Design of Pressure Vessels

Dr. Achchhe Lal

Department of Mechanical Engineering

SVNIT Surat-395007

Phone: (+91) (261) 2201993, Mobile: 9824442503

Email: lalachchhe@yahoo.co.in, URL: http://www.svnit.ac.in Kindly send your

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Basic References

Theory and Design of Pressure Vessels

John F. Harvey, P.E.

VAN NOSTRAND REINHOLD COMPANY INC., 1985.

Pressure Vessels: Design and Practice

Sobhanath Chattopadyay

CRC Press., 2000.

Pressure Vessels Design Manual

Denis Moss

Gulf Professional Company, 2004.

Mechanical Design of Heat Exchangers

K.P. Singh & A.L. Soler,, Arcturus Pub. Inc. N.J. 08003, USA.

1984.

Pressure Vessels and Stachs

Heith Escoe

Field repairs manuals

Introduction to diverse kinds of Pressure Vessels (PVs)

Overview of various parts (internal and external) of Pressure vessels and its

functions and applications.

Various failure modes of PVs, Brief introduction to different pressure vessels

code and importance

What factors to be considered for the selection of materials and different types of

materials with their characteristic and properties,

Theory of pressure vessels design on internal pressure basis and external pressure

basis, Autofretage of thick cylinders, Significant of thermal stresses and fatigue

Design of Shells and Heads for Internal and External Pressure

Importance and design of different kinds of openings and flanges

Pressure Vessel design for external loads– Wind/Seismic & Support design

Evaluation of pressure vessel for different conditions: Hydrotest condition, FEM

analysis,

What will you learn?

“A teacher’s job is to uncover and not cover the syllabus”- Richard M Felder

The following hyperlinks are to file-wise substructure. Content-wise substructure will appear in respective chapters.

1. CHAPTER 1: Introduction

1.1 Introduction to PVs

1.2 Types and Applications of PVs

CHAPTER 2: Factors influencing the design of vessels,

classification of pressure vessels, material selection,

loads & types of failures

3. CHAPTER 3: Stresses in pressure vessels

stresses in circular ring, cylinder & sphere,

membrane stresses in vessels under internal

pressure, thick cylinders, multilayered

cylinders, stress consideration in the selection

of flat plate & conical closures, elliptical,

torispherical,

4. CHAPTER 4: Autofretage of thick cylinders,

thermal stresses & their significance, fatigue of

pressure vessels

.

5. CHAPTER 5: Design of pressure vessels as per ASME & IS codes, externally pressurized

vessels, tall vertical vessels, support for

vertical & horizontal vessels, nozzles & flanges

5

Objectives of Chapter 1

Introduction of Pressure vessels with applications

in different engineering applications

Overview of various parts (internal and external)

of Pressure vessels and its functions and

applications.

Pressure vessels –An Introduction A pressure vessel are a closed container designed to hold gases or liquids at a pressure (inside the vessels) different from the out side pressure (known as ambient pressure or Atmospheric pressure).

Pressure vessels are the basic equipment for any fluid processing system.

The liquid and gaseous chemicals are storage in a pressurized chambers (pressure vessels) for a chemical reaction.

The inside pressure may be obtained from an external source or by the application of heat from direct or indirect source, or by other. PVs are also known as leak proof containers. They may be of any shape and range from bottles to the sophisticated ones in engineering construction

The pressure vessels is design of great care because of rapture

pressure vessels means an explosion which cause of may cause loss of

life property. The material of pressure vessels may be brittle such that

cast iron or ductile such mild steel.

They are used in

storage vessels (for liquified gases such as ammonia, chlorine, propane, butane, house hold gas cylinders, fire extinguishers, saving cream cans and LPG),

chemical industries (as distillation tower, domestic hot water storage tanks).

medical field (as autoclaves).

aero space field (as habitat of spaceship).

nuclear field (as a nuclear vessels).

pneumatic and hydraulic reservoirs under pressure.

In Automobiles: rail vehicle airbrake reservoir, road vehicle airbrake reservoir, power, food and many other industries.

In recent years, the use of pressure vessels has become very expansive due to phenomenal expansion in fertilizer, petrochemical paint, food, nuclear, drug and other allied industries.

Difference Applications of pressure vessels

Gas Cylinders

•Storage of medical gases.

•Storage of breathing gases in diving cylinder.

•Storage of gaseous fuels for internal combustion

engines,

•heating equipment and cooking such as LP gas,

butane and propane.

•Storage of gases used for oxy-fuel welding and

cutting.

2 and 3 liter diving cylinders.

Some Common Applications of Pressure Vessels

Typical industrial fractional distillation columns

Distillation columns used to

separate various gases in

petroleum refineries,

petrochemical and chemical

plants and natural gas

processing plants.

Chemical engineering

schematic of typical bubble-cap

trays in a distillation tower

Chemical Engineering Fields

An autoclave is a pressurized device

designed to heat aqueous solutions

above their boiling point to achieve

sterilization

Stovetop autoclaves - the

simplest of autoclaves A modern Front Loading Autoclave

Medical fields

A mine cart toilet used in mining

An oil refinery is an industrial process plant where crude oil is processed

and refined into more useful petroleum products, such as gasoline, diesel

fuel, asphalt base, heating oil, kerosine, and liquefied petroleum gas

Petrochemical fields

Petrochemicals are chemical products made from raw

materials of petroleum (hydrocarbon) origin

A nuclear reactor is a device in which nuclear chain reactions are

initiated, controlled, and sustained at a steady rate, as opposed to a

nuclear bomb, in which the chain reaction occurs in a fraction of a

second and is uncontrolled causing an explosion

In the nuclear fields

The Hubble Space Telescope.

In the aerospace applications

In Automobiles

An air brake is a conveyance braking system applied by

means of compressed air

To Be Continue…

Date: January 27, 2014

Continue... • In the industrial sector, pressure vessels are designed to

operate safely at a specific pressure and temperature, technically referred to as the "Design Pressure" and "Design Temperature".

• Second main important parameter is required thickness.

• A vessel that is inadequately designed to handle a high pressure constitutes a very significant safety hazard.

• Pressure vessels can theoretically be almost any shape, but shapes made of sections of spheres, cylinders and conical types are usually employed. More complicated shapes have historically been much harder to analyze for safe operation and are usually far harder to construct.

• Theoretically a sphere would be the optimal shape of a pressure vessel. Unfortunately the sphere shape is difficult to manufacture, therefore more expensive, so most of the pressure vessels are cylindrical shape with 2:1 semi elliptical heads or end caps on each end.

TYPES OF PRESSURE VESSELS

There are three main types of pressure vessels

in general

• Horizontal Pressure Vessels

• Vertical Pressure Vessels

• Spherical Pressure vessels

However there are some special types of Vessels like

Regeneration Tower, Reactors but these names are given

according to their use only.

HORIZONTAL PRESSURE VESSEL

VERTICAL PRESSURE VESSEL

• The max. Shell

length to diameter

ratio for a small

vertical drum is

about 5 : 1

TALL VERTICAL TOWER

• Constructed in a wider

range of shell diameter

and height.

• They can be relatively

small in dia. and very

large (e.g. 4 ft dia. And

200 ft tall distillation

column.

• They can be very large in

dia. and moderately tall

(e.g. 3 ft dia. And 150 ft

tall tower).

• Internal trays are

needed for flow

distribution.

VERTICAL REACTOR

• Figure shows a typical

reactor vessel with a

cylindrical shell.

• The process fluid

undergoes a chemical

reaction inside a

reactor.

• This reaction is normally

facilitated by the

presence of a catalyst

which is held in one or

more catalyst beds.

SPHERICAL PRESSURIZED

STORAGE VESSEL

MAIN COMPONENTS OF

PRESSURE VESSEL

Following are the main components of pressure

Vessels in general

• Shell

• Head

• Nozzle

• Support

SHELL

It is the primary component that contains the

pressure.

Pressure vessel shells in the form of different

plates are welded together to form a

structure that has a common rotational axis.

Shells are either cylindrical, spherical or

conical in shape.

SHELL

Horizontal drums have cylindrical shells and

are constructed in a wide range of diameter

and length.

The shell sections of a tall tower may be

constructed of different materials, thickness

and diameters due to process and phase

change of process fluid.

Shell of a spherical pressure vessel is

spherical as well.

HEAD

• All the pressure vessels must be closed at

the ends by heads (or another shell section).

• Heads are typically curved rather than flat.

• The reason is that curved configurations are

stronger and allow the heads to be thinner,

lighter and less expensive than flat heads.

• Heads can also be used inside a vessel and

are known as intermediate heads.

• These intermediate heads are separate

sections of the pressure vessels to permit

different design conditions.

NOZZLE

• A nozzle is a cylindrical component that

penetrates into the shell or head of pressure

vessel.

• They are used for the following applications.

• Attach piping for flow into or out of the vessel.

• Attach instrument connection (level gauges,

Thermowells, pressure gauges).

• Provide access to the vessel interior at

MANWAY.

• Provide for direct attachment of other equipment

items (e.g. heat exchangers).

SUPPORT

• Support is used to bear all the load of

pressure vessel, earthquake and wind loads.

• There are different types of supports which

are used depending upon the size and

orientation of the pressure vessel.

• It is considered to be the non-pressurized part

of the vessel.

TYPES OF SUPPORTS

SADDLE SUPPORT:

Horizontal drums are typically supported at two

locations by saddle support.

It spreads over a large area of the shell to prevent an

excessive local stress in the shell at support point.

One saddle support is anchored whereas the other is

free to permit unstrained longitudinal thermal

expansion of the drum.

TYPES OF SUPPORTS

LEG SUPPORT:

Small vertical drums are typically supported on legs

that are welded to the lower portion of the shell.

The max. ratio of support leg length to drum diameter

is typically 2 : 1

Reinforcing pads are welded to the shell first to

provide additional local reinforcement and load

distribution.

The number of legs depends on the drum size and

loads to be carried.

Support legs are also used for Spherical pressurized

storage vessels.

Cross bracing between the legs is used to absorb wind

or earth quake loads.

TYPES OF SUPPORTS

LUG SUPPORT:

Vertical pressure vessels may

also be supported by lugs.

The use of lugs is typically

limited to pressure vessels of

small and medium diameter (1

to 10 ft)

Also moderate height to

diameter ratios in the range of

2:1 to 5:1

The lugs are typically bolted to

horizontal structural members

in order to provide stability

against overturning loads.

TYPES OF SUPPORTS

SKIRT SUPPORT:

Tall vertical cylindrical pressure vessels are typically

supported by skirts.

A support skirt is a cylindrical shell section that is

welded either to the lower portion of the vessel shell

or to the bottom head (for cylindrical vessels).

The skirt is normally long enough to provide enough

flexibility so that radial thermal expansion of the shell

does not cause high thermal stresses at its junction

with the skirt.

THIN WALLED PRESSURE

VESSELS

• Thin wall refers to a vessel having an inner-radius-to-wall-

thickness ratio of “10” or more (r / t ≥ 10).

• When the vessel wall is thin, the stress distribution

throughout its thickness will not vary significantly, and so

we will assume that it is uniform or constant.

• Following this assumption, the analysis of thin walled

cylindrical and spherical pressure vessel will be carried out.

• In both cases, the pressure in the vessel will be considered

to be the gauge pressure, since it measure the pressure

above atmospheric pressure existing at inside and outside

the vessel’s walls.

THIN WALLED PRESSURE

VESSELS

• The above analysis indicates that an element of material

taken from either cylindrical or spherical pressure vessel is

subjected to biaxial stress, i.e. normal stress existing in only

two directions.

• Actually material of the vessel is also subjected to a radial

stress, σ3, which acts along a radial line. This stress has a

max. value equal to the pressure p at the interior wall and

decreases through the wall to zero at the exterior surface of

the vessel, since the gauge pressure there is zero.

• For thin walled vessels, however, the redial stress

components are ignored because r / t = 10 results in σ1 & σ2

being, respectively, 5 & 10 times higher than the max. radial

stress, (σ3)max = p

THIN WALLED PRESSURE

VESSELS

• It must be emphasized that the formula derived for thin

walled pressure vessels should be used only for cases

of internal pressure.

• If a vessel is to be designed for external pressure as in

the case of vacuum tank, or submarine, instability

(buckling) of the wall may occur & stress calculations

based on the formulae derived can be meaningless.

Types of pressure vessels

Storage Tank to Heat Exchanger

Pressure Vessels & Reactors

storage tanks from carbon steel,

stainless steel and nickel alloy vessels

Single Pass & Multiple Pass Heat Exchangers used in the chemical process industry.

Stainless Steel Pressure Vessel (painted)

Stainless Steel Pressure Vessels and

Heat Exchangers

Components of Pressure Vessels

Vessels with hemispherical head

Classification of pressure Vessels

Based on Construction:

• Mono wall: Depending on the specific

conditions, either monowall or multilayer construction

can be used, with finished high-pressure vessels

having unit weights of up to and in excess of 300t.

• Multi Wall: Various layered construction, used for all

types of PVs, large diameters, length, and wall thickness.

• Thermal conduction is lowers and easily made by reinforced

by shrinkage of one seamlessly forged cylinders on to the

core of shell

• The use of a multiwall pressure vessel is often necessary in

carrying out a reaction process under high pressure, and

when the reaction substances are corrosive, a multi-walled

pressure vessel provided with a special lining is often

utilized.

•

Analysis of PV based on internal pressure

Two types of analysis are commonly applied to pressure vessels. 1. Analysis based on a simple mechanics approach 2. Analysis based on based on elasticity solution The most common method is based on a simple mechanics approach and is applicable to “thin wall” pressure vessels which by definition have a ratio of inner radius, r, to wall thickness, t, of r/t≥10.

The second method is based on elasticity solution and is always applicable regardless of the r/t ratio and can be referred to as the solution for “thick wall” pressure vessels.

Both types of analysis are discussed here, although for most engineering applications, the thin wall pressure vessel can be used.

Cylindrical or spherical pressure vessels (e.g., hydraulic cylinders, gun barrels, pipes, boilers and tanks) are commonly used in industry to carry both liquids and gases under pressure. When the pressure vessel is exposed to this pressure, the material comprising the vessel is subjected to pressure loading, and hence stresses, from all directions. The normal stresses resulting from this pressure are functions of the radius/diameter of the element under consideration, the shape of the pressure vessel (i.e., open ended cylinder, closed end cylinder, or sphere) as well as the applied pressure.

Pressure Vessels: Combined Stresses

Thin-Walled Pressure Vessels

under internal pressure

1) Plane sections remain plane

2) r/t ≥ 10 with t being uniform and constant

3) The applied pressure, p, is the gage pressure (note that p is the difference between the absolute pressure and the atmospheric pressure)

4) Material is linear-elastic, isotropic and homogeneous.

5) Stress distributions throughout the wall thickness will not vary, however, stress distribution varies parabolic nature for thick walled pressure vessels.

6) Working fluid has negligible weight.

1.1. Stresses in Cylinders and Spheres

Longitudinal Stress in Spherical Pressure Vessel Thin Wall type

Thin-walled pressure vessels are one of the most typical applications of plane stress. Consider a spherical pressure vessel with radius r and wall thickness t subjected to an internal gage pressure p. The normal stresses σ can be related to the pressure p by inspecting a free body diagram of the pressure vessel. To simplify the analysis, we cut the vessel in half as illustrated. Since the vessel is under static equilibrium, it must satisfy Newton's first law of motion. In other words, the stress around the wall must have a net resultant forces acting in the pressure vessel to balance the internal pressure across the cross-section.

Hoop Stress Cylindrical Pressure

Vessel To determine the hoop stress σh, we make a cut along the longitudinal axis and construct a small slice as illustrated on the right. The free body is in static equilibrium. According to Newton's first law of motion, the hoop stress yields,

Hoop and longitudinal stress in a thin sphere subjected to internal pressure may be found to be equal to and same as longitudinal stress in a Cylinder

The above formulas are good for thin-walled pressure vessels. Generally, a pressure vessel is considered to be "thin-walled" if its radius r is larger than 5 times its wall thickness t (r > 5 · t). When a pressure vessel is subjected to external pressure, the above formulas are still valid. However, the stresses are now negative since the wall is now in compression instead of tension. The hoop stress is twice as much as the longitudinal stress for the cylindrical pressure vessel. This is why an overcooked hotdog usually cracks along the longitudinal direction first (i.e. its skin fails from hoop stress, generated by internal steam pressure).

Important Remarks

For example, the ASME Boiler and Pressure Vessel

Code (BPVC) (UG-27) formulas are:

Spherical shells:

Cylindrical shells:

where E is the joint efficient, and all others variables

as stated above.

The Factor of safety is often included in these

formulas as well, in the case of the ASME BPVC this

term is included in the material stress value when

solving for Pressure or Thickness.

Dilation or radial growth of pressure vessels

Axi-symmetric Pressure Vessels • provides the derivation of the

governing equations for membrane stress in pressure vessels having circular crosssection, which includes cylinders and any other shape having a revolved axis of symmetry

• Consider an element of size ds1 by ds2 by thickness t, extracted from the internally pressurized thin-shelled enclosure shown in Figure 2.1.1

• Note that for computational simplicity, the chosen element is oriented along the principal (longitudinal and circumferential) directions of the part, so that only normal forces act on its sectioned faces.

Ellipsoidal vessels under internal pressure

Thick Walled Cylindrical Vessels

When the thickness of the cylindrical vessel is relatively large, as in the case of gun barrel, high pressure hydraulic ram cylinders etc., the variation in the stress from the inner surface to outer surface becomes appreciable and the ordinary membrane or average stress formula are not satisfactory indication of significant stress.

Deformation (Radial) of thick cylinder

Thermal Stresses and their significance

Uniaxial Thermal

Strain=

Thermal Stress=

Thermal Stresses and their significance

Uniaxial Thermal

Strain=

Thermal Stress=

Assigments-1

Solve the unsolved numerical problem of Hohn F Harvey

Problems 1 to 16 Page no. 97 to 100

17. Explain the Shink-fit stresses in built-up cylinders.

18. Explain the autofrettage phenomenon in thick cylinders.

19. Explain the importance of brusting strength in Pressure

vessels.

20.Expalin the effect of thermal stresses and significant in

cylindrical vessels.

Shrink-fit stresses in builtup cylinders

Autofrettage of thick cylinders

• Autofrettage is a metal fabrication technique in which a pressure vessel is subjected to enormous pressure, causing internal portions of the part to yield and resulting in internal compressive residual stresses.

• The goal of autofrettage is to increase the durability of the final product.

• Inducing residual compressive stresses into materials can also increase their resistance to stress corrosion cracking; that is, non-mechanically-assisted cracking that occurs when a material is placed in a suitable environment in the presence of residual tensile stress.

• The technique is commonly used in manufacturing high-pressure pump cylinders, warship and tank gun barrels, and fuel injection systems for diesel engines. While some work hardening will occur, that is not the primary mechanism of strengthening.

The tube (a) is subjected to internal pressure past its elastic limit (b), leaving an inner

layer of stressed metal (c).

• The start point is a single steel tube of internal diameter slightly less than the desired calibre. The tube is subjected to internal pressure of sufficient magnitude to enlarge the bore and in the process the inner layers of the metal are stretched beyond their elastic limit.

• This means that the inner layers have been stretched to a point where the steel is no longer able to return to its original shape once the internal pressure in the bore has been removed. Although the outer layers of the tube are also stretched the degree of internal pressure applied during the process is such that they are not stretched beyond their elastic limit.

• The reason why this is possible is that the stress distribution through the walls of the tube is non-uniform. Its maximum value occurs in the metal adjacent to the source of pressure, decreasing markedly towards the outer layers of the tube.

• The strain is proportional to the stress applied within elastic limit; therefore the expansion at the outer layers is less than at the bore. Because the outer layers remain elastic they attempt to return to their original shape; however, they are prevented from doing so completely by the now permanently stretched inner layers.

• The effect is that the inner layers of the metal are put under compression by the outer layers in much the same way as though an outer layer of metal had been shrunk on as with a built-up gun.

• The next step is to subject the strained inner layers to low temperature heat treatment which results in the elastic limit being raised to at least the autofrettage pressure employed in the first stage of the process.

• Finally the elasticity of the barrel can be tested by applying internal pressure once more, but this time care is taken to ensure that the inner layers are not stretched beyond their new elastic limit.[1]

• When autofrettage is used for strengthening gun barrels, the barrel is bored to a slightly undersized inside diameter, and then a slightly oversized die is pushed through the barrel. The amount of initial underbore and size of the die are calculated to strain the material past its elastic limit into plastic deformation, sufficiently far that the final strained diameter is the final desired bore.

• The technique has been applied to the expansion of tubular components down hole in oil and gas wells. The method has been patented by the Norwegian oil service company, Meta, which uses it to connect concentric tubular components with sealing and strength properties outlined above.

Factors to be Considered for Selection of Material

The art of material selection lies in designing an economic system with maximum

reliability in operation.

Factors to be Considered for Selection of Material

• Mechanical strength at design conditions

– UTS

– Yield

– Impact

– Creep Rupture

– Fatigue

• Operating conditions and environment

– Corrosive/Non corrosive

– Cryogenic/Low Temp./Moderate Temp/High Temp.

– Steady load/Cyclic or fluctuating load

• Fabricability

• Cost

• Availability in market

Commonly used materials

ASME MATERIALS CODE

Theory of pressure vessels design

Lecture 4

Design of Shell and Head for Internal Pressure