Question

You are asked to calculae the minimum amount of work required to first separate CO2 and then N2 from natural gas (methane). the methane product needs to have 2 mol% CO2 and 3 mol% N2 such that the purity of the recovered methane is 95%. There are no purity requirements for the CO2 and N2 remeved. Assume the separation is carried out at 1 bar and 298.15K. Initially, there is 50 mol% methane, 40 mol% CO2, and 10 mol% N2.

Answer 1

Suppose mixture has 100 moles. Moles of CO₂ = 40, Moles of methane = 50 & moles of nitrogen = 10 moles

So n_i =100

now after removing x moles of CO₂ and y moles of N₂ ;

total moles left (n_f) = 50 + (40-x) + (10-y) = 100 - (x+y)

therefore 0.02*n_f = 40-x

100 - (x+y) = 50*(40-x)

49x - y =1900 ------------- (1)

and 0.03*n_f = 10-y

-3x + 97y = 700 -------------------- (2)

Solving (1) and (2) we get x = 38.95 and y = 8.55

So n_f = 100 - (38.95 + 8.55) = 52.5

So work done = |(n_f - n_i)|RT = 117.7 KJ