A gas line between the high and low pressure separators of a hydrocracking unit failed in service, probably through material fatigue caused by vibration. An additional 3-way stop was fitted just downstream of the TSO valve to reduce vibration levels, and vibration was then measured at nine locations on the line, which runs between the two separators and on to a power recovery turbine, to confirm that the remaining life of the line would be long enough.
The measured velocity peaks were assessed against VDI 3842, a guideline of typical vibration levels for piping, and several were classified as concerning. Most of those points were measured at the actuators of the valves, which are not typical piping. On the piping itself the most critical vibration, 5.7 Hz at the first support downstream of the high pressure separator, stays below the marginal classification line.
The guideline gives a qualitative indication only. It identifies where vibration is high, but not what stress that vibration puts into the pipe wall, so it could not settle the question of remaining life.
The piping material is St 35.8 (P235GH). The fluid is two-phase, liquid and gas together, with an average density of 772 kg/m³. Operating conditions reach 92.0 bar and 200 degC, and design conditions 117.9 bar at the same temperature. The line carries 150 mm of insulation.
Setting up the model
The line was rebuilt as a pipe stress model in CAESAR II, with component weights, reducer lengths and fluid properties taken from an earlier stress report for the system. The flexibility of the nozzle connections at the two separators was calculated separately and included in the model, since those connections yield slightly under load and that changes how the line moves. The connections to the turbine are stiff by comparison and were treated as anchors. For three supports the structural steel beneath them was modelled from site photographs, because support stiffness has a strong influence on vibration behaviour.
The insulation density was taken at twice the specified value, 260 kg/m³, because the line is steam traced and the insulation may be saturated with water. One limitation remained: the pipe rack, which was reported to move with the system, is not in the model, so not all of the vertical movement measured on site could be reproduced. The measurements were taken at operating conditions, so those conditions were used for the vibration calculations, and the design conditions only to check the line against the ASME B31.3 code, over six load cases.
Ruling out turbine, resonance and flow regime
The power recovery turbine runs at 76 Hz, well above the frequencies being measured, and the vibration continued when the turbine was offline. That eliminated it as the source.
Resonance was considered next. Every piping system has natural frequencies at which a small periodic disturbance can build into a large movement, and if that were happening the measured peaks would coincide with the calculated natural frequencies. They did not, and refining the model with more detail from site did not bring the two closer, so resonance was discounted.
That left the two-phase flow. Slug and other intermittent regimes generate unbalanced forces as the liquid travels through the line. The liquid and gas fractions worked out from the fluid composition show 5.6 times more liquid than gas by volume, which places the flow in the bubbly regime: gas carried as discrete bubbles through a continuous liquid, behaving effectively as a single-phase flow. Bubbly flow does not produce those unbalanced forces, so no obvious excitation mechanism remained at that stage.
A standing pressure wave in the fluid
The measurements were then converted from velocity into displacement, which changed which frequencies stood out. The largest displacements fall within the first 10 Hz of the spectra, and the largest measured amplitude on the piping itself is only 0.2 mm. More usefully, several of the peak frequencies proved to be multiples of one another, which points to a standing pressure wave in the fluid, with a base frequency and higher harmonics above it.
The hypothesis was checked against the geometry. The longest wave the system can hold is a quarter sine wave across the 39.2 m run from the high pressure separator to the turbine, taking the separator as a fixed pressure boundary and the large pressure drop at the turbine as a fixed velocity boundary. At the calculated speed of sound for this two-phase mixture that gives a base frequency of 1.7 Hz, against a lowest measured frequency of 1.9 Hz, with the instruments resolving in steps of 0.63 Hz. Such a wave is most likely initiated and sustained by flow disturbances at a restriction, a valve or a reducer.
Stresses calculated from the modelled vibration
To turn that into stress, the wave was applied in the model as unbalanced loads acting between pairs of elbows, at the middle of the straight sections that vibrate, with the magnitudes tuned until the model reproduced the measured displacements. Thirteen models were run, one for each measured peak frequency, nine with the turbine online and four with it offline; the difference between the two states is explained by closure of the valve in the line to the turbine.
Adding the maximum stress amplitude from every model algebraically, an intentionally conservative step since the peaks occur at different locations, gives 17.4 MPa with the turbine online and 12.2 MPa offline.
Both totals are well below the fatigue limit and, in the assessor’s opinion, a formal fatigue assessment is not required. The calculated amplitudes remain available should the operator want one carried out.
The valve actuators were assessed separately, in three models covering control valves 8.1, 8.2 and 11.1, because an actuator swings on its own natural frequency and the short pipe connecting it to the valve is the weakest link. The dimensions had to be estimated from photographs, so the result is an order of magnitude rather than a precise value, but the stresses are small, the highest single figure being 11.2 MPa. If the movement is uncomfortable for people working nearby, a bracket or bracing tying the actuator back to the main pipe would reduce it.
One exceedance, at design conditions rather than in service
At operating conditions every calculated static stress falls within the ASME B31.3 allowable limits. At design conditions the expansion case, the stress arising when the line is restrained as it expands, reaches 474.3 MPa at the small end of the reducer upstream of control valve 8.2, against an allowable of 278.0 MPa. The mechanism there is low cycle fatigue, driven by a small number of large temperature swings rather than by continuous vibration, and extrapolation of the code curve indicates roughly 500 cycles between ambient and design conditions would be tolerable. The real wall thickness of that reducer is not known; 16 mm was assumed in the model, and the actual component may be thicker.
Assessment points for vibration-prone two-phase systems
- Guideline screening identifies risk but does not quantify it. VDI 3842 applies to typical piping systems and gives a qualitative idea only; most of the concerning points were measured at valve actuators, and on the piping itself the peak at 5.7 Hz stays below the marginal classification line.
- The displacement domain shows what the velocity domain does not. Translating the RMS velocities into displacement amplitudes revealed peak frequencies that are multiples of one another, which is what produced the standing pressure wave hypothesis.
- A low frequency, low amplitude vibration carries a low bending stress. The largest measured amplitude on the pipe work itself is only 0.2 mm, and a low frequency pipe bending mode corresponds to a low pipe bending curvature and hence a low bending stress.
- A line within the allowables at operating conditions can still exceed them at design conditions. The expansion case at design conditions reaches 474.3 MPa against a 278.0 MPa allowable, with low cycle fatigue as the related failure mechanism.
- Assumed dimensions and excluded structure bound the result. The thickness of the overstressed reducer is not known and is set at 16 mm, the actuator connection thicknesses were assumed, and the pipe rack was not modelled, so not all vertical displacements could be reproduced.