Hydrocarbon Processing - September 2021 - 73

Process Optimization
For a sample study, an un-stiffened cylindrical shell with
20-mm wall thickness of material of construction 316 grade
SS was considered. The varied support-to-support length
and maximum allowable external pressure (MAEP) capabilities
have been determined as per various codes to obtain the
trend of conservativeness across the pressure vessel codes on
an external pressure design approach.
Assumed data for MAEP study and result table/plot.
TABLE 2 represents the MAEP per various pressure vessel
codes vs. the varied support-to-support length. FIG. 2 shows
the plot of the same data.
The MAEP, as tabulated/plotted here, was calculated based
on DBRs of various pressure vessel codes and other standards,
such as AWWA M11. Additionally, the MAEP based on the
DBA approach per ASME B & PVC Section VIII, Div. 2, Part
V was calculated using the procedure below and compared
with the DBR result set.
FIG. 3 represents a finite element model result of a linear
buckling analysis with a support-to-support length of 30 m
(with a 2,130-mm diameter SS 316 shell with 20-mm thickness
at 21°C) and with the same properties shown in TABLE 1.
Therefore (Eq. 3):10
MAEP 3[ ] =
=
where,
ΦB
βCR
Applied external preuure load multiplier (LM)
design factor B per part. V, div ii
(
1.03 4.20
2.5
= 2/βCR
= 1.73 kgf⁄cm2
= 2/0.80 = 2.5
= 0.8 for external pressure on the shell.
Similarly, for a varied support-to-support length starting
from 10 m to 60 m, the result was tabulated in the sixth column
(from left) of TABLE 2.
Observations/discussion on comparative study. ASME
B & PVC Section VIII, Div. 2 DBR for external pressure design10
is
the most conservative, followed by EN-13445/PD5500
and B & PVC Section VIII, Div.
2 design by rules per the data and plot
shown in TABLE 2 and FIG. 2.
Also in TABLE 2 and FIG. 2, DBA (linear
buckling, Type 1) per ASME B & PVC
Section VIII, Div. 2, Part V8
provides
a non-conservative result for certain
support-to-support length based on the
outer diameter of the pipe (in this case,
2,130 mm), after which the result converges
and the MAEP is almost independent
of support-to-support length.
The AWWA - M11/Timoshenko formula
(without an FOS) is basically an
overestimate of the MAEP compared to
other code rules and does not include the
effect of support-to-support length.
DBA: Type 1 linear buckling of actual
piping configuration/layout with
restrained condition. FIG. 3 represents
FIG. 3. FEA result with first Eigen mode
of buckling with LM 11.90. Inset figure shows
the buckled shape of the shell
at the first buckling mode.
)
(3)
a piping FEA buckling result under external pressure from
one piece of equipment to another (anchor-to-anchor), with
the properties shown in TABLE 1. A linear buckling analysis
(Type 1) was performed to evaluate the allowable external
pressure, as per the DBA approach of ASME B & PVC, Section
VIII, Div. 2, Part V.
Piping model properties. The piping model properties
have been kept the same as TABLE 1 except that the configuration/layout
was considered per FIG. 3 with the length of each
leg as 10 m, a total developed length of 30 m, and a restraint
boundary condition where both ends are fixed (equipment
end). Result summary: For the linear Type 1 buckling analysis,
Eq. 4 is used:
MAEP =
=
Applied external preuure
(
= 2/0.80 = 2.5
load multiplier (LM)
1.03 11.90
2.5
where,
ΦB
βCR
= 2/βCR
= 0.8 for the external pressure on the shell.
DBA Type 2 non-linear buckling analysis of actual
piping configuration with restrained condition. A nonlinear
Type 2 buckling analysis was performed on the same
piping configuration as FIG. 3 as per Part V of B & PVC,
Div. 2.8 FIG. 4 represents the non-linear FEA result plot, and
the inset figure shows the load factor plot for non-linear time
step analysis. Result summary: For the non-linear Type 2
buckling analysis11
, Eq. 5 is used:
MAEP =
=
Applied external preuure × Load factor
design factor ΦB per sect.−V,div −ii
(
15.29 × 0.7
2.08
= 5.14 kgf⁄cm2
where,
ΦB
βCR
= 1.667/βCR
= 1.667/0.8 = 2.08
= the effect of shell imperfection =
0.8 for external pressure on the shell.
DBA Type 1 and Type 2 analysis results
comparison. TABLE 3 represents
the summary of the buckling analysis
results from Sections IV and V for actual
piping configuration/layout with
restrained condition.
One intriguing observation is that the
non-linear Type 2 analysis MAEP without
the design factor stipulated by the
Div. 2 code is slightly less than that of the
linear Type 1 (10.70 kgf/cm2
vs. 12.25
kgf/cm2). However, for this particular
application, the final MAEP for the Type
2 analysis is greater than Type 1 due to a
significant difference in design factor for
these two types of analysis.12,13,14,15
Hydrocarbon Processing | SEPTEMBER 2021 73
)
(5)
design factor B per sect. V,B&PVC, div ii)
= 4.90 kgf⁄cm2
(4)
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