The 10″ inlet and outlet lines of furnace H301 carry two-phase content during all process conditions. Under certain process conditions, staff reported feeling like getting seasick when standing on the platform of the furnace, and the piping was seen vibrating mainly near the furnace. The impact of these dynamic effects on the integrity of the lines had to be assessed.
A second, separate concern affected the outlet line. The section just downstream of the furnace had not been supported according to the original design, and because of the counteracting support functions it was expected that the as-built support would lead to static stresses exceeding the allowable stresses. Both concerns had to be resolved together, because altering the supporting to reduce the static stresses might lead to an increased level of vibrations.
Static analysis: expansion stress above the EN-13480 allowable
A CAESAR II pipe stress model, made for static purposes, was received from the client and modified after a site visit to reflect the observed support conditions; some of the furnace structural steel was included so that a realistic stiffness could be modelled for the supporting connected to the furnace. The static assessment of both lines, Sch. 80 in A312-TP321, was made against the EN-13480 code. The y-piece just downstream of the furnace is not a standard fitting described in that code, so the flexibility and stress intensification factor of its latrolets were calculated with the finite element package FE/Pipe, giving an in-plane SIF of 2.85 and an out-plane SIF of 4.364.
At the small branch of that y-piece the expansion load case gave a code stress of 582.3 MPa, 308.6% of the allowable, and the expansion stress at two 10″ elbows also exceeded the allowable, explained by the lateral restriction at the axial stop upstream of the expansion loop, where concrete restricts the lateral movement of at least 40 mm required at design conditions. The inlet line remained within the allowable stresses for every load case, although only after the structural steel was incorporated. For the outlet line, implementing the originally intended supporting design did not suffice, because two counteracting vertical support functions remained.
Flow regime assessment, slug loads and modal analysis
Before the vibration could be modelled the flow regime had to be determined. Slug flow, a moving liquid mass pushed by gases in between, is the most hazardous two-phase scenario mechanically, because the change in flow direction at elbow pieces, reducers and tees produces a change in momentum and an unbalanced reaction force. Six sets of process conditions, two for the inlet line and four for the outlet line, were assessed against the Taitel and Dukler flow pattern maps for horizontal flow, which covers the majority of the piping, and against the Baker map. All data points fall within the annular flow regime but near the transition to slug flow, and since the transition lines should be interpreted as broad bands rather than distinct lines, slug flow might occur from time to time, especially for the low vaporisation condition in the inlet line; conditions at higher temperature sit further into the annular domain. The vibrations are very likely caused by the unbalanced reaction forces of liquid slugs on the bends, although gentler vibrations might alternatively arise from unsteadiness within the liquid film layer of the annular regime.
With slug flow taken as the worst case, the slug forces were calculated from the gas velocity, the liquid velocity conservatively assumed equal to it and no gas assumed to pass the slug. Worst case liquid slug forces of 1160 N on the 10″ sections and 1145 N on the 5″ sections were obtained for the inlet line, and 1800 N on the 10″ section and 1240 N on the 6″ sections for the outlet line; only the magnitude was determined, not the duration of the impact. The larger slug loads for the outlet line explain the larger dynamic displacements found there.
The slug length, and therefore the frequency of occurrence, cannot be determined a priori, and no vibration data were available, so a slug sensitivity study was performed: the time-dependent slug loads were represented by a harmonic function with an amplitude equal to the calculated worst case forces, applied to all elbow pieces, with the slug intermittency covered from 0.1 to 15 Hz. This is an approximate and conservative approach, since slug load magnitudes would not in reality be constant across frequencies, and the resulting stresses and displacements are relevant only when the system operates within the slug flow regime.
A mode shape analysis preceded the harmonic analysis; for a piping system likely to be subject to multiphase flow it is recommended that all dynamic natural mode shapes have frequencies larger than 10 Hz. Ten mode shapes below 10 Hz were found for the inlet line and six for the outlet line, and the supporting of the two expansion loops of both lines is limited dynamically. The flexible inlet piping just upstream of the furnace agrees with the field reports, whereas the outlet piping near the furnace appears relatively stiff apart from a coupled piping and furnace mode at 9.5 Hz.
Support modifications on the inlet and outlet lines
To avoid creating very large static stresses by adding supports for a dynamic purpose, a different supporting philosophy was chosen for the inlet line. Two axial stops in the expansion loop near the furnace push the north-south expansion of that loop in the opposite direction, creating a pivoting effect on the section downstream, and a guide at the neutral pivoting point of that section keeps additional reaction loads off supporting fixed to the furnace. Three new supports are proposed and five existing supports modified, after which the highest code stress is 177.1 MPa in the expansion case, 92.2% of the allowable.
On the outlet line, three modifications with a static purpose bring the expansion stresses within the EN-13480 allowable limits, one of them removal of the concrete restricting the axial stop upstream of the expansion loop so that the piping has at least 40 mm of movement in the north direction, the axial stop itself being retained; the maximum code stress is then 166.1 MPa in the expansion case, 85.9% of the allowable. The client intends to implement these three changes first and the dynamic changes only during a shutdown, so the static-only configuration was assessed separately.
Releasing that axial stop in the guide direction introduces a mode shape at 8.5 Hz and raises the dynamic response, so two new supports and three modified supports are proposed on top of the static changes. One is a hold-down support with a 40 kN pre-load, whose friction acts dynamically as a damper while still allowing the 40 mm static thermal displacement in guide direction at that support, calculated to give a critical damping ratio of approximately 10% for the mode shape at 9.5 Hz; 3% is applied for the other slug load frequencies.
Fatigue assessment and reduced dynamic displacements
Structural integrity was assessed against the design fatigue curve of the ASME B&PV code, Section VIII Division 2, using Curve C, which applies to a stress range above 188 MPa, with dynamic stresses from CAESAR II multiplied by a factor 2 where they do not occur in a plain pipe section. On this basis the maximum dynamic stress amplitudes of the as-built lines remain below the endurance limit, so there is no piping integrity problem, but the dynamic displacements are considerable and might give field personnel the perception of an unsafe situation. With the three static modifications alone the amplitude remains just below the endurance limit, and after the full packages the amplitudes for both lines fall further below it.
On the inlet line the modifications reduce the maximum dynamic displacement from 2 mm to around 0.5 mm and raise the first mode shape from 3.4 Hz to 8.4 Hz, leaving three mode shapes below 10 Hz. On the outlet line the as-built maximum dynamic displacement is 10 mm at a slug frequency of 6 Hz, rising to 16 mm with the three static modifications alone; with the full package it is 4 mm at 13 Hz, three mode shapes remain below 10 Hz, and the static stresses stay within the EN-13480 allowable limits. Two dynamic stress peaks remain around 12 to 13 Hz, caused by mode shapes near the reactor, where there is no structural steel to attach additional supporting; these are not considered a significant issue, since no vibrations were reported near the reactor and the frequency is relatively high.
Static compliance, dynamic response and friction damping
The inlet line remained within the allowable stresses on every static load case and still carried ten mode shapes below 10 Hz, against a guideline that they should all lie above it.
- Static code compliance does not qualify a line for multiphase flow. The as-built supporting of the inlet line is sufficient from a static stress perspective, but it does not seem to be laid out for the dynamic phenomena related to multiphase flow.
- A remedy designed for static stress can worsen the dynamic response. On the outlet line, relieving the expansion stress raised the maximum dynamic displacement from 10 mm to 16 mm, and only the dynamic package brought it back down to 4 mm.
- Friction can damp where a rigid restraint cannot be used. The hold-down support with a 40 kN pre-load generates a friction force that acts dynamically as a damper, giving approximately 10% critical damping at the 9.5 Hz mode while still allowing the 40 mm static thermal displacement in guide direction at that support.
