Simulation predictions

The central result of the developed simulation is the prediction of the sorption behaviour of the storage system, which must be validated on the basis of experimental results. The comparison of simulation results and experiments supports the determination of suitable assumptions of parameters and conditions for reliable simulations. The boundary condition of the energy equation at the interior of the sintered metal filter (B1, see Fig. 4.3) is taken as example to illustrate the effect of different assumptions on the simulation results. In particular, the definition of this boundary condition may be ambiguous, and the validation should hint at the most suitable assumption. The predictions from the simulation and the experimental results obtained in the tank station are plotted in Fig. 4.4. The assumptions of the simulations in Fig. 4.4 are described in Table 4.6. A further feature of the simulation is the prediction of the porosity of the hydride bed. Figure 4.5 shows the profile of the predicted porosity of the hydride bed during the absorption.

Table 4.6: Assumptions for the evaluated simulations presented in Fig. 4.4

Simulation Boundary condition assumption for heat transfer at B1 (see Fig. 4.3)

SIM-1

Heat flux

       

1 1 B

B p g g

inlet eff g g

p T u T c T u

c







SIM-2

Convective flux

  ⁰

n





SIM-3

Constant temperature

inlet

T

T _B1 ; T _inlet 80 °C

Figure 4.4: Experimental and predicted absorption behaviour in the tubular reactor filled with sodium alanate material: (a) absorbed hydrogen content and (b) course of temperature evolution close to the sintered metal filter

The simulation results of desorption are shown in Fig. 4.6. Boundary condition for the heat transfer at the interior of the sintered metal filter, interface B1 in Fig. 4.3, is redefined for desorption, since in this case the temperature of the hydrogen flowing out corresponds to the same temperature as at this interface (in the case of absorption the temperature of the hydrogen flowing into the sintered filter was different as the temperature at this interface).

Figure 4.6: Experimental and predicted desorption behaviour in the tubular reactor filled with sodium alanate material: (a) total hydrogen content and (b) course of temperature evolution close to the sintered metal filter

Figure 4.5: Evolution of the porosity according to absorption simulation results

4.2.5 Discussion

Figure 4.4 reveals that best predictions of the experimental results are obtained with the assumptions of simulation SIM-1, in terms of hydrogen sorption behaviour and achieved hydrogen contents, and specifically the profile of the temperature close to the sintered metal filter. SIM-2, in which the cooling effect of the hydrogen inlet-flow is neglected, predicts higher temperature levels. SIM-3, on the other hand, overestimates this cooling effect. The boundary condition of SIM-1 for the energy transport is called Danckwerts condition and was theoretically proposed for the inlet interface of metal hydride storage tanks by Na Ranong [65]. The present results validate the suitable boundary conditions of SIM-1 and therefore it is chosen as the final valid simulation for further analysis. On its basis, the predicted temperature field of the tubular tank during absorption is presented in Fig. 4.7.

Initially the hydride bed is isothermal, Fig. 4.7a. When the absorption proceeds, Fig. 4.7b and 4.7c, the released heat of reaction increases the temperature of the bed of hydride and its hottest region is located at a middle radius between the tank wall and the sintered filter. The lower temperature level close to the sintered filter is explained by the convective cooling effect of the hydrogen inlet-flow at the beginning of the absorption. Later on during the absorption, Fig. 4.7d and Fig. 4.7e, the hottest region shifts inwards to the sintered metal filter, because the total hydrogen inlet-flow diminishes and consequently its cooling effect. On the other hand, the coldest region in the hydride bed is close to the tank wall. Although at some moment the temperature in some part of the hydride bed is higher than the equilibrium value for the second absorption step, further reaction is predicted. This can happen since in some other regions of the hydride bed the temperature does not increase beyond this equilibrium value. The temperature of the tank wall remains practically constant and almost identical to the temperature of the heat transfer oil in this example. In contrast to the hydride bed, the thermal conductivity of the tank wall is higher and does not have any heat source. As expected from the resistance analysis of Fig. 4.2, heat transfer through the bed has a strong effect on the sorption performance of the hydride bed. The simulation confirms the resistance analysis also by the predicted pressure gradients in the hydride bed. The analysis predicted a negligible resistance due to hydrogen transport, confirmed by the extremely low pressure gradient in the reactor in the results of the simulated sorption. Nevertheless, it must be stressed that simulation of the hydrogen transport is required due to the heat convection from hydrogen flow, with stronger effect at the beginning of the sorption process. The determined most suitable boundary condition of heat transfer in the inner boundary (B1 in Fig. 4.3) of the simulation strengthens this requirement.

The porosity of the hydride bed changes as the absorption proceeds, Figure 4.5. The simulation does not assume constant bulk density and thus neither constant porosity of the hydride bed. The porosity depends on the mass concentrations and solid densities of the materials, as shown in Eqs. 4.25 to 4.27.

The porosity changes from 70 %, initial state of the hydride bed, to 59 %, final state of the hydride bed. This is due to the lower solid density of the material at the desorbed state in comparison to the absorbed state, also enhanced by the higher total solid mass of the system at the desorbed state.

The simulation results of desorption, Fig. 4.6, show that both predicted temperature profiles and hydrogen content are in good agreement with the experimental results. Heat transfer is not decisive, as desorption is not expected to occur in short time periods. A temperature decrease of only 30 °C during the first part of desorption is predicted, even by high rates of desorption. As desorption proceeds, e.g.

after 10 minutes, no noticeable temperature decrease is observed. In other applications at which desorption proceed at a constant rate, smaller temperature decreases may be expected that actually do not influence the overall rate of hydrogen desorption. Further implementation of desorption simulations are e.g. simulations of system integrations of the hydrogen storage tanks being heated-up by the waste heat coming out of hydrogen-based fuel cells.

a bb cc

dd ee f

Figure 4.7: Temperature profile of the tubular reactor at different times according to simulation SIM-1: (a) 0.1 min, (b) 1 min, (c) 1.5 min, (d) 2 min, (e) 3 min, (f) 10 min

with sodium alanate material

The use of sodium alanate in a practical hydrogen storage system requires the highest gravimetric capacity and volumetric capacity as possible. This chapter presents combined approaches that optimise hydrogen storage systems based on sodium alanate material. In the first Section of the Chapter, optimisation of the volumetric hydrogen storage capacity is experimentally demonstrated by powder