Coker A.K. Fortran Programs for Chemical Process Design, Analysis, and Simulation

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Mass Transfer 537

DIA

0.2830

Avg. 0.28325

0.2835

DIA

0.9009

Avg. 0.90115

0.9014

A d

0.2326

Avg. 0.2329

0.2332

That is

Ad = 0.2329

The downcomer area, A d, is (0.2329) (28.27)

= 6.584 ft 2

The weir length, L, is (0.90115 x 72)

= 64.88 in.

65 in.

The computed liquid flow rate is 1.482 fl3/sec or 664.907 USgpm.

conversion" 1 fl3/sec - 448.655 USgpm

The liquid flow per inch of weir -

664.907

= 10.23 USgpm per inch of weir

A single-pass tray is selected.

Problem 7-4

A packed tower with 1-inch Raschig rings are to be used to absorb

ammonia from air by contacting the gas stream with water. The entering

gas flow is 40 lb mol/h and contains 5.0% NH 3. Ninety percent of the

NH 3 is to be removed from the air. The entering water flow rate is 3,200

lb/h. Absorption is to be carried out at 1 atm. abs. and 20~ Estimate:

1. The diameter of the tower for a AP of 1.0 in.

HzO/ft.

packing.

2. The vapor rate at 70% of flooding condition.

538

Fortran Programs for Chemical Process Design

Physical properties"

(,//273/

p~ - (28.4) ~ -~

= 0. 0737 lb/ft 3

PL - 62.3 lb/ft 3

~L - lcP

Fp - 155

Solution

When calculating the tower diameter, conditions at the bottom of the

tower should be used because this corresponds to the maximum flow rates.

At the bottom of the column:

MWga~ -

0.05 • 17 + 0.95 X 29

= 28.4 lb/lb, mol.

Molecular weight of ammonia (MW

NHs

-17

lb /

lb. mol

NH 3 removed from the air - (0.9)(0.05)(40)

/,8,b moll( ,b /

9 hr 17 lb. mol

= 30.6 lb/hr

Gas flow rate at the bottom - (40

'b m~ 4 ,b)

hr lb. mol

= 1,136 lb/hr

Liquid flow rate at the bottom- 3200 + 30.6

= 3230.6 lb/hr

The computer program PROG74 calculates the diameter of a packed

tower for pressure drops of 0.05, 0.10, 0.25, 0.50, 1.0 and 1.5 in

HzO/ft.

Mass Transfer 539

The simulation is based on the generalized pressure drop correlation of

Sherwood

et al.

[20].

The curves have been fitted to a series of equations developed by

B lackwell [13]. In addition, the program computes the vapor rate and

vapor velocity at 70% of flooding condition. Table 7-21 illustrates the

input data and computer output of the packed tower.

Problem 7-5

A column is to be designed to separate 1000 moles/hr of a binary

mixture of benzene

(C6H6)

and toluene (C7H8). The feed will contain 40%

benzene and 60% toluene. A distillate that is 99% benzene and a bottoms

that is 1% benzene are desired at a reflux ratio of 3 to 1. For this mixture,

the average value of relative volatility (c~) is 2.50. Estimate the number of

equilibrium stages at this reflux ratio and the optimum feed stage location.

Solution

The computer program PROG75 uses the analytical method of a qua-

dratic equation to determine the number of stages in the rectifying and

stripping sections of a distillation column. The program uses Smoker's

equations involving two components to calculate the required number

of stages. Table 7-22 gives the input data and computer output. The

Table 7-21

Input Data and Computer Output for Packed Tower Design

DATA74.DAT

3230.6 1136.0 0.0737

62.3 155.0 1.0 1.0

PACKED TOWER DESIGN

*****************************************************************************

LIQUID FLOW RATE,

Ib/hr.:

GAS FLOW RATE,

ib/hr.:

GAS DENSITY, ib/ft.^3:

LIQUID DENSITY, ib/ft.^3:

TOWER PACKING FACTOR:

PRESSURE DROP, INCH-H20:

LIQUID VISCOSITY,

cP:

X CO-ORDINATE IN THE GENERALIZED PLOT:

Y CO-ORDINATE IN THE GENERALIZED PLOT:

CALCULATED VAPOR RATE, ib/s.ft^2:

X CO-ORDINATE AT FLOODING CONDITION:

Y CO-ORDINATE AT FLOODING CONDITION:

VAPOR RATE AT 70% FLOODING CONDITION, Ib/s.ft^2:

VAPOR VELOCITY AT 70% FLOODING CONDITION,

ft./sec:

TOWER AREA,

ft^2:

TOWER DIAMETER,

inches:

TOWER AREA AT 70% FLOODING CONDITION,

ft^2:

TOWER DIAMETER AT 70% FLOODING CONDITION,

inches:

3230.600

i136.000

.0737

62.3000

155.0

1.000

.0979

.0719

.2617

.0978

.1335

.2496

3.39

1.21

14.87

1.67

17.49

540

Fortran Programs for Chemical Process Design

Table 7-22

Input Data and Computer Output for Calculating Equilibrium

Number of Stages Using Smoker's Equations

DATA75.DAT

2.5 2.5

0.40 0.99 0.01

EQUILIBRIUM NUMBER OF STAGES BY SMOKER'S EQUATION

THE RELATIVE VOLATILITY OF COMPONENT i.:

THE RELATIVE VOLATILITY OF COMPONENT

2.:

THE MOLE FRACTION OF THE FEED:

THE MOLE FRACTION OF THE DISTILLATE:

THE MOLE FRACTION OF THE BOTTOMS:

THE REFLUX RATIO:

THE NUMBER OF STAGES IN THE RECTIFYING SECTION:

THE NUMBER OF STAGES IN THE STRIPPING SECTION:

TOTAL NUMBER OF STAGES:

FEED STAGE LOCATION:

2.500

.4000

.9900

.0100

3.00

7.87

7.76

15.63

7.8

required number of stages between benzene and toluene mixture is 16.

The optimum feed location is 8.

Problem 7-6

The feed to a butane-pentane splitter of the following composition is

to be fractionated into a distillate product that contains 95% of the

n-butane contained in the feed. The bottoms product contains 95% of

the iso-pentane in the feed. The reflux ratio for the fractionation will be

1.3 Rm~ n, and the column pressure will be 100 psia at the top plate. The

reflux and feed are at their bubble point temperatures. The feed compo-

sition and equilibrium constant are:

Number

Component

iC4Hlo

nC4Hio (LK)

iCsHl2 (HK)

nCsH12

0.06

0.17

0.32

0.45

2.15

1.70

0.835

0.70

Use the short-cut method to determine:

1. The recoveries of the components in the distillate and bottoms.

2. The minimum number of stages.

3. The minimum reflux ratio.

4. The actual number of theoretical plates.

5. The optimum location of the feed plate.

Mass Transfer 541

Solution

The computer program PROG76 gives the multicomponent distribu-

tion calculations based on a series of equations developed by

Hengstebeck-Geddes [35,36], while the minimum tray calculations (at

total reflux) use the equations developed by Fenske [37]. The number

of theoretical equilibrium stages is determined using Gilliland's [38,39]

empirical correlations. The program listed calculates the following: feed

component recovery in both the distillate and bottoms products, the

minimum number of stages, Underwood constant, minimum reflux ra-

tio, actual reflux ratio, total number of theoretical plates, and the opti-

mum location of the feed plate in a distillation column. The user has an

option of entering the feed components (moles) and the equilibrium

constants or the feed and the relative volatilities. Feed components must

be entered in order of decreasing relative volatility, with the light key

(LK) and heavy key (HK) components adjacent to each other. Table 7-23

shows the input data and computer output of the butane-pentane splitter.

Table 7-23

Input Data and Computer Output for Multicomponent

System Fractionation

DATA76.DAT

EQUIL

0.06 2.15

0.17 1.70

0.32 0.835

0.45 0.70

0.95 0.95

3 1 1.3

MULTICOMPONENT SYSTEM FRACTIONATION

COMPONENT FEED REL VOLATILITY DISTILLATE BOTTOMS

NUMBER MOLES ALPHA % MOLES % MOLES

1 .0600 2.5749 99.2532 .0596 .7468 .0004

2 .1700 2.0359 95.0000 .1615 5.0000 .0085

3 .3200 1.0000 5.0000 .0160 95.0000 .3040

4 .4500 .8383 1.2067 .0054 98.7933 .4446

THE HEAVY KEY COMPONENT NUMBER:

PERCENTAGE RECOVERY OF THE LIGHT KEY COMPONENT

IN THE DISTILLATE (%):

PERCENTAGE RECOVERY OF THE HEAVY KEY COMPONENT

IN THE BOTTOM~ (%):

MINIMUM NUMBER OF STAGES:

TOTAL MOLES IN THE DISTILLATE:

TOTAL MOLES IN THE BOTTOMS:

UNDERWOOD CONSTANT:

MINIMUM REFLUX RATIO:

ACTUAL REFLUX RATIO:

NUMBER OF THEORETICAL PLATES IN THE COLUMN:

THE POSITION OF THE FEED PLATE:

95.00

8.3

.2425

.7575

1.6213

2.8036

3.6447

16.2

6.7

542 Fortran Programs for Chemical Process Design

References

1. Humphrey, J. L. and A. F. S iebert, "New Horizons In Distillation",

Chem. Eng.,

Dec. 1992, pp. 86-98.

2. Reid, R.C., Prausnitz, J. M. and T. K. Sherwood,

The Properties of

Gases and Liquids,

3rd. ed., McGraw-Hill Book Company, N.Y.,

1997.

3. Walas, S. M.,

Phase Equilibria In Chemical Engineering,

Butterworths Publishers, Boston, 1985.

4. Dodge, B. E,

Chemical Engineering Thermodynamics,

McGraw-

Hill, New York, 1944.

5. Hines, A. L. and R. N. Maddox,

Mass Transfer Fundamentals and

Applications,

Prentice-Hall Inc., New Jersey, 1985.

6. Coker, A. K., "Equilibrium Flash Calculations Quickly Computed

on PC,"

Oil & Gas J.,

Jan 1991, pp. 55-58.

7. Oliver, I. H., "Hand Calculator Program Speeds Flash Calculations,"

Oil & Gas J.,

March 31, 1980, p. 130.

8. Kostecke, S. T., "Speed of Hand Calculator Programs Can Be

Improved,"

Oil & Gas J.,

August 11, 1980, p. 107.

9. De Priester, C. L., Chem. Eng. Progr. Symposium Ser. 7:49, 1953.

10. Hadden, S. T. and H. G. Grayson, Petrol, Refiner, September 1961,

p. 207.

11. Engineering Data Book,

Gas Processor Suppliers Association,

Vol. 2, 10th ed., Section 19, Tulsa, Oklahoma, 1987.

12.

Nutter Float Valve Design Manual,

Nutter Engineering Co., Tulsa,

Oklahoma, August 1981.

13. B lackwell, W. W.,

Chemical Process Design On A Programmable

Calculator,

McGraw-Hill Book Co., New York, 1984.

14. Hoak, E J.,

Large and Small Scale Liquid Maldistribution in Packed

Column,

Ph.D. Thesis, Delft University, Netherland, 1983.

15. Eckert, J. S., "Selecting the Proper Distillation Column Packing,"

Chem. Eng. Progr.,

Vol. 66, No. 3, March 1970, p. 39.

16. Leva, M.,

Tower Packing and Packed Tower Design,

2nd. ed., U.S.

Stoneware Co., Akron, OH, 1953.

17. Van Winkle, M.,

Distillation,

McGraw-Hill, New York, 1967, p. 635.

18. Bain, W. A., Jr., and O. A. Hougen, "Flooding Velocities in Packed

Columns", Trans.

A.ICh.E.,

40, (1944), p. 22.

19. Lobo, W. E., E Hashmall, L. Friend, and E A., Zenz, "Limiting

Capacity of Dumped Tower Packings", Trans.

AICh.E.,

41, 1945,

p. 693.

Mass Transfer 543

20. Sherwood, T. K., G. H. Shipley, and F. A. I. Holloway, "Flooding

Velocities in Packed Columns", Ind. Eng. Chem., 30, 1938, p. 765.

21. Eckert, J. S., "Design Techniques for Sizing Packed Towers," Chem.

Eng., Progr., 57, 9, Sept. 1961, p. 54.

22. Kessler, D. E and E C. Wankat, "Correlations for Column Param-

eters," Chem. Eng., Sept. 26, 1988, p. 72.

23. Nguyen, H. X., "Program Expedites Packed Tower Design", Chem.

Eng., Nov. 20, 1978, p. 181.

24. Nguyen, H. X., "Easy Way to Size Packed Towers," Hydroc. Proc.,

Feb. 1979, p. 101.

25. Branan, C., The Process Engineer's Pocket Handbook, Gulf Pub-

lishing Co., Houston, Texas, 1976, p. 87.

26. Eckert, J. S., "How Tower Packings Behave", Chem. Eng,. April 14,

1975, p. 70.

27. Walas, S. M., Chemical Process Equipment: Selection and Design,

Butterworths, Boston, 1988.

28. Morrris, G. A. and J. Jackson, Absorption Towers, Butterworth,

Woburn, MA, 1953.

29. Bolles, W. and J. E Fair, "Improved Mass-Transfer Model Enhances

Packed-Column Design", Chem. Eng., 89, 14, July 12, 1982, p. 109.

30. Fair, J. F., "Continuous Mass Transfer," Chapter 13 in Scale up of

Chemical Processes, A. R. B isio and R.L. Kabel, Eds., Wiley,

New York, 1985.

31. Coker, A. K., "Understand The Basis of Packed-Column Design,"

Chem. Eng. Progr., Nov. 1991, pp. 93-99.

32. Smoker, E. H., "Analytic Determination of Plates in Fractionating

Columns," Trans,. A.I. ChE., Vol 34, 1938, p. 165.

33. McCabie, W. L. and E. W. Thiele, "Graphical Design of Fractionat-

ing Columns", 17, 1925, pp. 605-611.

34. Underwood, A. J. V., Trans. Inst. Chem. Eng., 10, 1932, pp. 112-152.

35. Geddes, R. L., "A General Index of Fractional Distillation Tower

for Hydrocarbon Mixtures," A.I. ChE.J., Vol. 4, No. 4, 1958, p. 389.

36. Hengstebeck, R. J., "A Simplified Method for Solving Multicom-

ponent Distillation Problems," A.I. Ch.E.J., 1944, p. 389.

37. Fenske, M. R., "Fractionating of Straight-Run Pennsylvania Gaso-

line," Industrial Engineering Chemistry, Vol. 24, No. 5, 1932, p. 482.

38. Brown, C. G. and Marton, H. Z., Trans. A.I. ChE.,J., Vol. 35, 1939,

p. 679.

39. Gilliland, E. R., "Estimate of the Number of Theoretical Plates as a

Function of Reflux Ratio," Ind. Eng. Chem., Vol. 32, 1940, p. 1220.

544

Fortran Programs for Chemical Process Design

40.

41.

42.

43.

44.

45.

46.

47.

48.

49.

50.

51.

Underwood, A. J.

V.,

"Fractional Distillation of Multicomponent

Mixtures," Chem. Eng. Progr., Vol. 44, 1948, p. 603.

Coker, A. K., "Program Provides Short-cut Distillation Tower Cal-

culations," Oil & Gas J., June 25, 1990, pp. 33-38.

Hengstebeck, R. J., Distillation, Reinhold, New York, 1961.

Liddle, C. J., "Improved Short-cut Method for Distillation Calcula-

tions," Chem. Eng., Oct. 21, 1968, p. 137.

Van-Winkle, M. and Todd, W. G., "Optimum Fractionation Design

by Simple Graphical Methods," Chem. Eng., Vol. 78, Sept. 20, 1971,

p. 136.

Molkavov, Yu. K., Koralina, T. E, Mazurina, N. I., and Nikiforov,

G. A., "An Approximation Method for Calculating the Basic

Parameters of Multicomponent Fractionation," Int. Chem. Eng.,

Vol. 12, No. 2, 1972, pp. 29-212.

Hohman, E. C. and Lockhart, F. J., Chemical Technology, Vol. 2,

1972, p. 614.

Eduljee, H. E., "Equations Replace Gilliland Plot," Hydroc. Proc.,

Vol. 54, No. 9, 1975, p. 120.

Chang, H. Y., "Gilliland Plot In One Equation," Hydro. Proc., Vol. 64,

No. 3, 1985, p. 48.

Harg. K., "Equation Proposed," Hydroc. Proc., Vol. 64. No. 3, 1985,

p. 48.

McCormick, J. E., "A Correlation for Distillation Stages and

Reflux," Chem. Eng., Sept. 26, 1988, p. 75.

Kirkbride, C. G., "Process Design Procedure for Multicomponent

Fractionators," Petroleum Refiner, Vol. 23, No. 9, 1944, p. 87.

PROGRAM PROG71

i00

Ii0

120

130

140

150

160

CALCULATION OF THE DEW POINT AND BUBBLE POINT OF GAS MIXTURE.

THIS PROGRAM WILL CALCULATE DEW POINT AND BUBBLE POINT BASED

ON THE SUPPLIED K-VALUES.

THE PROGRAM WILL COVER FEED STREAMS CONTAINING UP TO 15

COMPONENTS.

***************************************************************

Ki = EQUILIBRIUM FLASH CONSTANT FOR EACH FEED STREAM

Mi = TOTAL MOLES OF COMPONENT i IN THE FEED STREAM

Ni = MOLE FRACTION OF COMPONENT i IN THE FEED STREAM

***************************************************************

CHARACTER*f0 FEED

COMMON/DATA/BP,DP,J,K,N

REAL K(20), M(20), N(20), BP(20), DP(20)

OPEN (UNIT = 3, FILE='DATA71.DAT', STATUS='OLD', ERR=IS)

OPEN (UNIT = I, FILE='PRN')

READ EITHER THE DEW POINT OR BUBBLE POINT TEMPERATURE

READ THE TOTAL NUMBER OF COMPONENTS

READ THE MOLES OF EACH FEED COMPONENT

READ THE K-VALUE OF EACH COMPONENT

READ (3, 10, ERR=19) FEED

FORMAT (A6)

READ (3,*,ERR=19) T

READ (3,*,ERR=19) J

READ (3,*,ERR=19)(M(I),K(I),I=I,J)

WRITE (1, 100)

FORMAT (///,20X,'DEW AND BUBBLE POINTS CALCULATIONS',/IH ,

* 76(IH*))

WRITE (I, ii0) FEED

FORMAT (/,6X, A6, 2X,'POINT CALCULATION')

WRITE (i, 120) T

FORMAT (/,6X,'TEMPERATURE oF:',FI0.2)

WRITE (I, 130) J

FORMAT (/,6X,'NUMBER OF COMPONENTS IN THE FEED STREAM:',I2)

WRITE (1, 140)

FORMAT (/,6X,'NUMBER OF COMPONENTS',6X,'FEED COMPOSITION (MOLE %)',

* 6X,'K-VALUE',/IH ,76(IH-))

DO I = 1, J

WRITE (i, 150) I,M(I),K(I)

FORMAT (13X, I2, 24X, F8.4, 16X, F8.4)

END DO

GO TO 20

WRITE (1, 160)

FORMAT (6X,'DATA FILE DOES NOT EXIST')

GO TO 999

545

170

180

190

999

200

WRITE (i, 170)

FORMAT (6X,'ERROR MESSAGE IN THE DATA VALUE')

GO TO 999

SUM=0.0

DO I = i, J

SUM=SUM+M(I)

END DO

WRITE (i, 180)

FORMAT (IH ,76(IH-))

WRITE (i, 190)SUM

FORMAT (6X,'TOTAL COMPOSITION:', T40, F8.4)

CALCULATE THE MOLE FRACTION OF COMPONENT IN THE FEED STREAM

DO I = i, J

N(I)=M(I)/SUM

END DO

CHECK WHETHER THE FEED IS AT BUBBLE POINT OR DEW POINT.

IF (FEED .EQ. 'DEW' .OR. FEED .EQ. 'dew') THEN

GO TO 30

ELSEIF (FEED .EQ. 'BUBBLE' .OR. FEED .EQ. 'bubble') THEN

CALL BUBBLE

GO TO 999

ENDIF

CALL DEW

GO TO 999

CLOSE (3,STATUS='KEEP')

CLOSE (i)

STOP

END

***************************************************************

THIS PROGRAM CALCULATES THE DEW POINT

***************************************************************

SUBROUTINE DEW

COMMON/DATA/BP,DP,J,K,N

REAL N(20), K(20), DP(20) , BP(20)

DPT = 0.0

DO I = i, J

DP(I)=N(I)/K(I)

DPT=DPT+N(I)/K(I)

END DO

WRITE (i, 200)

FORMAT (/,6X,'NUMBER OF COMPONENTS',6X,'MOLE FRACTION',I6X,

'X=Y/K',/IH ,76(IH-))

DO I =i, J

546