A novel method combined signal flow graph of a single heat exchanger with the transfer function of streams is developed for the dynamic behaviors of heat exchanger networks problems, which are determinate factors of the process control and operation optimization in the processing industries. The transfer functions between any two nodes of heat exchanger networks including the inlet and the outlet are obtained based on the signal flow graph of the networks by block-diagram reduction, Mason’s rule and the seeking-up method. The developed method is solved by a numerical inverse Laplace transform and the analytical solution to the dynamic behavior of heat exchanger networks is presented in the time domain. The numerical results demonstrate that the presented method is more efficient and more accurate for the dynamic behaviors of heat exchanger networks problems.

Introduction

The dynamic behavior of heat exchanger networks (HEN) has been taken into consideration because its dynamic response of outlet parameters to the disturbances of inlet parameters is important for the process controllability and operation optimization of the HEN problems [1–۳]. Nowadays, substantial numerical and experimental investigations have been carried out for the dynamic behavior of HEN, even including a single heat exchanger due to its wide applications [4–۹]. For a single heat exchanger, many dynamic mathematics models [10–۱۶] have been presented by scholars. The results showed that the transient temperature responses of streams can be obtained using analytic methods [17,18] or numerical methods [19,20]. For the HEN problems, the excessive simplifications of the dynamic mathematics model lead to low quality of dynamic simulations, whereas more consideration of the actual conditions in HEN would make the model complicated and increase computational cost. Therefore, the dynamic mathematics model is far from sufficient to apply to the dynamic characteristics of HEN with consideration into more factors [21]. Above all, achieving an efficient and high-accurate solution for the dynamic behavior of the HEN problems is more important than proposing a dynamic mathematics model which can be solved based on the modeling of single heat exchanger. During the past few decades, many effective numerical methods benefiting from the progress of the dynamic modeling of HEN have been presented to investigate the dynamic behavior of HEN [22– ۲۹]. Mathisen et al. [22] proposed a dynamic model of relatively simple HEN taking the structure, pipe residence time, model order of bypasses and the connecting pipes into consideration. The dynamic model based on the lumped model for a single heat exchanger was solved using the state-space method for the dynamic behavior of HEN and was implemented in Simulink. It’s shown that the presented dynamic model can be not for more complicated HEN owing to modeling complexity, computational speed, and numerical stability. Several dynamic models for HEN have been developed for the dynamic behavior of HEN problems in different practical requirements [23–۲۶]. Boyaci et al. [27] used a distributed-parameter model consisting of multi-tube, singlepass heat exchangers to construct a dynamic model of the HEN and investigated numerically the transient behavior of the HEN. Baldea et al. [28] presented a procedure deriving reduced-order, non-stiff models, which was focused on the dynamics and control of HEN consisting of a reactor connected with an external heat exchanger through a large material recycle stream that acts as an energy carrier. Guha and Ghaudhuri [29] developed a mathematical model to describe the transient heat exchange between the process streams of HEN and solved the developed model by a finite difference numerical scheme and solution algorithm.