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1 HATER 6 ressure (Welded) Vessel Design ressure Vessel is a closed vessel having an inernal pressure beween 15 psig o 3000 psig (erry and Green, 1997). Whereas, amospheric and low pressure anks are designed o operae a pressures beween amospheric o 0.5 psig, and, 0.5 o 15 psig respecively (Kohan, 1987). The American Sociey of Mechanical Engineers (ASME) Boiler and ressure Vessel ode conains rules for he design, fabricaion and inspecion of boilers and pressure vessels. ASME ode is accepable in mos of he Saes in he US and all anadian provinces. Secion VIII Division I of ASME Boiler and ressure Vessel ode deals specifically wih pressure vessels. Mos pressure vessels used in he process indusry in he US are designed in accordance wih he specificaion of his secion. ressure vessels may include reflux drum, sorage anks, hea exchangers, chemical reacors, disillaion columns, absorpion ower, sripping columns and many more. SHELL THIKNESS In general, he minimum wall hickness of welded meal plaes subjec o pressure, excluding corrosion allowances, should no be less han 2.4 mm (eers e al., 2004). To provide for he vessel sufficien rigidiy especially a low pressures, he minimum wall hickness a differen cylindrical shell diameers should be (Seider, 2004). Vessel inside diameer (f) Minimum wall hickness (inch) Up o 4 ¼ 4-6 5/ / / /2 In pracical designaion, he shell is considered hin if he raio of circumferenial radius of curvaure o wall hickness is greaer han 10. Many pressure vessels are relaively hin, having radius of hickness raio beween 10 o 500 (Bhaduri, 1984). Shell Thickness Working Equaions The needed Shell hickness of pressure vessels is a funcion of he ulimae ensile srengh of he meal a operaing emperaure, operaing pressure, vessel diameer and welding join efficiency (eers e al, 2004). In he recen American Sociey of Mechanical Engineers (ASME) ode (VIII-I), he working equaion for he deerminaion of shell hickness of cylinder subjeced o inernal pressure based on inside diameer is given as: p SE R 0.6 eq 6-1

2 RESSURE WELDED VESSEL DESIGN 2 where p = shell hickness required (inch) [m] = Inernal gauge pressure (psig) [kn/m 2 ] R = Inside Radius (inch) [m] S = Allowable sress (psi) [kn/m 2 ] E = oin efficiency facor (Table 6-4) = orrosion allowance (inch) [m] rovided ha 1. p less han or equal o 2 R and 2. ressure is less han or equal o SE (awad and Farr, 1988). Alernaive ASME equaion based on ouside diameer of a cylindrical shell is given as: p SE R 0.4 eq 6-2 ASME ressure Vessel ode formula excludes corrosion, wind and earhquake allowances (Mule, 1981) as cied by (Seider, 2004). The recommended wall hickness, v, requiremen of verical pressure vessel or ower incorporaing wind load based on wind velociy of 140 miles/hr, which is subsanially sufficien o handle addiional earhquake load is, v = p [ E ( L/Di) 2 / d } eq 6-3 The above equaion is applicable for 10 > ( L/Di) 2 / d > 1.34 If he raio is less han 1.34, hen v = p Table 6-1. Design equaions and daa for pressure vessels based on he ASME Boiler and ressure Vessel/ode. Adaped from ASME as cied by eers e al., Recommended design equaions for vessels Under inernal pressure Limiing condiions For cylindrical shells ri SE r i SE SE 1/2 c r i c or ri SE For spherical shells ri SE c or ri SE r i 2SE 2SE 2 1/3 r i c

3 RESSURE WELDED VESSEL DESIGN 3 For ellipsoidal head Da 2SE For orispherical (spherically dished) head c or 0.356r i 0.665SE 0.5 (minor axis) 0 = 0.25D a La SE For hemispherical head Same as for spherical shells wih r i = L a ***Nomenclaure for Table 6-1 c r = knuckle radius = 6% of inside crown radius and is no less han 3 a = 2 for hickness < m and 3 for hickness m c = allowance for corrosion, m D a = major axis of an ellipsoidal head, before corrosion allowance is added, m E = efficiency of joins expressed as a fracion IDD = inside deph of dish, m L a = inside radius of hemispherical head or inside crown radius of orispherical head, before corrosion allowance is added, m n = 1.2 for D 1.55m, 1.21 for D = m, 1.22 for D = m, and 1.23 for D > 2.7 m OD = ouside diameer, m = maximum allowable inernal pressure, ka (gauge) r = knuckle radius, m r i = inside radius of shell, before corrosion allowance is added, m S = maximum allowable working sress, ka = minimum wall hickness, m = densiy of meal, kg/m 3 + See he laes ASME Boiler and ressure Vessel ode for furher deails. Shell Wall hickness for vacuum vessels may be calculaed (Kalis, 1986) wih his equaion c Te D 2.6 o Te D o E m Te D o 0.5 eq 6-4 where c T e D o E m = ollapsing pressure (psi) = Thickness o wihsand exernal pressure (inch) = Ouside diameer (inch) = Maerial s modulus of elasiciy T e mus be high enough so ha c is five imes greaer han he difference beween amospheric pressure and design vacuum pressure

4 RESSURE WELDED VESSEL DESIGN 4 Mule e al, 1981, as cied by Seider, 2004, presened an alernaive equaion for he calculaion of cylindrical wall hickness a vacuum, E, E = 1.3 ( d L/E M D o ) 4 eq 6-5 a correcion facor is added, E E = L ( 0.18D i -2.2 ) x eq 6-6 Thus, he wall hickness of vessels a vacuum incorporaing wind and earhquake loads is, V = E + E eq 6-7 p = wall hickness (for inernal pressure) D i = inside diameer L = cylindrical shell lengh d = inernal design gauge pressure lb S = maximum allowable sress 2 in E = fracional weld efficiency o = operaing gauge pressure v = wall hickness of vessels or ower incorporaing wind and earhquake loads E = wall hickness of vessel or vacuum E = correcion added o E,, ( V = E + E ) To include corrosion allowance, c, Seider (2004) recommended 1/8 inch for noncorrosive condiions. Backhurs and Harker (1973) recommended 1/8 up o 3/16 corrosion allowance for noncorrosive and ¼ for corrosive environmens. where s = V + c eq 6-8 s = cylindrical wall hickness incorporaing wind, earhquake and corrosion allowances. For Spherical Shell, ASME code as cied by Kohan (1987) provide for equaion o calculae he maximum allowable inernal working pressure. SE p R 0.2 eq 6-9 p where = inernal working gauge pressure (psig) R = Inside Radius (inch) p = Minimum required hickness (inch) E = Lowes join efficiency S = Max allowable sress (psi)

5 RESSURE WELDED VESSEL DESIGN 5 Maerial of onsrucion In a noncorrosive environmen, carbon seel and low alloy seel are commonly used maerial of consrucion for pressure vessel a low emperaure (-20 o 650 o F) and high emperaure ( o F) respecively. arbon seel, SA 285 grade has a maximum allowable sress of 13,750 psi, while a low alloy seel, SA 387B has a maximum allowable sress of 15, 00 psi (Seider, 2004). Sainless seel 304 and 316 also known maerials for pressure vessel (eers e al., 2004). Sainless seel 300 series could even be used up o 1,500 o F (erry and Green, 1997). Maximum allowable sress varies from maerial o maerial and design emperaures. Tables 6-2 and 6-3 show maximum allowable sress of differen pressure vessel maerials. Table 6-4 shows modulus of elasiciy for carbon seel and low allow seel a differen emperaure (Seider, 2004). Table 6-2. Recommended sress values. Adaped from ASME as cied by eers e. al., Recommended sress values Meal Temp., º S, ka oin efficiencies For double-welded bu joins If fully radiographed = 1.0 If spo-examined = 0.85 If no radiographed = 0.70 arbon seel (SA-285, Gr. ) -29 o ,500 82,700 57,200 In general, for spo examined If elecric resisance weld = 0.85 If lap-welded = 0.80 If single-bu-welded = 0.60 Low-alloy seel for resisance o H 2 and H 2 S (SA-387, Gr ) -29 o ,500 75,800 34,500 6,900 High-ensile seel for heavy-wall vessels (SA-302, Gr.B) -29 o , ,800 69,000 42,750 High-alloy seel for cladding and corrosion resisance Sainless 304 (SA-240) ,900 77,200 72,400 66,900 Sainless 316 (SA-240) Nonferrous meals opper (SB-11) Aluminum (SB-209, ) ,900 79,300 75,800 73,100 46,200 20,700 15,900 6,900

6 RESSURE WELDED VESSEL DESIGN 6 Table 6-4. Modulus of elasiciy values, E M for carbon seel and low-alloy seel as a funcion of emperaure (Seider, 2004). si x 10 6 Temperaure (ºF) arbon Seel Low-alloy Seel Recommended Design ressure and Temperaure Design pressure used in he calculaion of wall hickness should always be greaer han he operaing pressure. Similarly, design emperaure may be equal o operaing emperaue plus 50 o F. The following are recommended design pressures a differen operaing pressure (Seider, 2004); Operaing ressure, o (psig) Design ressure, d (psig) ,000 = exp{ [ln o ] [ ln o ] 2 } 1, o Welding Welding will hea he meal surrounding he welding area which could resul in warping, shrinking of he welded area (Kennedy, 1982). I is for his reason ha a imes, sress relieving is required o release locked-up localized sresses. Sress relieving may be accomplished eiher by annealing or hammering. Afer welding, es are ofen employed o locae weld defecs and oher srucural rouble inside he weld. Radiographing is ofen used o find hese weld defecs. Radiography is an inspecion es where welded joins are exposed o x-ray o deec excessive porosiy, defecive fusion and oher defecs in he welding process (Kennedy, 1982). Weld efficiency, E, reflecs he inegriy of he welding. arbon seel having hickness up o 1.25 inch requires only a 10% spo X-ray check where he weld efficiency is 85 %. However, for hicker walls, a 100% X-ray check is required, allowing a value of 100% efficiency (Seider, 2004). Longiudinal joins are more highly sressed han circumferenial joins requires a minimum bu welding. Similarly, all vessels in lehal applicaion shall have an all bu weld connecion and fully radiographed. Also all vessels fabricaed on carbon or low alloy seel requires pos-hea reamen (erry and Green, 1997). All welded joins of cryogenic anks mus be bu welded, posweld hea reaed and X- ray examined (Kohan, 1987). Depending on he degree of radiograph examinaion used o check he inegriy of he welded join, and he ype of welded join, compuaion of wall

7 RESSURE WELDED VESSEL DESIGN 7 hickness of pressure vessel will have differen join efficiencies. ASME secion VIII classifies radiographic examinaion as full radiography, spo radiography and no spo radiography. For double bu join, he following are he corresponding efficiencies Full radiography 100% Spo radiography 85% No radiography 70 % This decrease in join efficiency from full o no spo radiography would resul o a more shell wall hickness. Hence, as a rule, when welded join efficiency is no known, assume a no spo radiography and use 70% join efficiency if double bu join is o be used (Kohan, 1987). This will provide for an allowance on wall hickness, bu should laer be check for he appropriae ype of welded join. Table 6-5 shows differen ype of welded joins and corresponding efficiencies and limiaions (awad and Farr, 1988). Figure 5-1. Welded oin aegories.

8 RESSURE WELDED VESSEL DESIGN 8 Table 6-5. Maximum Allowable oin Efficiencies 1 for Arc and Gas Welded oins. Adaped from awad, M. H., and. R. Farr, Degree of Radiographic Typ oin Descripion Limiaions oin Examinaion e aegory a b c No. Full Spo None (1) Bu joins as aained by double-welding or by oher means which will obain he same qualiy of deposied weld meal on he inside and ouside weld surfaces o agree wih he requiremens of UW- 35; welds using meal backing srips which remain in place are excluded. None A, B, & D (a) None excep as shown in (b) A, B, & D 0, (2) Single welded bu join wih backing srip oher han hose included in (1) below (b) ircumferenial bu joins wih one plae offse, see UW- 13(c) and Fig. UW-13.1 (k). ircumferenial bu joins (3) Single-welded bu join only. No over 5/8in. hick and wihou use of backing srip no over 24in ouside diameer Double full fille lap join longiudinal joins no over 4) Double full fille lap join 3/8in. hick circumferenial joins no over 5/8in. hick (a) ircumferenial joins 2 for aachmen of heads no over Single full fille lap joins wih 24in. ouside diameer o shells plug welds confirming o UW- no over 1/2in. hick. 17 (b) ircumferenial join for he (5) aachmen o shells of jackes no over 5/8in. in nominal Single full fille lap joins wih hickness where he disance plug welds confirming o UW- from he cener of he plug 17 weld o he edge of he plae is no less han 1-1/2 imes he diameer of he hole for he plug. (a) For he aachmen of heads convex o pressure o shells no over 5/8in. required hickness. only wih use of fille weld on (6) Single full fille lap joins inside of shells, or wihou plug welds (b) For aachmen of heads having pressure on eiher side. To shells no over 24in. inside diameer and no over 1/4in. required hickness wih fille weld on ouside of head flange only. 1 E = 1.0 for bu joins in compression. 2 joins aaching hemispherical heads o shells are excluded. A, B & A, B & NA NA 0.60 A NA NA 0.55 B & NA NA 0.55 B NA NA 0.50 NA NA 0.50 A & B NA NA 0.50

9 RESSURE WELDED VESSEL DESIGN 9 lae hickness incremens I is noeworhy o emphasize ha vessels fabricaed from meal plaes may be assumed o come in he following incremens (Seider, 2004). Final vessel wall hickness is esablished by rounding off o he nex incremen. Meal plae hickness, inch Incremens, inch 3/16 o 1/2 1/16 5/8 o 2 /8 2 ½ o 3 ¼ HESSE AND RUSHTON METHOD In chemical engineering pressure vessel course, he classical book on rocess Equipmen Design auhored by Hesse and Rushon (1975) has been in used as he course exbook. In he succeeding paragraphs, calculaion mehods, condiions and daa were reproduced in oo from he said exbook. Shell Thickness Shell hickness of welded pressured vessel may be calculaed using he given equaion (Hesse and Rushon, 1975): where D p 2Se p = shell hickness (inch) = Max allowable working pressure (psi) D = Inside diameer (inch) S = Max allowable ensile sress (psi) (Table 6-6) e = Efficiency of welded join (Table 6-7) = orrosion allowance The above equaion is applicable as long as he following condiions are me: 1. p < 0.10D 2. p > min eq 6-10 where D 100 min eq

10 RESSURE WELDED VESSEL DESIGN 10 Table 6-6. Maerials and Allowable Working Sresses for Unfired ressure Vessels, Adaped from ASME-UV ode by cied by Hesse, H.E. and.h. Rushon, (1975) rocess Equipmen Design. Specified ASME Minimum Allowable Uni Tensile Sress, Thousands psi ode Tensile a Various Temperaures, F Spec. Maerial Daa Srengh - 20 No. and Descripion Grad 1000 psi o e S-2 Seel plaes - flange and A firebox qualiy B S-1 arbon seel for boilers arbon-silicon seel, A S-42 ordinary srengh range B S-44 Molybdenum seel A S-43 Low-carbon nickel seel A S-55 arbon-silicon seel, high 65 srengh range, 4-1/2 A plaes and under S-44 B S-43 B S-55 B S S S-28 hrome-manganesesilicon A alloy seel B 85 Design Sress Design sress, S maybe esimaed using he given equaion: S = S u x F m x F s x F r x F a eq 6-12 Where S u = Minimum Specified Tensile Srengh F m = Maerial Facor F m = 1 for Grade A maerial F m = 0.97 for Grade B maerial F m = 0.92 for Grade maerial F s = Temperaure Facor (Use Table 6-8) F r = Sress Relief (SR) Facor F r = 1.06 When SR is applied F a = Radiographing Facor F a = 1.12 when Radiographing is applied and subsequen repair of defecs Noe: Boh Sress Relief and Radiographing facors are equal o uniy when no applied on welded joins.

11 RESSURE WELDED VESSEL DESIGN 11 Welding may induce inernal srain and sress on welded joins. In his case, sress relieving such as by annealing or hammering may be employed o release localized sresses. A 6% increase in he allowable design sress is allowed in some cases. Radiographing, on he oher hand, is an applicaion of X-ray on welded joins o examine defecive fusion and oher defecs ha may affec he inegriy of he pressure vessel. If subsequen repair of a deeced defec is done, a 12% increase in he allowable design sress may also be allowed. Sress relieving is mandaory for: 1. p > 1¼ D p (For hinner plaes) 120 where D has a minimum value of 20 inches 3. ASTM A ASTM A 149 (under cerain condiions) Whereas, Radiographing is mandaory for 1. ASTM A ASTM A 149 (under cerain condiions) 3. Lehal gases applicaion 4. Nuclear Reacor applicaions Table 6-7. Types of Welded oin and orresponding Efficiencies. EFFIIENY RITERIA LA WELD (For circumferenial oin) Single Lap Single Lap wih plug weld Double Lap BUTT WELD (For circumferenial and longiudinal joins) Single Bu Single Bu wih Back-up Srip Double Bu Double Bu wih reinforce a cener 55% 65% 65% 70% 80% 80% 90% p < ⅝ p < ⅝ p > ⅝ p < ⅝ p < 1¼ p > 1¼ p > 1¼

12 RESSURE WELDED VESSEL DESIGN 12 Table 6-7. Temperaure Facor. Meal Temperaure, lae and Forged F Seel, % as Seel, % Up o Adaped from Hesse, H.E. and.h. Rushon, rocess Equipmen Design (1975) Head Thickness To esimae head hickness requiremen for pressure vessel wih inernal pressure load (concave), he following are he working equaions for differen head configuraions. For exernal pressure load, hickness compued from inernal pressure load is muliplied by 5/3. Sandard Ellipsoidal D 2SE Hemispherical Sandard Dished where D 4SE LW 2SE L = crown radius in inches = D o 6 K r = knuckle radius = 0.06 D o

13 RESSURE WELDED VESSEL DESIGN 13 Values for W or dished heads Kr/L W For fla heads designed o permi fasening by means of lap joins wih or wihou plug welds; he required head hickness is given by d 0.3 S where = is he head hickness d = is he inner diameer of he flanged head For fla heads which may be aached by single or double vee or V bu welds; he required head hickness is given by d 0.25 S And for fla heads cu from a solid plae, he required head hickness is given by d 0.5 S

14 RESSURE WELDED VESSEL DESIGN 14 roblem 1. Deermine he hickness of a 10 meer diameer spherical ank a 300Ka and 27F. The maerial of consrucion is made of carbon seel. Use minimum corrosion allowance. roblem 2. A 12 in diameer S-2 Grade A seel has a working pressure and emperaure of 500 psi and 300F respecively. Deermine he ype of weld o be used and plae hickness using Hesse and Rushon mehod. roblem 3. Grade A S2 seel, bu welded pressured vessel for lehal gas applicaion has an inside diameer of 20 inches. If he working pressure is 900 psi and he working emperaure is 250ºF, wha is he shell hickness of he vessel? (Use minimum corrosion allowance and Hesse and Rushon mehod).