Pipeline Fatigue Assessment

Transcription

1 Pipeline Fatigue Assessment The purpose of this MathCAD sheet is to calculate cumulative pipeline fatigue damage using the well defined 'rainflow counting' process. The algorithms herein use pipeline variable stresses (as consequence of internal pressure and temperature variations) and uses the Rainflow counting method to determine the stress cycle ranges and the number of cycles per stress range. This will then allow the prediction of pipeline fatigue life. The rainflow counting routine used herein is that which is taken from Downing, S. D. and Socie, D. F., 'Simple Rainflow Counting Algortihms', International Journal of Fatigue, Vol 4, No. 1, January Algorithm one (of Downing et al) was made use of in this sheet. The calculation is performed in three discrete steps as follows: Sorting of the data in order to start and end with a maximum peak, and filter for peaks and valleys. The sorting is a necessary pre-conditioning step. Rainflow cycle counting; the data are then rearranged and filtered to provide an array of cyclic and mean values for each cycle. In addition, the array is also set to contain the maximum cyclic and corresponding mean for the entire data array. The data can also be factored for wall losses on account of corrosion. Summary Details Name of Asset UKCS Pipeline Operator UKCS Operator Designation 36-Inch Main Oil Export Pipeline Assessment Case Description Rainflow Counting Method: Operating Hoop Stresses This sheet calculates the pipeline fatigue life based on operational pressures (hoop stresses) Units Definitions deg C K BBL 42 gal BBLD BBL day 1 SCF ft 3 SCFD SCF day 1 MMSCFD 1 6 SCFD SCM m 3 SCMD SCM day 1 Author: KL Consulting (UK) Limited Page 1 of 6 Date: 7/7/214

2 Pipeline Operating Pressure Data Input Pipeline Operating Pressure History DATA Pressures.xlsx Assign Time Record t r DATA s Assign Pressure Record P r DATA 1 psi Duration of Time Record n period max( t r ) Average Operating Pressure μ p mean( P r ) Standard Deviation Operating Press σ p stdev( P r ) Maximum Operating Pressure P max max( P r ) n period = yr μ p = psi σ p = psi P max = psi Operating Pressure (psi) Time (Years) Hoop Stress Data Pipeline Outside Diameter D s 36 in Nominal Wall Thickness t nom 18.1 mm Author: KL Consulting (UK) Limited Page 2 of 6 Date: 7/7/214

3 Cumulative Corrosion at COP (Estimated) C loss 5.5 mm Estimated Wall Thickness at COP t wall t nom C loss t wall = 12.6 mm Number of Data Points k length( P r ) Data Range j.. k 1 P rj D s Operational Hoop Stresses σ hj 2 t wall Operational Hoop Stress (MPa) Time (Years) Material of Construction API 5L X52 Youngs Modulus E 27 GPa Average Hoop Stress (Normal Operating) μ h mean( σ h ) μ h = MPa Lambda (Eqn D.8-13 DNV-RP-C23) 12 μ h λ λ = m 1 2 E t wall Length Parameter (in D.8-12 DNV-RP-C23) π D s l f 8 l f = mm Author: KL Consulting (UK) Limited Page 3 of 6 Date: 7/7/214

4 Rainflow Counting of Time-Record and Fatigue Life Estimate The analysis below makes use of the above routines to calculate the range and mean stresses of the above time-record of data. These data may then be used with the material S-N data in order to calculate the fatigue life of the pipeline. Vector of Stresses σ σ h MPa Peak and Valley of Sorted Data y PVF( σ) Rainflow Counting y rfc RFC( y) Define Stress Range (MPa) S y rfc MPa 1 Define Mean Stress (MPa) S mean y rfc MPa S Define Maximum Stress (MPa) S max S mean + 2 ( ) Length of Column Vector b length S mean Define Range (for Matrix Values) n.. b 1 S-N Curve F1 (with Cathodic Protection) Intercept with Log N Axis loga Characteristic Fatigue Strength Constant for LHS of Curve Inverse Slope of Left-Hand of Bi-linear Curve Inverse Slope of Right-Hand of Bi-linear Curve loga 1 a 1 1 m 1 3 m 2 5 No of Cycles Where Slope Change Occurs Stress Value at SN Curve Intersection N s 1 6 a 1 log N s m 1 S si 1 MPa SsI = MPa Author: KL Consulting (UK) Limited Page 4 of 6 Date: 7/7/214

5 Characteristic Fatigue Strength Constant for RHS of Curve Girth Weld Joint Misalignment (for Calculation of SCF) S si logn s m 2 log + MPa a 2 1 a 2 = ( ) δ m min.15 t nom, 3 mm δ m = mm Out of Roundness (Maximum per DNV-OS-F11) D max D min δ OOR_max = D.3 Out of Roundness (for Calculation of SCF) Stress Concentration due to Joint Misalignment (See DNV-RP-C23) Stress Concentration due to Out-of-Roundness (See D.8-12 DNV-RP-C23) δ OOR D s.3 δ OOR = mm 3 δ m t nom SCF circ 1 + exp SCF t nom D circ = s 1.5 δ OOR SCF OOR 1 + tanh( λ l t nom λ l f ) SCF OOR = f Select Stress Concentration Factor SCF a SCF circ Damage Due to a Single Stress Reversal for Stress Range 'x' (DNV S-N Curve) D( x) x SCF a m 1 MPa if x > S a si 1 x SCF a MPa a 2 m 2 otherwise Fatigue Damage Per Stress Range D fatn D S n Cumulative Fatigue Damage D cum D fatn D cum = n Author: KL Consulting (UK) Limited Page 5 of 6 Date: 7/7/214

6 D cum Annual Fatigue Damage D ann D n ann = yr 1 period Design Fatigue Factor DFF 6 1 Unfactored Fatigue Life Life unf D ann Life unf = yr Life unf Factored Fatigue Life L f L DFF f = yr DNV-OS-F11 Design Fatigue Factor (Section 5, Table 5-11) 15 Stress Range (MPa) RFC Point 4 Mean Stress (MPa) RFC Point Author: KL Consulting (UK) Limited Page 6 of 6 Date: 7/7/214