Question

1000 kg/h of a hydrocarbon mixture containing 25% xylene by mass is fed to an extraction unit which partially removes the xylene by contacting the hydrocarbon stream with 2000 kg/h of an immiscible solvent initially containing 0.5% xylene by mass. The raffinate stream will contain 2% xylene by mass. Calculate the mass flowrates of the extract and raffinate streams and the composition of the extract.

Answer 1

First, let us draw the diagram

Clearly, we can perform the next mass balances:

F + S = E + R

overall mass balance over X:

F*Xf + S*Xs = E*Xe + R*Xr

substitute values:

F + S = E + R turns:

1000+2000 = E + R

F*Xf + S*Xs = E*Xe + R*Xr turns to

1000*0.25 + 0.005*2000 = E*Xe + 0.02*R

we have

3000 = E + R

260 = E*Xe + 0.02*R

Note that:

we have 2 equations and 3 unkown, so

Degrees of Freedom = 3-2 = 1 , we need an extra variable

i.e. set either E, R, or final Xe

We can't assume Xe = 0, since the extract will always have higher concentration than that of the raffinate

So the best conclusions is:

System is not set, it has 1 Degree of Freedom