(497d) Optimal Heat Exchanger Network Design for Rapid Start-up Operation of Fuel Cell Systems

A fuel cell system needs to be designed taking account of frequent start-up, shutdown and load change operations, since it is generally operated on demand manner. Though the conventional design approach such as a pinch technology gives us the optimal structure of a heat exchanger network of a fuel cell system during the steady state operation, the extra devices need to be added in the derived structure later for transitional operations.

The synthesis problem discussed in this paper is to determine a heat exchanger network and their heat transfer areas for a system with operation profiles of process streams. The objective function of this problem is to minimize the start-up time required for dynamically transferring the state of the system's main devices from an initial condition to the specified final condition. Here, main devices are defined as the minimum combination of necessary devices for the system to function in the desired way.

The synthesis problem of a heat exchanger network considering non-steady state operations is generally formulated as a Mixed Integer Dynamic Optimization Problem (MIDOP). However, MIDOP is too difficult to solve directly. Therefore, in this research, a two-step optimization approach is proposed. In the first step, the optimal heat exchanger network is derived by solving the optimization problem based on the dynamic transshipment model explained in the next paragraph. In the second step, the optimal operation profile is derived by solving the dynamic optimization problem, where the structure of the heat exchanger network obtained in the first step is fixed. A dynamic optimization problem with a detailed process model is solved by gPROMS^TM.

The extended transshipment model is a powerful tool for designing the optimal heat exchanger network because the model includes all the possibilities of heat transfer between streams (Papoulias et al., 1983). However, this model does not take into account any transitional behavior of the process, which is very important for the optimal design problem considering non-steady state operations. Therefore, we develop the dynamic transshipment model by modifying the extended transshipment model via following steps. First, the whole period of the non-steady state operation is divided into a set of sub-periods, and in each sub-period, the process is assumed to be in a pseudo steady state. By introducing this assumption, the dynamic model of the process can be transformed to the discrete model. Second, for each main device, the ideal temperature profile is defined as a function of sub-period to calculate the amount of heat accumulated in the main device during each sub-period. By representing the dynamic behavior of the main devices as a discrete model using the modified transshipment model, the optimal design and operation problem can be formulated as a linear problem.

Effective use of the proposed two-step optimization method is demonstrated through a case study of a fuel cell system. The proposed method only requires information related to temperature profiles of process streams and heat capacities and heat transfer areas of main devices to derive the optimal heat exchanger netwrok considering non-steady state operations, and those design specifications can usually be obtained at an early stage of the process design. The obtained design result can be used as the initial design for more precise optimization step. The proposed two-step optimization method that considers the non-steady state operation can also be applied to other chemical processes where the transitional operation is essential.

[References]

Papoulias, S. A., and I. E. Grossmann; ?A Structural Optimization Approach to Process Synthesis-II. Heat Recovery Networks,? Comp. and Chem. Eng., 7, 707 (1983)

Biegler, L. T., I. E. Grossmann, and A. W. Westerberg; ?Systematic Methods of Chemical Process Design,? Prentice Hall PTR (1997)