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

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Equipment Sizing 277

The Equations

Natural length, 1: the distance below the gas outlet where the vortex turns.

/1/3

1-2 3D D~

9 e

--~

(4-46)

For 1 < (H- S), the cyclone volume at the natural length (excluding the

core) is Vn~"

Vn 1

=n:D~4 (h- S) + [TrD~4 ](1+$3- h)[l+ Dcd

+ ~2-c2 )d 2

~D~I

(4-47)

The diameter of a central core at a point of vortex turns, d:

d- Dc-(D c-B)( S-l-h)H-h

(4-48)

For 1 > (H- S), the cyclone volume below the exit duct (excluding the

core) VH:

4 (h - S) + - B

B 2

4 3 D c D c

7'l~--eD2 (n- S)

For a vortex exponent, n:

(4-49)

n-1-{1-(12Dc)~ ~ 530

(4-50)

The cyclone volume constant, K c, using

Vnl or

VH:

KC ---

(2V s

+ Vnl,H )

2D~

(4-51)

where

c -De) t

Vs _ rt(S- a/2)(D 2 2

(4-52)

278

Fortran Programs for Chemical Process Design

The relaxation time

(~i)

for particle species i of

diameter dpi

pp(dpi)2

- (4-53)

18la

Cyclone configuration factor G: This is specified by the geometric

ratios that describe the cyclone's shape. The cyclone configuration fac-

tor G is a function only of the configuration and is specified by the

seven geometrical ratios that describe its shape. G is expressed as:

G - 8K c (4-54)

2 2

KaKb

where

a b

K a = --,

K b - (4-55)

Dc Dc

Substituting the values of K a,

K b,

and K c in Equation 4-54.

(4-56)

The fractional or grade efficiency,

r~i , can

be expressed as"

qi -1-exp -2 GI: (n+l)

/(n+l)

(4-57)

Saltation Velocity

Koch and Licht [12] expressed the saltation velocity as"

9 The minimum fluid velocity necessary to prevent the settling out

of solid particles carried in the stream.

9 The necessary velocity that picks up deposited particles and trans-

ports them without settling.

Zenz [ 13] has shown that the velocity given by the latter differs from

the former by a factor of 2 to 2.5. Kalen and Zenz [14] have applied the

saltation concept to cyclone design by assuming"

Equipment Sizing 279

9 There is no slippage between fluid and particles. The cyclone inlet

width is the effective pipe diameter for calculating saltation effects.

9 Grain loading (dust concentration) is less than 10 grains/ft 3.

9 The diameter effect on the saltation velocity is proportional to the

0.4 power of the inlet width.

The saltation velocity, v~, is dependent on cyclone dimensions, particle

and fluid properties, v s is expressed as:

V~ - 2. 0550){ b/Dc }

0.067_ 2/3

(1 - b/D c)l/3 D c vi

ft/s (4-58)

where

4gla(9 p

_ Pf ) }1/3

O) m 2

3pf

(4-59)

Inlet velocity,

Vi: ft/s

W i "- Q (4-60)

(ab)

Kalen and Zenz have shown that maximum cyclone collection efficiency

occurs at vi/v s = 1.25, and Zenz has found experimentally that fluid

reentrainment occurs at vi/v s = 1.36.

Pressure Drop (AP)

Several attempts have been made to calculate the frictional loss or

AP of a cyclone, although none has been very satisfactory. These are

because assumptions made have not considered entrance compression,

wall friction, and exit contraction, all of which have a major effect.

Consequently, no general correlation of cyclone AP has been adopted.

Pressure drop in a cyclone with collection efficiency is important in

evaluating its cost. Correlations for the pressure drop have been empiri-

cal and are acceptable up to AP = 10 in.

H20.

The pressure drop (AP) or

the frictional loss is expressed in terms of the velocity head based on the

cyclone inlet area. The frictional loss through cyclones is from 1 to 20

inlet velocity heads and depends on the geometric ratios. AP through a

cyclone is given by

AP - 0 003 2

9 9fviNn

(4-61)

280

Fortran Programs for Chemical Process Design

where

(ab /

N.-K ~-7

D e

(4-61)

K = 16 for no inlet vane

K = 7.5 with a neutral inlet vane

AP depends strongly on the inlet velocity and high velocities can cause

both reentrainment and high pressure drop. However, entrainmnent can

be reduced to a minimum, if the cyclone has a small base angle.

Trouble Shooting Cyclone Maloperations

In general, cyclones are used to separate particles from the gas stream,

but recent developments have enabled cyclones to function as reactors.

Some cyclone reactors can separate cracking catalyst from vaporized

reaction products in the range of 950~ and 1,000~ or can function as

regenerators for flue gases between 1,250~ and 1,500~ In both cases,

the high particle velocities can cause rapid erosion of the cyclone mate-

rial. This often results in poor performance of the cyclone. Other causes

of poor cyclone performance are:

9 Hole in cyclone body

9 Cyclone volute plugged

9 Dipleg unsealed

9 Dipleg plugged

9 Dipleg failure

Lieberman [ 15] has reviewed the causes of these maloperations, which

often result in loss catalyst and reduced efficiency. A deficient cyclone

reactor is identified by bottom sediment and water levels in the slurry

oil product. For a regenerator cyclone, problems are visibly identified

by the increased opacity of the regenerator flue gas or by reduced rates

of spent catalyst withdrawal.

Cyclone Collection Efficiency

Many theories have been proposed to predict the performance of a

cyclone, although no fundamental relationship has been accepted.

Attempts have been made to predict the critical particle diameter,

(Dp)crit.

Equipment Sizing 281

This is the size of the smallest particle that is theoretically separated

from the gas stream with 50 percent efficiency. The critical particle di-

ameter is defined by [ 16]

]0.5

9~tDc

(Dp)cnt - 4rtN,vi(P- 98)

(4-62)

where

N t =

effective number of turns made by the gas stream in the

cyclone, and is defined by

N t - (vi)[0.1079- 0.00077v i + 1.924(10-6)vi ]

(4-63)

and v i = is the inlet linear velocity.

Figure 4-8 shows the percentage removal of particles in a cyclone as

a function of the ratio of the particle to the critical diameter.

Cyclone Design Factor

Cyclones are designed to meet specified AP limitations. The factor

that controls the collection efficiency is the cyclone diameter, and a

smaller diameter cyclone at a fixed AP will have a higher efficiency.

Therefore, small diameter cyclones require a multiple of units in parallel

for a given capacity. Reducing the gas outlet diameter results in an

increased collection efficiency and AE High-efficiency cyclones have

cone lengths in the range of 1.6 to 3.0 times the cyclone diameters.

Collection efficiency increases as the gas throughput increases. Kalen

and Zenz [ 14] reported that collection efficiency increases with increas-

ing gas inlet velocity to a minimum tangential velocity. This reaches

the point where the dust is re-entrained or not deposited because of

saltation. Koch and Licht [ 12] showed that saltation velocity is consis-

tent with cyclone inlet velocities in the range of 50 to 90ft/sec.

Cyclones offer the least expensive means of dust collection. They

give low efficiency for collection of particles smaller than 5~tm. A high

efficiency of 98 percent can be achieved on dusts with particle sizes of

0.1 to 0.2~tm that are highly flocculated.

Cyclone Design Procedure

The following design procedures can be used to size a cyclone with a

specified fluid flow rate and physical property data:

282

Fortran Programs for Chemical Process Design

JO mm

6 - i

_ ,

4,.a

, ill

"06

0,4

mmmmm(

mmmml

~ ~ mpm~'. ;,,iN m

m~~v~mm

immmlm!

mm,,immm

mmm,,Jmmm

/inN/iilnmilill

i~~mm~Rnm~~~mnl

i~~miv~nmm~~~mnl

n~~i~Rnmm~~~inl

mmmmvAmmmmimmimnlm

mmmmmmmmmmmmmmt

imuimnmmmiimmmil

immimilimmmmili

mlimmmmmmmimmml

0.2 ~~i, -

0. I

2 5 I0 20 40 60 80 90 95 98 o.~

co.

0% 0"~ 0"%

Percent removed

Figure

4-8. Percentage removal of particles as a function of particle diameter relative to

the critical diameter.

1. Select either the high-efficiency or high-throughput design

depending on the performance required.

2. Obtain an estimate of the particle size distribution of the solids in

the stream to be treated.

3. Estimate the number of cyclones needed in parallel.

4. Calculate the cyclone diameter for an inlet velocity of 50 ft/sec.

Equipment Sizing 283

5. Calculate the scale-up factor for the transposition of grade effi-

ciency and particle size.

6. Calculate the cyclone performance and overall efficiency

(recovery of solids). If unsatisfactory, try a smaller diameter.

7. Calculate the cyclone pressure drop and, if required, select a suit-

able blower.

8. Cost the system and optimize to make the best use of the pressure

drop available or, if a blower is required, to give the lowest oper-

ating cost.

Nomenclature

a = inlet height, ft

b = inlet width, ft

B = cyclone dust-outlet diameter, ft

d = diameter of central core at a point where vortex turns, ft

dpi- diameter of particle in size range i, ft

D c = cyclone diameter, ft

D e = cyclone gas-outlet diameter, ft

g = acceleration due to gravity, 32.2 ft/s 2

G = cyclone configuration factor

h = cylindrical height of cyclone, ft

i = subscript denotes interval in particle size range

Ka= a]O c

K b =

b/D c

K c = cyclone volume constant

1 = natural length (distance below gas outlet where vortex turns), ft

n = vortex exponent

N H - number of inlet velocity heads

AP = pressure drop, in

H20

Q = total gas flowrate, actual ft3/s

S = gas outlet length, ft

T = temperature, ~

v~ = inlet velocity, ft/s

v s = saltation velocity, ft/s

V H = volume below exit duct (excluding core), ft 3

Vn~ = volume at natural length (excluding core), ft 3

V s = annular volume above exit duct to middle of entrance duct, ft 3

rli = grade efficiency for particle size at midpoint of interval i, %

/.t- fluid viscosity, lbm/ft.s

9f = fluid density, lbm/ft 3

284

Fortran Programs for Chemical Process Design

13p - particle density, lbm/ft 3

I: = relaxation time, s

= Equation 4-59

GAS DRYER (DEHYDRATION) DESIGN

Liquid water and sometimes water vapor are removed from natural

gas to prevent corrosion and formation of hydrates in transmission lines

and to attain a water dew point requirement of the sales of gas. Many

sweetening agents employ an aqueous solution for treating the gas. There-

fore dehydrating the natural gas that normally follows the sweetening

process involves:

9 dehydration by refrigeration

9 absorption by liquid desiccants

9 adsorption by solid desiccants

Adsorption is a process that involves the transfer of a material from

one phase to a surface where it is bound by intermolecular forces. The

process involves the transfer from a gas or liquid to a solid surface. It

could also involve the transfer from a gas to a liquid surface. The adsor-

bate is the material being concentrated on the surface and the material

that it accumulates is defined as the adsorbent.

The oil and chemical industries use the adsorption process in the

cleanup and purification of wastewater streams and for the dehydration

of gases. The process is also used in gas purification involving the

removal of sulfur dioxide from a stack gas. In addition, adsorption is

employed to fractionate fluids that are difficult to separate by other sepa-

rating methods. The amount of adsorbate that is collected on a unit of

surface area is negligible. Therefore, porous desiccants (adsorbent) hav-

ing a large internal surface area are used for industrial applications.

There are many solid desiccants that can adsorb water from natural

gas. The common commercial desiccants are alumina, silica gel, and

molecular sieves. The molecular sieves possess the highest water

capacity, will give the lowest water dew points, and can be applied to

sweeten dry gases and liquids. Figure 4-9 shows how desiccants can be

used in dehydrators containing two or more towers. One of the towers

operates using steam to adsorb water from the gas, while the other tower

is regenerated and cooled. The regenerated gas is heated to a range of

450~ and 600~ depending on the type of solid desiccant and the

nature of service [ 17].

Equipment Sizing

285

..,,t REGENERATION GAS

r REGEN GAS

| |

w "~c~ w~.

~g,~' ..............

REGENERATING

COOLING

600 "F

-- VALVE OPEN

'-- VALVE CLOSED

REGENERATION GAS

REGEN GAS i~

HEATER

DRY

GAS

Figure

4-9. Solid desiccant dehydrator twin tower system. Courtesy: Gas Processors

Suppliers Association Engineering Data Book, Tenth Edition.

The use of solid desiccant is limited to applications such as those

with very low water dewpoint requirements, simultaneous control of

water and hydrocarbon dewpoints, and in very sour gases. In cryogenic

plant, solid-desiccant dehydration is much preferred over methanol

injection to prevent hydrate and ice formation.

The basic design procedures for dehydrating saturated natural gas at

a specified dew point are:

1. Determine the process conditions and the dryer process flow

diagrams.

2. Select a drying cycle and calculate the water load.

3. Select the type of desiccant and compute the capacity and volume

required.

4. Size the dryer and check for the pressure drop.

5. Calculate the desiccant reactivation heating and cooling requirements.

Here, design procedures are presented for sizing a solid desiccant dryer

in removing moisture from gas streams. The process involves the fol-

lowing calculations.

1. the water pickup

2. desiccant volume

286 Fortran Programs for Chemical Process Design

3. desiccant bed

4. gas velocity through the bed

5. vessel weight

6. dryer regeneration requirements

The design is based upon the following assumptions [2]"

1. The temperature difference between the heater outlet temperature

and the peak vessel outlet temperature is 50~

2. The average bed temperature is based on 75 percent of the bed at

heater outlet temperature and 25 percent at the peak vessel outlet

temperature Equation 4-73.

3. Specific heats: steel, 0.12 Btu/lb ~ and desiccant 0.25 Btu/lb ~

4. Heat of water desorption 1400 Btu/lb

H20

adsorbed.

5. Flat heads used on vessel ends; steel density is 480 lb/ft 3.

6. Total vessel weight increased by 10 percent for supports.

7. Heat losses to the dryer during heating period calculated at 5 percent.

The Equations

The equations used for calculating these requirements are:

The total water adsorbed, lb

H20

load -

(Flow)(Cycle)(H20 Cont)

MMstd

ft 3 /(

day

( lb )

h) MMstd ft3

(h/day)

(4-64)

Desiccant volume

VDES =

(H20

load)(100) (4-65)

(pickup) (9D)

The calculated area based on desiccant volume

ApES = DES (4-66)

The bed diameter