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1
Pressure Vessels
Pressure Vessels
Cylinders or tanks used to store fluids under pressure subjected to a pressure difference of more than one bar Fluid may be compressed or under vacuum Fluid may undergo change of state or chemical reaction Design with great care because rupture means an explosion
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Design considerations for Pressure Vessels
Design Pressure
Code of Specifications or Standards
Shell and Head Thickness
Design Stress
Temperature
Material of Construction
Welded Joint Efficiency
Corrosion Allowance
Design Equations: Minimum Thickness
Design Loads
Design Pressure
Design Pressure based on Maximum Allowable Working
Pressure(MAWP)
MAWP = Operating Pressure + 10% Safety factor
Vessels subjected to Internal or External Pressure Under internal pressure: Pinside > Poutside
Set pressure relief device (burst if working pressure exceeds MAWP)
Hydrostatic pressure added (if significant)=
Under external pressure Poutside > Pinside For vacuum service, design pressure is at 1 bar
Set vacuum breaker (else vessel collapse)
rgh
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Failure of Pressure Vessels
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Thickness of Pressure Vessels
Shell Thickness (Cylinder or Spherical Shell) Thin walled vessels: thickness: diameter (t/D) < 1:10
Most vessels in chemical & allied industry are thin
Thick walled vessels: thickness: diameter (t/D) >= 1:10 High pressure applications involve thick vessels
Heads Thickness
Flat head
Dome head
Dish head
Types of heads for cylindrical pressure vessels
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Choice of Heads (Caps)
Flat plates covers for manways and as the channel covers of heat exchangers Formed flat ends or flange-only ends, are manufactured by turning over a flange
with a small radius on a flat plate. The corner radius reduces the abrupt change of shape, at the junction with the cylindrical section, which reduces the local stresses
flange-only heads are the cheapest type of formed head to manufacture limited to low-pressure and small-diameter vessels.
Dished ends Torispherical heads used end closure up to operating pressures of 15 bar Ellipsoidal head is most economical for pressures above 15 bar
Dome ends Hemispherical head Convex Disc strongest shape, capable of resisting about twice the pressure of a torispherical
head of the same thickness. More costly to form than torispherical head. used for high pressures.
Types of heads for cylindrical pressure vessels
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Types of heads for cylindrical pressure vessels
Flange
A protruding rim, edge, rib, or collar, as on a wheel or a pipe shaft, used to strengthen an object, hold it in place, or attach it to another object.
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Principal stresses on an
element of vessel
Thin vessels
s3 can be neglected
s1 and s2 can be taken as constant over the wall thickness.
Thick vessels
s3 is significant
s1 and s2 will vary across the wall.
radial stress s3
longitudinal stress s1
circumferential stresses s2
Failure due to Stress
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Design Stress Nominal design strength yield strength
Maximum allowable stress = of design strength
Factor of safety is 1.5 to 4
Safety ofFactor
Strength Yield StressDesign
Design Stress
For materials not subjected to high temperature
Yield or Proof stress (failure takes place)
Tensile strength or ultimate tensile stress
For materials subjected to creep (Creep defined as a time-dependent deformation at elevated temperature and constant stress.)
Average stress to produce rupture after 105 hrs
Average stress to produce 1% strain after 105 hrs
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Creep - may be defined as a time-dependent
deformation at elevated temperature
Standards and Code of Specifications for Pressure Vessels
Standards ASME Boiler and Pressure Vessel Code British Code or British Standards (BS) European Standard
Pressure vessels must be designed, constructed, and tested in accordance with part or all of the design code. The primary purpose of the design codes is to establish rules of safety relating to the
pressure integrity of vessels provide guidance on design, materials of
construction, fabrication, inspection, and testing.
Pressure Stress Temperature Thickness Material of Construction Nominal Diameter
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Design Temperature
Strength decreases with temperature
Maximum allowable design stress based on maximum operating temperature
Heuristics
For operating temperature between 30 to 350oC, Design T = Operating T + 30oC
Below 30oC, special steel required
Above 350oC, allowable design stress falls sharply
Material of Construction
Usual materials
Carbon steel
Low and high alloy steels
Alloys
Clad plate
Reinforced plastics
Choice of Material of construction
Ease of fabrication particularly welding
Compatibility with process environment
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Joint Efficiency Welded/Riveted
Strength depends on
Type of Joint: lap and butt
Quality of weld/rivet
Welded Joint Efficiency Soundness of weld check
Visual inspection
Nondestructive test (radiographic)
Radiographing is an inspection process whereby welded joints are examined by X-ray equipment sufficiently powerful to reveal excessive porosity, points of defective fusion and other defects.
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Radiographing to determine weld defects
Welded Joint Efficiency
Singlewelded butt joint with bonding strips 0.90 for fully radiographed
0.80 for spot examined (radiographed)
0.65 if not radiographed
Single/Doublewelded butt joints 1.00 for fully radiographed
0.85 for spot examined (radiographed)
0.70 if not radiographed
plate virgin unwelded ofStrength
plate weldedofStrength JE Strength=P (Newtons)
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Welded Joint Efficiency
In general, for spot examined (in the absence of available precise data)
EJ =
0.85 for electric resistance weld
0.80 for lap welded
0.60 for singlebutt welded
0.55 for double full fillet lap joint
0.50 for single full fillet lap with plugs
0.45 for single full fillet lap joint
1.0 for seamless shells and heads
Corrosion Allowance For carbon and low alloy steel
2 mm minimum where severe corrosion is not expected
4 mm minimum for severe corrosion
Most design codes and standards specify 1 mm minimum
Heuristics
0.250.38 mm/yr or 3 mm for 10 yr life
9 mm for vessel in contact with corrosive fluids
3 mm for noncorrosive fluids
For steam and air service, corrosion allowance is 1.5 mm
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Design Equations Shells
Cylindrical
Spherical
Heads/Closures/Ends Flat
Plates
Formed ends
Shaped Pierced/ Unpierced
Domed
Dished
Conical
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Openings in Pressure Vessels Necessary to allow
the mounting of equipment the insertion of instrumentation connection of piping to facilitate
the introduction and extraction of content.
Types Handholes are provided in vessels
to permit interior inspection Manways allow personnel to gain
access to their interiors.
Openings are generally made in both vessel shells as well as heads.
Weaken the containment strength of a pressure vessel
Thickness of Shells Thin Cylindrical Shells
P = intensity of internal pressure
d = diameter of the cylindrical shell
L = length of the cylindrical shell
t = thickness of the cylindrical shell
sh = circumferential or hoop or girth stress, tangential stress
Efficiency of the longitudinal joint Ej = E
Total Force acting on a longitudinal section = Intensity of pressure x projected area = p d L
Total resisting force acting on the cylinder walls = sh 2t L
= sh 2
sh =
2
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Thickness of Shells Thin Cylindrical Shells
P = intensity of internal pressure
d = diameter of the cylindrical shell
L = length of the cylindrical shell
t = thickness of the cylindrical shell
sl = longitudinal stress Efficiency of the
longitudinal joint Ej = E
Total Force acting on a section = Intensity of pressure x projected area
= p
4 2
Total resisting force acting on the cylinder walls =sl t
p
4 2 = sl t
sl =
4=
sh2
Minimum wall thickness
=
2
If t is the minimum thickness required: d = di + t and s = S = max allowable Stress
= ( + )
2 =
2
If we allow for the welded-joint efficiency, E, this becomes
=
2
The equation specified by the ASME BPV Code (Sec. VIII D.1 Part UG-27) is:
=
2 1.2
Simplifying
In terms of the radius, di=2R
=
.
Thickness based on circumferential stress
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Shell Design Equations
Cylindrical Shells
ci C
PSE
rPt
6.0
cii CrPSE
PSErt
2
1
SEPr
rt i
385.0 o
5.0 where
SEPr
rt i
385.0 o
5.0 where
Shell Design Equations
Spherical Shells
c
J
i CPSE
rPt
2.02
ci
J
Ji Cr
PSE
PSErt
3
1
2
22
J
i
SEP ro
rt where
685.0
356.0
J
i
SEP ro
rt where
685.0
356.0
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Head Design Equations
Flat Head
Hemispherical Head Same as spherical shell
Radius crown radius
Usual ratio of hemispherical head thickness to cylinder thickness is 7/17. Optimal thickness ratio is usually 0.6.
ci CS
Prt
3.02
Head Design Equations
Ellipsoidal Head
(for 2:1 ratio)
ca
J
a Ch
D
PSE
PDt
2
22
1.012
1
c
J
a CPSE
PDt
2.02
62 h
D where a
Da h
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Head Design Equations
Torispherical Head
aL.060r where k
c
J
a CPSE
PLt
1.0
885.0
c
k
a
J
a Cr
L
PSE
PLt
3
1.0
885.0
8
1
tr
trL
LrL where
k
ia
aka
3
22
06.0
Head Design Equations
c
J
cs CPSE
PDCt
2
Conical Head (for any point on a cone)
at conecylinder junction
c
J
c CPSE
PDt
cos2
1
6.0
20o 30o 45o 60o
Cs 1.00 1.35 2.05 3.20
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Design of Vessels under Internal Pressure