Equilibrium Stage Processes - Distillation[1].

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



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



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:



Fig 10:

Fig 11:

Type B

(e.g. Acetone-Chloroform)

Fig 12:



Fig 13:

Fig 14:

Fig 15:



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,



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



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



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



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.



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

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



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



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)



Fig 33:

Fig 34:

Fig 35:

Lower Operating Line



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



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) )



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



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)



Fig 41:

Importance of Reflux Ratio

Fig 42:

Total Reflux



Fig 43:

Minimum Reflux

Fig 44:



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 )



Fig 47:

© Christopher J. Hill, 2000

Index of figures.


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