Introduction
Delayed coking is an important process used by most oil refineries to upgrade heavy crude oil to usable products including but not limited to gasoline, gas oil, and petroleum coke. Vertically-oriented insulated cylindrical pressure vessels commonly referred to as coke drums are used to facilitate this process. In practice, each process cycle consists of several stages with temperatures fluctuating between ambient and 482 °C (900 °F). Hence, the drums are subjected to excessive thermal-mechanical stresses due to severe thermal cycling. The most common failure mechanisms for coke drums are related to cracking, bulging deformation, and low cycle fatigue [1].
Several studies on coke drum failure and design optimisation have been conducted by using a combination of material testing, measurement data, and numerical simulation [2–11]. Ramos et al. [2] concluded that fatigue cracks form primarily in the clad material, circumferential shell seam welds, and on the skirt-to-shell attachment welds. A separate study conducted by Ramos et al. [3] gave evidence for the existence of localised hot and cold regions randomly occurring during the quenching stage. It was determined that the temperature difference between these hot/cold regions and the areas immediately adjacent to them can cause stresses and strains severe enough to result in bulging and cracking of the coke drum shell. This finding was confirmed later by thermocouple data published by Oka et al. [4]. More recently, a study carried out by Yan et al. [5] presented a statistical method to estimate the fatigue life of coke drums while taking into consideration the randomness of these hot and cold regions.
Different types of cracks found in coke drums and their likely sources were identified in a metallurgical study done by Penso et al. [6]. The deepest cracks were found in the heat affected zones of internal welds, while the largest number of cracks was found in the stainless steel clad material. The cracks were attributed to a number of possible sources such as corrosion, stress concentrations caused by weld geometry, cyclic thermal stress, differences in material properties such as coefficient of thermal expansion (CTE) and tensile strength, thermal shock, and heat affected zones around welds. Xia et al. [7] conducted a finite element analysis of a coke drum for a complete operating cycle. The results showed that the clad material experiences a biaxial stress cycling with a maximum value higher than that of the yield limit of the material. The critical stress value was attributed to bending caused by thermal cycling and differences in CTE between the clad and base materials. The authors suggest that low cycle fatigue is the main failure mechanism of the simulated coke drum, which aligns both with previous studies and the real case. Several studies [9–11] have since been conducted in an effort to improve the selection of materials for coke drums. Nikic [8] used material properties given in ASME Boiler and Pressure Vessel Code and conducted finite element analyses to explore the effect of different clad/base material combinations. Chen [9] and Rahman [10] carried out extensive material testing to more accurately characterize the thermal-mechanical material properties of common coke drum materials. In addition, the thermal-mechanical properties of weld material and heat-affected base metals were also experimentally determined [9].
One of the areas on the coke drum, which is most susceptible to fatigue failure, is the circumferential junction weld joining the skirt support structure to the vessel. The skirt support structure is used to support the vessel on a raised platform to allow the petroleum coke to exit through the conical bottom head at the end of each process cycle. Presently, the most commonly used type of skirt for coke drums is an insulated thin-walled cylindrical shell joined tangentially to the vertical portion of the vessel by a continuous fillet weld [11]. The shape of the skirt, location of attachment point on the vessel, and cyclic thermal stresses are the main factors leading to failure. Previous research [12] has shown that the inner side of the upper part of the skirt experiences the most severe thermal-mechanical strains. During each cycle, two peak strains occur at this point which are compressive at the beginning of the oil filling stage and tensile at the beginning of the water quenching stage. The measured strains exceed the yield strain of the material used, which indicates plastic deformation and potential fatigue failure. Furthermore, the location of the peak strains is in the heat-affected zone (HAZ) of the junction weld, which is a disadvantage. According to the 1996 API Coke Drum Survey [1], 56% of the surveyed drums had experienced cracking in the skirt-to-shell junction weld, while 43% of those reported cracks had propagated into the vessel shell.
Several attempts at optimizing skirt design have recently been made by minimizing thermal gradients and localized stresses at the skirt attachment weld in various ways. Stewart et al. [13] reported that Chicago Bridge and Iron (CB&I), a large multinational conglomerate engineering and construction company based out of Texas, owns patents to two skirt support structure designs named “T-Rex” and “wrapper”. The T-Rex skirt is joined tangentially to the vertical portion of the vessel using discontinuous attachment welds separated by slots which penetrate to the top of the skirt. Additionally, the design includes a hot box which, as mentioned in an earlier section, results in a more gradual thermal gradient. The main advantage of the T-Rex skirt is a less stiff point of attachment compared to a conventionally slotted skirt due to the discontinuous welds and slots which are considerably wider than the conventional slots. However, stress concentrations will inevitably occur near the slot ends and points of attachment. The effectiveness of this design would be determined by the magnitude of these elevated stresses compared to the conventional slot. The wrapper skirt is designed to support the coke drum primarily by bearing and frictional forces rather than load bearing weld attachments. To accomplish this, the skirt conforms to the geometry of the cone at the knuckle bend. Therefore, as the authors note, the skirt provides a flexible connection absent of the large pre-stresses associated with weld-induced heat-affected zones. Furthermore, the extended contact between the shell and the skirt theoretically improves the heat transfer between the two components, which may cause a reduction in thermally induced stresses compared to a conventional skirt. In the opinion of the author of the current study, the functionality of the wrapper skirt is heavily dependent on how similarly the constructed skirt behaves to the theoretical skirt. For example, the constructed skirt will likely not conform perfectly to the vessel, which would severely compromise its effectiveness.
Recently, a patent for a coke drum skirt filed by Lah [14] demonstrates a shift of tendency away from continuous circumferential fillet attachment welds. The basic principle of the design is to eliminate the restriction normally imposed by a conventional cylindrical shell skirt and to allow the drum to freely expand and contract instead. As shown in Fig. 1, the weight of the vessel is transferred through welded attachment plates and support ribs to circumferential horizontal plates which are free to slide in the radial direction relative to the vessel. The number of attachment plates and thickness of support ribs are dependent on the loading conditions as outlined by the Code. The horizontal slide plates are sandwiched between a lower supporting plate and upper retaining plates which prevent the coke drum from tipping or falling over. The lower plate is anchored to a concrete support similarly to the conventional skirt design. In order for the design to be effective, the surfaces of the plates are coated with a low friction material or machined to reduce friction. Theoretically, the added degree of freedom should reduce the stress level near the points of attachment. However, the design is inherently more complex than the conventional skirt in its geometry. The attachment plates, support ribs, and sliding plates all form re-entrant corners between one another, which may be the source of excessive stress concentration effects. The effectiveness of this design will be examined in more detail in a later chapter.
Sasaki and Niimoto [15,16] conducted a study in which an integral machined plate or forging, instead of the conventional weld build-up, was proposed as an alternative shell-to-skirt attachment. The authors cite high stress near the weld and heat affected zones and lower fatigue strength of the weld metal (compared to the base metal) as the principal cause of fatigue failure in the conventional skirt attachment. The fatigue life can be improved simply by having the high-stress area occur in base metal as opposed to the weld metal since the integral design, shown in Fig. 2, effectively replaces the weld build-up with base metal. The welds joining the drum body and skirt to the integral plate are aligned vertically, such that any forces associated with the weight of the coke drum and its contents are directed downwards and there is no bending moment on the support structure. Furthermore, the authors note that the machining process allows for a larger inner radius, more accurate dimensions, and complex shapes such as ellipses in order to further mitigate stress concentration effects. The results of a finite element analysis conducted by the authors provide conclusive evidence that the integral skirt attachment has a longer fatigue life than the conventional attachment method. However, a major drawback of this design is its manufacturing cost.
A study conducted by Oka et al. [12] examined the effect of hot feed injection time on the fatigue life of the shell-to-skirt junction area. In the study, four coke drums identical in geometry and cycle time were fitted with strain and temperature gauges to provide empirical data over each cycle. The hot feed injection time for each drum was averaged over 35–40 cycles and maximum axial strain data was used in conjunction with fatigue failure theory to determine operational life of each coke drum. The injection time was found to significantly affect the operational life, as an increase in injection time corresponded with a decrease in maximum axial strain. A similar study by Oka et al. [17] explored the effect of switching temperature on the fatigue life of the junction area. The switching temperature is defined as the temperature of the drum just before the hot feed material is injected. The same coke drums fitted with strain and temperature gauges from the previous study [12] were used. The results show that an increase in switching temperature improved operational life. The authors attribute the improvement of operational life to a decrease in thermal shock as a result of the difference between the coke drum and feed material temperatures. The results from these studies [12,17] suggest that the fatigue life of the skirt-to-shell junction is heavily influenced by the process cycle parameters.
One of the most inexpensive methods which has been employed to reduce stress in the skirt-to-shell junction weld is to add vertical slots to the upper portion of the skirt. The reduction of stress is attributed to the decrease of local stiffness near the junction due to the presence of the slots. While this method has been shown to be effective at protecting the junction weld [18], 89% of the drums with slotted skirts included in the 1996 API Coke Drum Survey experienced cracking around the slots [1]. Thus, it is apparent that further research into the design of skirt support structures and skirt slots may contribute to improved reliability of coke drums.
In one commonly implemented skirt slot design, the slots are thin relative to their circumferential spacing and terminate in drilled keyholes to mitigate the effects of stress concentration at the ends of each slot. However, despite these efforts cracks form in most of the skirts with this slot design as mentioned previously. To improve this design, a new slot design has been proposed which uses a larger width and keyhole radius. The advantages of the proposed design are as follows:
1) Further reduction in local stiffness near the junction due to wider slot;
2) Further mitigation of the stress concentration effect at slot ends due to larger keyhole radius.
The objective of this study is to determine the relative effectiveness of the proposed skirt slot design to the original design. Finite element analysis (FEA) is used to study the real-time temperature and stress/strain fields of coke drum models over several complete operating cycles. Special care is taken to ensure appropriate mesh density in the areas of interest and properly applied boundary conditions to simulate operating conditions. In addition to the slotted skirt models, a theoretical model of a coke drum with a solid (un-slotted) skirt is also solved to provide a basis of comparison.
Coke drum geometry and materials
Vessel and skirt geometry
The main dimensions for the vessel and skirt of the considered coke drum and detailed dimensions of the junction weld are shown in Fig. 3.
Skirt slot geometry
The skirt slot dimensions optimization follows two basic shapes as shown in Fig. 4. For thin slot design (on the left) dimensions L and d, for wide slot design (on the right) dimensions d, L and w are independently altered and a separate model is created for each incremental change. Through this detailed parametric study, an optimal slot dimension design has been obtained. In the following, only results of the original slot design and proposed optimal slot design will be presented.
The original slots are thin (3 mm) relative to their circumferential spacing (101.6 mm), and the keyhole radius is 3 times larger than the width of the slot.
The proposed optimal slot design is significantly wider (50.8 mm) while maintaining the circumferential spacing of the original slot design. Additionally, the slots are made shorter to prevent buckling failure in the slotted region. The dimensions of both designs are summarized in Table 1.
Tab.1 Dimensions for considered skirt slot designs |
| Parameter | Original slot value/mm | Proposed slot value/mm |
|---|---|---|
| d | 76.2 | 92.1 |
| L | 304.8 | 203.2 |
| w | 3.175 | 50.8 |
| rk | 9.525 | 25.4 |
| s | 101.6 | 101.6 |
Materials
The coke drum vessel consists of SA387 Gr.12 Cl.2 cylindrical shell cladded with SA240-TP410S stainless steel. The skirt support structure is made from the same SA387-12-2 material. The important thermal and mechanical properties for both materials are summarized in Table 2 [5]. The thermal conductivity, specific heat capacity, and density can be found from the ASME Boiler and Pressure Vessel Code (BPVC) Section II [19]. All material properties are temperature dependent.
Tab.2 Material properties of SA387-12-2 and TP240-410S [5] |
| Temperature, T/°C | SA387-12-2 | TP240-410S | |||||||
|---|---|---|---|---|---|---|---|---|---|
| Ea)/GPa | Syb)/MPa | Etc)/MPa | CTEd)/(10−6°C−1) | E/GPa | Sy/MPa | Et/MPa | CTE/(10−6°C−1) | ||
| 20 | 202.4 | 435 | 10714 | 12.3 | 178.0 | 272 | 13333 | 11.0 | |
| 100 | 192.9 | 393 | 10333 | 12.8 | 175.8 | 270 | 9705 | 11.2 | |
| 250 | 185.0 | 362 | 10000 | 13.6 | 161.1 | 220 | 11111 | 11.6 | |
| 480 | 170.7 | 330 | 8441 | 14.7 | 161.5 | 188 | 6878 | 12.1 | |
a) Young’s modulus; b) yield strength; c) tangent modulus; d) coefficient of thermal expansion |
Thermal-elastoplastic finite element model setup
Solid models of each of the considered skirt designs are analyzed using ANSYS® Workbench, Release 15.0. The element type is dependent on the analysis being solved. Within the thermal analysis, the SOLID90 20-node thermal element is used. The elements are replaced by SOLID186 20-node structural elements for the structural analysis. The SOLID186 element was chosen because it supports plasticity, stress stiffening, and large deflection and strain capabilities. The element sizes in the critical junction area and around the slot are set to 2 and 5 mm, respectively. The mesh is set to become increasingly coarse further away from the critical areas.
In areas where excessive penetration between elements is found, such as in the crotch formed by the shell and skirt, contact and target elements are specified. The convex outer surface of the toroidal vessel section is specified as the contact surface and meshed using 8-node CONTA174 surface elements, which is intended for general flexible-flexible contact analysis. The cylindrical inner surface of the skirt is specified as the target surface and meshed using the corresponding TARGE170 target segments. Suggestions for best practice provided by the ANSYS Help Guide were taken into account when selecting the contact and target surfaces. The contact type is set to ‘frictionless’ and the formulation method is set to ‘augmented Lagrange’ with a normal stiffness of 0.1. These settings allow for some penetration to occur for a significant decrease in computational expense. The maximum penetration found in any analysis solution in this chapter is about 0.02 mm.
Each of the solid models is given a similar mesh to ensure the differences in stress values come from changes in the geometry, rather than changes in the mesh itself. To accomplish this, mesh controls are used in various areas of the models to enforce element size and shape. These mesh controls are kept consistent between models. Sweep meshing is specified on all regular surfaces, such as rectangular and circular surfaces, to ensure a regular mesh that is easily duplicated. An unstructured mesh is used anywhere that a swept mesh will fail due to complex geometry, such as the area around the slot. One particular advantage of using an unstructured mesh around the slot area is the ability of the mesh to adapt to constantly changing geometries between models, as is the case in this optimization study. Due to the large circumferential deformation normally experienced by coke drums, bending stresses and contact near the junction corner are of particular concern. Thus, an adequate number of elements are specified through thickness in order to accurately capture the bending stress profile.
A total of 3 models are created: No slot (NS), original slot (OS), and proposed slot (PS). Several mesh constraints are deployed in order to ensure that the mesh of each model is as geometrically similar as possible. Due to the large computational expense of solving 3-D analyses, several steps are taken to simplify the models, which are explained as follows. As shown in Fig. 5, the model domain extends circumferentially between the midpoints of a column and a slot. In other words, a cyclic symmetric “slice” (shown on right side of Fig. 5) of the entire coke drum is taken as the model domain. Also, the models are cut radially at an axial distance equal to from the junction weld where r and t are the radius and thickness of the vessel, respectively. This distance represents the minimum distance for the calculation of surface temperature differences for the purposes of fatigue analysis screening as detailed in ASME Sec. VIII Div. 2 [20]. The section above the cut is discarded since it is not the focus of the current study.
The bilinear kinematic hardening model is used to simulate plasticity since the coke drum is subjected to cyclic thermal and mechanical loadings. In this way, low cycle fatigue and ratcheting behavior of the materials can be analyzed. To ensure stability of stress and strain results, three complete process cycles are solved. Results from the final process cycle of each solution are used to compare designs.
Boundary conditions
Each process cycle stage is modelled using convective and pressure loads specified to the inner surfaces of the vessel. The corresponding pressures P, heat transfer coefficients h, and bulk temperatures Tb are summarized in Table 3 [7]. Adiabatic boundary conditions are specified on insulated surfaces and all cut surfaces. Fixed support boundary condition is specified at the skirt bottom, where the skirt would normally be mounted to a concrete support. Circumferential displacement is set to zero at all cyclic symmetry cut boundaries. To simulate the discarded sections of the vessel, tensile loads equal to the loads caused by the internal and hydrostatic pressures and plane-remains-plane condition are applied to the cut surfaces.
Tab.3 Prescribed boundary conditions for each process stage [7] |
| Process stage | Time/s | h/(W·m−2·oC−1) | Tb /°C | P/kPa |
|---|---|---|---|---|
| Steam testing | 7200 | 113.4 | 142 | 300 |
| Vapor heating | 7200 | 54.9 | 316 | 300 |
| Oil filling | 36000 | 141.0 | 482 | 300+ Psb) |
| Water quenchinga) | 7200 | 345.0 | 93 | 300+ Ps |
| Unheading | 5400 | 63.7 | 38 | 120 |
a) Water quench thermal boundary conditions are applied with a rise speed of 3 mm/s to mimic the effect of rising water; b) Ps is the hydrostatic pressure due to the coke, oil and water slurry at 80% capacity of the drum |
Areas of interest
In the current study, the skirt slot designs are compared using equivalent stress and plastic strain data from two areas of interest:
1) The interface between the top of the skirt and weld build-up (“junction face”);
2) The solid body upon which the slot exists (“slot area”).
Data extraction from each area of interest is made possible by the creation of virtual faces and solid bodies within each model. The geometries of the junction faces and slot areas are made identical between models.
Thermal analysis of coke drum skirt
The temperature profile does not vary significantly between each skirt design. Thus, thermal results from only the NS model are shown and discussed. The calculated temperature history of a point on the inner surface of the junction face is shown in Fig. 6 for a single cycle. It is obvious from the plotted temperature history that the coke drum experiences several episodes of thermal shock corresponding to the start of each cycle phase, resulting in severe thermal gradients. Each of these points in time is labeled with a letter in Fig. 6. Evidently, the most severe temperature gradient along the skirt axial (z) direction occurs during the quenching phase. During the quench phase, the temperature of the vessel in contact with the water quickly drops while the skirt maintains a relatively elevated temperature.
Stress analysis of coke drum skirt designs
Skirt deformation
During the oil filling stage, the hot vessel encounters the cold skirt and forces it outward causing high compressive and tensile axial stresses on the inner and outer junction surfaces, respectively. The rising water level during the quench phase causes a bending effect in the vessel wall which travels upward as the quench stage progresses. This effect is referred to as “vasing” due to the resultant shape of the vessel caused by the contraction of the rapidly cooling material below the water level while the relatively hot material above remains in its expanded state. As the water level passes through the junction area, this effect causes further bending stresses in the weld. This deformation response, shown in Fig. 7, occurs in each of the coke drum analyses conducted in this study and do not differ significantly when compared to differences in stress and strain.
Junction face stress response
In each model, maximum junction equivalent stress and plastic strain occur on the inner junction surface during the water quenching stage. As can be seen by the numerical results shown in Figs. 8 and 9, the addition of slots causes a significant change in the stress response near the junction weld. The most notable change is a significant decrease in junction stress and plastic strain in the OS model compared to the NS model. Furthermore, it can be seen that the PS design is a slight improvement on the OS model from the standpoint of junction stress and plastic strain. The junction stress and strain results from the final process cycle of each analysis are summarized in Table 4.
Tab.4 Junction inner surface stress and strain result summary |
| Design | Equivalent stress/MPa | Equivalent plastic strain/% | |||
|---|---|---|---|---|---|
| Maximum | Range | Maximum | Range | ||
| NS | 452.5 | 258.5 | 0.92 | 0.69 | |
| OS | 369.5 | 256.3 | 0.17 | 0.14 | |
| PS | 373.9 | 258.8 | 0.16 | 0.10 | |
Slot area stress response
It can be seen from Figs. 8 and 9 that for both skirt slot designs, the maximum equivalent stress and plastic strain in the slot area occur at the top end (keyhole) of each slot during the water quenching stage. Additionally, both values occur at mid-thickness in both designs. The analysis results show that the maximum stress and plastic strain in the top keyhole of the OS model is higher than experienced by the junction face in the NS model. Furthermore, the PS model causes a significant reduction in maximum slot area stress and plastic strain when compared to the OS model. The top keyhole stress and strain results from the final process cycle of each analysis are summarized in Table 5.
Tab.5 Top keyhole stress and strain result summary |
| Design | Equivalent stress/MPa | Equivalent plastic strain/% | |||
|---|---|---|---|---|---|
| Maximum | Range | Maximum | Range | ||
| OS | 469.1 | 442.0 | 1.30 | 1.15 | |
| PS | 403.3 | 390.5 | 0.66 | 0.63 | |
Fatigue life estimation
The method used in this study to estimate the fatigue life is based on procedures and fatigue design curves from ASME Sec. VIII Div. 2, Part 5 [20]. The assessment relies on the calculation of an effective strain range Dεeff using equivalent stress and plastic strain ranges directly obtained from a finite element stress analysis. The effective strain range is then used to determine the effective alternating equivalent stress Salt. Finally, the permissible number of cycles N can be determined for the alternating equivalent stress from the fatigue curves also provided in ASME Sec. VIII Div. 2, Annex 3-F [20].
It should be noted that methods used in this study are not to be used to accurately predict fatigue life since previous research [15] has shown that the ASME fatigue curve does not perfectly match experimentally determined fatigue curves for materials similar to the coke drums in the current study.
The estimated junction area and slot area fatigue lives of each design are summarized and compared in Tables 6 and 7, respectively.
Tab.6 Estimated fatigue life of junction weld |
| Design | Deeff/% | Salt/MPa | N |
|---|---|---|---|
| NS | 0.69 | 636.8 | 1343 |
| OS | 0.28 | 256.7 | 29332 |
| PS | 0.24 | 221.9 | 51138 |
Tab.7 Estimated fatigue life of slot area |
| Design | Deeff/% | Salt/MPa | N |
|---|---|---|---|
| OS | 1.27 | 1174.0 | 282 |
| PS | 0.79 | 730.9 | 911 |
Conclusions
The OS design significantly improves fatigue life of junction weld compared to NS design. However, the skirt slot area has very short fatigue life. As predicted, the PS design further improves on junction weld fatigue life, while also providing an improvement on slot area fatigue life when compared to the OS design. The results from this study suggest that wider skirt slots with larger keyholes are better suited to protect the junction weld of coke drums than the current accepted design.