Lines assessed | 4 |
Pipe content | Two-phase gas-liquid flow, all process conditions |
Flow regime, start-up | Slug flow |
Flow regime, normal operation | Annular flow |
Pipe material | A 358 type 321, main material |
Design temperature | 400 °C |
Design pressure | 77.5 bar, Lines 1 and 3; 81.0 bar, Lines 2 and 4 |
Liquid slug forces | 4 to 6.5 kN |
Software | CAESAR II |
Dynamic methods | Shock response spectrum and time history |
Fatigue criterion | ASME Section VIII Division 2 endurance limit, infinite number of cycles |
Static allowables | ASME B31.3 |
Final arrangement | 13 rigid-restraint modifications, 5 shock dampers |
Large-amplitude vibration on lines that see start-up one day a year
A refinery gasoil hydrofiner unit exhibited large-amplitude piping vibration, prompting a dynamic stress and vibration assessment of four pipelines connecting the furnace, heat exchanger, and reactor. The lines carry two-phase gas-liquid flow under all process conditions.
Eye witnesses reported the most severe motion during the start-up phase, a condition that occurs on average only one day per year. Vibration measurements were available for normal running only. Those measurements were classified as non-concerning at first sight against the VDI 3842 vibration level limit guideline, which gives a qualitative indication only for typical piping systems, with a largest measured displacement of 0.5 mm. They were taken at one location on each line, all near the furnace, and the cut-off frequency of the measurement device was 2.7 Hz.
The objective was twofold: reproduce the observed vibration in the models, and reduce vibration levels regardless of whether the resulting dynamic stresses were already acceptable.
Identifying slug flow as the excitation mechanism
Two-phase flow settles into several regimes, and the mechanical consequences differ sharply between them. A flow-regime assessment was performed using the Taitel and Dukler flow pattern maps, a method suited to the predominantly horizontal piping in the system and valued because it applies different axes to different regime transitions.
Across the studied process conditions, including soaking, two pre-sulfiding phases, and start and end of run, the data points clustered near the boundary between slug flow and annular flow, transitions that are themselves to be read as broad bands rather than sharp lines. This agreed with earlier observations made using the Mandhane, Gregory and Aziz map.
Slug flow is the most hazardous two-phase regime from a mechanical point of view. It consists of a moving liquid mass propelled by intervening gas pockets. Each time that mass changes direction at an elbow, reducer, or tee, the change in momentum produces an unbalanced reaction force. These repeated impacts were the probable cause of the heavy start-up vibration. The gentler motion during normal operation was attributed to unsteadiness in the liquid film of an annular flow pattern.
Because the assessment showed all conditions sitting close to the slug transition, the study conservatively treated every condition as slug flow and concentrated on the start-up phase.
Quantifying the slug force and selecting the slug length
Using the gas and liquid properties for each line and condition, and the conservative assumption that liquid velocity equals gas velocity with no gas bypassing the slug, the fully developed slug forces were calculated in the range of 4 to 6.5 kN. The highest value, 6400 N, was obtained on the 8 inch sections of Lines 1 and 3 during the pre-sulfiding 2 phase, reducing to 4075 N where those lines expand to 10 inch. On the 10 inch Lines 2 and 4 the value was 4077 N during the pre-sulfiding 1 phase.
At this stage only the magnitude of the unbalanced reaction force was known, not the duration of the impact. That duration was harder to pin down. No analytical theory gives the exact length of a slug, and two theories produced average estimates of 5 m and 70 m, a scatter so wide that the values can only be read as approximate extremes.
With no measurements available during start-up, the slug length had to be estimated. Since the gas-passage period behind a slug is fixed by the process conditions, slug length was the only free parameter. Three slug lengths were tried on each line, so that the slug impact frequency, the slug intermittency, coincided in turn with each of the first three eigen modes. The length producing the largest dynamic stresses was carried forward.
Line | Selected slug length | Tuned to |
Line 1 | 7580 mm | Third mode |
Line 2 | 5750 mm | Second mode |
Line 3 | 4570 mm | First mode |
Line 4 | 6420 mm | Second mode |
Shock response input spectrum for three trial slug lengths on one line. The dashed vertical lines mark the first, second and third natural frequencies, showing how each slug length places a local peak of the spectrum on a natural frequency.
Two dynamic response methods in CAESAR II
Each line was modelled individually in CAESAR II using mechanical and fluid properties drawn from isometrics, piping specifications, process conditions, and a thermal photograph of the furnace casing.
| Time history | Shock response spectrum |
Principle | Numerical solution of the time-dependent equations of motion | System transformed into modal coordinates, each mode a single degree of freedom |
Output | Actual response over time | Maximum modal response; the real time history is lost |
Phase differences | Preserved between slug impacts on successive bends | Not represented; all modal contributions occur simultaneously |
Modal contributions | Not readily attributable to individual eigen modes | Identifies the modes to be eliminated or shifted up |
Conservatism | Results probably the more realistic of the two | Extremely conservative |
Both methods used a train of six consecutive slugs, a number chosen so that slug forces still act on bends early in the system when the flow reaches the last bend, and one that produces a stable input spectrum. The spectra were attached at the inlet and outlet of every elbow; the time-dependent force profiles were applied at the inlet and outlet of all bends and on reducers and tees. Modifications were developed using the spectrum results and then verified against the time history method.
Closing guide gaps and adding shock dampers
Guide supports on the long straight sections had clearances so large that thermal expansion did not close them at either operating or design conditions, leaving the system dynamically flexible and prone to slug-driven motion. The short sections near the furnace were similarly flexible.
The remedy was to reduce guide gaps and add guides, stops and a vertical restraint, and at one location on Line 1 to remove an existing guide, so that the problematic modes were eliminated or shifted upward in frequency. Stiffening the system increased static restraint reaction forces on Lines 1, 3 and 4, so flange and nozzle loads were re-checked. On Line 2 the additional supports sit at points with no thermal displacement in the restrained direction, so the reaction forces they introduce stay small, the largest being 4 kN on the stop at the dummy near the furnace. The flange at one of the restraint locations on Line 3 carries a 7.5 per cent higher total equivalent pressure, its in-plane and out-of-plane bending moment rising from 22.5 kNm to 27 kNm, and was checked according to ASME VIII Division 1, where the operating stresses are high but within allowable limits. On Line 4 the heat exchanger nozzle loads remained within the allowables given on the referenced drawing.
Rigid restraints alone did not remove every dominant mode. On Line 1 they brought the peak spectrum stress amplitude from 111 MPa to 88 MPa and lifted the lowest natural frequency from 2.1 Hz to 5.4 Hz, but left a local fourth mode at 7.2 Hz contributing 36 per cent of the stress.
Where thermal displacement was too large to permit additional rigid supports, Gerb viscofluid shock dampers were specified. These act in all six degrees of freedom and produce force proportional to velocity, so they resist fast dynamic motion while allowing slow thermal travel. CAESAR II cannot model the damping directly, so the dampers were represented as snubbers with an effective stiffness of 4000 N/mm in all three directions, a value derived from the selected RRD-300 vendor data, giving a support that is not fully rigid and better reflects reality. On Line 1 the damper eliminated that local mode.
The client preferred shock dampers over the initially advised snubbers.
Final Arrangement
- Line 1, furnace to reactor: five modifications on rigid restraints and one shock damper.
- Line 2, heat exchanger to furnace: three modifications on rigid restraints, being two guides and one stop, and one shock damper.
- Line 3, furnace to reactor: three modifications on rigid restraints and one shock damper.
- Line 4, heat exchanger to furnace: two modifications on rigid restraints, being one vertical restraint and one reduced guide gap, and two shock dampers.
That is thirteen rigid-restraint modifications and five shock dampers across the four lines.
Model of one of the four analysed lines, running between a vertical vessel and a horizontal exchanger, with the restraint positions used in the analysis shown along the run.
Stresses, frequencies and displacements after modification
The modifications brought every dynamic stress amplitude below the endurance limit of the ASME Section VIII Division 2 fatigue curve for an infinite number of cycles. On Lines 1, 3 and 4 this came at the cost of increased static restraint reaction loads.
Line | Stress amplitude, spectrum method, as built | Spectrum method, modified | Stress amplitude, time history, as built | Time history, modified | Lowest natural frequency, as built | Lowest natural frequency, modified |
Line 1 | 111 MPa | 31 MPa | 48 MPa | 22 MPa | 2.1 Hz | 5.4 Hz |
Line 2 | 97 MPa | 31 MPa | 17 MPa | 9 MPa | 2.5 Hz | 3.9 Hz |
Line 3 | 101 MPa | 37 MPa | 53 MPa | 26 MPa | 3.0 Hz | 6.0 Hz |
Line 4 | 154 MPa | 28 MPa | 42 MPa | 15 MPa | 2.4 Hz | 4.3 Hz |
Maximum dynamic displacements from the time history method fell from 10 mm to 4 mm on Lines 1 and 2, from 11 mm to 6 mm on Line 3, and from 21 mm to 5.3 mm on Line 4.
On Line 3 the client did not deem an additional guide pair on the long vertical section near the reactor feasible, so vibration in that section may persist. The 6.0 Hz value quoted for Line 3 excludes that section’s modes at 3.6 Hz and 3.9 Hz, which remain in the modified configuration.
Harmonic models tuned to the normal-operation measurements returned low dynamic stresses on both the as-built and the modified configurations, and the modifications also reduce the overall dynamic effects during normal running, although the maximum displacements did not fall in every case. All static stresses stayed within the ASME B31.3 allowables, for all ten assessed load cases from hydrotest to expansion at start-up conditions.
Close-up motion plot of a natural mode of one line at the vessel end, with restraint and damper elements shown in green.
What the work shows for two-phase piping systems
Guide clearances sized purely for thermal relief can leave a line dynamically flexible enough to resonate under slug impact. |
Reducing those clearances lowers the dynamic stresses, and it obligates a re-check of restraint, flange and nozzle loads, since the reaction forces the clearances previously kept small return to the restraints. Where thermal displacement does not allow additional rigid supports, shock dampers resist the dynamic motion while leaving slow thermal travel free. On this unit the rigid-restraint modifications shifted the low-frequency modes up, and the dampers removed local modes that remained after those modifications.
Damper travel is a constraint on installation. The 40 mm displacement limit of the standard units is exceeded at two of the five damper locations by the calculated thermal displacement at normal operating conditions, and is closely met at the others. The pistons may therefore be installed with an offset inside the housing, or special dampers allowing displacements up to 120 mm may be used. Where structural attachment is not deemed feasible, as on the long vertical section near the reactor on one line, residual vibration may persist.