Pressure Vessel Handout

CHAPTER 6

Pressure (Welded) Vessel Design

Pressure Vessel is a closed vessel having an internal pressure between 15 psig to 3000 psig (Perry and Green, 1997). Whereas, atmospheric and low pressure tanks are designed to operate at pressures between atmospheric to 0.5 psig, and, 0.5 to 15 psig respectively (Kohan, 1987). The American Society of Mechanical Engineers (ASME) Boiler and Pressure Vessel Code contains rules for the design, fabrication and inspection of boilers and pressure vessels. ASME Code is acceptable in most of the States in the US and all Canadian provinces. Section VIII Division I of ASME Boiler and Pressure Vessel Code deals specifically with pressure vessels. Most pressure vessels used in the process industry in the US are designed in accordance with the specification of this section.

Pressure vessels may include reflux drum, storage tanks, heat exchangers, chemical reactors, distillation columns, absorption tower, stripping columns and many more.

SHELL THICKNESS In general, the minimum wall thickness of welded metal plates subject to pressure, excluding corrosion allowances, should not be less than 2.4 mm (Peters et al., 2004). To provide for the vessel sufficient rigidity especially at low pressures, the minimum wall thickness at different cylindrical shell diameters should be (Seider, 2004).

Vessel inside diameter (ft) Minimum wall thickness (inch) Up to 4 ¼ 4-6 5/16 6-8 3/8 8-10 7/16 10-12 1/2

In practical designation, the shell is considered thin if the ratio of circumferential radius of curvature to wall thickness is greater than 10. Many pressure vessels are relatively thin, having radius of thickness ratio between 10 to 500 (Bhaduri, 1984). Shell Thickness Working Equations The needed Shell thickness of pressure vessels is a function of the ultimate tensile strength of the metal at operating temperature, operating pressure, vessel diameter and welding joint efficiency (Peters et al, 2004). In the recent American Society of Mechanical Engineers (ASME) Code (VIII-I), the working equation for the determination of shell thickness of cylinder subjected to internal pressure based on inside diameter is given as:

0.6

p

PRt C

SE P eq 6-1

PRESSURE WELDED VESSEL DESIGN 2

where tp = shell thickness required (inch) [m] P = Internal gauge pressure (psig) [kN/m2] R = Inside Radius (inch) [m] S = Allowable stress (psi) [kN/m2] E = Joint efficiency factor (Table 6-4) C = Corrosion allowance (inch) [m] Provided that

1. tp less than or equal to 2

R and

2. Pressure is less than or equal to 0.385 SE (Jawad and Farr, 1988). Alternative ASME equation based on outside diameter of a cylindrical shell is given as:

0.4

p

PRt C

SE P eq 6-2

ASME Pressure Vessel Code formula excludes corrosion, wind and earthquake allowances (Mulet, 1981) as cited by (Seider, 2004). The recommended wall thickness, tv, requirement of vertical pressure vessel or tower incorporating wind load based on wind velocity of 140 miles/hr, which is substantially sufficient to handle additional earthquake load is, tv = tp [ 0.75 + 0.22 E ( L/Di)2/Pd } eq 6-3 The above equation is applicable for 10 > ( L/Di)2/ Pd > 1.34 If the ratio is less than 1.34, then tv = tp Table 6-1. Design equations and data for pressure vessels based on the ASME Boiler and Pressure

Vessel/Code. Adapted from ASME as cited by Peters et al., 2004.

Recommended design equations for vessels Under internal pressure

Limiting conditions

For cylindrical shells

ci

1/2

J

Ji

c

J

i

CrPSE

PSErt

C0.6P-SE

Prt

For spherical shells

ci

1/3

J

Ji

cJ

i

CrP2SE

P22SErt

C0.2P-SE

Prt

J

i

SE385.0Por

2

rt

J

i

SE385.0Por

2

rt


For ellipsoidal head

cJ

a C0.2P-2SE

PDt

For torispherical (spherically dished) head

cJ

a C0.1P-SE

PL 0.885t

For hemispherical head Same as for spherical shells with ri = La

J

i

SE665.0Por

r356.0t

0.5 (minor axis) 0 = 0.25Da r = knuckle radius = 6% of inside crown radius and is not less than 3t

***Nomenclature for Table 6-1

a = 2 for thickness <0.0254 m and 3 for thickness 0.0254 m Cc = allowance for corrosion, m Da = major axis of an ellipsoidal head, before corrosion allowance is added, m EJ = efficiency of joints expressed as a fraction IDD = inside depth of dish, m La = inside radius of hemispherical head or inside crown radius of torispherical head, before corrosion allowance is added, m

n = 1.2 for D 1.55m, 1.21 for D = 1.55-2.0 m, 1.22 for D = 2.0-2.7 m, and 1.23 for D > 2.7 m OD = outside diameter, m P = maximum allowable internal pressure, kPa (gauge) r = knuckle radius, m ri = inside radius of shell, before corrosion allowance is added, m S = maximum allowable working stress, kPa

t = minimum wall thickness, m = density of metal, kg/m3

+See the latest ASME Boiler and Pressure Vessel Code for further details.

Shell Wall thickness for vacuum vessels may be calculated (Kalis, 1986) with this equation

2

0.5

2.6

0.45

em

o

c

e e

o o

TE

DP

T T

D D

eq 6-4

where Pc = Collapsing pressure (psi) Te = Thickness to withstand external pressure (inch) Do = Outside diameter (inch) Em = Material’s modulus of elasticity Te must be high enough so that Pc is five times greater than the difference between atmospheric pressure and design vacuum pressure


Mulet et al , 1981, as cited by Seider, 2004, presented an alternative equation for the calculation of cylindrical wall thickness at vacuum, tE,

tE = 1.3 ( PdL/EMDo ) 4 eq 6-5

a correction factor is added ,tEC

tEC = L ( 0.18Di-2.2 ) x 10 -5- 0.19 eq 6-6

Thus, the wall thickness of vessels at vacuum incorporating wind and earthquake loads is,

tV = tE + tEC eq 6-7

tp = wall thickness (for internal pressure) Di = inside diameter L = cylindrical shell length Pd = internal design gauge pressure

S = maximum allowable stress 2in

lb

E = fractional weld efficiency Po = operating gauge pressure tv = wall thickness of vessels or tower incorporating wind and earthquake loads tE = wall thickness of vessel or tower @ vacuum tEC = correction added to tE, , (tV = tE + tEC) To include corrosion allowance, tc, Seider (2004) recommended 1/8 inch for noncorrosive conditions. Backhurst and Harker (1973) recommended 1/8 up to 3/16 corrosion allowance for noncorrosive and ¼ for corrosive environments.

ts = tV + tc eq 6-8

where

ts = cylindrical wall thickness incorporating wind, earthquake and corrosion allowances. For Spherical Shell, ASME code as cited by Kohan (1987) provide for equation to calculate the maximum allowable internal working pressure.

p

p

t2.0R

SEtP eq 6-9

where P = internal working gauge pressure (psig) R = Inside Radius (inch)

tp = Minimum required thickness (inch) E = Lowest joint efficiency S = Max allowable stress (psi)


Material of Construction In a noncorrosive environment, carbon steel and low alloy steel are commonly used material of construction for pressure vessel at low temperature (-20 to 650oF) and high temperature (650 – 900oF) respectively. Carbon steel, SA 285 grade C has a maximum allowable stress of 13,750 psi, while a low alloy steel, SA 387B has a maximum allowable stress of 15, 00 psi (Seider, 2004). Stainless steel 304 and 316 also known materials for pressure vessel (Peters et al., 2004). Stainless steel 300 series could even be used up to 1,500oF (Perry and Green, 1997). Maximum allowable stress varies from material to material and design temperatures. Tables 6-2 and 6-3 show maximum allowable stress of different pressure vessel materials. Table 6-4 shows modulus of elasticity for carbon steel and low allow steel at different temperature (Seider, 2004). Table 6-2. Recommended stress values. Adapted from ASME as cited by Peters et. al., 2004.

Joint efficiencies

Recommended stress values

Metal Temp., ºC S, kPa

For double-welded butt joints If fully radiographed = 1.0 If spot-examined = 0.85 If not radiographed = 0.70 In general, for spot examined If electric resistance weld = 0.85 If lap-welded = 0.80 If single-butt-welded = 0.60

Carbon steel (SA-285, Gr. C) Low-alloy steel for resistance to H2 and H2S (SA-387, Gr. 12C1.1) High-tensile steel for heavy-wall vessels (SA-302, Gr.B) High-alloy steel for cladding and corrosion resistance Stainless 304 (SA-240) Stainless 316 (SA-240) Nonferrous metals Copper (SB-11) Aluminum (SB-209, 1100-0)

-29 to 343

399 454

-29 to 427 510 565 649

-29 to 399

454 510 538

-29 343 427 538

-29 345 427 538

38

204 38

204

94,500 82,700 57,200

94,500 75,800 34,500 6,900

137,900 115,800 69,000 42,750

128,900 77,200 72,400 66,900

128,900 79,300 75,800 73,100

46,200 20,700 15,900 6,900


Table 6-4. Modulus of elasticity values, EM for carbon steel and low-alloy steel as a function of temperature (Seider, 2004).

Temperature (ºF)

Psi x 106

Carbon Steel Low-alloy Steel

-20 30.2 30.2

200 29.5 29.5

400 28.3 28.6

650 26.0 27.0

700 - 26.6

800 - 25.7

900 - 24.5

Recommended Design Pressure and Temperature Design pressure used in the calculation of wall thickness should always be greater than the operating pressure. Similarly, design temperature may be equal to operating temperatue plus 50oF. The following are recommended design pressures at different operating pressure (Seider, 2004); Operating Pressure ,Po (psig) Design Pressure ,Pd (psig) 0 -5 10 10 – 1,000 P= exp{0.60608+0.91615[ln Po] + 0.0015655 [ ln Po ]2 } 1,000 + 1.1Po Welding Welding will heat the metal surrounding the welding area which could result in warping, shrinking of the welded area (Kennedy, 1982). It is for this reason that at times, stress relieving is required to release locked-up localized stresses. Stress relieving may be accomplished either by annealing or hammering. After welding, test are often employed to locate weld defects and other structural trouble inside the weld. Radiographing is often used to find these weld defects. Radiography is an inspection test where welded joints are exposed to x-ray to detect excessive porosity, defective fusion and other defects in the welding process (Kennedy, 1982). Weld efficiency, E, reflects the integrity of the welding. Carbon steel having thickness up to 1.25 inch requires only a 10% spot X-ray check where the weld efficiency is 85 %. However, for thicker walls, a 100% X-ray check is required, allowing a value of 100% efficiency (Seider, 2004). Longitudinal joints are more highly stressed than circumferential joints requires a minimum butt welding. Similarly, all vessels in lethal application shall have an all butt weld connection and fully radiographed. Also all vessels fabricated on carbon or low alloy steel requires post-heat treatment (Perry and Green, 1997). All welded joints of cryogenic tanks must be butt welded, postweld heat treated and X- ray examined (Kohan, 1987). Depending on the degree of radiograph examination used to check the integrity of the welded joint, and the type of welded joint, computation of wall


thickness of pressure vessel will have different joint efficiencies. ASME section VIII classifies radiographic examination as full radiography, spot radiography and no spot radiography. For double butt joint, the following are the corresponding efficiencies Full radiography 100% Spot radiography 85% No radiography 70 % This decrease in joint efficiency from full to no spot radiography would result to a more shell wall thickness. Hence , as a rule, when welded joint efficiency is not known, assume a no spot radiography and use 70% joint efficiency if double butt joint is to be used (Kohan, 1987). This will provide for an allowance on wall thickness, but should later be check for the appropriate type of welded joint. Table 6-5 shows different type of welded joints and corresponding efficiencies and limitations (Jawad and Farr, 1988).

Figure 5-1. Welded Joint Categories.


Table 6-5. Maximum Allowable Joint Efficiencies1 for Arc and Gas Welded Joints. Adapted from Jawad, M. H., and J. R. Farr, 1988.

Typ

e No.

Joint Description

Limitations

Joint

Category

Degree of Radiographic Examination

a b c

Full Spot None

(1)

Butt joints as attained by double-welding or by other means which will obtain the same quality of deposited weld metal on the inside and outside weld surfaces to agree with the requirements of UW-35; welds using metal backing strips which remain in place are excluded.

None

A, B, C & D

1.0

0.85

0.70

(2) Single welded butt joint with backing strip other than those included in (1)

(a) None except as shown in (b) below

A, B, C & D 0,90 0.80 0.65

(b) Circumferential butt joints with one plate offset, see UW-13(c) and Fig. UW-13.1 (k).

A, B & C 0.90 0.80 0.65

(3)

Single-welded butt joint without use of backing strip

Circumferential butt joints only. Not over 5/8in. thick and not over 24in outside diameter

A, B & C NA NA 0.60

4)

Double full fillet lap joint Double full fillet lap joint

longitudinal joints not over 3/8in. thick

A NA NA 0.55

circumferential joints not over 5/8in. thick

B & C NA NA 0.55

(5)

Single full fillet lap joints with plug welds confirming to UW-

17

Single full fillet lap joints with plug welds confirming to UW-

17

(a) Circumferential joints2 for

attachment of heads not over 24in. outside diameter to shells not over 1/2in. thick.

B

NA

NA

0.50

(b) Circumferential joint for the attachment to shells of jackets not over 5/8in. in nominal thickness where the distance from the center of the plug weld to the edge of the plate is not less than 1-1/2 times the diameter of the hole for the plug.

C

NA

NA

0.50

(6)

Single full fillet lap joints without plug welds

(a) For the attachment of heads convex to pressure to shells not over 5/8in. required thickness. only with use of fillet weld on inside of shells, or (b) For attachment of heads having pressure on either side. To shells not over 24in. inside diameter and not over 1/4in. required thickness with fillet weld on outside of head flange only.

A & B

NA

NA

0.50

1 E = 1.0 for butt joints in compression. 2 joints attaching hemispherical heads to shells are excluded .


Plate thickness increments It is noteworthy to emphasize that vessels fabricated from metal plates may be assumed to come in the following increments (Seider, 2004). Final vessel wall thickness is established by rounding off to the next increment. Metal plate thickness, inch Increments, inch 3/16 to 1/2 1/16 5/8 to 2 /8 2 ½ to 3 ¼

HESSE AND RUSHTON METHOD In chemical engineering pressure vessel course, the classical book on Process Equipment Design authored by Hesse and Rushton (1975) has been in used as the course textbook. In the succeeding paragraphs, calculation methods, conditions and data were reproduced in toto from the said textbook. Shell Thickness Shell thickness of welded pressured vessel may be calculated using the given equation (Hesse and Rushton, 1975):

CPSe

PDt p

2 eq 6-10

where tp = shell thickness (inch)

P = Max allowable working pressure (psi) D = Inside diameter (inch) S = Max allowable tensile stress (psi) (Table 6-6) e = Efficiency of welded joint (Table 6-7) C = Corrosion allowance

The above equation is applicable as long as the following conditions are met:

1. tp < 0.10D 2. tp > tmin

where

1000

100min

Dt eq 6-11


Table 6-6. Materials and Allowable Working Stresses for Unfired Pressure Vessels, Adapted from ASME-UPV Code by cited by Hesse, H.E. and J.H. Rushton, (1975) Process Equipment Design.

Specified ASME Minimum Allowable Unit Tensile Stress, Thousands psi Code Tensile at Various Temperatures, °F

Spec. Material Data Strength - 20 No. and Description Grad

e 1000 psi to

650 700 750 800 850 900 950 1000

S-2 Steel plates - flange and A 45 9.0 8.8 8.4 6.9 5.7 4.4 2.6

firebox quality B 50 10.0 9.6 9.0 7.5 6.0 4.4 2.6

S-1 Carbon steel for boilers 11.0 10.4 9.5 8.0 6.3 4.4 2.5

Carbon-silicon steel, A 55 11.0 10.4 9.5 8.5 7.2 5.6 3.8 2.0

S-42 ordinary strength range B 60 12.0 11.4 10.4 9.1 7.4 5.6 3.8 2.0

S-44 Molybdenum steel A 13.0 13.0 13.0 12.5 11.5 10.0 8.0 5.0

S-43 Low-carbon nickel steel A

S-55 Carbon-silicon steel, high 65 strength range, 4-1/2” A 13.0 12.3 11.1 9.4 7.6 5.6 3.8 2.0 plates and under

S-44 B 14.0 14.0 14.0 13.5 12.0 10.2 8.0 5.0

S-43 B 70 14.0 13.3 11.9 10.0 7.8 5.6 3.8 2.0

S-55 B 14.0 13.3 11.9 10.0 7.8 5.6 3.8 2.0

S-44 C 15.0 15.0 15.0 14.4 12.7 10.4 8.0 5.0

S-43 C 75

S-28 Chrome-manganese-silicon

A 15.0 14.1 12.4 10.1 7.8 5.6 3.8 2.0

alloy steel B 85

Design Stress Design stress, S maybe estimated using the given equation:

S = Su x Fm x Fs x Fr x Fa eq 6-12 Where Su = Minimum Specified Tensile Strength

Fm = Material Factor Fm = 1 for Grade A material

Fm = 0.97 for Grade B material Fm = 0.92 for Grade C material

Fs = Temperature Factor (Use Table 6-8) Fr = Stress Relief (SR) Factor

Fr = 1.06 When SR is applied Fa = Radiographing Factor

Fa = 1.12 when Radiographing is applied and subsequent repair of defects Note: Both Stress Relief and Radiographing factors are equal to unity when not applied on welded

joints.


Welding may induce internal strain and stress on welded joints. In this case, stress relieving such as by annealing or hammering may be employed to release localized stresses. A 6% increase in the allowable design stress is allowed in some cases. Radiographing, on the other hand, is an application of X-ray on welded joints to examine defective fusion and other defects that may affect the integrity of the pressure vessel. If subsequent repair of a detected defect is done, a 12% increase in the allowable design stress may also be allowed. Stress relieving is mandatory for: 1. tp > 1¼”

2. 120

50Dt p (For thinner plates)

where D has a minimum value of 20 inches 3. ASTM A – 150 4. ASTM A – 149 (under certain conditions)

Whereas, Radiographing is mandatory for 1. ASTM A – 150

2. ASTM A – 149 (under certain conditions) 3. Lethal gases application 4. Nuclear Reactor applications

Table 6-7. Types of Welded Joint and Corresponding Efficiencies.

EFFICIENCY CRITERIA

LAP WELD (For circumferential Joint) Single Lap Single Lap with plug weld Double Lap BUTT WELD (For circumferential and longitudinal joints) Single Butt Single Butt with Back-up Strip Double Butt Double Butt with reinforce at center

55% 65% 65%

70% 80% 80% 90%

tp < ⅝” tp < ⅝” tp > ⅝”

tp < ⅝” tp < 1¼” tp > 1¼” tp > 1¼”


Table 6-7. Temperature Factor.

Metal Temperature, Plate and Forged °F Steel, % Cast Steel, %

Up to 650 25.0 16.7

700 23.7 16.4 750 21.0 14.7 800 18.0 12.9 850 15.0 11.1 900 12.0 9.3 950 9.0 7.5

1000 6.2 5.7

Adapted from Hesse, H.E. and J.H. Rushton, Process Equipment Design (1975) Head Thickness To estimate head thickness requirement for pressure vessel with internal pressure load (concave), the following are the working equations for different head configurations. For external pressure load, thickness computed from internal pressure load is multiplied by 5/3.

Standard Ellipsoidal SE2

PDt

Hemispherical SE4

PDt

Standard Dished SE2

PLWt

where L = crown radius in inches = Do – 6 Kr = knuckle radius = 0.06 Do


Values for W or dished heads Kr/L W 0.06 1.8 0.07 1.7 0.08 1.65 0.09 1.6 0.10 1.55 0.11 1.50 0.12 1.47 0.13 1.44 0.14 1.41 0.15 1.40 0.16 1.38 0.17 1.37 0.18 1.35 0.19 1.32 0.20 1.30 0.25 1.25 0.50 1.12 1.0 1.0 For flat heads designed to permit fastening by means of lap joints with or without plug welds; the required head thickness is given by

S

P3.0dt

where t = is the head thickness d = is the inner diameter of the flanged head For flat heads which may be attached by single or double vee or V butt welds; the required head thickness is given by

S

P25.0dt

And for flat heads cut from a solid plate, the required head thickness is given by

S

P5.0dt


Problem 1. Determine the thickness of a 10 meter diameter spherical tank at 300KPa and 27F. The material of construction is made of carbon steel. Use minimum corrosion allowance.

Problem 2. A 12 in diameter S-2 Grade A steel has a working pressure and temperature of 500 psi

and 300F respectively. Determine the type of weld to be used and plate thickness using Hesse and Rushton method.

Problem 3. Grade A S2 steel, butt welded pressured vessel for lethal gas application has an inside

diameter of 20 inches. If the working pressure is 900 psi and the working temperature is 250ºF, what is the shell thickness of the vessel? (Use minimum corrosion allowance and Hesse and Rushton method).

Pressure Vessel Handout

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