In the design of chemical process units, the tradeoff between capital cost and operating cost can often be seen. It is important to identify the design variables to capture such a tradeoff and a balance between the capital cost and operating cost can be made [1-2]. A notable example is in the design of a distillation column. For a given design specification (product purity), the tradeoff between the number of stages (capital cost) and the heat input (operating cost) can be seen as one varies the reflux ratio. It shows that an increase in reflux ratio results in a larger operating cost (energy) while having a smaller capital cost (total number of trays). Thus, the reflux ratio is a dominant design variable and optimal design can be obtained by minimizing the total annual cost [1]. The concept can also be extended to proton exchange membrane (PEM) fuel cell systems and this is the objective of this work.

The process performance of a PEM fuel cell system is characterized by the polarization (I-V) curve which can be obtained experimentally. The I-V curve describes the response of the voltage to the change in the current density. The major operating cost comes from the cost of fuel, namely hydrogen. The capital cost of a PEM fuel cell system includes: membrane electrode assembly (MEA) (which is the most expensive component), the bipolar plates, and auxiliaries such as humidifiers, blower, and heater, which is a strong function of the MEA area. The I-V curve reveals that the PEM fuel cell system is hydrogen economical when operates at low current density region, but, in practice, it is generally operated at medium-to-high current density which gives 0.6-0.7V. This comes from the tradeoff between the operating cost and the capital investment. Given the same specification, a much larger MEA area (higher capital cost) is required to achieve the desired power output when operating at the low current density region while possessing better fuel economy (lower operating cost). In this work, analytical expression is derived to describe the tradeoff between the capital cost (MEA area) and operating cost (hydrogen flow rate) for a desired power output. First, a linear approximation of a polarization curve is assumed [3-4], and then fuel cell area hydrogen flow rate can be expressed in terms of the dominant design variable, current density, using simple cost model. Given a desired power output, it can be shown that the tradeoff between the MEA area (capital cost) and hydrogen flow rate (operating cost) under different current densities. Capital costs can be reduced by using a smaller, less expensive MEA, but this increases the hydrogen flow requirement thus pushing up operating costs. Alternatively, a larger, more expensive, MEA requires less hydrogen to produce equivalent power output. With cost model parameters available, one can strike a balance between the capital cost and the operating cost for the design of PEM fuel cell system. Finally, different scenarios are used to illustrate the optimal design of the PEM fuel cell system as economic situation changes.

Reference 1. J. M. Douglas, Conceptual Process Design, McGraw-Hill, New York, 1988. 2. M. S. Peters, K. D. Timmerhaus, R. E. West, Plant Design and Economics for Chemical Engineers, McGraw-Hill, New York, 2003. 3. F. Barbir, PEM Fuel Cells: Theory and Practice, Elsevier Academic Press, New York, 2005. 4. F. Barbir, T. Gomez, Efficiency and economics of proton exchange membrane (PEM) fuel cells, Int. J. Hydrogen Energy, (1996), 21, 891-901.