Code: ASME VIII-1Year: 2007 Cust: Pressure Vessel Engineering

Addenda: 2009 Desc: Sample Vessel 4MAWP: 150 psi Dwg: Sample 4

MEAWP: 0 psi ID: Sample 4Max. Temp.: 120 F

MDMT: -20 FMDMT Press.: 150 psi

Min. Thk. (UG-16b): 0.09375 inCorrosion Allowance: 0.125 in

Hydrotest: 195 psiImpact Testing: No

Impact Exemption: UG-20(f)Radiography: None

Internal Press.: YesExternal Press.: NoVessel Weight: Yes

Weight of Attachments: NoAttachment of Internals: No

Attachment of Externals: YesCyclic or Dynamic Reactions: No

Wind Loading: NoSeismic Loading: Yes

Fluid Impact Shock Reactions: NoTemperature Gradients: No PVEcalc-Sample 4 Calulations

Differential Thermal Expansion: No Author: Brian MunnAbnormal Pressures: No Reviewer: Laurence Brundrett

Hydrotest Loads: No

www.pveng.cominfo@pveng.com

Phone 519-880-9808

Pressure Vessel Engineering Ltd.120 Randall Drive, Suite B

Waterloo, Ontario, Canada, N2V 1C6

Pressure Vessel Engineering Ltd.ASME Calculations - CRN Assistance - Vessel Design - Finite Element Analysis

Design ConditionsASME Section VIII-1 Calculations

UG-22 Loadings Considered

Conclusion: The sample vessel has been calculated to ASME Section VIII-1 and found acceptable.

Table of Contents 15-Apr-10 Page 2 of 21

Contents PageCover 1Table of Contents 2Material Properties 3Rolled Plate Shell 4F&D Heads 5N1 - 4" Sch. 160 6N2 - 4" Sch. 160 on Head 7N1 & N2 - Flange 8N3 - 1" NPT 6000# H.Cplg 9N4 & N5 - 4" Process Conn. 10N4 & N5 Flange 11 - 12M1 - 12"x16" MWY on Head 13 - 14M2 - 12"x16" MWY on Shell 15Vessel Weight & Volume 16Lifting Lugs 17Seismic - Vessel on Beams 18

Rev Date By1 06/03/02 LB2 12/18/08 ART3 4/08/10 BEMRevised

Revision(s)Description

ReleaseRevised

1 Material Properties ver 2.01 www.pveng.com 15-Apr-10 Page 3 of 212

3

1 Pipe and Shell ver 4.08 Page 4 of 212 Description3 Options:4 Interior ip? - Calculate interior pressure5 No Exterior ep? - Calculate exterior pressure6 Rolled Plate pr? - Pipe or rolled plate7 Non-Threaded pt? - Type of pipe8 No relief? - Stress Relief Calculations Required

9 Dimensions:10 60.000 Do [in] - outside diameter11 0.5000 t [in] - nominal wall thickness12 0.094 tminUG16b [in] - minimum wall per UG-16(b)13 120.000 L [in] - length for volume and weight14 0.125 Corr [in] - corrosion allowance

15 Material and Conditions:16 SA-516 70 Material17 20,000 S [psi] - allowable stress level18 0.70 El - longitudinal efficiency (circ. stress)19 0.70 Ec - circ. connecting efficiency (longitudinal stress)20 0.000% UTP [%] - undertolerance allowance21 0.000 UTI [in] - undertolerance allowance22 155.20 P [psi] - interior pressure

23 Stress Classification:24 NOTE: Both validity checks need to be "Acceptable" in order to use this sheet25 If not, refer to sheet "Thick Cylindrical Shell"26 ckValidity1 = tmin < 0.5*(Do/2) 0.331 < 0.5*(60/2) = Acceptable27 ckValidity2 = P< 0.385*S*El 155.2< 0.385*20000*0.7 = Acceptable

28 Variables:29 Td = 0.000 0 = 0.00030 UT [in] = t*UTP+UTI 0.5*0+0 = 0.00031 nt [in] = t-Corr-UT-Td 0.5-0.125-0-0 = 0.37532 Ri [in] = Do/2-nt 60/2-0.375 = 29.62533 Volume [cuft] = ((Do/2-t)^2)*p*L/1728 ((60/2-0.5)^2)*3.1416*120/1728 = 189.859

34Weight [lb] = (Do-t)*p*L*t*40.84/144

(60-0.5)*3.1416*120*0.5*40.84/144 = 3180.8435 Interior Pressure: VIII-1 UG-27(c)(1,2)36 ta [in] = P*Ri/(S*El-0.6*P) 155.2*29.625/(20000*0.7-0.6*155.2) = 0.33137 tb [in] = P*Ri/(2*S*Ec+0.4*P) 155.2*29.625/(2*20000*0.7+0.4*155.2) = 0.16438 tmin [in] = MAX(ta,tb,tminUG16b) MAX(0.331,0.164,0.094) = 0.33139 tr1 [in] = P*Ri/(S*1-0.6*P) 155.2*29.625/(20000*1-0.6*155.2) = 0.23140 Checkt = tmin = 155.2 = Acceptable

Rolled Plate Shell

(S*El*nt)/(Ri+0.6*nt)

t

Do

Leng

th

Long

Sea

m

39 Heads ver 4.15 Torispherical www.pveng.com 15-Apr-10 Page 5 of 2140 NO Appendix 1-4(f)22

30 Nozzle Reinforcement ver 3.90 UW16(c)

30 Nozzle Reinforcement ver 3.90 UW16(c)

18 B16.5/16.47 Flange Ver 2.61 SlipOn 15-Apr-10 Page 8 of 2119 #VALUE!20

21

15 Coupling ver 2.11 UW16.1Z1M 15-Apr-10 Page 9 of 2116 www.pveng.com22

30 Nozzle Reinforcement ver 3.90 UG40(a-2)

1 Flange ver 4.27 Page 11 of 212 ASME VIII Div I Appendix 23 Description4 Dimensions:5 Fig2-13.2modified fd? - Select a flange design6 9.000 A [in] - flange OD7 4.500 Bn [in] - ID, uncorroded8 1.500 t [in] - flange thickness9 0.500 tn [in] - nozzle wall thickness

10 Gasket:11 5.500 GOD [in] - gasket OD12 4.500 GID [in] - gasket ID13 3.00 m - gasket factor14 1,800 gy - gasket factor y

15 Bolting:16 7.500 varC [in] - bolt circle dia17 0.625 BoltOD [in] - bolt size18 8.0 Nbolt - number of bolts19 1.000 DepthT [in] - thread depth20 0.500 Leg1 [in]

21 Operating Conditions:22 0.125 Corr [in] - corrosion allowance23 155.2 P [psi] - internal operating pressure

24 Material Properties:25 NonCast CastMaterial? - Cast Or NonCast26 20,000 Sf [psi] - allowable flange stress at DESIGN temp.27 20,000 Sfa [psi] - Allowable Flange Stress at ASSEMBLY temp.28 27,900,000 Efo [psi] -Operating Flange Modulus29 27,900,000 Efs [psi] - Seating Flange Modulus30 20,000 Sb [psi] - allowable bolt stress at DESIGN temp31 20,000 Sba [psi] - allowable bolt stress at ASSEMBLY temp

32 Geometry Constraints:33 tmin = min(0.75,tn,t) MIN(0.75,0.5,1.5) = 0.50034 tc = max(0.25,0.7*tmin) MAX(0.25,0.7*0.5) = 0.35035 ThroatLeg1 = 0.7*Leg1 0.7*0.5 = 0.35036 ChTL1 = ThroatLeg1 >= tc 0.35 >= 0.35 = Acceptable37 Calculated Dimensions:38 B = Bn+2*Corr 4.5+2*0.125 = 4.75039 varN = (GOD-GID)/2 ~~ Gasket width in contact (5.5-4.5)/2 = 0.50040 b0 = varN / 2 ~~ Gasket seating width 0.5 / 2 = 0.25041 varb =42 0.25043 varG =44 5.00045 ThreadMin =46 0.75047 CheckTrdMin = ThreadMin

Flange ver 4.27 Page 12 of 21

1 Wm1 = H + HP ~~ bolt load 3046 + 3655 = 6,7012 Wm2 = pi()*varb*varG*gy ~~ seating load PI()*0.25*5*1800 = 7,0693 Am =4 0.3535 RootArea [sq. in] = PVELookup("BoltSizing","Lookup","Root Area",BoltOD) 0.2086 Ab = RootArea*Nbolt 0.208*8 = 1.6647 CheckExcess = Ab>=Am 1.664>=0.353 = Acceptable8 Flange Loads: (App 2-5)9 W [lb] = (Am + Ab)*Sba/2 ~~ seating conditions (0.353 + 1.664)*20000/2 = 20,17410 HG [lb] = Wm1 - H ~~ operating conditions 6701 - 3046 = 3,65511 TBoltLoad [lb] = (W+Wm1)/Nbolt (20174+6701)/8 = 3,35912 Flange Moment Arms: (Table App 2-6 - loose flanges)13 mhD [in] = (varC-A)/2 (7.5-9)/2 = -0.75014 mhT [in] = (varC-(A+varG)/2)/2 (7.5-(9+5)/2)/2 = 0.25015 mhG [in] = (varC-varG)/2 (7.5-5)/2 = 1.25016 Flange Moments: (App 2-6)17 MD [in-lb] = HD * mhD ~~ end pressure 9873 * -0.75 = -7,40518 MT [in-lb] = HT * mhT ~~ face pressure -6827 * 0.25 = -1,70719 MG [in-lb] = HG * mhG ~~ gasket load 3655 * 1.25 = 4,56920 Mo1 [in-lb] = MD+MT+MG ~~ total operating -7405+-1707+4569 = -4,54321 Mo2 [in-lb] = W*(varC-varG)/2 ~~ total seating 20174*(7.5-5)/2 = 25,21822 Graph: App 2-7.1 Value of Y23 K = A/B 9/4.75 = 1.89524 Y = PVELookup("Y","FlangeFactorK",K) 3.20525 Flange Seating Stress: (App 2-7,8)26 STs = Y*ABS(Mo2) / (t^2*B) 3.205*ABS(25218) / (1.5^2*4.75) = 7,56327 CheckSTs = ABS(STs)

30 Nozzle Reinforcement ver 3.90 UW16(h)

175 Sample 4 M1 - 12" x 16" Manway on Head c/w 3" x 3/4" Ring 15-Apr-10 Page 14 of 21207 Area Replacement: Fig UG-37.1 Pressure From: Internal External208 A = 1.0*d*tr*F + 2*tn*tr*F*(1-fr1) A Required (internal) = 6.690209 = 1.0*16*0.413*1 + 2*0.75*0.413*1*(1-0.855)212 Ae = 0.5*(d*trE*1 + 2*tn*trE*1*(1-fr1)) = 0.5*(16*0*1 + 2*0.75*0*1*(1-0.855)) A Required (external) = 0.000215 A1 = max(d, 2*(t+tn)) * (E1*t-F*tr)-2*tn*(E1*t-F*tr)*(1-fr1) A1 = 2.170216 = 219 A1e = max(d, 2*(t+tn)) * (E1*t-F*trE)-2*tn*(E1*t-F*trE)*(1-fr1) A1e = 8.680220 = 223 A2 = min((tn-trnR)*fr2*min(5*t,2*L) , (tn-trnR)*(Min(2.5*tn+te,L)*fr2*2) A2 = 1.592224 = 228 A2e = min((tn-trnE)*fr2*Min(5*t,2*L) , 2*(tn-trnE)*Min(2.5*tn+te,L)*fr2) A2e = 1.763229 = 233 A3 = Min(5*t*ti*fr2, 5*ti*ti*fr2, 2*h*ti*fr2) A3 = 0.802 0.802234 = Min(5*0.55*0.75*0.855, 5*0.75*0.75*0.855, 2*0.625*0.75*0.855)236 A5 = (Dp - d - 2tn)te*fr4 =(21.5 - 16 - 2*0.75)*0.5*1 A5 = 2.000 2.000241 A41 = Leg41^2*fr3 A41 = 0.5^2*0.855 A41 = 0.214 0.214244 A42 = Leg42^2*fr4 A42 = 0.375^2*1 A42 = 0.141 0.141247 A43 = (Leg43-nca)^2*fr2 = (0.375-0)^2*0.855 A43 = 0.120 0.120249 Actual Area = 7.038 13.720250 Acceptable Actual-Required = 0.348 13.720256 Internal Weld Load: (UG-41)257 WmaxI = (A - A1 + 2*Tn*Fr1*(E1*t-F*tr))*Sv, min0 = (6.69 - 2.17 + 2*0.75*0.855*(1*0.55-1*0.413))*20000 WmaxI = 93,927260

261 W1-1 = MIN((A2 + A5 + A41 + A42)*Sv,WmaxI) = MIN((1.592 + 2 + 0.214 + 0.141)*20000,93927) W1-1 = 78,923262 W2-2 = Min((A2 + A3 + A41 + A43 + 2*Tn*t*frone)*Sv,WmaxI) = Min((1.592 + 0.802 + 0.214 + 0.12 + 2*0.75*0.55*0.855)*20000,93927)W2-2 = 68,654266 W3-3 = Min((A2 + A3 + A5 + A41 + A42 + A43 + 2*Tn*t*fr1)*Sv,WmaxI) Weld load W3-3 = 93,927267 = Min((1.592 + 0.802 + 2 + 0.214 + 0.141 + 0.12 + 2*0.75*0.55*0.855)*20000,93927)271

272 External Weld Load: (UG-41)273 WmaxE = (Ae - A1e + 2*Tn*Fr1*(E1*t-F*tr))*Sv, min0 = (0 - 8.68 + 2*0.75*0.855*(1*0.55-1*0.413))*20000 WmaxE = 0276

277 W1-1 = MIN((A2e + A5 + A41 + A42)*Sv,WmaxE) Weld load W1-1e = 0278 = MIN((1.763 + 2 + 0.214 + 0.141)*20000,0)279 W2-2 = Min((A2e + A3 + A41 + A43 + 2*Tn*t*frone)*Sv,WmaxE) = Min((1.763 + 0.802 + 0.214 + 0.12 + 2*0.75*0.55*0.855)*20000,0)W2-2e = 0283 W3-3 = Min((A2e + A3 + A5 + A41 + A42 + A43 + 2*Tn*t*fr1)*Sv,WmaxE) Weld load W3-3e = 0284 = Min((1.763 + 0.802 + 2 + 0.214 + 0.141 + 0.12 + 2*0.75*0.55*0.855)*20000,0)288

294 Component Strength (UG-45(c), UW-15(c))295 A2 shear = PI()/2*(Do-tn)*tn*Sn*0.7 A2s = 236,206296 g tension = PI()/2*Do*LegG*Min(Sv,Sn)*0.74 gt = 234,795297 A41 shear = PI()/2*Do*Leg41*Min(Sn,Sp)*0.49 A41s = 115,165301 A42 shear = PI()/2*DP*Leg42*Min(Sv,Sp)*0.49 A42s = 124,113308

309 Failure mode along strength path (Greater than Weld Load, see App L-7) 312 S1-1 = A42s + A2s >= W1-1 Acceptable S1-1 = 360,318313 = 124113 + 236206 >= 78923320 S2-2 = A41s + gt >= W2-2 Acceptable S2-2 = 349,960321 = 115165 + 234795 >= 68654326 S3-3 = gt + A42s >= W3-3 Acceptable S3-3 = 358,908327 = 234795 + 124113 >= 93927331 Tstd = Standard pipe wall thickness from chart Tstd = 0.375332 Swre = tr * Pa / P = 0.413 * 0 / 155.197 Req. Exterior pressure Swre = 0.000333 Nact = Nt * (1-UTp) = 0.75 * (1-0) Actual Wall Thick. Nact = 0.750334 Tt = 0.8/Nth = 0.8/0 Ug-31(c)(2) threads Tt = 0.000335 UG-45 Acceptable336 UG45 = Max(UG45a, UG45b)

30 Nozzle Reinforcement ver 3.90 UW16(c)mod

1 Vessel Weight and Volume ver 4.03 Page 16 of 212 Description3 Volume:4 2 nhead - Number of heads?5 1.00 SG - Fluid Specific Gravity6 12.00 VE [ft3] - Volume of Each Head7 190.00 VS [ft3] - Volume of Shell

8 Construction:9 789 Wh [lb] - Weight of Each Head10 3181 Ws [lb] - Weight of Shell11 650 Wm [lb] - Misc Weight

12 Calculations:13 V [ft3] = VE*nhead + VS total volume 12*2 + 190 = 214.0014 V2 [Imp. Gallons] = V*6.229 214*6.229 = 1,333.0115 V3 [US Gallons] = V*7.4805 214*7.4805 = 1,600.8316 Wf [lb] = 62.37*SG*V fluid weight 62.37*1*214 = 13,347.1817 WC [lb] = Wh*nhead + Ws + Wm construction weight 789*2 + 3181 + 650 = 5,409.8318 WT [lb] = WC + Wf total weight 5409.83 + 13347.18 = 18,757.01

Sample 4

1 Lifting Lugs ver 4.01 Page 17 of 212 Description3 Dimensions:4 5,410 Load [lb] - vessel weight empty5 8.000 W [in] - width6 0.500 Thick [in] - lug thickness7 2.500 H [in] - hole height8 1.500 Dia [in] - hole diameter9 2.500 OR [in] - outside radius10 0.250 Weld [in] - leg size

11 SA-516 70 Material12 20,000 SA [psi] - allowed stress in tension13 All of load assumed carried by one lug14 All load cases analyzed independently15 Never load lug perpendicular to face16 Contour lug to fit vessel17 Do not move or support vessel with this lug when full or pressurized18 SB = UG-34(b) Max Bending Stress, SS = IID Tbl 1A(d) Max Shear Stress, SSw = UW-15(c) UW-15 Max Weld Shear

19 SB [psi] = SA * 1.5 20000 * 1.5 = 30,00020 SS [psi] = SA * 0.8 20000 * 0.8 = 16,00021 SSw [psi] = SA * 0.49 20000 * 0.49 = 9,80022 Tensile Stress (case 1):23 A1 [in2] = Thick*(OR-Dia/2) 0.5*(2.5-1.5/2) = 0.87524 A [in2] = A1 * 2 0.875 * 2 = 1.75025 Stress [psi] = Load / A 5410 / 1.75 = 3,09126 CheckTenStr = Stress

15 Vessel On Beams Ver 2.24 15-Apr-10 Page 18 of 2116

17

115 Sample 4 Vessel On Beams 15-Apr-10 Page 19 of 21117 Horizontal Seismic Force at Top of Vessel118 Ftmax = 0.25*V = 0.25 * 1623 Ftmax = 406119 Ftp = 0.07 * T * V = 0.07 * 0.02 * 1623 Ftp = 2.25120 Ft = if (T < 0.7, 0, min(0.07*T*V, Ftmax)) Ft = 0121

122 Horizontal Seismic Force at cg123 Fh = V - Ft = 1623 - 0 Fh = 1,623124

125 Vertical force at cg126 Fv = W Fv = 5,410127

128 Overturning Moment at Base129 Mb = L*Fh + H*Ft = 90 * 1623 + 162.5 * 0 Mb = 146,065130

131 Overturning Moment at Bottom Tangent Line132 Mt = (L-ls)*Fh + (H-ls)*Ft = (90 - 27) * 1623 + (162.5 - 27) * 0 Mt = 102,246133

134 Maximum eccentric load135 f1 = Fv/n + 4*Mto/(n*Do) = 5409.82819109538/4 + 4*102246/(4 * 60) f1 = 3,057136

137 Axial Load138 f2 = Fv/n + 4*Mb/(n*ds) = 5409.82819109538/4 + 4*146065/(4 * 60.5) f2 = 3,767139

140 Leg Loads141 f3x = 0.5*V*Ix/(Ix+Iy) =0.5* 1623*29.1 /( 29.1+9.32) f3x = 615142 f3y = 0.5*V*Iy/(Ix+Iy) =0.5* 1623*9.32 /( 29.1+9.32) f3y = 197143

144 Leg Bending Moments145 e = (ds-Do)/2 =(60.5-60)/2 e = 0.25146 Mx = f1*e + f3x*ls =3057*0.25 + 615*27 Mx = 17,359147 My = f1*e + f3y*ls =3057*0.25 + 197*27 My = 6,079148

149 Leg Bending Stress150 Sbmax = Sb * 1.25 =17100 * 1.25 Sbmax = 21,375151 fx = Mx*cx/Ix =17359 * 3 / 29.1 Acceptable fx = 1,790152 fy = My*cy/Iy =6079 * 3 / 9.32 Acceptable fy = 1,957153

154 Leg axial stress155 K1*ls/fFactor = =0.8 * 27 / 1.46 K1*ls/fFactor = 14.795156 Fa max = AISC code lookup based on K1*ls/r Fa max = 25,675157 fa = f2/A =3767 / 4.43 Acceptable fa = 850158

159 Maximum Euler Stress160 Fe = 12*pi^2*E/(23*(K1*L/r)^2)161 = 12*pi^2*30000000/(23*14.795^2) Fe = 705,785162

163 Combined Stress164 Fc1 = fa/Famax + 0.85*fx/((1-fa/Fe)*Sbmax) Acceptable165 = 850/25675 + 0.85*1790/((1-850/705785)*21375) Fc1 = 0.10166 Fc2 = fa/Famax + 0.85*fy/((1-fa/Fe)*Sbmax) Acceptable167 = 850/25675 + 0.85*1957/((1-850/705785)*21375) Fc2 = 0.11168

171 Sample 4 Vessel On Beams 15-Apr-10 Page 20 of 21172

173 Beam to Shell Attachment Stresses174

175 Beam Dimensions176 cx = 2cx/2 cx = 3.000177 cy = 2cy/2 cy = 3.000178

179180

181 C dimensions for weld stress182 weld area = ws*lw wa = 4.500183 wcx = lw/2 wcx = 9.000184 wcz = cy + ws wcz = 3.250185 wcy = sqrt(wcx^2 + wcy^2) = sqrt(9^2 + 9.569^2) wcy = 9.569186

187 Shear Force Distribution188 Vx = (V*Ix)/((n/2)*(Ix+Iy)) = (1622.948*29.1)/((4/2)*(29.1+9.32)) Vx = 615189 Vy = (V*Iy)/((n/2)*(Ix+Iy)) = (1622.948*9.32)/((4/2)*(29.1+9.32)) Vy = 197190 Vg = W/n gravity = 5409.828/4 Vg = 1,352191

192 Weld Moments of Inertias193 Iwx = (ws*lw^3/12)*2 = (0.25*18^3/12)*2 Iwx = 243.0194 Iwz = (lw*ws^3/12 + wa*(cy+ws/2)^2)*2 Iwz = 87.9195 = (18*0.25^3/12 + 4.5*(3+0.25/2)^2)*2196 Iwy = Iwx + Iwz = 243 + 88 Iwy = 330.9197

198 Weld Moments199 Mx = Vx*(ls+lw/2) + Vg*(ds-Do)/2 Mx = 22,465200 = 615*(27+18/2) + 1352.457*(60.5-60)/2201 My1 = Vy*(ls+lw/2) = 197*(27+18/2) My1 = 7,087202 Mz = Vy*(ds-Do)/2 = 197*(60.5-60)/2 Mz = 49203

204 Weld Stresses205 Sx = Mx*wcx/Iwx Bending = 17359*9/243 Sx = 643206 Sy = My1*wcy/Iwy Twisting = 7087*9.569/330.9 Sy = 205207 Sz = Mz*wcz/Iwz Torision = 49*3.25/87.9 Sz = 2208 Sg = Vg/(wa*2) Gravity = 1352/(4.5*2) Sg = 150209

210 Stress Limits and Ratios211 Slim = min(Sb,Sa)*0.49 = min(17100,20000)*0.49 Slim = 8,379212

213 SxR = Sx/Slim = 643/8379 SxR = 0.077214 SyR = Sy/Slim = 205/8379 SyR = 0.024215 SzR = Sz/Slim = 2/8379 SzR = 0.000216 SgR = Sg/Slim = 150/8379 SgR = 0.018217 Acceptable total (

231 15-Apr-10 Page 21 of 21

232 WRC 107 - shell local stress at support233

234 Loads (psi and lb)235 614.6