The crude heating system serves one of two distillation trains: crude is preheated in a convection box, heated in the radiant section of the furnace and carried by a feed line to the tower. Crude heating generates two-phase flow, whose fluctuations impose the unsteady unbalanced loads at elbows and tees responsible for the vibration in the passes between the two and in the feed line.
Field inspection found no guides or axial restraining: the supporting appeared designed for static loads only, leaving the system flexible and sensitive to dynamic loads. Several rest supports showed clearances during operation, losing their function; steel plates appeared to have been added under several pipe shoes, but whether this restored the function was unclear. Vibration amplitudes were clearly visible and at some locations estimated in the order of centimetres peak to peak.
Snubbers added during the past few years were mostly installed laterally, whereas the most likely vibration direction due to two-phase flow is the longitudinal, axial pipe direction, for which they are not efficient; the lines stayed sensitive. The 36″ flange joint at the tower nozzle also leaked crude from the bottom after a trip from steady state, with temperature sensor data spanning 20°C to 377°C.
Beam Element Stress Modelling, Measured Vibration Spectra and Axisymmetric Flange FEA
A beam element model was built in CAESAR II as two uncoupled submodels: the passes between convection box and radiant section, and the piping from furnace to distillation tower.
The manifold, a non-standard fitting under ASME B31.3, was modelled by finite elements for its stress intensification factors. No detail was available for the 24×8″ tees, type PRBC Type 3 set-in, so these were conservatively modelled as unreinforced fabricated tees. Static assessment followed ASME B31.3 for ASTM 335 Gr. P5 against basic allowable stresses of 116.4 MPa at 299°C (submodel A) and 100.9 MPa at 386°C (submodel B).
An accelerometer recorded RMS acceleration in three directions at several locations; FFT gave the Fourier spectra, integrated to RMS velocity and displacement, scaled by √2 for absolute displacement magnitude. Velocities were classified against VDI 3842, the lower “Design” curve conservatively taken as the limit, velocities above it being critical.
Eigen modes were calculated; where a dominant frequency revealed a pronounced eigen mode, the model was tuned to match it. Each critical displacement was applied as a harmonic displacement and the amplitudes summed, constructive addition at every oscillation being conservative. The up and down vibration measured at 4.1 Hz corresponded to a modelled mode at 3.0 Hz, a difference attributed to estimated spring stiffnesses, so displacements were applied conservatively at 3.0 Hz. Amplitudes were evaluated against the ASME VIII-2 fatigue curve for carbon steel with a factor 2 applied to fittings: with no critical vibration above 10 Hz, a 20-year lifetime gives an allowable amplitude of 25 MPa in fittings, the cut-off.
The flange joint was modelled in AxiPRO as a 9° section with rotation symmetric boundary conditions, including bolt and spacer. The ¾” rotabolts’ 17.4 mm diameter is reduced by a 7 mm inside pin to an effective 15.9 mm, so stresses were factored by 1.20. Bolt-up at 71.6 kN per bolt, pressure at 2.69 barg, thermal loading and external loads were evaluated, the latter converted by the equivalent pressure rule with the gasket reaction diameter per ASME VIII-1 App. 2; the total pressure then gives 56 MPa axial stress in each of the 40 bolts, which does not add to the bolt stress state, bolt-up being much larger. Two steady state temperature fields were used, one from estimated film and conduction coefficients and one tuned to contact probe measurements.
Static Stresses and Dynamic Amplitudes at the Tee and Manifold, and Bolt Yield at the 36" Flange Joint
In submodel A static stresses stayed below allowable: sustained 54 MPa, 46% of the 116.4 MPa allowable, secondary 42 MPa at 14%. In submodel B, thermal expansion of the header to the South produced 381 MPa secondary stress at the tee at node 520, 132% of the expansion allowable, from reduced flexibility of the vertical 8″ connection at the sway-brace.
The East/West vibration measured at 2.5 Hz matched a modelled eigen mode at 2.6 Hz and produced a 29.9 MPa stress amplitude in the manifold (node 30); the up and down mode gave 22.1 MPa in the tee (node 520). Summed amplitudes were 43.2 MPa at node 520 and 41.6 MPa at node 30, both above the cut-off; elsewhere the amplitude gives at least 20 years of fatigue life.
A guide in the East/West direction at the rest support under the manifold is recommended to prevent the 2.5 Hz mode, which contributes 72% of the node 30 amplitude; with that mode removed the manifold amplitude falls to acceptable levels and node 520, less its 9.5 MPa contribution, to 33.7 MPa. Verification that the tee is of welding type brings that amplitude below 25 MPa. At the flange, bolt-up alone gives 583 MPa with the 1.2 factor, 97% of the bolt’s 601.9 MPa hot yield stress. With thermal load it reaches 937 MPa (conservative) and 730 MPa (tuned), both above hot yield, so the bolt is expected to deform plastically and sealing pressure to be lost on cooling. The two models give required bolt lengths of 219 mm and 170 mm against the existing 140 mm; at least 219 mm clamped length with spacers between nut and flange is recommended.
Results were anchored to measurement: modelled 2.6 Hz against measured 2.5 Hz, and film coefficients tuned to those probe measurements.
Conservative assumptions should be resolved before hardware is changed: a tee modelled as unreinforced fabricated carries a large stress intensification factor, so the amplitude at the branch is raised by the assumption rather than by a larger load, and verifying the tee detail may clear the remaining exceedance. For bolted joints on hot lines the condition to check is the forced displacement from the flange-to-bolt temperature difference rather than pressure, absorbed by bolt flexibility, which is set by clamped length.