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

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Equipment Sizing 267

9 There should be no bends within 10-pipe diameters of the inlet

nozzle except:

for knockout drums and demisters, a bend in the feed pipe is per-

mitted if this is in a vertical plane through the axis of the feed nozzle.

for cyclones, a bend in the feed pipe is allowed if this is in a hori-

zontal plane and the curvature is in the same direction as the

cyclone vortex.

9 A pipe reducer may be used in the vapor line leading from the

separator, but it should be no nearer to the top of the vessel than

twice the outlet pipe diameter.

9 A gate or ball type valve that is fully opened in normal operation

should be used, where a valve in the feed line near the separator

cannot be avoided.

9 High pressure drops that cause flashing and atomization should be

avoided in the feed pipe.

9 If a pressure reducing valve in the feed pipe cannot be avoided, it

should be located as far upstream of the vessel as practicable.

Nomenclature

A = cross-sectional area of vertical separator,

ft 2

A L = cross-sectional area of horizontal vessel occupied by liquid

phase, fff

A T - total cross-sectional area of horizontal vessel,

ft 2

A v = minimum cross-sectional area of vertical separator,

ft 2

D = vessel diameter, ft

H L = liquid height, ft

H v - vapor height, ft

K = proportionality constant

K H = vapor velocity factor for horizontal separator

K v = vapor velocity factor for vertical separator

L = horizontal vessel level, ft

S.Fac = separation factor

QL = liquid volumetric flow, ft3/s

Qv = vapor volumetric flow, ft3/s

T- liquid surge time, min.

Vma x --

maximum vapor velocity, ft/s

VVE s = horizontal vessel volume, ft 3

WL = liquid flow rate, lb/h

WV = vapor flow rate, lb/h

268 Fortran Programs for Chemical Process Design

X = In (S.Fac)

9L = liquid density, lb/fl 3

9v = vapor density, lb/ft 3

SIZING OF PARTLY FILLED VESSELS AND TANKS

Cylindrical vessels and horizontal tanks are used for the storage of

fluids in the chemical process industries. Various level instruments are

employed to determine the liquid level in process vessels. The exact

liquid volume can be obtained either by calibration of the vessels or by

tedious calculations. Partial volumes for horizontal, cylinders with flat,

dished, elliptical, and hemispherical ends, and for vertical cylinders are

employed for storing process fluids.

Kowal [4] presented charts that allow designers to determine the vol-

ume of vessels for different dimensions. In addition, parameters for tray

designs and tray layout in distillation columns, such as chord length and

circle area, are computed in this chapter.

The Equations

Calculate the area of the segment of a circle from Figure 4-6:

R-H

Cos(c~) = (4-24)

or-C~

(4-25)

Area of the triangle:

Area of A = (R - H)(2RH - H 2)

(4-26)

Therefore, area of the segment of a circle from Figure 4-6 is:

A~ -R2Cos-'(R-H/-(R-H)(2RH-H2)~

(4-27)

Figure 4-7 is a nomograph based upon the area of the segment of a

circle [5]. The nomograph converts the height (rise) over diameter ratios

directly to percent of area. The procedure in using the nomograph is:

1. Start at the left-hand side of the nomograph with the trial diameter.

Equipment Sizing

269

-- I

R _H

Figure

4-6. Area of the segment.

2. Align the internal diameter with the height of the vapor space and

then with the rise of the minimum liquid level. Read the area

occupied by these segments.

3. Subtract the sum of these segments from 100%. The difference is

the area available for liquid holding time.

Chord length of segmental area, CL:

CL = 2(DH - H 2)~

Partial volume of a horizontal cylinder:

VHC = A~.L

Partial volume of dished heads:

VDH -- 0.215483H 2(1.5D - H)

Partial volume of elliptical heads:

VECL -- 0. 52360H 2 (1.5D - H)

(4-28)

(4-29)

(4-30)

(4-31)

270

Fortran Programs for Chemical Process Design

12--

I I ""

I0"

9--

8--

7"-"

6--

=:"

w 5-"

,~. ,=

4-"

.n,

,~ 3--

1'-6" -

0.04

'~ 0.06

~ 3

0: 4 O.OB z "~

5~/t.i 1-~

20.,,:

,,~

//~

30-

tG//

_j 40--

== 70 0.6

o =

w 90 0.8

SEGMENTAL I00 I

AREA

- 0.2~,,, w I

--0.3 ~

" W

--0.4 v~

I f

U')

--s

---7

"-'8

--'9

"- I0

"--

~--4o

"-60

-:--

~ IIX)

150

Figure 4-7. Nomograph to find segmental area available for liquid holding time.

Partial volume of hemispherical heads:

VHs = 2VEL L (4-32)

The total volume VT:

V T = VHc q-V

(4-33)

where

V H =

head volume

/~.D 2

Area

= (4-34)

Volume of a vertical tank:

VvT - 0.25rtD2H

Conversions:

ft 3 --"

in 3/1728

gal - (in 3)(0. 004329)

bbl = (in 3)(0. 00010307)

Nomenclature

Area = circle area, in 2

A~ = segmental area of a circle, in 2

CL = chord length of segmental area, inch

bbl = volume in barrels

d = vessel tank, or circle diameter, inch

H = chord or liquid height, inch

L = vessel length, inch

R = radius of vessel or tank, inch

VD~ = volume of dished head, in 3

VEL L = volume of elliptical heads, in 3

V H - head volumes, in 3

VHC = volume of horizontal cylinder, in 3

Vus = volume of hemispherical heads, in 3

V T = total volume of horizontal vessel, in 3

VvT = volume of vertical tank, in 3

Equipment Sizing 271

(4-35)

PRELIMINARY VESSEL DESIGN

Columns and towers are the most essential aspects of the refinery

system in the petrochemical or in the process chemical industries. They

are divided into three separate functions" distillation, fractionation, and

chemical operations. Stills are cylindrical chambers in which the appli-

cation of heat to the charge stock changes from a liquid to a vapor. The

vapor is then condensed in another vessel. Columns and towers are stills

that increase the degree of separation that can be obtained during the

distillation of crude oil. Fractionation towers are used for light end

products. Generally, towers are large cylindrical vessels that have plates

272

Fortran Programs for Chemical Process Design

(trays spaced inside the shell) to promote mixing of the downward flow

of liquid with the upward flow of the vapors. These vessels require

self-supporting, especially when they are exposed to high winds or to

seismic risk.

Process conditions in the CPI often change, and a tower that is ini-

tially designed for vacuum operation may at a later stage be employed

at pressure greater than atmospheric. Therefore, thin-walled vessels are

often rated for both pressure and vacuum conditions. If the vessel is

thick-walled and designed for high pressure service, no vacuum rating

will be required. Tall vessels have one of a number of closures such as

hemispherical, ellipsoidal, torispherical, conical, or flat ends.

The ellipsoidal shape is usual for closures of vessels that are six feet

in diameter or greater. The hemispherical shape is preferred for vessels

of a lesser diameter. The basic relationships for thin cylindrical shells

under internal pressure assume that circumferential stress is dependent

on the pressure and vessel diameter, but independent of the shell thickness.

That is:

P.D

f - (4-36)

P.D

t - (4-37)

Equation 4-36 is for membrane shells with a negligible thickness. As

the pressure and the shell thickness increase, the stress distribution across

the thickness is non-uniform. Therefore, some correction to the mem-

brane theory is required. The modified code equation as given by the

ASME Unfired Pressure Code, Section VIII, Division 1 is"

P.R

t - + c (4-38)

S.E- 0.6P

where c is the corrosion allowance

For a hemispherical head:

P.R

t.. = (4-39)

2S.E- 0.2P

For ellipsoidal dished head:

Equipment Sizing 273

P.D

ELL -- "1-

c (4-40)

2S.E- 0.2P

For torispherical head"

0.885P R c

t TOR = " + C (4-41)

S.E- 0.1P

The weight of the vessel shell is:

(t)

WTS =

Z(OD--~-t)(rt)(SL) ~ (gs) (4-42)

The head blank diameter is:

BD - {(OD)(H. Fac) + 2SF}

(4-43)

Weight of head:

It/

WT.

0.25(BD) z(rt) ~ (ps)(2)

(4-44)

The total weight"

WTOT -- Wvs + WTH

(4-45)

The total weight excludes the nozzles, attachments, and vessel internals.

Table 4-3 shows the head blank diameter factor for different types

of head.

Nomenclature

B D = head blank diameter, inch

c = corrosion allowance, inch

D - inside diameter of shell or head, inch

E = joint efficiency

H.Fac = head blank diameter factor

OD - outside diameter of head, inch

P- internal design pressure, psig

R = inside radius, inch

R c = crown radius of torispherical head, inch

S = allowable stress, lb/in 2

274

Fortran Programs for Chemical Process Design

Table 4-3

Head Blank Diameter Factor (H.Fac)

Head Type OD/t

H.Fac

Torispherical

Ellipsoidal

Hemispherical

>50

30-50

20-30

>20

10-20

>30

18-30

10-18

1.09

1.11

1.15

1.24

1.30

1.60

1.65

1.70

SF = straight flange length, inch

SL = shell length, ft

t = shell thickness, ft

tEL L = ellipsoidal head thickness, inch

tHH = hemispherical head thickness, inch

tTo R = torispherical head thickness, inch

WTH = weight of head, lb

WTs = weight of vessel shell, lb

WTo T = total weight of vessel, lb

P~- density of vessel material, lb/ft 3

CYCLONE DESIGN

Introduction

Cyclones are widely used for the separation and recovery of industrial

dusts from air or process gases. Pollution and emission regulations have

compelled designers to study the efficiency of cyclones. Cyclones are

the principal type of gas-solids separators using centrifugal force. They

are simple to construct, of low cost, and are made from a wide range of

materials with an ability to operate at high temperatures and pressures.

Cyclones are suitable for separating particles where agglomeration

occurs. These types of equipment have been employed in the cement

industry, and with coal gases for chemical feedstock, and gases from

Equipment Sizing 275

fluidized-bed combustion, as well as in the processing industry for the

recovery of spray-dried products, and recently, in the oil industry for

separating gas from liquid.

Cyclone reactors permit study of flow pattern and residence time dis-

tribution [6,7]. See for example, the studies by Coker [8,9] of synthetic

detergent production with fast reaction. Reactor cyclones are widely

used to separate a cracking catalyst from vaporized reaction products.

Reverse flow cyclones, in which the dust-laden gas stream enters the

top section of the cylindrical body either tangentially or via an involute

entry, are the most common design. The cylindrical body induces a spin-

ning, vortexed flow pattern to the gas-dust mixture. Centrifugal force

separates the dust from the gas stream; the dust travels to the walls of

the cylinder and down the conical section to the dust outlet. The spin-

ning gas also travels down the wall toward the apex of the cone, then

reverses direction in an air-core and leaves the cyclone through the gas

outlet tube at the top. This tube consists of a cylindrical sleeve and the

vortex finder, whose lower end extends below the level of the feed port.

Separation depends on particle settling velocities, which are governed

by size, density, and shape.

Stairmand [10], Strauss [11 ], Koch and Licht [12] have given guide-

lines for designing cyclones. The effects of feed and cyclone param-

eters on the efficiency are complex, because many parameters are

interdependent. Figure 4-3 shows the design dimensions of a cyclone

and Table 4-4 gives the effects on cyclone performance in the important

operating and design parameters.

Cyclone Design Procedure

The computation of a cyclone fractional or grade efficiency depends

on cyclone parameters and flow characteristics of particle-laden gases.

The procedure involves a series of equations containing exponential

and logarithmic functions. Koch and Licht [12] described a cyclone using

seven geometric ratios in terms of its diameter as:

a b D c S h H B

Dc Dc Dc Dc Dc Dc Dc

They further stated that certain constraints are observed in achieving a

sound design. These are:

a<S to prevent short circuiting

276 Fortran Programs for Chemical Process Design

Table 4-4

Effects of Variables on Cyclone Performance

Variable

Pressure drop increases

Solids content of feed increases

(Pp- Of)

increases

Viscosity of liquid phase increases

Cyclone diameter (D c) increases

Cyclone inlet (a) diameter increases

Overflow diameter increases

Underflow diameter increases

Cyclone shape becomes longer

Effect

Cut size (diameter of particles of

which 50% are collected) decreases,

flow rate increases; sharpness

increases.

Cut size increases (large effect

above 15-20% v/v).

Cut size decreases.

Little effect below 10 mPas.

Cut size increases; pressure drop

usually decreases.

Gravitational force in cyclone

decreases; cut size increases;

capacity falls; pressure drop

decreases.

Cut size increases; risk of coarse

sizes appearing.

Brings excess fines from liquid

phase into underflow.

Decreases cut size; sharpens separation.

b < -(D c

- De)

to avoid sudden contraction

S+I<H

to keep the vortex inside the cyclone

S<h

h<H

AP < 10 in

H20

v~/v~ < 1.35

to prevent reentrainment

V i/V s ~ 1.25

for optimum efficiency