Results and discussions

Based on experiments carried out by the Hydrogen Research Institute of the University of Quebee at Trois-Rivieres, a lab-seale model with a volume of 2.5 L was developed and discussed in our early works [7, 8l . The small hydrogen storage tank was cooled by ice water [7J and liquid nitrogen [8] respeetively. The model established in Comsol was validated by comparing the simulation resu1ts with the experiment data. The large-scale hydrogen delivery tank with a volume of 51.4 m3 is unfit for realistie experiments and measurements. However, the validated model can be extended to simulate a large-scale hydrogen delivery tanle In addition, the large-scale model can be used to study the thermal effects during the charging process and improve the efficiency of hydrogen delivery tanks. Hydrogen can be viewed from a modeling perspective as existing in the storage tank in the form of an adsorbed phase and a gaseous phase. Fig.2.2a shows the variation of pressure during the charging process and the mass balance of hydrogen in the tank. In this work, the target pressure is set to 10 MPa, the mass flow rate is equal to 10 000 SLPM (about 0.013907 kg/s), and the temperature of hydrogen filling in charging process is set to 298 K. It takes 29 140 s to reach the target pressure. Fig.2.2a also shows the pressure during the filling process, which increases linearly.

The parameter mg represents the mass in the gas phase, the ma represents the mass of hydrogen adsorbed by activated carbon bed, and the ml is the total mass of hydrogen present in the tank. The initial mass ofhydrogen stored in the tank was 3.2379 kg. The simulation results indicate that the sum of ma and mg is equal to ml. The total mass of hydrogen is approximately equal to 408 kg wh en the pressure reaches to 10 MPa. Fig.2.2b shows the evolution of the temperature at different monitor points. The 6 monitor points are located along the axial direction from Tl to T6, and 4 monitor points are located along the radial direction from T6 to T9. The temperature monitor point T8 is placed on the internai steel wall, and T9 close to the outside steel wall. During the charging process, the temperature in the hydrogen storage tank increases as a result of adsorption heat revealed and pressure work. The curves oftemperature at Tl , T2 and T3 rise quickly in the earlier process, and the changes are relatively tiny in the latter process. The temperature of the area near the inlet is greatly influenced by the filling hydrogen, and the variation oftemperature at T5, T6 and sorne other position along the axial direction trend to be uniform. The curves of tempe rature at T6 and T7 are broadly similar, but obviously different from those of T8 and T9. In other words, the heat generated in the tank is not transferred effectively to the environment along with radial direction due to the poor thermal conductivity of activated carbon.

Thermodynamic analysis for hydrogen storage system using metal hydride This section has been published in: Xiao J S, Tong L, Bénard P, et al. Thermodynamic analysis for hydriding-dehydriding cycle of metal hydride system. Energy 2019. https://doi .orgIl0.1016/j .energy.2019.116535. My specific contributions in this work was to obtain analytical solutions of thermodynamic model for metal hydride system, which can be used as a basic benchmarks to validate numerical models. In general, a mathematical model can be a lumped parameter model (O-dimensional in space, expressed as an ordinary differential equation on time) or a distributed parameter model (1-, 2- or 3-dimensional in space, expressed as a partial differential equation on time and space), and they can be solved numerically and sometimes analytically. Among them, the lumped parameter model has more possibilities to be solved analytically. A numerical model is a mathematical model whose solution relies on numerical methods and algorithms, such as the Euler method or Runge-Kutta method for ordinary differential equation (ODE) model, finite difference method or finite element method for partial differential equation (PDE) model. A numerical model, either a lumped parameter model or a distributed parameter model, can be validated by analytical solutions under simplified boundary conditions and material properties.

Considering an example of heat conduction of a metal hydride reactor, a distributed parameter model will reduce to a lumped parameter model wh en a uniform boundary condition and an infinity thermal conductivity is applied to the reactor. From the point of engineering applications, the numerical model should be further validated by experiments. The analytical solutions are solved from the thermodynamic model based on the principles of mass conservation and energy conservation under certain assumptions of conditions. Although these analytical solutions are applicable for ideal or theoretical problems only and not for real engineering problems, they are exactly correct under the assumed conditions and they can be used to validate numerical models by comparing the numerical solutions of the numerical models for the same problems with same conditions. Analytical solutions are valid un der the assumptions they are obtained and do not need to be validated experimentally,especially since the idealized conditions required for their solution are difficult to reproduce in experiments.

We have developed validated lumped parameter models to study the performances of hydrogen storage and purification systems using metal hydrides [601. In addition, sorne thermodynamics models and analytical solutions for the compressed and adsorptive hydrogen storage systems were developed and studied in previous works [13, 141. The metal hydride hydrogen storage system is based on the hydriding-dehydriding chemical reaction, which is more complicated than the compressed and adsorptive hydrogen storage systems. The analytical solutions for the metal hydride hydrogen st orage system are important to understand the hydriding-dehydriding process and the basic theory. The analytical solutions can be considered as a benchmark to validate lumped parameter or distributed parameter numerical models, reducing the need for extensive sets of experimental data required for validation. In this section, based on the mass and energy balance equations, the thermodynamic analyses for the hydriding-dehydriding cycle ofmetal hydride hydrogen storage system are carried out for various processes, including hydriding, dormancy and dehydriding processes. The analytical solutions for the metal hydride hydrogen storage system are obtained from the thermodynamic mode\.

Validation ofnumerical model by analytical solution

A lumped parameter model can be solved numerically and sometimes analytically. The analytical solution can be considered as a simple benchmark to validate the lumped parameter numerical mode!. For simplification, the hydrogen mass source term SH in 2 each stage is set as constant in the numerical model and the analytical solution. The mass flow rate used in the present work refers to that in Case 2 from Ref. [52] in order to maintain a hydrogen production of 2 kgH2/h. The time of an absorption-desorption cycle in Case 2 [52] is 3600s. The hydrogen is produced during desorption (about 720s), and the mass outflow rate is about 1.389g/s in the dehydriding process. The absolute values of the mass flow rate and the hydrogen mass source term are both assumed as 1.389 gis during hydriding and dehydriding. The ratio of the hydrogen mass source term to the mass flow rate is assumed as -). The hydriding/dehydriding reaction is ignored during dormancy. The mass flow rate is a positive quantity and the hydrogen mass source term is a negative quantity during hydriding.

On the contrary, the mass flow rate is a negative quantity and the hydrogen mass source term is a positive quantity during dehydriding. The inflow temperature is assumed as constant while the outflow temperature is variable. Fig.3.1 shows the comparisons between the Matlab/Simulink numerical solutions and the analytical solutions, inc1uding the variations of the lumped temperature, the pressure, the mass source term of metal hydride, the mass of metal hydride, the equilibrium pressure and the mass of gaseous hydrogen, in order to validate the lumped parameter numerical mode!. In general, the numerical solutions of the lumped parameter model with constant mass source term agree well with the analytical solutions. The lumped tempe rature of the metal hydride reactor increases during hydriding and decreases during dehydriding. The temperature increases during dormancy since the reactor is heated, which is good for the dehydriding reaction. The metal hydride mass increases during hydriding and decreases during dehydriding. The sum of the mass flow rate and the hydrogen mass source is 0, and the mass of gaseous hydrogen in the metal hydride reactor is a fixed value. The variation curve of pressure is as same as that oflumped temperature, which is according to the equation of state in the assumed conditions. The equilibrium pressure is presented in Fig.le, which is calculated by Eq. (11). The equilibrium pressure is related to the lumped temperature and the mass of metal hydride, and the effect of the lumped temperature on the equilibrium pressure is more obvious than that of the mass of metal hydride. The equilibrium pressure shows the same trend as the lumped temperature.