VII – CONCLUSIONS

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A. Bertei VII – CONCLUSIONS

183

VII – CONCLUSIONS

VII.1 – Conclusions on simulation results; VII.2 – General conclusions on the model; VII.3 – Future developments; VII.4 – References.

VII.1 – Conclusions on simulation results

It is possible to draw some conclusions concerning simulations results performed in the base-case. In particular, it is important to emphasize that base-case represents a situation close to the actual state of the art, i.e. properties of the CM and working conditions are quite the same used in experiments with real samples of IDEAL-Cell.

The main feature of the base-case is that it is in ohmic regime (par. VI.3), i.e. ohmic resistances are the main source of energy loss in the CM. In this situation, reaction occurs only in the proximity of CM-electrolytes interfaces while the internal part of the membrane is useless for the happening of the reaction (i.e. it contributes to increase ohmic losses). Moreover, this yields low gradients of pressure and molar fraction of water; in particular, evacuation of water is not problematic and it is mainly due to diffusion in gas phase.

In order to improve the performance of the CM, a design analysis has been performed (par. VI.5). The performances of the central membrane are expected to increase significantly for a decrease of porosity (fig. VI.14) and of the thickness down to about 130

µ

m as in fig. VI.18; radius of CM and mean dimension of particles have a smaller influence on global performance. Thus, it is important to exit from ohmic regime.

Simulation results are submitted on several unknown or uncertain parameters, in particular:

• exchange current i0: the global performance of the CM is strongly dependent on

this parameter (fig. VI.6). The value i0 = 8·10-9A/m, estimated in par. VI.2 for the

system BCY15-YDC15 at 873K by best fitting with experimental polarization curves made for 2 different samples, is only a rough estimation because it is difficult to determine the kinetics of water recombination reaction in ohmic regime. In particular, 8·10-9A/m is the minimum value, i.e. it is reasonable that i0

will be equal or higher than the value assumed in simulations. A more accurate estimation of i0 is needed and it can be performed by comparison of experimental

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184 and simulated results in kinetic regime, i.e. by using samples of CM with thickness in the order of 100

µ

m or less;

• kinetic constant of water adsorption kd: it is an unknown parameter, at the

moment a guess value 5·10-13mol/(m2_{·Pa·s) is used for BCY15 at 873K.} Sensitivity analysis (sec. VI.4.2) shows that kd is not a key parameter but it affects

pressure and molar fraction of water in gas phase and, obviously, the distribution of water adsorbed in PCP; so it could have a significant role in gas transport regime. Specific measurements on materials are needed in order to obtain this kinetic parameter;

• capacitance of double layer cdl: we set cdl = 5·10-2C/(m2·V) in simulations but it is

a guess. It has a role only in dynamics (i.e. in impedance curves). It will be estimated by comparison between simulated and experimental impedance curves after the validation of the model (i.e. when other parameters will be known);

• correction factor for apparent conductivity σapp/σ: it is an uncertain parameter estimated by computer simulations made on ordered structures (par. III.4). It is a key parameter (fig. VI.9), especially when CM is in ohmic regime, so a more accurate investigation is needed. In theory, it is possible to correlate σapp/σ with composition of the mixture, granulometric distribution of particles and mean angle of contact. The dependence of σapp/σ on these parameters can be revealed by experimental measurements of conductivity on packing of overlapping particles (as in sec. III.4.1, in particular fig. III.16) or by computer simulations (as described by Choi et al, 2009);

Thus, more experimental investigations are needed in order to estimate unknown parameters and to check uncertain parameters. It is important to emphasize that experiments can be performed by using the existing set up (par. II.8). Our suggestion is to use wet nitrogen in the third chamber (in particular with a molar fraction of water in the order of 0.03-0.05) and to wait stabilization time before starting impedance measurements (see par. V.7) in order to obtain stable and reproducible results.

Only after a stronger validation of the model and estimation of parameters a more accurate design analysis will be possible. Due to the rough knowledge of the system and the lack of specific experimental measurements on properties of materials (useful to estimate unknown parameters) and on performances of samples not in ohmic regime (useful to validate the model), the performed design analysis is indicative. This does not

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185 mean that the model does not work well but that in order to optimize cell design the model needs good estimations of parameters.

VII.2 – General conclusions on the model

The model presented takes into account several phenomena occurring in the central membrane as charge transport, electrochemical kinetics, gas transport and adsorption of water in PCP. For each phenomenon a physical description has been performed and, according to this description, a submodel of behaviour has been proposed according to existing elementary models in literature (e.g. Dusty Gas model to describe gas transport). Each submodel is consistent with experimental evidences and has been used to derive constitutive laws such as equations of transport and kinetics. These mathematical relationships enter in the model of the CM, that is made of charge and mass balances. Due to this approach, the model is therefore mechanistic and not a representation of the CM by an equivalent circuit.

The model is based on several assumptions, the strongest one is to model the CM as a continuum with uniform morphological properties by using consistent balance equations and apparent properties. Moreover, reaction is assumed to occur at the TPB following a Butler and Volmer kinetics while water adsorption in PCP follows a kinetic law consistent with its equilibrium description; mixed conduction of both ionic species is neglected in both solid phases. It is straightforward to understand that the model may use other kinetic laws or different equations of transport (e.g. a different kinetics for water recombination reaction).

The model can be used to perform steady-state or dynamic simulations, in particular polarization and impedance curves in different conditions can be obtained. Simulations are used both to interpret experimental results and to predict performance in order to optimize the design of the central membrane.

VII.3 – Future developments

The determination of unknown parameters by specific measurements, such as the estimation of the adsorption kinetics and of the water recombination kinetics, is of primary importance to have the knowledge of all parameters that the model needs. It is also important to obtain a stronger validation of the specific model for the determination

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186 of morphological properties and, in particular, the estimation of apparent conductivity: simulation results of the model of the central membrane are strictly dependent on parameters that come from the morphological description of the system. In this direction, tomographic measurements will be very useful to determine first of all the sintering effects (i.e. angles of contact among particles, mean dimensions of grains, etc.) and also to estimate functional parameters (e.g. length of TPB per unit volume) in order to compare theoretical results, obtained with percolation theory or computer simulations (as in chap. III), with results from image analysis.

In the following, a stronger validation of the model of the central membrane will be possible. In particular, it is important to validate the model with different samples in different conditions, i.e. in different regimes (ohmic, kinetic or gas transport regime). More experimental measurements are needed not only to validate the model but also to understand if other phenomena, not considered yet, characterize the central membrane.

After this step, the model will be used for the design in order to increase the performances of the system. So, indications on materials, geometry, morphology, procedures and manufacturing of the central membrane will lead to the optimization of the system. In this procedure, simulations of impedance curves will have a central role because they describe the stationary and the dynamic behaviour of the system.

VII.4 – References

Choi H.W., Berson A., Kenney B., Pharoah J.G., Beale S., Karan K., “Effective

Transport Coefficients for Porous Microstructures in Solid Oxide Fuel Cells”,