McCabe

~~

Chapter

Fractionation Concepts

The concepts concepts describe described d in i n this th is chapter ar e foundations foundations of of distilladistill ation engineering. thorough understanding of these concepts is essential sen tial for for distillation practitioner. practitioner. This is one chapter th at th e novic novic can ill-afford to skip. The author stresses an d applies applies th e visual approac approach h (i.e., (i.e., graphical methods) when introducing these concepts. This approach was deemphasized when computers began to make rapid inroads into distillation design. For some time, graphical techniques were considered tool f th e past, never to be used agai n. undesirable undesirab le by-produ by-product ct was th at he distillation column column becam becam “black box,” box,” and e engineers’ understanding of distillation distillatio n suffere suffered. d. The last decade decade saw th e pendulum swing the other o ther way. It was ap preciated that there is no conflict between computer and graphical techniques, and that the two can coexist. It was realized that the graphical techniques themselves can be programm programmed ed and an d used side by side with computer simulation. This hybrid approach combined the speed and accuracy of the computer with the analytical and visual value of the graphical techniques. This chapter first discusse discussess t e stage concept concept,, and ho stages put together in column column.. It then presents th e principl principles es of x- diagram, agr am, whic is th e main graphical tool tool for for distillation distillation analysis. I t applies plies this th is graphical graph ical technique technique to define define and an d illustr illu strate ate several key distillation concepts: pinching, minimum and total reflux, minimum stripping, strippin g, effect of the thermal thermal stat of th e feed, and column compl complexexities (e.g., (e.g., multifeed multifeed columns). The chapter cha pter then th en reviews th e basic conconcepts of multicomponent distillation, and the application of graphical techniques such systems. Finally, the chapter describes the use of graphical techniques techniques i n analyzing analy zing compu computer ter simulation simul ation results. 19

Chapter Tw

Theo retical Stages Stages

2.1 2.1.1

Ideal and nonideal stages

The ideal distillation stage is

device device

It operates in steady state and has product.

t meets these criteria: liquid product and

vapor

All vapor and liquid entering the stage are intimately contacted and perfectly mixed. Total vapor leaving the stage is in equilibrium with t o t a l liquid leaving leaving the stage illustrates the first criterion. criter ion. The system in Fig. Examples. Figure ha vapor product and liquid product product a nd therefore obeys thi criterion. The systems in Fig. 2 . l b nd have no vapor products and therefore are not equilibrium stages. Generating vapor phase in these systems (Fig. 2 . l d an renders them equilibrium stages. stages. Figre 2 . l c an depict t o t a l an partial condenser, respectively. The total condenser is not distillation stage, whereas the partial condenser is. Figure illustr ates commo common n distillation distillation stage ar range ments Al satisfy criterion 1. Criteria an determine which arrangements are ideal stages. Nonideal stages can still be modeled using the ideal stage model, model, but th e nonideality m ust be accounted accounted for. Figure 2 . 2 a an shows thermosiphon reboiler arrangements. The system in Fig. 2 . 2 a is not a n ideal stage. The liquid product product is made up from from liquid leaving t he reboiler reboiler and liquid descending from from th e botto tra y. Although Although th e former former is perfectly mixed with the leaving vapor, th e latte la tterr does does not conta contact ct th e vapo vaporr and a nd is not i n equilibrium with it The system in Fig. 2 . 2 b is n idea idea stage. Here the liquid product is made up from the liquid leaving the reboiler only. This liquid is equilibrium with vapor vapor leaving th e reboiler, which which is th e vapor prodproduct from the stage. Figure 2 . 2 ~nd shows shows distillation tray arran geme nts. The syste in Fig. 2 . 2 ~s typical. typical. t does not satisfy criterion and therefore, is not an ideal stage. stage. Further F urther , only only th e vapo vaporr leaving the s tage at point can be in equilibrium equilibrium with the th e liquid liquid leaving th e tray . Vapor Vapor leaving the tray at point can only only be in equilibrium with th e tra y inl et liquid, liquid, but not with liquid liquid leaving the t ray . The system system in Fig 2 . 2 d is rarely encountered, but it satisfies criterion Here liquid composition tion acro across ss the t ray is uniform and a nd equa e quals ls th e composition f liquid leaving leaving t he tray. Vapo Vapo both points an with th is in contact with liquid product stream. Providing there is suffic sufficien ientt time and a re

Chapter Tw

Theo retical Stages Stages

2.1 2.1.1

Ideal and nonideal stages

The ideal distillation stage is

device device

It operates in steady state and has product.

t meets these criteria: liquid product and

vapor

All vapor and liquid entering the stage are intimately contacted and perfectly mixed. Total vapor leaving the stage is in equilibrium with t o t a l liquid leaving leaving the stage illustrates the first criterion. criter ion. The system in Fig. Examples. Figure ha vapor product and liquid product product a nd therefore obeys thi criterion. The systems in Fig. 2 . l b nd have no vapor products and therefore are not equilibrium stages. Generating vapor phase in these systems (Fig. 2 . l d an renders them equilibrium stages. stages. Figre 2 . l c an depict t o t a l an partial condenser, respectively. The total condenser is not distillation stage, whereas the partial condenser is. Figure illustr ates commo common n distillation distillation stage ar range ments Al satisfy criterion 1. Criteria an determine which arrangements are ideal stages. Nonideal stages can still be modeled using the ideal stage model, model, but th e nonideality m ust be accounted accounted for. Figure 2 . 2 a an shows thermosiphon reboiler arrangements. The system in Fig. 2 . 2 a is not a n ideal stage. The liquid product product is made up from from liquid leaving t he reboiler reboiler and liquid descending from from th e botto tra y. Although Although th e former former is perfectly mixed with the leaving vapor, th e latte la tterr does does not conta contact ct th e vapo vaporr and a nd is not i n equilibrium with it The system in Fig. 2 . 2 b is n idea idea stage. Here the liquid product is made up from the liquid leaving the reboiler only. This liquid is equilibrium with vapor vapor leaving th e reboiler, which which is th e vapor prodproduct from the stage. Figure 2 . 2 ~nd shows shows distillation tray arran geme nts. The syste in Fig. 2 . 2 ~s typical. typical. t does not satisfy criterion and therefore, is not an ideal stage. stage. Further F urther , only only th e vapo vaporr leaving the s tage at point can be in equilibrium equilibrium with the th e liquid liquid leaving th e tray . Vapor Vapor leaving the tray at point can only only be in equilibrium with th e tra y inl et liquid, liquid, but not with liquid liquid leaving the t ray . The system system in Fig 2 . 2 d is rarely encountered, but it satisfies criterion Here liquid composition tion acro across ss the t ray is uniform and a nd equa e quals ls th e composition f liquid leaving leaving t he tray. Vapo Vapo both points an with th is in contact with liquid product stream. Providing there is suffic sufficien ientt time and a re

(d)

The distillation stage concept. (a eneral presentation of an ideal distillation and (c) single-phase single-ph ase prod produc uctt (these (th ese are not ideal distillation dist illation stages); sta ges); an (e) two-phase two-phas e prod produc uctt (thes ( these e are ideal distilla dist illation tion stages). Figure 2. stage;

22

Chapter Two

22

Chapter Two

(d

Figure 2.2 Ideal and nonideal stages in distillation systems. ( a ) , Thermosiphon reboiler arrangements; (c), fractionation tray arr&gements; (e), inter(b), condenser arrangements. Arrangements and are ideal stages. Arrangements ( a ) , an (e) are nonideal stages.

vapor-liquid contact, equilibrium will be established. Criterion will be satisfied, making arra ngement 2.2d ideal stage. Figure 2.2e an shows intercondenser arrangements. The system in Fig. 2.2e is not a n ideal stage. Liquid leaving th e stage is made up from liquid condensed in the intercondenser and liquid from the top column. While the condensate is in equilibrium with vapor leaving th e stage, e liquid from th e column does not mix with th is vapor an is not in equilibrium with it. Mixing th e column liquid with th e vapor

Key Fractlonatlon Concepts

Vapor product stream

23

Vapor product stream

(e) Figure 2.

(Continued)

liquid mix ture leaving th e condenser (Fig. converts th e nonideal into a n ideal stage, provided th e line downstream of th e mixing point is sufficiently long. the nonideality of stage. The Stage efficiency. This accounts number of ideal stages is equal the number of nonideal stages multiplied by t e stage efficiency. The nonideality may lower enhance th e separation; if it enhances the separation, th e stage efficiency can exceed percent. Stage efficiencies ar e discussed in Chaps. and 9.

Stripping, rectification, and fractionation 2.1.2

Vapor leaving distillation stage is richer tha n the feed in t he morevolatile components. Liquid leaving the stage is richer than the feed in the less-volatile components. In order to improve the separation, multiple stages are used. Stripping stages (Fig. 2 . 3 ~ )oncentrate t he less-volatile component in liquid stream. vapor recycle vaporizes (“strips”) e morevolatile components from the liquid. generate the vapor recycle, heat is supplied vaporize portion of the bottom-stage liquid. This vapor recycle is termed boilup.

Chapter Tw

24

Vapor product

Vapor product

v1

Feed

Ji-7-1

Feed

v2

Vapor

Heat

Liquid product

Liquid product

(a) Vapor product Vapor

Vapor product

v3

Feed

Feed

Liquid produc

Liquid product (b)

Flgure

Multiple-stage arrangem ents.

Stripping;

ectifying;

fractionator,

Rectifying stages (Fig. 2 . 3 b ) concentrate the more-volatile components in vapor stream. liquid recycle condenses the less-volatile components from the rising vapor. generate the liquid recycle, cool ing is applied condense portion of th e overhead vapor. The liquid recycle is termed reflux. The stripping and rectifying stages shown in Fig. 2.3a an ca be combined into single separation process with internal recycle (Fig. 2 . 3 ~ ) .his process is termed fractionation. In single-feed fractionator, stages above the feed are rectifying

Key Fractionation Concepts

25

Vapor product Cooling

Feed

Heat

Liquid product

Liquid product

Figure

(Continued)

(c

and those belo it ar e stripping (Fig. 2 . 3 ~ ) .n multifeed fractionators, the more precise functional criterion below is used to distinguish th rectifying from stripping sections. The stripping section has net downflow f material. The vapor serves as the quantity of liquid exceeds the quantity of vapor in the stripping section. The converse applies in t e rectifying section. This section has net upflow of material, and t he quantity of vapor exceeds e quan tity of liquid. Figure 2. shows multifeed fractionator. The top three sections have net upflow f material and a re therefore rectifying. The bottom thre sections have net downflow of material, and a re therefore stripping. 2.1.3

Material and energy balance

For single binary distillation stage (Fig. 2.5a) the following equations apply:

Chapter Tw

F4

800

F3

300

F2

500

F,

1000

500

1700

Flgure 2.4 Stripping

rectifying sections.

Heat input or removal AH

Feed

(a

Fractionation-stage model nomenclature. (a Each stage; ractionator.

Figure 2.5

Key Fractionation Concepts

27

Stage Stage Stage 3 Stage Stage Stage Stage Stage

Stage Stage Stage

Stage Stage Stage

(b

Figure 2.5

(Continued)

M a s s Balance Fn

V n + , Ln-l

Ln

(2.1)

Component Balance Fnzn

Vn+IYn+l

Ln-A-1

VJ

(2.2)

Chapter

28

Energy Balanc

AHn

FnHf,n

Vn+lHV,n+l Ln-lHL,n-l

VnHv,n

LnHL,

(2.3)

Equilibrium Relationship

In multicomponent distillation of components, there are component balances a equations describing the equilibrium relationship. Equations (2.1) (2.4) apply to each stage. rigorous solution (Chap. 4) simultaneously solves these equations each stage and each component. The equations can be simplified and solved by analytical shortcut procedures (Chap. or graphically. The rest of thi s chapter focuses on th e graphical procedures, whic are applied introduce and illustrate several key fractionation concepts. Multiple stages (Fig. 2.5b).

2.

x-y Diagrams

Computers have superseded graphical techniques as the main distillation design and performance evaluation tool. Nevertheless, graphitechniques a re still widely used in modern distillation technology Their prime application is as an analytical tool. They provide means of visualizing the process and enable spotting pinched conditions, excessive reflux, incorrect feed points, and nonoptimum thermal condition of th e feed. They ar e powerfu analyzing computer solutions (Sec. 2.4.1). Other applications ar e screening and optimization of de sign options, providing initial estimates for computer calculations and engineer trainin g. The graphical technique most frequently used in distillation is th or McCabe-Thiele diagram (1).The H-x, Ponchon-Savarit diagram (2,3), is harder visualize and cannot be readily extended multicomponent distillation. Due their limited application, diagrams were excluded from thi s book, and are discussed elsewhere

(4-6).

2.2.1

McCabe-Thiele diagrams: fundamentals

mass balance th e “envelope” shown in Fig. 2.6a, cutting belo any plate in t e rectifying section, gives

Key Fractionation Concepts

Mater ial balances ping section; overall. Figure 2.6

Rectifying section;

V,,, Similarly,

trip-

(2.5)

Ln

component balance gives Dx

Instead of

29

(2.6)

ene rgy balance, th e McCabe-Thiele method assumes

30

Chapter Tw

XD

(C

Figure 2.6

(Continued)

constant molar overflow (Sec. 2.2.2). Mathematically, this assumption means

...

(2.7)

From Eqs. (2.5) an (2.7) it follows t

v, v,

..

These equations simplify Eq. (2.6)

Vn+1

(2.8)

Key Fractionation Concepts

31

similar derivation for the stripping section (Fig. 2.6b) ives

(2.10) Equations (2.9) nd (2.10) re basic building blocks McCabe-Thiele diagrams. They ar e discussed further in Sec. 2.2.3. quations (2.7) nd (2.8) also simplify Eq. (2.5)

V = L t D

(2.11)

similar derivation for th e stripping section give

v = L ' - B

(2.12)

An overall column mass balance (Fig. 2.6~)ives

F = B t D

(2.13)

Combining Eqs. (2.11), 2.12), nd (2.13) ives relationship th at can also be derived from feed stage mass balance (Fig. 2.6~)

(L

(2.14)

An overall column component balance gives

FZ

(2.15)

The definition of reflux ratio is

(2.16) Similarly, the stripping ratio is

(2.17) 2.2.2 Constant molar overflow and o ther assumptions

Constant molar overflow. This assumption is substitute the en ergy balances. I states th at t he mixture has constant hea of vaporization and that sensible heat and heat of mixing effects are negligible. Equations (2.7) nd (2.8) ive mathematical expression of this assumption. Detailed thermodynamic implications of this assumptio e described elsewhere (e.g., Refs. 6-8). Generally, constant molar overflow holds well systems where the components ar similar in nature and molecular weights, and

32

Chapter

where heat-of-solution effects ar not significant. When heat-of-solution effects ar small, th ratio of the molar latent heats of the pur components provides insight into the suitability of the assumption (Table 2.1). The assumption holds well for t e benzene-toluene, isobul butane, propane-normal butane, and normal heptane ethylbenzene systems, where the late nt hea ratios ar e close unity. The assumption is less satisfactory the acetone-water and methaneethylene systems, where this ratio is higher. The assumption is poor th e ammonia-water system where the latent heat ratio is close to When in doubt, it is best adjust th diagram heat effects. This can be achieved by one of t e following techniques. When computer simulation is available, the component balance lines (Sec. 2.2.3) can be constructed from compositions printed out by the simulation. The simulation energy balances adjust the component balance lines heat effects. These heat effects convert each component balance line t hus constructed into curve (Sec. 2.4.1). Using an diagram adjust Eqs. (2.9) nd (2.10) latent heat effects. This approach also converts each component balance line into -x diagram instead of curve, but the curv is constructed using a computer simulation, Further details ar e described by Fisher (10). Using an diagram derive pseudo molecular weights and pseudo latent heats of vaporization for t e components. These pseud properties ar e then applied construct an diagram. This methd is described in detail by Robinson and Gilliland (6). Other assumptions. diagram method:

o additional assumptions ar e inherent in th

x-

1. The separation is at constant pressure. This assumption is usually good unless the column operates under vacuum. For vacuum systems, the equilibrium curve needs adjustment pressure variations.

The feed stream mixes with th e feed-stage fluids prior to an y separation. This assumption is good single-phase feed, but less satisfactory fo partially vaporized feed (11). partially vaporized feed splits prior mixing; e feed liquid then mixes with liquid of th e tr ay below, while vapor mixes with vapor f the tray above. Ledanois and Olivera-Fuentes (11)derived simple correction to the diagram construction alleviate the inaccuracy. Their correction is valid where t ra y efficiency is high (i.e., above 60 to 70 percent); at lower tray efficiencies, th e inaccuracy is more difficult to quantify.

Using Latent Heat Ratio as a Guide to the Application of Constant Molar Overflow

TABLE

Boiling points, "F Component no Benzene Isobutane Propane n-heptane Acetone Methane Ammonia NOTES:

Component no. 2

Pressure, psia

Toluene n-butane n-butane Ethylbenzene Water Ethylene Water

14.7 75 200 14.7 14.7 470 295

Component no. 176 100 100 210 133 140 120

Latent heat, Btd b-m ole

Component no. 2

Component no.

Component no. 2

Latent heat ratio, (comp. 2)/ (camp. 1)

Note

231 122 201 277 212 10 413

13300 790 5900 13600 12800 2200 7700

14500 8300 6700 15500 17500 3100 15200

1.09 1.05 1.13 1.14 1.37 1.41 1.97

2

(1)Data from Gallant, Ref. 9; (2) data from Robinson and Gilliland, Ref. 6; (3

ata

from

Van Winkle, Ref. 4.

Chapter Tw

The inaccuracy due this assumptio is usually minor. It is substantial (11)only where the feed split significantly affects the separation; typically with very few stages (about five or fewer) and very high relative volatility

Mc Cab e-Thlele diagrams: line equations

2.2.3

Equilibrium curve (Figs. 1.18, 2.9b). This curve is th e locus of all equilibrium points. For given liquid composition it gives th e equilibrium vapor composition, and vice versa. An equilibrium stage is represented point (x,,y,) on the equilibrium curve where an ar e the liquid and vapor compositions leaving th e stage. 45 diagonal line (Fig. 2.9b). This line is the locus of all the points where Yn+l

(2.18)

Com ponent balance (operating) lines (Fig. 2.9b). The component balance equations, Eqs. (2.9) and (2.10),can be represented as straight lines on x-y diagram. The rectifying section component balance line is the locus of points th at obey e rectifying section component balance, Eq. (2.9). Similarly, t e stripping section component balance line is the lo

Chapter Tw

The inaccuracy due this assumptio is usually minor. It is substantial (11)only where the feed split significantly affects the separation; typically with very few stages (about five or fewer) and very high relative volatility

Mc Cab e-Thlele diagrams: line equations

2.2.3

Equilibrium curve (Figs. 1.18, 2.9b). This curve is th e locus of all equilibrium points. For given liquid composition it gives th e equilibrium vapor composition, and vice versa. An equilibrium stage is represented point (x,,y,) on the equilibrium curve where an ar e the liquid and vapor compositions leaving th e stage. 45 diagonal line (Fig. 2.9b). This line is the locus of all the points where Yn+l

(2.18)

Com ponent balance (operating) lines (Fig. 2.9b). The component balance equations, Eqs. (2.9) and (2.10),can be represented as straight lines on x-y diagram. The rectifying section component balance line is the locus of points th at obey e rectifying section component balance, Eq. (2.9). Similarly, t e stripping section component balance line is the lo cus of points t ha t obey e stripping section component balance, Eq. (2.10). Unfortunately, component balance lines are referred "operating lines." The autho r believes th operating lines is poor choice of words, since it states little about the physical nature of these lines. The term component balance lines is more descriptive and appropriate, and will be used in this book. Slopes of component balance (Operating) lines. Equations (2.9) and (2.10) indicate t ha t th e slopes of th e component balance lines a LIV an the rectifying and stripping sections, respectively. As V' Eq. (2.1211, e slope of e rectifying [Eq. (2.11)l an section component balance line is smaller th an unity, while t ha of stripping section component balance line is greater th an unity When latent hea t varies from stage to stage, o LIV nd ratios. For this reason, when th e constant molar overflow assumption (Sec. 2.2.2) does not apply, the component balance relationship becomes curve instead of straight line. intersection of component balance (operating) lines with diagonal. The point where the rectifying section component balance line intersects

Ke Fractionation Concepts

35

th 45 diagonal line satisfies both Eqs. (2.9) nd (2.18). olving these simultaneously and then using Eq. (2.11) ives

(2.19) Both Eqs. (2.9) nd (2.19) column equipped with total confo denser (Fig. 2.74.Since t o t a l condenser is not a n equilibrium stage (Sec. 2.1.11, he first equilibrium stage is inside the column. f t he condenser is p a r t i a l (Fig. 2.7b), he it is the first equilibrium stage. In this case, replaces in Eq. (2.9), is identical V,, nd zero. Substituting in Eq. (2.9) ives

(2.20)

Yntl

Condenser compoTotal connent balances. denser; partial condenser. Figure 2.7

Chapter Tw

Therefore, the rectifying section component balance line intersects th 5" diagonal line at the point an for t o t a l and partial condenser, respectively, The intersection point can be expressed (2.21)

product composition

similar derivation fo the stripping section shows that the stripping section component balance line intersects the " diagonal line at the point bottom product composition

(2.22)

Intersection of the two-com ponent b alance (operating) lines. Intersection takes place at point ( x i , y i ) ha t satisfies both Eqs. (2.9) and (2.10). Multiplying both sides of Eq. (2.9) by and both sides of (2.10) by V' and subtracting one from the other yields (V

L'hi

V')yi

DxD

(2.23)

Using Eq. (2.151, this simplifies

L')xi

V)yi

FZ

(2.24)

Let (2.25) Dividing both sides of Eq. (2.14) by

and substituting Eq. (2.25),gives (2.26)

Substituting Eqs. (2.25) and (2.26) in Eq. (2.241, and dividing both sides by (q 1)F i-

q-lX

(2.27)

Equation (2.27) represents the locus of the points at which the rectifying section component balance line intersects t e stripping sectio component balance line. This equation is called the q-line equation. The q-line is illustrated lat er in Fig. 2.9b

Intersection of the gl ine w ith the 45 diagonal. gives Therefore, th e q-line intersects at th e poin (z,z).

z, then Eq. (2.27) e 45" diagonal line

per Eq. (2.27). Equation Slope of the gline. The slope is q/(q , which defines q, can be rewritten as

Key Fractionation Con cepts

37

(2.28) is From this equation, th e quantity is th e fraction f t e feed liquid. The product q F is the quantit of liquid contained in the feed. This quantity joins t he liquid descending from th e rectifying section to is provide th e liquid the stripping section. Similarly, (1 quantity of vapor in the feed; this vapor joins the vapor ascending from th e stripping section to provide th e rectifying section vapor flow Table summarizes the relationship betwee q, the thermal condition f th e feed, slope of th e q-line, and column flows. Figure 2 . 8 ~llustrates the slope of the q-line for each these conditions. Figure 2.8b illustrates t he effect of th e slope on th e component balance line, assuming t he rectifying section component balance line (and therefore th e reflux ratio) is fixed. draw straight line on an x-y diagram, the Summary. In order slope of th e line and one point on the line need be determined. The derivations above enable the determination of e slope and one point on th e following lines: 1. The rectifying section component balance (operating) line.

The stripping section component balance (operating) line.

3. The q-line. In each case th e point defined is th e intersection of the line with th 45" diagonal line. The slopes and intersection points of each of these lines ar e summarized in Tabl 2.3. In addition, it has been shown at the rectifying section component balance line and the stripping section component balance line meet on the q-line.

McCabe-Thiele diagrams: construction

2.2.4

benzene an 60% toluene mixture into top product containing 95% benzene and bottom stre am containing 90% toluene. The feed mixtur is 25 percent vaporized. The reflux ratio is 3:1, an total condenser is to be used. How many theoretical stages ar e required At what stage should the feed be introduced Example 2.1

is required to separate 200 lb-moleh of

40

Obtain an overall material balance for the column. (Refer to solution STEP Figs. 2 . 6 ~ nd 2.9a.I 1. Given

0.4, x, 200 lb-mol eh, 2. Overall mass balance, Eq. (2.13)

0.95,

200 Overall component balance on benzene, Eq. (2.15) 20

0.4

0.1B

0.950

Chapter Tw

38

.o

LIVE GRAP H Click here to view

0. .-

OO

0.6 0.2 0. 0.4 mole fraction benzene in liquid (a

1.0

.o

LIVE GRAPH Click here to view

0.

0.6

.4

0.6 liquid mole fraction benzen 0.

(b)

1.0

The q-line and its implications. The q-line ffect of q as function of th e therm al state of th e feed; on stripping section component balance line at constant reflux ratio. Figure .8

Key Ractlonatlon,Concepts Relationship between 9, qLlne, and Column Flows

TABLE 2.2

Relationship between Feed condition

calculate

Subcooled

q = l t

liquid Saturated liquid

Slope of line

Lan d

Vand

Line in Fig.

V'

CpL(TBp

2.8a (a

V

1

Vapor-liquid mixture

=,mol ar liqui fraction of feed

(c

-u

Saturated vapor

L'=L

C p d T f TDp)

Superheated apor

V'
(d)

V' V

(e)

Mc Cab eTh lele Diagram Lines

TABLE 2.

What the line describes

Line

Point through which line passes

Slope

L/

(xD,xD) if total condenser (yD,yD) f partial condenser

Rectifying section component balance (operating) line

Rectifying section component balances

Stripping section component balance (operating) line

Stripping section component balances

(.ZBJB)

Locus of points of intersection of rectifying and stripping componen balance lines

(2,Z)

3. q-line

45" diagonal line

Locus of points where At total reflux it represents the component balance lines

(0,O) nd (1.0,l.O)

129.

Solving t he equations simultaneously, STEP

39

Set vapor an d liquid flow in th e column.

Find

from

e definitio

of reflux [Eq. (2.1613

21

b-moleh

Find Vfrom Eq (2.11).

21

28

b-moleh

Chapter Tw

20 0. 0.75

Legend: Initially given Calculated in Step Calculated in Step

xs

0.

(a

Figure 2.9 Solution to Example 2.1. (a Steps 1,

tep

c)

step 4.

3. Since 25 percent of the feed is vaporized, 0.75. Find rom t he definition of q, q. (2.28) 21 0.75 200 363 lb-mo leh qF L’ (2.12). 4. Find V’ rom

L’

36 29 234 Ib-moleh The material balances and flows are shown in F g. STEP

2.3.

3 Establish component balance and q-lines. Us e th e equations in Table

1.0

Equiiibr um curve

0.8

a-line Rec tifyin g section component balance ("operating)Iile

0)

.-

(0.95,0.95

diagonol line

0.4 (0.4,0.4) 0.2 '( 0 . 1 , O . l ~

S t r i p p i n g s e ct io n compone nt ba a nce ("operating) line

.o

0. 0. mole fraction benzene in liquid

(b

.o 0.8

0.

0.6 mole fraction benzene in liquid

(c Figure 2.8

(Continued) Lin e

S lo pe

section component balance (operating) l in Str ipp ing section component balance (operating) l in

3. q - l i n e

Point through whic

passes

(0.95, .95 v-284-

23

1,55

L=o.750.25

-3'0

(0.10, .10)

(0.40, 0.40) 41

Chapter These lines are shown in Fig. 2.9b. Note th at the q-line passes through the intersection of the two component balance lines. Step off the stages. Start off t the poin ( z D , x D ) .Move horizontally to th left until you meet the equilibrium curve. The point of intersection with th equilibrium curve represents the vapor and liquid compositionsof stage Then move vertically down the point (x,,y,), which is located on the component balance line [Eq. (2.9)].Move horizontally to the left u ntil you meet the equilibrium curve at point (zz,yz).Continue stepping off stages until reaching the bottom compositio x,. The number of times the equilibrium curve is met is the number of stages. Note that the optimum feed point is where the component balance lines intersect. The number of stages above the intersection point is th number of rectifying stages. The number of stages below is the number of stripping stages. This procedure is illustrated in Fig. 2 . 9 ~ . or this example,just over stages are required; stages will ensure t ha t the separation is achieved. The best fee point is stage giving rectifying and stripping stages. f the Condenser were a partial condenser, the condenser would have been stage 1. In this case, the numbe of stages in the column would have been re9. duced from 10 STEP

2.2.5

Optimum feed stage and pinching

In Sec. 2 . 2 . 4 , it was assumed that the feed enters the column at optimum feed stage, which is located at th e intersection of e component balance lines. At t t point, th e construction was switched fro th e rectifying section component balance line to t e stripping sectio component balance line. This switch could have been made earlie later, depending on the location of actual feed point. Figure 2 . 1 0 ~ hows switch taking place earlier, because t e column feed point is located between stages an (compared stage an in Sec. 2 . 2 . 4 ) . Figure 2.10b shows switch taking place later, because the column feed point is located between stage an 9. In either case, more stages ar e required and 12 stages in Fig 2 . 1 0 ~ nd respectively, compared to 10 stages in Fig. 2 . 9 ~ ) . The reason fo the greater number of stages is that steps become smaller as th e component balance line moves close the equilibriu curve, and therefore more steps re required. The optimum feed point is therefore achieved when e “active” component balance line is as as possible from the equilibrium curve.

Pinching. As t e component balance line approaches th e equilibrium curve, the steps become smaller. An infinite number of stages is required reach t e intersection of th e component balance line an d th equilibrium curve. This intersection is termed the pinch point. The bottom pinch point is ( 0 . 2 2 , 0.4) in Fig. 2.10bJ and t e top pinch point

Key Fractionatlon Concepts

LIVE GRAPH Click here to view

0.8

.-

0.

0.

0.6

0.8 mole fraction benzene in liquid

.4

1.0

(a)

.o

LIVE GRAP H Click here to view

.8

0.8

.4

1.0

mole fraction benzene in liquid (b

Nonoptimum feed points. (a Feed point located too hig h; feed point located too low; (c) increasin g reflux and reboil in order to accommodate for feed point located too high. Figure 2.10

43

44

Chapter Tw

.o

LIVE GRAP H Click here to view

0.8

0.2

0.

0.8

1.0

mole fraction benzene in liquid

Figure 2.10

(Continued)

is (0.47, 0.69) in Fig. 2.10~.hese points change when th e component balance lines do. column is said to be “pinching” when th e component balance line is close he equilibrium curve. Physically, this represents situation where several stages are doing very little separation and ar practically wasted. Pinching in column design does only waste stages, thereby leading n oversized column, but is also risky. Even minor inaccuracies in relative volatilities and enthalpies may brin g th e componen balance line and th e equilibrium curve closer, or even cross, earlie th an anticipated. This exponentially escalates th e stage requirement. f th e additional stages required a re unavailable, t e colum will not accomplish th e desired separation. It is therefore imperative to design column away from the pinched region. In a n existing column, mechanical reasons often make it difficult change feed location. pinch can then be remedied by increasing reflux and reboil. This draws the component balance line and the equilibrium curve furthe r ap art , enlarging th e steps, and thereby per-

Key Fractionation Concepts

45

mitting the required separation be achieved with the existing feed location. Example illustrates this. Increasing reflux and reboil in order to overcome pinch, however, is achieved at the penalty of greater energy consumption, higher operating costs, and greater vapor and liquid traffic through the column. When the column or its heat exchangers are close to capacity limit, the greater vapor and liquid traffic may reduce column feed-handling capacity. In the field symptom of pinching is very small temperatu re difference across many trays, particularly near the feed. This symptom can also suggest flooding, dry, otherwise inefficient trays. distinguishing feature of pinching is that reboil and reflux ratios a re increased, the temperature difference becomes larger and operation returns normal. Note t ha t “dry tray s” is specific case pinching. When the slope of the component balance line is 0, it will become horizontal until it meets the equilibrium curve. field test check whether column is pinching is described elsewhere (12). 10-stage column, with feed enter ing between stag e 4 an was used separate benzene-toluene mixture similar to that described in Example 2.1. The composition of feedstock has changed, and the new feedstock contai ns 40% benzene. Relocating the feed nozzle requires column shutdown, which is costly. Is t necessary? (Product composition specifications given in Example 2.1.) Example 2.

McCabe-Thiele diagram is shown in Fig. 2 With 10 stages, th overhead product can be kept on-spec, but t he bottoms product will contain 17% benzene, compared th e 10% specification. If this can be tolerated, shutdown change column feed nozzle is unnecessary. If 17%benzene i s unacceptable in t he bottom product, reflux and reboil can be raised to achieve th e required separation in 10 stages. The slope of th e rectifying section component balance line is increased, a nd t ha of the stripping section component balance line is lowered. This is trial-and-error calculation, which ends when 10 theoretical stages ar e accommodated between th e component balance line and the equilibrium curve, the top and bottom products are at their desired specifications, and the feed enters between stages 4 an The slopes of th e component balance line will determine the new required reflux and boilup rate. The final result is shown in Fig. 2. 10 ~. rom this diagram, solution

0.758 (slope of rectifying section component balance line) 1.54 (slope f stripping section component balance line) o calculate the actu al vapor a nd liquid rates, proceed as follows: 1. From Eq. (2.111, and since

(above)

71 lb-moleh (Example 2.1) and

0.758V

46

Chapter Tw

0.758V

b-molelh 0.758 Find

2.1)

from Eq. (2.28, nd since

L' Find

qF

0.76

22 0.75

20

rom Eq. (2.12), nd since

37 is the sam Check that ponent balance line.

b-molelh 20

37

b-moleh (Example

b-mole/h

lb-moleh (Example 2.1)

b-molelh

th at determined from

slope of the com-

Comparison of Examples 2.1 an 2.2. Table .4 gives measure of the effect f nonoptimum feed point on th e column in this example. Table 2. shows th at nd and therefore reboiler and condenser duties, increase by about to percent in Example 2.2. This roughly corresponds to percent increase in energy consumption a nd operatat its pacity limit, the column feed rate will need be reduced by to percent. If these consequences can be tolerated shutdown to change e column feed nozzle will be unnecessary. Note th t in thi s example th e effect of nonoptimum feed was quite mild. In other cases, it may be more detrimental.

TABLE 2.4

Variable

Comparlson of Examples 2. and 2. This variable gives measure of Rectifying section liquid load Rectifyingsection vapor load Condenser duty Stripping section liquid load Strippingsection vapor load Reboiler duty

Example 2.1, lb-moleh

Example 2.2, lb-moleh

Effect of nonoptimum feed in Example

21

222

4% greater

28

293

3% greater

363

372

2.5 greater

234

243

4% greater

Key Fractionation C oncepts

2.2.6

47

Minimum reflux ratio

Using Eqs. (2.11) an

(2.161, Eq. (2.9)

e rectifying section com-

XD

t l

R t l

(2.29)

As the reflux ratio decreases, so does the slope of the upper component

balance line. The effect of reflux ratio on th e component balance lines is illustrated in Fig 2.11, using the benzene-toluenesystem in Example 2.1. Any practical separation requires t t the component balance lines intersect below the equilibrium curve, reflux ratio of 3. in Fig. The McCabe-Thiele construction corresponding to thi ratio is shown in Fig. 2 . 9 ~ .f insufficient reflux is provided, th e component balance lines intersect above the equilibrium curve, as reflux ratio of 1. in Fig. 2 . 1 1 ~ . he McCabe-Thiele construction (Fig. 2.11b) these conditions shows that even with an infinite number of stages, th e separation cannot be achieved. The separation is theoretically possible if the component balance lines intersect at point just below t e equilibrium curve. The corresponding reflux ratio is termed minimum reflux. The separation at minimum reflux requires an infinite number of stages. In Fig. 2.11, he minimum reflu ratio is 2.0. The McCabe-Thiele construction for this ratio is shown in Fig. 2 . 1 1 ~ . At minimum reflux, t e pinch occurs at th e intersection f t e component balance line and the q-line when the equilibrium curve has no inflection points (Fig. 2 . 1 1 ~ ) . his would be expected because t e component balance lines intersect on the q-line. When the equilibrium curve has point of inflection (Fig. 2.12), e pinch between t e equilibrium curve and the component balance line may occur at th e poin of tangency instead f the intersection of th e q-line and the componen balance line. This conditio is termed tangent pinch. o determine minimum reflux, construct t e q-line and identify its point of intersection with the equilibrium curve. Then draw line from th e product composition point on t diagonal line this intersection point. From Eq. (2.291, the slope of the line is Rmin/ axis is xD/(Rmin 1). (Rmin nd th e intercept of this line on th Minimum reflux can be determined from either of these. If minimum reflux occurs at tangent pinch, the minimum reflux is independent of th e q-line and t he feed composition. t can then be determined fro the equilibrium curve alone (13). Neither minimum reflux nor tangent pinch is an operable condition. Either will require an infinite number of stages in th e column, and this is physically impossible. Nevertheless, operation can some-

40

Chapter Tw

LIVE GRAPH Click here to view

0.6 0. mole fraction benzene in liquid

.o

LIVE GRAPH Click here to view

=1.0

.6 ._

0.

mole fraction benzene

liquid

(b

Effect f reflu x ratio on compon ent balance lines. Overall; Rmi,, impossible operation; (c) Rmi,, minimum reflux; t o t a l reflux.

Figure 2.1 1

Ke Fractlonatlon C oncepts

.o

49

LIVE GRAPH Click here to view

0.

._

0.8 mole fraction benzene in liquid (C

LIVE GRAPH Click here to view

.-

0.

.4 0. mole fraction benzene in liquid (d Figure 2.11

(Continued)

times approach minimum reflux when cess of stages. 2.2.7

column contains

large ex-

Minimum stripping

Using Eqs. (2.12) (2.171,he stripping section component balance line [Eq. 2.1011 can be expressed in terms of the stripping ratio