A coil anchored at both ends, with the cross-over overloaded
In a refinery furnace, the radiant coil carries crude. Under a project designated high TAN, the existing carbon steel radiant coil piping is to be replaced by stainless steel, grade A312 TP316Ti. This account presents the stress analysis of the new coil arrangement.
The coil enters the furnace at grade level, runs along the refractory lined furnace wall making 21 loops, crosses over to the roof of the furnace, makes a further 8 loops against the roof, and leaves the furnace at roof level. The inlet and the outlet are at opposite furnace walls. The furnace consists of two compartments, each equipped with two geometrically mirror symmetrical radiant coil geometries, giving four coil pipes in the furnace. The coil is supported from the wall and the roof of the furnace by rest supports with a guiding function and a lateral clearance, so the coil is free to expand and is only restrained by frictional forces.
In the original arrangement both the inlet and the outlet were anchored at furnace wall level. The preliminary stress analysis showed that in that case the counter acting thermal expansion left the cross-over, and in particular the bends adjacent to the cross-over, overloaded in terms of stress.
Shifting the fixed point to the first bend downstream of the inlet
It was therefore decided to shift the fixed point from the coil pipe inlet to the first bend in the loop downstream of the inlet, model node 2031, which is located close to the opposite furnace wall. With the fixed point in that position the wall coil and the roof coil expand thermally in the same direction and the stress problem is resolved.
Because of the mirror symmetry of the coil pipe geometries, only one of the four coil pipes in the furnace was modelled. The remaining coils are identical or mirror symmetrical geometries, so their stress analysis results are identical. To increase the model accuracy, part of the furnace wall was included in the model, to simulate the thermal expansion of the furnace wall and thereby the thermal displacements of the support locations. The furnace wall was modelled as carbon steel, rigid, at 80 °C. The geometry and the supporting were modelled in accordance with the detail shown on four layout drawings, all at rev. 08. All flexibility of the bend to which the fixed point is attached was taken out of the model by the introduction of a double flanged elbow. Node numbers larger than 10000 belong to the furnace model and not to the coil model, and are irrelevant to the stress and load results.
Two load cases, from an installation temperature of 15 °C
The coil piping was assessed to the Dutch Rules for Pressure Vessels (RtoD ed 2005-9), in accordance with the applicable technical requisition. Two identical models were used, one for each load case, and in both the installation temperature was assumed to be 15 °C. For the coil material, A312 TP316Ti, Rm is 515 MPa, and Re is 205 MPa at 15 °C, 119.2 MPa at 495 °C and 69 MPa at 650 °C, the value at 650 °C being governed by Rmg tensile after 100,000 hr.
| Load case 1, maximum operating temperature | Load case 2, normal operating temperature |
Coil temperature | 650 °C | 430 to 495 °C, design temperature given as 495 °C |
Coil pressure | 14.5 Barg | 14.5 Barg |
Coil contents | Crude at 800 kg/m³ flashing to vapour at 2.7 kg/m³ | Crude at 800 kg/m³ |
Content distribution | Specific weight varying linearly between those values, from the 18th row in the furnace wall to the outlet | Coil filled |
The bend at the fixed point assessed as a local detail
The bend carrying the fixed point was assessed in its own right. A two dimensional rotationally symmetric thermal and stress model of the bend and the dummy stop was run for a start-up case with no coke deposition and for an end of run case, with a furnace gas temperature of 775 °C and radiation included, a gas temperature outside the furnace of 15 °C, a gas temperature in the dummy of 200 °C and a fluid temperature in the coil of 330 °C. The two cases differ in the film coefficient on the coil fluid, 600 W/(m²°C) at start-up against 60 W/(m²°C) at end of run.
A three dimensional finite element model of the same detail was then run in FE/Pipe for three load cases, sustained, thermal only and operating, with a bend temperature of 600 °C, a bend pressure of 1.45 N/mm² and an axial load on the dummy of 14.5 kN, made up of 11 kN from the downstream coil and 3.5 kN from the upstream coil. In that model the bend is 114.3 mm outside diameter and 8 mm thick at a bend radius of 101.6 mm, and the dummy is 60.32 mm outside diameter with a net thickness of 6.6 mm.
The calculated metal temperature in the bend is 423.9 °C to 433.3 °C at start-up and 651.2 °C to 656.1 °C at end of run, and the field falls along the dummy from the bend to the outside face of the wall. The stress intensity plots for the two cases range up to 227.8 MPa at start-up and 207.7 MPa at end of run. These sheets state no allowable, so no ratio is reported for them.
Stresses below the allowable limits in the coil and at the detail
With the fixed point at its new location, both the primary (sustained) and the secondary (thermal expansion) stresses in the coil piping were well below the allowable limits and hence acceptable, and the support loads were moderate. On that analysis the system as proposed is fit for purpose.
The local three dimensional model was assessed against ASME Section VIII Division 2, with the allowables derived from a cold allowable stress of 136.7 MPa and a hot allowable stress of 69 MPa. The highest ratio to allowable reported anywhere in that model is 63 per cent.
Stress category | Location | Load case | Calculated | Allowable | Ratio |
Primary membrane, Pl | Dummy adjacent to bend weld | Sustained | 54 MPa | 103 MPa, 1.5kSmh | 52 % |
Primary bending, Qb | Bend adjacent to dummy weld | Sustained | 83 MPa | 207 MPa, 3Smh | 40 % |
Primary plus secondary, Pl+Pb+Q, inner | Bend adjacent to dummy weld | Operating | 197 MPa | 309 MPa, 3Smavg | 63 % |
Primary plus secondary plus peak, Pl+Pb+Q+F, inner | Bend adjacent to dummy weld | Operating | 133 MPa | 494 MPa, Sa | 26 % |
The fatigue check at that location was computed with a stress concentration factor of 1.35 and gives 4,533,977 allowable cycles.
What the work shows for a coil with a wall section and a roof section
| The position of the fixed point sets the direction in which each section of the coil expands, and with it whether the counter acting expansion overloads the cross-over. |
With the inlet and the outlet both anchored at furnace wall level, the counter acting thermal expansion left the cross-over, and in particular the bends adjacent to it, overloaded in terms of stress. Shifting the fixed point to the first bend in the loop downstream of the inlet, close to the opposite furnace wall, brought the wall coil and the roof coil into thermal expansion in the same direction and resolved the stress problem.
The second point concerns temperature dependent material properties. For A312 TP316Ti, Re is 205 MPa at 15 °C and 69 MPa at 650 °C, the value at 650 °C being governed by Rmg tensile after 100,000 hr. The properties from which the allowable limits are derived therefore depend on the temperature at which the coil runs, so a flexibility arrangement has to be verified against the properties at that temperature.
The third point concerns the detail at the fixed point itself. The relocated fixed point is a three way dummy stop that passes through the furnace wall, so it carries both the reaction load and a thermal gradient, calculated in the three dimensional model as 600 °C to 250 °C along the dummy. Choosing where to put a fixed point settles a system level flexibility question and at the same time creates a local detail that has to be verified separately, here against a different code from the one applied to the coil piping.