CHEE 470 Course Notes
PROCESS DESIGN-FRACTIONATION
1
A Review
1
Types of Fractionation Operations
2
Calculation Procedures.
5
Component Designations:
7
Separation Specifications
7
BATCH DISTILLATION
10
Advantages of Batch Distillation
10
Disadvantages of Batch Distillation
11
SHORT-CUT METHODS
11
RIGOROUS FRACTIONATION METHODS
12
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CHEE 470 Course Notes
CHEE 470
FRACTIONATION
A Review
Fractionation is a distillation carried out in such a way that the rising vapour
repeatedly and successively contacts condensed portions of the vapour previously
produced which is known as reflux. Transfers of heat and material result from
these contacts which serve to enrich the vapour and deplete the liquid in the more
volatile components. This operation is carried out in a vessel called a tower (or
column) which contains devices to enhance mass and heat transfer between the
liquid and vapour phases. These devices can be packing such as Rashig Rings,
Saddles or the more modern materials such as a Glitsch Grid (structured packing),
or alternatively trays. There are basically three types of trays: Sieve trays, Bubble
Caps, and Valve trays.
In order to carry out calculations involving fractionation, a theoretical model
is used based on the concept of an equilibrium stage. An equilibrium stage is not
the same thing as a Tray. The question of tray efficiency determines the number of
trays required to equal an equilibrium stage. This number is unlikely to be an
integer. In the case of packing, the term HETP is used, which simply means the
height of packing equivalent to a theoretical stage.
By definition, the vapour and liquid leaving a theoretical stage are in
equilibrium with each other. Provided the composition of the vapour and liquid at
equilibrium differ, then separation of a mixture by fractionation is possible. The
degree to which the composition of the two phases differ will determine the ease
with which the components may be separated. In the case of an azeotrope, there
is no difference in the vapour and liquid compositions, hence separation by simple
fractionation is impossible.
In order to carry out a rigorous quantitative design calculation of a fractionation, the
equilibrium relationships between the liquid and vapour phase must be known.
There are many cases where the situation is complicated by the presence of two
liquid phases. There are also situations where a chemical reaction takes place in
a stage, which further complicates the situation.
In the design of any fractionation system, there are three conditions that must be
satisfied.
1)
MATERIAL BALANCE. The amount of material entering a column for
any and all components must equal the amount leaving the column.
This same rule must be satisfied for all equilibrium stages in the
column. An exception to this rule would be the situation where a
chemical reaction occurs in a one or more stage of the column.
Lecture Notes: Fractionation
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CHEE 470 Course Notes
2)
HEAT BALANCE. The amount of heat entering a column must equal
the amount of heat leaving the column. Likewise, the amount of
heat entering any particular equilibrium stage must equal the amount
of heat leaving that stage. The exception to this rule would be a
situation where a chemical reaction occurring in a stage may
contribute or remove heat from that stage.
3)
PHASE EQUILIBRIUM. Vapour and liquid leaving the stage must be in
equilibrium with each other. It must be recognized that should a
chemical reaction occur which results in a change in composition.
This may have an effect on Phase Equilibria.
Types of Fractionation Operations
Although there are many variations of fractionation operations, the following
schematics illustrate the most common.
1)
A SIMPLE FLASH OPERATION. Flash operations are used to separate a
wide-boiling mixture into a liquid and vapour stream.
2)
SIMPLE ABSORBER. There are situations where it is difficult to
condense a top product without the help of a "lean oil absorbent ". A
rich gas is fed to the bottom of the absorber and the fat oil which has
absorbed the desired components from the gas leaves the column at
the bottom.
3)
RECTIFIED ABSORBER. A rectified (reboiled) absorber is used to give a better
separation than possible from a simple absorber. In a rectified absorber the
rich gas is fed in at an intermediate point in the column.
Lecture Notes: Fractionation
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CHEE 470 Course Notes
4)
TYPICAL FRACTIONATION COLUMN. This schematic illustrates a typical
single feed fractionation column. It is not unusual for a column to
have more than one feed and a side-cut product in addition to the
normal tops and bottoms stream. Occasionally a tower will contain a
pasteurization section. In this situation the top product is withdrawn
some trays below the top of the tower. This is done to remove trace
light impurities in the net tops product.
5)
REBOILED STRIPPER. In the case of a reboiled stripper the feed enters
the tower on the top tray. This system is often used for streams that
contain only small amounts of light components.
6)
STEAM STRIPPER. The normal reboiler is replaced by direct steam
injection as a heat source. If the column bottom product has a very
high boiling point, this can be an effective system.
Lecture Notes: Fractionation
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CHEE 470 Course Notes
7)
AZEOTROPIC DISTILLATION TOWER. In this case an "entrainer" has
been added to alter the individual component a values in such a way
that azeotropes can be "broken" and either permit separation or
enhance the economics of difficult separations.
8)
EXTRACTIVE DISTILLATION. This schematic shows a typical extractive
distillation column-solvent stripper arrangement. Here the extractive
solvent is added at the top of the column. Extractive distillation (as is
the case with Azeotropic Distillation) is used where there is a
problem with normally tight  systems. The addition of a solvent
changes the environment to such an extent that the  values are
increased and the separation becomes more economically attractive.
Lecture Notes: Fractionation
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CHEE 470 Course Notes
As a general rule extractive distillation is more economical than
azeotropic as the solvent is not vapourized to any extent, hence the
heat loads are significantly less.
Calculation Procedures.
It would be very easy to spend a great deal of time writing the equations for
the mass and energy balances and phase equilibria for fractionation calculations.
We have made the choice that we will review concepts rather than mathematics,
since the equations are available in any number of texts.
The next figure should be familiar. It is a classic McCabe-Thiele Diagram
for a binary system. Although this type of diagram is often used as an excellent
illustrative tool, it has little practical application in terms of design.
There are a few equations that we should look at. The equilibrium curve of a
binary system is given as follows:
 L,H * X L
YL=
1 + (  L,H - 1)* X L
The liquid molal composition is:
XL=
Lecture Notes: Fractionation
Yl
 L,H - (  L,H - 1)* Y L
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CHEE 470 Course Notes
The equation for the operating line for the rectifying section (RS) is as follows.
Ln+1 * xi,n+1 d * xi,d
+
Y i,n =
Vn
Vn
In the same fashion, the equation describing the operating line for the stripping
section is as follows:
Lm+1 * xi,m+1 b* xi,b
Y i,m =
Vm
Vm
The other straight line, commonly called the Q line, represents the feed state and
has the following equation:
L f * xL - x f
yL =
L f -1
The nomenclature for these equations is as follows:
xi, yi Liquid and Vapour mole fractions for component i
L and H are the light and heavy components of a binary
i, j is the relative volatility between two components i, j and equal to Ki / Kj
L is the liquid flow rate, moles per unit time
V is the vapour flow rate moles per unit time
d is the distillate or top product, moles per unit time
b is the bottoms product moles per unit time
f is the feed in moles per unit time
n and m are stage numbers in the rectifying and stripping sections
respectively
A McCabe-Thiele Diagram may be used to step off the required number of
equilibrium stages required to achieve a separation with a true binary system. As
mentioned previously, these diagrams and the other graphical procedure (the
Ponchon-Savarit which incorporates enthalpy) really have little practical value for
fractionation design purposes.
With the more or less general availability of computers, Short-Cut or
Rigorous design procedures are used almost exclusively. Before discussing some
of the concepts behind these methods, some additional definitions are in order.
Lecture Notes: Fractionation
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CHEE 470 Course Notes
Component Designations:
In any multicomponent fractionation system the separation is usually
specified in the terms of key components. Assuming a nine component system
the components are arranged as follows in order of decreasing volatility.
1.
2.
3.
4.
5.
6.
7.
8.
9.
Lightest component
.
Primary Key (Light Key)
.
.
.
Secondary Key (Heavy Key)
.
Heaviest Component
In this system, components 1 and 2 are often referred to as light diluents,
components 4,5 and 6 as sandwiched components, and components 8 and 9 are
heaviest diluents. The lightest and heaviest components are also often referred to
as terminal components.
Separation Specifications
There are many ways that one may specify a separation, but generally they
are specified in terms of recovery fractions of the keys. For a given number of
stages, it is then necessary to calculate the reflux required to achieve this
separation, the condenser and reboiler heat duties and the distribution of the nonkey components. Rather than specifying a secondary key, any of the following
variables may be specified as being equivalent, Lt, which is the top internal reflux,
Vr the reboiler vapour, Qc the condenser duty, or Qr the reboiler duty. It is not
recommended that one use external reflux rather than the internal reflux, as it is
subject to changes in external conditions while the internal reflux is not.
There are several other concepts that are often mentioned with respect to
fractionation. Some of them are as follows:
Constant Molal Overflow
This concept ignores the effect of heat balance in the shaping of the vapour
and liquid flow profiles in a fractionation column. It is a simplification sometimes
used in elementary calculation procedures, however it really is not valid except in
the case of close boiling feeds.
Minimum Reflux
Lecture Notes: Fractionation
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CHEE 470 Course Notes
The minimum reflux ratio is that below which the desired separation
between two key components is impossible to achieve, even with an infinite
number of stages. As an example of this, we can return to the McCabe-Thiele
Diagram. Minimum reflux would occur when the two sectional operating lines and
the "Q" line all intersect at the equilibrium curve. This point of intersection is also
called a point of infinitude, or the "pinch point". Minimum reflux is a concept that
has no meaning if only one key is specified, since there is no basis on which to
calculate it.
Minimum Stages
Minimum stages assume the condition of total reflux. A column is under
total reflux when there is no feed to the tower. All of the overhead vapour is
condensed and returned to the tower as reflux and all of the bottom liquid is
vapourized and returned to the tower. If we can assume constant molal overflow
the vapour and liquid flows throughout the column are identical, and the two
sectional operating lines have a slope of unity and become the 45 degree
diagonal. The Fenske equation (1932) calculates the minimum number of stages
required for a given separation.
DRlk
log(
)
DR
hk
N min +1=
log  l,havg
This equation is normally used by counting the "1" as an equilibrium stage
reboiler. Nmin refers to the number of stages in the column, and this equation
assumes that a total condenser is present.
Optimum Feed Stage Location
When one designs a fractionation column there are always several
economic criteria to consider. The optimum feed stage location is quite important.
The optimum feed stage location is that which gives the lowest reflux requirements
for a given number of stages for a two key separation. Although it is only possible
to specify the recovery fraction of two key components, the distribution of a third
component may be important.
Lecture Notes: Fractionation
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CHEE 470 Course Notes
It is sometimes possible to enhance the distribution of a third component by
deliberately displacing the location of the feed stage. This is most effective for
sandwiched components. As the feed stage is lowered from its optimum location,
the recovery fraction of sandwiched components is increased relative to the value
at the optimum location. Of course, the opposite will hold. In addition, as one
increases the length of the stripping section the rejection of the very light diluents is
improved for a given separation.
Stages-Reflux Curve
The two following figures are stage-reflux curves for an easy separation and
a difficult separation. In the first case, the knee or breakpoint is easily
distinguishable. In the second case, for a difficult separation requiring 50 or more
stages and an l,h of no more than 1.3, the curve is much flatter. The asymptote of
this type of curve has not really developed and the knee is not readily
distinguishable.
Lecture Notes: Fractionation
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CHEE 470 Course Notes
BATCH DISTILLATION
Batch distillation was the predominant type of distillation practiced in the first
20 to 30 years of this century. Although continuous systems have superseded
batch, there are probably still many more batch stills used commercially than
continuous.
In a batch distillation, an amount of feed is charged to a still pot and then
boiled overhead. Components in the feed charge are separated due to their
different volatilities. In a simple batch system there is no column or reflux and, in
its limit, (conducted at equilibrium) is a simple differential distillation or Rayleigh
distillation. A column or reflux can be provided and then the system is referred to
as batch rectification or batch fractionation.
Advantages of Batch Distillation
1)
Normally the most economical for small volumes.
2)
Very flexible, a given system can handle large variations in feed
quality and different feeds.
3)
There are cases where a batch system can be more efficient than a
continuous system when recovery of a single component at high
purity from a complex mixture is desired.
4)
The control systems are usually very simple and inexpensive.
5)
Operation is usually very simple, as there is no need to balance feed and
product rates.
Lecture Notes: Fractionation
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CHEE 470 Course Notes
Disadvantages of Batch Distillation
1)
Only relatively small volumes can be processed economically.
2)
Under normal circumstances a batch system cannot be used for
heat sensitive materials because of the long residence times at high
end point conditions.
3)
Since batch distillation is a non-steady state system, design and
analysis are very much more difficult.
For highly non-ideal
multicomponent mixtures the procedure can become hopelessly
complex.
SHORT-CUT METHODS
There are basically three short-cut or approximate methods for solving
multicomponent separation problems: the Fenske-Underwood-Gilliland method,
the Kremser group method and the Edmister group method. Monor variations of
each method are also used.
Before the advent of computers that could handle the rigorous procedures,
the only practical methods were the short-cut or approximate methods. With the
ever-decreasing cost of computing power and the ready availability of
sophisticated rigorous procedures, the short-cut methods are rarely used these
days. They can be used in preliminary design studies, parametric studies to
establish optimum design conditions, and in process synthesis studies to
determine optimal separation sequences. Although the methods can be solved by
hand calculations, a practical approach only provided the physical properties are
independent of composition. Since the calculations are iterative in nature, the
most likely approach today is to use computer solutions.
A typical algorithm for the Fenske Underwood Gilliland Correlation is shown
on the following page. The Underwood equation is exact for the conditions of
constant  and constant molal overflow, the equation being an analytical
representation of the McCabe-Thiele diagram. The order of the calculation is that
the Fenske correlation is used to calculate the minimum number of stages and
estimate the overhead compositions and rate. The Underwood equations are then
used to estimate the minimum reflux corresponding to the estimated overhead
composition. The Gilliland correlation is then used to relate Nmin and the Rmin to
the actual required N and R. The resultant vapour and liquid rates can then be
used to calculate the required column diameter by means of vapour loading
equations, i.e. the Glitsch method.
Lecture Notes: Fractionation
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CHEE 470 Course Notes
The biggest problem with this approach is that it assumes a constant  across the
column as well as constant molal overflow. This situation simply doesn't exist.
The degree of deviation varies from an insignificant degree for close-boiling,
similar components to extreme deviations for non-ideal mixtures.
RIGOROUS FRACTIONATION METHODS
It should be emphasized that the rigorous procedures for column
calculations are not necessarily recent developments. In many instances, the
theoretical basis of these calculations has been around for a long time. What are
new in most cases are the algorithms that have been developed in order to solve
these quite involved problems. Some of the more common approaches are as
follows.
Lecture Notes: Fractionation
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CHEE 470 Course Notes
1)
The Lewis and Matheson Method
2)
The Stripping Factor Method
3)
The Thiele and Geddes Method
4)
Matrix Methods
If anyone is interested in the details of these procedures they are covered in
some detail in the references. We will only comment on the Matrix methods. The
matrix methods (which are definitely not hand methods) have largely taken over
the field of rigorous computer solutions, as they are believed to have superior
numerical stability.
A typical approach is to derive a set of simultaneous equations, which
express the mass balance and phase equilibria for the column for all components
taken one at a time. The solution of the set usually gives the liquid flow profile or
mole fraction from which the corresponding values for the vapour phase may be
derived. The matrix solution does not require that the sum of all the liquid mole
fractions equal zero, accordingly the temperature profile must be revised in an
appropriate fashion so that the mass balance does converge to a summation of
1.0 within reasonable tolerance. Conversion problems may arise if the K values
are strongly composition dependent. These algorithms are constantly being
improved. Some of the more exotic techniques involve the solution of Jacobian
(partial differential) matrices by inversion techniques.
Having solved the material balance/phase equilibria matrix, it is then
necessary to derive the appropriate set of simultaneous equations describing the
column heat balance. Upon solving this set, a new set of vapour flow rates are
obtained which are then used in conjunction with the new set of K values to reach
a new solution for the mass and heat balance. An iterative procedure is followed
until the mass balance, the heat balance, and all the phase equilibria meet
tolerance.
As you can appreciate from this brief description of a typical matrix solution
procedure, we are dealing with an extremely complex mathematical technique in
order to achieve a rigorous solution. Consider the complex mathematics involved
in the computation of the K values, for example. The solution of an equation of
state in itself may not be particularly robust for the given conditions, and before
one even gets involved with the complexities of the matrix solution for the mass
and heat balances, it is not surprising that a rigorous column calculation often
does not converge. These computerized systems have improved enormously over
the last several years in this regard.
There will continue to be improvements in the mathematical stability of the
computer algorithms, however at the present time there would appear to still be a
Lecture Notes: Fractionation
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CHEE 470 Course Notes
place for short-cut methods, provided one is fully aware of the severe limitations of
these procedures. (Except in a few rare instances where the assumption of
constant  and constant molal overflow are reasonable.) Recently a colleague of
ours, Ross Taylor of Clarkson University has developed a rate-based algorithm
which is incorporated into his fractionation program ChemSep. This is a novel
approach, and if successful will obviate the need to estimate tray efficiencies, an
arcane piece of "black art" at best.
Some recommended references are as follows:
DISTILLATION, Principles and Design Procedures
R.J Hengstebeck
Reinhold Publishing Corp
EQUILIBRIUM STAGED SEPARATIONS
Phillip C. Wankat
Elsevier
EQUILIBRIUM-STAGE SEPARATION OPERATIONS
ENGINEERING
Ernest J. Henley and J.D. Seader
John Wiley & Sons
IN CHEMICAL
DESIGN OF EQUILIBRIUM STAGE PROCESSES
Buford D. Smith
McGraw Hill
Fair, J.R., and W.l. Bolles, Chem. Eng., 75(9), 156-178 (April 22,1968)
Lecture Notes: Fractionation
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