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

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Mass Transfer 527

Kirkbride's Feed Plate Location

After the minimum number of stages and the minimum reflux ratio

have been determined, the number of theoretical stages is then calcu-

lated. The ratio of the number of plates above the feed stage (including

the partial condenser) to the number below the feed stage (including the

reboiler) can be obtained using Kirkbride's empirical equation [51 ]. The

equation was developed on the basis that the ratio of rectifying trays to

stripping trays depends on"

9 The fraction of the heavy key component (in the feed) removed in

the overhead.

9 The fraction of the light key component removed in the bottoms.

9 The concentration of the heavy key component in the overhead.

9 The concentration of the light key component in the bottoms.

Kirkbride's feed plate equation is expressed as:

( ( /[ ]2}

[el S )B

log -o.2o61og LK

XLK F (XHK)D

(7-131)

where B = molar flow bottoms product

D = molar flow top product

m = number of theoretical stages above the feed plate, including

any partial condenser

p = number of theoretical stages below the feed plate, including

the reboiler

(XLK)F = concentration of the light key in the feed

(XnK)F = concentration of the heavy key in the feed

(XLK)B = concentration of the light key in the bottoms product

(XnK)D = concentration of the heavy key in the top product

Nomenclature

A~,B~ = correlation constants in Hengstebeck-Geddes equation

b = number of moles of a component in the bottoms

B = bottoms flow rate moles/hr

d = number of moles of a component in the distillate

D = distillate flow rate moles/hr

F = feed flow rate moles/hr

f = number of moles of a component in the feed

528

Fortran Programs for Chemical Process Design

FACTOR - multiplier for the reflux ratio (that is, FACTOR

Rmin)

K = equilibrium constant for a component in the feed

n = number of components

N - number of theoretical plates

Nmi n :

minimum number of theoretical plates at total reflux

q = pseudo-ratio of liquid to vapor for the feed

R = reflux ratio

Umi n =

minimum reflux ratio

x = mole fraction of a component where x B, x D, x F = mole frac-

tions in the bottoms, distillate, and feed, respectively

Greek Letters

~z = relative volatility with respect to the heavy key

0 = Underwood's constant

= summation

HK, LK = heavy and the light key components

i = individual component identifier

PROBLEMS AND SOLUTIONS

Problem 7-1

A multicomponent hydrocarbon gas mixture is composed as follows:

Component Mol % K

Methane

(CU4)

27.52 7.88

Ethane (C2H6) 16.34 2.77

Propane (C3H8) 29.18 1.18

Isobutane

(iC4Hl0)

5.37 0.61

Normal butane

(nC4Hl0)

17.18 0.48

Isopentane (iCsH12)

1.72 0.264

Normal pentane(nCsH~2) 2.18 0.225

Hexane

(C6Hl4)

0.47 0.102

Heptane (C7H16)

0.04 0.048

Operating temperature and pressure are 178~ and 400 psia. Determine

the dew point temperature of the gas mixture.

Mass Transfer 529

Solution

The computer program PROG71 calculates the dew and bubble points

of any multicomponent hydrocarbon mixture based on the user sup-

plied K-values. The program will handle feed streams containing up to

15 components. The feed entries may be moles, mole fraction, or mole

percent. The dew point (~X = ~Y/K) should be 1.0 or very close to 1.0,

depending on the tolerance the user will accept. If the sum printed is not

equal to 1.0 (within the user tolerance), a message is printed instructing

the user to assume a new temperature. The iteration is repeated using

the Ki's corresponding to the new temperature chosen. The temperature

supplied does not affect the computation, but is printed and stored as a

reminder to the user of which temperature (and corresponding K-values)

was used for the last iteration. Table 7-15 shows the input data and com-

puter output instructing the user that the dew point temperature is increased.

At 200 psia, calculate the bubble point temperature of the following:

Component Mol % K @ 260~ K @ 235~ K @ 237~

iC4Hl0

18.2 1.92 1.62 1.65

nCaH 10

23.8 1.58 1.35 1.35

iCsHl2

33.7 0.93 0.76 0.77

nCsHl2 12.1 0.81 0.64 0.64

C6H14

12.2 0.42 0.315 0.32

Solution

The computer program PROG71 determines the bubble points of

the hydrocarbon mixture. As with the dew point, the bubble point

(~Y = ~KX) is computed until the sum is 1.0 or very close to 1.0,

depending on the tolerance the user will accept. If the sum printed is not

equal to 1.0 (within tolerance), the iteration is repeated using the K~'s

corresponding to the new temperature. Tables 7-16, 7-17, and 7-18 give

both the data input and computer outputs for the bubble points of the

hydrocarbon mixture at 260~ 235~ and 237~

Problem 7-2

The composition of the feed to a natural gas liquefaction plant is

shown in the feed stream data. The feed will be flashed at 600 psia and

Table 7-15

Input Data and Computer Output for Dew

and Bubble Points Calculations

DATA71.DAT

DEW

178

27.52 7.88

16.34 2.77

29.18 1.18

5.37 0.61

17.18 0.48

1.72 0.264

2.18 0.225

0.47 0.102

0.04 0.048

DEW AND BUBBLE POINTS CALCULATIONS

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

DEW POINT CALCULATION

TEMPERATURE oF: 178.00

NUMBER OF COMPONENTS IN THE FEED STREAM: 9

NUMBER OF COMPONENTS FEED COMPOSITION (MOLE %) K-VALUE

1 27.5200 7.8800

2 16.3400 2.7700

3 29.1800 1.1800

4 5.3700 .6100

5 17.1800 .4800

6 1.7200 .2640

7 2.1800 .2250

8 .4700 .1020

9 .0400 .0480

TOTAL COMPOSITION:

NUMBER OF COMPONENTS

i00.0000

MOLE FRACTION

X=Y/K

1 .2752 .0349

2 .1634 .0590

3 .2918 .2473

4 .0537 .0880

5 .1718 .3579

6 .0172 .0652

7 .0218 .0969

8 .0047 .0461

9 .0004 .0083

TOTAL DEW POINT:

RAISE THE DEW-POINT TEMPERATURE: oF

1.0036

530

Mass Transfer 531

Table 7-16

Input Data and Computer Output for Dew

and Bubble Points Calculations

DATA71.DAT

BUBBLE

260

18.2 1.92

23.8 1.58

33.7 0.93

12.1 0.81

12.2 0.42

DEW AND BUBBLE POINTS CALCULATIONS

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

BUBBLE POINT CALCULATION

TEMPERATURE oF: 260.00

NUMBER OF COMPONENTS IN THE FEED STREAM: 5

NUMBER OF COMPONENTS FEED COMPOSITION (MOLE %) K-VALUE

1 18.2000 1.9200

2 23.8000 1.5800

3 33.7000 .9300

4 12.1000 .8100

5 12.2000 .4200

TOTAL COMPOSITION:

NUMBER OF COMPONENTS

I00.0000

MOLE FRACTION Y=KX

1 .1820 .3494

2 .2380 .3760

3 .3370 .3134

4 .1210 .0980

5 .1220 .0512

TOTAL BUBBLE POINT: 1 . 1881

LOWER THE BUBBLE POINT TEMPERATURE: oF

20~ If the flow rate is 1,000 moles/h, calculate the flow rates of the

liquid and vapor streams and their compositions.

Feed stream data"

Component Feed Equilibrium

Number Name Mole Fraction Constant, K

1 CO 2 0.0112 0.90

2 CH 4 0.8957 2.70

3 C2H 6 0.0526 0.38

4 C3H8 0.0197 0.098

5 iC4Hl0

0.0068 0.038

(table continued on next page)

Table 7-16

(continued)

Component Feed Equilibrium

Number Name Mole Fraction Constant, K

nC4Hl0

0.0047 0.024

C5H12

0.0038 0.0075

C6HI4

0.0031 0.00019

9 C7H,6 and 0.0024 0.0007

heavier

Solution

The computer program PROG72 performs equilibrium flash calcula-

tions for an ideal multi-component mixture. The program listed deter-

mines the moles of each component in the liquid and vapor phases

Table 7-17

Input Data and Computer Output for Dew

and Bubble Points Calculations

DATA71.DAT

BUBBLE

235

18.2 1.62

23.8 1.35

33.7 0.76

12.1 0.64

12.2 0.315

DEW AND BUBBLE POINTS CALCULATIONS

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

BUBBLE POINT CALCULATION

TEMPERATURE oF: 235.00

NUMBER OF COMPONENTS IN THE FEED STREAM: 5

NUMBER OF COMPONENTS FEED COMPOSITION (MOLE %) K-VALUE

1 18.2000 1.6200

2 23.8000 1.3500

3 33.7000 .7600

4 12.1000 .6400

5 12.2000 .3150

TOTAL COMPOSITION:

NUMBER OF COMPONENTS

i00.0000

MOLE FRACTION

1 .1820 .2948

2 .2380 .3213

3 .3370 .2561

4 .1210 .0774

5 .1220 .0384

TOTAL BUBBLE POINT:

RAISE THE BUBBLE POINT TEMPERATURE: oF

.9881

Mass Transfer 533

Table 7-18

Input Data and Computer Output for Dew

and Bubble Points Calculations

DATA71.DAT

BUBBLE

235

18.2 1.65

23.8 1.35

33.7 0.77

12.1 0.64

12.2 0.32

DEW AND BUBBLE POINTS CAiEUI~TIONS

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

BUBBLE POINT CALCULATION

TEMPERATURE oF: 235.00

NUMBER OF COMPONENTS IN THE FEED STREAM: 5

NUMBER OF COMPONENTS FEED COMPOSITION (MOLE %) K-VALUE

1 18.2000 1.6500

2 23.8000 1.3500

3 33.7000 .7700

4 12.1000 .6400

5 12.2000 .3200

TOTAL COMPOSITION:

NUMBER OF COMPONENTS

I00.0000

MOLE FRACTION

Y=KX

1 .1820 .3003

2 .2380 .3213

3 .3370 .2595

4 .1210 .0774

5 .1220 .0390

TOTAL BUBBLE POINT:

RAISE THE BUBBLE POINT TEMPERATURE: oF

.9976

including the feed fraction condensed or vaporized. In addition, all feed moles

and K-values are printed. As an added feature, the program checks the feed

composition at the conditions given. This determines whether the feed is all

vapor or all liquid. These computations are performed before the flash calcula-

tions are started, and a message is printed if either condition exists. Table 7-19

gives the input data and the computer output of the multicomponent mixture.

Problem 7-3"

Size an absorber tower for a methy ethyl amine (MEA) system with

the following conditions:

534

Fortran Programs for Chemical Process Design

Table 7-19

Input Data and Computer Output for Multicomponent

Equilibrium Flash Calculations

DATA72.DAT

20.0

600.0

11.2 0.90

895.7 2.70

52.6 0.38

19.7 0.098

6.8 0.038

4.7 0.024

3.8 0.0075

3.1 0.00019

2.4 0.0007

MULTICOMPONENT EQUILIBRIUM FLASH CALCULATIONS

MULTICOMPONENT EQUILIBRIUM FLASH CALCULATION AT 20.0 DEG. F AND 600.0

psia

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

COMPONENT K-VALUE FEED LIQUID VAPOR

NUMBER Mols/h. Mol. frac. Mols/h. Mol. frac. Mols/h. Mol.

frac.

1 .900 11.200 .011 .510 .012 10.690 .011

2 2.700 895.700 .896 14.030 .341 881.670 .920

3 .380 52.600 .053 5.343 .130 47.257 .049

4 .098 19.700 .020 6.004 .146 13.696 .014

5 .038 6.800 .007 3.608 .088 3.192 .003

6 .024 4.700 .005 3.016 .073 1.684 .002

7 .007 3.800 .004 3.235 .079 .565 .001

8 .000 3.100 .003 3.086 .075 014 .000

9 .001 2.400 .002 2.362 .057 .038 .000

TOTALS 1000.000 1.000 41.195 1.000 958.805 1.000

Vapor

flow 40,000 lb/h.

Vapor density

0.295 lb/ft 3

Liquid

flow 330,000

lb/h.

Liquid density 61.85 lb/ft 3

Foam factor

0.75

Residence Time

4.5s

Tray Spacing

24in.

Surface tension 57.6 dyne/cm.

The author developed computer program PROG73 for solving problem

7-3 in the text, using Nutter's

Float Valve Design Manual.

The devel-

oped program and calculation of the tray geometry are the responsibil-

ity of the author. The author expresses his gratitude to Nutter Engineering

for the use of the photographs and the information from the Float Valve

Design Manual.

Mass Transfer 535

Solution

The computer program PROG73 determines the parameters required

for sizing a tower using valve trays. The program calculates the bub-

bling area, downcomer area, tower area, and diameter. The tower diam-

eter may be rounded to an appropriate value and the area is recalculated.

Once the tower diameter is set, the downcomer area ratio is determined

and the downcomer height is computed from Tables 7-5 to 7-9. Table 7-20

shows the input data and computer output for tower sizing using valve

trays. The computer output gives the tower area of 26.571 ft 2 and a

diameter of 5.816 ft.

Tray Geometry

From the tower size (normally by increasing the diameter to the near-

est 6-inch increment), the following procedure is used to calculate the

downcomer dimensions.

Table 7-20

Input Data and Computer Output for

Tower Design Using Valve Trays

DATA73.DAT

40000.0 330000.0 61.85

0.295 0.75 4.5

24.0 57.6

TOWER DESIGN FOR VALVE TRAYS

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

VAPOR FLOW RATE,

Ib/hr.:

VAPOR VOLUMETRIC RATE, ft^3/sec.:

LIQUID FLOW RATE,

Ib/hr.:

LIQUID VOLUMETRIC RATE, ft^3/sec.:

LIQUID DENSITY, ib/ft^3.:

VAPOR DENSITY, ib/ft^3.:

FOAM FACTOR:

DOWNCOMER RESIDENCE TIME,

sec.:

TRAY SPACING, in.:

SURFACE TENSION,

dyne/cm.:

SURFACE TENSION/VAPOR DENSITY (X):

SAFETY FACTOR:

DENSITY RADICAL:

BUBBLING AREA, ft^2:

DOWNCOMER AREA, ftA2:

TOWER AREA, ft^2:

TOWER DIAMETER,

ft:

DOWNCOMER AREA RATIO:

40000.0

37.665

330000.0

1.482

61.850

.295

.750

4.500

24.

57.60

195.254

.745

.069

10.905

4.446

26.571

5.816

.2246

536

Fortran Programs for Chemical Process Design

The downcomer area ratio is"

RDC A =

AD~

(2ADc

+ A b)

The calculated tower diameter is increased to 6.0 ft and the tower

area becomes

/17. d 2

A-

/rX6 2

= 28.27 ft 2

Using Tables 7-5 to 7-9 and

RDC A

will allow a direct computation of

chord height for the side downcomer. This is rounded up to the nearest

1/2-inch incremental dimension. Using this dimension, the corrected

downcomer area is calculated from Tables 7-5 to 7-9. The computed

output of the tower used by the downcomer

area (RDcA)

is 0.2246. That is,

= 0.2246

DIA

0.2760

DIA

0.8940

A d

0.2246

The corresponding downcomer height-to-tower-diameter ratio is 0.2760.

The downcomer height is (0.2760) (6) (12)

= 19.87 in. + 1/2 in.

= 20.4 in.

H 20.4

The new =

DIA 72

= 0.2833

This gives a downcomer-area-to-tower-area ratio of 0.2329.