Introduction to Carbon Capture - Introduction to Carbon Capture and Sequestration - page 152

Box 4.2.2 ( Continued )

The entropy of mixing is given by:

( )

NN + !

mix AB

∆= SSSSk − − = In

AB A B B

NN ! !

AB

For very large number of particles we can use the Stirling approximation:

ln N ! ≈ N ln N − N ,

which gives:

∆ S mix = k B ( N A + N B ) ln ( N A + N B ) − k B N A ln N A − k B N B ln N B

If we write for the mole fraction of component A:

N

A

x = ,

A

NN +

AB

we obtain for the entropy of the mixing:

mix

∆
∆=

S

mix

( ) ( )

s =− kxxk x ln − − 1 ln 1 − x

BA A B A A

N

where n is the fl ux in number of moles per second. The number of moles
of CO 2 is also conserved:

x fl ue n fl ue = x exh n exh + x cap n cap

As we think about how to design a separation process, it's important
to realize that that we cannot control the fl ux of the fl ue gas nor the