Operating line analysis of fuel processors for PEM fuel cell systems

Transcription

1 International Journal of Hydrogen Energy 30 (2005) Operating line analysis of fuel processors for PEM fuel cell systems Alan S. Feitelberg,1, Donald F. Rohr Jr Plug Power Inc., 968 Albany Shaker Road, Latham, NY 12110, USA Received 15 September 2004; accepted 2 February 2005 Available online 29 April 2005 Abstract At least three different definitions of fuel processor efficiency are in widespread use in the fuel cell industry. In some instances the different definitions are qualitatively the same and differ only in their quantitative values. However, in certain limiting cases, the different efficiency definitions exhibit qualitatively different trends as system parameters are varied. In one limiting case that will be presented, the use of the wrong efficiency definition can lead a process engineer to believe that a theoretical maximum in fuel processor efficiency exists at a particular operating condition, when in fact no such efficiency optimum exists. For these reasons, the objectives of this paper are to: (1) quantitatively compare and contrast these different definitions, (2) highlight the advantages and disadvantages of each definition and (3) recommend the correct definition of fuel processor efficiency International Association for Hydrogen Energy. Published by Elsevier Ltd. All rights reserved. Keywords: Fuel processor; Fuel processing; Fuel reforming; Reforming; Reformer; Efficiency; Reformer efficiency; PEM fuel cells; PEM fuel cell systems 1. Introduction Plug Power Inc. is a developer and manufacturer of proton exchange membrane (PEM) fuel cell systems intended for stationary power generation in residential and light commercial applications. Plug Power s current offering in this market is the GenSys TM family of products. These fuel cell systems can provide both heat and electric power, and can be fueled by either natural gas or liquefied petroleumgas (LPG). GenSys TM systems are capable of producing up to 5 kw of electric power and 9 kw of thermal energy, depending upon the specific model and installation configuration. Since January 2001, Plug Power has shipped more than three Corresponding author. Tel.: x1414; fax: address: alan_feitelberg@plugpower.com (A.S. Feitelberg). 1 This paper was presented at 3rd Fuel Cell Topical Conference, 2004, AlChE Spring National Meeting, April 25 29, hundred 5 kwe fuel cell systems to more than 50 customer sites around the world, and these units have generated a combined total of more than 2800 MW h of electric energy. The GenSys TM fuel cell systemconsists of five major modules: (1) a fuel processing module, which converts hydrocarbon fuel into a high H 2 -content, low CO-content reformate stream, (2) a power generation module, which includes the PEM fuel cell stack, (3) a power electronics module, which converts the DC power produced by the stack into AC power, (4) an electrical energy storage module, which ensures continuity of electric power during transients and (5) a thermal management module, which transfers heat to the installation location. The two modules with the largest impact on the overall AC electrical efficiency of the systemare the fuel processing module and the power generation module. A fuel processor intended for use in a PEM fuel cell system must comply with a fairly simple set of overall requirements, as will be discussed below. Our work has shown that the imposition of these requirements creates a special /$ International Association for Hydrogen Energy. Published by Elsevier Ltd. All rights reserved. doi: /j.ijhydene

2 1252 A.S. Feitelberg, D.F. Rohr Jr / International Journal of Hydrogen Energy 30 (2005) Nomenclature ATO H LHV ṅ i P PEM P vp Q T Z η anode tailgas oxidizer molar enthalpy lower heating value molar flow rate of species i total pressure proton exchange membrane vapor pressure steady-state heat input temperature mole fraction of water in reformate fuel processing module efficiency relationship between design variables we refer to as a fuel processor operating line. The operating line dictates the overall steam/fuel ratio and air/fuel ratio required by a fuel processor to comply with the given constraints, and can be derived froman overall mass balance around the fuel processor. The operating line is a simple, graphical representation of this relationship that the process design engineer may find to be quite illuminating, especially when coupled with an energy balance. We will show that the combined mass and energy balances can be used to calculate a maximum possible fuel processor efficiency. This efficiency calculation is somewhat complicated by the widespread use, within the fuel cell industry, of several different definitions of fuel processor efficiency. In some instances the different definitions of fuel processor efficiency are qualitatively the same and differ only in their quantitative values. However, in certain limiting cases, the different efficiency definitions exhibit qualitatively different trends as systemparameters are varied. As a consequence, using the wrong efficiency definition can lead the development engineer to make poor design choices. In the following sections of this paper, the operating line analysis will be presented and the different definitions of fuel processor efficiency will be compared. We will also recommend a specific definition of fuel processor efficiency. An overall block diagramof a typical PEM fuel processing module is shown in Fig. 1. In this figure, the fuel processing module has been divided into two major blocks: a reformer and an anode tailgas oxidizer (ATO). Depending upon the relative amounts of supplied fuel, air, and water, the reforming process shown on the left in Fig. 1 is either a net heat consumer or a net heat generator. When the reforming process is net endothermic, the ATO provides the thermal energy needed to run the reforming process by oxidizing the excess hydrogen returned fromthe PEM stack (the anode tailgas) and transferring that heat to the reformer. If the heat generated by oxidation of the anode tailgas is not sufficient to meet the heat demands of the reforming process, the ATO may need supplemental fuel, as shown in Fig. 1. Most practical reformers are net consumers of heat (especially when the heat needed to evaporate the feed water is considered) for one simple reason: fuel processing module efficiency generally increases with decreasing reformer air/fuel ratio. As the air/fuel ratio to the reformer approaches zero, the reforming process approaches the steam reforming limit, and the reformer has the largest heat requirements. An autothermal reformer can be net endothermic or net exothermic, depending upon the air/fuel and steam/fuel ratios. Fig. 1 shows the oxidant supplied to the ATO is cathode tail gas, or the oxygen-depleted air leaving the cathode side of the PEM stack. Although this is the convention used throughout this paper, fresh air can also be used as the oxidant in the ATO. If fresh air was supplied to the ATO, some of the numerical values calculated here for fuel processor efficiency would be slightly different, but the overall conclusions and trends would not be changed. The reformer shown on the left in Fig. 1 can be characterized by a unique operating line if four reasonable assumptions, or design specifications, are applied: (1) reformate must contain a negligible amount of carbon monoxide; (2) reformate must contain a negligible amount of oxygen; (3) fractional conversion of fuel in the reformer must be specified, (4) reformate dew point must be controlled to a specific value. The presence of CO and oxygen in the reformate are wellknown contributors to premature failure of the PEM stack, and are often constrained to very low concentrations. For example, the maximum allowable CO concentration in the reformate is typically specified to be 50 ppm by volume or less. The first two assumptions are justified for this reason. The third assumption can be motivated by a desire to minimize unburned hydrocarbon emissions, or to achieve a predictable hydrogen output for a given fuel input. Water management is also critical to PEM stack performance, which leads to the fourth assumption. 2. Operating line derivation In the operating line derivation presented here, a method for calculating maximum possible fuel processing module efficiency will be presented. This method will be illustrated for one particular fuel (CH 4 ), but the learned reader can easily generalize the results to a fuel of arbitrary composition C i H j O k. Using the four reformer design specifications given above, an overall mass balance around the reformer shown on the left in Fig. 1 requires CH 4 + x(o N 2 ) + yh 2 O =a CO 2 +b CH 4 +c H 2 +d H 2 O+3.76x N 2, (R1)

3 A.S. Feitelberg, D.F. Rohr Jr / International Journal of Hydrogen Energy 30 (2005) Fuel Air Water Reformer CO Free Reformate (to Fuel Cell) Heat Fuel processor Anode Tail Gas Cathode Tail Gas Additional Fuel (optional) Anode Tail Gas Oxidizer (ATO) Heat Exhaust Fig. 1. Overall block diagramfor a PEM fuel processor. Left: the reformer. Right: oxidation step which provides the heat needed (if any) to operate the reforming process on the left. Additional heat input is optional. Cathode tail gas is assumed here, but may be replaced with fresh air. where x is the O 2 /carbon mole ratio and y the water/carbon mole ratio of the reformer feed. The coefficient b represents the fraction of the fuel that has not reacted, so (1 b) is the fractional fuel conversion. Notice that the coefficients on O 2 and N 2 define the air compositions as 21% O 2 and 79% N 2, and completely dry. From an operational point of view, x and y are independent variables that can be set by the process design engineer. A steam reformer is a limiting case with x = 0. Coefficients a,b,c, and d are unknown dependent variables. The application of a carbon balance 1 = a + b (1) an oxygen balance 2x + y = 2a + d (2) and a hydrogen balance 4 + 2y = 4b + 2c + 2d (3) generates a systemof 3 equations with 4 unknowns. A fourth, independent equation comes from the specification of a reformate dew point temperature. Assuming all the water in the reformate is in the vapor phase, we have d/(a + b + c + d x) = P vp,h2 O/P, (4) where P is the total pressure of the reformate, and P vp,h2 O is the vapor pressure of water at the specified dew point temperature. Eqs. (1) (4) forma set of 4 equations with 4 unknowns (a,b,c, and d) that have a unique solution for given values of x and y. This set of equations can be rearranged to form a single expression involving x and y, yielding an equation which we call the fuel processor operating line: [ ] 3.76Z 2 y = x + 1 Z [ 3Z 2bZ 2b Z ], (5) where Z = P vp,h2 O/P is the mole fraction of water in the reformate. Eq. (5) has intentionally been arranged in the form y = (slope)x + (constant) to emphasize that (5) defines an operating line. The slope of the line is fixed by design specifications on the reformate pressure and dew point temperature. The intercept depends upon these design Steam / CH 4 Ratio Dew Point T=65 C 55 C 55 C P = 1 atm 98% CH 4 destruction 95% 98% 95% Reformer O 2 / CH 4 Ratio Fig. 2. Reformer operating lines for conditions typical of PEM fuel cell systemreformers (see Eq. (5)). specifications, as well as the design specification for the fractional conversion of fuel within the fuel processor. Eq. (5) is plotted in Fig. 2 for four combinations of conditions which are illustrative of an atmospheric pressure (P = 1 atm) reformer incorporated into a fuel cell system. The conditions are 95% or 98% CH 4 destruction in the reformer (b =0.05 or 0.02, respectively), and a reformate dew point of 55 or 65 C. Several observations can be drawn from Fig. 2. First, as the O 2 /CH 4 mole ratio is decreased, the steam/carbon ratio must increase to remain on the operating line. However, as the O 2 /CH 4 ratio is decreased, heat generation in the fuel processor will decrease. And yet to increase the steam/carbon ratio, more heat must be generated to vaporize more water. In other words, moving along the operating line has significant implications for the reformer energy balance. Second, although fractional methane destruction is constant along an operating line, the gas composition is not constant. In particular, the dry H 2 concentration changes significantly along the operating line. Fortunately, once the reformate dew point temperature and any two of (i) fractional CH 4 destruction, (ii) O 2 /CH 4 ratio, and (iii) H 2 O/CH 4 ratio have been specified, the gas composition is known and can be calculated fromthe equations above. For example,

4 1254 A.S. Feitelberg, D.F. Rohr Jr / International Journal of Hydrogen Energy 30 (2005) consider the operating line shown in Fig. 2 with reformate temperature = 65 C and methane destruction = 98% (b = 0.02). The dry H 2 concentration varies from61% at O 2 /CH 4 = 0.3 to 41% at O 2 /CH 4 = 0.7. Third, although the two sets of operating lines in Fig. 2 may appear to be parallel, they are not. The lines appear to be parallel because the two selected reformate dew point temperatures have similar magnitude. The lower set of operating lines actually have a slope of 1.43, while the upper set have a slope of The operating line slope is zero (i.e., horizontal) if the reformate dew point temperature is fixed at about 83.3 C. At this dew point temperature, the H 2 O/CH 4 ratio must be held constant, even as the O 2 /CH 4 ratio is varied, but otherwise this dew point temperature has no special significance. Note that a horizontal operating line does not mean the dry H 2 concentration is constant along the line. The fourth observation is that being on an operating line (i.e., setting a particular O 2 /CH 4 ratio and H 2 O/CH 4 ratio) does not guarantee any of the four design assumptions outlined above (e.g., reformate contains negligible CO) are satisfied. Being on the operating line is a necessary but not sufficient condition for achieving the design specifications. Other necessary conditions are properly designed and operating heat exchangers, functioning chemical reactors (active catalysts, sufficient residence time, etc.) and the proper amount of heat input. If these additional conditions are not satisfied, it is entirely possible that the one or more of the initial design specifications will not be satisfied. Finally, the meaning of off-line operation must be explored. One possible outcome of operating above a line is that the first three design specification above are satisfied, but the reformate contains more steam, or a higher dew point, than required. This suggests that energy has been wasted by vaporizing more water than required. One possible outcome of operating below a line is that the reformate has a lower dew point than specified, which may lead to premature PEM stack failure. This suggests that insufficient energy has been supplied to the reformer to comply with the design specifications. These last observations suggests that there is a maximum fuel processing module efficiency for any given specification of O 2 /CH 4 mole ratio, reformate dew point, and fuel conversion. The maximum efficiency occurs when the fuel processor is run on the corresponding operating line, and the heat produced in the anode tail gas oxidizer (the righthand side of Fig. 1) just matches the heat consumed by the reformer (the left-hand side of Fig. 1). If the heat generated by the ATO is less than the heat consumed by the reformer, one or more of the reformer design specifications will not be satisfied (e.g., the reformate dew point will be lower than specified). If heat generated in the ATO exceeds the heat demand of the reformer, fuel has been wasted and the excess heat must be handled in some way (e.g., rejected to ambient, or by vaporizing more water than desired into the reformate stream). From the preceding discussion, it should be clear that there is no value in discussing fuel processing module efficiency without providing a specification for reformate dew point. In the following development, we will illustrate the concept of maximum fuel processor efficiency with sample calculations at conditions representative of PEM fuel cell systems. We will perform energy balances on the reformer and ATO, and then require the heat output of the ATO to match the heat input requirements of the reformer. 3. Fuel processor efficiency If heat loss to ambient is neglected, an energy balance around the reformer (the left-hand side of Fig. 1) reveals Q reformer = ṅ i H i i reformate [ṅ CH4 H CH4 +ṅ air H air +ṅ water H water ], (6) where Q reformer is the steady-state heat input to the reformer (W), H i the mole specific enthalpy of species i in indicated stream(j/mol), and ṅ i the molar flow rate of species i in indicated stream(mol/s). For the remainder of this paper, we will assume the reformer fuel, air, and liquid water are supplied at a temperature of 25 C. The results of the energy balance around the reformer are shown in Fig. 3 for some typical input conditions. The required reformer heat input is directly proportional to methane flow rate, so the heat requirements in Fig. 3 have been normalized to 1 mol/ min of CH 4 input. The dashed horizontal line in Fig. 3 indicates the thermally neutral condition (heat input requirements are zero), the case in which the reformer is truly an autothermal Fuel Processor Heat Requirement (kw) C Reformate, 100%CH4 Destruction 65 C Reformate, 100%CH4 Destruction 65 C Reformate, 98%CH4 Destruction CH 4 input = 1mol/min O 2 /CH 4 Mole Ratio Fig. 3. Minimum reformer heat input requirements, neglecting any heat losses to ambient. Fuel, air, and water are assumed to be supplied to the fuel processor at 25 C. Heat input is proportional to methane input and has been normalized to 1 mol/min of methane input. Dashed horizontal line indicates the thermally neutral condition (heat required =0).

5 A.S. Feitelberg, D.F. Rohr Jr / International Journal of Hydrogen Energy 30 (2005) Table 1 Input parameters for the calculations shown in Figs. 4 and 5 Parameter Value CH 4 destruction in fuel processor 100% CH 4 temperature at fuel processor inlet 25 C Air temperature at fuel processor inlet 25 C Makeup H 2 O temperature at fuel processor inlet 25 C Anode tail gas temperature at ATO inlet 71 C Anode tail gas relative humidity at ATO inlet 92% Cathode tail gas temperature at ATO inlet 40 C Cathode tail gas dew point at ATO inlet 40 C O 2 concentration in cathode tail gas 13% by volume, dry basis Excess O 2 in ATO feed 10% reformer, and needs to exchange no heat with the surroundings. Fig. 3 shows that a perfectly insulated methane reformer needs no net heat input when the O 2 /CH 4 mole ratio of the feed is about , depending mainly upon the desired reformate dew point temperature, and to a lesser extent on the fractional CH 4 destruction in the fuel processor. At higher O 2 /CH 4 mole ratios, the fuel processor is a net generator of heat (thus the required heat input is negative, representing a heat output), and heat must be removed from the reformer. At lower O 2 /CH 4 ratios the fuel processor requires a net heat input. An energy balance around the ATO reveals Q ATO = ṅ i H i ṅ i H i i exhaust i anode tail gas ṅ i H i, (7) i cathode tail gas At this point the fuel processing module efficiency (η) must be defined. The term efficiency is usually reserved for quantities that describe useful energy (or work) produced divided by energy (or work) consumed. By inspection of Fig. 2, the logical definition of η is then η = (LHV of H 2) (flow rate of H 2 leaving reformer), [(LHV of fuel stream) (fuel streamflow rate)] where LHV is the lower heating value, and the summation is taken over all fuel streams entering the reformer and the ATO, including the anode tail gas. Note that unreacted fuel does not appear in the numerator of this expression. In the limiting case in which all the fuel passes through the fuel processor unreacted, the efficiency should be zero, as provided by this definition of η. Lower heating value has been used in this efficiency definition (rather than higher heating value) because we have assumed the heat of condensation in the exhaust gas is not recovered. We have not used Gibbs energy in the efficiency definition, even though Gibbs energy appears in the Nernst equation [1], because this presupposes that all of the H 2 produced by the reformer will be electrochemically converted into H 2 O in the PEM stack. This is not a good assumption. Under many conditions, the fraction of the H 2 that is consumed in the PEM stack is only 80%, and can be as low as 50%. For hydrogen that is oxidized in the ATO, enthalpy (or heating value) is the correct thermodynamic potential to be used in an efficiency calculation. Although the fuel processor design constraints we have outlined are typical to PEM systems, feeding the product H 2 to a PEM stack is not a requirement of this analysis. We prefer not to assume what the end user will do with the product hydrogen, and thus we try to keep our analysis as general as possible. For simplicity, we have also excluded the power required by blowers, pumps, and other auxiliary equipment from our efficiency definition. A parameter frequently used in the fuel cell industry, and often referred to as fuel processor efficiency, will herein be referred to as η, and is defined by (8) η = (LHV of H 2) (flow rate of H 2 leaving reformer flow rate of H 2 entering ATO) [(LHV of fuel stream) (fuel streamflow rate)]. (9) where Q ATO is the steady-state heat output fromthe ATO (W), and other terms have already been defined. To solve Eq. (7), the composition, flow rate, and temperature of each streammust also be specified. Of particular interest is the temperature and amount of heat removed from the ATO exhaust. In the remainder of this analysis, we will assume the ATO exhaust gas streamis always cooled to its dew point, but no further, so that no condensation occurs in the exhaust gas stream. In other words, the maximum amount of heat will be recovered fromthe ATO exhaust, subject to the constraint that no condensation occurs. Table 1 lists the other conditions we will use in this paper to illustrate the methodology. In this case, the summation is taken over all fuel streams except the anode tail gas. A third parameter that is sometimes called fuel processor efficiency will be given the symbol η, and is defined by η = (LHV of H 2) (flow rate of H 2 leaving reformer). [(LHV of fuel stream) (fuel streamflow rate)] (10) As in Eq. (9), the summation in the denominator is made over all fuel streams except the anode tail gas. The fuel processor efficiency η defined in Eq. (10) can easily exceed 100%. For a steam reformer with complete fuel conversion, η is approximately 120%. This high

6 1256 A.S. Feitelberg, D.F. Rohr Jr / International Journal of Hydrogen Energy 30 (2005) Maximum Fuel Processor Efficiency (%) η η Decreasing O 2 /CH Anode Stoichiometry Fig. 4. Comparison of fuel processing module efficiency definitions η and η at the conditions given in Table 1. Reformate dew point =65 C. efficiency results fromcompletely neglecting the heat input provided by the ATO in Eq. (10). In other words, using this definition suggests that the chemical energy of the hydrogen in the anode tail gas is not useful energy. Since anode tail gas frequently contains enough hydrogen to be produce temperatures as high as C upon oxidation, we find this suggestion unrealistic. We also find definitions of efficiency which allow theoretical values in excess of 100% to be unsatisfactory. For these reasons, this definition of fuel processor efficiency will not be discussed further here. Using the methodology outlined above (constraining the reformer to the operating line, and matching heat generation in the ATO to heat consumption in the reformer), Fig. 4 plots the maximum fuel processing module efficiency as a function of fuel cell anode stoichiometry for a particular set of systemoperating conditions, including reformate dew point T =65 C and b=0 (see Table 1). For these calculations, we have assumed that anode tail gas is the only fuel supplied to the ATO. As anode stoichiometry increases, the reformer O 2 /CH 4 mole ratio decreases from 0.49 to 0.14 to balance ATO heat generation with reformer heat consumption. The parameter η actually decreases with decreasing O 2 /CH 4 ratio, while η shows the expected trend of increasing efficiency as the process moves closer to the steam reforming limit. The opposite trends in η and η with varying O 2 /CH 4 ratio shown in Fig. 4 do not occur in other types of plots in which anode stoichiometry is held constant. When anode stoichiometry is constant, η and η show similar trends with changes in O 2 /CH 4 ratio, and are simply offset. As one might expect from the definitions, η is always less than or equal to η. However, variations in anode stoichiometry with load, or other operating conditions, are common in PEM fuel cell systems and are often of the magnitude shown in Fig. 4. Maximum Fuel Processor Efficiency, η or η (%) η η O 2 /CH 4 Mole Ratio Fig. 5. Additional comparison of fuel processing module efficiency definitions η and η at the conditions given in Table 1. Reformate dew point =65 C. Another example of the differences between η and η is shown in Fig. 5, which plots the maximum fuel processing module efficiency as a function of the overall O 2 /CH 4 mole ratio in the fuel processor for the conditions listed in Table 1. We have again assumed that anode tail gas is the only fuel supplied to the ATO. The efficiency η behaves as expected, and increases with decreasing O 2 /CH 4 mole ratio. There is an abrupt change in the slope of the efficiency curve at an O 2 /CH 4 mole ratio of about 0.605, because this is the point at which anode stoichiometry reaches unity. When anode stoichiometry is unity, the definitions of η and η are identical. Thus, the two curves lie on top of each other at O 2 /CH 4 > At higher O 2 /CH 4 mole ratios, the ATO is producing more heat than needed by the fuel processor, so efficiency decreases rapidly. In these calculations, the excess heat generated by the ATO was transferred to ambient so that the reformer could remain on the operating line. At lower O 2 /CH 4 mole ratios, the heat generated in the ATO just equals the heat consumed in the fuel processor. The efficiency-like parameter η behaves slightly differently compared to η. AtlowO 2 /CH 4 mole ratios, this parameter actually increases as the O 2 /CH 4 mole ratio increases, until the anode stoichiometry reaches unity. This is an unexpected and counterintuitive result. Once anode stoichiometry is unity, η and η coincide, and η begins to decrease with increasing O 2 /CH 4 mole ratio. The relatively shallow slope of η with changes in O 2 /CH 4 ratio (at least when anode stoichiometry > 1, or O 2 /CH 4 < 0.605) shown in Fig. 5 is noteworthy. A typical autothermal reformer operates at an O 2 /CH 4 ratio of about 0.5, while a steamreformer operates with an O 2 /CH 4 = 0. The value of η varies by only about 1% point between these two values of O 2 /CH 4 ratio. In other words, the theoretical maximum efficiency of a steam-reformer-based fuel processor is only about one percentage point higher than the theoretical maximum efficiency of a typical autothermalreformer-based fuel processor. This is a significant finding

7 A.S. Feitelberg, D.F. Rohr Jr / International Journal of Hydrogen Energy 30 (2005) and counter to the prevailing opinions held by many in the fuel cell industry. Since a steamreformer is usually significantly larger and more expensive than a comparable autothermal reformer, the design engineer must consider if this added cost is justified by the modest increase in efficiency. One way to look at the difference between η and η is that η, like η, considers the excess H 2 returned to the ATO as unusable energy. We believe this to be unwise, because most practical reformers are net heat consumers. Reformer heat requirements that are not met by H 2 oxidized in the ATO must simply be made up by supplying additional fuel to the ATO. We see no reason why the heat energy of supplemental fuel should be considered in the efficiency calculation, but heat energy of hydrogen returned fromthe PEM stack should not be included. As mentioned previously, typical anode tail gas can be oxidized to produce a streamwith temperature as high as C, or higher. We certainly consider heat at this temperature to be useful. 4. Conclusions We have demonstrated that the fuel processing module constraints typically applied to a reformer in a PEM fuel cell systemresult in the existence of an operating line. The operating line relates the required air/fuel and steam/fuel ratio to the design specifications on reformate dew point and fuel conversion in the reformer. This linear relationship provides a simple, graphical method for relating these important design variables. In addition, the operating line analysis leads to the conclusion that there is a maximum theoretical efficiency for a fuel processing module designed to meet the needs of a PEM fuel cell system. We have shown that there is no value in discussing fuel processing module efficiency without a specification on reformate dew point. Three different definitions of fuel processor efficiency for PEM fuel cell systems have been compared for conditions typical of PEM fuel cell systems. We find η to be unsatisfactory, because this definition of efficiency admits values in excess of 100%. When comparing η and η, we find the η exhibits unexpected behavior in certain limiting cases. For these reasons, we recommend using η, the fuel processor efficiency defined in Eq. (8). We have further shown that the maximum theoretical efficiency of a steam-reformer-based fuel processing module is only about one percentage point higher than the maximum theoretical efficiency of a typical autothermal-reformer-based fuel processing module. Reference [1] Larminie J, Dicks A. Fuel cell systems explained. New York: Wiley; 2000.