Pipeline Calculations - ASAB Gas Lift Lines [PDF]

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PIPELINE CALCULATIONS



Doc NO :



DES-C-1360-302-01-0



Date : REV.:



JUNE 05, 2015 A



Pipeline Calculations (Bend Radius, Buoyancy Forces, Thrust Block Calculations )



0 Rev.



First Issue DESCRIPTION



JUNE 29, 2015 MRQ / IMZ Date Prepared By



HMA SMW Checked By Approved By



INPUT PARAMETER Input Data



Unit



1



PIPE MATERIAL:



= API 5L GR X65Q



2 3



Pipe diameter Nominal pipe thk



D t



= 0.114 = 0.0050



m m



4.50 0.20



in in



4 5



Internal Dia Corrosion Allowance



d C



= 0.1043 = 1.500



m mm



4.11 0.06



in in



6 7



Design Pressure Product Specific Gravity



P



= 1.42E+07 = 0.13



pa



2060



psig



8 9



Fluid density Installation (backfill) Temp



pf



Kg/m3



Ti



= 25 = 21



o



C



1.561 70



lb/ft3 o F



10 11 12



Design Temperature Design Temp (Min. buried) FBE Thickness



Tdmax Tdmin t1



= 85 = -20 = 0



o



C C



185 -4 0.00



o



o



13 14



FBE density Adhesive Thickness



pfbe t2



= 1550 = 0



Kg/m3



96.76 0.00



lb/ft3 in



15 16



Adhesive density PP/PE Thickness



pad t3



= 900 = 0.0023



Kg/m3



56.19 0.09



lb/ft3 in



17 18



PP/PE Density Insulation Thickness of Pipe



ppp



= 960 = 0



Kg/m3



59.93 0.00



lb/ft3 in.



19 20 21 22 23



Insulation Density of Pipe Steel density Specified Minimum Yield Strength Modulus of Elasticity Yield Stress



= = = = =



Kg/m3



pa



0.00 490 65267 30022812 6.53E+04



lb/ft3 lb/ft3 psig psig psig



24 25



Poisson ratio Coefficent of Linear Thermal Expansion



Per oC



0.00000655



Per oF



26 28



Pipeline Cover depth Length of Pipe



29 30 31



Bend Angle of Pipe (for AG/UG Transition) Uplift coefficient Picode (As per K-Peter Method)



32 33



Gravity Soil density (uncompacted)



34 35



Water density Net allowable Bearing Capacity of Soil



36 37



Concrete Density Coefficent of friction between pipe & Soil



38 39



Soil density (compacted)



40 41



Calculation of Pipe Properties



ρs S E S ν



0 7850 450 2.07E+05 4.50E+08



m m m mm Kg/m3



Mpa Mpa



F F in. o



α



= 0.3 = 0.0000117



H L



= 1.0 = 7000



m m



39.37 275591



in in



DEG.



0.39



RAD.



fu



= 22.5 = 0.4 = 1.2 = 9.8 = 1575



m/sec2 Kg/m



386 98



= 1000 = 50



Kg/m3



62



KN/m2



1044.28



Kg/m



120



μ



= 1925 = 0.4



lb/ft2 lb/ft3



pbc



= 1900



Kg/m3



118.6



lb/ft3



g



pbuc pw qnet



(0.1 for uncompacted backfill & 0.5 for compacted backfill) 1 for B31.4 and 2 for B31.8 3



3



in/sec2 lb/ft3 lb/ft3



Pipe Outside Diameter Including Coating Metallic cross sectional area Pipe Section modulus Pipe flexural rigidity



OD



= D + 2 t1 + 2 t2 + 2 t3



=



0.1189



m



42 43 44



As I



= π/4 (D2-d2) = π/64 (D4-d4) = EI



= = =



0.00172 0.000003 5.32.E+05



m2 m4



45 46



Weight of Pipe Fluid cross sectional area



W Af



= =



13.478 0.009



47 48



Weight of contents FBE Weight



Wf Wfbe



= As x ρs = π/4 (D-2xt)2 = Af x ρf = π/4 [(D + 2 t1)² – D² ]ρfbe



= =



0.214 0.00000



m2 Kg/m Kg/m



49 50



Adhesive Weight PP/PE Weight



Wad Wpp



= π/4[(D + 2t1+2t2)² – (D+2t1)² ]ρad = π/4[(OD)² – (OD-2t3)² ]ρpp



= =



0.00000 0.80881



Kg/m Kg/m



51 52



Pipe Weight Including Coating Weight of pipe



Wte W



= W + Wfbe + Wad + Wpp = As x ρs x g



= =



14.286 132



Kg/m N/m



53 54



Weight of contents Total Weight + Contents



= As x ρs x g = Wte + Wf



= =



2.09 14.50



N/m Kg/m



55



Total Weight + Contents



Wf Wto Wto



= Wte + Wf



=



142



N/m



N.m2 Kg/m



K PETER'S METHOD Upheaval Buckling Calculation Introduction The aim of this calculation is to determine the allowable Bend Angle and Minimum Depth of Cover on the pipeline to prevent upheaval buckling as a result of axial compression. Input Data Pipe diameter Selected Wall Thickness Internal Dia Corrosion Allowance



D t d C



= = = =



0.114 0.0050 0.1043 1.500



Design pressure Steel density Specified Minimum Yield Strength Modulus of Elasticity Yield Stress Poisson ratio



P ρs S E S ν



= = = = = =



α T1 T2 Tdmin H fu



= = = = = =



Coefficent of Linear Thermal Expansion Installation (backfill) Temp Design Temp max buried Design Temp min buried Pipeline Cover depth Uplift coefficient Gravity



g



Soil density



pbuc



Fluid density



pf



Unit m m m mm



4.50 0.20 4.11 0.06



in in in in



1.42E+07 7.85E+03 450 2.07E+11 4.50E+08 0.300



pa Kg/m3 Mpa pa pa



2060 490 65267 30022812 65267



psig lb/ft3 psig psig psig



0.0000117 21 85 -20 1.00 0.4



Per oC o C o C o C m



0.00000655 70 185 -4



Per oF o F o F o F



= 9.8



m/sec2



386



in/sec2



= 1575.0



Kg/m3



98



lb/ft3



= 25.0



Kg/m3



2



lb/ft3



Corroded Wall Thickness



tw = (t-C)



= 0.0035



m



0.138



in



3LPP Coating Thickness



tpp



= 0.0023



m



0.091



in



3LPP Coating Density



ppp



= 960



Kg/m3



59.91



lb/ft3



Calculation of Pipe Properties & Weights Pipe Outside Diameter Including Coating Metallic cross sectional area Pipe Section modulus Pipe flexural rigidity



OD As I



= = = =



= = = =



0.1189 0.00172 0.000003 5.32.E+05



m m2 m4 N.m2



W Af Wf W Wf Wpp Wte



= = = = = =



As x ps π/4 (D-2xt)2 Af x pf As x ps x g Af x pf x g π/4[(OD)² – (OD-2tpp)² ]ρpp = W + Wpp = Wte + Wf



= = = = = =



13.478 0.009 0.214 132 2.09 7.93



Kg/m m2 Kg/m N/m N/m N/m



= =



140 142



N/m N/m



= As Eα (T2-T1) = (1-2v) P.Af = Tt + Pt



= = =



2.66.E+05 4.85.E+04 3.15.E+05



N N N



= 2 (pi) (EI/Frestr)0.5



=



= 0.9 x S



=



4.05.E+08



Pa



58740



psi



= (P x D)/2tw = α E (T2 - T1) - ν SH = Sa - SH - SL



= = = =



2.32.E+08 8.54.E+07 8.77.E+07 87.7



Pa Pa Pa Mpa



33629 12392 12719



psi psi psi



= =



7938.2 8080.3



N/m N/m



Weight of pipe Fluid cross sectional area Weight of contents Weight of pipe Weight of contents PP/PE Weight Pipe Weight including Coating Total Weight + Contents Compressive Restraining Force Thermal Expansion Forces Pressure Force Restraining Force Buckling Length Buckling Length



Wto



Tt Pt Frest



ƛ



Calculation of Stresses as per ASME B31.8 Maximum Allowable Stress Sa Tensile Hoop Stress Compressive Longitudinal Stress Allowable bending stress Allowable bending stress



SH SL σall σall



D + 2 tpp π/4 (D2-d2) π/64 (D4-d4) EI



8.17 m



Ultimate Soil Resistance The ultimate soil resistance, R is the sum of uplift resistance of soil and pipe weight. Soil Uplift Resistance q = pbuc H D (1+fu H/D) Ultimate soil resistance R = q + Wto



Bend Radius to prevent Upheaval Buckling Equation 12 of K Peters paper gives the minimum bending radius to prevent upheaval buckling as given below: r = Frest / R r



= Frest / R



=



38.94



m



Calculation of Critical Bend Angle The allowable overbend angle 'ϕ' is calculated on a buckling length 'ƛ' against utimate soil resistance 'R' and allowable bending stress 'σall' as per Equation 25 of K Peters paper as follows: 1/2 (1-πἠ Cosπἠ/Sinπἠ ) = σall. Frest / (D . E. R ) = 0.144 ἠ = 0 to1 Critical Buckling Length Allowable over bend angle



ἠ ƛ ϕall



= = =



= = ἠ. ƛ.R / Frestr



0.29 8.17 0.0602 3.45



Solving for ἠ using iterative method m Radian degree



Bending Angle Vs Burial Depth Overbend with bend angles more than the critical bend angle can be stabilised against buckling by increasing the burial depth thereby increasing soil resistance. Allowable burial depth 'Hreq' and ultimate soil resistance 'Rreq' for a given bend angle 'ϕ' is calculated as per Equation 26 of K Peters paper as follows: Assume Angle ϕ = 3.45 degree 1/2ἠ1 (1-πἠ1 Cosπἠ1/Sinπἠ1 ) ἠ1 = 0 to1 ἠ1 Ultimate Soil Resistance Required Rreq Minimum Burial Depth required Hreq



= = σall. ƛ / (D.E ϕ ) = = = = Frest ϕ / (ἠ1 ƛ) = = D/fu ((Rreq/g-Wto/g)x(fu/p buc.D2)+1/4)^0.5-1/2)



0.0602 0.5028 0.2885 8040 1.00



Radian Solving for ἠ1 using iterative method N/m m 3.27 ft



Bend Angle Vs Minimum Burial Depth Bend Angle is increased in steps of 0.25 degree and the Minimum Burial Depth is calculated. Bend angle vs depth of cover is summarized as below: Bend angle (rad)



Bend Angle (deg)



σall. ƛ / (D.E ϕ )



ἠ1



Rreq (N/m)



Hreq (m)



3.45



0.0602



0.5028



0.2885



8040



1.00



3.50 3.75 4 4.25 4.5 4.75



0.0611 0.0654 0.0698 0.0742 0.0785 0.0829



0.4956 0.4626 0.4337 0.4082 0.3855 0.3652



0.2848 0.2679 0.2520 0.2385 0.2262 0.2151



8262 9412 10669 11982 13375 14849



1.01 1.09 1.17 1.25 1.33 1.41



5 5.25



0.0873 0.0916



0.3469 0.3304



0.2049 0.1957



16403 18035



1.49 1.57



5.5 5.75 6 6.25 6.5 6.75



0.0960 0.1004 0.1047 0.1091 0.1134 0.1178



0.3154 0.3017 0.2891 0.2775 0.2669 0.2570



0.1872 0.1795 0.1723 0.1656 0.1600 0.1541



19747 21539 23414 25369 27311 29444



1.64 1.72 1.80 1.88 1.96 2.04



7 7.5 8 8.5 9 9.25



0.1222 0.1309 0.1396 0.1484 0.1571 0.1614



0.2478 0.2313 0.2168 0.2041 0.1927 0.1875



0.1487 0.1388 0.1303 0.1228 0.1166 0.1135



31657 36314 41274 46521 51891 54809



2.12 2.28 2.44 2.60 2.76 2.84



2.50 2.00 1.50



Depth of Cover (m)



3.00



1.00 0.50 0.00 3.50



4.50



5.50



6.50



7.50



8.50



9.50



Angle of Deflection (deg)



Results : a) Critical Bend angle to avoid upheaval buckling for a minimum depth of cover (1m) shall be 3.45degree b) Overbends with bend angle more than the critical bend angle can be stabilised by increasing the depth of cover as per the above table. c) Minim cover depth specified does not include the berm length over grade level. d) Bend Radius to prevent upheaval buckling is 39m. No buckling will occur if the calculated radius of curvature of profile is greater than this value.



OTC 6335 Upheaval Buckling Calculation Introduction The aim of this calculation is to determine the downward force required on the pipeline to prevent upheavalbuckling as a result of axial compression. Input Data PIPE MATERIAL: Pipe diameter Nominal pipe thk Internal Dia Corrosion Allowance



Unit API 5L GR X65Q D t d C



= = = =



P S E ν α



= = = = = =



T1 T2 Tdmin H fu μ



= = = = = =



Soil density, Fluid density



pbuc pf



= =



-20 1 0.4 0.4 1575 25



Calculation of Pipe Properties Metallic cross sectional area



As



=



π/4 (D2-d2)



=



I



π/64 (D4-d4) EI As x ρs π/4 (D-2xt)2 Af x ρf



=



Design pressure Steel density Specified Minimum Yield Strength Modulus of Elasticity Poisson ratio Coefficent of Linear Thermal Expansion Installation (backfill) Temp Design Temp max buried Design Temp min buried Pipeline Cover depth Uplift coefficient Coefficent of friction between pipe & Soil



ρs



0.1143 0.005 0.1043 1.5 1.42E+07



m m m mm



7850



Kg/m3



450



Mpa Mpa



2.07E+05



0.3 0.0000117 21 85



4.50 0.20 4.11 0.06 2060



N/m2



490 65267 30022812



Per oC



0.000006552 70 185



C



o



C



o



C



m



Kg/m3



98 1.561



Kg/m3



W Af Wf Wte



= = = = = =



Total Weight + Contents Total Weight + Contents



Wto Wto



= =



Wte + Wf Wte + Wf



=



HOOP STRESS Axial Stress due to Pressure Elongation Axial Stress due to Poison Shrinkage Axial Stress due to Thermal Expansion



SH



= = =



(P x D)/2t 0.5 SH ν SH



= = =



=



α E (Tdmax - Ti)



=



F = As (0.5SH + α E (Tdmax - Ti) - ν SH)



=



Net Axial Force



psig psig Per oF o F o F o F



-4 39.37 in (0.1 for uncompacted backfill & 0.5 for compacted backfill)



o



Pipe Section modulus Pipe flexural rigidity Weight of pipe Fluid cross sectional area Weight of contents Pipe Weight Including Coating



ST



in in in in psig lb/ft3



= = = = = =



0.00172 0.000003 531824.82 13.47751 0.00854 0.214 14.286 14.500 142



lb/ft3 lb/ft3



m2 m4 N.m2 Kg/m m2 Kg/m Kg/m Kg/m N/m



162306000



N/m2



81153000 48691800.0 155001600



N/m2



321851.20427



N/m2 N/m2 N



Required Downward Force (As per OTC Paper 6335): Equation 12 of OTC paper 6335 specifies down force required to prevent upheavel buckling for offshore pipeline. The same has been used by modifying to suit onshore pipeline. Wru = [1.16 – 4.76 (EI Wto / δ)0.5 / F] F ( δ Wto / EI) 0.5 where δ = imperfection height Uplift resistance from Soil : Equation 13 of OTC 6335 defines the uplift resistance by soil (cohsionless sand) as given below, q = H D pbuc [1 + fu (H / D)] Total Downward Force: The actual downward force is provided by the sum of pipe weight and the uplift resistance of soil cover. Q = q + Wto Stability Check For Stability of pipe in trench against upheaval bucking the actual download 'Q' shall be greater than required dowmload 'W ru'. Wru < Q Upheavel Buckling Assessment: The required down load ‘Wru’ and actual down load ‘Q’ for the different imperfection heights (500mm, 400mm, 300mm, 200mm & 100mm) are tabulated below: Imperfection Height, δ (m) 0.1 0.2 0.3 0.4 0.5



Wru (N/m)



q (N/m)



Q (N/m)



Stability Check



1253.46 2052.83 2666.21 3183.32



672.32 547.22 434.72 334.81



814.419481 689.317231 576.814981 476.912731



Not Stable Not Stable Not Stable Not Stable



3638.89



247.51



389.610481



Not Stable



MINIMUM ELASTIC BEND RADIUS Input Data PIPE MATERIAL: Specified Minimum Yield Strength PIPE Diameter PIPE ID Wall Thickness Design Pressure Installation (backfill) Temp DESIGN TEMP CHANGE OF TEMP Coefficent of Thermal Expansion Modulus of Elasticity POISSON'S RATIO Corrosion Allowance Corroded Wall Thickness Equivalent Stress Design Factor



= = = = =



Ti Tdmax (Tdmax - Ti) α E ν C



= = = = = =



1.5 mm



tw = (t-C)



3.5 mm 0.9



=



0.14 in.



Feq



= =



SH = (P x D)/2tw ν SH



= = =



231.9 Mpa 69.6 Mpa



= =



33629 psig 10089 psig



ST = α E (Tdmax - Ti) SLA= α E (Tdmax - Ti) - ν SH



= =



156.2 Mpa 86.7 Mpa



= =



22661 psig 12572 psig



(0.9 x S)



=



405.0 Mpa



=



58740 psig



SB = (0.9 x S) - SH - SL r = (E x D)/(2 x SB) r/D



= = =



86.5 Mpa 136.84 m 1197.2



= = =



12539 psig 5387.38 in 1197.2



Stresses in Fully Restrained Sections Hoop Stress Axial Stress due to Internal Pressure Axial Stress due to Thermal Expansion Compressive Longitudinal Stress Maximum Allowable Stress



API 5L GR X65Q 450 Mpa 114 mm. 104 mm. 5.00 mm. 14.20 Mpa



S D d t P



21 oC 85 oC 64 oC 0.0000117 Per oC 207000 Mpa



= = = = =



65267 4.50 4.11 0.20 2060



= = = = = = =



70 185 115 0.00000655 30022812 0.30 0.06



psig in. in. in. psig F F o F Per oF psig o o



in.



Minimum Bend Radius Margin for Elastic Bending Minimum Bend Radius Bend Radius to Diameter Ratio



Maximum Allowable Longitudinal Stess for both tensile and compresive conditions is given by: SLmax = [SH ± {SH2 – 4[SH2 – (Feq SMYS )2]}1/2] / 2 In Compression: Max. Allowable Longitudinal Stress Margin for Elastic Bending Minimum Bend Radius Bend Radius to Diameter Ratio



SLmax = (SH-[SH2-4 (SH2-(Feq x S)2]0.5)/2 SB = SLmax - SLA r = (E x D)/(2 x SB) r/D



= = = =



-235.8 Mpa -149.10 Mpa 79.3 m 694.2



= = = =



-34197.31 psig -21625.18 psig 3123.74 in. 694.2



In Tension: Max. Allowable Longitudinal Stress Margin for Elastic Bending Minimum Bend Radius Bend Radius to Diameter Ratio



SLmax = (SH +[SH2-4 (SH2-(Feq x S)2]0.5)/2 SB = SLmax - SL r = (E x D)/(2 x SB) r/D



= = = =



467.6 Mpa 554.33 Mpa 21.3 m 186.7



= = = =



67826.64 psig 80398.77 psig 840.20 in. 186.7



-235.78 Mpa



=



-9053.05 psig



=



30140.37 psig



From the above compression case is the more critical one; hence: Minimum Selected Bend Radius



=



Net Longitudinal Stress Net Longitudinal Stress



=



SL= α E (Tdmax - Ti) - ν SH + SB



The following criteria need to be satisfied for 'Net Longitudinal stress': SL R, ANCHOR BLOCK IS REQUIRED PIPELINE RADIAL BEND FORCES - ANCHOR BLOCK DESIGN ANCHOR BLOCK SIZE: WIDTH = DEPTH = LENGTH =



10 6 10



ft. ft. ft.



value to be put value to be put value to be put



CONCRETE DENSITY 1925 kg/m3 COEFF. OF FRICTION B/W CONCRETE & SOIL SOIL PRESSURE ON SIDES OF ANCHOR BLOCK SOIL RESISTANCE ON ANCHOR BLOCK,Ra Factor of Satety = CONCLUSION:



= = = =



ANCHOR BLOCK IS ADEQUATE



120 lb/ft3 0.40 120.00 lb/sft/ft DEPTH 139250.83 lb. 850%