DISTURBANCE REJECTION SENSITIVITY ANALYSIS IN AN INTEGRATED METHANOL REFORMING AND PEM FUEL CELL SYSTEM

Transcription

1 DISTURBANCE REJECTION SENSITIVITY ANALYSIS IN AN INTEGRATED METHANOL REFORMING AND PEM FUEL CELL SYSTEM Dimitris Ipsakis 1, Spyros Voutetakis 1, Simira Papadopoulou 1,2, Panos Seferlis 1,3 1 Chemical Process Engineering Research Institute (C.P.E.R.I.), CEntre for Research and Technology Hellas (CE.R.T.H.), P.O. Box 60361, Thermi-Thessaloniki, Greece 2 Department of Automation, Alexander Technological Educational Institute of Thessaloniki, P.O. Box 141, Thessaloniki, Greece 3 Department of Mechanical Engineering, Aristotle University of Thessaloniki, P.O. Box 484, Thessaloniki, Greece ipsakis@cperi.certh.gr, paris@cperi.certh.gr, shmira@teithe.gr, seferlis@auth.gr ABSTRACT A disturbance rejection sensitivity analysis is employed in an integrated methanol reforming and PEM fuel cell system that aims to evaluate alternative flowsheet configurations and control structures based on their performance to compensate for the effects of multiple disturbances affecting the plant. Hence, the selected design ensures a high overall efficiency and optimal characteristics of the complex and highly interactive system under real operating conditions. Disturbance rejection sensitivity analysis utilizes nonlinear models for all involved thermo-chemical and electro-chemical processes in the integrated power generation system for the calculation of the steady-state effort in terms of manipulated variables required for the maintenance of the controlled variables within predefined levels and the satisfaction of the operating specifications in an optimal fashion. Two steady-state controllability indices that describe the ability of the design and the selected control structure to meet the operating targets despite the effects of disturbances are useful metrics in assessing design decisions in a system consisted of diverse units and highly interactive components. Improved designs for power generation through methanol reforming and PEM fuel cell enable the efficient operation under severe catalyst deactivation and kinetic parameter variations. INTRODUCTION Power generation using methanol as a fuel involves the hydrogen production through autothermal steam reforming followed by a purification stage based on catalytic preferential oxidation that eliminates from the hydrogen stream the undesirable carbon monoxide to acceptable levels below 50ppm. The rich hydrogen stream is then directed to the anode of a polymer electrolyte membrane (PEM) fuel cell for the consequent electric power generation (Ouzounidou et al., 2009). The process flowsheet for such a system, especially in cases of autonomous operation, are quite complex in order to carefully balance the thermal requirements of the system and the achievement of high methanol to hydrogen conversion. Heat integration through the utilization of the thermal content of all available process streams in the most efficient way becomes of paramount importance in order to lower the thermal requirements and ensure a highly performing system. However, heat integration increases interaction among the various units in the system thus making it more susceptible to parameter variations such as catalyst deactivation and disturbances. Integrated systems for hydrogen production and subsequent power generation based on methanol at a pilot plant scale for power ranges from 10W p to 75kW p have been studied extensively (Liu et.al, 2008, Son et al., 2008). The design of these process flowsheets and the selection of the employed control structure have been performed based on heuristics without a systematic consideration of the complex interaction pattern associated with the process. Numerous research works provided mathematical models for the static (Stamps and Gatzke, 2006) and dynamic (Sharkh et al.,2004) simulation of methanol reforming and the PEM fuel cell. Control studies using fuzzy controllers for the operation of the extensive heat exchanger network of the system have been presented in (Wu and Pai, 2009). A disturbance sensitivity analysis study was presented in (Biset et al., 2009) for an ethanol processor, where steady-state mathematical models have been utilized in order to analyze the influence of some critical perturbations in the plant that caused controlled variables to move away from their setpoints. A number of alternative process diagrams and control structures have been assessed using simulations so that thermal specifications are met, without however attempting to optimize the system response. Clearly, the link between the design phase where significant decisions about the connectivity of the various process units, and the selection of the operating conditions are determined, and the operating performance of the selected design in a perpetually varying environment is not well established. The main scope of this work is to systematically evaluate the performance of candidate flowsheet configurations and alternative

2 control structures to satisfy the control objectives under the presence of multiple disturbances and model parameter variations in an integrated methanol reforming and PEM fuel cell system. The procedure involves nonlinear process models that enable the calculation of the optimal steady-state behavior of the process system in order to satisfy multiple control objectives translated into targets for the selected controlled and manipulated variables. Disturbance rejection capability is considered as an inherent property of the process design and the control system and independent of the selection of the control algorithm and the controller tuning. A meaningful indicator that encompasses the effort that the control system requires in terms of variations for the manipulated variables to maintain the controlled variables within the allowable range becomes the key factor for the assessment and subsequent rank-ordering of alternative flowsheet configurations for the hydrogen production and the power generation. Disturbances that affect the system involve mainly catalyst deactivation and changes in the kinetic parameter values that have a profound effect on the overall performance of the critically balanced reaction systems therefore enabling a realistic and objective account of the system operability. The flowsheet configurations under examination consider different levels of heat integration so that an autonomous operation is both feasible and efficient. DISTURBANCE REJECTION SENSITIVITY ANALYSIS The disturbance rejection sensitivity analysis follows the general framework described in (Seferlis and Grievink, 2001, 2004) and the main implementation steps are analyzed in the subsequent sections: Flowsheet Development Methanol reformer is considered to operate at autothermal conditions that surmount the conventional methods of steam reforming that requires an external heating source, and partial oxidation that requires a cooling jacket (Ouzounidou et al., 2009). Hence, a suitable ratio of methanol, water and air in the feed stream can maintain the desirable autothermal conditions. The feed streams are preheated utilizing the thermal content of the burner effluent stream before entering the reforming reaction. Through a series of reactions (Table 1) a gas mixture rich in hydrogen (~ 50-60%) is produced which after being cooled at ~100 o C in a heat exchanger enters a second reactor for the catalytic preferential oxidation (PROX) of carbon monoxide. Carbon monoxide blocks the access of hydrogen molecules to the Pt-anode electrode of the PEM fuel cells and therefore needs to be eliminated from the hydrogen stream. Inside this reactor, the reduction of CO levels lower than 50ppm is achieved with the use of air, while the cooling jacket maintains the reaction temperatures at the desired level. The hot PROX reactor output is cooled at ~150 o C for compatibility with the prevailing conditions in the fuel cell and in order to remove the contained water so that flooding conditions inside the sensitive PEM membrane of the fuel cell are prevented. The cathode inlet stream contains air that reacts with the anode-hydrogen stream towards electric power generation. The anode effluent that contains unreacted hydrogen, traces of methanol along with a mixture of gases (CO 2, CO and N 2 ) enters the burner. The burner generates the necessary heat for the preheating of the feed streams to the reformer by additional methanol and spare hydrogen oxidation. A schematic of the integrated flowsheet designated as design I (D-I) is shown in Figure 1. Table 1. Reaction in the reforming and the PROX reactors. Reforming reactor Steam Reforming: CH 3OH + H 2O CO 2 + 3H 2 ΔΗ R,298=49kJ/mol (R1) Partial Oxidation: CH 3OH +0.5O 2 CO 2 + 2H 2 ΔΗ R,298=-193kJ/mol (R2) Water Gas Shift: CO +H 2O CO 2 + H 2 ΔΗ R,298=-41.2kJ/mol (R3) CH3OH Decomposition: CH 3OH CO + 2H 2 ΔΗ R,298=90.1kJ/mol (R4) PROX reactor CO Oxidation: CO +0.5O 2 CO 2 ΔΗ R,298=-283kJ/mol (R5) H2 Oxidation: H 2+0.5O 2 H 2O ΔΗ R,298=-242kJ/mol (R6) D-I uses independent heat exchangers for the cooling of the reformer and PROX reactor streams leading to increased requirements in cooling water and methanol in the burner thus decreasing the overall efficiency of the system (~0.4kg methanol/kwh) (Ouzounidou et al., 2008). In order to improve the efficiency of the system the heat content of the reactor effluent streams is utilized in a series of feed-effluent heat exchangers (FEHE) for the preheating of the methanol-water feed stream. The flow diagram designated as D-II is shown in Figure 2. Such alternative reduces significantly the overall efficiency compared to D-I as much less methanol is required in the burner for heat generation (~0.35kg methanol/kwh) (Ouzounidou et al., 2008). Basically, D-II introduces more interaction among the various process units due to thermal recycling. For instance, disturbances in the operation of the reformer induced by catalyst deactivation would affect the reactor effluent temperature that consequently would alter the operation of the FEHE unit and the reformer

3 feed conditions. A thermal imbalance in the reforming reactive scheme can cause severe deterioration of the hydrogen production rate. In order to provide higher flexibility in the flow diagram, by-pass streams for the FEHE and extra coolers are being introduced as part of the control system structure. In general, D-II requires a greater number of heat exchangers than D-I leading to higher investment costs. CH3OH ΑIR (CATHODE) EFFLUENT BURNER GAS EFFLUENT (ΑNODE) VI FUEL CELL ENERGY LOAD CATHODE OUTLET ANODE STREAM H2O CH3OH CH3OH+H2O (gas) HX a TI_01 REFORMER HX TI_04 1 HX 2 PROX TI_03 COOLING JACKET CI CI TI_05 H2O HX b TI_02 EFFLUENT Fig.1. Alternative Process Flow Diagram-D-I CH3OH ΑIR (CATHODE) EFFLUENT BURNER GAS EFFLUENT (ΑNODE) FUEL CELL ENERGY LOAD VI CATHODE OUTLET ANODE STREAM CH3OH+H2O (gas) HXa REFORMER HX1 PROX HX2 H2O TI_01 TI_03 TI_04 CI TI_05 COOLING JACKET HXb TI_02 EFFLUENT TI_06 TI_07 H2O HXc HXd CH3OH Fig. 2. Alternative Process Flow Diagram-D-II The main difference between the two flowsheets configurations lies on the way the reforming reactor feed is heated. In the case of D-I the overall heating takes place only through the use of the burner effluent, whereas in the case of D-II, process streams are also implemented imposing significant heat recycling in the system. In order to analyze the advantages and disadvantages of the two alternatives, steady-state simulation preliminary analysis is performed for reference cases (e.g., power outputs 2-10kW p ) (Ouzounidou et al.,

4 2008). As reported, D-II utilizes less methanol fuel at the burner as the heat recycling favors the decrease on system utilities. Following the same trend, the coolant flowrates of the heat exchangers are also lower as compared to the base case of D-I. Nevertheless, such an analysis, despite providing insightful perspectives on the operation costs of the system, does not indicate behaviour of the system if a deviation from the normal operating conditions occurs. Such a behavior will be revealed by a disturbance rejection sensitivity analysis utilizing rigorous process models. Development of mathematical models The steady-state and dynamic models that describe in detail the operating features of the individual subsystems are reported in (Ouzounidou et al., 2009, Ipsakis, 2011) and are briefly outlined below: Reactors Partial differential equations in temporal and two spatial dimensions are used to describe the mass and energy balances in the reactors assuming plug flow conditions, whereas a nonlinear model describes the reaction kinetic mechanism. Heat Exchangers Time differential equations are used to describe the heat exchangers assuming a lumped heat transfer model. Burner and Fuel Cell Time differential equations are used to describe the mass and energy balances. Selection of alternative control structures The control structure defines the controlled and the manipulated variables in the control system. The controlled variables should be closely related to the control objectives of the system and further be easily, quickly and accurately measured. The manipulated variables should have a large impact on the associated controlled variables, and exhibit fast dynamics. In general, all independent valves in a process system can act as manipulated variables. In order to achieve the satisfaction of the control objectives as these are represented by the set of controlled variables, each controlled variables should be at least affected by one manipulated variable. In cases, where the number of manipulated variables exceeds the number of controlled variables then there is opportunity for satisfaction of the control objectives in an optimal sense through the optimization of a relevant criterion. However, in cases, where the number of manipulated variables is less than the number of controlled variables, the satisfaction of all control specifications is not possible and eventually some of them should be compromised. The main objective for the integrated methanol reforming and fuel cell system is the satisfaction of the desired power level. This is achieved though current control in the output of the fuel cell, assuming operation at a constant output voltage. The power level can be adjusted through the hydrogen flow in the fuel call and subsequently the methanol feed flow into the system. The desired hydrogen production rate is maintained through the careful control of the conditions in the reforming and the PROX reactors. Since, composition measurements are less accurate, usually with significant time delay, and definitely more costly, fast temperature measurements at the reactor effluent streams are used as controlled variables. Temperature measurements are then used for the monitor of the reactors conditions. Moreover, the temperature level at the inlet reactor streams are important for the thermal balance of the reacting system (i.e. the exothermic oxidation reactions should provide the necessary energy for the ignition and preservation of the endothermic reforming reaction). D-II offers additional manipulated variables through the bypass streams to the FEHE thus allowing extra degrees of freedom in the system for the anticipation of disturbances. Table 2 summarizes the control objectives and the candidate sets of controlled and manipulated variables for the methanol reforming and fuel cell system. Table 2. Control system structure and control targets. Controlled Variable Target value Manipulated Variable Reformer feed temperature 280 o C Burner methanol flowrate Reformer output temperature 280 o C H 2O/CH 3OH Ratio CO concentration at the outlet of PROX reactor 10ppm PROX operation temperature Fuel cell output current 53A Feed methanol flowrate Hot stream output temperature of ΗΧ1/ΗΧ2 200 o C/80 o C Coolant flowrate at ΗΧ 1/ΗΧ 2 Fuel cell operation temperature 47 o C Coolant flowrate at fuel cell jacket Hot stream output temperature of ΗΧc/ΗΧd (D-II only) 220 o C/150 o C Bypass of reactors output

5 Disturbance rejection problem formulation The objective function is introduced in a quadratic form that sums the steady-state deviations of the controlled variables from a set-point value and the manipulated variables from desired steady-state values in a least squares sense for different realizations of the process disturbances. The process modeling equations and operating constraints should be satisfied at all instances to ensure a feasible solution. The proposed procedure is mainly used for an efficient screening of those design configurations that exhibit poor static performance even though a complete study of the dynamic features of the system is necessary for the design of a good control system (Seferlis and Grievink, 2001, 2004). The optimization problem thus takes the form: Min f = ( y y u s. t. h( x, u, y, d, ε) = 0 g( x, u, y, d, ε) 0 l u l u x x x, u u u, sp T ) W ( y y y sp ) + ( u u l y y y u ss T ) W ( u u y ss ) (P1) Symbol f denotes the objective function value, y the vector of controlled variables, W y the penalty matrix for the variations of the controlled variables from setpoints, y sp, u the vector of manipulated variables, W u the penalty matrix for the variations of the manipulated variables from steady-state targets, u ss, h the vector of equality constraints derived from the modeling equations, g the vector of inequality constraints of the system derived from operational limitations, and x the system state variables. Superscripts u and l denote upper and lower bounds for the state, manipulated, and controlled variables. Symbol ε denotes the system disturbances and model parameters whereas d indicates the design parameters (e.g., reactor volumes, area of heat exchangers and so forth) of the integrated system. The static control objectives for the controlled variables (y sp ) should be satisfied are closely as possible despite the effect of disturbances ε, affecting the system. The penalty matrices W y and W u introduce the priorities in the satisfaction of the controlled variables and the preferences in the utilization of the available resources. During the solution of problem P1 the modelling equations and the process constraints are strictly satisfied. The overall objective of the problem formulation for fixed design parameters is to identify inadequate process designs and control structures that require large changes in the manipulated variables for small disturbance magnitudes (Seferlis and Grievink, 2001). Solution of the formulated problem The optimal solution of (P1) is obtained through the solution of the first-order Karush-Kuhn-Tucker optimality conditions for various realizations of the disturbance vector ε. The disturbances are varied along a specific direction in the multi-dimensional disturbance space as dictated by vector θ. An independent continuation parameter, ζ, determines the magnitude of relative disturbance variation, Δε, along the given direction of variability, θ. The resulting set of equations is as follows (Seferlis and Grievink, 2004): f F( x, u, y, d, ε, ζ ) = μ > 0 A + λ T h + μ h μ g i Δε θζ i T A g A = 0 (P2) The first entry in problem (P2) refers to the gradient of the Lagrangian function of problem (P1) with respect to variables x, y, and u. Vectors λ and μ A denote the Lagrange multipliers associated to the equality and active inequality constraints, h and g A, respectively. The second entry refers to the feasibility condition of the optimal solution, whereas the third entry along with the positivity condition for μ A refers to the strict complementarity condition for the active inequality constraints. Vector Δε refers to the relative changes of the disturbance vector ε from the reference values. The optimal solution path for (P2) is obtained using a predictor-corrector continuation method (Rheinboldt, 1986). The selection of the direction is usually based on process knowledge regarding the most likely disturbances that are expected to affect the plant during real

6 time operation. However, disturbance and model parameter correlation structures derived from experimental data may also be utilized. The optimal solution path in (P2) can trace active set changes (i.e. active constraints becoming inactive through the inspection of the sign for the Lagrange multipliers μ Α, and the violation of inequality constraints and variable bounds) as the magnitude of parametric and disturbance variation changes. Saturation of manipulated variables is explicitly handled and the effect of the variable bounds, a key design decision, can therefore be investigated Static controllability indices The evaluation of alternative flowsheet configurations is achieved through the calculation of two indices derived from the solution of (P2). Ω= ζ final ( ζ ) n y 2 ( ζ ) y m u ( ζ ) u 2 dζ i sp, i i ss, i w + 0 i= 1 ysp j = 1 uss, i (1) C Ω = w( ) n ui( ζ ) u ζ (2) i= 1 max, i Index Ω in eq. (1) refers to the static controllability index that takes into account the relative variation of controlled variables from their desired setpoints and the relative changes of the manipulated variables from their steady-state values under multiple disturbance variations. The weighting coefficient w(ζ) is used to adaptively stress the performance at various disturbance magnitude ranges. The second index, C Ω, in eq. (2) calculates the distance of the manipulated variables from their associated saturation limit. It can be considered as an indicator of proximity to the maximum allowable bound the system operates. The two indices are then utilized for the evaluation and rank-ordering of candidate flowsheet configurations and control structures. The method does not derive the optimal design but rather eliminates from further consideration those designs that exhibit poor steady-state disturbance rejection characteristics (i.e. high values for Ω and C Ω ) for a set of representative disturbance scenarios. In general, large changes in the manipulated variables would imply large errors in the controlled variables during dynamic transitions. Good steady-state characteristics for a given process design are a prerequisite for good dynamic performance by the control system. SIMULATED CASE SCENARIOS The behavior of the two alternative flowsheets D-I and D-II for the integrated methanol reforming and PEM fuel cell system is investigated under three different disturbance scenarios that are representative for the system under investigation. The three scenarios are summarized as follows: Disturbance Scenario 1 A maximum of 15% increase in the reaction rate of the endothermic reaction of steam reforming combined with a respective decrease in the reaction rate for the exothermic partial oxidation in the reformer. Disturbance Scenario 2 A maximum of 15% increase in the reaction rate of the exothermic reaction of partial oxidation combined with a respective decrease in the reaction rate for the endothermic steam reforming in the reformer. Disturbance Scenario 3 A maximum of 15% decrease in the reaction rate of the CO oxidation in the PROX reactor. Tables 3 and 4 report the values of the two indices for the three case scenarios at different disturbance magnitude levels. D-II shows an overall superior performance as reflected in the lower value for both Ω and C Ω indices, which implies better capability to reject disturbances from the control objectives. In general, the effort in the manipulated variables for the disturbance compensation is smaller in D-II than in D-I as indicated by index C Ω for all scenarios. Index Ω reflects also the impact of the disturbances on the controlled variable variations. The increased value of the static controllability index Ω in scenario 2 for D-II is mainly attributed to the variations of methanol fuel in the burner due to the higher thermal needs for the feed heating. The presence of FEHE in D-II makes the flowsheet more susceptible to catalyst deactivation as the reactor

7 effluent thermal content is utilized in the preheating of the feed stream. However, it should be noted that the indices record only relative changes from the base operating point and D-II requires less methanol amount per kwh than D-I hence achieving higher efficiency. Table 4 shows the variation of the C Ω index with respect to disturbance magnitude. As can be observed, D-II candidate flowsheet exhibits improved performance compared to D-I for all three scenarios. Similarly, Table 4 shows the variation of the static controllability index, Ω, with respect to disturbance magnitude changes. As can be observed, D-II design shows superior performance than D-I for scenarios 1 and 3. For the second scenario, results give a small advantage to D-I that is mainly attributed to the lower in absolute values operating methanol burner feed flowrate. Table 3. CΩ index for the two candidate flowsheets as a function of disturbance magnitude Disturbance Magnitude Candidate Flowsheet Scenario 1 Scenario 2 Scenario 3 5% D-I (C Ω) D-II (C Ω) % D-I (C Ω) D-II (C Ω) % D-I (C Ω) D-II (C Ω) Table 4 Static controllability criterion for the two alternative diagrams for all disturbance case scenarios Disturbance Magnitude Candidate Flowsheet Scenario 1 Scenario 2 Scenario 3 5% D-I (Ω) 4.3e e D-II (Ω) 4.18e e -4 10% D-I (Ω) D-II (Ω) % D-I (Ω) D-II (Ω) Figure 3 shows the relative change of the methanol feed flowrate, the total coolant flowrate and the methanol burner feed flowrate for scenario 1. D-II handles better the disturbance in the reaction rates with a relatively low increase in the cooling requirements due to the higher flexibility in the heat exchanger network. Methanol flowrate in the burner for D-II decreases at a much greater rate than D-I thus increasing the overall efficiency of the system. The sharp changes in the slope of the diagram at disturbance magnitudes of 3% and 12% are attributed to the fact that reformer feed and effluent temperatures have reached their maximum allowable levels, respectively. Both temperatures are controlled variables in the selected control structure as indicated in Table 2 that were allowed only small deviations around their setpoints. In general, both candidate flowsheets exhibited adequate performance under the influence of significant reaction rate variation. Even though no controller has been imposed the steady-state behavior of the system has optimally adjusted to satisfy multiple, diverse, and competing objectives. Methanol Feed, % D-I D-II Disturbance Magnitude, % a) Coolant Flowrate, % D-I D-II Disturbance Magnitude, % b) Methanol Burner Feed, % D-I D-II Disturbance Magnitude, % Fig. 3. Relative changes (a) methanol feed flow, (b) total coolant flow and (c) methanol burner feed under the disturbance effect for disturbance scenario 1. c)

8 CONCLUSIONS In this study, a procedure for the systematic evaluation of alternative flowsheet configurations and control structures based on nonlinear disturbance rejection sensitivity analysis for a methanol reforming and PEM fuel cell unit was successfully implemented. Two candidate flowsheet configurations of different degree of heat integration were analyzed in terms of efficient operation under the presence of multiple simultaneous disturbances. The employed objective function reflected the control objectives and further enabled the hierarchical ordering of the control targets and the prioritization in the use of available resources. Therefore, designs that enabled the preservation of high overall efficiency were obtained. If designed carefully a heat integrated flowsheet that inherently exhibits high interaction among the process units can achieve superior steady-state performance in disturbance rejection and simultaneously a higher efficiency compared to a conventional flowsheet with no or a small degree of heat integration. The key design features that enable such performance involve the existence of additional degrees of freedom in the flowsheet through suitable recycling and by-pass streams and the introduction of process units (e.g., burner and coolers) that provide the strength to the process to anticipate the effects of disturbances. REFERENCES Biset, S., L.N. Deglioumini, M. Basualdo, V.M. Garcia, and M. Serra Analysis of the control structures for an integrated ethanol processor for proton exchange membrane fuel cell systems, Journal of Power Sources, 192 (1): El-Sharkh, M.Y., A. Rahman, M.S. Alam, P.C. Byrne, A.A. Sakla, and T. Thomas A dynamic model for a stand-alone PEM fuel cell power plant for residential applications, Journal of Power Sources, 138 (1-2): Ιpsakis, D Optimal operation of energy systems using renewable and alternative energy sources, PhD Dissertation, Department of Chemical Engineering, Aristotle University of Thessaloniki Liu, N., Z. Yuan, C. Wang, L. Pan, S. Wang, S. Li, D. Li, and S. Wang Bench-scale methanol autothermal reformer for distributed hydrogen production, Chemical Engineering Journal, 139 (1): Ouzounidou, M., D. Ipsakis, S. Voutetakis, S. Papadopoulou, and P. Seferlis Experimental studies and optimal design for a small-scale autonomous power system based on methanol reforming and a PEM fuel cell, AIChE Annual Meeting, Philadelphia, PA, U.S.A., November Ouzounidou, M., D. Ipsakis, S. Voutetakis, S. Papadopoulou, and P. Seferlis. P A combined methanol autothermal steam reforming and PEM fuel cell pilot plant unit: Experimental and simulation studies, Energy, 34 (10): Rheinboldt, W.C Numerical analysis of parameterized nonlinear equations, Wiley, New York. Seferlis, P. and J. Grievink Process design and control structure screening based on economic and static controllability criteria, Computers & Chemical Engineering, 25 (1): Seferlis, P. and J. Grievink Process design and control structure evaluation and screening using nonlinear sensitivity analysis (Chapter B6), in The Integration of Process Design and Control, edited by P.Seferlis and M.C. Georgiadis, Netherlands, Elsevier B.V. Son, I.H., W.C. Shin, Y.K. Lee, S.C. Lee, J.G. Ahn, S.I. Han, H.G. Kweon, J.Y. Kim, M.C. Kim, and J.Y. Park. 2008, 35-We polymer electrolyte membrane fuel cell system for notebook computer using a compact fuel processor, Journal of Power Sources, 185 (1): Stamps, A.T., Gatzke, E.P Dynamic modeling of a methanol reformer PEMFC stack system for analysis and design, Journal of Power Sources, 161 (1): Wu, W., Pai, C.C Control of a heat-integrated proton exchange membrane fuel cell system with methanol reforming, Journal of Power Sources, 194 (2):