Vessel Design Course Notes

8/15/2019 Vessel Design Course Notes

1/29

Cairo University

Facul ty of Engineer ing

Chemical Engineer ing Department

Prof. Dr . Mohamed Hanafy

Eng. Hadir Wahid

Eng. Fady Gamal

2010 – 2011


2/29

Design of Vessels under Internal Pressure

(Pin > Pout)

1. Design of Spheri cal Vessels:

C P E

R P t

d all

id

sp

*2.0*2

*

Where:

tsp: Thickness of the spherical vessel, inch.

Pd : Design pressure, Pd = 1.1 Pmax

Pmax: Maximum internal pressure (gauge not absolute), psi

R i: Vessel internal radius, inch.

σall: Maximum allowable strength of the material of construction of the vessel,

psi

E: Welding efficiency, usually taken 0.8 (if not given)

C: Corrosion allowance,

C = 1/16" for mi ld corr osion

C = 1/8" for severe corrosion

2.

Design of Cylindr ical Vessels:

2.1. Design of Shell :

C P E

R P t

d all

id

sh

*6.0*

*

Where:

tsh: Thickness of the shell of the vessel, inch.

2.2. Design of H ead:

2.2.1. Hemispherical Head:

C E

D P t

all

ishd

h

*4

*

Where:

th: Head thickness, inch.

Dish: Shell inside diameter, inch.


3/29

2

2.2.2. Elliptical Head:

C K E

D P t

all

ishd

h **4

*

Where:

K: Constant depends on the ratio of head height to the diameter and

can be obtained from the following table:

K 6 4.2 3 2 1.5 1

h/D 0.14 0.162 0.193 0.25 0.33 0.5

Note:

We will take the value of h/D = 0.25 to get K = 2. This value will give

a head thickness near or equal to that of the shell to avoid "welding

bridge" between them.

2.2.3. Dished Head:

C K E

R P t

all

d

h **2

*

Where:

R: Crown radius, R ≤ Dish (Take R = Dish), inch.

K: Constant depends on the ratio between the knuckle radius 'r' and the

crown radius and can be obtained from the following table:

r/R 0.06 0.1 0.2

K 1.75 1.5 1.7

2.2.4. Flat Head:

C E

P Dt

all

d

ishh

*

5.0

2.2.5.

Conical Bottom:

C E

D P t

all

ishd

c

cos**2

*


4/29

3

Where:

tc: Thickness of the conical bottom, inch.

2α: Apex angle.

To get 'α' (if not given):

h

Dish

2tan

Where:

h: Conical bottom height, inch.

2.2.5.1. Special Parts for Conical Bottom:

a)

Compression ring ( If α ≤ 30° ):

We should get the dimensions of the ring: b, h

)1(*8

tan*

*

**

2

E

D P hb A

all

ishd ring

Where:

Aring: Area of the ring, inch.2

δ: An angle and can be obtained from the following table:

E P

all

d *

0.001 0.002 0.003 0.004 0.006

δ 13 18 22 25 30

Note:

The minimum dimensions for the ring is 1" * 1" so, we assume one

of them [b or h] and get the other from 'Aring':


5/29

4

If the calculated dimension "1 take it 1".

If the calculated dimension "1 take it as it is.

b) Intermediate Part (If 30° < α ≤ 75°)

C K E

D P t all

oshd i *

*2

*

Where:

ti: Thickness of the intermediate part, inch.

Dosh: Outside diameter of the shell, inch.

Dosh = Dish + 2 tsh

K: Constant can be obtained from the following table:

α 30 45 60 70

K 1.31 2.01 3.2 3.7

cos

*2 iosh

t D L

Where:

2L: Intermediate part length, inch.

Note:

If you calculate 'α' from the beginning and find that: α > 75°,

calculate the thickness of the conical bottom from the following

equation:

C

E

P Dt t

all

d

ishh c

*

5.0


6/29

5

Design of Vessels under Internal Pressure

(Pout > Pin)

1. Design of Shell :

3' )(*ish

shc

D

t E K P

Where:

Pc = The critical pressure, psi

Pc = 4 Pact

Pact = Pout – Pin

E' = The modulus of elasticity of the material of construction, psi

K = The collapse coefficient,

),( sh

ish

ish

sh

t

D

D

L f K

& can be obtained from the following chart:


7/29

6

1.1. Steps for calculating the shell thickness:

Assume:"

16

2 sht

Calculate:ish

sh

sh

ish

D

L

t

D,

Get (K) from the chart.

Calculate Pc)cal.

If .. )) givccal c P P , the thickness is o.k.,

tsh = assumed thickness + corrosion allowance

If .. )) givccal c P P , increase the thickness by"

161 and repeat the above steps

until .. )) givccal c P P .

1.2.

In case of tall vessels )6( m L :

In this case:

shcal c t P K L .)

So in order to avoid the large shell thickness, we put more than one ring

[stiffening rings] around the tower to protect it from collapse and reduce the

required shell thickness. In this case, the length used in the chart is the

distance between the rings not the shell height:

1

N

Ll shnew

Where:

Lnew = The distance between rings, inch.

Lsh = The shell height, inch.

N = No. of stiffening rings.

As the dimensions of the rings are required, we can calculate it as following:

'

.

24

**)

E

l D P I

newosh givc

12

4b I Or

12

3bh I [According to the shape of the ring]


8/29

7

Where:

I = Moment of inertia.

(Calculate (I) and from it calculate the ring dimensions)

2.

Design of heads:2.1. Hemispherical head:

2' )2

(2.1ish

hc

D

t E P

2.2. Dished head:

2'

)(2.1 R

t

E P h

c Where:

R = Crown radius, ish D R (Take R = Dish).

2.3. El li ptical head:

2

43

' )*

(2.1ish

hc

D

t E P

2.4. Conical bottom:

3' )(*ish

cc

D

t E K P

As the above rule contains the coefficient (K), the procedure of calculating the

thickness of the conical is the same as that of the shell. In this case the value of

L/D used in the chart depends on the apex angle:i. If 452 :

ish D

h

D

L

ii. If 120245 :

1 D

L

iii.

If 1202 :


9/29

8

Get the thickness of the conical bottom from:

C E

P Dt

all

act ishc

*

*162.0 .


10/29

9

Design of Openings

(Pipes & Manholes)

1. I n Case of Vessels Under I nternal Pressure:

1.1. Design of Neck:

C P E

R P t

d all

id neck

6.0*

*

Where:

tneck = Thickness of pipe or manhole, inch.

R i = Radius of pipe or man hole, inch.

Note: take the diameter of man hole = 70 cm (if not given).

σall = Allowable tensile strength of the material of construction of

pipe or man hole (the same value of the shell and its heads), psi.

C = Corrosion allowance (the same value used for shell and heads),

inch.

Pd = Design pressure, psi. Pd = 1.1 Pmax (Pmax is the internal pressure

inside the vessel).

E = Welding efficiency (the same value used for shell and heads).

1.2. Design of Gasket:

The gasket type is chosen according to temperature and pressure as shown in

the following table:

Gasket typem

(Gasket factor)

y

(Seating

pressure, psi)

Working

temperature

(°C)

Working

pressure (atm.)

Rubber flat 1 200

< 100 < 10Rubber with

cotton fabric

flat

1.2 400

Steel metal flat 5.5 18000

> 350 > 20Aluminum

metal flat4 88000

Ring steel 5.5 18000


11/29

1

Stainless steel 6.5 26000 > 350 > 20

Corrugated

metal

aluminum

2.3 2000

> 350


12/29

y

b

d Q

P mbd P bd Q

g

g g

mb

mmb

*2**

*****)*(

"

maxmax

2

32

4

'

Where:

Q' b = Sealing load, lbf

Q'' b = Seating load, lbf

Note: you will calculate the sealing load and the seating load, take the

largest one and substitute in the following equation to get the number

of bolts:

bolt all inb

b

bbbolts

C d f

f

Qor Qn

)*)(

)()(

2

4

"'

Where:

n bolts = The required number of bolts [4 – 8 – 12 – 16 – 20].

f b = The force exerted by one bolt, lbf

din = The diameter of the bolt, inch. [Take it 1/2" or 1"].

C = Corrosion allowance of bolt [Take it 1/16"].

σall) bolt = The allowable tensile strength of bolt [Take it 12000 psi].

1.4. Design of F lange:

bolt all inb

act bolt bb

d f

n f Q f

)**

)*

2

4

'

'

Where:

Q bf = The actual load on flange, lbf

f' b = The same as f b but without corrosion allowance.

"4opi s

D D if atm P 6

"7opi s

D D if atm P 256


13/29

2

Where:

Ds = The bolt circle diameter, inch.

E D D so f *2 Where:

Dof = The outside diameter of the flange, inch.

E = the edge distance, inch. "E" can be obtained from the next table:

din (inch.) E (inch.)

1/2 5/8

1 17/16

2 2

2

)*2(

*2

**

6**

'

'

h D D

l

h D D

C D

l Qt

f

f

f

i s

i f

all f

b

f

Where:

tf = The thickness of flange, inch.

Dif = The inside diameter of flange, inch.)(

op g f iii D D D

h' can be calculated from the following equation:

all i

i sb

act h D

h D DQ

h

f

f

f

)(

22*4.2

'

'

'

To get h':

- Assume h' = 1" and get h'act.

- If h'act ≤ h', so your assumption is correct and take h' = 1".

-

If h'act > h', assume new value for h' [e.g. 1.5"] and get h'act and so on.


14/29

3

1.5. Design of F lat Cover: (in case of man hole only):

C P

Dt all

d sC f

*162.0..

Where:

tf.c. = The flat cover thickness, inch.

1.6. Design of Reinforcement Ring: (for openings diameters > 2" )

30

2

321321 *)(*** t D Dt t t t t Dt neck neck bo Where:

t1 = The shell thickness.

t2 = The opening thickness.

t3 = The ring thickness, Take it 1".

D b = The outside diameter of the ring.

2. I n Case of Vessels Under External Pressure:

2.1. Design of Neck:

The thickness of opening (pipe or man hole) is calculated from the following

equation:

3

'*)

neck i

neck

cal c D

t E K P

Calculate tneck from the above equation in the same way used in calculating

tshell of vessel under external pressure and using the same chart of "K". In this

"K" will be function of:

neck n eck i

neck

i

neck

D

t

D

l ,

If "lneck " is not given take it in the range: 50 – 70 cm.

2.2. Design of Gasket:

-

Take the gasket type the same as the material of construction of the

shell.


15/29

4

- In the equation of "Dog" previously mentioned, put "Pact" instead of

"Pmax".

2.3. Design of Bolts:

-

The diameter of the bolt (din) will be always 1/2".-

Calculate Q" b only as it will has the largest value.

2.4. Design of F lange:

- For calculating "Ds" we will always use the equation:

"4opi s

D D

2.5. Design of F lat Cover:

- In calculating the thickness of flat cover (tf.c.

), put "Pact

" instead of

"Pmax" in the equation.


16/29

5

Design of Tall Vertical Vessels

(L > 6 m)

After calculating the shell thickness from previous design methods for vessels

under internal and external pressures, we should check that this thickness will

withstand the loads applied on it. This check is done on three cases: operation,

shutdown and erection.

1. Check for Operation:

The following conditions should be achieved:

External Internal

y

External Internal

E

p Ld wdw st comb

all Ld wuw st comb

"",""

3)

"",""

)

..

..

E C t

D P

sh

mshd L

)(4

Where:

Dmsh = The shell mean diameter, Dmsh = (Dish+Dosh) / 2.

"Pd" is used in case of vessels under internal pressures, and replaced by

"Pact" in case of vessels under external pressures.

E C t D

L L D P

shmsh

oinsw

w

*)(**

2*)**7.0*(

2

4

.

Where:

Doins. = The outside diameter of insulation, Doins. = Dosh + 2*tins.

(If there is no insulation, put Doins.= Dosh)

L = Shell length, inch.

Pw = The wind pressure, psi. The wind pressure can be obtained from

the following table:


17/29

6

Shell Height, inch.Wind Pressure (Pw, psi)

Internal Region Coastal Region

0 - < 360 0.138 0.2

360 - < 600 0.174 0.27600 - < 1200 0.2 0.347

1200 - < 6000 0.27 0.42

E C t D

wt

shmsh

d *)(**

1.1

liqiiiconiconconical

coninliq

iiiconiconconical iioconoconconical conical

linilinolinlining

ishtray

trays

trays

liqishliq

insiinsoinsins

spish sp

headshh sphead

sh ell ishosh sh ell

traysliqinsheads sh ell

d d D D H wt

d d D D H d d D D H wt

L D Dwt

L Dareaunit wt L

N wt

L Dwt

L D Dwt

Dished Rd elliptical Dd

N t d wt

L D Dwt

wt wt wt wt wt wt

*12

)(*)

28.0*12

*

12

*)

**)()

***).)()

)

**)

*)()

,

*)***()

*)()

...)))))

2

.

2

....

2

.

22

.

2

.

.

2

.

2

.4

2

4

.

2

4.

.

2

.

2

.4.

43

2

21

22

4

.

2. Check for Shutdown:

3))

))

..

..

p sh u td o wnd wd w st comb

a ll sh u td o wnd wu w st comb

y

E

Note: in case of shutdown, σd is calculated from the same equation of operation

but don't put the weight of liquid in Σwt.


18/29

7

3. Check for Erection:

3))

))

..

..

perectiond wd w st comb

a ll erectiond wu w st comb

y

E

Note: in this case we only put the weight of shell [or shell + one head] in Σwt. in

the equation of σd.

Design of Skir t Support:

Assume: Disk = 0.95 Dish

Dosk = 1.05 Dosh

2isk osk

sk D Dt

Where:

- Disk = The inside diameter of skirt support.

-

Dosk = The outside diameter of skirt support.

- tsk = The thickness of the skirt.

Check on the thickness of the skirt:

3))

))

..

..

poperationd wd w st comb

a ll erectiond wu w st comb

y

E

E C t D

l L D P

sk msk

sk osk w

w )(*

)2

(*7.0**

.2

.4

2

.

Where:

- lsk = The height of skirt support, lsk = 2 – 2.5 m

E C t D

wt wt wt

sk msk

skirt head sh ell erectiond

*)(**

))))


19/29

8

E C t D

wt wt

sk msk

skirt operationd

*)(**

)1.1)

Design of Bearing Plate:

Assume: Dib = 0.8 Disk

Dob = 1.2 Dosk

psioperationd wdw st comb 525))..

2

*

)2

(*7.0**

44

64

2

ob

ibob

sk osk w

w

D D D

l L D P

)(

)1.1)

22

4 ibob

skirt operationd

D D

wt wt

C

D D

t all

st combibob dw

.).3

2

Where:

- t = The thickness of the bearing plate.

Design of Anchor Bolts:

erectiond wtension ))max

Where:

-

σw is that calculated above in the bearing plate.- σd is calculated from:

)(

))))

22

4 ibob

skirt head sh ell operationd

D D

wt wt wt

If σtension) max = - ve value: the number of bolts equal 4 used for fixation.


20/29

9

If σtension) max = + ve value: the number of bolts calculated from the

following equation:

boltsall in

ibobtensionbolts

C d D D N

.

2

4

22

4

*)(*)

Where:

- σall).bolts = 12000 psi.


21/29

21

Design of Shor t Vertical Vessels

(L < 6m)

In designing short vessels, we firstly calculate the thickness of shell and heads

according to the operating pressure [i.e. internal or external]. In this case we will not

do checks on the thickness as done in tall vessels so, we will design the support

directly.

Design of Lug support:

N D

h H D P

N

wt f

bolt

ow s

*

7.0*****4.*1.1 '

Where:

- f s = The maximum compressive / support, lbf .

- N = Number of supports (lugs). Minimum No. of lugs = 4 [Take it 4 if

not given].

- Pw = Wind pressure, psi.

- D'o = The biggest diameter in the vessel, inch.

D'o = Dosh (If there is no insulation)

D'o = Doins. (If there is insulation)

- H = The shell length (tangent to tangent), inch.

- h = The length from the point at which wind effect appears to the end

of the lug length, inch.

h = h' + 0.25 H

- h' = The lug support height, inch.

h' ≥ 0.25 H + 2m [Use this rule only when h' is not given]

-

D bolt = The diameter of the circle passed through bolts, inch.

D bolt = D'o + 20"

After calculating f s, you should select the dimension of pipe (lug) and check on

your selected dimensions [i.e. check if the lug supports will withstand the load applied

on it]. Following are the steps used to select the suitable pipe dimensions:

1. From the following table, assume nominal diameter to get the inside

and outside diameter of the pipe:


22/29

2

Begin your assumption with nominal diameter = 2" [always take the

Schedule number = 80].

2. Calculate the radius of gyration (r) from the following equation:

22

4

44

64.

p p

p p

io pipe

iocal

pipe

D D A

D D I

A

I r


23/29

22

Where:

- Dop = The outside diameter of the pipe, inch.

-

Dip = The inside diameter of the pipe, inch.

- Ical = Moment of inertia, inch4.

- A pipe = The area of the pipe, inch2.

3. Calculate the value ofr

h' .

4. Make the check on the selected pipe dimensions according to the value

ofr

h'. Those values are summarized in the following table:

r

h' 60

'

r

h 200

'60

r

h 200

'

r

h

The Check

Relation pipeall

pipe

s

A

f

2

.

.

'*

11

r

h A

f

pipe

pipe

all

all

pipe

s

..min

.min

'2

'

**

*5

cal

critical

scritical

I I

h

I E F

f F

Note:

Take psi p ipeall 15000. if not given.

5. If the corresponding check is not correct, assume another nominal

diameter [greater than 2"] and repeat the above steps.

Note:

I f you increase the nominal diameter several times [for

example til l 20" ] and the check i s stil l not veri f ied, increase

the number of lug supports [6, 8,…].


24/29

23


Assume:

p

p p

p p

beffective

bb

ob

A A

D A

D D

8.07.0

)(

*2

2

4

Where:

- D bp = The diameter of the bearing plate, inch.

- A bp = The area of the bearing plate, inch2.

- Aeffective = The effective area of the bearing plate, inch2.

In order to check on this assumption, use the following formula:

N D A

h H D P

A

wt N

wt

psi

bolt effective

ow

w

effective

lug

d

wd compcomb

**

**7.0***4

.).1.1

525

'

.). max

If the check is not correct, increase the D bp till the check become correct.

Note:

I f you increase the diameter of bearing plate several times [f or

example til l 6D op ] and the check is sti l l not veri f ied, increase

the number of lug supports [6, 8,… ] or make more than plate

instead of one plate. Those plates are in the form of layers as

shown in the fi gure:


25/29

24

This wil l distribute the stress on the plates instead of being

concentrated on only one plate.


erectiond wtension ))max

Where:

- σw is that calculated above in the bearing plate.

- σd is calculated from:

effective

Lu g head sh ell

operationd A

wt N

wt wt ).))

)

If σtension) max = - ve value: the number of bolts equal 4 used for fixation.

If σtension) max = + ve value: the number of bolts calculated from the

following equation:

boltsall in

effectivetension

boltsC d

A N

.

2

4 *)(*

*)

Where:

- σall).bolts = 12000 psi.

Lug Support


26/29

25

Design of Horizontal Vessels

Like short vessels, in designing horizontal vessels, we firstly calculate the thickness

of shell and heads according to the operating pressure [i.e. internal or external]. Here

also we will not do checks on the thickness as done in tall vessels so, we will design

the support directly.

Design of Saddle Support:

The horizontal vessel is supported on at least 2 saddles supports. The saddle

support consists of sheet and rabbles:

Rabbles are used to reinforce the sheet and prevent its bending.

The distance between the two saddles "c" can be obtained from the following

equation:

al c 2' Or bl c 2' Where:

- l' = Lsh + h

Lsh = The shell length, inch.

h = The height of one head, inch.

In case of elliptical or dished head: h / Dish = 0.25 → get h.

- a = b = The distance from each support to the end of the shell, inch.

'*207.0 l ba

You should check if the distance between the supports "c" is sufficient or not.

The following are the two checks on the distance "c":

Sheet

Sheet

RabbleBearing

Plate


27/29

26

External Internal E

External Internal

y

all L M TenComb

P L M CompComb

"",""

*

"",""

3

...

..

E C t D

Moment Max

E C t

D P

sho M

sh

md

L

sh

sh

)(**

.

)(4

*

24

Where:

- Dmsh = The mean diameter of the shell, inch.

2

sh sh

sh

oi

m

D D D

-

In case of vessels under external pressure, put "Pact." Instead of "Pd"

the equation of "σL".

- Max. Moment can be calculated from:

'

.

'**. 2471

l

wt q

l q Moment Max

Where:

- q = The maximum weight / unit length, lbf / inch.

Note:

I f the above 2 checks are satisfied, the distance between the two

suppor ts is o.k. and if not we can decrease the distance between

the two supports or put a third saddle suppor t in between the

other two suppor ts or we can increase the thickness of shel l [by

1 / 16" ].


28/29

27

Now, we should choose the dimensions of the sheet:

Assume:

"*

"2"5.1

l t Area

t

sh eet sh eet

sh eet

Where:

- tsheet = the sheet thickness, inch.

- l" = The sheet width, inch.

180120*"

shi Dl

To check on this assumption:

N

wt f

y

Area

f

s

p

sh eet

s

.

3

Where:

- N = No. of saddles.


Rabble

Anchor BoltBearing Plate

Sheet


29/29

The dimensions of the bearing plate are:

Width = 12" – 15"

Length = l" + 6"

Assume:

)6"(*12 l A pb

Where:

- A bp = The area of the bearing plate, inch2.

Check on this assumption:

psi A

wt f

pb

saddle s

525

.)

Where:

steel rabblesrabbles

steel sadd le sheet sheet

rabbles sheet saddle

N wt

ht l wt

wt wt wt

**10*3*5.0*.)

**"*.)

.).).)

41

- hsaddle = The height of saddle, inch. [Take it 1.5 – 2m if not given].

-

Nrabbles = No. of rabbles = 8.

Note:

I f the check is not satisfied, increase the area of the bearing plate

[i.e. increase the width to 13" or 14" …. Or the length to l"+8 or

l " +9 Or increase both the width and the length].


As the wind has no effect on horizontal vessels, the number of bolts required

is 4 bolts only for fixation.

Documents

Vessel Design Course Notes