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Equilibrium Stage Processes -
Distillation.
Christopher J. Hill, 2000
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Introduction
This course is, in general, concerned with the processes effecting the separation in the outline
of a chemical process shown below.
Fig 1: Typical Chemical Process
One example of a separation process, liquid-liquid extraction, may be used to seperate
propionic acid from a mixture with kerosine as follows:
Fig 2: Batch liquid-liquid extraction.
For continuous operation,
Fig 3: Continuous liquid-liquid extraction.
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The ideal Equilibrium Stage?
The 'Ideal Equilibrium Stage', also known as a 'Theoretical Stage', 'Theoretical Plate' or 'Ideal
Stage', is one which has the exit phases/streams in thermodynamic equilibrium, each
phase/stream being removed from the stage without entraining any of the other phase /
stream.
Binary Distillation
Distillation is a process involving an equilibrium between two phases - liquid and vapour. For
a pure compound, in particular a pure ionic compound, a sharp boiling point usually exists.
For a mixture, however, a phase equilibrium exists over a range of temperature, as shown
below.
Fig 4: Isobaric (Constant Pressure) Temperature Composition Diagram.
The above diagram applies to the system:
Fig 5: Liquid and vapour space in equilibrium.
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Fig 8: X-Y Diagram for Constant Temperature.
Pmvc = partial pressure of more volatile componentPlvc = partial pressure of less volatile component
Azeotropes
Type A
(e.g. Acetone - CS2, Chloroform - methanol)
Fig 9:
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Fig 10:
Fig 11:
Type B
(e.g. Acetone-Chloroform)
Fig 12:
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Fig 13:
Fig 14:
Fig 15:
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Fig 16:
Flash Distillation
Flash distillation is a process typically used to effect seperation of crude oil. The process
involves heating a feed stream and then allowing it to expand into a vessel maintained at low
pressure. Partial vaporisation then occurs, and a phase equilibrium is (ideally) reached.
Fig 17: Flash Distillation.
A material balance gives:
F = L + V ...1
An m.v.c. balance gives:
FZF = Lxe + Vye ...2
Now from 2,
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Fig 19: Differential Distillation
The above diagrams represent classical simple laboratory distillation, attributed to Rayleigh,
1903. Heat is applied to vapourise some of the solution. The vapour is condensed and found
to contain a high m.v.c. composition (depending on amount vapourised).
Now in a small time increment dt, vapour of m.v.c. composition y is given off. The amount of
vapour given off is V kmol. Assuming x and y are equilibrium values throughout the process,
In time increment dt,
dV = -dS
m.v.c. balance
ydV = -d(Sx) = -Sdx - xdS
-ydS = -Sdx - xdS
xdS - ydS = -Sdx
(x - y) dS = -Sdx
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Fig 20:
The last equation above is known as Rayleigh Equation, where
S1 = total kmol solution to start with
S2 = total kmol solution left in bottoms
x1 = starting m.v.c. composition in liquid
x2 = finishing m.v.c. composition in liquid
Fig 21:
Continuous Fractionation
The system typically adopted for continuous fractionation is shown below.
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Fig 22: Continuous Fractionation.
where,
F = Feed flow rate (kmols/hr)
xf= m.v.c. composition of feed (mole fraction or mol percentage)V = Vapour flow rate (kmols/hr)
L = Reflux flow rate (kmols/hr)
D = Top Product flow rate (kmols/hr)
xD = m.v.c. composition of top vapour stream, top product, and reflux (mole fraction or mol
percentage)
V" = Reboiler exit stream flow rate (kmols/hr)
W = Bottom-product flow rate (kmols/hr)
xW = m.v.c. composition of bottom product and feed to reboiler (mole fraction or mol
percentage)
Comparison of Continuous Fractionation with Flash and
Rayleigh Distillation
Flash Distillation
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Fig 23: Flash Distillation.
Rayleigh Distillation (Simple Differential Distillation)
Fig 24: Rayleigh Distillation.
A single stage of the continuous fractionation column is now considered for comparison.
Continuous Simple Distillation
Fig 25: Continuous Distillation.
Multiple Continuous Simple Distillation
Fig 26: Multiple Continuous Distillation.
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Consider a fractionating column of N plates, where the condenser and reboiler are counted as
'plates'. A typical 'nth' plate has the streams shown below associated with it:
Fig 27: Column.
Fig 28: Temperature - Composition Diagram for nth Plate.
M.v.c balance for Nth
plate
Fig 29: mvc balance.
VN-1YN-1 + LN+1XN+1 = VNYN + LNXN
But XN+1 = XD
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VN-1YN-1 + LN+1XD = VNYN + LNXN
M.v.c. balance for plates n to N (where n,N in rectifying section)
Fig 30: M.v.c. balance for plates n to N.
(The balance is for the solid red line area)
Vn-1Yn-1 + LN+1XN+1 = VNYN + LnXn
But XN+1 = XD
Vn-1Yn-1 + LN+1XD = VNYN + LnXn
M.v.c. balance as above incorporating condenser.
(balance as above + dotted red line area)
Vn-1Yn-1 = LnXn + DXD
Conditions for Constant Molal Overflow
1. Heat losses negligable (achieved more easily in industrial columns)2. Negligable heat of mixing3. Equal or close heats of vaporisation
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In general, values of V and L very from stage to stage, and an enthalpy balance over each
stage is required to calculate L,V.
With constant molal overflow assumption,
Ln-1 = Ln = Ln+1 = ... etc.
Vn-1 = Vn = Vn+1 = ... etc.
M.v.c. balance for plate n to condenser continued.
Vn-1Yn-1 = LnXn + DXD
Assuming constant molal overflow,
VYn-1 = LXn + DXD
Note: V=Vapour from top of column
L = reflux
D = top-product
Dividing through by V gives
Yn-1 = (L/V)Xn + (D/V)XD
Y = m X + c
This material balance equation is called the Upper Operating Line. Note that (L/V) and
(D/V) are constants. This linear relationship links the compositions of passing streams
between stages.
The Lewis-Sorel Method
This uses the above equilibrium relationship and the operating line equation alternately to
step up or down the column.
e.g. at the top of the column:
YN = XD = (known)
Equilibrium XN
Operating Line YN-1 = (L/V)XN + (D/V)XD
Equilibrium XN-1
Operating Line YN-2 = (L/V)XN-1 + (D/V)XD
etc.
McCabe-Thiele
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Recognised the fact that the operating line is straight simple graphical construction.
On an x-y diagram, the operating line is a straight line of gradient (L/V) and passes through
XD, XD
Fig 31:
Fig 32:
Reflux Ratio, R = L / D
V = L + D
L / V = R / (R + 1)
D / V = 1 - (L / V)
= (R + 1 - R) / (R + 1)
1 / (R + 1)
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Fig 33:
Fig 34:
Fig 35:
Lower Operating Line
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L', V' may be different from L, V
m.v.c. balance
L' xm = V' Ym-1 + W Xw
Ym-1 = (L' / V') Xm - (W/V') Xw
This material balance is a straight line passing through the point (Xw,Xw)
The intersection of the upper and lower operating lines is determined by the feed.
Importance of the feed
The feed should be introduced where the appropriate stream in the column has the same
composition as the feed.
The thermodynamic state of the feed determines the relationships between L' and L and V'
and V
Different States of the Feed
1. Saturated Liquid, i.e. at bubble temperature
2. Saturated Vapour, i.e. at dew temperature
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3. Two-Phase Feed
Summary of McCabe Thiele Construction
Fig 39:
Plot equilibrium line Draw 45o line Locate Distillate (XD,XD) Draw Upper Operating Line (gradient R / (R + 1)) between (XD,XD) and (D,XD/(R +
1) )
Locate bottom product (XW,XW) Locate (XF,XF) Draw "q-line" with gradient q / (q - 1) Draw lower operating line (from q-line / upper operating line intersection to (XW,XW)
)
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hF = hv - qhv + qhL = (1-q)hv + qhL
FhF = FqhL + F(1-q)hv
c.f. FhF = LFhL + VFhV
LF = qF and VF = (1 - q)F
(q / (q - 1)) = - LF / VF
Now V = V' + VF = V' + (1 - q)F
and L = L' - LF = L' - qF
Rectifying Operation Line
Vyn-1 = Lxn + DxD
Stripping op line
V'ym-1 = L'xm - WxW
Let intersection occur at ( , )
then
(V - V') = (L - L') + DxD + WxW
i.e. (V - V') = (L - L') + FzF
from 1a, 1b
(1 - q)F = -qF + FzF
i.e. = (q / (q - 1)) - (zF / (q - 1)) equation of "q-line"
Straight line of gradient q / (q - 1) passing (zF, zF)
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Fig 41:
Importance of Reflux Ratio
Fig 42:
Total Reflux
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Fig 43:
Minimum Reflux
Fig 44:
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Fig 45:
Optimum R is often 1.2 - 1.5 x Rmin
Fig 46:
Relative Volatility
Volatility = y / x
Relative Volatility, AB = ( yA / xA ) / ( yB / xB )
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Fig 47: