L14 & 15 - Distillation & Assisted distillation Flashcards
Describe simple distillation (Rayleigh distillation)
-In stillpot, initially filled with mixture that is heated producing a vapour
-Vapour is condensed overhead and collected in reciever; no reflux, plates or packing
- Concentration of more volatile component (mvc) is higher in vapour than liquid - over time liquid mvc decreases and amount of mvc in overhead increases
-Quality of vapour decreases over time
Describe VLE curve at constant pressure - 2 component
Temp v mole fraction of mvc
Mvc has lower BP at mole fraction = 1; less volatile has higher BP at mole fraction = 0
Dew point (vapour) higher T; bubble point (liquid) lower T
Mass balance for simple distillation & Rayleigh eq. proof
No. moles of mvc in stillpot, Lm = x*L
Small amount of liquid dL evaporates- change in no. of moles of mvc is: y*dL = dLm
Differentiating (chain rule): dLm = xdL + Ldx
-> xdL + Ldx = ydL
-> ydL - xdL = Ldx
-> (y-x)dL = L*dx
Therefore, dL/L = dx/(y-x)
Integrating from Li to Lf & xi to xf:
ln[Li/Lf] = integral xf to xi: dx/y-x
Mean composition of what has been distilled over, xD
Lixi - Lfxf = xD*(Li-Lf)
-> xD = (Lixi - Lfxf)/(Li-Lf)
Relative volatility
y = ax/[1+(a-1)*x]
Rayleigh in terms of relative volatility
ln[Li/Lf] = [1/(a-1)]{ln[xi/xf] - aln[(1-xi)/(1-xf)]}
Overall mass balance and rectification operating line
Assume constant molal overflow:
V = L + D
Vyn+1 = Lxn + DxD
yn+1 = (L/V)xn + (D/V)xD
yn+1 = (R/R+1)xn + (1/R+1)*xD
Constant reflux ratio
Distillation proceeds, slope of operating line constant
As stillpot mole fraction, Xs, decreases, the distillate mole fraction, XD, decreases
In reality, performance of distillation better than equation prediction, why?
Vapour condenses on lid of vessels/pipes so refluxes back into boiler - rectification
(Vapour entering condenser richer in mvc)
Finding Li or Lf at constant reflux ratio
Graphically:
1) plot 1/(xD-xS) against xS
2) Find area under curve between xiS and xiF = ln[Li/Lf]
Minimum reflux ratio
Rmin/(Rmin+1) = [xD-y*(xS)]/[xD-xS]
Variable reflux ratio
xD remains constant -> vetter quality of distillate
Reflux ratio must increase as distillation proceeds as more difficult to get distillate of desired composition from stillpot residue of smaller and smaller mvc mole fraction
As distillation proceeds, amount of material in stillpot falls: heat transfer area falls as level falls so more time & fewer xD and vaporisation rate slower
Rayleigh eq. at variable reflux ratio
ln[Li/Lf] = integral xf to xi: dx/y-x
Now: ln[Li/Lf] = ln[(xD-xf)/(xD-xi)]
-> [Li/Lf] = [(xD-xf)/(xD-xi)]
Running costs of batch distillation
Depends on amount of material vaporised:
Constant reflux ratio:
Total amount vaporised over whole batch, Vb:
Vb = (R+1)*D, where Db = distillate amount collected
Variable reflux ratio:
Amount of vaporisation required to collect same distillate quantity will increase as distillation proceeds
Developing mass balance for Bogart Eq.
Mass balance of vaporisation from stillpot to rate of depletion of content of stillpot:
dV/dt = (R+1)[-dL/dt]
Variable reflux Rayleigh: [Li/L] = [(xD-x)/(xD-xi)]
-> L = Li[(xD-x)/(xD-xi)]
dL = (dL/dx)(dx/dt) = [Li(xD-xi)]/[(xD-x)^2]*(dx/dt)
