December 2021

Special Focus: Catalysts

Establish the maximum allowable pressure drop across the catalyst bed structure in a hydrocracker

The reaction section of a hydrocracker unit has three reactors configured in two stages.

The reaction section of a hydrocracker unit has three reactors configured in two stages. Most of the cracking takes place in the third reactor (of interest), which uses a high-activity hydrocracking catalyst in its top four beds. As the feed and recycle gas mixture enters the top of the reactor, it flows evenly over the reactor cross-sections before flowing down to each of the catalyst beds. The catalyst is designed to remove organic metals from the feed and is graded to provide maximum surface area to collect pipe scale and other solid particles with minimal impact on reactor pressure drop, as shown in FIG. 1.

As per original equipment manufacturer (OEM) specifications, each catalyst bed can handle an 85-psig pressure drop. Pressure differential transmitters measure the differential pressure over the reactor and can also be lined up to indicate the pressure drop over the top catalyst beds.

A steady increase in pressure drop is typically expected across the first catalyst bed structure during normal operations (FIG. 2). In operational runs, it was observed that this pressure drop approached the set value of 85 psig much earlier than the scheduled end-of-run (EOR) conditions. Operational adjustments were required to avoid this pressure drop from exceeding an 85-psig set value before the scheduled EOR, which often compromised the efficiency and productivity of the hydrocracker.

Problem statement

To establish the maximum allowable pressure drop that the reactor internal structural components can withstand, the mechanical strength of the a) catalyst bed support structure, b) expansion skirt structure, c) shell integral support ring, and d) expansion skirt plug weld to the shell wall, must be established. A preliminary assessment of the reactor’s mechanical design was completed, and several important characteristics of internal mechanical and fluid loads were identified for the existing maximum allowable 85 psid pressure drop permitted across the first catalyst bed and expansion skirt assembly, combined.

Basically, the dead weights for the reactor internals contributing toward the mechanical loads remain constant through the changing fluid loading scenarios. The correlation for pressure drop data across the various elevations of the reactor were obtained from the process trends of existing field instrumentation, which established that 86% of the pressure drop was found to occur across the catalyst beam structure of the first bed, while the remaining 14% was found to occur across the expansion skirt assembly of the first bed.

Among the contributions of the various fluid loads and the weights of the reactor internals contributing toward the mechanical loading of 398 psi on the top general surface of the shell integral support ring, the effect of the pressure drop across the first bed had the maximum impact of 94% when compared with the other. The contribution of the various fluid loads and the weights of the reactor internals toward the mechanical loading of 655 lb/in. (117 kg/cm) on the expansion skirt plug weld to shell is shown in FIG. 3. The effect of the pressure drop across the first bed had the maximum impact of 87% when compared with the other loads.

The complex geometry associated with the reactor internals, coupled with the thermo-mechanical loading, mandated an exhaustive and thorough stress analysis based on American Society of Mechanical Engineers ASME Sec-VIII Div-2 methodology.¹ The accurate stress distribution was simulated using the finite element method (FEM).

Finite element modeling

The reactor was modelled as a 90° 3D-solid model based on the cyclical symmetry shown in FIG. 4. This model enables the accommodation of the geometric details for applying the appropriate loads and boundary conditions. The catalyst weight, self-weight of the support beams and the grids, operating liquid static head, velocity head, pressure drop mechanical loading and temperature distribution were considered while establishing the mechanical strength of the shell integral support ring. Whereas, for establishing the mechanical strength of the expansion skirt plug weld to shell, the self-weight of the expansion skirt and the lower liquid distribution tray, liquid collection tray assembly, mixing chamber, rough liquid distribution tray assembly, the operating liquid static head, velocity head and pressure drop mechanical loading on each of the three trays, and temperature distribution, were considered.

Similarly, the mechanical strength of the individual structural components of the reactor internals was also established based on individual weight, fluid and temperature distribution loads. The temperature-dependent mechanical properties for reactor shell base metal A336 GrF22, weld overlay A312 Gr347, and shell internals A312 Gr321 were obtained from ASME Sec-II Part-D.²

Analysis methodology

The reactor internal structural components were evaluated primarily for protection against plastic collapse. Despite the steady nature of operating pressure and temperature of the reactors, the ratcheting and fatigue failure modes were only considered due to the hydrocracker unit startup and shutdowns cycles. The FEM with continuum elements provided the total stress distribution for evaluation and the simulated stresses were compared with stress limits defined in ASME Sec-VIII Div-2. This established the maximum load bearing capacity of the structure and, consequently, the maximum allowable pressure drop that the reactor can safely sustain.

Nomenclature used here includes:
P = Primary stress
P_m = General primary membrane equivalent stress
P_L = Local primary membrane equivalent stress
P_b = Primary bending equivalent stress
Q = Secondary equivalent stress
F = Peak stress produced by a stress conc. or a thermal stress over and above the nominal (P + Q) stress level
S = von Mises equivalent stress
S_m = Allowable stress intensity
S_y = Yield strength
S_alt = Alternating stress intensity
ΔS_n = Stress intensity range.

Temperature

A thermal stress was simulated for the reactor vessel as the thermal gradient along the radial direction was 40°F per 9 in. = 4.45°F/in., as shown in FIG. 5. The thermal gradient across the entire height (longitudinal) of the reactor was 8°F per 5 m = 0.04°F/in., which could be ignored as it was insignificant toward generating secondary stresses.

The FEM model in FIGS. 6 and 7 shows the quality of the mesh on the stress classification planes (SCPs) and the location of the stress classification lines (SCLs) selected at the critical locations of gross and local structural discontinuities for this analysis. The FEM model has been meshed using hexahedrons (20-node brick elements), which can effectively simulate the stress and deformation fields in solids in a structural analysis. The stress components were obtained from the linear elastic stress analysis and were then integrated along the SCLs through the wall thickness to compute the equivalent linearized membrane, bending stresses and peak stress components.

Catalyst bed support ring at Bed #1 (FIG. 6):

• SCL-1 is the shell thickness at the general area (P_m and P_b)
• SCL-2, -3 and -4 are the gross discontinuity of the shell (P_L and Q).

Expansion skirt assembly at Bed #1 (FIG. 7):

• SCL-1 is the gross discontinuity of the shell (P_L and Q)
• SCL-2 and -3 are the concentration plug weld-root, connecting the top and bottom rings (F)
• SCL-4 is the local discontinuity of the plug weld connecting the top and bottom rings (P_L and Q).

The cases for analysis were developed based on the “objective of assessment” and “methodology” for the below scenarios:

• Scenario 1: Internal design pressure (2,480 psig)
• Scenario 2: Radial thermal gradient of 760°F–720°F = 40°F per 9 in. = 4.45°F/in.
• Scenario 3: Internal maximum operating pressure 1 (2,226 psig)
• Scenario 4: Internal maximum operating pressure 2 (2,276 psig)
• Scenario 5: Internal maximum operating pressure 3 (2,326 psig)

Independent finite element analysis (FEA) simulations were completed for the following developed cases, as shown in TABLE 1.

The stress results from Case 1 were utilized to determine the primary membrane (P_m and P_L) and bending stresses (P_b) at the general and local locations for evaluating failure due to plastic collapse.

The stress results (P_m P_L P_b + Q) from Cases 2, 3 and 4 were combined with the zero-stress condition existing at equipment shutdown (ambient temperature and atmospheric pressure) to determine the ΔS_n (primary + secondary, equivalent stress range) required for evaluating failure due to cyclical loading (ratcheting).

The stress results (P_m P_L P_b + Q + F) from Cases 2, 3 and 4 were combined with the zero-stress condition existing at equipment shutdown (ambient temperature and atmospheric pressure) to determine the ΔS_p (primary + secondary + peak, equivalent stress range) and the S_alt.

The acceptance criteria for the fatigue evaluation were established as per ASME Sec-VIII Div-2. The applicable stress intensity factor was k = 1 for the design load condition for the kS_m.

The S_m values were chosen for the shell base metal = A-336 GrF22, as it is the lesser of the two materials considering the weld overlay (WOL):

• At a design temperature of 800°F, the S_m = 22.9 ksi.
• At an operating temperature of 740°F, the S_m = 23.3 ksi.

The S_m values for the shell internals A312 Gr321 are:

• At a design temperature of 800°F, the S_m = 16.9 ksi.
• At an operating temperature of 740°F, the S_m = 17.2 ksi.

The four basic stress intensity limits were satisfied as:

1. The allowable value of P_m produced by design internal pressure and other specified mechanical loads—but excluding all secondary and peak stresses—will be less than S_m.
2. The allowable value of P_L produced by design internal pressure and other specified mechanical loads—but excluding all secondary and peak stresses—will be less than 1.5S_m.
3. The allowable value of (P_L + P_b) produced by design pressure and other specified mechanical loads—but excluding all secondary and peak stresses—will be less than 1.5kS_m.
4. The allowable value of (P_L + P_b + Q) produced by design pressure and other specified mechanical loads—but excluding all secondary and peak stresses—will be less than 3.0kS_m.

Results: Elastic stress analysis

The values of the primary local (membrane + bending) stresses (P_L + P_b) at SCL-4 in the plug weld of the expansion skirt rings welded to the reactor shell (FIG. 8) were found to be slightly above the maximum allowable of 1.5S_m.

The maximum stress values obtained for the reactor internal structural components were acceptable and well within the design limits, corresponding to an 85-psid pressure drop across the first bed.

Further simulations for the Case 3 (116 psid) and Case 4 (159 psid) values of pressure drops across the catalyst structure and the expansion skirt structure of the reactor first bed were completed.

It was found that the stress (P_L + P_b) at the expansion skirt welded connection (SCL-4) location does not increase beyond 37 ksi even with an increased value of the pressure drop, which does not correlate to a primary load. It was found that the pressure drop load does not have a direct effect on values of the primary local (membrane + bending) stresses at SCL-4. Based on this finding, an important aspect was realized that the bending stress at SCL-4 in reality should be classified as “secondary” (Q), although membrane stress is classified as “primary” (P_L). As a result, evaluating (P + Q) at SCL-4 at its design-value load is no longer valid with a lower allowable stress limit of 1.5S_m. In the case of SCL-4, to evaluate the (P + Q) criteria, the more appropriate operating value loads were applied and a corresponding higher allowable stress limit of 3.0Sm was utilized. The maximum simulated stress values of the respective SCL-4 location were found to be well within the allowable limit of 3.0S_m.

For SCL-6 and SCL-7 in the longest catalyst support beam, as shown in FIG. 9, the stresses increased to a level that exceeded the corresponding maximum allowable stress intensity value of 16.9 ksi (S_m for primary general-membrane) and 25.23 ksi (1.5S_m for primary general-membrane + bending).

Takeaway

For the expansion skirt weld, at SCL-4 location on the internal expansion skirt weld as shown in FIGS. 8 and 10, it was found that the 9.5-in. thick reactor shell undergoes an insignificant amount of hoops deformation due to the internal pressure of 2,480 psi. The 1-in. thick internal expansion skirt rings are not designed for hoops stress, as the reactor shell internal pressure acts hydrostatically on all internal surfaces of expansion skirt rings. Owing to the weld between the internal expansion skirt rings and the shell, the shell imposes its hoop’s deformation on the internal expansion skirt rings at their connection (SCL-4). Although this hoop’s deformation is insignificant for the 9.5-in. thick reactor shell, but it becomes significant for the 1-in. thick internal expansion skirt ring, causing the internal expansion skirt ring to preferentially bulge at the welded connection (SCL-4) location, resulting in the above 36 ksi.

It has been found that the pressure drop load does not have a direct effect on values of the primary local (membrane + bending) stresses at SCL-4, but the stresses at the SCL-4 location are related to only the hoop’s deformation imposed by the shell on the internal expansion skirt rings at their connection (SCL-4). Therefore, the membrane + bending stresses are purely “secondary” (Q) in nature. In conclusion, the stress situation of 36 ksi will continue to exist at this magnitude with the presence of internal design pressure, irrespective of change in the magnitude of the pressure drop load.

For the catalyst support beam, an additional simulation was performed with a reduced pressure drop of 142 psid across the first bed, which resulted in a limiting value of the linearized stress intensity of 16.8 ksi at SCL-7 (in the direction of the beam axis) location (FIG. 9).

The analysis established that the longest catalyst support beam limits the pressure drop across the first bed of the reactor vessel to 140 psid. For operation of the hydrocracker reactor vessel, this pressure drop could be considered as the limiting value. HP

LITERATURE CITED

1. American Society of Mechanical Engineers (ASME), “Boiler and pressure vessel code ASME Sec-VIII Div-2.
2. American Society of Mechanical Engineers (ASME), “Boiler and pressure vessel code: Material properties,” ASME Sec-II.

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