# Measurements of Operating Parameters of a Metal Hydride Compressor with a Heat Pump
## 2 Description of the Designed MH Compressor Mechanism
As the pressure increased, the desorption was accompanied with a release of a small amount of hydrogen which increased the pressure of gaseous hydrogen that was present among the alloy grains; therefore, the shift of point C towards the zone with a lower concentration depended primarily on the grain size and on the free volume among the alloy grains. After the pressure was increased by heating the alloy, the hydrogen desorption began in the zone between points C and D. The total amount of the heat to be supplied to the tank for covering the heat of reaction and the heat loss was calculated as follows: \begin{table}
\begin{tabular}{c c} \hline
**Parameter** & **Value** \\ \hline Dimensions of the MH compressor, including & \(117\times 75\times 130\) \\ accessories H \(\times\) D \(\times\) W (cm) & \(124\) \\ \hline Heat pump input power (average) (W) & \(300\) \\ \hline Electric power input of the auxiliary water cooler (W) & \(2\times 36\) \\ \hline Circulation pump input power (W) & \(2\times 36\) \\ \hline Number of MH tanks & \(2\) \\ \hline m\({}_{\rm MH}\) (for 1 tank) (kg) & \(3.125\) \\ \hline Hydrogen volume in one cycle \(V_{\rm H2}\) (calculated) (litres) & \(200\) \\ \hline \end{tabular}
\end{table} 
Table 1: Description of the basic parameters of the MH compressor. \[Q_{\rm CD}=q_{\rm des\ H_{2}}\cdot\Delta V_{\rm desH_{2}}+k\cdot A\cdot(t-t_{\rm a })\cdot\Delta t\ ({\rm J}) \tag{3}\]  
The concentration could only be reduced to the value of 0.13%, because lower concentrations would result in an abrupt pressure drop. The pressure in point D amounted to 0.8 MPa, so the compression ratio for the hydrogen compression in a thermal cycle was calculated using the following equation:  
\[\varepsilon_{\rm k}=\frac{p_{\rm D}}{p_{\rm B}} \tag{4}\]  
where \(p_{\rm D}\) is the hydrogen pressure in point D (Pa) and \(p_{\rm B}\) is the hydrogen pressure in point B (Pa). During the operation of the compressor with a cyclical use of the La\({}_{0.85}\)Ce\({}_{0.15}\)Ni\({}_{5}\) alloy at temperatures ranging from 10 to 50 \({}^{\circ}\)C and with the mass concentrations of 0.16 and 0.66%, the theoretical value of the compression ratio, as measured on the PCI curves, was \(\varepsilon_{\rm k}\) = 4. In order to restore the baseline temperature and pressure (the values in point A), it was necessary to cool the tank and remove the heat, the quantity of which was calculated as follows:  
\[{\rm D}\ \mathbf{\times}\ {\rm A}\] \[Q_{DA}=\sum_{i}\left(m_{i}\cdot c_{i}\right)\cdot\Delta T-q_{\rm abs \ H_{2}}\cdot\Delta V_{absH_{2}}-\int k\cdot A\cdot(t-t_{\rm a})\cdot\rm d \tau\ ({\rm J}) \tag{5}\]  
where in \(q_{\rm abs\ H2}\) is the heat of reaction in hydrogen absorption (J\(\cdot\)m\({}^{-3}\)) and \(\Delta V_{\rm abs\ H2}\) is the amount of the absorbed hydrogen at a temperature decrease representing \(\Delta T\) (m\({}^{3}\)). The hydrogen compressor was designed for the compression of 200 litres of hydrogen in a single cycle. In order to identify the optimal amounts of the metal hydride material at the individual tandem stages of the compressor for the predefined volumetric flow rate of the hydrogen, it was necessary to calculate the mass concentration of the hydrogen using the following equation:  
\[\Delta c=\frac{m_{\rm H_{2}}}{m_{\rm MH}} \tag{6}\]  
The editing of Equation (6) yielded the equation for calculating the amount of the metal hydride material necessary for the compression of the proposed amount of hydrogen in one stage of the compression:  
\[m_{\rm MH}=\frac{V_{\rm H_{2}}\cdot\rho_{\rm H_{2}}}{\Delta c} \tag{7}\]  
where \(\Delta c\) is the change in the mass concentration of the stored hydrogen (1); \(V_{\rm H2}\) is the hydrogen volume (m\({}^{3}\)); \(\rho_{\rm H2}\) is the hydrogen density (kg\(\cdot\)m\({}^{-3}\)); \(m_{\rm MH}\) is the mass of the metal hydride alloy (kg). Using Equation (7), the amount of the alloy necessary for the compression of 200 litres of hydrogen in one cycle was calculated as ca 3.5 kg.