Multicomponent Distillation v Imp

7/29/2019 Multicomponent Distillation v Imp

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F. Grisafi


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The problem of determining the stage and reflux

requ remen s or mu componen s a ons s muc morecomplex than for binary mixtures.

With a multicom onent mixture, fixin one com onentcomposition oes not unique y etermine t e ot ercomponent compositions and the stage temperature.

Also when the feed contains more than two com onents it is

not possible to specify the complete composition of the topand bottom products independently.

usually specified by setting limits on two "key components",between which it is desired to make the separation.


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The normal procedure for a typical problem is to solve the MESH(Material balance, Equilibrium, Summation and Heat) balance

equations stage-by-stage, from the top and bottom of the columntoward the feed point.

For such a calculation to be exact the com ositions obtained rom

both the bottom-up and top-down calculations must mesh at thefeed point and mesh the feed composition.

assumed for the top and bottom products at the commencement ofthe calculations.

oug t s poss e to matc t e ey components, t e ot ercomponents will not match unless the designer was particularlyfortunate in choosing the trial top and bottom compositions.


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For a completely rigorous solution the compositions must be

adjusted and the calculations repeated until a satisfactory matchat the feed point is obtained by iterative trial-and-errorcalculations.

Clearly, the greater the number of components, the more difficultthe problem.

,complicated by the fact that the component volatilities will befunctions of the unknown stage compositions.

I more t an a ew stages are require , stage- y-stagecalculations are complex and tedious.


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Before the advent of the modern digital computer, various "short-

cut" methods were developed to simplify the task of designingmulticomponent columns.

Though computer programs will normally be available for therigorous solution of the MESH equations, short-cut methods arestill useful in the preliminary design work, and as an aid in definingproblems for computer solution.

Intelligent use of the short-cut methods can reduce the computertime and costs.


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The short-cut methods available can be divided into two classes:

1. Simplifications of the rigorous stage-by-stage procedures toenable the calculations to be done using hand calculators, orra hicall .

Typical examples of this approach are the methods given byHengstebeck (1961), and the Smith-Brinkley method (1960); which

are described in Section 11.7 (C&R Vol. VI).

2. Empirical methods, which are based on the performance ofoperating columns, or the results of rigorous designs.T ical exam les of these methods are Gilliland's correlation

which is given in (C&R Vol. II, Chapter 11) and the Erbar-Maddoxcorrelation given in Section 11.7.3 (C&R Vol. VI).

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The designer must select the two "key components between which it isdesired to make the separation.

bottom product, and the heavy key the component to be kept out of thetop product.

Specifications will be set on the maximum concentrations of the keys in.

The keys are known as "adjacent keys" if they are "adjacent" in a listing of

the components in order of volatility, and "split keys" if some othercomponent lies between them in the order; they will usually be adjacent.

If any uncertainty exists in identifying keys components (e.g. isomers),trial calculations should be made using different components as the keys todetermine the pair that requires the largest number of stages forse aration the worst case .

The "non-key" components that appear in both top and bottom productsare known as "distributed" components; and those that are not present, toany significant extent, in one or other product, are known as "non-

" .

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In multicomponent distillations it is not possible to obtain more than one, , .

If a multicomponent feed is to be split into two or more virtually pureproducts, several columns will be needed.

side stream from a stage where a minor component is concentrated willreduce the concentration of that component in the main product.

For separation of N components, with one essentially pure component taken, ,

needed to obtain complete separation of all components.

For example, to separate a mixture of benzene, toluene and xylene twocolumns are needed (3-1), Benzene is taken overhead from the first column

and the bottom product, essentially free of benzene, is fed to the secondcolumn.

This column separates the toluene and xylene.

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Costs considerationsThe order in which the com onents are se arated will determinethe capital and operating costs.

Where there are several components the number of possible,

number is 14, whereas with ten components it is near 5000.

When designing systems that require the separation of several,

optimum sequence of separation.

Separation schemesor a 4 components

mixture

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i i i i

1. Remove the components one at a time.

2. Remove any components that are present in largeexcess early in the sequence.

3. With difficult separations, involving close boilingcomponents, postpone the most difficult separation to

late in the sequence.Difficult separations will require many stages, so toreduce cost, the column diameter should be made asmall as ossible. As the column diameter is de endent

on flow-rate, the further down the sequence the smallerwill be the amount of material that the column has tohandle.

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Where a lar e number of sta es is re uired it ma be

necessary to split a column into two or more separatecolumns to reduce the height of the column, even

, ,have been obtained in a single column.

This may also be done in vacuum distillations, to reducethe column pressure drop and limit the bottom

.

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Short-cut methods for stage and refluxrequ remen s

Some of the more useful short-cut rocedures which

can be used to estimate stage and reflux requirementswithout the aid of computers are given in this section.

os o e s or -cu me o s were eve ope or edesign of separation columns for hydrocarbon systems

in the petroleum and petrochemical systems industries,an cau on mus e exerc se w en app y ng em oother systems (as it is assumed almost ideal behavior ofmixtures).

They usually depend on the assumption of constantrelative volatility, and should not be used for severely

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If the presence of the other components does not significantly,

treated as a pseudo-binary pair.

The number of stages can then be calculated using a McCabe-,

systems.

This simplification can often be made when the amount of the non-,mixtures.

Where the concentration of the non-keys is small, say less than, .

For higher concentrations the method proposed by Hengstebeck(1946) can be used to reduce the system to an equivalent binary

.

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'For any component i the Lewis-Sorel material balancee uations and e uilibrium relationshi can be written in

terms of the individual component molar flow rates; inplace of the component composition:

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To reduce a multicom onent s stem to an e uivalent

binary it is necessary to estimate the flow-rate of thekey components throughout the column.

Hengstebeck considers that in a typical distillation the

flow-rates of each of the light non-key components, ,section; and the flows of each of the heavy non-keycomponents approach limiting flow-rates in the strippingsec on.

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Putting the flow-rates of the non-keys equal to these

m ng ra es n eac sec on ena es e com neflows of the key components to be estimated.

eav er spec esspecies

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The method used to estimate the limiting flow-rates is

a propose y enny . e equa ons are:Stripping sectionRectifying section

di and bi = corresponding top and bottom flow rate of component i.

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Estimates of the flows of the combined keys enable operating lines to be.

The equilibrium line is drawn by assuming a constant relative volatility forthe light key:

where y and xrefer to thevapor and liquid concentrations of the light key.Hengstebeck shows how the method can be extended to deal withs ua ons w ere e re a ve vo a y canno e a en as cons an , an

how to allow for variations in the liquid and vapor molar flow rates.

He also ives a more ri orous ra hical rocedure based on the Lewis-Matheson method (see Section 11.8).

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Ki=F(T) [De Priester charts]

i

1 1

( ) 1 ( ) ( ) 1c c

i i i ii i

K T x f T K T x= =

= = i

1 1

1 ( ) 1( ) ( )

c ci i

i ii i

y yf TK T K T

= =

= =

Solution: find the temperature Tby trial-and-error procedure as f(T)=0

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Estimate the number of ideal stages needed in the butane-pentanesplitter defined by the compositions given in the table below.

. ,

R=2.5. The feed is at its boiling point (q=1).Assumed composition

xd xb

C3

0.111 0.000

4. .

nC4

0.533 0.018

iC5

0.022 0.345

. .

.rigorouscomputer method and it was found that 10 stages were needed.

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Example 11.5 - solutionThe top and bottom temperatures (dew points and bubble points)were calculated by the methods illustrated in Example 11.9.

Relative volatilities are given by equation 8.30:

Equilibrium constants were taken from the De Priester charts.

Relative volatilities estimated:

Light non-key comp.

g t non- ey comp.

Heavy non-key comp.

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-Stripping sectionRectifying section

Calculations ofnon-key flows:

Strippingsection

Rectifying

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-Flow of combined keys:

tripping sectionecti ying section

L=RDV=(R+1)DV=V-(1-q)F

R= reflux ratio; q= feed thermal index (1 for boiling liquid; 0 for saturated vapour)

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Equilibrium points

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Example 11.5 - solutionThe McCabe-Thiele dia ram is shown in Fi ure: 12 sta es re uired;feed on seventh from base.

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Empirical correlations methodsThe two most fre uentl used em irical methods for estimatin thestage requirements for multicomponent distillations are thecorrelations published by Gilliland (1940) and by Erbar and Maddox(1961).

These relate the number of ideal stages required for a givenseparation, at a given reflux ratio, to the number at total refluxminimum ossible and the minimum reflux ratio infinite number

of stages).

Gilliland's correlation is given in C-R Vol. 2, Chapter 11.

The Erbar-Maddox correlation is given in this section, as it is nowgenerally considered to give more reliable predictions.

Their correlation is shown in Fi ure 11.11 which ives the ratio of

number of stages required to the number at total reflux, as afunction of the reflux ratio, with the minimum reflux ratio as aparameter.

To use Figure 11.11, estimates of the number of stages at totalreflux and the minimum reflux ratio are needed.

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Number of stages calculationFig.11.11

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correlation(1961)

R/(R+1)=0.6

Example:Rm=1.33R=1.5

Rm/(Rm+1)=0.57R/(R+1)=0.6

Nm/N=0.34

m = .

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Gilliland correlation (1940), C&R II Vol.

Log-log plot

Linear plot

+

=+ 5.02.11711

.exp1

1nm

1+

=

Rmwhere:

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Minimum number of sta es Fenske E uationThe Fenske equation (Fenske, 1932) can be used to estimate theminimum stages required at total reflux.

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Vol. 2, Chapter 11. The equation applies equally to multicomponentsystems and can be written as:

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Minimum number of sta es Fenske E uation

Normally the separation required will be specified in terms of thekey components, and equation 11.57 can be rearranged to give anestimate of the number of stages.

where LK is the average relative volatility of the light key withrespect to the heavy key, and xLK and xHKare the light and heavy keyconcentrations.

e re a ve vo a y s a en as e geome r c mean o e va ues

at the column top and bottom temperatures.To calculate these temperatures initial estimates of the

,number of stages by the Fenske equation is a trial-and- errorprocedure.

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Lar e relative volatilities and feed locationIf there is a wide difference between the relative volatilities atthe top and bottom of the column the use of the average value in

.

In these circumstances, a better estimate can be made bycalculating the number of stages in the rectifying and strippingsec ons separa e y.

The feed concentration is taken as the base concentration for thesection, and estimating the average relative volatilities separatelyfor each section.

s proce ure w a so g ve an es ma e o e ee po n oca on

cannot be taken as constant.

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i iIf the number of stages is known, equation 11.57 can be usedto estimate the split of components between the top and

.

It can be written in a more convenient form for calculatingthe split of components:

Fenske Equation

where diand biare the flow-rates of the component i in the topsand bottoms, dr and br are the flow-rates of the reference (lightey componen n e ops an o oms.

Note: from the column material balance:

i i= iwhere fi is the flow rate of component iin the feed.

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Minimum reflux ratio Underwood equation

estimating the minimum reflux ratio for multicomponentdistillations. These equations are discussed in C-R Vol. 2, Chapt. 11.As the Underwood equation is more widely used it is presented in

s sec on. e equa on can e s a e n e orm:

1 LK

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Multicomponent Distillation v Imp