Biogas temperature [closed]








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What would be the temperature of Biogas when it is delivered to a boiler through a pipeline by a gas blower. Inlet pressure at gas blower is zero and at delivery it is 3.0 psi.




The compression by the blower can be used as an example of adiabatic compression.
$$pV^\gamma=\text{constant}$$
or
$$p\_1V\_1^\gamma=p\_2V\_2^\gamma$$
where $\gamma$ is the ratio of the heat capacities $\gamma=C\_p/C\_V=C\_{\mathrm m,p}/C\_{\mathrm m,V}=c\_p/c\_V$. You need to find a value of $\gamma$ suitable for your biogas, which is probably mainly a mixture of $\ce{CH4}$ and $\ce{CO2}$.


According to the ideal gas law,
$$p\_1V\_1=nRT\_1$$
and
$$p\_2V\_2=nRT\_2$$
Therefore,
$$\begin{align}p\_1\left(\frac{nRT\_1}{p\_1}\right)^\gamma&=p\_2\left(\frac{nRT\_2}{p\_2}\right)^\gamma\\[6pt]
p\_1^{1-\gamma}T\_1^\gamma&=p\_2^{1-\gamma}T\_2^\gamma\\[6pt]
\frac{T\_1}{T\_2}&=\left(\frac{p\_1}{p\_2}^{\frac{1-\gamma}{\gamma}}\right)\end{align}$$


The given initial temperature of $40\ \mathrm{^\circ C}$ needs to be converted to the corresponding thermodynamic temperature $T\_1=313.15\ \mathrm K$.


Note that, unfortunately, the given pressures are actually gauge pressures (also note that the use of the unit $\mathrm{psi}$ is deprecated). Assuming an ambient pressure of about $1\ \mathrm{bar}=14.5\ \mathrm{psi}$, the corresponding pressures are $p\_1=0\ \mathrm{psi}+14.5\ \mathrm{psi}=14.5\ \mathrm{psi}$ and $p\_2=3.0\ \mathrm{psi}+14.5\ \mathrm{psi}=17.5\ \mathrm{psi}$.


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