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2.2 Mathcad This Mathcad calculation determines the requirement for a buckle arrestor (BA) according to DNV-OS-F101, to find the collapse pressure and propagation pressure in order to determine the minimum geometry for an integral buckle arrestor for welded pipe. 2.2.1 References 1. DNV-OS-F101 "Submarine Pipeline Pipeli ne Systems" August 2012. (Section 5: Design - Limit state Criteria)
2.2.2 2.2.2 Desig Desig n Consi deration s To ease procurement of the BA, the design is based on UOE line pipe and a normal material strength factor. 2.2.3 2.2.3 Input Data Pipe Dimensions Total Length of pipe
Material strength factor for pipeline Table 5-4 (supplementary requirement U)
UBA := 1
Material strength factor for BA material Table 5-4 (supplementary requirement U
fab := 0.85
Fabrication factor for the Pipeline Table 5-5 (UOE)
fabBA := 0.85
Fabrication factor for BA Table 5-5 (UOE)
sc := 1.04
Pipeline safety class Table 5-3 (for other load cases)
sc_arr := 1.04
Arrestor safety class Table 5-3 (for other load c ases)
Material resistance factor (SLS / ULS / ALS) Table 5-2
m := 1.15
Environmental Characteristics kg
sw := 1025
Density of Seawater
3
m
Maximum Design Water Depth
h := 148.3m
Tidal Surge
ht := 2.95m
Highest expected wave
hw := 22.98m
General Desig n facto rs co := 0.0
Content Density
kg 3
m
Pi := 0.0MPa
Internal Pressure
10
2.2.4 Calcul ation s Manufact uring tol erances fr om DNV-OS-F101 (Table 7-17 & Table 7-18)
Construction method is 0 for welded pipe or 1 for seamless pipe . Sheet does not cater for seamless Type of weld ( 0 if HFW, EBW, LBW or MWP and 1 if SAW) ttol_max :=
( 0.4mm) if WeldType = 0 tnom 6.0mm ( 0.7mm) if WeldType = 0 6.0mm < tnom 15.0mm ( 1.0mm) if WeldType = 0 15.0mm < tnom ( 0.5mm) if WeldType = 1 tnom 6.0mm ( 0.7mm) if WeldType = 1 6.0mm < tnom 10.0mm ( 1.0mm) if WeldType = 1 10.0mm < tnom ttol_min = 1 mm
Maximum thickness due to manufacturing tolerances
tmax := tnom + ttol_max
Minimum thickness due to manufacturing tolerances
tmin := tnom - ttol_min
11
tmax = 21.9 mm
tmin = 19.4 mm
Factor for determination of fabrication tolerance based on pipeline wall thickness
Dtol :=
tfab_fact :=
(tmax - tmin) tnom
tfab_fact = 0.1225
min ( 1.6mm , max( 0.5mm , 0.005 OD)) if 60.3mm OD 610mm ( 1.6mm) if 610mm < OD 1422mm Dtol = 1.6 mm Dmax := OD + Dtol
Maximum diameter due to ovality
Dmax = 763.6 mm Dmin := OD - Dtol
Minimum diameter due to ovality
Dmin = 760.4 mm
Ovality tolerance (Equation 5.14)
f o :=
(Dmax - Dmin) OD
f o = 0.0042
System co llapse Criterion Table 5-6 (operation)
Pipe wall thickness
t1 := tnom - tcorr - ttol_min
t1 = 17.9 mm
Pipe wall thickness
t2 := tnom - tcorr
t2 = 18.9 mm
The system collapse criterion is based on the pipe body material and shall fulfill the following criteron: pe
External pressure check along the pipeline (Equation 5.10)
( )
P c t1
m sc
and the characteristics resisitance for collapse P c is given by the solution (Equation 5.11) :
(Pc ( t) - Pel ( t)) (Pc (t)
2
- Pp (t)
2
Do
) = Pc (t) Pel (t) Pp (t) f o t
1
12
Where,
t1 2 E OD Pel :=
Elastic collapse pressure
1-
(Equation 5.12)
3
2
Pel = 5.9 MPa
(
)
f y := Y - f ytemp U
Characteristics yield stress (Equation 5.4)
f y = 450 MPa
t1 Pp := 2 f y fab OD
Plastic collapse pressure (Equation 5.13)
Pp = 17.97 MPa The analytical solution for P c as defined in DNV-OS-F101
Pc = y -
b 3
(Equation 13.13)
Where,
6
b := -Pel
b = -5.897 10 Pa
OD 2 c := - Pp + P p Pel f o t1
c = -3.419 10
d := Pel Pp u :=
1
v :=
1
3
2
2
d = 1.904 10
14
21
-1 2 b + c
u = -1.178 10
v = 6.086 10
3 2
27
:= acos
3
b -
1 3
b c + d
-v (-u) 3
y := -2 -u cos
+ 60 180 3 13
Pa
14
= 118 deg
y = 3.6 MPa
20
Pa
2
3
Pa
Pa
3
2
Pc := y -
Characteristics resisitance against collapse
b 3
Pc = 5.5 MPa htot := h + ht + hw
Maximum water depth
htot = 174.23m Pe := sw g htot
Hydrostatic Pressure
Pe = 1.75 MPa Collapse Pressure Check This is to confirm the characteristic resisitance against external over-pressure. (Equation 5.10)
Collapse :=
"Pipeline collapse initiated"
if Pe P c
"Pipeline collapse prevented"
otherwise
Collapse = "Pipeline collapse prevented" Buckle Propagation Check This buckle propagation check is to determine if the pipeline will buckle under external pressure. (Equation 5.15)
Propagation pressure in the pipeline (Equation 5.16)
t2 Ppr := 35 f y fab OD Ppr = 1.3 MPa
