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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