Model-based analysis of water management at anode of alkaline direct methanol fuel cells

Chemical Engineering Science 143 (2016) 181–193

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Model-based analysis of water management at anode of alkaline direct methanol fuel cells C. Weinzierl a,b, U. Krewer a,n a b

TU Braunschweig, Institute of Energy and Process Systems Engineering, Franz-Liszt-Str. 35, 38106 Braunschweig, Germany1 Max Planck Institute for Dynamics of Complex Technical Systems, Sandtorstr. 1, 39106 Magdeburg, Germany2

H I G H L I G H T S








First modelling study of water management at anode of anion-exchange membrane ADMFCs. Effect of unstable water level in the anodic loop of an ADMFC is demonstrated. Conditions that lead to stable water level in the anodic loop are identified. Full humidification of inlet gases is detrimental for stable water level in AFCs. Importance of quantification of water diffusion for design of ADMFC-systems revealed.

art ic l e i nf o

a b s t r a c t

Article history: Received 25 August 2015 Received in revised form 7 December 2015 Accepted 11 December 2015 Available online 7 January 2016

Alkaline direct methanol fuel cells (ADMFCs) produce water at the aqueous fed anode. This complicates water management at anode which is analysed in this study by modelling three extreme case scenarios assuming different conditions for water transport or removal. All scenarios include recycling of methanol solution at anode outlet to achieve high methanol efficiencies. One scenario reveals that high operation times and high methanol efficiencies necessitate active stabilisation of anodic water level since both water accumulation and depletion can take place depending on operation conditions. Another scenario shows that water level can be stabilised by adjusting cathodic evaporation and the corresponding water removal from the system. The results indicate that feeding cathode with water-saturated gas is detrimental for stabilising water level. The last scenario suggests the addition of a gas flow to anodic outlet to remove excess water for water level stabilisation. Minimization of additional methanol loss requires to reach high humidities by evaporation. The present paper reveals the impact of processes occurring in ADMFCs on anodic water management and indicates the necessity to quantify water transport through membrane. Knowledge of the influence of operation conditions on water level in the anodic loop are beneficial for design of ADMFC systems. & 2015 Elsevier Ltd. All rights reserved.

Keywords: ADMFC Fuel cell system Anion exchange membrane Alkaline fuel cell Water management Mathematical modelling

1. Introduction One of the main reasons why fuel cells are not commercialised yet is the high cost which mainly comes from expensive materials. A potential way of reducing the cost of fuel cells is to use fuel cells of the alkaline type which do not require platinum as catalyst. Due to higher activity and stability in alkaline media, even nonprecious metals like nickel can be used as catalyst. However, alkaline fuel cells used to be operated with liquid electrolyte n

Corresponding author. Tel.: þ 49 0531 391 3030; fax: þ49 0531 391 5932. E-mail addresses: [email protected] (C. Weinzierl), [email protected] (U. Krewer). 1 Present address of both authors. 2 Address during research work. http://dx.doi.org/10.1016/j.ces.2015.12.006 0009-2509/& 2015 Elsevier Ltd. All rights reserved.

which causes, among others, corrosion and carbonation problems. The latter is quite intense in alkaline direct methanol fuel cells (ADMFCs) since CO2, which causes the carbonation, is permanently produced at anode during operation. In order to avoid these problems, anion exchange membranes were introduced as electrolyte in alkaline fuel cells as reported by Varcoe et al. (2006). Thus, research of alkaline fuel cells mainly focusses on new catalysts (Varcoe et al., 2008; Yu et al., 2010) or new membrane material (Merle et al., 2011; Cheng et al., 2015). A very detailed overview over state of the art of anion exchange membranes (AEMs) and their application in electrochemistry is given by Antanassov et al. (2014) who also state that low conductivity and poor stability of AEMs are still challenging topics. Up to now alkaline anion exchange membrane fuel cells do not show the same performance as acidic fuel cells (Varcoe and Slade, 2006) or

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alkaline fuel cells with liquid electrolyte (Coutanceau et al., 2006; Janarthanan et al., 2015). The reason for that low performance is not clear yet since removing the alkaline solution effects several things such as ionic conductivity, reaction kinetics, and water management. Most studies about anion-exchange membrane fuel cells focus on performance of the fuel cells with new component materials (Janarthanan et al., 2015; Yu and Scott, 2004; Sun et al., 2012; Poynton et al., 2010). Modelling studies also describe and analyse mainly the performance of AFCs (Kimble and White, 1991; Jo et al., 2000; Mohan and Shrestha, 2010; Verhaert et al., 2009; Jiao et al., 2014; Verma and Basu, 2007; Deng et al., 2014; An et al., 2013) considering ion conduction and reaction kinetics while process engineering issues remain unstudied. Due to the low performance without liquid electrolyte, most studies about alkaline direct alcohol fuel cells include potassium or sodium salts mixed to alcohol solution for a better performance as summarized by Antanassov et al. (2014). Likewise, the few models of alkaline direct alcohol fuel cells mostly include KOH or NaOH solution in addition to the electrolyte membrane (Verma and Basu, 2007; Deng et al., 2014; An et al., 2013; Bahrami and Faghri, 2012). Only few exceptions consider solely an anion-exchange membrane as electrolyte in ADMFCs (Weinzierl and Krewer, 2014; Deng et al., 2015). Although water transport through the membrane has already been identified as a possible limiting factor for performance of AFCs by Poynton et al. (2010), water management attracted little attention so far. Only in few studies, water transport coefficients through anion-exchange membranes have been determined experimentally (Li et al., 2010; Follain et al., 2012; Garca-Nieto and Barragn, 2015) or have been estimated by modelling (Myles et al., 2011; Yamanaka et al., 2009). Whereas water transport processes have been included in many mathematical models of AFCs (Kimble and White, 1991; Jiao et al., 2014; Deng et al., 2014; Weinzierl and Krewer, 2014; Deng et al., 2015; Bjornbom and Yang, 1993; Yang and Bjornbom, 1992; Huo et al., 2012; Deng et al., 2013), the effect of water management was only studied for AFCs with liquid electrolyte by Verhaert et al. (2011) and Rowshanzamir et al. (1998), for the anode of hydrogen fuelled AEMFCs by Huo et al. (2012) and Deng et al. (2013) and for an AEM ADMFC cathode by Weinzierl and Krewer (2014) so far. Direct methanol fuel cells (DMFCs) are highly attractive for portable and off-grid applications due to the high energy density of methanol. To reduce the weight of DMFC-systems and to achieve high methanol efficiencies, recycling of methanol solution is applied. This causes a special need to maintain constant amount

and composition of the liquid in the anode loop. Stable and autonomous operation of methanol fuel cell systems without refilling water or storing waste solution has already been analysed for acidic DMFC-systems by Zenith et al. (2010). In acidic DMFCs, water is lost at anode and needs to be recovered from the cathode exhaust whereas it is not clear yet whether water accumulation or depletion takes place in the anode compartment of an alkaline DMFC. Therefore, our previously published model (Weinzierl and Krewer, 2014) that was used to analyse water management at cathode is extended in the present paper in order to analyse water management at anode of an ADMFC. It targets to determine conditions that lead to stable water level and to reveal the effect of unstable water level on methanol efficiency and operation time. Furthermore, this study identifies the influence of conditions at cathode on the anodic water level as well as one way of removing water from anodic liquid and the consequences of that removal on efficiency.

2. ADMFC-system structure and relevance of water management The anode of an ADMFC is fed with water-methanol-solution and the methanol is electrochemically oxidised as follows: CH3 OH þ 6OH  ⟶CO2 ↑ þ5H2 O þ 6e 

ð1Þ

while cathode reaction is:   3 2 O2 þ 3H2 O þ 6e ⟶6OH

ð2Þ

This results in the following overall reaction: CH3 OH þ 32 O2 ⟶CO2 þ 2H2 O

ð3Þ 

Water is dragged along with the OH -ions from cathode to anode. Due to the methanol-water solution that is fed to anode, a gradient between high concentrations at anode and low concentrations at the gas fed cathode is formed which leads to water diffusion as well as methanol diffusion through membrane from anode to cathode. The latter is called methanol cross-over. In order to avoid fuel starvation, methanol is fed in excess. To prevent waste of methanol it is necessary to recycle the liquid leaving the anode 1 chamber. Methanol concentration is low (  1 moll ) to avoid high methanol losses due to cross-over. Hence, most of the recycled liquid is water. Fig. 1 shows an ADMFC connected to an anodic loop to recycle methanol solution. The gas in the flow leaving the anode needs to be removed for example by a membrane separator

Fig. 1. Schematic of an ADMFC system including fuel tank, membrane separator, mixer and ADMFC with anode, cathode and membrane electrode assembly (MEA).

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as described by Kraus and Krewer (2011). Neat methanol is mixed to the liquid in order to compensate methanol consumption. The methanol solution is then fed to the anode of the fuel cell, closing the anodic loop. The cathode is flushed with ambient air. Recycling of gas is not necessary due to abundancy of ambient air. Recycling the methanol solution at anode also effects water management. Ideally, the amount of water in the anodic loop should stay constant to prevent methanol from being diluted or concentrated. Water is produced by anode reaction, Eq. (1), and it is added by electro-osmotic water drag along with OH  -transport from cathode to anode. Water is removed from anode by diffusion through the membrane and by humidification of the produced CO2 at anode. Water transport through membrane couples water management at anode and cathode. At cathode, water is consumed due to oxygen reduction, Eq. (2), and electro-osmotic water drag. Ambient air is fed to the cathode containing only little amount of water. This inlet flow does not supply sufficient water for the reaction (Weinzierl and Krewer, 2014). In case of insufficient water supply to the cathode, oxygen reduction rate is reduced and the power of the fuel cell decreases. This reveals two big challenges regarding water management in ADMFCs: Sufficient water supply to cathode which has already been analysed in a previous study (Weinzierl and Krewer, 2014) and water level stabilisation in the anodic loop which is analysed in the present paper.

3. General mathematical model A general mathematical model that solely describes a single ADMFC with membrane electrolyte was published in our previous work (Weinzierl and Krewer, 2014). In this general model, anode and cathode are modelled as continuous stirred tank reactors and, thus, do not contain any local gradients. The membrane is included as a semipermeable volume-free wall that allows methanol and water transport. Since most experimental studies about mass

183

transport through membranes in literature use Fick's law of diffusion for determination of diffusion coefficients, methanol crossover is calculated according to Fick's law (Eq. (A.28)) even though this is a strong simplification. Calculation of water transport is described separately for each modification of this general model. It is assumed that temperature and pressure in all chambers are constant and gas and liquid phase are in equilibrium at anode. Despite diffusion of liquid components through membrane, no liquid components exist at cathode since methanol is assumed to be completely oxidised at cathodic catalyst layer persuant to Eq. (3) producing water, and liquid water is consumed by oxygen reduction reaction Eq. (2) or evaporated to the air flow. Since the model is used to analyse steady state conditions and no kinetics, reaction rates are described by Faraday's law. From this general model, two scenarios have been derived to analyse the challenge of sufficient cathodic water supply (Weinzierl and Krewer, 2014). The results of this analysis already indicate the necessity of including an anodic loop to achieve reasonable methanol efficiencies. Therefore, the above-mentioned general model is extended in the following by adding an anodic loop for liquid recycling in order to analyse water management at anode. Those equations that are modified, added to the existing model or needed for derivation of the new equations are given in the following. The remaining equations of the general model given by Weinzierl and Krewer (2014) that are also used for the modelling of the present paper are listed in A.1. A sketch of the modelled ADMFC including anodic loop in Fig. 2 shows three interconnected chambers: Anode, cathode and anodic loop. The molar balances of a general component β in anode and cathode are taken from Weinzierl and Krewer (2014): A

VA

dcβ

VC

dcβ

dt

A ¼ n_ Aβ;in  n_ Aβ;out  n_ diff β þ σβ

ð4Þ

C ¼ n_ Cβ;in  n_ Cβ;out þ n_ diff β þ σβ

ð5Þ

C

dt

Fig. 2. Sketch of the general ADMFC model including fuel cell and anodic loop. The chambers are well mixed (no local gradients) and the reactions only occur at anode and cathode.

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A=C A=C A=C with n_ β;out ¼ cβ F out

ð6Þ

cA M M β;liq n_ diff β ¼ Dβ A M d

ð7Þ

are The terms of sources and sinks σ β and the inlet flows defined in Appendix A.1. The anodic loop is solely a storage and mixing unit for methanol solution. Consequently, no reactions or phase transitions occur in the loop and no other source or sink terms appear. Hence, the molar balances of water and methanol (Me) in the anodic loop simplify to: A=C n_ β;in

L

dnH2 O ¼ n_ LH2 O;in  n_ LH2 O;out dt

ð8Þ

n_ Sys H2 O;out ¼

n_ Sys Me;out ¼

yad H2 O ad 1  yad H2 O yMe



yad H2 O;in 1  yad H2 O;in

yad Me n_ ad dry ad 1  yH2 O  yad Me

! n_ ad dry

ð12Þ

ð13Þ

Methanol concentration in the anodic loop may change during operation. As a consequence, either anodic inlet volume flow or methanol excess ratio cannot be fixed to a constant value. In this study, volume flow rate F Ain from loop to anode is kept constant during operation and is fixed to an initial methanol excess ratio of λA ðt ¼ 0Þ ¼ 10 with cAMe;in ðt ¼ 0Þ ¼ 1 moll  1 : F Ain ¼

λA ðt ¼ 0Þ AM i cAMe;in ðt

ð14Þ

¼ 0Þ 6F

The high initial value for λ is chosen in order to reduce residence time in the anode chamber and to diminish difference between concentrations in anode chamber and anodic loop. This allows consumption of most of a substance stored in the loop if its concentration decreases during operation. The consequences of the high excess ratio are discussed in the results sections. Water is solely recycled from anode and not refilled from an external source whereas a feed forward control of methanol is implemented to keep amount of methanol in the loop constant. Hereby, the amount of neat methanol fed to the anodic loop is set equal to the amount of methanol consumed by reaction, evaporation and methanol cross-over: A

L

dnMe ¼ n_ LMe;in þ n_ LMe;new  n_ LMe;out dt

ð9Þ

As shown in Fig. 2, outlet of the anodic loop is connected to inlet of the anode. Furthermore, it is assumed that gas and liquid phase are completely separated at anodic outlet. Deducting additional losses n_ Sys ζ ;out which are explained in detail later, the liquid leaving the anode is fed to the loop while the gas leaves the system. For liquid components ζ A fH2 O; Meg, it yields: n_ Lζ;in ¼ n_ Aζ;out  n_ Sys ζ ;out

ð10Þ

n_ Lζ;out ¼ n_ Aζ;in ¼ cLζ;out F Ain

ð11Þ

As discussed later, an additional gas flow can be mixed to anodic outlet causing additional losses of water and methanol. Correlation between additional losses and the dry part of the additional gas flow n_ ad dry is defined as: Table 1 Operation conditions and initial conditions used for simulation. Parameter

Value

Parameter

Value

RH Cin nLMe;0

60%

λC

10

0.5 mol

λA0

10

nLH2 O;0

26.58 mol

V L0

0.5 l

_ Sys n_ LMe;new ¼  σ AMe þ n_ co Me þ n Me;out

ð15Þ

Most parameters used for simulation are adopted from the previous paper (Weinzierl and Krewer, 2014) and listed in A.2 unless specified otherwise. Operation parameters include an operation temperature of 50 °C, a gas feed of un-humidified 1 ambient air at 1 bar to cathode and a liquid feed of 1 moll methanol solution at anode as used by Scott et al. (2008). Values for membrane thickness and water drag coefficient are based on coefficients of Tokuyama A201 membrane published by Li et al. (2010) and the used methanol diffusion coefficient given by Li and Wang (2005) is relatively low even for anion exchange membranes (compare Antolini and Gonzalez, 2010) which is beneficial for methanol efficiency. The few additional parameters and initial conditions required for the anodic loop are listed in Table 1.

Fig. 3. Structure diagram of all scenarios that are based on the same general model. Scenarios 1 and 2 are analysed previously (Weinzierl and Krewer (2014)); Scenarios 3–5 are analysed in the present paper.

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thus calculated by:

4. Modelling and analysis of different scenarios The structure diagram in Fig. 3 displays five scenarios of water management in ADMFCs. Scenarios 1 and 2 solely analyse an ADMFC fulfilling cathodic water demand in various ways (Weinzierl and Krewer, 2014). In the present paper, three further scenarios (Scenarios 3–5) are derived from the extended general model (Section 3) to study conditions for stable water level in the anodic loop. Scenario 3 satisfies cathodic water demand and also includes an anodic loop to demonstrate the importance of water level stabilisation. Scenarios 4 and 5 show two different ways of water level stabilisation in the anodic loop. The modelling of these scenarios and the analysis of the results are described in this section. All scenarios analysed in this paper are implemented in Matlab and numerically integrated with ode15s until steady state is reached or until simulation is stopped due to lack of a substance. The latter only occurs in Scenario 3. 4.1. Scenario 3 - water supply by mass transport through membrane including an anodic loop This scenario is modelled and analysed to understand the behaviour of water level in an anodic loop without active stabilisation. In this scenario, net water transport from anode to cathode is identical to water consumption and evaporation at cathode and, consequently, satisfies the demand for sufficient water supply to cathode. Mathematical modelling In order to create a scenario with methanol recycling that also fulfils the demands for sufficient water supply, the general model is modified as follows. As in Scenario 2 from the previous paper (Weinzierl and Krewer, 2014), water diffusion through membrane exactly satisfies cathodic water demand. Hence, the required water diffusion can be calculated from Eq. (5) for water in steady state: C _C _C n_ diff H2 O ¼ n H2 O;out  n H2 O;in  σ H2 Og

σ

ð16Þ

C H2 Og

is a term including all sources and sinks of water at cathode which is defined by Eq. (A.8). In the present scenario, no additional gas is added to the anodic outlet, i.e. n_ ad dry ¼ 0, and water level is not actively controlled. As a consequence, volume of the anodic loop is changing during operation depending on operation conditions. Total volume of the loop and the resulting concentrations are calculated by: VL ¼

nLMe nLH2 O þ cnMe cnH2 O

cLMe ¼

nLMe

cLH2 O ¼

VL nLH2 O VL

185

ð17Þ

ð18Þ

ð19Þ

with concentrations of pure methanol cnMe and water cnH2 O . Methanol efficiency which is used for analysis of this scenario is defined as the ratio between amount of methanol used to provide current during operation and total amount of methanol fed to the system. The latter consists of the amount of methanol inside the system at the beginning of simulation in addition to the methanol fed to anodic loop during operation. The efficiency is

iA t end 6F ηMe ¼ A Rt A A A L cMe;0 V  cMe;end V þ nMe;0 nLMe;end þ 0end n_ new Me dt

ð20Þ

The change of water level ξH2 O is defined as the ratio between water accumulation in the loop and the amount of water which initially is inside anode and anodic loop:

ξH2 O ¼

n_ AH2 O;out  n_ AH2 O;in cAH2 O;0 V A þ nLH2 O;0

ð21Þ

Results and discussion In this scenario, anodic water level can change during operation. If water level sinks, the system runs out of water and methanol concentration rises. If water level rises, methanol gets diluted and, due to the constant volume flow to anode, fuel cell runs out of methanol after some time. Simulation is stopped if one of the concentrations becomes zero or if a maximum simulation time t max ¼ 5000 h is reached. Values at the end of simulation are displayed in the graphs. This scenario is analysed for five cases with different operation conditions. The first case considers reference conditions which include methanol cross-over and evaporation to RH C ¼ 100% with C an air excess ratio of λ ¼ 10. In order to investigate the effect of methanol cross-over on the water level in the anodic loop, this process is excluded in one of the other analysed cases. The impact of water evaporation at cathode on the water level at anode is analysed by three other cases. One assumes that no evaporation at cathode takes place at all. The other two cases consider reduced C evaporation by including smaller air excess ratio of λ ¼ 4 or C assuming lower achieved relative humidity of RH ¼ 60%, respectively. Since water diffusion is assumed to exactly satisfy cathodic water demand, water diffusion rises with increasing current density and electro-osmotic drag of water does not have an influence on the anodic water level because the water dragged from cathode to anode is assumed to be transported back by diffusion according to Eq. (16). As shown in Fig. 4(a), water can be accumulated or depleted in the loop – positive or negative change of water level – depending on operation conditions. Without methanol cross-over, water depletion in the anodic loop occurs for all current densities during whole operation time as indicated by the grey dotted line. The depletion increases with increasing current density due to a rise in water consumption at cathode. E.g. at a current density of approximately i  280 mA cm  2 the loop looses 1% of the initial amount of water each hour of operation. As a consequence, methanol concentration rises until pure methanol remains with 1 cAMe ¼ 24:66 moll (Fig. 4(b)) and simulation is stopped (Fig. 4(c)) because no water is left at anode cAH2 O ¼ 0. This is only a theoretical consideration since nearly pure methanol solutions would require infinite diffusion coefficient of water which obviously is not possible in reality. Hence, fuel cell performance would drop distinctly before pure methanol is reached because of insufficient water supply to cathode. However, this scenario is supposed to demonstrate the consequences of uncontrolled anodic water level and is therefore carried to the unachievable extreme. The resulting methanol efficiency (Fig. 4(d)) is below 50% due to high methanol evaporation caused by high methanol concentration. The reference conditions include methanol cross-over which leads to a stabilising effect for small current densities (Fig. 4(a)) which is explained as follows. As in the case without methanol cross-over, water production at anode is smaller than water transport through membrane and methanol concentration rises dur-

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Fig. 4. Simulation results of Scenario 3 for the case with reference conditions (methanol cross-over and full evaporation to RHC ¼ 100% at cathode occur with λC ¼ 10), and for four other cases that differ from the reference condition in one of the mentioned conditions. (a) Change of anodic water level at the end of simulation, (b) anodic methanol concentration at the end of simulation, (c) simulated operation time of fuel cell system, maximum operation time is set to 5000 h and (d) methanol efficiency at end of simulation.

Fig. 5. Temporal change of methanol concentration for three different current densities: i ¼ 100 mA cm  2 , i ¼ 150 mA cm  2 and i ¼ 200 mA cm  2 . (a) At reference conditions (b) in case without evaporation at cathode.

ing operation (Fig. 5(a)). As a consequence, methanol cross-over is increased which results in higher water production at cathode and lower required water diffusion which slows down water depletion. Fig. 5(a) shows that methanol concentration stabilises for small current densities while simulation is stopped for a current density of 200 mA cm  2 when concentration of pure methanol is reached. Increasing current density causes an increase in steady state methanol concentration until only pure methanol is remaining

(Fig. 4(b)). Since methanol cross-over cannot increase further, further increase of current density leads to water depletion during whole operation. However, the stabilising effect causes a low methanol efficiency of below 30% for reference conditions (Fig. 4 (d)). For the cases of reduced evaporation rates, i.e. evaporation to RH C ¼ 60% and λC ¼ 4, water consumption and, accordingly, water diffusion are smaller and the stabilising effect is extended to

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higher current densities. The simulation is not stopped before the maximum simulation time (Fig. 4(c)) since final methanol concentration is smaller than concentration of pure methanol (Fig. 4 (b)) for the investigated range of current density. As such, an important feature to stabilise water level for higher current densities without active control is to decrease cathodic water evaporation. However, in case without water evaporation at cathode, the anodic loop accumulates water for all current densities (Fig. 4 (a)). The system does not reach steady state (Fig. 5(b)) and for high current densities, simulation is stopped when cAMe ¼ 0. For small current densities, the system can still be operated longer than the set maximum simulation time but Fig. 5(b) proves that no steady state is reached. Since methanol concentration is very small, methanol losses are negligible and efficiency at the end of simulation is close to 100% (Fig. 4(d)). In contrast, methanol efficiencies below 50% are achieved in the cases that lead to high methanol A concentrations. The high volume flow rate F Ain caused by λ ðt ¼ 0Þ ¼ 10 delays substance starvation since concentration of a substance needs to drop to a small value in the whole loop to cause total consumption in the anode chamber. Hence, maximum operation time decreases with decreasing volume flow rate from loop to anode if concentrations are not maintained stable during operation. It should also be mentioned that a quite low value for diffusion coefficient of methanol through membrane is used for simulations. A higher diffusion coefficient increases the effect of methanol cross-over and decreases methanol efficiency. On the other hand, higher methanol cross-over decreases the required water diffusion and, thus, water depletion is reduced. However, the qualitative statements remain same. This also holds true for the next two scenarios. It can be concluded from Scenario 3 that stabilisation of water level is essential for operation of ADMFCs with respect to stability, operation time and efficiency, if methanol solution is recycled. It should also be mentioned that high methanol concentration and high methanol cross-over are strongly detrimental to electrochemical performance and, thus, maintaining a low methanol concentration is also essential for high fuel cell performance. 4.2. Scenario 4 - water level stabilisation by diffusion through membrane Scenario 3 reveals the necessity to stabilise water level in an anodic loop in order to achieve high methanol efficiencies at long term operation. This scenario is designed to study conditions that lead to stable water level in the anodic loop and to determine the diffusion coefficient needed to stabilise anodic water level. Mathematical modelling The model of this scenario is similar to the model of Scenario 3. However, in this model, water diffusion does not fulfil cathodic water demands but stabilises anodic water level without water removal from anode: n_ Sys H2 O;out ¼ 0. Water level in the anodic loop is stable if the molar flow of water entering the loop n_ LH2 O;in is equal to the molar flow leaving the loop n_ LH2 O;out . Since these flows are coupled to the convective flows entering and leaving the anode (Eq. (10) and (11)), this constraint can be applied for the anode: n_ AH2 O;out  n_ AH2 O;in ¼ 0

ð22Þ

In order to achieve this in steady state, the amount of water received at anode needs to be equal to the amount removed from anode. Water is gained by electrochemical oxidation of methanol and by electro-osmotic water drag. Water removal at anode takes place by evaporation and by diffusion through the membrane to

187

the cathode. Hence, the mass balance Eq. (4) for water at anode in steady state including Eqs. (A.2) and (22) results in: A n_ diff H2 O ¼ σ H2 O

ð23Þ

This diffusive flux of water is required to remove sufficient amount of water from anode. Since results of diffusion experiments are usually visualized by diffusion coefficients according to Fick's law, this diffusive flux is also visualised by Fick's diffusion coefficient of water through membrane. This required diffusion coefficient to stabilise water level by sufficient water transport through membrane is calculated by: ! M yAH2 O 5i i i d DM  þ ¼ κ ð24Þ H2 O A A A 6F 1  yMe  yH O 6F F cH O;liq 2 2 The water diffusing through the membrane is partly transported back due to electro-osmotic water drag and partly consumed by the electrochemical reduction reaction Eq. (2). The remaining water at cathode gained by water diffusion and methanol oxidation needs to leave cathode in order to prevent water accumulation and flooding. It is assumed that this water evaporates, humidifying cathodic gas to a certain relative humidity. This humidity arises from the mass balance for water at cathode Eq. (5) in steady state and is calculated by: ! C yCH2 O;in yAH2 O AM i 3 λ 2 þ þ 4n_ co Me 3F 1 yAH2 O  yAMe 2 0:21 1 yCH2 O;in pC C ! RH ¼ M C A o 2yH2 O pH2 O ðT C Þ A i 3λ 1 1 þ þ3n_ co Me C A A 6F 1 yH2 O  yMe 0:21 1  yH2 O;in ð25Þ as derived in A.3. Results and discussion Since material properties and the conditions at anode (T A , pA , RH A and cAH2 O;liq ) are assumed to be constant in this scenario, the required diffusion coefficient for stable water level is solely depending on water drag and current density. Its dependency on current density is displayed in Fig. 6 (black curve) for two cases: Including electro-osmotic water drag (Fig. 6(a)) and neglecting water drag (Fig. 6(b)). It is compared to the corresponding diffusion coefficients of Scenarios 2 and 3 presented in the previous paper (grey curves in Fig. 6) at equal conditions for the cases of full evaporation and no evaporation at cathode. Diffusion coefficients below the black curves lead to water accumulation while diffusion coefficients above lead to water depletion. In case that no water drag occurs, the water diffusion needed for water level stabilisation is expectedly smaller than in the case with water drag. However, in both cases, the diffusion coefficient required to stabilise water level in the anodic loop lies in between the cases of sufficient water supply without and with full evaporation. This implies that the water diffusion which is required for stable water level also supplies sufficient water for the electrochemical reaction at cathode but not for full evaporation to 100% relative humidity for all current densities. It further implies C that no liquid water accumulates for an air excess ratio of λ ¼ 10 C since relative humidity stays below RH r 100% for all current densities. The corresponding relative humidity, calculated by Eq. (25), depends on methanol cross-over, on air excess ratio and on the conditions in the fuel cell and at the cathodic inlet. Relative humidity at cathodic inlet and in anode chamber as well as all pressures and temperatures are assumed to be constant in this study. Hence, relative humidity at cathode solely changes with current density and air excess ratio. Fig. 7 displays the relative

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Fig. 6. Diffusion coefficients of Scenario 4 (black lines) required for stable water level compared to diffusion coefficients of Scenario 2 (grey lines) required for sufficient water supply according to Weinzierl and Krewer (2014): (a) Including electro-osmotic water drag (b) without electro-osmotic water drag.

Fig. 7. Relative humidity at cathode needed for water level stabilisation in the anodic loop in Scenario 4 as a function of air excess ratio for current densities of i ¼ 4 mA cm  2 and i ¼ 400 mAcm  2 and without methanol cross-over.

humidity in the cathode chamber, which is the same as at the cathodic outlet, as a function of air excess ratio. These curves can be used to identify change in water level in real ADMFC-systems in which water diffusion does not exactly stabilise anodic water level. Relative humidities above the curves lead to water depletion while humidities below the curves result in water accumulation. The figure displays three cases: without methanol cross-over, with cross-over for a current density of i ¼ 4 mA cm  2 and with cross over for i ¼ 400 mA cm  2 . The smaller the current density, the higher is the required relative humidity in the cathode chamber. For high current densities, the curve of relative humidity converges to the case of no methanol cross-over which is independent of current density (see Eq. (25)). This is attributed to a smaller effect of the water production by methanol oxidation caused by methanol cross-over for higher current densities. Furthermore, the needed relative humidity decreases with increasing excess ratio and lies below the maximum relative humidity of RH C ¼ 100% for most air excess ratios. However, for C small λ , the corresponding relative humidity is above 100% which would cause formation of liquid water at cathode. Therefore, the minimum air excess ratio which is needed to remove sufficient C C water from cathode is λ Z 10 for i ¼ 4 mA cm  2 and λ Z 2:5 for high current densities or without methanol cross-over. A In case of a smaller methanol excess ratio, e.g. λ ¼ 4, the methanol concentration at anode decreases. As a consequence, the influence of methanol cross-over also decreases and the quantity

of the curve for small current density of i ¼ 4 mA cm  2 changes slightly. However, the tendencies and conclusions remain same. A change of methanol excess ratio has no influence on anodic water level and, thus, no influence on the required diffusion coefficient to stabilise water level. The results of this scenario assume that water diffusion through membrane is sufficient to stabilise water level at anode. Since diffusion coefficients for real material do not change with current density, comparing the value for water diffusion coefficient of a given membrane material with the black curve shown in Fig. 6 yields a maximum current density imax that allows water level stabilisation. Water diffusion coefficients through AEMs given by Li et al. (2010) are in the order of 10  6 cm  2 s  1 which allow sufficient water diffusion for stable water level for current densities up to 360 mA cm  2 as well as sufficient water supply to cathode for 400 mA cm  2. Due to the linearity of the curves in Fig. 6, achievable current densities change with the same factor as the water diffusion coefficient. For higher current densities than imax , water will be accumulated in the anodic loop. Current densities below imax might cause water depletion in the loop. However, diffusion also depends on the concentration gradient which is diminished if water concentration at anode is decreased or concentration at cathode is increased. The latter happens if spare water at cathode is not evaporated but stays in the electrolyte membrane as liquid water. As a result, water diffusion through membrane will decrease and adjust itself to the required value. If this self adjusting effect fails, excess water needs to be removed from cathode to avoid flooding and water recovery from cathodic exhaust gas as described by Zenith et al. (2012) is required. Humidification of inlet gas decreases water evaporation and can help to diminish water loss for current densities below imax but needs to be considered when adjusting air excess ratio and relative humidity according to Fig. 7. Optimal inlet gas humidification depends on fuel cell structure and used materials and cannot be generalised. Though, according to Fig. 7, inlet humidity at cell C temperature above 70% for λ  10 would definitely lead to water accumulation. For current densities above imax , humidification of cathodic inlet gas up to RH C ¼ 100% at cell temperature might help for cathodic water supply. However, these conditions definitely lead to water accumulation at anode and require further water removal to stabilise anodic water level. 4.3. Scenario 5 - water removal at anodic outlet Scenario 4 reveals that water level stabilisation by sufficient water diffusion through membrane is limited to current densities

C. Weinzierl, U. Krewer / Chemical Engineering Science 143 (2016) 181–193

below a maximum value imax which depends on the diffusion coefficient of water through membrane. Current densities above imax lead to water accumulation in the anodic loop and water needs to be removed from anode in addition to water diffusion. Scenario 5 is modelled to analyse the possibility of removing water from anodic outlet. Mathematical modelling The model of this scenario includes an active stabilisation of water level in the anodic loop by feeding an additional gas flow n_ ad gas to the anodic outlet in order to evaporate excess water. Subsequently, liquid and gas are separated (see Fig. 2). Liquid is recycled while gas including additionally evaporated water n_ Sys H2 O;out is removed from the system. For stable water level, the molar flow of recycled liquid water fed to anodic loop needs to be equal to molar flow of water leaving the loop which is equal to the flow fed to anode: n_ LH2 O;in ¼ n_ LH2 O;out ¼ n_ AH2 O;in

ð26Þ

Combining this equation with Eq. (10) results in: _A _A n_ Sys H2 O;out ¼ n H2 O;out  n H2 O;in

ð27Þ

The molar flow that has to be removed from system can be calculated by including this equation in the mass balance of water at anode, Eq. (4), in steady state: A _ diff n_ Sys H2 O;out ¼ σ H2 O  n H2 O

ð28Þ

As in Scenario 3, water diffusion is assumed to satisfy cathodic water demand and is calculated by Eq. (16). It is assumed that additional gas is fed to anodic outlet with ad T ad in ¼ 293:15 K and RH in ¼ 60% and that it is saturated with water at anode temperature T A ¼ 323:15 K when leaving the system. Thus, the molar flow of additional gas n_ ad gas required to remove excess water is calculated as follows: n_ ad gas ¼

ad 1  yad H2 O  yMe ad ad ad yad H2 O  yH2 O;in þ yH2 O;in yMe

n_ Sys H2 O;out

ð29Þ

The derivation of this equation is displayed in A.3. The additional gas also causes evaporation of methanol which is leaving the system along with the evaporated water. This additional loss of methanol is calculated by Eq. (13). The resulting methanol efficiency is calculated by: AM i 6F ηMe ¼ co n_ Me  σ AMe þ n_ Sys Me;out

ð30Þ

Additional parameters needed to simulate this scenario are listed in Table 2. Results and discussion In this scenario, it is again assumed that water diffusion satisfies cathodic water demand and, thus, depends on current density, water drag, evaporation and methanol cross-over. Due to this definition, water dragged from cathode to anode is assumed to be transported back by diffusion. Consequently, electro-osmotic Table 2 Additional parameters used for simulation of Scenario 5. Parameter

Value

Parameter

Value

RH ad in

60%

T ad in

293.15 K

pad in

1 bar

RH ad

100%

189

water drag does not influence the anode and is neglected in this scenario. In reality, water diffusion is not adjusted to water consumption and, thus, water drag influences anodic water level. Hence, this scenario is a qualitative study. Conditions that lead to water accumulation in Scenario 3 and, hence, need additional water removal from anodic loop are chosen as reference conditions for the analysis of this scenario. These conditions include that methanol cross-over occurs, but no evaporation takes place at cathode, and that water is removed from anodic loop as water vapour with RHad ¼ 100%. The scenario is further analysed for three other cases which differ from reference conditions in one of the mentioned conditions. One case assumes that cathodic air is humidified to RH C ¼ 30%. As a consequence, water diffusion is increased to satisfy both reaction and evaporation. Partial humidification can happen in real systems e.g. if water diffusion is bigger than water consumption at cathode by electrochemical reaction and the cathodic gas takes up some excess water. Another case implies that additional gas is only humidified to RH ad ¼ 80% and, thus, a higher flow rate of additional gas is needed. Finally, the influence of methanol cross-over on the results is analysed by a case that excludes methanol cross-over. Water production at anode is proportional to current density. Consequently, additional water evaporation needs to increase with rising current density as shown in Fig. 8(a). This increase is nearly linear for high current densities and has an offset for the case without methanol cross-over which is equal to the water production by methanol oxidation at cathode. For very low current densities, the curves for the cases that include methanol crossover in Fig. 8(a) show non-linear behaviour which is caused by the strong influence of methanol cross-over at low current densities. In the case that cathodic gas is partly humidified, only little amount of water needs to be removed from anodic loop. The achieved relative humidity in the additional gas flow has no impact on the required additional water evaporation. Fig. 8(b) displays the corresponding additional gas flow which is required to evaporate excess water as a function of current C density as well as the cathodic air flow for λ ¼ 10 for comparison. ad n_ gas shows similar behaviour as the additional water evaporation. For reference conditions, it is about 25% of cathodic air flow for λC ¼ 10. In case of water evaporation at cathode to RH C ¼ 30%, a much lower additional gas flow is needed than at reference conditions, since water is already removed by diffusion through membrane. Reduction of achieved humidity to RH ad ¼ 80% requires a higher additional gas flow because the same gas flow takes up less water. Furthermore, the gas flow also needs to be slightly lower if no methanol cross-over occurs since water diffusion is slightly higher in that case. However, in all cases, the required additional gas flow is much smaller than cathodic gas C flow with λ ¼ 10 for all relevant current densities. Thus, cathodic gas flow is sufficient for water removal which can be realised by mixing part of cathodic outlet to anodic outlet. This is similar to a water transport through membrane with subsequent evaporation at the cathode as described in Scenario 4 (Fig. 7). Nevertheless, there is a large difference between Scenario 4 and Scenario 5. Feeding additional gas to anodic outlet also leads to evaporation of methanol and, thus, decreases methanol efficiency. The additional efficiency losses caused by additional methanol evaporation may reach up to 20%. This is indicated by Fig. 8(c) which displays the corresponding methanol efficiencies. In the case without methanol cross-over, methanol efficiency is not changing with current density because all terms in Eq. (30) are directly proportional to current density which can be cancelled causing methanol efficiency to be independent of current density. The additional efficiency loss in case of reference conditions is approximately 10%. This efficiency loss is increased if lower

190

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Fig. 8. Results of Scenario 5 for reference conditions: methanol cross-over occurs, cathodic gas is not humidified and water is removed with RH ad ¼ 100%, and for three other cases that differ from reference conditions in one of the mentioned conditions: (a) Amount of water that needs to be evaporated to stabilise water level, (b) required additional gas flow to evaporate sufficient water and, for comparison, cathodic gas flow for λC ¼ 10, (c) resulting methanol efficiency.

relative humidities are achieved due to a higher required additional gas flow. However, these efficiencies are acceptable especially compared to those obtained due to the stabilising effect in Scenario 3 (see Fig. 4(d)). In case that water level in the anodic loop is stabilised, methanol excess ratio can be decreased. This results in a lower methanol concentration at anode and a higher methanol efficiency.

All scenarios identify the membrane as the key component for water management in ADMFCs and, in order to enable stable operation and high efficiencies, water diffusion through membrane should be considered when developing new anion exchange membranes.

Appendix A. Additional equations, parameters and derivations 5. Conclusions

A.1. Additional model equations

Stabilising water level at anode is essential for methanol efficiencies during long term operation of ADMFCs if methanol solution is recycled by an anodic loop. Water diffusion coefficient and thickness of membrane define a maximum current density above which diffusion through membrane cannot sufficiently remove excess amount of water from anode. For current densities below maximum current density, water level can be stabilised by adjusting relative humidity and gas flow rate at cathode and, thus, controlling the amount of water removed from system. Current densities above the maximum current density require active water removal from anodic loop which is coupled with an additional loss of methanol. Since active water removal from anode complicates the fuel cell system and reduces methanol efficiency, water removal from anode should preferably be realised by diffusion through membrane as described by Scenario 4 and only extended by direct water removal from anode as described by Scenario 5 if necessary.

The following equations constitute the general model of the previous study (Weinzierl and Krewer, 2014) and are also part of the extended general model of the present paper. Sources and sinks:

σ AMe ¼ 

σ AH2 O ¼

yAMeg AM i  6F 1  yAMeg  yAH

yAH Og 5AM i 2  A 6F 1  yMeg  yAH

σ ACO2 ¼

AM i 6F

σ AMeg ¼

yAMeg A 1  yMeg  yAH Og 2

AM i 6F Og

ðA:1Þ

AM i AM i þκ 6F F Og

ðA:2Þ

2

2

ðA:3Þ AM i 6F

ðA:4Þ

C. Weinzierl, U. Krewer / Chemical Engineering Science 143 (2016) 181–193

yAH

AM i 1  yAMeg  yAH Og 6F

σ AH2 Og ¼

g 2O

ðA:5Þ

n_ Cdry;out ¼ n_ Cdry;in 

ðA:6Þ

n_ CH2 Og ;in=out ¼

191

AM i 1 co  n_ 4F 2 Me

ðA:26Þ

2

σ CN2 ¼ 0 σ CO2 ¼  σ

M

A i 3 co  n_ 4F 2 Me

ðA:7Þ

M

M n_ co Me ¼ DMe

M

A i A i þ 2n_ co ¼ Me  κ 2F F

C H2 Og

σ CCO2 ¼ n_ co Me

ðA:8Þ ðA:9Þ

Conditions inside the chambers and at the cathodic inlet: ðcACO2

V Agas ¼

þ cAMeg þ cAH Og Þ A 2 V nA cgas

V Aliq ¼ V A  V Agas cAβ;liq ¼

cAH2 O V A

ðA:13Þ

V Aliq

pA=C

nA=C

ðA:14Þ

RT A=C

yAβ ¼ X β

yβðinÞ ¼

ðA:12Þ

V Aliq

cgas ¼

C

ðA:11Þ

cAβ V A

cAH2 O;liq ¼

ðA:10Þ

yCH

2O

1  yCH

g

;in=out

n_ Cdry;in=out

ðA:27Þ

g 2 O ;in=out

AM d

cA M Me;liq

ðA:28Þ

A.2. Parameters from general model The parameters of the general model used by Weinzierl and Krewer (2014) which are also used to simulate the scenarios of this paper are listed below: Data on chemical media: AMe BMe C Me DMe AH2 O BH2 O

 8.54582 0.67266  2.54743  2.71874  7.71374 1.31467

C H2 O DH2 O

 2.51444  1.72542

T crit Me

512.5 K

DM Me pcrit Me

T crit H2 O

647.1 K

pcrit H2 O

32.04 g mol  1 18.02 g mol  1 44.01 g mol  1 32.00 g mol  1 24.66 mol l  1 55.4 mol l  1

M Me M H2 O M CO2 M O2 cnMe cnH2 O

κ

4 1.23  10  7 cm2 s  1 80:8  105 Pa 220:6  105 Pa

Physical constants and geometry parameters:

poβ ðT A Þ

ðA:15Þ

pA

F

96485 As mol  1 12.5 ml

VA

poβ ðT CðinÞ Þ RH CðinÞ pCðinÞ

ðA:16Þ

M

25 cm

A

2

R

8.31 J mol  1K  1

VC

12.5 ml

d

30 μm

M

Operation, initial and inlet conditions: X H2 O ¼

cAH2 O

ðA:17Þ

cAMe þ cAH2 O

X Me ¼ 1  X H2 O

ðA:18Þ "

1  A ð1  T r;β Þ þ Bβ ð1  T r;β Þ1:5 poβ ðTÞ ¼ pcrit exp T r;β β  þ C β ð1  T r;β Þ3 þ Dβ ð1  T r;β Þ6  T r;β ¼

T

F Aout ¼ F Ain 

F Cout ¼

cnH2 O



n_ co Me cnMe

n_ diff H O F Cin þ nC2 C cH Og pC T in 2 pCin T C

λC AM i

þ

þ

X σ Aβ nA β cβ

X σ Cβ nC

β cβ

ðA:19Þ

ðA:21Þ

ðA:22Þ

323.15 K

1.013 bar

T Cin

293 K

RH A

100%

λC

10

1

¼

n_ CO2 ;in

¼ 0:21 n_ Cdry;in

ðA:24Þ

n_ CN2 ;in ¼ 0:79 n_ Cdry;in

ðA:25Þ

ðA:23Þ

cCO2 ;0=in

1 mol l 53.15 mol l  1

cACO2 ;0=in cAH Og ;0=in 2 cAMeg ;0=in

0 mol l

1

0 mol l

1

0 mol l  1

7.92  10  3 mol l  1

cCN2 0=in

29.8  10  3 mol l  1

cCCO2 ;0=in cCH Og ;0=in 2

0 mol l  1

0 mol l  1

A.3. Derivations of equations of the scenarios The equation to calculate the relative humidity at cathode required in Scenario 4 to remove sufficient water is derived in the following. Starting with the molar balance of water at cathode Eq. (5) in steady state and including Eq. (A.27) leads to: C 0 ¼ n_ CH2 O;in  n_ CH2 O;out þ n_ diff H2 O þ σ H2 Og

0¼

n_ Cdry;in

0:21 4F

T A=C

cAH2 O;0=in

The vapour pressure is described by the Wagner equation Eq. (A.19) taken from Verein Deutscher Ingenieure, VDI-Gesellschaft Verfahrenstechnik und Chemie Ingenieurwesen GVC (2006). Volume and molar flows: n_ diff H2 O

1.013 bar

pCin cAMe;0=in ;

ðA:20Þ

T crit β

pA=C

yCH2 O;in 1 yCH2 O;in

n_ Cdry;in 

yCH2 O 1  yCH2 O

n_ Cdry;out þ σ AH2 O þ σ CH2 Og

Considering Eqs. (A.2), (A.8), (A.23) and (A.26) results in: ! yCH2 O;in yCH2 O λC AM i λC AM i AM i 1 _ co    n 0¼ þ… 4F 2 Me 1 yCH O;in 0:21 4F 1  yCH O 0:21 4F 2

2

ðA:29Þ

ðA:30Þ

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C. Weinzierl, U. Krewer / Chemical Engineering Science 143 (2016) 181–193

yAH Og 5AM i 2  …þ A 6F 1  yMeg  yAH

2

! AM i AM i þκ þ 6F F Og

! AM i AM i co _  þ 2n Me  κ 2F F

) yCH2 O ¼

A i 3F AM i 6F

!

C yAH Og yCH2 O;in 3 2 2 þ þ 4n_ co Me C 1  yAMeg  yAH Og 1  yH2 O;in 0:21 2 2 ! C 2yAH Og 3 1 2 1 þ þ 3n_ co Me A A 1  yMeg  yH Og 0:21 1  yCH2 O;in 2

λ

λ

Including Eq. (A.16) results in Eq. (25) to calculate the resulting relative humidity at cathode: ! C yAH Og yCH2 O;in AM i 3 λ 2 2 þ 4n_ co þ Me o A A 3F 2 0:21 1  yCH O;in 1  y g y g pH2 O ðT C Þ Me O H 2 2 ! ) RH C ¼ A C M pC 2yH Og A i 3λ 1 2 1 þ 3n_ co þ Me C A A 6F 1  yMeg  yH Og 0:21 1  yH2 O;in 2

The molar flow of dry gas that needs to be added to anode outlet in order to remove excess water in Scenario 5 (Eq. (29)) is derived in the following. The amount of water that is evaporated by the additional gas is supposed to be equal to the amount that needs to be removed:

¼

yad H2 O

yad H2 O;in

! n_ ad dry

 ad 1 yad 1  yad H O  yMe H2 O;in 2   1 0 ad ad ad ad  y yad 1 y n_ ad H2 O H2 O;in H2 O;in 1  yH2 O  yMe dry A ¼@ ad ad 1  yad 1  yH2 O  yMe H2 O;in ! ad ad ad yad  y þ y y H2 O H2 O;in H2 O;in Me ¼ n_ ad gas;in ad 1  yad H2 O  yMe ) n_ ad gas;in ¼

ad 1  yad H2 O yMe n_ Sys H2 O;out ad ad ad yH2 O  yH2 O;in þ yH2 O;in yad Me

Appendix B. Nomenclature area of membrane (m2 ) AM Aβ , Bβ , C β , Dβ Wagner coefficients of component β for vapour pressure cβ concentration of component β in mol l  1

β in mol l β through

cnβ

concentration of pure substance

DM β

diffusion coefficient of component membrane in m2 s  1 thickness of membrane in m

M

d F F in=out i nβ n_ β n_ new Me p poβ ðTÞ RH T Tr t t max

mole fraction of component

β in liquid phase

ηMe κ λ σβ

Superscripts A ad C co crit diff drag g L M Sys

methanol efficiency water drag coefficient excess ratio of reactant sources and sinks of component

β in mol s  1

at anode additional at cathode cross-over critical value diffusion electro-osmotic water drag vapour in loop membrane system

Subscripts

_ ad g _ ad g n_ Sys H2 O;out ¼ n H2 O ;out  n H2 O ;in n_ Sys H2 O;out

volume in m3 mole fraction in gas phase

Greek

Rearranging this equation yields: M

V y Xβ

1

Faraday constant in As mol  1 volume flow rate at inlet/outlet in m3 s  1 current density in A m  2 amount of substance of component

β in mol

molar flow of component β in mol s  1 molar flow of neat methanol to the loop in mol s1 pressure in Pa vapour pressure of β at temperature T in Pa relative humidity in % temperature in K temperature related to critical temperature time in s maximal simulated operation time in s

β ζ

general component

0 dry end evap gas in liq max out Me Meg CO2 H2O H2Og N2 O2

at start of simulation dry gas at end of simulation evaporation of gas phase at inlet of liquid phase maximum at outlet methanol methanol vapour carbon dioxide water water vapour nitrogen oxygen

Abbreviations AEM ADMFC AFC DMFC MEA

anion exchange membrane alkaline direct methanol fuel cell alkaline fuel cell direc methanol fuel cell membrane electrode assembly

liquid component

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