Calculation of compression energy

Single compressor

The pressure increase through compression can be either isothermal, polytropic, or isentropic. The required energy for compression increases from isothermal to isentropic. EnergyModelsHydrogen incorporates isentropic compression. Depending on the input parameters, this can however be translated to polytropic compression. In the following, ideal gas behaviour is assumed.

Given the ideal gas constant $R$ (8.314 J/mol/K), the inlet temperature $T_1$ (in K), the specific heat ratio $\kappa$ (no unit), the efficiency $\eta$ (no unit), the inlet pressure $p_1$, and the outlet pressure $p_2$ (both pressures require the same unit), the compression energy $W_p$ in J/mol can be calculated as

\[W_p(p_1, p_2) = \frac{\kappa R T_1}{\kappa-1} \left(\left(\frac{p_2}{p_1}\right)^{\frac{\kappa-1}{\kappa}}-1\right) \frac{1}{\eta}\]

The compression energy requirement is implemented through the function compression_energy. This function requires as default only the pressures $p_1$ and $p_2$ while all other parameters can be included as keyword arguments. The included standard values are $T_1=298.15~\text{K}$, $\kappa = 1.41$, and $\eta = 0.75$. This values are representative for hydrogen.

Compression train

It is in general not advisable to have a large compression ratio as the temperature increase results in an increased compression energy requirment. It is instead beneficial to utilize multiple compressors with interstage cooling.

If the delivery pressure $p$ is larger than the inlet pressure $p_{in}$, we first calculate the different pressure levels for a compressor traing of $n_{comp}$ compressors and a maximum pressure ratio of $PR$ in each compressor as

\[\begin{aligned} p_{i+1,1} & = p_{in} PR^{i} \quad \text{for} ~ i \in 0, \ldots, n_{comp}-1 \quad & \text{if} ~ p > p_{in}PR^i \\ p_{i,2} & = p_{in} PR^{i} \quad \text{for} ~ i \in 1, \ldots, n_{comp} \quad & \text{if} ~ p > p_{in}PR^i \\ \end{aligned}\]

As can be seen from above equations, we have one more pressure $p_{i,1}$ than $p_{i,2}$. Hence, the pressure $p$ is added to $p_{i,2}$.

The total compression energy requirement (without unit, as fraction of the stored energy) is then given by

\[W = \frac{\sum_{i} W_p(p_{i,1}, p_{i,2})}{1000 M \times \text{LHV}}\]

using the molar mass $M$ (in g/mol) and the lower heating value LHV (in MJ/kg).

The energy demand in a compressor train is implemented through the function energy_curve.