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

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Equipment Sizing 287

DBED (4ADEs /0"5

- (4-67)

71;

actual desiccant bed area

A-

~J~--BED

132

(4-68)

The actual gas flowrate at flowing conditions, ft3/min

Q - (Flow)( P

147 l/w/( 1

+14.7 5-~ 1440

T )(Z)(19.6314)

=(Flow) P+14.7

(4-69)

Superficial gas velocity, ft/min

VGA S = --

(4-70)

Superficial gas velocities for adequate contact time should range

between 30 and 60ft/min

Dryer shell thickness, inch

t - (4-71)

SE- 0.6P

Vessel weight

It/

WVE s --

480gD ~ (L + h + R)(1.10)

(4-72)

Add an extra 2 ft (h - 2) of straight side (i.e., for 6 in. of 3/8-in. inert balls

above and below the desiccant bed and 1 ft for an inlet-gas distributor).

Temperature of desiccant bed, ~

TBE o --

0.75(HT) + 0.25(HT - 50)

(4-73)

Total heat required to regenerate the dryer (ideal), Btu

HTO T

- {(WvEs)(0.12)(TBE

D -- T) + (WD)(0.25)(TBE D -- T)

+ (H20

load)(1400)}(1.05)

(4-74)

288 Fortran Programs for Chemical Process Design

where

loss factor for non-steady state heating, F

F-ln(HT- T/50 (4-75)

Heat added to regeneration gas to regenerate the desiccant bed

HREG

HTOT. F

The total regeneration gas requirement, lb

(4-76)

HGA s = HREG

(4-77)

H l

- H 2

Standard cubic feet of regeneration gas

SCF = HGAS (380) (4-78)

Pressure Drop (AP)

The pressure drop is estimated from the desiccant manufacturer's

data and correlations. In addition, AP can be calculated by Wunder's

[18] graphical correlation of gas superficial velocity against AP in ft

water per ft bed. Wunder used a factor of 1.6 for a fouled bed. AP through

a new desiccant bed is initially low. After a short time in service, AP

rises because of bed settling and then slowly increases over the active

life of the desiccant because of more settling and some attrition. Figure

4-10 shows AP for an 8-inch silica gel desiccant. These data are based

on air. For other gases, the given values should be multiplied by (MW

gas/MW air) ~ The pressure drop for a clean bed is given by:

AP - ( ft H20/( 0" 4335psi )( MWgas )~ bed ft H 20 MW air

(4-79)

Fouled bed:

AP = clean bed AP x 1.6

(4-80)

Desiccant attrition due to high gas velocities is controlled by proper

bed design. The superficial gas velocity is used to estimate Alcoa's

Equipment Sizing 289

Figure 4-10. Pressure drop for an 8 mesh silica gel desiccant (by permission Oil &

Gas Journal).

momemtum downflow velocities [18]. However, desiccant attrition

should not be a problem when the momentum number is equal to or less

than 30,000. Although, this number is based on granular alumina, it can

be used for silica gel, which has crushing characteristics similar to alu-

mina. The momentum is expressed as:

Momentum

-(VGAs)(MW)( P +

14.7~ < 30,000

(4-81)

14.7

)

where VGA s = superficial gas velocity, ft/min

MW = molecular weight of gas

P = system pressure in psig

290

Fortran Programs for Chemical Process Design

Desiccant Reactivation

The desiccant bed is reactivated at as high a temperature as permissible

to start optimum capacity and minimum dew points. In natural gas dry-

ing service, the normal reactivation temperature for silica gel is between

350~ and 400~ Because the feed gas contains high pentanes-plus

materials, Wunder [ 18] suggested that reactivation can be carried out at

450~ to desorb the heavy hydrocarbons.

At a temperature above 450~ the attrition rate for silica gel is high.

However, occasionally at 600~ reactivation will restore some

desiccant's initial activity thus extending the life of the silica gel. There-

fore, the reactivation procedure is designed to periodically heat the des-

iccant to 600~ [ 18].

Nomenclature

A = actual desiccant bed area,

ft 2

ApE s =

calculated area based on desiccant volume,

ft 2

Cycle - drying cycle, h

DBE D -"

calculated bed diameter, ft

E - joint efficiency

F = loss factor for non-steady state heating

Flow = gas flow rate, 106 std ft3/day

h - additional shell height for desiccant supports and distribu-

tor, ft

H~, H 2 - enthalpy of regeneration gas before and after regeneration

heater, Btu/lb

HaA s -"

total regeneration gas requirement, lb

HRE G --

heat added to regeneration gas to regenerate desiccant bed

HTo T = heat required to regenerate dryer (ideal), Btu

HT = heater temperature, ~

H20 load = total water adsorbed, lb

H20

Cont - water content of gas, lb/106 std ft 3

L = desiccant bed length, ft

MW = molecular weight of regeneration gas

P - dryer operating pressure, psig

PICKUP = useful design capacity of desiccant, %

Q - actual gas flow rate at flowing conditions, ft3/min

R - radius of desiccant bed, ft

S - allowable stress, lb/in 2

SCF - standard cubic feet of regeneration gas

Equipment Sizing

291

t = dryer shell thickness, inch

T = gas flowing temperature, ~

TB = temperature of desiccant bed, ~

VDES = desiccant volume, ft 3

VGA s -- superficial gas velocity, ft/min

W D = desiccant weight, lb

WS = steel weight of shell and heads, lb

WvE s = vessel weight, lb

Z- compressibility factor

9D = desiccant density, lb/ft3

PROBLEMS AND SOLUTIONS

Problem 4-1

Size a vertical separator under the following conditions:

WL = 5000 lb/h

9L = 61.87 lb/ft 3

WV = 37,000 lb/h

Pv = 0.374

lb/ft 3

The liquid surge time is five minutes.

Size a horizontal separator for the following conditions:

WL = 56,150 lb/h

PL = 60.0 lb/ft 3

WV = 40,000 lb/h

9v = 1.47 lb/ft 3

The liquid surge time is six minutes.

Use L/D = 3.0

Solution

The computer program PROG41 sizes both the vertical and horizontal

separators. Table 4-5 shows the input data and computer output for both

separators. From the computed output, the diameter of the vertical sepa-

rator with the given flow data and physical properties is 2.88 ft, the

liquid height is 1.03 ft and the vessel volume is 6.74 ft 3. The computer

output for the horizontal separator gives its diameter as 4.13 ft, the ves-

sel length is 12.39 ft, and volume is 165.82 ft 3.

Figure 4-7 gives a nomograph of the vapor rise in horizontal vessels.

A check of the vapor area with 20 percent of the total cross-sectional

292

Fortran Programs for Chemical Process Design

Table 4-5

Input Data and Computer Output for

Vertical and Horizontal Separators

DATA41.DAT

5000.0 37000.0

61.87 0.374

5.0

56150.0 40000.0

60.0 1.47

3.0

6.0

VERTICAL SEPARATOR SIZING

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

LIQUID FLOWRATE, ib/hr.:

VAPOR FLOWRATE, ib/hr.:

LIQUID DENSITY, ib/ft^3.:

VAPOR DENSITY, ib/ft^3.:

LIQUID VOLUMETRIC RATE, ft^3/sec.:

VAPOR VOLUMETRIC RATE, ft^3/sec.:

LIQUID SURGE TIME,

min.:

SEPARATION FACTOR:

VAPOR VELOCITY FACTOR:

MAXIMUM VAPOR VELOCITY, ft/s.:

VESSEL DIAMETER, ft:

MINIMUM VAPOR-LIQUID NOZZLE VELOCITY, ft/s.:

MAXIMUM VAPOR-LIQUID NOZZLE VELOCITY, ft/s.:

REQUIRED VESSEL VOLUME, ft^3:

LIQUID HEIGHT, ft.:

5000.

37000.

61.870

.374

92.1232

.0224

5.0

.0105

.329

4.213

2.882

27.481

153.539

6.735

1.032

HORIZONTAL SEPARATOR SIZING

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

LIQUID FLOWRATE, ib/hr.:

VAPOR FLOWRATE, ib/hr.:

LIQUID DENSITY, Ib/ft^3.:

VAPOR DENSITY, ib/ft^3.:

LIQUID VOLUMETRIC RATE, ft^3/sec.:

VAPOR VOLUMETRIC RATE, ft^3/sec.:

LIQUID SURGE TIME,

min.:

LENGTH TO DIAMETER RATIO (L/D):

SEPARATION FACTOR:

VAPOR VELOCITY FACTOR:

VAPOR VOLUMETRIC RATE, ft^3/s.:

MAXIMUM VAPOR VELOCITY, ft/s.:

VESSEL DIAMETER, ft.:

VESSEL LENGTH, ft.:

VESSEL VOLUME, ft^3.:

CALCULATED LIQUID SURGE TIME,

min.:

56150.

40000.

60.000

1.470

.2600

7.5586

6.000

3.0

.220

.447

7.559

2.823

4.129

12.386

165.815

8.5O5

area and the computed diameter of 4.13 ft shows that the vapor rise is

approximately 12 inches.

Problem 4-2

Estimate the liquid volume in a horizontal storage tank that has a

diameter of 120 inches, a length of 200 inches, and contains 40 inches

of liquid. Calculate the liquid volume for a vertical tank and for tanks

with either flat heads, dished heads, elliptical and hemispherical.

Equipment Sizing 293

Solution

The computer program PROG42 calculates the liquid volume in a hori-

zontal tank and for tanks with flat, dished, elliptical and hemispherical

heads. Table 4-6 shows the input data and computer output for a vertical

tank and tanks with flat, dished, elliptical and hemispherical heads.

Problem 4-3

Estimate the weight of a pressure vessel with hemispherical heads.

The vessel is 2 ft 6 in ID x 10 ft- 0 in T/T and has a design pressure of

1000 psig.

2SF - 4 in

c = 0.125 in

P~ = 489.024 lb/ft 3

Eshen = 0.85

Ehead ---- 1.0

S = 17,500 lb/in 2

Solution

The computer program PROG43 determines the vessel weight of the

pressure vessel with hemispherical, elliptical, and torispherical heads.

Table 4-7 gives input data and computer output for 2 ft 6 in.-diameter

vessel. The output gives the shell and head thicknesses, the weights of

the shell and head, and the total weight of the vessel with hemispheri-

cal, elliptical and torispherical heads.

Problem 4-4

Determine the efficiency and pressure drop (AP) based on cyclone

dimensions and the gas flow rate at 516.7 ft3/s, and a density of 0.075

lb/ft 3 containing particles with density of 62.43 lb/ft 3.

The dimensions and data required are:

Cyclone gas inlet height, ft

Cyclone gas inlet width, ft

Cyclone gas outlet length, ft

Cyclone gas outlet diameter, ft

Cyclone overall height, ft

Cyclone cylindrical height, ft

Cyclone diameter, ft

4.5

1.896

3.448

3.792

26.333

8.552

6.333

(text continued on page 296)

Table 4-6

Input Data and Computer Outputs for Tank Volume

with Flat, Dished, Elliptical and Hemispherical

Heads, and Vertical Tank Volume

DATA42.DAT

120. 40. 200.

TANK VOLUME WITH FLAT HEADS

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

TANK DIAMETER, in.: 120.000

LIQUID DEPTH, in.: 40.000

TANK LENGTH, in.: 200.000

TANK VOLUME, in.^3: .660017E+06

TANK VOLUME, ft.^3: .381954E+03

TANK VOLUME, gal: .285721E+04

TANK VOLUME, bbl: .680279E+02

TANK VOLUME WITH DISHED HEADS

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

TANK DIAMETER, in.: 120.000

LIQUID DEPTH, in.: 40.000

TANK LENGTH, in.: 200.000

TANK VOLUME, in^3: .662430E+06

TANK VOLUME, ft.^3: .383351E+03

TANK VOLUME, gal: .286766E+04

TANK VOLUME, bbl: .682767E+02

TANK VOLUME WITH ELLIPTICAL HEADS

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

TANK DIAMETER, in.: 120.000

LIQUID DEPTH, in.: 40.000

TANK LENGTH, in.: 200.000

TANK VOLUME, in.^3: .894589E+06

TANK VOLUME, ft.^3: .517702E+03

TANK VOLUME, gal: .387268E+04

TANK VOLUME, bbl: .922053E+02

TANK VOLUME WITH HEMISPHERICAL HEADS

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

TANK DIAMETER, in.: 120.000

LIQUID DEPTH, in.: 40.000

TANK LENGTH, in.: 200.000

TANK VOLUME, in.^3: .I12916E+07

TANK VOLUME, ft.^3: .653450E+03

TANK VOLUME, gal: .488814E+04

TANK VOLUME, bbl: .I16383E+03

VERTICAL TANK VOLUME

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

TANK DIAMETER, in.: 120.000

LIQUID DEPTH, in.: 40.000

TANK LENGTH, in.: 200.000

294

Table 4-6

(continued)

TANK VOLUME, in.^3:

TANK VOLUME, ft.^3:

TANK VOLUME, gal:

TANK VOLUME, bbl:

.452389E+06

.261799E+03

.195839E+04

.466278E+02

Table 4-7

Input Data and Computer Outputs for Vessel Design with

Hemispherical, Ellipsoidal and Torispherical Heads

DATA43.DAT

30.0 i0.0 i000.0

2.0 0.125 489.024

0.85 1.0 17500.

30.0 i0.0 i000.0

2.0 0.125 489.024

0.85 1.0 17500.0

30.0 i0.0 i000.0

2.0 0.125 489.024

0.85 1.0 17500.0 2.0

VESSEL DESIGN WITH HEMISPHERICAL HEADS

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

INTERNAL DIAMETER, in.:

SHELL LENGHT, ft.:

INTERNAL DESIGN PRESSURE, psig:

STRAIGHT FLANGE LENGTH, in.:

CORROSION ALLOWANCE, in.:

DENSITY OF VESSEL MATERIAL, Ib/ft^3.:

JOINT EFFICIENCY OF SHELL:

JOINT EFFICIENCY OF HEAD:

ALLOWABLE STRESS, ib/in^2.:

CALCULATED SHELL THICKNESS, in.:

CALCULATED HEAD THICKNESS, in.:

WEIGHT OF VESSEL SHELL, ib:

WEIGHT OF VESSEL HEAD, ib:

TOTAL VESSEL WEIGHT, ib:

30.000

I0.000

i000.000

2.000

.125

489.024

.85O

1.000

17500.000

1.176

.431

4205.77

595.80

4801.58

VESSEL DESIGN WITH ELLIPSOIDAL HEADS

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

INTERNAL DIAMETER, in.:

SHELL LENGTH, ft.:

INTERNAL DESIGN PRESSURE, psig.:

STRAIGHT FLANGE LENGTH, in.:

CORROSION ALLOWANCE, in.:

DENSITY OF VESSEL MATERIAL, ib/ft^3.:

JOINT EFFICIENCY OF SHELL:

JOINT EFFICIENCY OF HEAD:

ALLOWABLE STRESS, ib/in^2.:

CALCULATED SHELL THICKNESS, in.:

CALCULATED HEAD THICKNESS, in.:

WEIGHT OF VESSEL SHELL, ib:

WEIGHT OF VESSEL HEAD, ib:

TOTAL VESSEL WEIGHT, ib:

30.000

i0.000

i000.000

2.000

.125

489.024

.850

1.000

17500.000

1.176

.987

4205.77

853.98

5059.75

VESSEL DESIGN WITH TORISPHERICAL HEADS

(table continued on next page)

295

296

Fortran Programs for Chemical Process Design

Table 4-7

(continued)

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

INTERNAL DIAMETER, in.: 30.000

SHELL LENGTH, ft.:

INTERNAL DESIGN PRESSURE, psig.:

STRAIGHT FLANGE LENGTH, in.:

CORROSION ALLOWANCE, in.:

DENSITY OF VESSEL MATERIAL, ib/ft^3.:

JOINT EFFICIENCY OF SHELL:

JOINT EFFICIENCY OF HEAD:

ALLOWABLE STREES, Ib/in.^2:

CALCULATED SHELL THICKNESS, in.:

CALCULATED HEAD THICKNESS, ft.:

WEIGHT OF VESSEL SHELL, ib:

WEIGHT OF VESSEL HEAD, ib:

TOTAL VESSEL WEIGHT, ib:

i0.000

i000.000

2.000

.125

489.024

.850

1.000

17500.000

1.176

.227

4205.77

155.37

4361.15

(text continued from page 293)

Cyclone dust-outlet diameter, ft

Gas rate,

ft3/s

Gas density, lb/ft 3

Gas viscosity, lb/ft s

Temperature, ~

Particle size, ft

2.533

516.7

0.075

1.28 x 10 -5

110

3.281 x 10 -5

Solution

The computer program PROG44 calculates the pressure drop and the

efficiency of the cyclone using the cyclone geometry, fluid and particle

specifications. Table 4-8 gives the input data and computer results with

an efficiency of 63.305%, and a pressure drop of 7.834 in

H20.

The

calculated ratio of the particle diameter relative to the critical diameter

is 0.51. From Figure 4-8, the percentage removal of the particle is 23%.

Problem 4-5

Size a dryer to operate under the following conditions as shown in

Table 4-9 using silica gel as the adsorbent.

Solution

The computer program PROG45 calculates the size of the dryer using

silica gel, and Table 4-10 illustrates the input data and computer output.

The total regeneration flow is 44649.0 lb and the momentum is 30,584.

The heat requirement for dryer regeneration is 5.6 x 108 Btu. The calcu-

lated superficial gas velocity is 34.95ft/min.