Furnace F-501 at a refinery heats crude through radiant coils made of A312 TP316Ti stainless steel. Each coil enters the radiant section at grade level, runs 21 loops parallel to the refractory lined furnace wall, crosses over to the roof section, makes 8 further loops against the roof, and leaves the radiant section at roof level. The coil is supported from the wall and the roof of the furnace, basically on rest supports with a guiding function and a lateral clearance, so it is free to expand and is restrained only by frictional forces. The coil is analysed at 650 °C and at 495 °C, in both cases at 14.5 Barg.
In 2009 a stress analysis was performed for the radiant coil, which at that time replaced an existing carbon steel coil. The inlet and the outlet are at opposite furnace walls. The preliminary 2009 analysis showed that in the original arrangement, with both anchored at furnace wall level, the counteracting thermal expansion left the cross-over and in particular the bends adjacent to the cross-over stress wise overloaded. The anchor point was therefore moved from the coil pipe inlet to the first bend in the loop downstream of the inlet, close to the opposite furnace wall, so that the roof coil and the wall coil expand thermally in the same direction, and the stress problem was resolved. At the outlet side an anchor, a fixed point, was introduced close to the furnace wall penetration.
In 2013/2014 the furnace outlet piping was revised. The anchor foreseen in 2009 at the coil outlet wall penetration was removed and a new three way stop was introduced in the revised outlet piping at some distance from the outlet flange. Eliminating the anchor introduced an interaction between the revised outlet piping and the coil piping in the furnace: the axial thermal expansion of the revised outlet piping between the old anchor and the new three way stop has to be accommodated by the flexibility of the furnace coil.
How Header Expansion Defined the Most Unfavourable Outlet
The outlet piping of all furnace units is connected to a common header. The header expands thermally, so the connected furnace outlets are exposed to different header displacements. The outlet pipe connecting to the extreme end of the collector pipe experiences the largest of these displacements, and that most unfavourable outlet pipe was included in the analysis. A flange displacement was imposed at the downstream end of the outlet piping, taken from information received from the client. For the sustained case the imposed displacements are 27.6 mm in x, 94.7 mm in y and -250.3 mm in z, with rotations of 0.056, -0.238 and 0.086 degrees about x, y and z. For the operational case they are -26.0 mm in x, -3.0 mm in y and 7.0 mm in z, with rotations of -0.023, 0.043 and -0.025 degrees.
The analysis therefore had to cover both the stresses in the coil piping and the coil displacements at the side opposite the outlet, since displacements that are too large would let the coil clash with the furnace wall.
Extending the 2009 Model Rather Than Rebuilding It
Only one radiant coil was modelled. The furnace consists of several identical units. Each compartment is equipped with two geometrically mirror symmetrical radiant coil geometries, and the remaining coils are either identical or mirror symmetrical, so the stress analysis results are identical. The 2009 model was extended to include the applicable outlet pipe and its support, with a spec break at the coil pipe outlet flange between the A312 TP316Ti coil and the A 316 type outlet piping. In the 2009 edition of the report external loads were included at both the furnace inlet and the outlet; in the present analysis the external loads at the furnace outlet flange were eliminated, since the model now includes the relevant part of the outlet piping.
Part of the furnace wall was included in the model in 2009 to increase model accuracy, modelled as carbon steel, rigid, at 80 °C, to simulate the thermal expansion of the furnace structural wall and thereby the thermal displacements of the support locations. The geometry and the supports were modelled in accordance with the lay-out drawings listed in the report and the isometrics included in appendix 1. The analysis was performed the same way as the 2009 analysis, in accordance with technical requisition A00607/24/05 rev 2, and the assessment code is the Dutch Rules for Pressure Vessels, RToD, Stoomwezen, edition 2005-9. 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 last value based on Rmg tensile after 100,000 hr.
The two existing load cases were reused. In the first the coil is at 650 °C and only partly filled with crude, the content specific weight varying linearly between 800 kg/m³ and 2.7 kg/m³ from the 18th row in the furnace wall to the outlet, and the outlet pipe is at 425 °C with vapour as content. In the second the coil is at 495 °C and filled with crude, with the outlet piping at 425 °C and crude as content. The coil pressure is 14.5 Barg in both load cases. The outlet pipe was analysed for one temperature and pressure case only, 425 °C and 14.5 Barg, with the content differing between the two coil load cases. The installation temperature is assumed to be 15 °C in both models.
Handling Two Support Uncertainties in the Model
It was communicated by the client that the last support in the furnace upstream of the outlet wall penetration had been installed in the field as a spring support, but the spring stiffness and spring load could not be retrieved. In the adjusted 2014 model the spring support was introduced with a spring stiffness of 4.1 N/mm and a spring cold load of 1000 N, based on an educated guess. In principle the stress results are also acceptable if the support were removed completely.
A second uncertainty was the deflection of the supporting steel under the dummy support at node 6000. Two further models were added to simulate this deflection as a support gap of 10 mm, so that the support first moves 10 mm downwards before a support reaction force builds up. Four models were analysed in total: the maximum operating case and the normal operating case, each with and without the 10 mm gap.
Stresses Within RToD Allowable Levels and Displacements Left for Evaluation
The models show acceptable stress results for all cases, both normal operating and maximum operating, with the stresses within allowable levels in accordance with RToD, Stoomwezen. A deflection of up to 10 mm under the dummy support at node 6000 does not create a stress problem either. The support loads in the furnace are moderate and only slightly different from the 2009 results.
The coil displacements at the side opposite the outlet were listed for fifteen bends, for evaluation against the separation from the furnace wall. The largest values occur at bend node 70, where the displacement in x is 148.3 mm in the maximum operating case and 112.5 mm in the normal operating case. Two checks were left with the client: the dummy support at node 6000, to be evaluated load and deflection wise against the capability of the supporting steel, and the coil bend displacements, to be evaluated for clashes with the furnace wall. Upon successful verification of those two items the system as proposed is fit for purpose.
What the Reanalysis Shows for Comparable Furnace Layouts
Eliminating the outlet anchor and introducing the three way stop gave acceptable stress results, with the axial thermal expansion of the revised outlet piping accommodated by the flexibility of the furnace coil. The modelling decision behind that result was extending the analysis boundary to include the outlet piping and the imposed header displacement, so that the interaction was represented in the model rather than applied as external loads at the outlet flange.
On a shared header the outlet pipe connecting to the extreme end of the collector takes the largest imposed displacement, which is why the most unfavourable outlet pipe was analysed. Where spring support data could not be retrieved, the support was represented by an estimated stiffness and cold load, and the stress results are in principle also acceptable with that support removed completely. The two items on which the outcome depends are the capability of the supporting steel at node 6000 and the coil bend clearances to the furnace wall, and the fit for purpose statement is conditional on verification of both.