An 8-inch line carrying two-phase content from a heat exchanger to a gasoil stripper at a refinery had been vibrating for years, mainly in the two shorter horizontal sections, one downstream of the heat exchanger and one just upstream of the stripper. The operator had reported vibration for 5 to 10 years, and half a year before the assessment the process conditions changed and the flow rate increased.
Large amplitude movements were observed approximately every 3.6 seconds, each followed by damped vibration, which led to the view that there might be a liquid slug impact at that interval. Two events were also recorded: the support originally designed as a 3-way stop, in the long horizontal section, was no longer acting as one, its welds having broken, and a cut-out in the insulation shell was pressing against a vertical structural steel beam, which damps lateral vibration there and was taken into account in the dynamic calculations.
For both process conditions the operator measured plus or minus 10 mm in the x-direction and plus or minus 5 mm in the y- and z-directions at the spring support, plus or minus 5 mm in all directions at a second node, at average excitation intervals of 5 seconds under the current conditions and 6 seconds under the previous ones.
If liquid slugs were driving the vibration, the resulting cyclic stress could accumulate fatigue damage at the bends.
Flow regime maps, a field-tuned pipe stress model and nine mode shapes below 10 Hz
A CAESAR II pipe stress model was built from the received isometrics, supplemented by dimensions taken during the inspection where the drawings were incomplete. A static stress and flexibility analysis to ASME B31.3 gave maximum stresses well within the allowable levels for all load cases, so apart from repairing the weld that had come loose, no modifications with a static purpose were required.
Slug flow is the most hazardous two-phase scenario mechanically, since it involves a moving liquid mass pushed by gas in between. On the Taitel and Dukler flow pattern map for horizontal flow within a tube, both sets of process conditions fall in the transition area between slug and annular flow with a tendency to slug flow, and the Baker map gives a similar picture. Those transition lines are to be interpreted as broad bands, but with the site observations they gave confidence that liquid slugs occur in the line.
The superficial gas velocity follows from the gas mass flux, the gas density and the internal cross-sectional area, and the actual gas velocity from the void fraction, taken from the Lockhart and Martinelli experimental two-phase flow model. Assuming conservatively that the liquid travels at gas velocity with no gas surpassing the slug, the actual gas velocity is 13.2 m/s for the current process conditions and 11.8 m/s for the previous ones, giving fully developed slug loads of 3.9 kN and 3.0 kN on the 90 degree bends.
The time-history method applies the impacts to each elbow individually and maintains the phase differences between them, giving the most accurate stresses and displacements; the spectrum response method loses the time phase but identifies the mode shapes contributing most, and is likely to overestimate, since it loads every bend at once. Because the calculated loads assume the gas fills the full cross-section between slugs, the applied magnitudes were scaled until calculated displacements matched measured ones.
Nine natural mode shapes lie below 10 Hz, against a rule of thumb that they preferably lie above 10 Hz for lines subject to multi-phase flow, indicating a system relatively sensitive to dynamic loads.
An axial stop at the spring support, a fourfold reduction of the gas volume flow and a medium term support package
The spectrum response method gives 79.4 MPa at the bend downstream of the spring support, where the maximum time-history fitting stress also occurs, 42 per cent of it from the third mode shape at 4.4 Hz, so that mode shape was to be eliminated in the short term. Support functionality was added at the spring support, restraining the piping axially, which could be done while the system was operating and without significant steel structure extensions. A vertical vibration component remains there and could be removed by locking the springs; the operator chose instead to combine the axial stop with a pressure increase.
The slug load relates in the second order to the actual gas velocity. Raising the operating pressure from 0.57 to 2.56 barg, by throttling at the downstream instead of the upstream end of the line, gives almost a fourfold reduction of the gas volume flow and brings the actual gas velocity from 13.2 to 4.5 m/s. A repeated flow regime assessment places these conditions in the slug flow regime even more clearly, but the calculated slug load falls to 0.45 kN; with a design pressure of 10.4 barg the increase is not an issue statically.
A medium term package was developed as well: three new supports at new locations and two support functionality changes at existing ones, with the guide along the stripper rotated 90 degrees, both to eliminate certain mode shapes and to reduce the static reaction forces added by the axial stop. Replacement of the bends, which might have accumulated micro fatigue cracks, is advised during a shut-down.
Amplitudes exceeded at the fittings, and the modified configurations within the allowable cycle counts
Dynamic stresses were assessed against the design fatigue curve of the ASME B&PV code (Section VIII, Division 2), lower curve, applicable to A106 B and API-5L B, a stress in a fitting being doubled first to account for the baseline fitting used by Markl in determining the stress intensification factor.
The exceedance is at the fittings: the fitting amplitude of 43.8 MPa doubles to 87.6 MPa for the current conditions, allowing 1 million cycles against the 6 million accumulated in half a year at a 5 second interval and two stress cycles per impact, and 36.6 MPa doubles to 73.2 MPa for the previous conditions, allowing 11 million against 105 million over 10 years at the 6 second interval. The plain pipe amplitudes stay below their allowables. The combined cumulative usage factor is well above the allowed value of 1.0, and that no fatigue failure had occurred is explained by the safety factors in the curve, a minimum of 15 to 20 on cycles and a minimum of 2 on stress.
The dynamic stress in the bend downstream of the spring support falls from 43.8 to 16.6 MPa, and the fitting amplitude becomes 24.1 MPa at the second bend downstream of the heat exchanger, 48.2 MPa doubled, allowing at least 5 × 1010 cycles.
With the 0.45 kN load applied to the as-built model without the axial stop, the maximum fitting amplitude is 3.7 MPa, 7.4 MPa doubled, and the maximum dynamic displacement 1.1, -0.1, 1.7 mm at the elbow downstream of the spring support, against 13.0, -15.6, -2.1 mm at the bend upstream of it for the as-built line under the same conditions; over 1011 cycles are allowed, and this load was not scaled to the measurements. Combining the pressure increase with the axial stop would also eliminate the x-component of that displacement.
Assessed for the current conditions with the tuned slug forces, it gives 17.6 MPa at that same second bend downstream of the heat exchanger, 35.2 MPa doubled, again over 1011 cycles, with static stresses below the ASME B31.3 allowables; the heat exchanger nozzle load increases, mainly Mz, and might need checking against vendor specified nozzle load allowables, which were not in the received documentation. Both short term measures had already been implemented by the operator.
What the work shows about the supports, the drawings and the conservative slug loads
The design fatigue limit was exceeded without a fatigue failure, and the safety factors in the curve are the reason; consuming that margin is a far from ideal situation.
- The support package was not designed for a line carrying two-phase content. The flexibility of the two vibrating sections is caused mainly by the lack of axial stops and lateral guide supports there, and the medium term package answers that with three new supports at new locations and two support functionality changes at existing ones.
- The isometrics did not give a complete picture of the supporting. Neither the 3-way stop with the broken welds, included in the model with the functionality of a 3-way stop and in need of an improved construction, nor the insulation contact, taken into account as lateral damping, could be read from them.
- Scaling the conservative slug loads to the measured displacements made the dynamic stresses assessable. Without it the fatigue assessment would rest on loads deliberately set high rather than on the measured behaviour of the line, and every cycle count reported here would carry that conservatism.
