Chapter-2 Pressure vessels_Akash ver2.pdf

pressure vessel iit

1. INDIAN INSTITUTE OF TECHNOLOGY ROORKEE
Process Equipment Design
Dr. Deepak K Ojha
Department of Chemical Engineering
IIT Roorkee
Chapter-2

2. 2
Design of Head and Closures
•It is used to close the ends of the cylindrical pressure vessel.
•The design of head/closures require knowledge of ‘discontinuity stress’.
•Discontinuitystressesinpressurevesselsarelocalized,highstressesthat
occuratpointswherethereareabruptchangesingeometry,material
properties,orloadingconditions.
•Theseareas,calleddiscontinuityareas,canleadtoincreasedstress
concentrations,potentiallycausingleaks,bursting,ordeformation

3. 3
Design of Head and Closures
DiscontinuityAreas:Thesearelocationswherethevessel'sshape,material,or
howit'sloadedchangessuddenly.Examplesincludethejunctionofacylinderand
ahead(likeahemisphericalorellipsoidalendcap),orchangesinwallthickness.
StressConcentration:Atthesepoints,thestressdistributionisn'tuniform.The
stressishigherthanwhat'spredictedbysimplemembranetheory,whichassumes
uniformstressdistributionacrossthevesselwall.
Causes:
•DifferentMaterialProperties:Ifdifferentmaterialsarejoined,theydeform
differentlyunderload,leadingtostressbuildupatthejoint.
•GeometricDiscontinuities:Changesinshapecausethevesseltobendand
twistinwaysthatcreatehigherstresses.
•ExternalLoads:Applyingloadslikeforcesorthermalexpansioncanalsocause
stressconcentrationsatthesepoints.

4. 4
Types of Head and Closures
Flat Heads
•Used in small dia, low pressure vessels.
•Also used as manhole in low pressure vessels.
•For large diaor high-pressure vessels, it is too bulky .
•Discontinuity stress is too high near head and shell junction.
•Fabrication cost is low, but material cost is high.

5. 5
Types of Head and Closures
Flanged only Heads
•Gradualchangeintheshapeat
thecornerresultsinreduced
discontinuitystress.
•Economicalandusedinhorizontal
storagevesselsatatmospheric
pressure.
•Suitabletostoreliquidatlow
vaporpressuresuchasfueloil.

6. 6
Types of Head and Closures
Flanged shallow dished & Flanged standard dished (Torispherical)
Two important parameters
Crown radius (R
i): It's the radius of the sphere that
forms the main curved surface of the head.
Knuckle radius (r
i): It's the radius of the smaller curve
that connects the crown to the straight flange or the
shell. It's crucial for stress distribution and structural
integrity.
If the
•Crown radius (R
i) > Shell outer dia(D
0), vessel is
called ‘shallow dished’.
•Crown radius (R
i) ≤ Shell outer dia(D
0), vessel is
called ‘standard dished’.
Application:
•Vertical/horizontal process vessels with small/large dia. for low pressure (upto15 bar).
•Suitable for volatile liquid storage.

7. 7
Shallow & standard dished (Torispherical)
Design Consideration as per IS codes
•r
i≥ 3t
•r
i≥10% of D
i
•r
i<D
o
Example:Foravessel,iftheinnerdiameterandthicknessaregivenas1.0mand
2.0mm.
(a)Whatwouldbetheknuckleradius.
(b)Whatwouldbethecrownradiusfordishedenclosure.

8. 8
Types of Head and Closures
Elliptical dished head:
•Recommended for pressure range upto15 bar.
•Economicsbasisshouldbeappliedtochoose
betweentheshallow/standarddishedand
ellipticaldished.
Hemispherical head:
•Foragiventhisisstrongestamongtheformedheads.
•Theheadcanbeuseduptotwicethepressurerating
ofanellipsoidalheadvesselofsamediameterand
thickness.
•Mostexpensiveamongtheotherheads.
•Usedinveryhigh-pressureapplications.

9. 9
Types of Head and Closures
Conical heads and reducers:
•Usedasbottomforavarietyofprocessequipmentssuch
asevaporators,spraydriers,crystallizers,settlingtanks,
silos,etc.
•Idealforsolidhandlingsystems.
•Alsousedasreducer,providingasmoothtransition
betweentwopartsofdifferentdiameterincylindrical
processvessels.
•Difficulttofabricatewhenthedesiredapexangle>60.
Inthiscaseatransitionknuckleismust.

10. 10
Design of flat heads
Plate thickness, t =&#3627408438;&#3627408439;
0
Τ&#3627408477;&#3627408467;
Where,
C =factor of attachment
D
e= Effective diameter
p= load intensity or pressure
f= allowable stress
Plate welded on inside and both sides

11. 11
Plate welded to the end; additional fillet weld
Design of flat heads

12. 12
Design of flat heads
Coversrivetedor
boltedwithafull-
facegasketsto
shells
Coverswitha
narrowfacebolted
flange joint.
Gasketisplaced
withinboltholes.

13. 13
S. NoMethod of attachment C De
1 Flanged flat heads butt welded 0.45 Di
2 Plates welded to the Inside of the shell 0.55 Di
3 Plate welded to the end of the shell 0.7 Di
4 Plate welded to the end of the shell with additional fillet welt
on inside
0.55 Di
5 Cover rivetted or bolted with a full-face gaskets to shells0.42 Bolt dia
6 Covers with a narrow face bolted flange joint * Dg
Design of flat heads
*C=0.31+190
&#3627408441;??????ℎ??????
&#3627408477;&#3627408439;
??????
3
Τ
1
2
F
B= Bolt load
ℎ
&#3627408442;=
1
2
&#3627408437;&#3627408476;&#3627408473;&#3627408481;&#3627408464;??????&#3627408479;&#3627408464;&#3627408473;&#3627408466;&#3627408465;??????&#3627408462;&#3627408474;&#3627408481;&#3627408466;&#3627408479;−&#3627408439;
&#3627408466;
D
g= mean diameter of gasket

14. 14
Design of flat heads
Problem:Apressurevesseltobedesignedforamax.operatingpressureof500
kN/m
2
.Thevesselhasnominaldiameterandheightof1.2m,2.4mrespectively.
ThevesselismadeofIS:2002-1962Grade2Bstainlesssteelhavingallowable
designstressvalueof118MN/m
2
atdesigntemperature.Consideringthelifespan,
thecorrosionallowanceisrecommendedas2mm.Thevesselistobefabricated
asclass-IIofIndianStandardwhichstipulatetheweldjointefficiencyof0.85.
Determinethethicknessoftheflangedflatcoversoftheprocessvessel?
Plate thickness, t =&#3627408438;&#3627408439;
0
Τ&#3627408477;&#3627408467;
Where,
C =factor of attachment
D
e= Effective diameter
p= load intensity or pressure
f= allowable stress

15. 15
Design of Torispherical (Standard dished) heads
Any dished head consists of 3 integral
parts:
1)Central dishing
2)Corner torus
3)End straight flange
There are two junctions of discontinuity existing in a formed
head:
1)Between knuckle (torus) and crown (dish)
2)Second one between knuckle and straight flange.

16. 16
Design of Torispherical (Standard dished) heads
Head thickness:
t =
&#3627408477;&#3627408439;0&#3627408438;
2&#3627408467;??????
Shape factor C depends on:
A)hs/Doand t/Dofor the head without any opening or openings completely
reinforced.
B)he/Doand
&#3627408465;
√??????&#3627408439;&#3627408476;
for the heads containing unreinforced opening
d is the diameter of the largest uncompensated opening in the
head.

17. 17
hEis the effective external height of the head without straight flange and equal to
the minimum of
h0 or Do
2
/4 Ro or (Doro/2)
1/2
The external height, h
0of a dished head, the approximate blank diameter of the plate with
which formed ends can be fabricated:
h
0(excluding straight flange): R
o–[(R
o–
&#3627408439;
&#3627408476;
2
) ×(R
o+
&#3627408439;
&#3627408476;
2
–2r
o)]
1/2
Blank diameter = D
o+
D
o
42
+
2
3
r
i+ 2 S
f ( for t ≤25mm)
= D
o+
D
o
42
+
2
3
r
i + 2 S
f+ t ( for t > 25 mm)
Design of Torispherical (Standard dished) heads

18. 18
Design of Torispherical (Standard dished) heads

19. 19
Problem:Apressurevesseltobedesignedforamax.operatingpressureof500
kN/m
2
.Thevesselhasnominaldiameterandheightof1.2m,2.4mrespectively.The
vesselismadeofIS:2002-1962Grade2Bstainlesssteelhavingallowabledesign
stressvalueof118MN/m
2
atdesigntemperature.Consideringthelifespan,the
corrosionallowanceisrecommendedas2mm.Thevesselistobefabricatedas
class-IIofIndianStandardwhichstipulatetheweldjointefficiencyof0.85.
Determinethethicknessoftheplaterequiredtofabricateastandarddished
head.
Itmaybeassumedthattherewillbenouncompensatedopeninginthehead.
Specificationsfortheheadaregivenbelow:
R
i=Do;r
i=0.06Do;S
f=40mm
Whatshouldbethethickness&blankdiameter(i.e.thediameteroftheplate)
forthehead?
Design of Torispherical (Standard dished) heads

20. 20
Design of Torispherical (Standard dished) heads
What if the top has an opening?
Head thickness:
t =
&#3627408477;&#3627408439;0&#3627408438;
2&#3627408467;??????
Rearrange this to have a correlation between d/sqrt(tD0) and C, to use Table 4(B)
1
&#3627408481;&#3627408439;
0
=
2&#3627408467;??????
&#3627408477;&#3627408439;
0
2
&#3627408438;
Multiply the opening diameter ‘d’ on both sides

21. 21
Design of Torispherical (Standard dished) heads
Problem: For the process vessel discussed in the previous example, a 10 mm thick 2:1 ellipsoidal
head with an uncompensated opening is to be fabricated. What max. diameter opening will be
possible?
Thickness without corrosion allowance, t = 10-2 = 8 mm
Calculate C, using the formulat =
&#3627408477;&#3627408439;0&#3627408438;
2&#3627408467;??????
For 2:1 ellipsoidal head, h
e= h
0= D
0/4; h
e/D
0=0.25

22. 22
Design of Conical heads
Geometryofaconemaybecomparedwiththatofacylinderinwhichthediameteris
continuouslychanging.
&#3627408477;D
k
2&#3627408467;??????−&#3627408477;
×
1
&#3627408464;&#3627408476;&#3627408480;∝
&#3627408481;=
Calculation is divided in two parts: Thickness of conical section, thickness of cylindrical section
&#3627408481;=
&#3627408477;D
eZ
2&#3627408467;??????
Where D
kis the diameter at slanting distance
&#3627409359;
&#3627409360;
(D
et/cos α)
1/2
from the junction.
α 20° 30° 45° 60°
Z 1.00 1.35 2.05 3.2
The conical-cylindrical junction is welded hence weld efficiency must be considered.

23. 23
Problem:Apressurevesseltobedesignedforamax.operatingpressureof500kN/m
2
.The
vesselhasnominaldiameterandheightof1.2m,2.4mrespectively.Thevesselismadeof
IS:2002-1962Grade2Bstainlesssteelhavingallowabledesignstressvalueof118MN/m
2
at
designtemperature.Consideringthelifespan,thecorrosionallowanceisrecommendedas2
mm.Thevesselistobefabricatedasclass-IIofIndianStandardwhichstipulatetheweldjoint
efficiencyof0.85.
Iftheprocessvesselistobeprovidedwithaconicalheadhavingthehalf-apexangle30°,
determinethethicknessofthehead.
Design of Conical heads
Retry the problem with half apex angle of 45
o
.

24. 24
Summary of the head design
Type of Head Thickness with allowance
(Std. plate thickness)
Flat 40.2 mm (45 mm)
Torispherical 9 mm (10 mm)
Conical 7 mm (8 mm)
Vessel thickness: 6mm (8mm)

25. 25
Summary of the head designprocedure
Flat head
Torrispherical head
Conical head
t =&#3627408438;&#3627408439;
0
Τ&#3627408477;&#3627408467;
Valueof‘C’
shouldbechosen
forattachment
type.
2. Calculate h
E/D
0
1.Estimate h
Eby
ℎ
&#3627408440;=&#3627408474;??????&#3627408475;ℎ
0,
&#3627408439;
0
2
4??????0
,
&#3627408439;
0??????
0
2
3.Reorganizethethickness
equationforheadwith/without
openingtoalignwiththeTable
4.1(A)&(B)
4. For without opening
&#3627408481;
&#3627408439;
0&#3627408438;
=
&#3627408477;
2&#3627408467;??????
5. For head with opening
&#3627408465;&#3627408438;
&#3627408481;&#3627408439;
0
=&#3627408465;
2&#3627408467;??????
??????&#3627408439;
0
2
6.Usetable4.1(A&B)andlinearinterpolationsto
estimatethethickness
1.Estimate the thickness
of cylindrical part by
&#3627408481;=
&#3627408477;&#3627408439;
&#3627408466;&#3627408461;
2&#3627408467;??????
2. Estimate the thickness of
the conical section using
&#3627408481;=
&#3627408477;&#3627408439;
??????
2&#3627408467;??????−&#3627408477;
×
1
cos??????
2. Estimate D
kat a slanting
distance of
1
2
Τ&#3627408439;
&#3627408466;&#3627408481;cos??????

26. 26
Design of Vessel heads

27. 27
Practice Problem
Problem:Apressurevesseltobedesignedforamax.operatingpressureof500
kN/m
2
.Thevesselhasnominaldiameterandheightof1.2m,2.4mrespectively.The
vesselismadeofIS:2002-1962Grade2Bstainlesssteelhavingallowabledesign
stressvalueof118MN/m
2
atdesigntemperature.Consideringthelifespan,the
corrosionallowanceisrecommendedas2mm.Thevesselistobefabricatedas
class-IIofIndianStandardwhichstipulatetheweldjointefficiencyof0.85.
Determinethethicknessoftheplaterequiredtofabricateastandarddished
head.
Notethatthevesselhasanuncompensatedopening(dia.0.25m)inthehead.
Specificationsfortheheadaregivenbelow:
R
i=Do;r
i=0.06Do;S
f=40mm
Whatshouldbethethicknessofthehead?

28. 28