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Development and modeling for process control purposes in PEMs
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( 2 0 1 4 ) 1 e9
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Development and modeling for process control purposes in PEMs* Yasemin Saygılı*, Serkan Kıncal, Inci Eroglu Department of Chemical Engineering, Middle East Technical University, Ankara 06800, Turkey
article info
abstract
Article history:
To maintain suitable operating conditions, polymer electrolyte membrane (PEM) fuel cell
Received 17 July 2014
stacks require additional equipment and control systems. Fuel supply, power and thermal
Received in revised form
management, purge strategy and individual cell voltage control must be in place and
19 October 2014
operate reliably for a fuel cell system to achieve similar levels of performance as con-
Accepted 27 October 2014
ventional energy generators. System design, auxiliary equipment selection and selection of
Available online xxx
control strategies have effects on fuel cell efficiency, durability and reliability. In this study we report on our efforts to develop the piping and instrumentation diagram of a 3 kW PEM
Keywords:
fuel cell, including the control instrumentation. A semi-empirical model was put together
PEMFC
to understand dynamic system behavior for purpose of evaluating possible operating
Fuel cell piping and instrumentation
scenarios, in an effort to have useful insight into the system during the equipment se-
diagram
lection stage. The model complexity was reduced by ignoring the spatial variations and
Integrated fuel cell modeling
assuming isothermal stack operation. The stack, cooling system, humidifier, compressor,
Fuel cell control
inlet and outlet manifold were modeled and integrated to formulate a comprehensive prototype model. This model was subsequently used to generate predictions for the responses of the compressor, humidifier, humidification of the stack, power and heat generation for a multitude of dynamic changes in load. With the predictive capability enabled by the model, equipment and algorithm selections can be made in a more directed fashion, reducing the initial design and development costs by delivering a hardware configuration that is close to an ideal one with minimal iterations. Copyright © 2014, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.
Introduction PEM fuel cells are the electrochemical reactors that directly convert chemical energy of hydrogen into DC (direct current) electricity. A single PEM fuel cell consists of a proton conducting membrane that is sandwiched between a pair of
catalyst and gas diffusion layers encapsulated by bipolar plates. In order to deliver useful power levels, single cells are connected in series to build a stack. This stack of multiple individual cells must be complemented by auxiliary equipment and control systems in order to fulfill the requirements for efficient and reliable power generation. The auxiliary equipment and process control algorithms can be divided into
*
Presented in International Conference on Clean Energy (ICCE) 2014, 8e12 June, istanbul. * Corresponding author. Tel.: þ 90 542 5705381; fax: þ 90 312 210 2600. E-mail addresses: [email protected] (Y. Saygılı), [email protected] (S. Kıncal), [email protected] (I. Eroglu). http://dx.doi.org/10.1016/j.ijhydene.2014.10.116 0360-3199/Copyright © 2014, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.
Please cite this article in press as: Saygılı Y, et al., Development and modeling for process control purposes in PEMs, International Journal of Hydrogen Energy (2014), http://dx.doi.org/10.1016/j.ijhydene.2014.10.116
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Nomenclature area, m2, cm2 constant pressure heat capacity, J kg1 K1 constant volume heat capacity, J kg1 K1 membrane water concentration, mol cm3 Diameter, m diffusion coefficient of water, cm2 s1 friction factor enthalpy, J kg1 stack current density, A cm2 inertia, kg m2 mass, kg mass flow rate, kg s1 M molecular weight, kg mol1 L Length, m electroosmotic drag coefficient, e nd number of cells, e ncell Nv,membrane water flux, mol cm2 s1 P pressure, bar P power, W Q heat transfer, W t membrane thickness, cm T temperature, K, C u overall heat transfer coefficient, W m2 K1 U internal energy, J V Mean velocity V voltage, V volume, m3 Vi W mass Flow rate, kg s1 wcp compressor speed, rad sec1 Tlm log-mean temperature, e A Cp Cv Cv,i D Dw f c Hi i J m m_
Greek letters h efficiency, e r density, kg m3 t torque,N m Subscripts cm compressor motor cp Compressor i,anode anode compartment i,cathode cathode compartment v Vapor ∞ ambient air
subsystems of fuel supply, water management, thermal management, power management, purge strategy and cell voltage tracking. To assure uninterrupted power, the reactants should be delivered to the stack in sufficient amounts and proper molar ratios under all load conditions. Undersupply, low partial pressures and mis-matched molar ratios must be avoided by properly adjusting the hydrogen and oxygen supplies while minimizing parasitic losses to deliver these requirements. Hydrogen is generally delivered from a pressurized tank by adjusting the hydrogen flow with proportional regulation valves according to the pressure difference between cathode and anode. Fuel delivery systems can be
designed to recirculate the excess hydrogen to avoid extra fuel usage [1]. Air is the preferred supply of oxygen in most configurations and is usually provided by compressors, blowers or similar equipment from the ambient, which can consume significant amounts of parasitic power and tend to react slower than the regulation valves used on the hydrogen side. The air line should contain filters and leakproof lubrication systems to eliminate contamination risks [2]. Different control strategies for fuel cell air supply are reported in the literature [3,4]. Water management subsystem provides the required level of humidity for proton conduction in the porous media of the system. Too little water reduces conduction while too much water causes flooding. External humidifiers such as nozzle spray, static injector, gas bubbling, enthalpy wheel and membrane humidifiers are used to regulate the water content in the stack [4e7]. Membrane type humidifiers with different geometries exchange heat and water in the presence of temperature and vapor concentration gradients. Stack exhaust gas is often used for humidification in membrane type humidifiers [8,9]. Purging can be utilized as both a water management and an impurity elimination approach. Particularly for dead-end operation of the anode, a purge valve is opened at required intervals to remove the water and impurities that have accumulated at the anode. Unless effective purging is applied, both in frequency and duration, uneven distribution of hydrogen and fuel starvation is observed [10]. The frequency and duration of purges should be determined for an efficient purge while ensuring minimum fuel consumption [11]. Fuel cell system thermal management has a significant role on safe and efficient operation of fuel cells. Stack overheating can cause dehydration in the polymer membrane, resulting in performance losses. High temperatures can also cause membrane leaks formed by hot spots which can result in an unsafe position due to the mixing of hydrogen and oxygen [12]. Some of these modes of damage may be permanent, some are recoverable. Air cooled [3] and water cooled [13,14] systems with different designs can be used for thermal management of fuel cells e the selection usually depending on the capacity of the stack impacting the amount of heat to be removed. The individual cell voltages in the stack should ideally be monitored for safety, control and long-term analysis. Cell voltage losses can be caused by internal problems appearing in the membrane electrode assembly, such as water droplets that prevents gas flow or pinholes and hotspots. Cell voltages quickly respond to the conditions such as impurity accumulations, water droplets in the gas pathways, unequal gas distribution, membrane drying or flooding and electrical connectivity problems, allowing them to be used for control, monitoring and troubleshooting purposes [15]. Cell voltage monitoring also allows for the tracking of fuel cell degradation over extended periods of operation [16]. While the current delivered from the system is increased, the reactant consumption and water production rates also increase. This manifests itself as a decrease in cell voltages, observed in typical polarization curves. In operation, the current density should be limited by keeping the individual cell voltages above 0.4 V to prevent reactant starvation and water flooding [17].
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The purpose of this work is the investigation of the performance and competence of the auxiliary equipment for a 3 kW fuel cell prototype following a model based strategy. A piping and instrumentation diagram for this prototype was generated; a dynamic model for the system developed and this model used to evaluate the performance of candidate equipment and control strategies. Many fuel cell models of various levels of complexity are reported in the literature. For this study, we develop an integrated fuel cell system model including humidifier, compressor, manifolds and cooling system to observe subsystem interactions and dynamics. The model is as complex as necessary and as simple as possible e in an effort to optimize the resources invested in the model development and the accuracy of the feedback it provides the prototype development efforts. The developed system model allows for the design, analysis and evaluation of any desired component of the system such as humidifier and cooling system.
Piping and instrumentation diagram For the PEM fuel cell under study, a pressurized hydrogen tank was selected as the hydrogen source. The auxiliary equipment for the system and the associated control instrumentation is given in Fig. 1. The hydrogen line involves a solenoid valve, relief valve, pressure indicator and a pressure regulator. Solenoid valve is opened at start-ups, the pressure indicator indicating whether there is proper hydrogen pressure in the line and tank or not by initiating an alarm at pressures lower than a set-point. High pressures in the line are avoided by the relief valve. The pressure regulator lets the hydrogen flow to the anode compartment when the hydrogen inside anode is
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depleted, indicated by a drop of the cathode pressure. The solenoid valve is closed at shut-down and emergency conditions. A scroll compressor accompanied by a filter is used to regulate the air flow. The compressor command voltage is determined according to the stack current, defining the motor speed and the compressed air flow rate through the stack. Air requirement is calculated by Faraday's Law, coupled by a PI (proportional integral) controller following the feedback of the difference of required and supplied air amount. Finally the compressor voltage command corresponding to this air flow rate is determined. The compressor outlet pressure was set at 1.2 atm. The stack is cooled down by a cooling system involving a pump, radiator and a fan. Stack temperature is inferred by tracking the temperature of the cooling water outlet. This temperature feedback can be used for different control strategies by changing the pump and fan voltages. Power management subsystem involves a battery, DC/DC converter and DC/AC converter to control the power drawn from the fuel cell system. While the load connected to the system increases, the parasitic power losses also increase and the net power delivered from the stack can be complemented by the battery if necessary. In case of low voltages the battery would be used exclusively, such as start-ups and shut-downs. Battery would be recharged when excessive power is available. To remove the water and impurities accumulated at anode compartment, the anode is to be purged. Purge valve can be operated at a fixed frequency and duration setting or be dynamically controlled based on the voltage across the cells nearest to the anode exit. At voltage levels below a certain threshold, the purge valve is to be opened to eliminate
Fig. 1 e Prototype piping and instrumentation diagram with control instrumentation. Please cite this article in press as: Saygılı Y, et al., Development and modeling for process control purposes in PEMs, International Journal of Hydrogen Energy (2014), http://dx.doi.org/10.1016/j.ijhydene.2014.10.116
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impurities to recover the voltage. To prevent flooding, the individual cell voltages should be kept below 0.4 V.
System model Within the scope of this study, a semi-empirical model was developed for the specific PEM fuel cell prototype. Spatial variations were ignored in an effort to reduce the complexity and allow for quick feedback for the prototype development activities. With perfect cooling assumption and considering the slow response time of the stack temperature an isothermal model was utilized for the stack. Stack voltage test data and cooling system test data were integrated to the model to determine the unknown coefficients appearing in the model equations, resulting in a semi-empirical model. Individual models for the stack, cooling system, humidifier, compressor, inlet and outlet manifold were integrated for the prototype model. Although the resulting model is specific to the fuel cell system under study, the approach is generic and can be quickly adapted to the response of similar systems through generation of limited experimental datasets.
Stack model Stack model consists of stack voltage model, anode and cathode flow models and membrane hydration model. The general assumptions involved in the stack modeling are: Isothermal operation e temperature dynamics have larger time constants among the other processes involved in fuel cell stack. Therefore stack temperature can be considered as a constant instantly. By assuming a perfect cooling system that directly remove generated heat from the stack, isothermal operation at any time was justified and the energy balance in the stack model was neglected. Gases behave ideally. Uniform system e the anode and cathode outlet properties such as temperature, pressure, relative humidity are the same as those within the subsystem. This is based upon the assumption that the anode and cathode channels are uniform by ignoring the spatial variations. This eliminates the need to solve partial differential equations, reducing the model into equations that involve time derivatives only. The Nafion® membrane is taken to be impermeable to the species other than water due to its structure. Pressure drop in the stack was taken as 24 mbar. This is based upon a detailed computational fluid dynamics model of the flow channel geometry in the stack. The stack voltage model estimates the stack voltage for all current, temperature, humidity and reactant partial pressure conditions and combinations. It quantifies ohmic losses, concentration losses and activation losses e predicting the total deviation from the theoretical cell voltage of 1.23 V. Eq. (1) gives the cell potential, where E is OCV (open circuit voltage) value and Vactivation, Vohmic, Vconcentration are the activation, ohmic and concentration polarizations respectively [4].
Vsinglecell ¼ E Vactivation Vohmic Vconcentration
(1)
Cathode flow model is based on the air flow in the cathode volume and the governing electrochemical reactions. For through flow mode operation, the mass balances for cathode species are completed with the ideal gas law and Faraday's law as in Eqs. (2)e(4). The water transfer rate through the membrane involved in Eq. (4) is assumed to be at a pseudosteady state since it is considered to be a small value. Amounts of oxygen reacted and water produced by the electro-chemical reactions were determined by Faraday's law [4]. dmO2 ;cathode ¼ WO2 ;cathodein WO2 ; cathodeout WO2 ; reacted dt
(2)
dmN2 ;cathode ¼ WN2 ;cathode_in WN2 ; cathode_out dt
(3)
dmH2 O;cathode ¼Wvapor;cathode_in Wvapor;cathode_out þ Wvapor;cathode_gen dt þ Wvapor; membrane WH2 Oliq; cathode_out (4) Anode flow model is based on the hydrogen and water balance in the anode compartment. The anode side of the stack considered in this work was operated in a dead-end mode. A pressurized hydrogen tank was used as the hydrogen source, and the anode pressure is to be adjusted with a diaphragm valve and check valve installed on the hydrogen line. The anode side mass balance can be written for hydrogen and water as in Eq. (5) and Eq. (6), where mi,anode (kg) denotes the amount of gas accumulated in the anode for hydrogen or water and W (kg s1) is the amount of hydrogen or water inlet, outlet, reacted or transferred. For dead-end mode the outlet terms for hydrogen and water would appear only during purge conditions [11]. dmH2 ;anode ¼ WH2 ;anodein WH2 ; anodeout WH2 ; reacted dt
(5)
dmH2 O;anode ¼Wvapor;anode_in Wvapor; anode_out Wvapor; membrane dt WH2 Oliquid; anode_out (6) Membrane hydration model estimates the water transfer through the membrane via the mechanisms of electro osmotic drag and diffusion. For membrane hydration model it is assumed that the water transfer is uniform over the fuel cell active area and the water concentration changes linearly within the membrane thickness. Water flux, Nvapor,membrane (mol s1 cm2)), through a membrane is given in Eq. (7). The overall water transfer, Wvapor,membrane(kg s1), for the stack is given by Eq. (8) [4]. Nvapor;membrane ¼ Nvapor;osmotic Nvapor;diffusion
(7)
Wvapor;membrane ¼ Nvapor;membrane Mvapor Afuelcell ncell
(8)
Water transfer by the electro-osmotic drag is captured by Eq. (9), where nd is the electroosmotic drag coefficient which is a function of membrane water content, the current density i
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(A cm2) and Faraday's constant [4,18]. Water content can be expressed in terms of the water activities of anode, cathode or membrane [19]. Membrane water activity can be calculated as the arithmetic mean of anode side and cathode side water activities, where activities are defined as the ratio of vapor pressure and saturation pressure. Nvapor;osmotic ¼ nd
i F
DTlm ¼
ðT∞ Tout Þ ðT∞ Tin Þ out Þ ln ðTðT∞∞T T Þ
(14)
in
(9)
Water generation due to chemical reactions and electroosmotic drag establishes a concentration gradient between anode and cathode. The diffused water amount,Nvapor,diffusion(mol cm2 s1), can be expressed as in Eq. (10), where Dw is the diffusion coefficient (cm2 s1), Cvapor_i is the concentration of anodic and cathodic sides (mol cm3) and tmembrane is the membrane thickness. Water concentrations for anode and cathode compartments can be expressed as functions of the membrane dry density, membrane equivalent weight and the water content [4]. The diffusion coefficient depends on the stack temperature Tfuelcell (K) and the membrane water content [18]. Nvapor;diffusion ¼ Dw
radiator is the average of radiator inlet and outlet temperatures. The log-mean temperature is given in Eq. (14) where T∞(K) is the ambient air temperature assumed to be constant [20].
Cvapor_cathode Cvapor_anode tmembrane
(10)
Cooling system model For the purposes of modeling the cooling system, the system is defined as the contents of the radiator. The mass balance for the radiator can be written as in Eq. (11), where m_ in ðkg s1 Þ is the hot water coming out of the stack and entering the radiator, m_ out ðkg s1 Þ is the cooled water exiting the radiator and mradiator (kg) is the water contained within the radiator volume. The coolant circuit is assumed to be completely filled under all operating conditions, making the water amount in the radiator a constant. Thus the radiator inlet and outlet flow rates would be equal and dependent on the pump voltage as stated by Eq. (12). dmradiator m_ in m_ out ¼ dt
(11)
m_ in ¼ m_ out ¼ m_ ¼ m_ Vpump
(12)
The energy balance is given in Eq. (13), by neglecting the kinetic and potential energy terms and assuming constant physical properties. The inlet energy term contains the hot water leaving the stack and entering the radiator while the energy removal term captures the energy of the cold water leaving the stack and heat removed by the radiator surface to surroundings. Heat conduction and radiation terms are also neglected. m_ Vpump $Cpwater $ðTin Tout Þ ðu A DTlm Þ ¼ Vradiator $r$Cpwater $
dT dt
Overall heat transfer coefficient depends on the water flow rate and air flow rate that correspond to pump and fan voltages, allowing for u to be estimated as a function of fan and pump voltages as u ¼ u(Vfan,Vpump). The final form of the general energy balance is represented in Eq. (15). _ Cpwater ðTin Tout Þ m Vpump 0
1
B ðT∞ Tout Þ ðT∞ Tin ÞC C B @u Vfan ; Vpump A A out Þ ln ðTðT∞∞T Tin Þ 1 dTin dTout þ ¼ Vradiator r Cpwater 2 dt dt
(15)
The integration with the stack and cooling system is given by the Eq. (16), where the stack efficiency is proportional to the stack power and heat generation proportional to the lack of efficiency. Thus heat generation can be expressed as in Eq. (17) where h is the efficiency (Eq. (18)) and Pstack (W) is the stack power. dTstack ¼ Q_ generation Q_ removed dt
(16)
ð1 hÞ Q_ generation ¼ Pstack h
(17)
h¼
vsinglecell 1:23
(18)
Cooling system test data were analyzed using the MATLAB® nonlinear regression, lsqcurvefit method. The regression was carried out by substituting several sequences of the experimentally generated data points of radiator inlet and outlet temperatures, pump and fan voltages into Eq. (15). Different functional forms for u(Vfan,Vpump) were tried to obtain the best fit. The function obtained by regression is stated in Eq. (19). Mass flow rate through the pump was expressed as a function of pump voltage as in Eq. (20). 2:08 uA ¼ 0:782 0:551 Vfan þ 3:639 0:815 0:913 Vpump 3:97
(19)
while Vpump 4.5 V m_ Vpump ¼ 0:023Vpump 0:0944
(20)
(13)
Here, Cpwater (J kg1 K1) is the heat capacity of water, T (K) is the temperature, u (W m2 K1) is the overall heat transfer coefficient, A (m2) is the heat transfer area of the radiator, r (kg m3) is the density of the radiator contents, specifically water in this case. It is assumed that the temperature of the
Humidifier model In this system, a membrane type humidifier with a shell and tube geometry was utilized to humidify the air entering the stack. To increase system efficiency the cathode exhaust stream is used as the humidification source for the dry gas of
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compressor output. The arrangement of the humidifier is very similar to shell and tube heat exchangers. The dry gas passes through the bundle of Nafion® tubes (stream-4), while the cathode exhaust gas (stream-1) surrounds these Nafion® tubes, providing both moisture and heat for the gas entering to the stack (stream-2). The assumptions made for the humidifier modeling are listed below: Ideal gas law is applicable. There is no liquid water in the system and no condensation occurs. The stack exhaust is assumed to contain no liquid water and the temperature change in humidifier is compensated by the vapor transfer that prevents condensation. The humidifier operates isothermally. The insulation is assumed to be preventing any heat exchange between the humidifier and the ambient. Heat capacities are constant. The changing temperature and pressure effects on heat capacities are ignored. The kinetic and potential energy terms in the energy balance are neglected. Tube side is considered to be a single tube whose area and volume is equal to the cumulative area and volume of the multiple tubes that the humidifier is constructed from. The air permeation through the Nafion® membrane is negligible and only water can permeate through the membrane, dry air cannot pass from shell side to tube side or vice versa. Pressure drop in the humidifier was taken as 725 Pa as suggested by the manufacturer specifications. The model was developed over two control volumes; the bundle of Nafion® tubes and shell side. Wet gas coming from the stack (m_ 1 kg s1 ), passes through the shell volume while the dry gas (m_ 4 kg s1 )) passes counter-currently through the Nafion® tubes. Mass transfer between the two mediums occurs due to concentration difference in the shell and tube volumes, along with heat transfer due to the temperature difference. The mass and energy balance equations are developed over control volumes A and B for the dry air and vapor. Mass balances for the tube side and shell side are given by the Eqs. 21e24 dmA;vapor m_ 4;vapor þ m_ vapor m_ 2;vapor ¼ dt
(21)
dmA;dryair m_ 4;dryair m_ 2;dryair ¼ dt
(22)
dmB;vapor m_ 1;vapor m_ vapor m_ 3;vapor ¼ dt
(23)
m_ 1;dryair m_ 3;dryair
dmB;dryair ¼ dt
(24)
Tube and shell side energy balances are given by the Eqs. 25e28, where Q_ (W)is the heat transfer and m_ vapor is the water 1 transfer from shell side to tube side, ( c Hi J kg ) is the enthalpy of the relevant species, U (J) is the internal energy accumulated in the control volume and Cv (J kg1 K1) is the constant volume heat capacity [5].
Tube side(A): b 4 þ m_V H b vapor þ Q_ m_ 2 H b 2 ¼ dUA ¼ mA CvA dTA þ CvA TA dmA m_ 4 H dt dt dt (25) where TA ¼ ðT4 þ T2 Þ=2
(26)
Shell side(B): c1 þ m_V H b vapor Q_ m_ 3 H c3 ¼ dUB m_ 1 H dt
¼ mB Cv3
dTB dmB þ Cv3 TB dt dt (27)
where TB ¼ ðT1 þ T3 Þ=2
(28)
Compressor model Air supply to the fuel cell stack is provided by a compressor. The compressor model needs to map the compressed air flow rate to the compressor supply signal. A compressor model consisting of a compressor map, compressor and motor inertia is available in the literature. The compressor map gives static information reflecting the air flow rate according to the desired pressure, motor speed and power. Compressor and motor inertia provides the compressor speed which is to be used in the compressor map to find flow rate. The dynamics related to compressor speed wcp (rad sec1) is given in Eq. (29) where Jcp (kg m2) is the combined inertia for the motor and compressor, tcm (N m) is the torque input to the compressor motor, tcp (N m) is the torque need by the compressor [4].
Jcp
ducp ¼ tcm tcp dt
(29)
Inlet and outlet manifolds The inlet and outlet manifolds deliver the gases to the stack and therefore characterize the connection between the humidifier and the stack on both ends. To avoid any heat losses in the system these manifolds need to be properly insulated, allowing the manifolds to be assumed at constant, uniform temperature. Eq. (30) shows the mass balance for a manifold, where i represents inlet and outlet manifolds. dPi Rair T ¼ mair;in mair;out Vi dt
(30)
The pressure drop in the tube shaped manifolds were calculated by Eq. (31), where L (m) is the tube length, D (m) is the tube diameter, r (kg m3) is the fluid density, V (m s1) is the mean velocity of the flow and f is the friction factor defined in Eq. (32) [21]. 2LrV2 DPi ¼ f $ D
(31)
Please cite this article in press as: Saygılı Y, et al., Development and modeling for process control purposes in PEMs, International Journal of Hydrogen Energy (2014), http://dx.doi.org/10.1016/j.ijhydene.2014.10.116
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( 2 0 1 4 ) 1 e9
f ¼ 0:0014 þ
0:125 Re0:32
7
(32)
The block diagram of the integrated model is given in Fig. 2
Results and discussion In fuel cell systems, the main disturbance is the stack current since this value is adjusted to deliver the desired load at any given time. This subsequently sets-off a chain reaction, impacting the required reactant amounts, amount of heat that needs to be removed, sufficient humidification level and so on. Hydrogen and air amounts are related to the current driven from the stack. Therefore the fuel and oxidant supply equipment need to deliver desired amounts of reactants to the system at any load conditions. Similarly, high stack currents will cause higher heat generation that necessitates changes in cooling system manipulated variables. The integrated fuel cell SIMULINK® model, involving compressor, humidifier, stack, cooling system, inlet and outlet manifolds with controllers was analyzed by applying multiple step changes in stack current as a disturbance, which is given in Fig. 3 with the resulting stack voltage. The model outputs such as power and heat generations, humidifier responses and membrane water contents are shown in Figs. 3e6. At 328 K, the OCV value is observed to be 0.96 V, corresponding to a stack voltage of 42.3 V for 44 cells as given in Fig. 3. The experimental OCV value for the stack was obtained to be 41.4 V indicating a reasonable agreement with the model. According to the model, while power demanded by the load is 150 A, individual cell voltages remains about 0.61 V, which is the desired level to attain for high power densities as shown on Fig. 4. Humidifier responses for step changes and compressor output air flow rate are given in Fig. 5. Two commercial
Fig. 3 e Stack current applied as the disturbance and the resulting stack voltage.
humidifiers analyzed, Permapure FC200 and FC300 models, which include 780 and 1660 tubes respectively. It is observed that for the first 5 s the dry system begins to be humidified by the electrochemical reactions, the stack exhaust reaching full humidification by the 7th second. Although the water production increases by the increase in stack current, the air flows at higher levels as well due to the increasing voltage command for compressor by the 8th second. At 8th second and beyond, the air flow rate through the compressor is increased within a short response time, the stack exhaust humidity becomes insufficient and a sharp decrease is observed for the relative humidity of the fresh air. The FC300 humidifier, with the larger the heat and mass transfer area, shows better performance to humidify the dry air. Fig. 6 shows the change in water contents, the ratio of water molecules to the charge sites, of anode, cathode and membrane with respect to time when the stack current
Fig. 2 e Block diagram of the integrated system model. Please cite this article in press as: Saygılı Y, et al., Development and modeling for process control purposes in PEMs, International Journal of Hydrogen Energy (2014), http://dx.doi.org/10.1016/j.ijhydene.2014.10.116
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vapor pressure at cathode. Membrane water content, the arithmetic mean of cathode and anode water contents, also shows a decreasing trend due to the decrease in anode water content with increasing electro-osmotic drag.
Conclusion
Fig. 4 e Power and heat generation simulation results for the current disturbance.
Fig. 5 e Simulation of humidifier performances and air flow rate in terms of a step change in stack current.
disturbance given in Fig. 5 was applied. While the inlet air humidity increases as in Fig. 5, water contents of anode, cathode and membrane also show an increasing trend. After the 6th second, cathode water content reaches a maximum, when cathode vapor pressure becomes equal to the saturation pressure. As stack current increases, the anode water content decreases due to the increase in electro-osmotic drag but cathode water content stays constant due to the constant
Fuel cell system design plays an important role in terms of safe and efficient operations. Equipment selection defines and restricts the system process conditions, process control requirements and parasitic losses. In this study, a 3 kW PEM fuel cell is designed and piping and instrumentation diagram with the necessary control instrumentation is generated. A scroll compressor, a cylindrical-membrane humidifier, a cooling system consisting of a pump, fun and radiator are the main auxiliary equipment selections for this system. To check both the effectiveness and adequacy of these equipment prior to purchase and installation on the system, a dynamic semiempirical model of the system is developed and implemented in the MATLAB-SIMULINK® environment. The model was utilized to evaluate possible cooling and humidification equipment and algorithms. The simulations on the integrated model show that individual cell voltages at no load condition and with 150 A load are 0.96 V and 0.61 V respectively which are consisted with the experimental data and design basis. The heat generation rate in the system reaches to 3900 W levels while the power generation is 4300 W. The properly selected cooling system with a radiator and fan maintains the stack at 328 K. For water management it is observed that the fuel cell can be humidified by a membrane type humidifier that uses stack exhaust air without installing additional humidity sources. Higher heat and mass transfer areas in the membrane type humidifier provides better humidification, the particular size of this membrane type humidifier has an impact on how quickly the humidification adapts to dynamic changes. This model based equipment selection and design approach enhances the equipment and algorithm selection process by providing some predictive capability without necessarily having to put together the entire integrated fuelcell system. This reduces costs and resources involved during the design stage.
Acknowledgments UNIDO-ICHET is acknowledged for the project ‘Development of a 3 kW PEM Fuel Cell- TF/INT/03/002’.Prof Dr. Nurcan Bac¸, Asst. Prof. Dr. Ays‚e Bayrakc¸eken, Dr. Yılser Devrim, and Hu¨seyin Devrim are acknowledged for their contributions.
references
Fig. 6 e Water contents of anode, cathode and the membrane obtained by SIMULINK®.
[1] He J, Ahn J, Choe S. Analysis and control of a fuel delivery system considering a two-phase anode model of the polymer electrolyte membrane fuel cell stack. J Power Sources 2011;196(10):4655e70.
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[2] Matraji I, Laghrouche S, Jemei S, Wack M. Robust control of the PEM fuel cell air-feed system via sub-optimal second order sliding mode. Appl Energy 2013;104:945e57. n F, Garcı´a C, Brey JJ. Design [3] Vega-Leal AP, Palomo FR, Barraga of control systems for portable PEM fuel cells. J Power Sources 2007;169:194e7. [4] Pukrushpan JT, Stefanopoulou AG, Peng H. Control of fuel cell power systems. Principles, modeling, analysis and feedback design. New York: Springer; 2004. [5] Park YH, Caton JA. Development of a PEM stack and performance analysis including the effects of water content in the membrane and cooling method. J Power Sources 2008;179:584e91. [6] Chen D, Li W, Peng H. An experimental study and model validation of a membrane humidifier for PEM fuel cell humidification control. J Power Sci 2008;180:461e7. [7] Kang S, Min K, Yu S. Two dimensional dynamic modeling of a shell-and-tube water-to-gas membrane humidifier for proton exchange membrane fuel cell. Int J Hydrogen Energy 2010;35:1727e41. [8] Chen D, Peng H. A thermodynamic model of membrane humidifiers for PEM fuel cell humidification control. Trans ASME 2005;127:424e32. [9] Woo-Ann J. Control and analysis of air, water and thermal systems for a polymer electrolyte membrane fuel cell. Phd Thesis. Mechanical Engineering.Alabama, Auburn University; 2011. guy P, Candusso D, Hissel D. A [10] Yousfi-Steiner N, Moc¸ote review on polymer electrolyte membrane fuel cell catalyst degradation and starvation issues: causes, consequences and diagnostic for mitigation. J Power Sources 2009;194:130e45.
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[11] Barbir F. PEM fuel cells: theory and practice. New York: Elsevier Academic Press; 2005. [12] Park S, Choe S, Choi S. Dynamic modeling and analysis of a shell-and-tube type gas to gas membrane humidifier for PEM fuel cell applications. Int J Hydrogen Energy 2008;33:2273e82. [13] Hu P, Cao G, Zhu X, Hu M. Coolant circuit modeling and temperature fuzzy control of proton exchange membrane fuel cells. Int J Hydrogen Energy 2010;35:9110e23. [14] Rabbani A, Rokni M. Dynamic characteristics of an automotive fuel cell system for transitory load changes. Sustain Energy Technol Assessments 2013;1:34e43. [15] Mulder G, Coenen P, Ridder FJ, Martens A. An advanced cell voltage monitoring device for fuel cell control. Boeretang B2400 Mol, Belgium: VlaamseInstellingvoorTechnologischOnderzoek; 2008. [16] Collier AH, Wang XZ, Yuan JZhang, Wilkinson DP. Degradation of polymer electrolyte membranes. Int J Hydrogen Energy 2006;35:1838e54. [17] Ous T, Arcoumanis C. Degradation aspects of water formation and transport in proton exchange membrane fuel cell: a review. J Power Sci 2013;240:558e82. [18] Dutta S, Shimpalee S, Van Zee JW. Numerical prediction of mass-exchange between cathode and anode channels in a PEM fuel cell. Int J Heat Mass Transf 2001;44:2029e42. [19] Zhang Y, Zhou B. Modeling and control of a portable proton exchange membrane fuel cell-battery power system. J Power Sci 2011;196:8413e23. [20] Incropera FP, DeWitt DP, Bergman TL, Lavine AS. Fundamentals of heat and mass transfer. New York: Wiley; 2007. [21] Mccabe WL, Smith JC, Harriott P. Unit operations of chemical engineering. New York: McGraw-Hill; 2001.
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Available online at www.sciencedirect.com
ScienceDirect journal homepage: www.elsevier.com/locate/he
Development and modeling for process control purposes in PEMs* Yasemin Saygılı*, Serkan Kıncal, Inci Eroglu Department of Chemical Engineering, Middle East Technical University, Ankara 06800, Turkey
article info
abstract
Article history:
To maintain suitable operating conditions, polymer electrolyte membrane (PEM) fuel cell
Received 17 July 2014
stacks require additional equipment and control systems. Fuel supply, power and thermal
Received in revised form
management, purge strategy and individual cell voltage control must be in place and
19 October 2014
operate reliably for a fuel cell system to achieve similar levels of performance as con-
Accepted 27 October 2014
ventional energy generators. System design, auxiliary equipment selection and selection of
Available online xxx
control strategies have effects on fuel cell efficiency, durability and reliability. In this study we report on our efforts to develop the piping and instrumentation diagram of a 3 kW PEM
Keywords:
fuel cell, including the control instrumentation. A semi-empirical model was put together
PEMFC
to understand dynamic system behavior for purpose of evaluating possible operating
Fuel cell piping and instrumentation
scenarios, in an effort to have useful insight into the system during the equipment se-
diagram
lection stage. The model complexity was reduced by ignoring the spatial variations and
Integrated fuel cell modeling
assuming isothermal stack operation. The stack, cooling system, humidifier, compressor,
Fuel cell control
inlet and outlet manifold were modeled and integrated to formulate a comprehensive prototype model. This model was subsequently used to generate predictions for the responses of the compressor, humidifier, humidification of the stack, power and heat generation for a multitude of dynamic changes in load. With the predictive capability enabled by the model, equipment and algorithm selections can be made in a more directed fashion, reducing the initial design and development costs by delivering a hardware configuration that is close to an ideal one with minimal iterations. Copyright © 2014, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.
Introduction PEM fuel cells are the electrochemical reactors that directly convert chemical energy of hydrogen into DC (direct current) electricity. A single PEM fuel cell consists of a proton conducting membrane that is sandwiched between a pair of
catalyst and gas diffusion layers encapsulated by bipolar plates. In order to deliver useful power levels, single cells are connected in series to build a stack. This stack of multiple individual cells must be complemented by auxiliary equipment and control systems in order to fulfill the requirements for efficient and reliable power generation. The auxiliary equipment and process control algorithms can be divided into
*
Presented in International Conference on Clean Energy (ICCE) 2014, 8e12 June, istanbul. * Corresponding author. Tel.: þ 90 542 5705381; fax: þ 90 312 210 2600. E-mail addresses: [email protected] (Y. Saygılı), [email protected] (S. Kıncal), [email protected] (I. Eroglu). http://dx.doi.org/10.1016/j.ijhydene.2014.10.116 0360-3199/Copyright © 2014, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.
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Nomenclature area, m2, cm2 constant pressure heat capacity, J kg1 K1 constant volume heat capacity, J kg1 K1 membrane water concentration, mol cm3 Diameter, m diffusion coefficient of water, cm2 s1 friction factor enthalpy, J kg1 stack current density, A cm2 inertia, kg m2 mass, kg mass flow rate, kg s1 M molecular weight, kg mol1 L Length, m electroosmotic drag coefficient, e nd number of cells, e ncell Nv,membrane water flux, mol cm2 s1 P pressure, bar P power, W Q heat transfer, W t membrane thickness, cm T temperature, K, C u overall heat transfer coefficient, W m2 K1 U internal energy, J V Mean velocity V voltage, V volume, m3 Vi W mass Flow rate, kg s1 wcp compressor speed, rad sec1 Tlm log-mean temperature, e A Cp Cv Cv,i D Dw f c Hi i J m m_
Greek letters h efficiency, e r density, kg m3 t torque,N m Subscripts cm compressor motor cp Compressor i,anode anode compartment i,cathode cathode compartment v Vapor ∞ ambient air
subsystems of fuel supply, water management, thermal management, power management, purge strategy and cell voltage tracking. To assure uninterrupted power, the reactants should be delivered to the stack in sufficient amounts and proper molar ratios under all load conditions. Undersupply, low partial pressures and mis-matched molar ratios must be avoided by properly adjusting the hydrogen and oxygen supplies while minimizing parasitic losses to deliver these requirements. Hydrogen is generally delivered from a pressurized tank by adjusting the hydrogen flow with proportional regulation valves according to the pressure difference between cathode and anode. Fuel delivery systems can be
designed to recirculate the excess hydrogen to avoid extra fuel usage [1]. Air is the preferred supply of oxygen in most configurations and is usually provided by compressors, blowers or similar equipment from the ambient, which can consume significant amounts of parasitic power and tend to react slower than the regulation valves used on the hydrogen side. The air line should contain filters and leakproof lubrication systems to eliminate contamination risks [2]. Different control strategies for fuel cell air supply are reported in the literature [3,4]. Water management subsystem provides the required level of humidity for proton conduction in the porous media of the system. Too little water reduces conduction while too much water causes flooding. External humidifiers such as nozzle spray, static injector, gas bubbling, enthalpy wheel and membrane humidifiers are used to regulate the water content in the stack [4e7]. Membrane type humidifiers with different geometries exchange heat and water in the presence of temperature and vapor concentration gradients. Stack exhaust gas is often used for humidification in membrane type humidifiers [8,9]. Purging can be utilized as both a water management and an impurity elimination approach. Particularly for dead-end operation of the anode, a purge valve is opened at required intervals to remove the water and impurities that have accumulated at the anode. Unless effective purging is applied, both in frequency and duration, uneven distribution of hydrogen and fuel starvation is observed [10]. The frequency and duration of purges should be determined for an efficient purge while ensuring minimum fuel consumption [11]. Fuel cell system thermal management has a significant role on safe and efficient operation of fuel cells. Stack overheating can cause dehydration in the polymer membrane, resulting in performance losses. High temperatures can also cause membrane leaks formed by hot spots which can result in an unsafe position due to the mixing of hydrogen and oxygen [12]. Some of these modes of damage may be permanent, some are recoverable. Air cooled [3] and water cooled [13,14] systems with different designs can be used for thermal management of fuel cells e the selection usually depending on the capacity of the stack impacting the amount of heat to be removed. The individual cell voltages in the stack should ideally be monitored for safety, control and long-term analysis. Cell voltage losses can be caused by internal problems appearing in the membrane electrode assembly, such as water droplets that prevents gas flow or pinholes and hotspots. Cell voltages quickly respond to the conditions such as impurity accumulations, water droplets in the gas pathways, unequal gas distribution, membrane drying or flooding and electrical connectivity problems, allowing them to be used for control, monitoring and troubleshooting purposes [15]. Cell voltage monitoring also allows for the tracking of fuel cell degradation over extended periods of operation [16]. While the current delivered from the system is increased, the reactant consumption and water production rates also increase. This manifests itself as a decrease in cell voltages, observed in typical polarization curves. In operation, the current density should be limited by keeping the individual cell voltages above 0.4 V to prevent reactant starvation and water flooding [17].
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The purpose of this work is the investigation of the performance and competence of the auxiliary equipment for a 3 kW fuel cell prototype following a model based strategy. A piping and instrumentation diagram for this prototype was generated; a dynamic model for the system developed and this model used to evaluate the performance of candidate equipment and control strategies. Many fuel cell models of various levels of complexity are reported in the literature. For this study, we develop an integrated fuel cell system model including humidifier, compressor, manifolds and cooling system to observe subsystem interactions and dynamics. The model is as complex as necessary and as simple as possible e in an effort to optimize the resources invested in the model development and the accuracy of the feedback it provides the prototype development efforts. The developed system model allows for the design, analysis and evaluation of any desired component of the system such as humidifier and cooling system.
Piping and instrumentation diagram For the PEM fuel cell under study, a pressurized hydrogen tank was selected as the hydrogen source. The auxiliary equipment for the system and the associated control instrumentation is given in Fig. 1. The hydrogen line involves a solenoid valve, relief valve, pressure indicator and a pressure regulator. Solenoid valve is opened at start-ups, the pressure indicator indicating whether there is proper hydrogen pressure in the line and tank or not by initiating an alarm at pressures lower than a set-point. High pressures in the line are avoided by the relief valve. The pressure regulator lets the hydrogen flow to the anode compartment when the hydrogen inside anode is
3
depleted, indicated by a drop of the cathode pressure. The solenoid valve is closed at shut-down and emergency conditions. A scroll compressor accompanied by a filter is used to regulate the air flow. The compressor command voltage is determined according to the stack current, defining the motor speed and the compressed air flow rate through the stack. Air requirement is calculated by Faraday's Law, coupled by a PI (proportional integral) controller following the feedback of the difference of required and supplied air amount. Finally the compressor voltage command corresponding to this air flow rate is determined. The compressor outlet pressure was set at 1.2 atm. The stack is cooled down by a cooling system involving a pump, radiator and a fan. Stack temperature is inferred by tracking the temperature of the cooling water outlet. This temperature feedback can be used for different control strategies by changing the pump and fan voltages. Power management subsystem involves a battery, DC/DC converter and DC/AC converter to control the power drawn from the fuel cell system. While the load connected to the system increases, the parasitic power losses also increase and the net power delivered from the stack can be complemented by the battery if necessary. In case of low voltages the battery would be used exclusively, such as start-ups and shut-downs. Battery would be recharged when excessive power is available. To remove the water and impurities accumulated at anode compartment, the anode is to be purged. Purge valve can be operated at a fixed frequency and duration setting or be dynamically controlled based on the voltage across the cells nearest to the anode exit. At voltage levels below a certain threshold, the purge valve is to be opened to eliminate
Fig. 1 e Prototype piping and instrumentation diagram with control instrumentation. Please cite this article in press as: Saygılı Y, et al., Development and modeling for process control purposes in PEMs, International Journal of Hydrogen Energy (2014), http://dx.doi.org/10.1016/j.ijhydene.2014.10.116
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impurities to recover the voltage. To prevent flooding, the individual cell voltages should be kept below 0.4 V.
System model Within the scope of this study, a semi-empirical model was developed for the specific PEM fuel cell prototype. Spatial variations were ignored in an effort to reduce the complexity and allow for quick feedback for the prototype development activities. With perfect cooling assumption and considering the slow response time of the stack temperature an isothermal model was utilized for the stack. Stack voltage test data and cooling system test data were integrated to the model to determine the unknown coefficients appearing in the model equations, resulting in a semi-empirical model. Individual models for the stack, cooling system, humidifier, compressor, inlet and outlet manifold were integrated for the prototype model. Although the resulting model is specific to the fuel cell system under study, the approach is generic and can be quickly adapted to the response of similar systems through generation of limited experimental datasets.
Stack model Stack model consists of stack voltage model, anode and cathode flow models and membrane hydration model. The general assumptions involved in the stack modeling are: Isothermal operation e temperature dynamics have larger time constants among the other processes involved in fuel cell stack. Therefore stack temperature can be considered as a constant instantly. By assuming a perfect cooling system that directly remove generated heat from the stack, isothermal operation at any time was justified and the energy balance in the stack model was neglected. Gases behave ideally. Uniform system e the anode and cathode outlet properties such as temperature, pressure, relative humidity are the same as those within the subsystem. This is based upon the assumption that the anode and cathode channels are uniform by ignoring the spatial variations. This eliminates the need to solve partial differential equations, reducing the model into equations that involve time derivatives only. The Nafion® membrane is taken to be impermeable to the species other than water due to its structure. Pressure drop in the stack was taken as 24 mbar. This is based upon a detailed computational fluid dynamics model of the flow channel geometry in the stack. The stack voltage model estimates the stack voltage for all current, temperature, humidity and reactant partial pressure conditions and combinations. It quantifies ohmic losses, concentration losses and activation losses e predicting the total deviation from the theoretical cell voltage of 1.23 V. Eq. (1) gives the cell potential, where E is OCV (open circuit voltage) value and Vactivation, Vohmic, Vconcentration are the activation, ohmic and concentration polarizations respectively [4].
Vsinglecell ¼ E Vactivation Vohmic Vconcentration
(1)
Cathode flow model is based on the air flow in the cathode volume and the governing electrochemical reactions. For through flow mode operation, the mass balances for cathode species are completed with the ideal gas law and Faraday's law as in Eqs. (2)e(4). The water transfer rate through the membrane involved in Eq. (4) is assumed to be at a pseudosteady state since it is considered to be a small value. Amounts of oxygen reacted and water produced by the electro-chemical reactions were determined by Faraday's law [4]. dmO2 ;cathode ¼ WO2 ;cathodein WO2 ; cathodeout WO2 ; reacted dt
(2)
dmN2 ;cathode ¼ WN2 ;cathode_in WN2 ; cathode_out dt
(3)
dmH2 O;cathode ¼Wvapor;cathode_in Wvapor;cathode_out þ Wvapor;cathode_gen dt þ Wvapor; membrane WH2 Oliq; cathode_out (4) Anode flow model is based on the hydrogen and water balance in the anode compartment. The anode side of the stack considered in this work was operated in a dead-end mode. A pressurized hydrogen tank was used as the hydrogen source, and the anode pressure is to be adjusted with a diaphragm valve and check valve installed on the hydrogen line. The anode side mass balance can be written for hydrogen and water as in Eq. (5) and Eq. (6), where mi,anode (kg) denotes the amount of gas accumulated in the anode for hydrogen or water and W (kg s1) is the amount of hydrogen or water inlet, outlet, reacted or transferred. For dead-end mode the outlet terms for hydrogen and water would appear only during purge conditions [11]. dmH2 ;anode ¼ WH2 ;anodein WH2 ; anodeout WH2 ; reacted dt
(5)
dmH2 O;anode ¼Wvapor;anode_in Wvapor; anode_out Wvapor; membrane dt WH2 Oliquid; anode_out (6) Membrane hydration model estimates the water transfer through the membrane via the mechanisms of electro osmotic drag and diffusion. For membrane hydration model it is assumed that the water transfer is uniform over the fuel cell active area and the water concentration changes linearly within the membrane thickness. Water flux, Nvapor,membrane (mol s1 cm2)), through a membrane is given in Eq. (7). The overall water transfer, Wvapor,membrane(kg s1), for the stack is given by Eq. (8) [4]. Nvapor;membrane ¼ Nvapor;osmotic Nvapor;diffusion
(7)
Wvapor;membrane ¼ Nvapor;membrane Mvapor Afuelcell ncell
(8)
Water transfer by the electro-osmotic drag is captured by Eq. (9), where nd is the electroosmotic drag coefficient which is a function of membrane water content, the current density i
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(A cm2) and Faraday's constant [4,18]. Water content can be expressed in terms of the water activities of anode, cathode or membrane [19]. Membrane water activity can be calculated as the arithmetic mean of anode side and cathode side water activities, where activities are defined as the ratio of vapor pressure and saturation pressure. Nvapor;osmotic ¼ nd
i F
DTlm ¼
ðT∞ Tout Þ ðT∞ Tin Þ out Þ ln ðTðT∞∞T T Þ
(14)
in
(9)
Water generation due to chemical reactions and electroosmotic drag establishes a concentration gradient between anode and cathode. The diffused water amount,Nvapor,diffusion(mol cm2 s1), can be expressed as in Eq. (10), where Dw is the diffusion coefficient (cm2 s1), Cvapor_i is the concentration of anodic and cathodic sides (mol cm3) and tmembrane is the membrane thickness. Water concentrations for anode and cathode compartments can be expressed as functions of the membrane dry density, membrane equivalent weight and the water content [4]. The diffusion coefficient depends on the stack temperature Tfuelcell (K) and the membrane water content [18]. Nvapor;diffusion ¼ Dw
radiator is the average of radiator inlet and outlet temperatures. The log-mean temperature is given in Eq. (14) where T∞(K) is the ambient air temperature assumed to be constant [20].
Cvapor_cathode Cvapor_anode tmembrane
(10)
Cooling system model For the purposes of modeling the cooling system, the system is defined as the contents of the radiator. The mass balance for the radiator can be written as in Eq. (11), where m_ in ðkg s1 Þ is the hot water coming out of the stack and entering the radiator, m_ out ðkg s1 Þ is the cooled water exiting the radiator and mradiator (kg) is the water contained within the radiator volume. The coolant circuit is assumed to be completely filled under all operating conditions, making the water amount in the radiator a constant. Thus the radiator inlet and outlet flow rates would be equal and dependent on the pump voltage as stated by Eq. (12). dmradiator m_ in m_ out ¼ dt
(11)
m_ in ¼ m_ out ¼ m_ ¼ m_ Vpump
(12)
The energy balance is given in Eq. (13), by neglecting the kinetic and potential energy terms and assuming constant physical properties. The inlet energy term contains the hot water leaving the stack and entering the radiator while the energy removal term captures the energy of the cold water leaving the stack and heat removed by the radiator surface to surroundings. Heat conduction and radiation terms are also neglected. m_ Vpump $Cpwater $ðTin Tout Þ ðu A DTlm Þ ¼ Vradiator $r$Cpwater $
dT dt
Overall heat transfer coefficient depends on the water flow rate and air flow rate that correspond to pump and fan voltages, allowing for u to be estimated as a function of fan and pump voltages as u ¼ u(Vfan,Vpump). The final form of the general energy balance is represented in Eq. (15). _ Cpwater ðTin Tout Þ m Vpump 0
1
B ðT∞ Tout Þ ðT∞ Tin ÞC C B @u Vfan ; Vpump A A out Þ ln ðTðT∞∞T Tin Þ 1 dTin dTout þ ¼ Vradiator r Cpwater 2 dt dt
(15)
The integration with the stack and cooling system is given by the Eq. (16), where the stack efficiency is proportional to the stack power and heat generation proportional to the lack of efficiency. Thus heat generation can be expressed as in Eq. (17) where h is the efficiency (Eq. (18)) and Pstack (W) is the stack power. dTstack ¼ Q_ generation Q_ removed dt
(16)
ð1 hÞ Q_ generation ¼ Pstack h
(17)
h¼
vsinglecell 1:23
(18)
Cooling system test data were analyzed using the MATLAB® nonlinear regression, lsqcurvefit method. The regression was carried out by substituting several sequences of the experimentally generated data points of radiator inlet and outlet temperatures, pump and fan voltages into Eq. (15). Different functional forms for u(Vfan,Vpump) were tried to obtain the best fit. The function obtained by regression is stated in Eq. (19). Mass flow rate through the pump was expressed as a function of pump voltage as in Eq. (20). 2:08 uA ¼ 0:782 0:551 Vfan þ 3:639 0:815 0:913 Vpump 3:97
(19)
while Vpump 4.5 V m_ Vpump ¼ 0:023Vpump 0:0944
(20)
(13)
Here, Cpwater (J kg1 K1) is the heat capacity of water, T (K) is the temperature, u (W m2 K1) is the overall heat transfer coefficient, A (m2) is the heat transfer area of the radiator, r (kg m3) is the density of the radiator contents, specifically water in this case. It is assumed that the temperature of the
Humidifier model In this system, a membrane type humidifier with a shell and tube geometry was utilized to humidify the air entering the stack. To increase system efficiency the cathode exhaust stream is used as the humidification source for the dry gas of
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compressor output. The arrangement of the humidifier is very similar to shell and tube heat exchangers. The dry gas passes through the bundle of Nafion® tubes (stream-4), while the cathode exhaust gas (stream-1) surrounds these Nafion® tubes, providing both moisture and heat for the gas entering to the stack (stream-2). The assumptions made for the humidifier modeling are listed below: Ideal gas law is applicable. There is no liquid water in the system and no condensation occurs. The stack exhaust is assumed to contain no liquid water and the temperature change in humidifier is compensated by the vapor transfer that prevents condensation. The humidifier operates isothermally. The insulation is assumed to be preventing any heat exchange between the humidifier and the ambient. Heat capacities are constant. The changing temperature and pressure effects on heat capacities are ignored. The kinetic and potential energy terms in the energy balance are neglected. Tube side is considered to be a single tube whose area and volume is equal to the cumulative area and volume of the multiple tubes that the humidifier is constructed from. The air permeation through the Nafion® membrane is negligible and only water can permeate through the membrane, dry air cannot pass from shell side to tube side or vice versa. Pressure drop in the humidifier was taken as 725 Pa as suggested by the manufacturer specifications. The model was developed over two control volumes; the bundle of Nafion® tubes and shell side. Wet gas coming from the stack (m_ 1 kg s1 ), passes through the shell volume while the dry gas (m_ 4 kg s1 )) passes counter-currently through the Nafion® tubes. Mass transfer between the two mediums occurs due to concentration difference in the shell and tube volumes, along with heat transfer due to the temperature difference. The mass and energy balance equations are developed over control volumes A and B for the dry air and vapor. Mass balances for the tube side and shell side are given by the Eqs. 21e24 dmA;vapor m_ 4;vapor þ m_ vapor m_ 2;vapor ¼ dt
(21)
dmA;dryair m_ 4;dryair m_ 2;dryair ¼ dt
(22)
dmB;vapor m_ 1;vapor m_ vapor m_ 3;vapor ¼ dt
(23)
m_ 1;dryair m_ 3;dryair
dmB;dryair ¼ dt
(24)
Tube and shell side energy balances are given by the Eqs. 25e28, where Q_ (W)is the heat transfer and m_ vapor is the water 1 transfer from shell side to tube side, ( c Hi J kg ) is the enthalpy of the relevant species, U (J) is the internal energy accumulated in the control volume and Cv (J kg1 K1) is the constant volume heat capacity [5].
Tube side(A): b 4 þ m_V H b vapor þ Q_ m_ 2 H b 2 ¼ dUA ¼ mA CvA dTA þ CvA TA dmA m_ 4 H dt dt dt (25) where TA ¼ ðT4 þ T2 Þ=2
(26)
Shell side(B): c1 þ m_V H b vapor Q_ m_ 3 H c3 ¼ dUB m_ 1 H dt
¼ mB Cv3
dTB dmB þ Cv3 TB dt dt (27)
where TB ¼ ðT1 þ T3 Þ=2
(28)
Compressor model Air supply to the fuel cell stack is provided by a compressor. The compressor model needs to map the compressed air flow rate to the compressor supply signal. A compressor model consisting of a compressor map, compressor and motor inertia is available in the literature. The compressor map gives static information reflecting the air flow rate according to the desired pressure, motor speed and power. Compressor and motor inertia provides the compressor speed which is to be used in the compressor map to find flow rate. The dynamics related to compressor speed wcp (rad sec1) is given in Eq. (29) where Jcp (kg m2) is the combined inertia for the motor and compressor, tcm (N m) is the torque input to the compressor motor, tcp (N m) is the torque need by the compressor [4].
Jcp
ducp ¼ tcm tcp dt
(29)
Inlet and outlet manifolds The inlet and outlet manifolds deliver the gases to the stack and therefore characterize the connection between the humidifier and the stack on both ends. To avoid any heat losses in the system these manifolds need to be properly insulated, allowing the manifolds to be assumed at constant, uniform temperature. Eq. (30) shows the mass balance for a manifold, where i represents inlet and outlet manifolds. dPi Rair T ¼ mair;in mair;out Vi dt
(30)
The pressure drop in the tube shaped manifolds were calculated by Eq. (31), where L (m) is the tube length, D (m) is the tube diameter, r (kg m3) is the fluid density, V (m s1) is the mean velocity of the flow and f is the friction factor defined in Eq. (32) [21]. 2LrV2 DPi ¼ f $ D
(31)
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f ¼ 0:0014 þ
0:125 Re0:32
7
(32)
The block diagram of the integrated model is given in Fig. 2
Results and discussion In fuel cell systems, the main disturbance is the stack current since this value is adjusted to deliver the desired load at any given time. This subsequently sets-off a chain reaction, impacting the required reactant amounts, amount of heat that needs to be removed, sufficient humidification level and so on. Hydrogen and air amounts are related to the current driven from the stack. Therefore the fuel and oxidant supply equipment need to deliver desired amounts of reactants to the system at any load conditions. Similarly, high stack currents will cause higher heat generation that necessitates changes in cooling system manipulated variables. The integrated fuel cell SIMULINK® model, involving compressor, humidifier, stack, cooling system, inlet and outlet manifolds with controllers was analyzed by applying multiple step changes in stack current as a disturbance, which is given in Fig. 3 with the resulting stack voltage. The model outputs such as power and heat generations, humidifier responses and membrane water contents are shown in Figs. 3e6. At 328 K, the OCV value is observed to be 0.96 V, corresponding to a stack voltage of 42.3 V for 44 cells as given in Fig. 3. The experimental OCV value for the stack was obtained to be 41.4 V indicating a reasonable agreement with the model. According to the model, while power demanded by the load is 150 A, individual cell voltages remains about 0.61 V, which is the desired level to attain for high power densities as shown on Fig. 4. Humidifier responses for step changes and compressor output air flow rate are given in Fig. 5. Two commercial
Fig. 3 e Stack current applied as the disturbance and the resulting stack voltage.
humidifiers analyzed, Permapure FC200 and FC300 models, which include 780 and 1660 tubes respectively. It is observed that for the first 5 s the dry system begins to be humidified by the electrochemical reactions, the stack exhaust reaching full humidification by the 7th second. Although the water production increases by the increase in stack current, the air flows at higher levels as well due to the increasing voltage command for compressor by the 8th second. At 8th second and beyond, the air flow rate through the compressor is increased within a short response time, the stack exhaust humidity becomes insufficient and a sharp decrease is observed for the relative humidity of the fresh air. The FC300 humidifier, with the larger the heat and mass transfer area, shows better performance to humidify the dry air. Fig. 6 shows the change in water contents, the ratio of water molecules to the charge sites, of anode, cathode and membrane with respect to time when the stack current
Fig. 2 e Block diagram of the integrated system model. Please cite this article in press as: Saygılı Y, et al., Development and modeling for process control purposes in PEMs, International Journal of Hydrogen Energy (2014), http://dx.doi.org/10.1016/j.ijhydene.2014.10.116
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vapor pressure at cathode. Membrane water content, the arithmetic mean of cathode and anode water contents, also shows a decreasing trend due to the decrease in anode water content with increasing electro-osmotic drag.
Conclusion
Fig. 4 e Power and heat generation simulation results for the current disturbance.
Fig. 5 e Simulation of humidifier performances and air flow rate in terms of a step change in stack current.
disturbance given in Fig. 5 was applied. While the inlet air humidity increases as in Fig. 5, water contents of anode, cathode and membrane also show an increasing trend. After the 6th second, cathode water content reaches a maximum, when cathode vapor pressure becomes equal to the saturation pressure. As stack current increases, the anode water content decreases due to the increase in electro-osmotic drag but cathode water content stays constant due to the constant
Fuel cell system design plays an important role in terms of safe and efficient operations. Equipment selection defines and restricts the system process conditions, process control requirements and parasitic losses. In this study, a 3 kW PEM fuel cell is designed and piping and instrumentation diagram with the necessary control instrumentation is generated. A scroll compressor, a cylindrical-membrane humidifier, a cooling system consisting of a pump, fun and radiator are the main auxiliary equipment selections for this system. To check both the effectiveness and adequacy of these equipment prior to purchase and installation on the system, a dynamic semiempirical model of the system is developed and implemented in the MATLAB-SIMULINK® environment. The model was utilized to evaluate possible cooling and humidification equipment and algorithms. The simulations on the integrated model show that individual cell voltages at no load condition and with 150 A load are 0.96 V and 0.61 V respectively which are consisted with the experimental data and design basis. The heat generation rate in the system reaches to 3900 W levels while the power generation is 4300 W. The properly selected cooling system with a radiator and fan maintains the stack at 328 K. For water management it is observed that the fuel cell can be humidified by a membrane type humidifier that uses stack exhaust air without installing additional humidity sources. Higher heat and mass transfer areas in the membrane type humidifier provides better humidification, the particular size of this membrane type humidifier has an impact on how quickly the humidification adapts to dynamic changes. This model based equipment selection and design approach enhances the equipment and algorithm selection process by providing some predictive capability without necessarily having to put together the entire integrated fuelcell system. This reduces costs and resources involved during the design stage.
Acknowledgments UNIDO-ICHET is acknowledged for the project ‘Development of a 3 kW PEM Fuel Cell- TF/INT/03/002’.Prof Dr. Nurcan Bac¸, Asst. Prof. Dr. Ays‚e Bayrakc¸eken, Dr. Yılser Devrim, and Hu¨seyin Devrim are acknowledged for their contributions.
references
Fig. 6 e Water contents of anode, cathode and the membrane obtained by SIMULINK®.
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