According to thermodynamic principle

synthesis of the heat exchanger network (HEN) with multi-pass was performed based on pinch technology

and a two-stage method was presented by using the mathematical programming methodology and pinch technology simultaneously. Firstly

the minimum temperature difference for the multi-pass HEN was optimized based on thermodynamic analysis

and then utility costs were calculated. At the second stage

according to the obtained optimal minimum temperature difference the pinch location was defined

and the corresponding HEN could be divided into two sub-networks: above the pinch point and under the pinch point. Then streams matches were optimized by using the superstructure model for the multi-pass HEN. Consequently

to minimize total cost

the multi-pass HEN was synthesized by balancing capital cost and operation cost. Case studies demonstrated the effectiveness and application prospect of the presented method.