Equilibrium Stage Processes - Distillation.
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.
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
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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.
The first bubble of vapour formed when a liquid (subcooled) is heated is formed at the bubble curve.
The first drop of liquid formed when a vapour (superheated) is cooled is formed at the dew curve.
x = mole fraction m.v.c. in liquidy = mole fraction m.v.c. in vapour
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The temperature - composition diagram is used for isobaric conditions. For isothermal (constant temperature) conditions a pressure - composition diagram is used.
Fig 6: Isothermal (constant temperature) Pressure-Composition Diagram.
X-Y Diagrams for Constant Pressure
If the isobaric temperature-composition diagram is drawn or plotted, the x and y data for different temperatures may be utilised to form the x-y diagram (i.e. the plot of y against x). The x-y diagram will correspond to the pressure for which the temperature-composition diagram was plotted.
Fig 7: X-Y Diagram for Constant Pressure.
X-Y Diagrams for Constant Temperature
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Fig 8: X-Y Diagram for Constant Temperature.
Pmvc = partial pressure of more volatile component
Plvc = 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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Vye = FZF - Lxe
ye = (FZF / V) - (Lxe/V)
y = c + mx
Putting xe = ZF gives
ye = ZF[ (F / V) - (L/V) ]
but from 1, (F / V) = (L / V) + 1, so (F / V) - (L / V) = 1
thus ye = ZF when xe = ZF
(this is not surprising considering the fact that with a feed of composition ZF and a liquid bottom product of composition ZF the
top product cannot be of any composition other than ZF).
For the constant pressure at which the flash vessel is operated, a y against x diagram may be plotted and the material balance line (which is straight) is seen to pass through ZF, ZF and xe, ye (corresponding to the temperature Te).
Fig 18:
Simple Differential Distillation
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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’s 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
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But XN+1 = XD
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 mixing
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3. Equal or close heats of vaporisation
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 columnL = refluxD = top-product
Dividing through by V gives
Yn-1 = (L/V)Xn + (D/V)XDY = 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
3. Two-Phase Feed
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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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Fig 40:
The q-line
For a two phase feed (assumed in equilibrium)
F hF = LF hL + VF hv
where,hF = specific enthalpy of feed
hL = specific enthalpy of saturated liquid
hv = specific enthalpy of saturated vapour
Generalize by defining q:
q = Enthalpy change reqd to vaporise 1 mole of feed (change it to saturated vapour) / molar enthalpy of vaporisation
= (hv - hF) / (hv - hL)
IncreasingSpecificEnthalpy
Superheated Vapour q<0
hv Saturated Vapour q = 0
2-phase feed 0 < q < 1
hL Saturated Liquid q = 1
Sub-cooled Liquid q > 1
qhv - qhL = hv - hF
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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, αAB = ( yA / xA ) / ( yB / xB )
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Fig 47:
© Christopher J. Hill, 2000
Index of figures.
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