and solved using the built-in Solver™ module, which provides simple-to-apply and flexible tools for HEN synthesis.