Speeds of sound for a biogas mixture $CH_{4}$ + $N_{2}$ + $CO_{2}$ + $CO$ from $p$ = (1-12) MPa at $T$ = (273, 300 and 325) K measured with a spherical resonator

The present work aims to measure speeds of sound $c$ in a biogas mixture of $CH_{4}$ + $N_{2}$ + $CO_{2}$ + $CO$, at $p$ = (1-12) MPa and $T$ = (273, 300 and 325) K, using a spherical acoustical resonator. The results are fitted to the virial acoustic equation of state, and the virial acoustic coefficients are obtained, $\beta_{a}$ and $\gamma_{a}$ and extrapolated to zero pressure, determining the adiabatic coefficient as perfect gas, $\gamma^{pg}$, and the isobaric and isochoric heat capacities as perfect gas, $C_{p}^{pg}$ and $C_{V}^{pg}$, respectively. The speeds of sound are acquired with a mean expanded relative uncertainty of 165 parts in $10^{6}$ ($k$ = 2) and are compared with the results predicted by the reference equation of state for this kind of mixture (natural gas-like mixtures), EoS GERG-2008. Relative deviations between experimental data and values estimated by this model were less than 700 parts in $10^{6}$ at $T$ = 325 K, and below 400 parts in $10^{6}$, and within measurement uncertainty of at $T$ = 300 K, although appreciably higher at isotherm $T$ = 273 K at the highest pressure data for this work, and even reaching values above 3 400 parts in $10^{6}$.