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Question 1 - Compression of a C H 4 C O 2 mixture ( van der Waals EoS ) A mixture of methane ( C

Question 1- Compression of a CH4CO2 mixture (van der Waals EoS)
A mixture of methane (CH4) and carbon dioxide (CO2) is produced as off-gas in a
composting process, comprising of 85 mol% methane and 15 mol% carbon dioxide. This
gas is to be stored in compressed form to be used as fuel gas for a thermal process in the
operation. The off-gas is available at the temperature and pressure of 293K and 1bar,
respectively, and needs to be compressed to the pressure of 10 bar in a steady-state
process. The efficiency of the available adiabatic compressor is 85%. The gas mixture
can be described using the van der Waals equation of state:
(p+amixV??(2))*(V-bmix)=RT with amix=0.2378*Pa*m6mol2 and bmix=4.311*10-5*m3mol
The rest of required data are available in Table 1.
35.699 I
Table 1. Properties of methane and carbon dioxide
(a) Make a drawing of the process and define your system by the relevant balances.
(b) Show that the final temperature upon compressing the gas from 1 bar to 10 bar is
474K, if the gas obeys the Ideal Gas Law.
(c) Show that the gas mixture is close to ideal at both the inlet and the outlet
conditions of the compressor.
(d) Determine the amount of work required if the flow rate of the gas mixture is 1.0
mols.
(e) What is the actual final temperature of the gas leaving the compressor
considering its efficiency?
17.6493+3.8637+0.048435T
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