Compressor

Introduction and Model¶

The compressor increases the pressure of the biogas from the anaerobic digester, reducing its volume to prepare it for the biogas storage.

The compressor is implemented as a black box model, as its internal workings are not considered critical and are too complex to model in detail. The power consumption of the compressor is calculated with the maximum electrical power uptake and the current utilization of the compressor. The utilization rate \(k_{load}\) depends on the gas flow \(\dot V_{gas}\) of the anaerobic digester. The following cases are assumed:

Gas flow (\(0 \lt \dot V_{gas} \le \dot V_{gas,max}\)): Compressor is utilized (\(0 \lt k_{load} \le 1\))
No gas flow (\(\dot Q_{gas} = 0\)): Compressor is not utilized (\(k_{load} = 0\))

Equations¶

Power consumption¶

\[ P_{el} = k_{load} \cdot P_{el,max} \]

Symbol	Description	Unit
\(P_{el}\)	Power consumption of the compressor	kW
\(k_{load}\)	Utilization rate of the compressor	-
\(P_{el,max}\)	Maximum electrical power uptake	kW

Maximum electrical power uptake¶

\[ P_{el,max} = \frac{1}{3600} \cdot \frac{c_{p,gas} \cdot (t_{gas} + 273,15) \cdot \dot V_{gas,max} \cdot \rho_{gas} \cdot \left( \left( \frac{p_{out}}{p_{in}} \right)^{\frac{\kappa - 1}{\kappa}} - 1 \right)}{\eta} \]

Symbol	Description	Unit
\(P_{el,max}\)	Power consumption of the compressor	kW
\(c_{p,gas}\)	Specific heat capacity of the biogas	kJ \(\cdot\) kg^-1 \(\cdot\) K^-1
\(t_{gas}\)	Input temperature of the biogas	°C
\(\dot V_{gas,max}\)	Maximum gas flow uptake	Nm³ \(\cdot\) h^-1
\(\rho_{gas}\)	Density of the biogas	kg \(\cdot\) Nm^-3
\(p_{out}\)	Pressure of the biogas storage	bar
\(p_{in}\)	Pressure of the influent biogas	bar
\(\kappa\)	Isotropic exponent of the biogas	-
\(\eta\)	Electrical efficiency of the compressor	-

Source code documentation¶

mod compressor

mod compressor_init