August 2022

Maintenance and Reliability

Pressure swing adsorption vessels fatigue analysis

The hydrogen (H₂) plant in a refinery produces high-purity (99.9+ vol%) H₂ products using a licensed pressure swing adsorption (PSA) purification process to fulfill the H₂ makeup needs of refinery hydroprocessing facilities.

The hydrogen (H₂) plant in a refinery produces high-purity (99.9+ vol%) H₂ products using a licensed pressure swing adsorption (PSA) purification process to fulfill the H₂ makeup needs of refinery hydroprocessing facilities, as shown in FIG. 1. The H₂ recovery/purification process consists of two trains. The PSA process purifies H₂ by filtering heavier gases/impurities from the process stream as it passes through an adsorber vessel. Each train has 12 identical adsorbers in four groups of three vessels. Each vessel goes through four stages in a cycle: adsorption, depressurization, desorption (regeneration) and repressurization. Adsorption at high pressure pulls all the heavier gases/impurities from the feed gas, producing 99.9% pure H₂. The vessels can handle 40,000 cycles/yr of pressure/de-pressure between 50 psig and 335 psig. This fluctuating pressure range allows for a fatigue design life of 20 yr.

Problem statement

The original equipment manufacturer (OEM) design completed during the manufacturing of the vessels was based on expectations of the pressure cycling range being between 5 psi and 340 psi. The operating cycle time was anticipated to be 12.08 min, which would result in 870,000 cycles in 20 yr. The fatigue design life was acceptable with negligible cumulative usage factors on almost all sections of the vessel except at the joint located between the skirt, and the bottom head was at 87.6%. As a result, the adsorber vessels were designated at 20 yr of design fatigue life with a safety margin of 12.4% at the previously mentioned location, all based on the nominal thicknesses of the vessel components. Since the PSA vessels were nearing their end of fatigue-designed life based on the OEM design, a complete replacement of 24 vessels was required as they were approaching 20 yr in service. However, since the H₂ plant has been in operation, the PSA vessels have experienced changed operating conditions, wherein the actual pressure cycling range was reduced to between 16 psig to 285 psig, as shown in FIG. 2.

For an accurate and representative remaining life assessment of the PSA vessel, the thickness of the vessel components was available, and the presence of objectionable flaws had been detected and geometrically characterized by non-destructive examination (NDE)-based inspections. The inspections confirmed that all 24 inspected vessels showed good health, apart from two vessels with linear indications on the shell parent plate and the circular and longitudinal weld seams. These factors established the need for a fitness-for-service (FFS) assessment. The estimated OEM fatigue design life calculations were deemed completed during the manufacturing of the vessels as an unacceptable technical basis for the forthcoming replacement strategy of PSA vessels.

A stress-fatigue evaluation in accordance with the American Society of Mechanical Engineers (ASME) Sec-VIII³ Div-2/American Petroleum Institute (API)-579¹ Annex B1.52 was required for the components (head, nozzle, flanges, shell and skirt) of the PSA vessels in pressure cyclical service to evaluate protection against failure from cyclical loading. In the assessment, embedded flaws were identified in the vessel wall during the inspection findings and classified as crack-like flaws. In addition to the stress-fatigue analysis, the API-579¹ FFS assessment was required to establish the behavior of the embedded flaws detected during the inspections of the vessel components. Based on the estimated fracture toughness properties of the vessel shell, this analysis would predict the future crack growth and further validate the life extension of the vessel.

Finite element modeling

The finite element method (FEM) with continuum elements was utilized in this analysis, which provided the total stress distribution in the vessel components. The PSA vessel was modeled as a 30° 3D-solid model based on the cyclical symmetry, as shown in FIG. 3.

This model enables the accommodation of the geometric details responsible for the predicted failure due to fatigue. A varying finite element mesh size ranging from 0.1 in.–0.25 in. was chosen appropriately to accommodate a minimum of five elements in the thickness direction of each pressure vessel component, as shown in FIGS. 5–10. The properties shown in TABLE 1 were obtained from ASME Sec-II Part-D2 and were utilized as input for the analysis.

For carbon steels with C ≤ 0.30% (all the components in TABLE 1), the Modulus of Elasticity E value of 29.31 × 10⁶ psi at a temperature of 105°F, and the Modulus of Elasticity E value of 29.5 × 10⁶ psi at a temperature of 70°F were utilized. The applied loads were appropriately factored down to a 30° (1/12th of full load) sector model basis. Symmetric boundary conditions were applied on the entire longitudinally cut edges of the 30° sector model. The loads per FIG. 4 were applied for the stress and finite element analysis (FEA) model.

The secondary stresses due to general thermal effects were not considered since it was assumed that there were no significant thermal gradients because the operating temperature for the adsorber vessel was 105°F. Stresses and strains produced by any load or thermal condition that does not vary during the cycle were not considered in a fatigue analysis, as the fatigue curves utilized in the evaluation were adjusted for mean stresses and strains and the degree of conservatism employed.

Analysis methodology

A fatigue assessment was carried out using the elastic stress analysis and equivalent stresses method. The FEM with continuum elements provided the total stress distribution, which was linearized on a stress component basis (membrane and bending stresses categories) using the stress-integration method, and the equivalent stresses were calculated using the maximum distortion energy (von Mises) yield criteria. The effective total equivalent stress amplitude was utilized to evaluate the fatigue damage.

The evaluation for fatigue was made based on the number of applied cycles of the equivalent stress range at every point in the vessel’s component. The allowable number of cycles was then evaluated to determine adequacy for the duration of operation to ascertain the suitability for continued operation. The assessment of the embedded flaws in the vessel shell was based on linear stress analysis, where the numerical model does not include the crack explicitly. The acceptance criteria were based on a two-parameter failure assessment diagram (FAD) approach to evaluate the combined effects of fracture and plastic collapse per API-579¹ Part 9. The stress values were post-processed to tie into existing K_I and σ_ref solutions, as the geometry of the embedded flaws were approximated by simple shapes addressed in Annex C and Annex D of API-579¹. The crack growth model based on the Paris equation was employed to estimate the remaining life of the vessels with a crack-like flaw based on the linear elastic fracture mechanics approach, where each increment of crack extension shall correlate to a certain increment of stress cycles.

FIGS. 5–10 show the FEM model and the quality of the mesh on the stress classification planes and the location of the stress classification lines (SCLs) selected at the critical locations of gross and local structural discontinuities for this analysis. The stress components will be integrated along the SCLs through the wall thickness to compute the equivalent linearized membrane, bending stresses and peak stress components.

The cases for analyses performed have been developed based on the objective of assessment and methodology for the two scenarios encountered during operation. The stress analysis was performed for the below scenarios:

• CASE I: OPE-MAX internal pressure of 285 psig
• CASE II: OPE-MIN internal pressure of 16 psig.

The stress results from Cases I and II were combined to determine the ΔS_n,k (primary + secondary, equivalent stress range) and ΔS_p,k (primary + secondary + peak, equivalent stress range). The fatigue analysis was completed for the scenario that the PSA vessels of both trains have witnessed 480,000 pressure cycles over the 15 yr in operation based on the available operating data for the uptime of the H₂ plant.

RESULTS—ELASTIC STRESS ANALYSIS

The equivalent stress consisting of primary + secondary + peak was derived from the highest value across the thickness of the section (head, nozzle, flanges, shell and skirt) and was produced by specified operating pressures and other mechanical loads, including the effects of gross and local structural discontinuities. The stress distribution plots have been provided in FIGS. 11–13. The graphical comparison of the simulated values of equivalent stress range (P + Q) at the various SCL locations has been illustrated in FIG. 14, whereas FIG. 15 shows the values of equivalent stress range (P + Q + F) at the various SCL locations. The maximum accumulated fatigue of 13.5% was calculated at SCL-11 and was found acceptable, as it was within the specified limits. The SCL-11 corresponds to the PSA vessel’s skirt section, which was also not a part of the vessel’s pressure boundary shell.

The damage factors were calculated based on the stress-fatigue analysis (K_e = 1.0 and K_f = 1.2 were assumed for the calculations), and all SCL locations in the adsorber vessels were found acceptable for continued operation well beyond the previously established fatigue-design life. However, due to embedded flaws, the effect of crack growth has been considered in the following section, which provides the additional criteria to limit the fatigue design life. This shall be based on the crack growth from its size (yr) to its critical size.

Crack criticality assessment

The PSA vessels in pressure cycling service containing the crack-like flaw are subject to loading conditions that may result in crack growth. As a result, the Level 1 and 2 assessment procedures in API-579¹ Part 9 do not apply as conditions are not satisfied. As the embedded flaw is anticipated to be subjected to subcritical crack growth during future operation, it has been evaluated using a Level 3 assessment procedure that provides the best estimate of the structural integrity of a component with a crack-like flaw. A Method A assessment has been utilized, such that the FAD was utilized for the acceptance criteria with user-specified partial safety factors (PSFs) based on a risk assessment.

The flaw characterization rules in API-579¹ will allow existing or postulated crack geometry to be modeled by a geometrically simpler one to make the actual crack geometry more amenable to fracture mechanics analysis. As a result, these linear indications were categorized as embedded cracks [FIG. 16 (cylinder—embedded crack, longitudinal direction and elliptical shape)] and [FIG. 17 (cylinder—embedded crack, circumferential direction and elliptical shape)] of API-579¹. The crack depth, length, angle and distance to other embedded cracks were typically required to be determined using the angle beam ultrasonic testing (UT) examination techniques, such as time of flight diffraction (TOFD) and pulse-echo techniques, as shown in TABLE 3.

The Mode I stress intensity factor solution representing a fourth-order polynomial stress distribution (KPECE2) was chosen to represent the cylinder—embedded crack, elliptical shape in the longitudinal direction and circumferential direction. For the FAD, the Level 2 recommended curve was used in the assessment (Level 3).

Stress analysis results from the previous section were used in a crack-like flaw assessment, such that the numerical model did not include the crack explicitly. This approach entails post-processing the stress values in such a way as to tie into existing K_I and σ_ref solutions in Annex C and Annex D, respectively. This approach was applied because it is best suited to the case where the PSA vessel’s shell could be approximated by simple shapes, such as a cylinder addressed in Annex C and Annex D of API-579¹. The stress results were linearized based on the crack location within the section thickness—this linearization method employed K_I estimation, as the stress distribution was uniform. The reference stress σ_ref was determined from the membrane and bending stresses derived from the linearization of stress results. The lower-bound estimate of fracture toughness 69.141 ksi√in. used in this assessment was based on the API-579¹ equation F.54 (Eq. 1):

K_IC = 33.2 + 2.806 exp [0.02(T – T_ref + 100)]              (1)

The primary stress, material fracture toughness and flaw size should be modified using the PSF. However, as the conservative estimate of lower-bound fracture toughness has been established, the applicable PSF equal to 1.0 would have normally been permissible. However, for conservatism, a PSF = 1.3 was used in this assessment.

The toughness ratio (K_r) was calculated based on the applied stress intensity due to the primary stress distribution and was plotted as the ordinate of the above FAD assessment point. The load ratio was calculated using the reference stress for primary loads (L^P_r) and plotted as the abscissa of the above FAD assessment point. The FAD plot in FIG. 18 shows that all existing flaws are well within the acceptable region and were deemed non-critical.

Crack growth assessment

It is anticipated that these cracks may grow by fatigue when the adsorber vessels continue operating, witnessing a PSA pressure cycle that results in cyclic stresses. Each increment of crack extension correlates to a certain increment of stress cycles.

The following basis was adopted for the crack growth assessment methodology:

1. During the crack growth, crack dimensions a and c will grow simultaneously, with the a/c ratio being assumed to remain constant during crack growth of 12.5%.
2. Crack dimension d₁ has been taken from the closest of the two edges, such that d₁ ≤ 0.5, and is assumed not to change during crack growth.
3. 1st limitation on crack growth (for those cracks that exceed the a/d₁ ≥ 0.8 criteria before exceeding the cut-off limit for steel): During the crack growth, crack dimension a will increase, resulting in a possible highest a/d₁ ≥ 0.8. As the crack face nears the thickness boundary, a becomes = d₁. This limiting/highest crack ratio a/d₁ = 0.8 will correspond to the critical size.
4. 2nd limitation on crack growth (for those cracks which exceed the cut-off limit for steel before exceeding a/d₁ ≥ 0.8 criteria): During the crack growth, crack dimension a will increase, resulting in a FAD position in the unacceptable region. The crack dimension will correspond to the crack ratio a/d₁. It is taken as the critical crack size when it touches this limit.

A crack growth model and associated constants were utilized to estimate the remaining life of the adsorber shell locations with the crack-like flaws based on a fracture mechanics approach. The Paris model was chosen for the assessment, as it accounted for environmental effects and was related to cyclic behavior da/dN. The fatigue crack growth equation was used with the Paris Equation (F-1.23) in FFS assessments completed in this analysis, as these equations are valid for materials with yield strengths less than or equal to 600 MPa (87 ksi), shown in Eq. 2:

(da/dN) = 8.61(10^–10)(∆K)^3.0       (2)

Where the below threshold stress intensity value (Eq. 3) was used:

∆K_th =1.8 ksi√in                         (3)

FIG. 19 provides the graphical illustration of the years required by each recorded crack to reach its respective critical sizes while the concerned PSA continued to operate in the H₂ plant. Following this assessment, the NDE-based inspection of the embedded flaws was completed after a 5-yr gap by entering the PSA vessels in an emptied state during the scheduled catalyst change-out activity. The UT-based TOFD technique was employed to establish the data of any growth of these previously detected flaws during this period. The results confirmed that there was no observable crack growth based on the prior baselined NDE results for characterized geometries of the flaws.

Takeaway

Based on the stress-fatigue analysis in accordance with the requirements of API-579¹, all SCL locations in the adsorber vessels were found to be acceptable for continued operation well beyond the previously established fatigue design life. Considering the presence of 18 embedded flaws in two out of the 24 PSA vessels, the least fatigue remaining life of 13 yr was estimated for at least three flaws. On average, all other remaining embedded flaws have a fatigue remaining life of at least an additional 20 yr. To understand that the operational PSA adsorber vessels had been assessed for life extension beyond their originally estimated fatigue design life, it was deemed essential that the embedded flaws be subjected to rigorous NDE-based monitoring to guarantee the continued safe and reliable operation of the PSA vessels. This analysis established that the actual fatigue life of these adsorber vessels exceeded the originally anticipated fatigue life of 20 yr. This had a positive impact on cost projection and lifecycle value analysis of these assets and will also help as the basis for a phased replacement approach of the PSA vessels in the near future. HP

LITERATURE CITED

1. “API-579, Fitness for Service,” 2022.
2. “ASME Boiler and Pressure Vessel Code ASME Sec-II, Material Properties,” 2021.
3. “ASME Boiler and Pressure Vessel Code ASME Sec-VIII, Pressure Vessels,” 2022.
4. “ANSYS Theory & Application Guide,” November 2013.

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