DESIGN PROCEDURE FOR PRESSURE VESSEL

DESIGN PROCEDURE FOR PRESSURE VESSEL

TABLE OF CONTENTS

S NO TITLE

PAGE NO 1 INTRODUCTION TO PRESSURE VESSELS 4

1.1 BASIC TERMINOLOGIES USED 5

1.2 CYLINDERS AND SPHERS 19

2 ANALYTICAL DESIGN OF METHANATOR 26

2.1 GIVEN DATA 28

2.2 REQUIRED DIMENTIONS OF METHANATOR 29

2.3 METHANATOR AS A THIN CYLINDER 30

2.4 THICKNESS OF SHELL 32

2.5 THICKNESS OF 2:1 ELLIPSOIDAL HEAD 34

2.6 OPENING IN THE PRESSURE VESSELS 35

2.7 SELECTION OF FLANGES 37

2.8 THICKNESS OF SKIRT OR DESIGN OF SUPPORTS 39

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2.9 LOADINGS 44

2.10 STRESSES IN RESPONSE TO DIFFERENT LOADS 45

a) INTERNAL PRESSURE

45 b) WEIGHT

46 c) WIND LOAD

49 d) SEISMIC LOAD

54 2.11 COMBINATION OF STRESSES 57

2.12 COMPARISION 58

2.13 DESIGN OF ANCHOR BOLTS 58

2.14 WELDING OF PRESSURE VESSELS 62

3 ANALYSIS BY ANSYS

67 3.1 ANSYS 68

3.2 ANSYS INPUT METHODS 69

3.3 SHELL 51 70

3.4 ANALYSIS OF METHANATOR UNDER INTERNAL PRESSURE USING SHELL 51 71

3.5 ANALYSIS OF METHANATOR TO COMMAND WINDOW 72

3.6 ANALYSIS OF METHANATOR THROUGH GUI 72

3.7 TO FIND THE HOOP AND LONGITUDINAL STRESS ON ANSYS 88

3.8 DISPLACEMENTS OF NODES 91

4.1 MEMBRENE STRESSE IN METHANATOR 93

4.2 COMARISION OF ANSYS AND ANALYTICAL SOLUTION 94

4.3 CONCLUSION 96

REFERENCES -TABLES

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TO PRESSUREVESSE LS

A metal container generally cylindrical or spheroid, capable or

withstanding various loadings

STRESSES IN PRESSURE VESSEL:

 Longitudinal S1 stress

S1 and S2 called membrane (diaphragm) stress

For vessel having a figure of revolution

Bending stress

Shear stress

Discontinuity stress at an abrupt change in thickness or

Shape of the vessel

The requirements for determining the test pressure based on

calculations are out lined in UG-99(c) for the hydrostatic test and UG-100(b)for the pneumatic test The basis for calculated test pressure in either of these paragraphs is the highest permissible internal pressure as determined

by the design formulas, for each element of the vessel using nominal

THERMAL STRESS:

A self-balancing stress produced by a non uniform distribution oftemperature or by differing thermal coefficients of expansion Thermal stressdeveloped in a solid body whenever a volume of material is prevented fromassuming the size and shape that it normally should under a change intemperature

THICKNESS OF VESSEL WALL:

1 The “required thickness” is that computed by the formulas in this division, before corrosion allowance is added

2 The “design thickness” is the sum of the required thickness and the corrosion allowance

3 The “nominal thickness” is the thickness selected as commercially available, and as supplied to the manufacturer; it may exceed the design thickness

UNIT STRAIN:

Unit tensile strain is the elongation per unit length; unit compressive strain is the shortening per unit length; unit shear strain is the change in angle (radians) between two lines originally at right angles to each other

The metal joining process in making welds

In the construction of vessels the welding process is restricted by the code (UW-27) as follows;

1 Shielded metal arc, submerged arc, gas metal arc, gas tungsten arc, atomic hydrogen metal arc, oxy fuel gas welding, electro-slag, and electron beam

2 Pressure welding process: flash, induction, resistance, pressure

Thermit, and pressure gas

YIELD POINT:

The lowest stress at which strain increases without increase in stress For some purpose it is important to distinguish between the upper yield point, which is the stress at which stress-stain curve first become horizontal, and the lower yield point, which is the somewhat lower and almost constant stress under which the metal continues to deform Only a few materials exhibit a true yield point; for some materials the term is sometimes used as synonymous with yield strength

SPECIFIC GRAVITY:

The ratio of the density of a material to the density of some standard

Or (for gases) air at standard conditions of pressure and temperature

STABILITY OF VESSEL:

(Elastic stability) The strength of the vessel to resist buckling or

wrinkling due to axial compressive stress The stability of a vessel is

severely affected by out of roundness

RESIDUAL STRESS:

Stress remaining in a structure or member as a result of thermal or mechanical treatment, or both

RESISTANCE WELDING:

A pressure welding process wherein the heat is produced by the

resistance to the flow of an electric current

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SECONDARY STRESS:

A normal stress or a shear stress developed by the constraint of

adjacent parts or by self-constraint of a structure The basic characteristic of

a secondary stress is that it is self-limiting Local yielding and minor

distortions can satisfy the conditions which cause the stress to occur and failure from one application of the stress is not to be expected Examples of secondary stress are: general thermal stress; bending stress at a gross

POSTWELD HEAT TREATMENT:

Heating a vessel to a sufficient temperature to relieve the residual stresses which are the result of mechanical treatment and welding

Pressure vessels and parts shall be post weld heat treated

PREHEATING:

Heat applied to base metal prior to welding operations

is not classified as primary stress Primary membrane stress is divided into local and general categories A general primary membrane stress is one which is so disturbed in the structure no redistribution of load occurs as a result of yielding Examples of primary stress are: general membrane in a circular cylindrical or a spherical shell due to internal pressure or to

distributed live load; bending stress in the central portion of a flat head due

to pressure

OPERATING PRESSURE:

The pressure at the top of a vessel at which it normally operates It shall not exceed the maximum allowable working pressure and it is usually kept at a suitable level below the setting of the pressure relieving devices to prevent their frequent opening (Code UA-60)

OPERATING TEMPERATURE:

The temperature that will be maintained in the metal of the part of the vessel being considered for the specified operation of the vessel (Code UA-60)

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NEUTRAL AXIS:

The line of zero fiber stress in any given section of a member subject

to bending; it is the line formed by the intersection of the neutral surface andthe section

MOMENT OF INERTIA OF AN AREA (SECOND MOMENT OF AN AREA)

The moment of inertia of an area with respect to an axis is the sum of the products obtained by multiplying each element of the area by the square

of its distance from the axis The moment of inertia (I) for thin walled

such as wood, it is necessary to distinguish moduli of elasticity in different directions.

MODULUS OF RIGIDITY:

The rate of change of unit shear stress with respect to unit shear strain,for the condition of pure shear within the proportional limit

MAXIMUM ALLOWABLE STRESS VALUE:

The maximum unit stress permissible for any specific material that may be used in the design formulas given in the code (UG-23)

MAXIMUM ALLOWABLE WORKING PRESSURE:

The maximum gage pressure permissible at the top of a completed vessel in its operating position for a designed temperature This pressure is based on the weakest element of the vessel using nominal thickness

exclusives of allowances for corrosion and thickness required for loading other than pressure (Code UA-60)

MEMBRANE STRESS:

The component of normal stress which is uniform ally distributed and equal to the average value of stress across the thickness of the section under consideration

ISOTROPIC:

Having same properties in all directions In discussion pertaining to strength of materials, isotropic usually means having the same strength and elastic properties

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LOW-ALLOY STEEL:

A harden able carbon steel generally containing not more than about 1% carbon and one or more of the following components; ‹ (less than) 2% manganese, ‹ 4%nickel, ‹ 2%chromium, 0.6% molybdenum, and

‹ 0.2%vanadium

HEAT TREATMENT:

Heat treating operation performed either to produce changes in

mechanical properties of the material or to restore its maximum corrosion

resistance There are three principle types of heat treatment; annealing,

normalizing, and post weld heat treatment

pressure to be marked on the vessel or 1 ½ the design pressure by

agreement between the user and the manufacturer (Code UG-99)

sometimes used to denote this stress at the point or points most remote from

the neutral axis, but the term stress in extreme fiber is preferable for this

purpose Also, for convenience, the longitudinal elements or filaments of

which a beam may be imagined as composed are called fibers.

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FACTOR OF SAFETY:

The ratio of the load that would cause a failure of a member or

structure, to the load that is imposed upon it in service

EFFICIENCY OF A WELDED JOINT:

The efficiency of the welded joint is expressed as a numerical quantityand is used in the design of a joint as a multiplier of the appropriate

allowable stress value (Code UA-60)

ELASTIC:

Capable of sustaining stress without permanent deformation; the term

is also used to denote conformity to the law stress-strain proportionality An elastic stress or elastic strain is a stress or strain within the elastic limit

ELASTIC LIMIT:

The least stress that will cause permanent set

DESIGN PRESSURE:

The pressure used in determining the minimum permissible thickness

or physical characteristics of the different parts of the vessel (Code UG-60)

compressive stress is usually called plastic flow or flow.

CORROSION:

Chemical erosion by motionless or moving agents Gradual

destruction of a metal or alloy due to chemical process such as oxidation or action of a chemical agent

CLAD VESSEL:

A vessel made from plate having a corrosion resistant material

integrally bonded to a base of a less resistant material (Code UA-60)

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Any of a large no of substances having metallic properties consisting

of two or more elements; with few exceptions, the components are usually metallic elements

CYLINDERS AND SPHERES:

Vessels such as steam boilers, air compressors, storage tanks,

accumulators and large pipes are subjected to internal fluid pressure which isuniformly distributed All the above mentioned vessels are classified as cylinders or spheres

The following stresses are illustrated in fig (1) and fig (2)

CIRCUMFERENTIAL OR HOOP STRESS:

The stress which acts tangent to the circumference and perpendicular

to the axis of the cylinder is called circumferential or hoop stress It is

denoted by fh.

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LONGITUDINAL STRESS:

The stress which acts normal to circumference and parallel to the axis

RADIAL STRESS:

The stress which acts in a direction perpendicular to the internal

ANALYSIS OF THIN CYLINDER:

Consider the equilibrium of half cylinder of length ‘L’ sectioned through a diameteral plane as shown in fig, (3)

Total vertical force =prL 0∫180Sinθδθ

Resisting force = stress * resisting area

= fh * 2tLFor equilibrium of cylinder

Bursting force = Resisting force

pdL = fh*2tL

LONGTUDINAL STRESS:

This force tries to burst the cylinder at the ends of cylinder and is called ‘bursting force’

Resisting force = stress * resisting area

Fl = pd/4t eq (B)Comparing (A) and (B)

Fl =1/2 fh

THIN SPHERICAL SHELL:

In case of spherical shell also, the radial stress will be neglected and the circumferential or hoop stress will be assumed to be constant

Bursting force = resisting force

P * Π /4d2 = f * dt

f = pd/4t

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CYLINDERICAL SHELL WITH HEMISPHERICAL ENDS:

thickness of the hemisphere, the internal diameter being assumed the same for both

STRESSES IN THE CYLINDERICAL PORTION:

If the shell is subjected to an internal pressure p, stresses in the

cylinder will be;

STRESSES IN THE SPHRICAL PORTION:

Єl ΄ = pd/4t2E (1 -ν)Therefore for spherical portion

Єh΄ = Єl΄

At the junction of cylindrical and spherical portion

Єh = Єh΄ Pd/4t1E (2 -ν) = pd/4t2E (1 -ν)

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ANALYTICAL DESIGN

OF METHANATOR

GIVEN DATA

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PARAMETETS:-

Working temperature = 364 °C Design temperature = 454 °C Working pressure = 380 Psi.g Design pressure = 435 Psi.g

DIMENSIONS:-Inside diameter = 102" = 2590.8 mmTangent to tangent length = 150" = 3810mmType of dished ends = 2:1 semi ellipsoidalHydrostatic test pressure = 806 Psi.gWelded joint efficiency = 100 %Corrosion allowance = 1.6 mm

UG-36 (b) (1) (2))

appendix G)

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So incase of methanator the radial stresses can be neglected And there will

be only circumferential or hoop stress & longitudinal stress in the

methanator Further the governing stress will be the greater of the two & we

base our design on it

2.4 THICKNESS OF SHELL

According to specifications in UG-27 (c) which deals with the thickness of shells under internal pressure and clause “c” with the cylindrical shells, gives formulae for the thickness based on either longitudinal joint or

circumferential joint

a) CIRCUMFERNTIAL STRESS (LONGITUDINAL JOINTS)

It means that the governing stress will be the circumferential stress (hoop stress) in the long seam For this it has to satisfythat P does not exceed 0.385SE In which case we shall use the following formulae for thickness of shell

t = PR/ (SE -0.6P)

b) LONGITUDINAL STRESS (CIRUMFERENTIAL JOINTS)

stress in the circumferential joint For this it has to satisfy that P does not exceed 1.25SE OR if the circumferential joint efficiency is less than than ½ the longitudinal joint efficiency In which case we use the formula for

t = min required thickness of shell, in

P = internal design pressure, psi

R = inside radius of shell, in

S = max Allowable stress, psi

E = joint efficiency (min)

Putting the values in the above equation for methanator

Allowable stress for the material to be used is also given (16394.966 psi)

we shall take a plate of 1 ½" for safety

2.5 THICKNESS OF 2:1 ELLIPSOIDAL HEAD

It will be found by UG-32 (d) which states

The required thickness of a dished head of semi ellipsoidal form, in which half the minor axis (inside depth of the head minus the skirt)equals one-forth of the inside diameter of the head skirt, shall be determined by

t = PD / (2SE – 0.2P)

An acceptable approximation of a 2: 1 Ellipsoidal head is one with a knuckleradius of 0.17D and a spherical radius of 0.90D

2.6 OPENINGS IN A PRESSURE VESSEL

The clause of the code concerning with the design of openings is UG-36(a) (b)

a) shape of openings

1) Openings in cylindrical or conical portions of vessels, or in formed heads, shall preferably be circular, elliptical or round opening exceeds twice the short dimensions, the reinforcement across the short dimensions shall be increased as necessary to provide against excessive distortion due to twistingmoment (The opening made by a pipe or a circular nozzle, the axis of which

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is not perpendicular to the vessel wall or head, may be considered as

elliptical opening of design purposes)

2) Openings may be of other shapes than those given in (1) above, and all corners shall be provided with a suitable radius When the openings are of such proportions that their strength cannot be computed with assurance of accuracy, or when doubt exists as to the safety of a vessel with such

openings, the part of the vessel affected shall be subjected to a proof

hydrostatic test as prescribed in UG-101

b) size of openings

1) Properly reinforced openings in cylindrical shells are not limited as to size except with the following provisions for design The rules in UG-36 through UG-43 apply to openings not exceeding the following: for vessels

60 in in diameter and less, one half vessel diameter, but not to exceed 20 in.; for vessel over 60 in in diameter, one third the vessel diameter, but not

to exceed 40 in For openings exceeding these limits, supplement rules of

1-7 shall be satisfied in addition to UG-36 through UG-43

2) Properly reinforced openings in formed heads and spherical shells are not limited in size For an opening in end closure, which is larger than one half of inside diameter of the shell, various alternatives to reinforcement may also be used

FOR METHANATOR

As there are five openings in the methanator all of them are in its heads Two of them are elliptical & three are circular.

As for methanator there is the maximum opening is of size 24" &

LENGTH OF STUD BOLTS

2.8 THICKNESS OF SKIRT OR DESIGN OF SUPPORTS

A skirt is the most frequently used and the most satisfactory support for vertical vessels It is attached by continuous welding to the head and usually the required size of this welding determines the thickness of the skirt

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D = Outside diameter of skirt, in

E = efficiency of skirt to head joint

(0.6 for butt weld, fig A, 0.45 for lap weld, fig B)

R = outside radius of skirt, in

S = stress value of the head or skirt material whichever issmaller, psi

t = required thickness of skirt, in

W = weight of tower above the skirt to head joint, in