At a refinery, a branch connection designated W31056, the 2″ line that ties in to the high-pressure steam attemperator J-3103 (a desuperheater), failed in service. A similar failure had occurred about twenty years earlier, in 1992.
On-site observations report periodic movement of the connecting header, line 6″-S31022, which contains the desuperheater, indicating that the failure is likely a fatigue failure. The objective of the analysis was to provide a permanent solution to the movement of line 6″-S31022, thereby preventing future cracks in the branch connection W31056. The work proceeded in two stages: a static stress analysis of the existing line, followed by a dynamic analysis to determine the possible vibration modes that have caused the line failure.
The header has a design pressure of 47 barg, a design temperature of 538 °C, an operating temperature of 484 °C and a fluid density of 12.4 kg/m³. The adjoining line W31056 has the same design pressure of 47 barg, a design temperature of 170 °C, an operating temperature of 152 °C and a fluid density of 915 kg/m³.
Model scope, load cases and static assessment to ASME B31.3
Only the piping connecting to the desuperheater is modelled; the model has boundaries where the piping is truncated, together with a number of natural boundaries. The modelled section covers five pipe classes, all with a 1 mm corrosion allowance, and the insulation is calcium silicate. Part of the piping connects to vessel A-3101, where the piping is anchored. Thermal expansion of the vessel displaces the connecting piping and adds static displacement stresses, but information on the thermal growth of the vessel is not available, so the predicted static stress near the model boundaries is not reliable. For the dynamic behaviour the thermal growth is less important, provided the initial thermal displacement of the piping does not change support functions. The analysis focuses on the region close to the failure, away from the model boundaries.
The static stress analysis was performed to ASME B31.3, and the static stresses were assessed to the same code. Three load cases are defined: a sustained case SUS1, covering pipe and content weight, design pressure and the hanger and support loads; an operating case OPE1, adding the design temperature, which is not a code case; and an expansion case EXP1, taken as OPE1 minus SUS1. Of these, the two stress cases SUS1 and EXP1 are assessed against the code. During the operating case there is lift-off from one of the supports, as a result of a combination of unfavourable weight distribution and pipe expansion; that support is therefore not active during the sustained load case. Reports from on-site engineers confirm this non-sitting support.
The results, expressed as a percentage of the allowable at design conditions, show part of the system overstressed in both the sustained and the expansion case. The main reason for this stress excess is the low allowable stress at the design temperature. The material A335 P11 has an allowable stress S of 137.9 MPa at ambient temperature (21 °C), 86.7 MPa at 484 °C and 43.3 MPa at 538 °C: the design-temperature value is more than a factor of three below the ambient value, and the operating-temperature value is double the design-temperature value.
There is no indication of a failure of this statically overstressed line during its normal static operational lifetime. This is most probably because the strength of the pipe at operating temperature is twice the strength at design temperature; a safety factor of 1.5 is also incorporated in the design.
Natural vibration modes and the limits of the modal analysis
The second stage, the modal analysis, determined the structural natural frequencies and related mode shapes of the piping. If a load is periodic with a period close to one of the natural periods, resonance may occur, which may result in large amplitude vibrations and ultimately failure due to fatigue. Low frequency mode shapes, typically below 5 Hz, are more easily excited than higher frequency modes.
The analysis identifies low frequency modes at 1.1, 1.2, 1.5, 2.3, 2.9 and 3.9 Hz, all below 5 Hz, and these correspond to the movements observed on site. The lines are insufficiently restrained when exposed to dynamic loads and allow much dynamic movement.
The modal analysis does not establish the potential excitation mechanism, and because the displacement magnitudes are unknown a quantitative description of the dynamic stress levels cannot be made; the approach is therefore more qualitative than quantitative.
Support modifications that restrict the modes and retain thermal flexibility
The proposed modifications to the support arrangement have the objective of restricting the natural vibration modes identified in the modal analysis, so that the frequency of the lowest natural mode shape is increased and the observed movements are restricted. When restricting the vibration modes, attention has to be paid to the resulting thermal stresses: the additional restraining has to be designed with sufficient resulting flexibility to allow thermal displacement of the piping without stress excess. A further objective is to reduce the primary stresses due to pipe weight to within allowable levels at design temperature.
Modifications are specified at seven support locations. A hanger gains a guide function at node 560; a resting guide is added at node 620 and a three way stop at node 680, where there was no support previously; three existing rest supports gain an axial restraint function, at nodes 715, 735 and 1840; and a rest support is added at node 1980, where there was no support previously. Because of the additional restraining of the system, the hanger load at node 560 is modified from 10 kN to 6 kN in order to prevent a potential negative effect of the hanger.
Reduced stress percentages and improved behaviour under the modified support arrangement
The same three load cases were re-run in CAESAR II for the modified support arrangement with the revised hanger load, and stresses, displacements and restraint loads are reported for that arrangement.
The modified support arrangement results in an overall improvement of the static stress level in the system. The support modifications are such that they do not significantly influence the expansion stresses near the vessel connection, where the expansion stress check remains inaccurate. The conclusion drawn is that the new support locations, together with the modified functions of existing supports, produce a substantial improvement in both the dynamic and the static behaviour of the system.
Assessment points for high-temperature steam piping
The allowable stress at an elevated design temperature is more than a factor of three below the ambient value, so a layout assessed against design-temperature allowables can show an exceedance that an ambient-temperature comparison would not.
- The check is made against the design-temperature allowable. For A335 P11 the allowable stress falls from 137.9 MPa at ambient temperature to 43.3 MPa at the design temperature of 538 °C, and against the allowables at design conditions the sustained case reached 119 per cent and the expansion case 132 per cent.
- Operating strength most probably explains the absence of static failure. There is no indication of a failure of this statically overstressed line during its normal static operational lifetime, most probably because the strength at operating temperature is twice the strength at design temperature, with a safety factor of 1.5 also incorporated in the design.
- A support that lifts off is not active in the sustained case. Lift-off during the operating case, from a combination of unfavourable weight distribution and pipe expansion, left one support not active during the sustained load case, and reports from on-site engineers confirm this non-sitting support.
- Mode shapes below 5 Hz are the ones to restrain. Six modes between 1.1 and 3.9 Hz correspond to the movements observed on site, and restricting them raises the frequency of the lowest natural mode shape.
- Additional restraint has to retain flexibility for thermal displacement. The additional restraining is designed with sufficient resulting flexibility to allow thermal displacement without stress excess, and the hanger load at node 560 was modified in order to prevent a potential negative effect of the hanger.
- Boundary conditions limit what can be concluded. Thermal growth data for the connecting vessel was not available, so the expansion stress check remains inaccurate near the model boundaries, and the analysis focuses on the region close to the failure, away from the model boundaries.
