Part 2:
Background Material
64
I.
INTRODUCTION
Pressure vessels are used in many industries (e.g., hydrocarbon processing,
chemical, power, pharmaceutical, food and beverage). The mechanical design
of most pressure vessels is done in accordance with the requirements contained
in the ASME Boiler and Pressure Vessel Code, Section VIII. Section VIII is
divided into three divisions. This course provides an overview of pressure vessel
mechanical design requirements. It focuses on Division 1, highlights the
differences in scope among the three divisions of Section VIII, and discusses
several factors related to pressure vessel design that the ASME Code does not
cover. The following summarizes the main sections of the course:
•
•
•
•
General
-
Main Pressure Vessel Components
-
Primary Process Functions of Pressure Vessels
-
Scope of ASME Code Section VIII
-
Structure of Section VIII, Division 1
Materials of Construction
-
Material Selection Factors
-
Maximum Allowable Stress
Design
-
Design Conditions and Loadings
-
Weld Joint Efficiency and Corrosion Allowance
-
Design for Internal Pressure
-
Design for External Pressure and Compressive Stresses
-
Reinforcement of Openings
-
Flange Rating
-
Flange Design
-
Maximum Allowable Working Pressure
Other Design Considerations
-
Vessel Support
-
Local Loads
65
•
•
Vessel Internals
Fabrication
-
Acceptable Welding Details
-
Postweld Heat Treatment Requirements
Inspection and Testing
-
Inspection
-
Pressure Testing
This course is nominally only ½ day in length. Therefore, it cannot provide an indepth treatment of all aspects of pressure vessel design. However, the topics
are covered in sufficient depth to provide participants with a general
understanding of pressure vessel design requirements, to design pressure vessel
components to a limited extent, or to review pressure vessel designs prepared by
others. It also prepares individuals who require a more thorough understanding
of pressure vessel design to attend a more in-depth course or to acquire the
necessary knowledge on their own.
66
II.
General
This section describes the various components of pressure vessels through the
use of conceptual drawings. It also describes the scope of the ASME Boiler and
Pressure Vessel Code Section VIII, and the basic structure of Section VIII,
Division 1.
A.
Main Pressure Vessel Components
Pressure vessels are containers for fluids that are under pressure. They
are used in a wide variety of industries (e.g., petroleum refining, chemical,
power, pulp and paper, food, etc.)
1.0
Shell
The shell is the primary component that contains the pressure.
Pressure vessel shells are welded together to form a structure that
has a common rotational axis. Most pressure vessel shells are
either cylindrical, spherical, or conical in shape.
•
Figure 2.1 illustrates a typical horizontal drum. Horizontal
drums have cylindrical shells and are fabricated in a wide range
of diameters and lengths.
•
Figure 2.2 illustrates a small vertical drum. Small vertical drums
are normally located at grade. The maximum shell length-todiameter ratio for a small vertical drum is about 5:1.
•
Figure 2.3 illustrates a typical tall, vertical tower. Tall vertical
towers are constructed in a wide range of shell diameters and
heights. Towers can be relatively small in diameter and very tall
(e.g., a 4 ft. diameter and 200 ft. tall distillation column), or very
large in diameter and moderately tall (e.g., a 30 ft. diameter and
150 ft. tall pipestill tower).
A tower typically contains internal trays in the cylindrical shell
section. These internal trays (noted in Figure 2.3) are needed
for flow distribution. Several types of tower trays are available,
such as the bubble -cap, valve, sieve, and packed. The
particular type of tray used depends on the specific design
conditions and process application.
The shell sections of a tall tower may be constructed of different
materials, thicknesses, and diameters. This is because
temperature and phase changes of the process fluid – two of
67
the factors that affect the corrosiveness of the process fluid vary along the tower’s length. Alloy material or a corrosionresistant lining are sometimes used in sections of a vertical
tower where corrosion is a critical factor.
•
2.0
Figure 2.4 illustrates a typical reactor vessel with a cylindrical
shell. The process fluid undergoes a chemical reaction inside a
reactor. This reaction is normally facilitated by the presence of
catalyst which is held in one or more catalyst beds.
Head
All pressure vessel shells must be closed at the ends by heads (or
another shell section). Heads are typically curved rather than flat.
Curved configurations are stronger and allow the heads to be
thinner, lighter, and less expensive than flat heads. Figures 2.1
through 2.4 show heads closing the cylindrical sections of the
subject pressure vessels. Heads can also be used inside a vessel.
These “intermediate heads” separate sections of the pressure
vessel to permit different design conditions in each section.
68
Nozzle
A
Shell
Head
Head
Saddle Support
(Sliding)
Saddle Support
(Fixed)
A
Section A-A
Horizontal Drum on Saddle Supports
Figure 2.1
69
Head
Shell
Nozzle
Head
Support
Leg
Vertical Drum on Leg Supports
Figure 2.2
70
Nozzle
Head
Trays
Shell
Nozzle
Cone
Nozzle
Shell
Head
Nozzle
Skirt
Support
Tall Vertical Tower
Figure 2.3
71
Inlet
Nozzle
Head
Upper
Catalyst
Bed
Shell
Catalyst Bed
Support Grid
Lower
Catalyst
Bed
Outlet
Collector
Head
Outlet
Nozzle
Support
Skirt
Vertical Reactor
Figure 2.4
3.0
Nozzle
A nozzle is a cylindrical component that penetrates the shell or
heads of a pressure vessel. The nozzle ends are usually flanged to
allow for the necessary connections and to permit easy disassembly
for maintenance or access. Nozzles are used for the following
applications:
•
Attach piping for flow into or out of the vessel.
•
Attach instrument connections, (e.g., level gauges, thermowells,
or pressure gauges).
72
•
Provide access to the vessel interior at manways.
•
Provide for direct attachment of other equipment items, (e.g., a
heat exchanger or mixer).
Nozzles are also sometimes extended into the vessel interior for
some applications, such as for inlet flow distribution or to permit the
entry of thermowells.
Figure 2.5 shows a pressurized storage vessel with a spherical
shell.
Shell
Support
Leg
Cross
Bracing
Spherical Pressurized Storage Vessel
Figure 2.5
4.0
Support
The type of support that is used depends primarily on the size and
orientation of the pressure vessel. In all cases, the pressure vessel
support must be adequate for the applied weight, wind, a nd
earthquake loads. The design pressure of the vessel is not a
consideration in the design of the support since the support is not
73
pressurized. Temperature may be a consideration in support design
from the standpoint of material selection and provision for differential
thermal expansion.
4.1 Saddle Supports
Horizontal drums (See Figure 2.1) are typically supported at two
locations by saddle supports. A saddle support spreads the
weight load over a large area of the shell to prevent an
excessive local stress in the shell at the support points. The
width of the saddle, among other design details, is determined
by the specific size and design conditions of the pressure
vessel. One saddle support is normally fixed or anchored to its
foundation. The other support is normally free to permit
unrestrained longitudinal thermal expansion of the drum.
4.2 Leg Supports
Small vertical drums (See Figure 2.2) are typically supported on
legs that are welded to the lower portion of the shell. The
maximum ratio of support leg length to drum diameter is
typically 2:1. Reinforcing pads and/or rings are first welded to
the shell to provide additional local reinforcement and load
distribution in cases where the local shell stresses may be
excessive. The number of legs needed depends on the drum
size and the loads to be carried. Support legs are also typically
used for spherical pressurized storage vessels (See Figure 2.5).
The support legs for small vertical drums and spherical
pressurized storage vessels may be made from structural steel
columns or pipe sections, whichever provides a more efficient
design. Cross bracing between the legs, as shown in Figure
2.5, is typically used to help absorb wind or earthquake loads.
4.3 Lug Supports
Lugs that are welded to the pressure vessel shell (See Figure
2.6) may also be used to support vertical pressure vessels. The
use of lugs is typically limited to vessels of small to medium
diameter (1 to 10 ft.) and moderate height-to-diameter ratios in
the range of 2:1 to 5:1. Lug supports are often used for vessels
of this size that are located above grade within structural steel.
The lugs are typically bolted to horizontal structural members to
provide stability against overturning loads; however, the bolt
holes are often slotted to permit free radial thermal expansion of
the drum.
74
4.4 Skirt Supports
Tall, vertical, cylindrical pressure vessels (e.g., the tower and
reactor shown in Figures 2.3 and 2.4 respectively) are typically
supported by skirts. A support skirt is a cylindrical shell section
that is welded either to the lower portion of the vessel shell or to
the bottom head (for cylindrical vessels). Skirts for spherical
vessels are welded to the vessel near the mid-plane of the shell.
It is normally not necessary for the skirt bolt holes to be slotted
(as with lug supports). The skirt is normally long enough to
provide enough flexibility so that radial thermal expansion of the
shell does not cause high thermal stresses at its junction with
the skirt.
Vertical Vessel on Lug Supports
Figure 2.6
B.
Scope of the ASME Code Section VIII
Pressure vessels are typically designed in accordance with the ASME
Code Section VIII, even for locations outside the US. Section VIII is
divided into three divisions: Division 1, Division 2, and Division 3. Division
1 is used most often since it contains sufficient requirements for the
majority of pressure vessel applications.
75
The main objective of ASME Code rules is to establish the minimum
requirements that are necessary for safe construction and operation. The
ASME Code protects the public by defining the material, design,
fabrication, inspection, and testing requirements that are needed to
achieve a safe design. Experience has shown that the probability of a
catastrophic pressure vessel failure is reduced to an acceptable level by
use of the ASME Code.
The ASME Code is written to apply to many industries. Accordingly, it
cannot anticipate and address every possible design requirement or
service application. Therefo re, users must supplement the ASME Code
by specifying additional requirements that are appropriate for their
particular industry and applications.
1.0
Division 1
The ASME Code Section VIII, Division 1 applies for pressures that
exceed 15 psig and through 3,000 psig. At pressures below 15 psig,
the ASME Code is not applicable. At pressures above 3,000 psig,
additional design rules are required to cover the design and
construction requirements that are needed at such high pressures.
The ASME Code is not applicable for piping system components
that are attached to pressure vessels. Therefore, at pressure vessel
nozzles, ASME Code rules apply only through the first junction that
connects to the pipe. This junction may be at the following
locations:
•
Welded end connection through the first circumferential joint.
•
First threaded joint for screwed connections.
•
Face of the first flange for bolted, flanged connections.
•
First sealing surface for proprietary connections or fittings.
The Code also does not apply to no n pressure-containing parts that
are welded, or not welded, to pressure-containing parts. However,
the weld that makes the attachment to the pressure part must meet
Code rules. Therefore, items such as pressure vessel internal
components or external supports do not need to follow Code rules,
except for any attachment weld to the vessel.
The ASME Code identifies several other specific items where it does
not apply. These include:
76
•
Fired process tubular heaters (e.g., furnaces).
•
Pressure containers that are integral parts mechanical devices
(e.g., pump, turbine, or compressor casings).
•
Piping systems and their components.
Note that all detailed design requirements discussed in this course
are based on Division 1. Refer to Divisions 2 and 3 for comparable
information in those documents
2.0
Division 2, Alternative Rules
The scope of Division 2 is identical to that of Division 1; however,
Division 2 contains requirements that differ from those that are
contained in Division 1. Several areas where the requirements
between the two divisions differ are highlighted below.
•
Stress. The maximum allowable primary membrane stress for
a Division 2 pressure vessel is higher than that of a Division 1
pressure vessel. The Division 2 vessel is thinner and uses less
material. A Division 2 vessel compensates for the higher
allowable primary membrane stress by being a more stringent
than Division 1 in other respects.
•
Stress Calculations. Division 2 uses a complex method of
formulas, charts, and design by analysis that results in more
precise stress calculations than are required in Division 1.
•
Design. Some design details are not permitted in Division 2
that are allowed in Division 1.
•
Quality Control. Material quality control is more stringent in
Division 2 than in Division 1.
•
Fabrication and Inspection. Division 2 has more stringent
requirements than Division 1.
The choice between using Division 1 and Division 2 is based on
economics. The areas where Division 2 is more conservative than
Division 1 add to the cost of a vessel. The lower costs that are
associated with the use of less material (because of the higher
allowable membrane stress) must exceed the increased costs that
are associated with the more conservative Division 2 requirements
in order for the Division 2 design to be economically attractive.
77
A Division 2 design is more likely to be attractive for vessels that
require greater wall thickness, typically over approximately 2 in.
thick. The thickness break point is lower for more expensive alloy
material than for plain carbon steel, and will also be influenced by
current market conditions. A Division 2 design will also be attractive
for very large pressure vessels where a slight reduction in required
thickness will greatly reduce shipping weights and foundation load
design requirements.
3.0
Division 3, Alternative Rules For Construction of High
Pressure Vessels
Division 3 applies to the design, fabrication, inspection, testing, and
certification of unfired or fired pressure vessels operating at internal
or external pressures generally above 10,000 psi. This pressure
may be obtained from an external source, a process reaction, by the
application of heat, or any combination thereof. Division 3 does not
establish maximum pressure limits for either Divisions 1 or 2, nor
minimum pressure limits for Division 3.
C.
Structure of Section VIII, Division 1
The ASME Code, Section VIII, Division 1, is divided into three subsections
as follows:
•
Subsection A consists of Part UG, the general requirements that
apply to all pressure vessels, regardless of fabrication method or
material.
•
Subsection B covers requirements that apply to various fabrication
methods. Subsection B consists of Parts UW, UF, and UB that deal
with welded, forged, and brazed fabrication methods, respectively.
•
Subsection C covers requirements that apply to several classes of
materials. Subsection C consists of Parts UCS (carbon and low-alloy
steel), UNF (nonferrous metals), UHA (high-alloy steel), UCI (cast
iron), UCL (clad and lined material), UCD (cast ductile iron), UHT
(ferritic steel with properties enhanced by heat treatment), ULW
(layered construction), and ULT (low-temperature materials).
Division 1 also contains the following appendices:
•
Mandatory Appendices address subjects that are not covered
elsewhere in the Code. The requirements that are contained in these
appendices are mandatory when the subject that is covered is included
78
in the pressure vessel under consideration. Examples of Mandatory
Appendices are:
•
III.
-
Supplementary Design Formulas
-
Rules for Bolted Flange Connections with Ring Type Gaskets
-
Vessels of Noncircular Cross Section
-
Design Rules for Clamped Connections
Nonmandatory Appendices provide information and suggested good
practices. The use of these nonmandatory appendices is not required
unless their use is specified in the vessel purchase order. Examples of
nonmandatory appendices are:
-
Basis for Establishing Allowable Loads for Tube-to-Tubesheet
Joints
-
Suggested Good Practice Regarding Internal Structures
-
Rules for the Design of Tubesheets
-
Flanged and Flued or Flanged Only Expansion Joints
-
Half-Pipe Jackets
Materials of Construction
This section discusses the primary factors that influence material selection for
pressure vessels and the maximum allowable material stresses specified by the
ASME Code. The mechanical design of a pressure vessel can proceed only
after the materials have been specified. The ASME Code does not state what
materials must be used in each application. It specifies what materials may be
used for ASME Code vessels, plus rules and limitations on their use. But, it is up
to the end user to specify the appropriate materials for each application
considering various material selection factors in conjunction with ASME Code
requirements.
A.
Material Selection Factors
The main factors that influence material selection are:
•
Strength
•
Corrosion Resistance
•
Resistance to Hydrogen Attack
•
Fracture Toughness
79
•
Fabricability
Other factors that influence material selection are cost, availability, and
ease of maintenance.
1.0
Strength
Strength is a material's ability to withstand an imposed force or
stress. Strength is a significant factor in the material selection for a
particular application. Strength determines how thick a component
must be to withstand the imposed loads.
The overall strength of a material is determined by its yield strength,
ultimate tensile strength, creep and rupture strengths. These
strength properties depend on the chemical composition of the
material. Creep resistance (a measure of material strength at
elevated temperature) is increased by the addition of alloying
elements such as chromium, molybdenum, and/or nickel to carbon
steel. Therefore, alloy materials are often used in elevated
temperature applications.
2.0
Corrosion Resistance
Corrosion is the deterioration of metals by chemical action. A
material's resistance to corrosion is probably the most important
factor that influences its selection for a specific application. The
most common method that is used to address corrosion in pressure
vessels is to specify a corrosion allowance. A corrosion allowance
is supplemental metal thickness that is added to the minimum
thickness that is required to resist the applied loads. This added
thickness compensates for thinning (i.e., corrosion) that will take
place during service.
The corrosion resistance of carbon steel could be increased through
the addition of alloying elements such as chromium, molybdenum,
or nickel. Alloy materials, rather than carbon steel, are often used in
applications where increased corrosion resistance is required in
order to minimize the necessary corrosion allowance.
3.0
Resistance to Hydrogen Attack
At temperatures from approximately 300°F to 400°F, monatomic
hydrogen diffuses into voids that are normally present in steel. In
these voids, the monatomic hydrogen forms molecular hydrogen,
which cannot diffuse out of the steel. If this hydrogen diffusion
80
continues, pressure can build to high levels within the steel, and the
steel can crack.
At elevated temperatures, over approximately 600°F, monatomic
hydrogen not only causes cracks to form but also attacks the steel.
Hydrogen attack differs from corrosion in that damage occurs
throughout the thickness of the component, rather than just at its
surface, and occurs without any metal loss. In addition, once
hydrogen attack has occurred, the metal cannot be repaired and
must be replaced. Thus, it is not practical to provide a corrosion
allowance to allow for hydrogen attack. Instead, materials are
selected such that they are resistant to hydrogen attack at the
specified design conditions.
Hydrogen attack is a potential design factor at hydrogen partial
pressures above approximately 100 psia. Material selection for
these hydrogen service applications is based on API 941, Steels for
Hydrogen Service at Elevated Temperatures and Pressures in
Petroleum Refineries and Petrochemical Plants. API 941 contains a
family of design curves (the Nelson Curves) that are used to select
appropriate material based on hydrogen partial pressure and design
temperature.
4.0
Fracture Toughness
Fracture toughness refers to the ability of a material to withstand
conditions that could cause a brittle fracture. The fracture toughness
of a material can be determined by the magnitude of the impact
energy that is required to fracture a specimen using Charpy V-notch
test. Generally speaking, the fracture toughness of a material
decreases as the temperature decreases (i.e., it behaves more like
glass). The fracture toughness at a given temperature varies with
different steels and with different manufacturing and fabrication
processes.
Material selection must confirm that the material has adequate
fracture toughness at the lowest expected metal temperature. It is
especially important for material selection to eliminate the risk of
brittle fracture since a brittle fracture is catastrophic in nature. It
occurs without warning the first time the necessary combination of
critical size defect, low enough temperature, and high enough stress
occurs.
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4.1 ASME Code and Brittle-Fracture Evaluation
The following pressure vessel components must be considered
in brittle fracture evaluations:
•
Shells
•
Manways
•
Heads
•
Reinforcing pads
•
Nozzles
•
Tubesheets
•
Flanges
•
Flat cover plates
•
Backing strips that remain in place
•
Attachments that are essential to the structural integrity of the
vessel when welded to pressure-containing components
(e.g., vessel supports)
The Minimum Design Metal Temperature (MDMT) is the lowest
temperature at which the component is designed to have
adequate fracture toughness. It is a function of the component’s
material specification and thickness. The Critical Exposure
Temperature (CET) is the minimum metal temperature that can
occur at the same time as a significant membrane stress in the
vessel (e.g., at a pressure that is greater than 25% of the design
pressure). The CET is determined by either ambient conditions
or process conditions, whichever results in the lowest metal
temperature. While the terms MDMT and CET are often used
interchangeably, they are separate parameters.
Each component must be evaluated separately for impact test
requirements based on its material, thickness, and MDMT. In
all cases, the MDMT must be no greater than the CET.
Division 1 contains a simplified approach to evaluate the
potential for brittle fracture in carbon and low-alloy steel.
Material specifications are classified within Material Groups A
through D for the purpose of brittle fracture evaluation (See
Table 3.1, excerpted from Figure UCS-66 of Division 1). The
Code contains exemption curves for these Material Groups that
82
identify the acceptable MDMT versus thickness (0 in. through 6
in.) where impact testing (Charpy V-notch) is not required. The
curves shown in Figure 3.1 are excerpted from Figure UCS-66.
If the design conditions do not permit exemption in accordance
with this basis, then material impact testing at the specified CET
is required to permit its use. The Code specifies the necessary
impact test procedure and acceptance criteria.
83
Material Group Applicable Materials
Curve A
Curve B
Curve C
Curve D
Bolting and Nuts
•
All carbon and low alloy steel plates, structural shapes, and bars not listed in Curves B, C,
and D.
•
SA-216 Gr. WCB and WCC, SA-217 Gr. WC6, if normalized and tempered or water-quenched and
tempered.
•
SA-216 Gr. WCA if normalized and tempered or water-quenched and tempered
•
SA-216 Gr. WCB and WCC for maximum thickness of 2 in., if produced to fine grain practice and
water-quenched and tempered
•
SA-217 Gr. WC9 if normalized and tempered
•
SA-285 Gr. A and B
•
SA-414 Gr. A
•
SA-515 Gr. 60
•
SA-516 Gr. 65 and 70 if not normalized
•
SA-612 if not normalized
•
SA-662 Gr. B if not normalized
•
Except for cast steels, all materials of Curve A if produced to fine grain practice and normalized which
are not included in Curves C and D
•
All pipe, fittings, forgings, and tubing which are not included in Curves C and D
•
Parts permitted under Para. UG-11 shall be included in Curve B even when fabricated from plate that
otherwise would be assigned to a different curve
•
SA-182 Gr. 21 and 22 if normalized and tempered
•
SA-302 Gr. C and D
•
SA-336 Gr. F21 and F22 if normalized and tempered
•
SA-387 Gr. 21 and 22 if normalized and tempered
•
SA-516 Gr. 55 and 60 if not normalized
•
SA-533 Gr. B and C
•
SA-662 Gr. A
•
All material of Curve B if produced to fine grain practice and normalized which are not included in
Curve D
•
SA-203
•
SA-508 Cl. 1
•
SA-516 if normalized
•
SA-524 Cl. 1 and 2
•
SA-537 Cl. 1, 2, and 3
•
SA-612 if normalized
•
SA-662 if normalized
•
SA-738 Gr. A
See Figure UCS-66 of Division 1for impact test exemption temperatures for specified material
specifications.
Material Groups for Impact Test Exemptions
Table 3.1
84
140
120
Minimum Design Metal Temperature, F
100
B
A
80
60
C
40
D
20
0
-20
-40
-55
-60
Impact testing required
-80
0.394
1
2
3
4
5
Nominal Thickness, in.
(Limited to 4 in. for Welded Construction)
Impact Test Exemption Curves for Carbon Steels
Figure 3.1
A capital letter that designates the corresponding Material Group
appears above each curve in Figure 3.1. If the CET of a pressure
vessel is equal to or above that shown by the intersection of the
Material Group curve and component thickness, then impact testing
is not required. For example, a Group B material that is 1.5 in. thick
does not require impact testing as long as the CET of the vessel is
approximately 50°F or higher.
Division 1 has additional impact test requirements, some of which
are highlighted below. Refer to the code for additional information.
•
Impact testing is required for all welded construction that is over
4 in. thick if the MDMT is below 120°F.
•
Impact testing is required for non-welded construction (e.g., a
seamless, bolted heat exchanger cover plate) if the component
is over 6 in. thick and the MDMT is below 120°F.
85
•
Impact testing is not required for ASME B16.5 or B16.47 ferritic
steel flanges if the design metal temperature is no colder than 20°F.
•
Unless specifically exempt by Fig. UCS-66, materials with a
minimum yield strength greater than 65 ksi must be impact
tested.
•
Low temperature grades of steel that are impact tested to
conform to the particular material specification (e.g., SA-333 or
SA-350) may be used at design metal temperatures as low as
the impact test temperature.
•
If PWHT is done on P-1 material when it is not required by
ASME Code rules, its impact test exemption temperature may
be reduced by 30°F from that provided in Fig. UCS-66 (Ref.
Para. UCS-68), as long as the resulting exemption temperature
is no lower than -55°F. This recognizes the fact that a material’s
fracture toughness is improved after stress relief.
•
The MDMT of a vessel component may be further reduced if the
general primary membrane stress in the vessel component is
less than the design allowable stress. This could occur in
situations where the nominal thickness of the component is
greater than that required for the design conditions plus
corrosion allowance (Ref. Fig. UCS-66.1).
Division 1 also contains impact-testing procedures and impactenergy requirements for cases that are subject to impact testing.
Refer to Division 1 for details.
5.0
Fabricability
Fabricability refers to the ease of construction and to any special
fabrication practices that are required to use the material. Of special
importance is the ease with which the material can be rolled or
otherwise shaped to conform to vessel component geometry
requirements.
Pressure vessels commonly use welded construction. Therefore, the
materials used must be weldable so that individual components can
be assembled into the completed vessel. The material chemistry of
the weld area must be equivalent to that of the base material so that
the material properties and corrosion resistance of the weld area will
be the same as those of the base material.
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B.
Maximum Allowable Stress
One of the major factors in the design of pressure vessels is the
relationship between the strength of the components and the loads (i.e.,
pressure, weight, etc.) imposed upon them. These loads cause internal
stresses in the components. The design of a pressure vessel must ensure
that these internal stresses never exceed the strength of the vessel
components.
Pressure vessel components are designed such that the component
stresses that are caused by the loads are limited to maximum allowable
values that will ensure safe operation. Maximum allowable stress is the
maximum stress that may be safely applied to a pressure vessel
component. The maximum allowable stress includes a safety margin
between the stress level in a component due to the applied loads and the
stress level that could cause a failure.
1.0
Maximum Allowable Stress Criteria
The ASME Code Section II, Part D, Appendix 1 discusses the basis
used to establish maximum allowable stress values for materials
other than bolting for Division 1 vessels. A similar discussion is
contained in Section II, Part D, Appendix 2 for bolting, and Section
VIII, Division 1, Appendix P for low-temperature, cast or ductile iron
materials. Refer to these appendices for the specific safety margins
and other considerations used in determining the maximum
allowable stresses.
Two sets of allowable stress values are provided in Division 1 for
austenitic materials and for specific non-ferrous alloys. The higher
alternative allowable stresses exceed two-thirds but do not exceed
90% of the minimum yield strength of the material at temperature.
The higher allowable stress values should be used only where
slightly higher deformation of the component is not in itself
objectionable (e.g., for shell and head sections). These higher
allowable stresses are not recommended for the design of flanges or
other strain-sensitive applications. In the case of flanges, for
example, the larger deformation that would be expected if the higher
allowable stresses were used could cause flange leakage problems
even though a major flange failure would not occur.
2.0
ASME Maximum Allowable Stress Tables
Tables in the ASME Code Section II, Part D contain the maximum
allowable tensile stresses of materials that are acceptable for use in
87
ASME Code Section VIII pressure vessels. The maximum allowable
stress varies with temperature because material strength is a
function of temperature.
Figure 3.2 (adapted from Table 1A of the ASME Code Section II,
Part D) shows examples of maximum allowable Division 1 tensile
stress for three different material specifications.
The first part of Figure 3.2 identifies the Spec. No. (i.e., material
specification number), the grade (a material specification may have
multiple strength grades), the nominal chemical composition, the PNo. and Group No., and the minimum yield and tensile strengths in
thousands of pounds per square inch (ksi). This first part of Figure
3.2 also helps identify similarities that may exist among the material
specifications (e.g., nominal alloy composition, yield strength, and
tensile strength). In some cases, these similarities may help select
the material to use for pressure vessel fabrication, given specific
process conditions. The maximum allowable stress va lues as a
function of temperature are presented in the second part of Figure
3.2.
The information that is contained in the ASME Code Table 1A has
been condensed and reorganized in Figure 3.2 in two parts to help
Participants compare the material types and to note variances in
maximum allowable stress that are determined by temperature and
alloy composition.
88
ALLOWABLE STRESS IN TENSION FOR CARBON AND
LOW-ALLOY STEEL
Spec No.
Grade
Nominal
P-No.
Group No. Min. Yield
Composition
(ksi)
Carbon Steel Plates and Sheets
SA-515
55
C-Si
1
1
30
60
C-Si
1
1
32
65
C-Si
1
1
35
70
C-Si
1
2
38
SA-516
SA-387
55
60
65
70
C-Si
C-Mn-Si
C-Mn-Si
C-Mn-Si
Plate - Low Alloy Steels
2 Cl.1
½ Cr-½ Mo
2 Cl.2
½ Cr-½ Mo
12 Cl.1
1Cr-½ Mo
12 Cl.2
1Cr-½ Mo
11 Cl.1
1 ¼ Cr-½Mo-Si
11 Cl.2
1 ¼ Cr-½Mo-Si
22 Cl.1
2 ¼ Cr-1Mo
22 Cl.2
2 ¼ Cr-1Mo
55
60
65
70
1
1
1
1
1
1
1
2
30
32
35
38
55
60
65
70
3
3
4
4
4
4
5
5
1
2
1
1
1
1
1
1
33
45
33
40
35
45
30
45
55
70
55
65
60
75
60
75
ASME Maximum Allowable Stress (Table 1A Excerpt)
Figure 3.2
89
Min. Tensile
(ksi)
ALLOWABLE STRESS IN TENSION FOR CARBON AND LOW ALLOY STEEL
Max Allowable Stress, ksi (Multiply by 1,000 to Obtain psi)
for Metal Temperature, °F, Not Exceeding
Spec
1050 1100 1150 1200
No.
Carbon Steel Plates and Sheets
----SA-515
----SA-515
----SA-515
----SA-515
650
700
750
800
850
900
950
1000
13.8
15.0
16.3
17.5
13.3
14.4
15.5
16.6
12.1
13.0
13.9
14.8
10.2
10.8
11.4
12.0
8.4
8.7
9.0
9.3
6.5
6.5
6.5
6.5
4.5
4.5
4.5
4.5
2.5
2.5
2.5
2.5
13.8
15.0
16.3
17.5
13.3
14.4
15.5
16.6
12.1
13.0
13.9
14.8
10.2
10.8
11.4
12.0
8.4
8.7
9.0
9.3
6.5
6.5
6.5
6.5
4.5
4.5
4.5
4.5
2.5
2.5
2.5
2.5
-----
13.8
17.5
13.8
16.3
15.0
18.8
15.0
17.7
13.8
17.5
13.8
16.3
15.0
18.8
15.0
17.2
13.8
17.5
13.8
16.3
15.0
18.8
15.0
17.2
13.8
17.5
13.8
16.3
15.0
18.8
15.0
16.9
13.8
17.5
13.4
15.8
14.6
18.3
14.4
16.4
13.3
16.9
12.9
15.2
13.7
13.7
13.6
15.8
9.2
9.2
11.3
11.3
9.3
9.3
10.8
11.4
5.9
5.9
7.2
7.2
6.3
6.3
8.0
7.8
Plate-Low Alloy Steels (Cont'd)
----SA-387
----SA-387
4.5
2.8
1.8
1.1
SA-387
4.5
2.8
1.8
1.1
SA-387
4.2
2.8
1.9
1.2
SA-387
4.2
2.8
1.9
1.2
SA-387
5.7
3.8
2.4
1.4
SA-387
5.1
3.2
2.0
1.2
SA-387
-----
-----
-----
SA-516
SA-516
SA-516
SA-516
ASME Maximum Allowable Stress (Excerpt), cont'd
Figure 3.2, cont'd
Note that the allowable stresses at temperatures between
-20°F and 650°F are the same as the allowable stress at 650°F for each
material presented in Figure 3.2 (except for SA-387, Grade 22 Cl. 2). The
allowable stress increases for SA–387, Grade 22 Cl. 2 material at
temperatures below 650°F to a maximum of 18.8 ksi at 100°F and below.
Note that each material specification has different Types, Grades, and/or
Classes within it. In some cases, these differences are due to different
chemical compositions, while in other cases they may be due to the
particular steel making process that is employed. Higher strength grades
of a particular material specification have higher maximum allowable
stresses.
90
Exercise 1
Material Selection Based on Fracture Toughness
A new horizontal pressure vessel is being designed for an application where the
CET is -2°F. The material being used for the shell and heads is SA-516 Gr. 70
plate. The heads are hemispherical in shape and are ½ in. thick. The cylindrical
shell is 1.0 in. thick. The supplier has not specified any impact testing for the
shell and head plate. Is this correct? If this is not correct, what should be done
to correct the situation?
91
IV.
Design
A.
Design Conditions and Loadings
The mechanical design of a pressure vessel begins with specification of
the design pressure and design temperature. Pressure imposes loads
that must be withstood by the individual vessel components. Temperature
affects material strength and, thus, its allowable stress, regardless of the
design pressure. Some pressure vessels have multiple sets of design
conditions that correspond to different modes of operation. For example,
during its operating cycle, a reactor may have a high pressure and
moderate temperature during normal operation, but it may operate at a
much lower pressure and a very high temperature during catalyst
regeneration. Both sets of design conditions must be specified because
either one or the other may govern the mechanical design.
All pressure vessels must be designed for the most severe conditions of
coincident pressure and temperature that are expected during normal
service. Normal service includes conditions that are associated with:
•
Startup.
•
Normal operation.
•
Deviations from normal operation that can be anticipated (e.g., catalyst
regeneration or process upsets).
•
Shutdown.
Pressure vessels must also be designed for other loading conditions and
service factors that may apply in particular situations. These are
highlighted later.
92
1.0
Pressure
1.1
Operating Pressure
The operating pressure must be set based on the maximum
internal or external pressure that the pressure vessel may
encounter. The following factors must be considered:
1.2
•
Ambient temperature effects.
•
Normal operational variations.
•
Pressure variations due to changes in the vapor pressure
of the contained fluid.
•
Pump or compressor shut-off pressure.
•
Static head due to the liquid level in the vessel.
•
System pressure drop.
•
Normal pre-startup activities or other operating conditions
that may occur (e.g., vacuum), that should be considered
in the design.
Design Pressure
Generally, design pressure is the maximum internal pressure (in
psig), that is used in the mechanical design of a pressure
vessel. For full or partial vacuum conditions, the design
pressure is applied externally and is the maximum pressure
difference that can occur between the atmosphere and the
inside of the pressure vessel. Some pressure vessels may
experience both internal and external pressure conditions at
different times during their operation. The mechanical design of
the pressure vessel in this case is based on which of these is
the more severe design condition.
The specified design pressure is based on the maximum
operating pressure at the top of the vessel, plus the margin that
the process design engineer determines is suitable for the
particular application. A suitable margin must also be provided
between the maximum operating pressure and the safety relief
valve set pressure. This margin is necessary to prevent
frequent and unnecessary opening of the safety relief valve that
may occur during normal variations in operating pressure. The
safety relief valve set pressure is normally set equal to the
design pressure.
93
Pressure vessels, especially tall towers, may have liquid in them
during normal operation. The maximum height of this liquid
normally does not reach the top of the vessel. The liquid level
that is required for design is specified by the process design
engineer.
The hydrostatic pressure that is exerted by the liquid must be
considered in the design of vessel components upon which it
acts. Therefore, the pressure that is used to design a vessel
component is equal to the design pressure at the top of the
vessel, plus the hydrostatic pressure of the liquid in the vessel
that is above the point being designed (i.e., P BH = P T + γH). See
Figure 4.1.
94
PT = Design Pressure at
Top of Vessel
γ = Weight Density of
Liquid in Vessel
H = Height
of Liquid
PBH = Design Pressure of
Bottom Head
Design Pressure
Figure 4.1
2.0
Temperature
2.1
Operating Temperature
The operating temperature must be set based on the maximum
and minimum metal temperatures that the pressure vessel may
encounter. The operation and vertical length of tall towers, and
the presence of liquid in the bottom section, sometime result in
large temperature reductions between the bottom and top of the
vessel. It is permissible to specify different operating
95
temperatures at different elevations of such a pressure vessel,
as long as the temperatures can be accurately predicted. This
approach results in dividing the vessel into sections along its
vertical length. Each section is designed for the temperature
that it will encounter, rather than for the most severe condition at
the bottom of the vessel. Figure 4.2 illustrates this concept.
Section 4
(T-Z)
Section 3
(T-Y)
Section 2
(T-X)
Section 1
(T) F
Support Skirt
Grade
Temperature Zones in Tall Vessels
Figure 4.2
2.2
Design Temperature
The design temperature of a pressure vessel is the maximum
fluid temperature that occurs under normal operating conditions,
plus an allowance for variations that occur during operation.
2.3
Critical Exposure Temperature (CET)
The CET must also be specified for pressure vessel design to
ensure that materials that have adequate fracture toughness are
selected for construction (i.e., MDMT ≤ CET). Fracture
toughness was previously discussed.
96
3.0
Other Loadings
Paragraph UG-22 of Division 1 specifies the loadings that must be
considered to determine the minimum required thicknesses for the
various vessel components. These design loadings are as follows:
B.
•
Internal or external design pressure.
•
Weight of the vessel and its normal contents under operating or
test conditions.
•
Superimposed static reactions from the weight of attached
equipment (e.g., motors, machinery, other vessels, piping,
linings, insulation).
•
Loads at attached of internal components or vessel supports.
•
Wind, snow, and seismic reactions.
•
Cyclic and dynamic reactions that are caused by pressure or
thermal variations, or by equipment that is mounted on a vessel,
and mechanical loadings.
•
Test pressure combined with hydrostatic weight.
•
Impact reactions such as those that are caused by fluid shock.
•
Temperature gradients within a vessel component and
differential thermal expansion between vessel components.
Weld Joint Efficiency and Corrosion Allowance
The weld joint efficiency and corrosion allowance are additional design
parameters that are required to calculate vessel component thicknesses.
1.0
Weld Joint Efficiency
Weld joint efficiency (E) accounts for the quality of a welded joint
and for the concentration of local stress. This higher local stress is
due to local material or structural discontinuities.
Paragraph UW-12 of Division 1 specifies weld joint efficiencies to be
used to calculate component thicknesses. Figure 4.3 identifies weld
joint categories, Figure 4.4 identifies weld types, and Figure 4.5
defines weld joint efficiencies based on the type of weld and degree
of radiographic examination.
97
The majority of pressure vessel welds use a Type 1 joint design. A
Type 1 joint has an efficiency of either 0.85 or 1.00, corresponding
with spot or full radiographic examination, respectively.
C
C
C
A
A
A D
B
D
B
A
C
D
A
D
B
D
A
C
Weld Joint Categories
Figure 4.3
2.0
Corrosion Allowance
Corrosion, erosion, or abrasion causes vessel components to thin
during their operating life. To compensate for this thinning,
components must have their thicknesses increased over those that
are calculated using the ASME Code design formulas. Internal
corrosion/erosion-resistant linings are sometimes used as an
alternative to the use of greater component thicknesses.
Process design and materials engineers typically specify the
corrosion allowance. The corrosion allowance is based on the
expected corrosion rate for the vessel material in the anticipated
process environment. The corrosion rate is multiplied by the
nominal design life of the vessel (normally 20 years) to determine
the corrosion allowance.
C.
Design for Internal Pressure
1.0
Cylindrical Shells
The idealized equations for the calculation of hoop and longitudinal
stresses, respectively, in a cylindrical shell under internal pressure
are as follows:
σθ =
C
B
Pr
Pr
and σ1 =
t
2t
98
B
These equations assume a uniform stress distribution through the
thickness of the shell. Note that the longitudinal stress is half the
hoop stress. Since this is an idealized state, the ASME Code
formulas (See Figure 4.6) have been modified to account for nonideal behavior.
Butt joints as attained by double-welding or by other
means which will obtain the same quality of deposited
weld metal on the inside and outside weld surface.
1
Backing strip, if used, shall be removed after
completion of weld.
Single-welded butt joint with backing strip which
remains in place after welding.
2
For circumferential
joint only
3
Single-welded butt joint without backing strip.
4
Double-full fillet lap joint.
5
Single-full fillet lap joint with plug welds.
6
Single-full fillet lap joint without plug welds.
Types of Welded Joints
Figure 4.4
99
Joint
Type
Acceptable Joint Categories
1
A, B, C, D
Degree of
Radiographic Examination
Full
Spot
None
1.00
0.85
0.70
2
A, B, C, D (See ASME Code for limitations)
0.90
0.80
0.65
3
A, B, C
NA
NA
0.60
4
A, B, C (See ASME Code for limitations)
NA
NA
0.55
5
B, C (See ASME Code for limitations)
NA
NA
0.50
6
A, B, (See ASME Code for limitations)
NA
NA
0.45
Maximum Weld Joint Efficiency
Figure 4.5
Longitudinal stress can govern the design of a cylindrical section
when loadings other than internal pressure induce longitudinal
stresses that are greater than one half of the hoop stress due to
internal pressure. One example where this could occur is in the
lower section of a ta ll tower where wind or earthquake loading could
cause high longitudinal stresses. In these cases, the longitudinal
stress that is due to these other loads is added to the longitudinal
stress due to internal pressure. The total combined longitudinal
stress is then limited to the maximum allowable stress.
Figure 4.6 summarizes the ASME Code equations used to calculate
the minimum required thickness for common pressure vessel
components. The equations have also been rearranged to calculate
pressure and stress as a function of thickness.
100
Part
Thickness,
tp, in.
Pressure,
P, psi
Stress,
S, psi
Cylindrical shell
Pr
SE1 − 0.6P
SE1t
r + 0.6t
P (r + 0.6t)
tE 1
Spherical shell
Pr
2SE1 − 0.2P
2SEt
r + 0.2t
P (r + 0.2t)
2tE
PD
2SE − 0 .2P
2SEt
D + 0.2t
P (D + 0.2t )
2tE
Torispherical head
with 6% knuckle
0.885PL
SE − 0.1P
SEt
0.885L + 0.1t
P (0.885L + 0.1t)
tE
Conical Section
(α = 30°)
PD
2 cos α(SE − 0.6P)
2SEt cos α
D + 1.2t cos α
P (D + 1.2t cos α )
2tE cos α
2:1
Semi -Elliptical head
Summary of ASME Code Equations
Figure 4.6
Where:
P
=
Internal design pressure, psig. When used in the
pressure calculation equations, this is the MAWP.
r
=
Internal radius, in. Add corrosion allowance to
specified uncorroded internal radius.
S
=
Allowable Stress, psi. When used in the thickness
calculation equations, this is the allowable stress for
the material used. When used in the stress
calculation equations, this is the calculated stress for
the given pressure and thickness.
E1, E =
Longitudinal weld joint efficiency
tp
=
Required wall thickness for internal pressure of the
part under consideration, in.
t
=
Actual wall thickness (less corrosion allowance) of the
part under consideration, in.
D
=
Inside diameter, in. Add twice the corrosion
allowance to specified uncorroded inside diameter.
DL
=
Cone inside diameter at large end, in. Add twice the
corrosion allowance to specified uncorroded inside
diameter.
101
DS
=
Cone inside diameter at small end, in. Add twice the
corrosion allowance to specified uncorroded inside
diameter.
L
=
Inside crown radius of torispherical head, in. Add
corrosion allowance to specified uncorroded inside
crown radius.
α
=
One half of the apex angle of the cone at the
centerline, degrees.
α = tan−1
2.0
0.5(D L − Ds )
(Cone Length)
Heads
Figure 4.7 shows typical types of closure heads. Elliptical,
hemispherical, and torispherical are the most commonly used head
types. Note in Figure 4.7 that all head types but the conical have a
straight flange (sf) section, which simplifies welding the head to the
adjacent cylindrical shell section. The elliptical and torispherical
heads have an indicated head depth (h), which is measured from
the straight flange to the maximum point of curvature on the inside
surface.
102
t
t
R
sf
sf
ID
ID
Flanged
Hemispherical
t
t
h
sf
h
Flanged and Dished
(torispherical)
Elliptical
α
sf
α
t
t
r
ID
ID
Conical
Toriconical
Typical Formed Closure Heads
Figure 4.7
As with shells, the internal head dimensions that are used to
calculate the required thicknesses must first be increased to account
for the corrosion allowance. The corrosion allowance must then be
added to the calculated thicknesses. See Figure 4.6 for the ASME
Code equations that are used to calculate the wall thickness of each
head type.
103
sf
2.1
Elliptical Heads - The 2:1 semi-elliptical head is the most
commonly used head type. Half of its minor axis (i.e., the inside
depth of the head minus the length of the straight flange
section) equals one-fourth of the inside diameter of the head.
The thickness of this type of head is normally equal to the
thickness of the cylinder to which it is attached.
2.2
Hemispherical Heads - The required thickness of a
hemispherical head is normally one-half the thickness of an
elliptical or torispherical head for the same design conditions,
material, and diameter. Hemispherical heads are normally
fabricated from segmented sections that are welded together,
spun, or pressed. Hemispherical heads are an economical
option to consider when expensive alloy material is used. In
carbon steel construction, hemispherical heads are generally
not as economical as elliptical or torispherical heads because of
higher fabrication cost. Carbon steel hemispherical heads may
be economical for thin, very large-diameter vessels, or in thick,
small-diameter vessels.
The thickness transition zone between the hemispherical head
and shell must be contoured to minimize the effect of local
stress. Figure 4.8 shows the thickness transition requirements
that are contained in the ASME Code.
2.3
Torispherical Heads - A torispherical (or flanged and dished)
head is typically somewhat flatter than an elliptical head and can
be the same thickness as an elliptical head for identical design
conditions and diameter. The minimum permitted knuckle
radius of a torispherical head is 6% of the maximum inside
crown radius. The maximum inside crown radius equals the
outside diameter of the head.
104
th
l ≥ 3y
Thinner Part
Thinner Part
th
l ≥ 3y
Tangent Line
y
Length of required taper, l,
may include the width
of the weld
ts
y
ts
Thickness Transition Between Hemispherical Head and Shell
Figure 4.8
2.4
3.0
Intermediate Heads – An intermediate head may be installed
inside a pressure vessel to separate two sections that can have
different design conditions. Most head types can be used as
intermediate heads. Intermediate heads are evaluated for
internal pressure in the same way as external heads.
Conical Sections
Tall towers may have sections with different diameters along their
length. The transition between the different diameters is made in a
conical section. The most common design for a conical transition
does not have formed knuckles at the ends of the cone. The
cylindrical sections of different diameter are welded to each end of
the cone. The required thickness for internal pressure of a conical
shell without transition knuckles is calculated using the equation
shown in Figure 4.6. This equation assumes that half of the coneapex a ngle is no greater than 30°.
Formed knuckles are sometimes used at the cone-to-cylinder
transition in order to reduce localized stresses. When knuckles are
used, the transition is called toriconical. The use of knuckles is
105
mandatory when the cone half-apex angle exceeds 30°. Knuckles
are also sometimes used for smaller angles when there is concern
about potentially high local stresses at the cone -to-cylinder junction.
The ASME Code has design procedures for toriconical sections.
106
Sample Problem 1 – Design for Internal Pressure
The geometry and design data of a vertical cylindrical pressure vessel are
specified in Figure 4.9. Cost estimates are being prepared for this vessel. It is
your job to estimate the required component thicknesses.
A. What are the minimum required thicknesses for the two cylindrical sections?
Hemispherical
DESIGN INFORMATION
Design Pressure = 250 psig
Design Temperature = 700° F
Shell and Head Material is SA-515
Gr. 60
Corrosion Allowance = 0.125"
Both Heads are Seamless
Shell and Cone Welds are Double
Welded and will be Spot
Radiographed
The Vessel is in All Vapor Service
Cylinder Dimensions Shown are
Inside Diameters
4' - 0"
60' - 0"
10' - 0"
6' - 0"
30' - 0"
2:1 Semi-Elliptical
Sample Problem 1
Figure 4.9
107
Solution
1. The required wall thickness for internal pressure of a cylindrical shell is
calculated using the following equation from Figure 4.6:
tp =
Pr
SE1 − 0.6P
2. Since the welds are spot radiographed, E = 0.85 (from Figure 4.5)
3. S = 14,400 psi for SA-515/Gr. 60 at 700°F (from Figure 3.2)
4. P is given as 250 psig.
5. For the 6 ft. - 0 in. shell, calculate r (including corrosion allowance)
r = 0.5D + CA = 0.5 x 72 + 0.125 = 36.125 in.
tp =
Pr
250 × 36.125
=
= 0.747 in.
SE1 − 0.6P 14,400 × 0.85 − 0.6 × 250
t = tp + c = 0.747 + 0.125
t = 0.872 in. required including corrosion allowance
6. For the 4 ft. - 0 in. shell, calculate r (including corrosion allowance)
r = 0.5 x 48 + 0.125 = 24.125 in.
tp =
250 × 24.125
14,400 × 0.85 − 0.6 × 250
= 0.499 in.
t = 0.499 + 0.125
t = 0.624 in. required (including corrosion allowance)
108
B.
For the same vessel, what are the minimum required thicknesses for the
top and bottom heads?
Solution
1. Since both heads are seamless, E = 1.0.
2. Top Head - Hemispherical head (Equation from Figure 4.6)
r = 24 + 0.125 = 24.125 in.
tp =
Pr
250 × 24.125
=
= 0.21 in.
2SE1 − 0.2P 2 × 14,400 × 1 − 0.2 × 250
t = tp + c = 0.21 + 0.125
t = 0.335 in. required including corrosion allowance
3. Bottom Head - 2:1 Semi-Elliptical Head (Equation from Figure 4.6)
D = 72 + 2 x 0.125 = 72.25 in.
tp =
250 × 72.25
PD
=
= 0.628 in.
2SE − 0.2P 2 × 14,400 × 1 − 0.2 × 250
t = 0.628 + 0.125
t = 0.753 in. required including corrosion allowance
109
D.
Design for External Pressure and Compressive Stresses
Pressure vessels are subject to compressive forces such as those caused
by dead weight, wind, earthquake, and internal vacuum. Pressure vessel
components behave differently under these compressive forces than when
they are exposed to tensile forces (e.g., from internal pressure). This
difference in behavior is due to elastic instability, which makes shells
weaker in compression than in tension. In failure by elastic instability, the
vessel is said to collapse or buckle. The paragraphs that follow discuss
buckling of cylindrical shells due to external pressure. These basic
principles also apply to other forms of shells as well as to heads and to
compressive loads other than external pressure.
1.0
Overview
The critical pressure that causes buckling is not a simple function of
the stress that is produced in the shell, as is true with tensile loads.
An allowable stress is not used to design pressure vessels that are
subject to elastic instability. Instead, the design is based on the
prevention of elastic collapse under the applied external pressure.
This applied external pressure is normally 15 psig for full vacuum
conditions.
The maximum allowable external pressure can be increased by
welding circumferential stiffening rings (i.e., stiffeners) around the
vessel shell. The addition of stiffening reduces the effective buckling
length of the shell, and this length reduction increases the allowable
buckling pressure. These stiffener rings may be welded on either
the inside or the outside of the shell. Figure 4.10 illustrates the use
of stiffeners on a pressure vessel cylinder.
Other factors also affect the design of a pressure vessel for external
pressure since they also influence its resistance to buckling.
•
At elevated temperature, the material stress-strain curves are
nonlinear with no definite yield point and with a variable
modulus of elasticity.
•
The shell diameter and thickness are additional geometric
parameters that affect shell stiffness.
Paragraphs UG-28 and UG-33 of Division 1 contain procedures to
calculate the allowable external pressure on cylindrical shells and
110
heads, respectively. These calculation procedures use an iterative
approach.
Moment Axis of Ring
h/3
L
L
L
L
L
L
L
L
L
L
h/3
h = Depth of Head
Stiffener Rings on Pressure Vessel Cylinders
Figure 4.10
The maximum allowable compressive stress in a pressure vessel
component that is due to loads other than external pressure is
limited to the lower of the following:
2.0
•
The allowable tensile stress, or
•
A value, Factor B (See Figure 4.13), determined using the
external pressure calculation procedure.
Shells
The allowable external pressure of a cylindrical shell is a function of
material, design temperature, outside diameter, corroded thickness,
and unstiffened length. See Division 1 for procedural details.
3.0
Heads
The allowable external pressure of a head is a function of material,
design temperature, outside radius, head depth, and corroded
thickness. Stiffening rings a re not used to increase the allowable
external pressure of heads. The head thickness is increased as
required to achieve the required external pressure. When an
intermediate head is installed inside a pressure vessel, it may be
111
necessary to design it for an external pressure that is higher than 15
psig. See Division 1 for procedural details.
4.0
Conical Sections
The allowable external pressure of a conical section is a function of
material, design temperature, outside diameters at the small and
large ends, conical section length, apex angle, and corroded
thickness. The allowable external pressure may be increased by the
addition of stiffener rings, or by increasing the cone thickness. See
Division 1 for procedural details.
112
Sample Problem 2 - External Pressure Calculation
This Sample Problem demonstrates the external pressure design procedure for
one example of a cylindrical pressure vessel shell. Refer to Division 1 for
additional details and procedures to use for heads and conical shells.
A tall cylindrical tower is being supplied. The geometry and design conditions
are specified in Figure 4.11. The vendor has proposed that the wall thickness of
this tower be 7/16 in., and no stiffener rings have been specified. Is the 7/16 in.
thickness acceptable for external pressure? If it is not acceptable, what minimum
thickness is required? Round your answer upward to the nearest 1/16 in.
DESIGN INFORMATION
Design Pressure = Full Vacuum
Design Temperature = 500° F
Shell and Head Material is
SA-285 Gr. B, Yield Stress = 27 ksi
Corrosion Allowance = 0.0625"
Cylinder Dimension Shown
is Inside Diameter
4' - 0"
150' - 0"
2:1 Semi-Elliptical
(Typical)
Sample Problem 2 - Solution
Figure 4.11
Solution
1.
First, calculate the unstiffened design length, L, and the outside diameter,
Do, of the cylindrical shell, both in inches.
113
L = Tangent Length + 2 × 1/3 (Head Depth)
The tangent length is given as 150 ft.
Since the heads are semi-elliptical, the depth of each head is equal to ¼
the inside diameter of the shell.
Head Depth = 48 /4 = 12 in.
L = 150 × 12 + 2/3 × 12 = 1,808 in.
Calculate outside diameter D o, in.
Do = 48 + 2 × 7/16 = 48.875 in.
Next, determine the ratios L/D o and D o/t.
Accounting for the corrosion allowance,
t = 7/16 – 1/16 = 6/16 = 0.375 in.
Do/t = 48.875 / 0.375 = 130
L/D o = 1808 / 48.875 = 37
2.
Determine the value of A using Figure 4.12 and the calculated D o/t and
L/D o.
Note: If L/D o > 50, use L/D o = 50. For L/D o < 0.05, use L/D o = 0.05.
114
A = 0.000065
D o/t = 125
D o/t = 150
3
Do/t = 200
2
1.2
1.6
1.4
2.0
1.8
2.5
3.0
3.5
4.0
5.0
6.0
7.0
0
0
0
0
,00
00
40 = 50 = 60
=1
=8
t
t
t
t
/
/
/
/
Do
Do
Do
Do
8.0
10.0
12.0
14.0
16.0
20.0
18.0
D
25.0
30.0
35.0
40.0
50.0
D o/t = 300
=
/t
o
9.0
D o/t = 250
Length + Outside Diameter = L/D
o
L/Do = 37
Factor A
Figure 4.12
3.
Move horizontally to the line for the value of D o/t = 130 determined in Step
2. Use interpolation for intermediate values of D o/t. Move vertically
downward from this intersection point to determine Factor A.
A = 0.000065
4.
Using the value of A from Step 4, enter the applicable material chart. For
this case, the applicable material chart is Figure CS-1, excerpted in Figure
4.13. Move vertically in this chart to the intersection with the correct
design temperature line. Use interpolation for intermediate temperatures.
Note that in this case, the value of A is to the left of all the temperature
curves.
115
.00001
D o/t = 130
.0001
4 5 6 789
Do/t = 100
500°F
14,000
700°F
12,000
800°F
10,000
9,000
8,000
900°F
7,000
E-29.0 = 106
6,000
E-27.0 = 106
E-24.5 = 106
5,000
E-22.8 = 106
4,000
E-20.8 = 106
3,500
3,000
2,500
2
3 4 5 6 789
.00001
2
3
4
.0001
5 6 789
2
3 4 5 6789
.001
2
3
4
2,000
5 6 789
.01
FACTOR A
A=0.000065
Figure CS-1
Figure 4.13
5.
Calculate maximum allowable external pressure for the value of t, psi.
Pa =
2AE
3(D o / t)
Where:
E=
Young's modulus of elasticity at design temperature for the
material, psi. Do not confuse this parameter with the weld joint
efficiency, E, that is used elsewhere.
E = 27 x 106 psi from Figure CS-1 (Figure 4.13) at T = 500°F
Pa =
2 × 0.000065 × 27 × 106
3 × 130.33
Pa = 9 psi
116
.1
FACTOR B
up to 300°F
20,000
18,000
16,000
GENERAL NOTE: See Table CS-1 for tabular values
Since the calculated P a < 15 psi, the proposed 7/16 in. shell thickness is
not sufficient.
Note: In cases where A is located under the temperature curves,
determine the Factor B by reading horizontally across from the
intersection point. Then determine the maximum allowable external
pressure, P a, from the following equation:
Pa =
6.
4B
3(D o /t)
Now determine how thick the shell must be in order to have P a ≥15 psi.
This is a trial-and-error process, by which the thickness is increased until
an acceptable value is found. The intent is to use the thinnest shell that
will meet the requirement. Without going through all the iterations, we will
assume a new shell thickness of 9/16 in. and thus a corroded thickness of
½ in.
D o 48.875
=
= 97.75
t
0.5
L
= 37 (as before)
Do
A = 0.000114
Pa =
2 × 0.000114 × 27 × 106
= 15.7 psi
3 × 130.33
117
Exercise 2
Required Thickness for Internal Pressure
Determine the minimum required thickness for the cylindrical shell and heads of
the following pressure vessel:
•
Inside Diameter
-
10’ - 6”
•
Design Pressure
-
650 psig
•
Design Temperature
-
750°F
•
Shell & Head Material
-
SA-516 Grade 70
•
Corrosion Allowance
-
0.125”
•
2:1 Semi-Elliptical heads, seamless
•
100% radiography of cylindrical shell welds
•
The vessel is in an all vapor service (i.e., no liquid loading)
118
E.
Reinforcement of Openings
Calculation of the required wall thickness of a nozzle is one step in the
design of openings in pressure vessels. This is done in the same manner
as for any other cylindrical shell. There is more to the design of openings
than calculating the nozzle thickness, cutting a hole in the vessel, and
welding the nozzle in.
The ASME Code uses simplified rules to ensure that the membrane
stresses are kept within acceptable limits when an opening is made in a
vessel shell or head.
Dp
tn
trn
te
2.5t or 2.5tn + t e
Use smaller value
t
2.5t or 2.5tn
Use smaller value
Rn
tr
c
h
d
d or Rn + t n + t
d or Rn + tn + t
Use larger value
Use larger value
For nozzle wall inserted
through the vessel wall
For nozzle wall abutting
the vessel wall
Cross-Sectional View of Nozzle Opening
Figure 4.14
When the opening is made, a volume of material is removed from the
pressure vessel. This metal is no longer available to absorb the applied
loads. The ASME Code simplifies the design calculations by viewing the
nozzle -to-vessel junction area in cross section (See Figure 4.14). This
simplification permits the nozzle reinforcement calculations to be made in
terms of metal cross-sectional area rather than metal volume. The ASME
Code requires that the metal area that is removed for the opening must be
replaced by an equivalent metal area in order for the opening to be
adequately reinforced. The replacement metal must be located adjacent
119
to the opening within defined geometric limits. The replacement metal
area may come from two sources:
•
Excess metal that is available in the shell or nozzle neck that is not
required for pressure or to absorb other loads.
•
Reinforcement that is added to the shell or nozzle neck.
Figure 4.15 shows several typical nozzle design configurations including
examples of inserted versus abutted nozzles, pad reinforcement versus no
reinforcement, and self-reinforced nozzles. Self-reinforced nozzles are
forged fittings that have extra thickness in the nozzle-to-vessel junction
area to provide reinforcement.
Additional reinforcement must be provided if the vessel shell and nozzle
do not have sufficient excess thickness that is not required for pressure or
other loads. Additional reinforcement can be in one of the following forms:
•
A reinforcement pad.
•
Additional thickness in the vessel shell or head.
•
Additional thickness in the nozzle near its attachment to the vessel.
The reinforcement must be located within defined boundaries in order for it
to be considered effective.
120
(a)
Full Penetration Weld
With Integral Reinforcement
(a-1)
(a-2)
(a-3)
Separate Reinforcement Plates Added
(b)
(c)
(d)
(e)
Full Penetration Welds to Which Separate Reinforcement Plates May be Added
(f-1)
(f-3)
(f-2)
(f-4)
(g)
Self - Reinforced Nozzles
Typical Nozzle Design Configurations
Figure 4.15
If a reinforcement pad is used, its material should have an allowable
stress that is at least equal to that of the pressure vessel shell or head
material to which it is attached. No credit can be taken for the additional
strength of any reinforcement that has a higher allowable stress. If
reinforcement material with a lower allowable stress is used, the
reinforcement area must be increased to compensate for this.
121
The ASME Code specifies circumstances under which no nozzle
reinforcement eva luations are needed. It also provides rules to evaluate
the reinforcement of openings that are located near each other. These
situations are not discussed in this course. Refer to the ASME Code for
details. Sample Problem 3 illustrates the procedure used to evaluate
nozzle reinforcement.
Sample Problem 3 - Reinforcement of Openings
You are reviewing the nozzle design details that are proposed by a vendor for a
new drum and have selected an NPS 8 nozzle into the shell for detailed
evaluation. The vendor has not provided any reinforcement for this nozzle, and
he has not provided any calculations to verify that use of the nozzle without
reinforcement is acceptable.
Determine if this nozzle requires additional reinforcement. If it does, assume that
a 0.5 i n. thick reinforcement pad of SA-516, Gr. 60 material is used. What must
the minimum pad diameter be? Neglect any contribution of weld areas in these
calculations since they are insignificant. The information that is needed to
perform your evaluation is in Figure 4.16. Use Figure 4.14 as a reference.
122
DESIGN INFORMATION
Design Pressure = 300 psig
Design Temperature = 200°F
Shell Material is SA-516 Gr. 60
Nozzle Material is SA-53 Gr. B, Seamless
Corrosion Allowance = 0.0625"
Vessel is 100% Radiographed
Nozzle does not pass through Vessel Weld Seam
NPS 8 Nozzle
(8.625" OD)
0.5" Thick
0.5625" Thick Shell, 48" Inside Diameter
Sample Problem 3
Figure 4.16
123
Solution
Calculate the required reinforcement area, A
A = dtrF
Where:
d =
Finished diameter of circular opening, or finished
dimension (chord length at mid surface of thickness
excluding excess thickness available for
reinforcement) of nonradial opening in the plane
under consideration, in.
tr =
Minimum required thickness of the shell using
appropriate ASME Code formula and a weld joint
efficienc y of 1.0, in.
F =
Correction factor normally equal to 1.0.
Calculate the diameter, d.
d = Diameter of Opening – 2 (Thickness + Corrosion Allowance)
d = 8.625 – 1.0 + .125 = 7.750 in.
Calculate the required thickness of the shell, tr (See Figure 4.6)
tr =
Pr
300 × (24 + 0.0625)
=
= 0.487 in.
SE1 − 0.6P 15,000 × 1 − 0.6 × 300
Assume a value of 1.0 for F.
Calculate the required reinforcement area, A
A = dtrF
A = (8.625 - 1.0 + 0.125) × 0.487 × 1 = 3.775 in.2 required area
Calculate the available reinforcement area in the vessel shell, A 1, as the larger of
A11 or A 12
A11 = (E lt - Ftr)d
124
A12 = 2 (E lt-Ftr )(t + tn)
Where:
El =
1.0 when the opening is in the base plate away from
the welds, or when the opening passes through a
circumferential joint in the shell (excluding head to
shell joints).
El =
The ASME Code joint efficiency when any part of the
opening passes through any other welded joint.
F =
1 for all cases except integrally reinforced nozzles
that are inserted into a shell or cone at an angle to the
vessel longitudinal axis. See Fig. UG-37 for this
special case.
tn =
Nominal thickness of the nozzle in the corroded
condition, in.
A11 = (E lt - Ftr)d = (0.5625 - 0.0625 - 0.487) x 7.75 = 0.1 in.2
A12
= 2(E lt - Ftr ) (t + tn)
= 2(0.5625 - 0.0625 - 0.487) (0.5625 - 0.0625 + 0.5 - 0.0625)
= 0.0243 in.2
Therefore, A1= 0.1 in.2 available reinforcement in shell
Calculate the reinforcement area that is available in the nozzle wall, A2,
as the smaller of A21 or A22.
A21 = (tn-trn)5t
A22 = 2(tn-trn)(2.5 tn + te)
Where:
trn =
Required thickness of the nozzle wall, in.
125
r
= radius of the nozzle, in.
te = 0 if there is no reinforcing pad.
te = Reinforcing pad thickness if one is installed, in.
te = As defined in Figure UG-40 of the ASME Code for
self-reinforced nozzles, in.
Calculate the required thickness of the nozzle, trn (See Figure 4.6)
t rn =
tm =
Pr
SE1 − 0. 6P
300 (3.8125 + 0.0625 )
= 0.0784 in.
15,000 × 1 − 0.6 × 300
Calculate the available reinforcement in the nozzle neck, A 2, as the smaller of
A21 or A 22.
A21
= (tn - trn)5t = (0.5 - 0.0625 - 0.0784) x 5(0.5625 - 0.0625)
A21
= 0.898 in.2
A22
= 2(tn - trn) (2.5 tn + te)
= 2(0.5 - 0.0625 - 0.0784) [2.5 x (0.5 - 0.0625) + 0]
= 0.786 in.2
Therefore, A2 = 0.786 in.2 available reinforcement in nozzle
Determine the total available reinforcement area, A T, and compare it to the
required area.
AT = A 1 + A 2 = 0.1 + 0.786 = 0.886 in.2
Since A T < A, the nozzle is not adequately reinforced, and a reinforcement pad is
required.
126
Determine the required reinforcement pad area, A 5, and pad diameter, D p.
Since the required reinforcement area is 3.775 in.2 and the available
reinforcement area is 0.886 in.2 , we need to calculate the required area for the
reinforcement pad.
A5 = A - AT
A5 = (3.775 - 0.886) = 2.889 in.2 required area in reinforcement pad.
Now, calculate D p
te
= 0.5625 in. (reinforcement pad thickness)
A5
= [D p - (d + 2 tn)] te
2.889 = [D p - (7.75 + 2(0.5 - 0.0625)] 0.5625
5.136 = [D p - 8.625]
Dp = 13.761 in.
Therefore, the minimum required reinforcement pad diameter is 13.761 in.
Confirm that this diameter does not extend beyond the outer limit of the permitted
reinforcement zone in the shell, 2d.
2d
= 2 x 7.75 = 15.5 in.
Therefore, D p = 13.761 in. is acceptable.
F.
Flange Rating
ASME B16.5, Pipe Flanges and Flanged Fittings, provides steel flange
dimensional details for standard pipe sizes through NPS 24. ASME B16.5
flanges are acceptable for most pressure vessel nozzles and for shell
flanges when the vessel diameter corresponds to a standard pipe size.
Specification of an ASME B16.5 flange involves selection of the correct
material and flange "Class." The paragraphs that follow discuss the flange
specification process in general terms.
127
Flange material specifications are listed in Table 1A in ASME B16.5, a
portion of which is excerpted as Figure 4.17. The material specifications
are grouped within specific Material Group Numbers. For example, if the
pressure vessel is fabricated from carbon steel, ASTM A105 is an
appropriate flange material specification in most applications. ASTM A105
material is in Material Group No. 1.1. Refer to ASME B16.5 for additional
acceptable material specifications and corresponding Material Group
Numbers.
Material Groups
Material
Group
Number
Nominal
Designation
Steel
1.1
Carbon
1.2
C-Mn-Si
Carbon
2 ½ Ni
3 ½ Ni
Product Forms
Forgings
Castings
Plates
Spec. No.
Grade
Spec. No.
Grade
Spec. No.
Grade
A105
A350
----A350
-LF2
----LF3
A216
--A216
A352
A352
A352
WCB
--WCC
LCC
LC2
LC3
A515
A516
A537
--A203
A203
70
70
Cl.1
--B
E
ASME B16.5, Table 1a, Material Specification List (Excerpt)
Figure 4.17
Table 2 of ASME B16.5 is used to select the appropriate flange Class for
the specified design conditions and Material Group Number. ASME B16.5
has seven Classes: 150, 300, 400, 600, 900, 1,500, and 2,500. Each
Class specifies the design pressure and temperature combinations that
are acceptable for a flange that has that designation. As the number of
the Class increases, the strength of the flange increases for a given
Material Group. Figure 4.18 is an excerpt from Table 2 and shows the
temperature and pressure ratings for three carbon steel Material Groups.
128
Material Group
No.
Classes
Temp., °F
-20 to 100
200
300
400
500
600
650
700
750
800
850
900
950
1000
1.1
1.2
1.3
150
300
400
150
300
400
150
300
400
285
260
230
200
170
140
125
110
95
80
65
50
35
20
740
675
655
635
600
550
535
535
505
410
270
170
105
50
990
900
875
845
800
730
715
710
670
550
355
230
140
70
290
260
230
200
170
140
125
110
95
80
65
50
35
20
750
750
730
705
665
605
590
570
505
410
270
170
105
50
1000
1000
970
940
885
805
785
755
670
550
355
230
140
70
265
250
230
200
170
140
125
110
95
80
65
50
35
20
695
655
640
620
585
534
525
520
475
390
270
170
105
50
925
875
850
825
775
710
695
690
630
520
355
230
140
70
ASME B16.5, Table 2, Pressure-Temperature Ratings (Excerpt)
Figure 4.18
Specification of the size, material, and Class completes most of the
selection requirements for flanges. Flange type and gasket material must
also be specified. Discussion of these factors is beyond the scope of this
course.
129
Sample Problem 4 – Determine Required Flange Rating
For the pressure vessel described below, use the following procedure to
determine the required flange rating (or Class) in accordance with ASME B16.5.
Pressure Vessel Material Specifications:
Shell and Heads:
SA-516 Gr.70
Flanges:
SA-105
Design Temperature:
700°F
Design Pressure:
275 psig
1. Identify the material specification of the flange.
SA-105
2. Go to Figure 4.17 (Table 1A of ASME B16.5) and determine the Material
Group No. for the selected material specification.
Group 1.1
3. Go to Figure 4.18 (Table 2 of ASME B16.5) with the design temperature and
Material Group No. determined in Step 3.
•
The intersection of design temperature with Material Group No. is
the maximum allowable design pressure for the flange Class.
•
Table 2 of ASME B16.5 contains design information for all seven
possible flange Classes (i.e., 150, 300, 400, 600, 900, 1500, 2500).
•
Select the lowest Class whose maximum allowable design pressure
is equal to or greater than the required design pressure.
At 700°F, for Group 1.1 flange material, the Lowest Class that will accommodate
a design pressure of 275 psig is Class 300. At 700°F a Class 300 flange of
Material Group 1.1 can have a design pressure up to 535 psig.
130
G.
Flange Design
For some pressure vessel applications, it is advantageous to have one or
more flanged joints in the vessel shell to facilitate entry, removal, and/or
replacement of internal components (e.g., cartridge trays). In most
applications such as these, the shell diameter is of a size that standardsized flanges designed in accordance with either ASME B16.5 or ASME
B16.47 may be used. Mechanical design calculations for these standard
flanges are not necessary.
Flanges must be custom-designed in situations where standard-sized
flanges are not appropriate. The most common application for customdesigned flanges is for the girth flanges of shell-and-tube heat
exchangers. All custom-designed flanges must meet the requirements of
Appendix 2 of Division 1. The Appendix 2 design procedure is
complicated and is best done using a computer program. The following
paragraphs briefly describe:
1.0
•
The main steps in the ASME flange design procedure.
•
The parameters that affect flange design and in-service
performance.
ASME Flange Design Procedure
The ASME flange design procedure consists of determining the:
•
Bolting requirements.
•
Flange design loads and moments.
•
Stresses in the flange ring and hub.
The first step is usually to determine the required number and size
of bolts. Bolting requirements are determined by calculating the
loads on the bolts for two separate cases:
•
Normal operation
•
Initial flange boltup
The bolt load during normal operation, W m1, is based on the design
conditions. The bolt load during initial flange boltup, W m2, is based
on the load (or stress) necessary to seat the gasket and form a tight
seal.
131
The bolt area that is required for each of these loads is then
calculated by dividing each bolt load by the bolt allowable stress at
design temperature and room temperature, respectively. Either the
operating case or the gasket seating case may result in the
minimum required bolt area, A m ; therefore, both cases must be
checked. Since bolts come in standard sizes, and there are
limitations on the spacing between bolts, the actual bolt area, A b, is
usually greater than the required bolt area.
The next step is to determine the design loads and moments on the
flange. These loads include the:
•
Design bolt load on the flange (W).
•
Hydrostatic pressure loads that act on the flange (HD and HT).
•
Gasket sealing force (H G).
These loads do not all act at the same location on the flange,
therefore, effective moment arms (hD, hT , and hG) are calculated
based on the locations of the bolts and gasket, and on the flange
geometry (See Figure 4.19). The appropriate loads are then
multiplied by the effective moment arms to determine flange design
moments for the operating and gasket seating cases.
Flange
Ring
Gasket
h
t
A
hG
W
hT
hD
C
g1
HT
G
HG
HD
B
g0
Flange Hub
Flange Loads and Moment Arms
Figure 4.19
132
The stresses in the flange ring and hub are then calculated using
stress factors specified in the ASME Code (based on flange
geometry), the applied moments, and the flange geometry. The
stresses are calculated for both the operating case and gasket
seating cases and are then compared to the appropriate Code
allowable stresses.
All flange stresses will be lower than the appropriate allowable
stresses if the flange is designed properly. It may be necessary to
increase the flange thickness, change the hub dimensions, or make
other changes to the flange design parameters to keep flange
stresses within their allowable limits. The computer programs that
suppliers use for flange design use iterative calculation procedures
to optimize flange design. In this sense, the goal of optimization,
from the supplier’s viewpoint, is to design a “least weight” (i.e.,
lowest cost) flange that will satisfy the design requirements.
2.0
Parameters That Affect Flange Design and In-Service
Performance
The following parameters affect flange design and in-service
performance:
•
ASME Code m and y parameters.
•
Specified gasket widths.
•
Flange facing and nubbin width, w.
•
Bolt size, number, and spacing.
The gasket factor, m, determines the amount of force required to
keep the gasketed joint tight. The minimum design seating stress, y,
determines how much gasket stress is required to initially seat or
deform the gasket. Both parameters are used in the flange design
calculations.
The ASME Code specifies m and y based on gasket type in its
Table 2 -5.1 (excerpted in Figure 4.20). Higher values of m and y
typically indicate that a gasket is harder to seal or seat. While this is
a consideration in gasket selection, gasket type and material are
usually selected based on historical service experience and the
corrosion resistance of the gasket material in the process
environment.
133
Heat exchanger flanges sometimes have leakage problems during
operation. When this occurs, there is often the tendency to change
the gasket to a different type that has provided leak-free
performance in other applications. This problem-solving method
should always be approached with caution because the flanges
were designed for a specific gasket type with its associated m and y
values. Therefore, the existing bolting may either impose too high a
load on the gasket (and possibly crush it) or the new gasket may
require a higher load to seat it (which might not be possible with the
existing bolting).
Gasket Type and Material
Gasket
Factor, m
Min.
Design
Seating
Stress y,
psi
Facing Sketch and
Column in ASME
Table 2-5.2
(Figure 4.21)
Flat metal, jacketed asbestos filled:
Soft aluminum
Soft copper or brass
Iron or soft steel
Monel
4-6% chrome
Stainless steels and nickel-base alloys
3.25
3.50
3.75
3.50
3.75
3.75
5,500
6,500
7,600
8,000
9,000
9,000
(1a), (1b), (1c), (1d);
(2);
Column II
Solid flat metal:
Soft aluminum
Soft copper or brass
Iron or soft steel
Monel or 4-6% chrome
Stainless steels and nickel-base alloys
4.00
4.75
5.50
6.00
6.50
8,800
13,000
18,000
21,800
26,000
(1a), (1b), (1c), (1d);
(2), (3), (4), (5);
Column I
ASME Code m and y Factors
Figure 4.20
The TEMA standard for shell-and-tube heat exchangers specifies a
minimum required width for the peripheral ring gaskets at external
joints (3/8 in. or ½ in. depending on shell size) and for pass partition
gaskets (¼ in. or 3/8 in. depending on shell size). These minimum
gasket widths are typically used over a wide range of service
conditions.
The gasket widths referred to in TEMA are actual minimum widths,
N. In addition to N, two other gasket widths are referred to in the
ASME Code: the basic seating width, b o, and the effective seating
width, b. The effective seating width is a function of the basic
seating width, and the basic seating width is a function of the actual
width and the type of flange face. See Table 2-5.2 in the ASME
134
Code (excerpted in Figure 4.21). In general, wider gaskets provide
better sealing, but a wider gasket also requires a larger bolt load
(i.e., more bolt area) to seat and seal the gasket. The required
flange thickness increases as the bolting area increases.
135
Facing Sketch
(Exaggerated)
Basic Gasket Seating Width bo
N
(1a)
Column I
Column II
N
2
N
2
w+ T w+N

;
max 
2
 4

w + T  w +N

;
max 
2  4

N
N
N
(1b)
w
T
w
(1d)
w≤N
N
(1c)
T
N
w≤N
HG
HG
hG
G
O.D. Contact Face
G
hG
CL Gasket
Face
b
For bo > ¼ in.
For bo < ¼ in.
ASME Code Gasket Widths (Table 2 -5.2 excerpt)
Figure 4.21
The effective seating width, b, is also a function of the flange facing
type and the nubbin width, w, for flat metal gaskets. Table 2 -5.1 in
the Code (excerpted in Figure 4.22) indicates which facing sketch is
applicable for a given gasket type and material.
136
Gasket Materials and Contact Facings
Gasket Factors m for Operating Conditions and Minimum Design Seating Stress y
Gasket Material
Gasket
Factor
m
Flat metal, jacketed asbestos filled:
Soft aluminum
Soft copper or brass
Iron or soft steel
Monel
4% - 6% chrome
Stainless steels and nickel-base alloys
3.25
3.50
3.75
3.50
3.75
3.75
Min. Design
Seating
Stress y,
psi
5500
6500
7600
8000
9000
9000
Sketches
Facing
Sketch and
Column in
Table 2-5.2
(1a), (1b),
2
2
(1c), , (1d) ,
2
(2) , Column
II
Gasket Materials and Contact Facings (Table 2-5.2 Excerpt)
Figure 4.22
The equations for determining b are based on w, N, and the type of
flange facing. Note that b is used in the Code equations to
determine the bolt load required for sealing the gasket during
operation, Wm1, and the bolt load required for seating the gasket
initially, Wm2. Once a gasket type, material, width, and facing are
selected, the required bolting area can be determined.
•
The bolt size, number, and spacing that are used to clamp the
flanges together are interrelated parameters that affect their
overall design.
•
The number of bolts multiplied by the bolt root area of a single
bolt must be greater than the minimum required bolt area, A m .
•
The bolts must be far enough away from the shell or hub of the
flange, and be far enough apart circumferentially, so that there
is adequate clearance to permit access for a wrench.
•
There must be adequate distance to other flange or vessel
surfaces to ensure adequate clearance for standard wrenches.
It may appear that maintaining these minimum bolt dimensions can
be easily achieved if a few large bolts are used. However, the bolts
should also be spaced as close together as practical for several
reasons.
•
Having fewer bolts increases the bolt load moment arms.
Larger moment arms increase the bending moments for which
the flange must be designed and thus increase the required
flange thickness.
137
H.
•
TEMA requires that the flange design moment be increased if
the bolts are widely spaced. This results in a thicker flange.
•
Excessive bolt spacing could make the flange more prone to
leakage. The portions of the gasket located between the bolts
might not be compressed sufficiently to maintain a tight seal.
Maximum Allowable Working Pressure (MAWP)
The MAWP of a pressure vessel is the maximum permissible gauge
pressure in the vessel. It is determined as the lowest MAWP of all the
vessel's components based on their actual supplied thicknesses. The
MAWP is specified at the top of the vessel when the vessel is in its
operating position. The MAWP is also specified at a "designated
temperature" (i.e., the design temperature) that is coincident with the
MAWP. The material thicknesses used in these calculations do not
include any excess thickness that was added for corrosion allowance or to
absorb loadings other than pressure.
The MAWP may be used later if a change in operation is being considered
that requires a more severe design pressure and/or temperature than
what were originally specified. The MAWP shows whether the same
pressure vessel may be used at the new design conditions.
138
V.
Other Design Considerations
A.
Vessel Support
The type of support that is used for a pressure vessel depends primarily
on the vessel’s size and orientation.
Shown in Figure 2.1, a saddle support spreads the weight load of a
horizontal drum over a large area of the shell. This prevents excessive
local stress in the shell at the support points. The size and design details
used for the saddle depend on the diameter and thickness of the drum
and the imposed load.
As shown in Figure 2.2, small vertical drums are typically supported on
legs that are welded to the lower portion of the shell. Support legs are
also typically used for spherical pressurized storage vessels (See Figure
2.5). The support legs for small vertical drums and spherical pressurized
storage vessels may be made from structural steel columns or pipe
sections, whichever provides a more efficient design. Cross bracing
between the legs (See Figure 2.5) is typically used to help absorb wind or
earthquake loads.
Lugs may also be used to support vertical pressure vessels. As shown in
Figure 5.1, the lugs are typically bolted to horizontal structural members.
It is common for a reinforcement pad to be first welded to the vessel shell,
and then the lugs welded to it.
A support skirt (See Figures 2.3 and 2.4) is a cylindrical shell section that
is welded either to the lower portion of the vessel shell or to the bottom
head. Support skirts are commonly used for tall towers.
B.
Local Loads
It is common for external loads to be applied to nozzles or lugs that are
attached to pressure vessel shells or heads. External loads cause local
stresses that are in addition to those caused by pressure, weight, and
wind loads. External loads may be caused by the following:
•
Piping system weight, wind, and thermal expansion loads that are
applied at vessel nozzles.
139
•
Loads from platforms, internal or external piping, internal components,
or equipment items supported from a vessel shell by lugs or clips
attached to the shell.
•
Loads at vessel supports, such as columns or lugs.
Vertical Vessel on Lug Supports
Figure 5.1
The total stress in the vessel shell, including that caused by locally applied
loads, must be kept to within allowable limits. Division 1 does not contain
detailed procedures for evaluating these local loads. Other industry
practices (e.g., Welding Research Council Bulletins 107 and 297) and
Division 2 are commonly used to evaluate local loads.
140
C.
Vessel Internals
1.0
Types of Internals
There are many different types of vessel internals used to perform
various process functions. The following highlights several (but not
all) of these types:
•
Trays. Located at various elevations along the length of a
tower. Provide liquid/vapor flow distribution and separation
along the length. Various tray types are available to suit specific
process needs.
•
Inlet distributor. Installed as an internal extension to the inlet
nozzle. Used to direct the inlet flow stream and properly
distribute it within the vessel.
•
Anti-vortex baffle. Installed at vessel outlet to prevent the
formation of flow vortices at the exit from the vessel.
•
Catalyst bed grid and support beams. An open steel gridwork
may be used to support one or more intermediate catalyst beds
installed inside fixed bed reactors. The gridwork is typically
covered by wire mesh screen to prevent the solid catalyst from
passing through the grid, while the gridwork permits process
flow. Supplementary beams are typically used to support the
grid from the vessel shell.
•
Outlet collector. Typically placed at the outlet of fixed bed
reactors. Designed to allow process flow while preventing
catalyst from passing into the downstream system.
•
Flow distribution grid. In fluidized solids processes (e.g., FCCU,
Fluid Coker, etc.), a flow distribution grid is used to direct and
distribute the fluidization media that is needed to keep the solids
(i.e., catalyst or coke) in a fluidized state inside a vessel.
•
Cyclone and plenum chamber system. In fluidized solids
processes (e.g., FCCU, Fluid Coker, etc.), a cyclone and
plenum chamber system separates entrained catalyst from
process vapor before the vapor exits the vessel through the
overhead line.
ASME Code design requirements only apply to the external,
pressure-containing “envelope” of the vessel (i.e., shell, heads,
nozzles, etc.) and not to items contained inside it. The only
exceptions to this are:
141
•
Loads that are applied from the internals to pressure-containing
parts must be considered in the vessel design.
•
All welding to pressure-containing parts must meet ASME Code
requirements.
The end-user, vessel vendor, internals supplier, prime contractor,
and/or a combination of these entities must develop the detailed
design requirements for all vessel internals.
2.0
Treatment of Corrosion Allowance.
Removable pressure vessel internals that are subject to corrosion
should typically have a corrosion allowance equal to that of the shell.
In this way, the design of removable internals considers only half of
the expected total corrosion. The rationale for this approach is that
removable internals that are designed for only the expected total
corrosion will cost less initially and can easily be replaced later,
based on the actual corrosion that occurs.
Most pressure vessel internals can corrode on both sides. From a
strength-design viewpoint, corrosion from both sides should be
considered with regard to non-removable internals. Non-removable
internals, and those that are major load-bearing members (e.g.,
catalyst bed supports), must typically have a total corrosion
allowance that is equal to twice that of the shell.
142
VI.
Fabrication
A.
Acceptable Welding Details
All pressure vessel welds, including the welds that attach heads, nozzles,
small fittings, and nonpressure components to a shell, must conform to
ASME Code requirements. Details that are used for the primary
circumferential and longitudinal welds were discussed earlier in
conjunction with weld joint categories.
The ASME Code specifies weld detail requirements for vessel fabrication
(e.g., type and size of weld, weld locations, etc.). It also specifies welder
and welding procedure qualification requirements. The paragraphs that
follow highlight several of the ASME Code requirements. Refer to the
ASME Code for further information related to these and other weld details.
1.0
Thickness Transitions
The thickness of a pressure vessel head sometimes differs from the
thickness of the shell it is attached to (e.g., when a hemispherical
head is attached to a cylindrical shell). The transition between the
component thicknesses must be made in a taper to avoid excessive
local stress. Head-to-shell thickness transitions are illustrated in
Figure 6.1.
2.0
Intermediate Heads
An intermediate head is attached to the inside of a cylindrical shell
when it is needed to separate two sections of the vessel. The butt
weld between shell sections also attaches to the head, and a fillet
weld is also located between the head and shell. The ASME Code
permits elimination of the fillet weld if there is no access and if the
service is noncorrosive. However, the fillet weld should generally be
used for all refinery applications to avoid the potential for
accelerated corrosion due to process fluid getting between the head
and shell. The attachment of an intermediate head to a cylindrical
shell is illustrated in Figure 6.1.
143
th
l
y
Thinner part
Thinner part
th
l
Tangent
Line
y
ts
ts
th
th
Tangent
Line
Thinner part
l
y
Thinner part
y
l
ts
ts
Fillet
Weld
Butt Weld
Intermediate Head Attachment
Typical Head-to-Shell Transitions
Figure 6.1
3.0
Openings
Fabrication details for various types of openings are specified.
These include unreinforced nozzles (e.g., a nozzle neck welded
directly to the vessel shell or head), a nozzle with a reinforcing pad
added, and a self-reinforced nozzle (i.e., where extra thickness is
144
provided in the nozzle neck to provide the necessary reinforcement).
These were illustrated in Figure 4.15.
In some cases, a nozzle neck that has a weld-end may be attached
to a pipe that is thinner. This attachment between components of
different thicknesses could occur if extra thickness was included in
the nozzle neck for reinforcement or if the pipe and nozzle materials
and/or allowable stresses differ. In such cases, the nozzle neck
must be tapered to the pipe thickness. Tapers are also used to join
shell sections that are of different thicknesses. Shell thickness and
nozzle thickness tapers are illustrated in Figures 6.2 and 6.3,
respectively.
C
L
In all cases, l shall not
be less than 3y.
C
L
y
l
l
CL
Typical Shell Transitions
Figure 6.2
Nozzle Neck Attachment to Thinner Pipe
Figure 6.3
4.0
Stiffener Rings
Stiffener rings may be attached to the vessel shell by continuous,
intermittent, or a combination of continuous and intermittent welds.
145
Intermittent welds must be placed on both sides of the stiffener and
may be either staggered or in-line. The ASME Code specifies
acceptable spacing, size, and length of the welds. Stiffener ring
attachment weld options are illustrated in Figure 6.4.
In-Line
Intermittent Weld
Staggered
Intermittent Weld
Continuous Fillet Weld On
One Side, Intermittent Weld
On Other Side
Stiffener Ring Attachment
Figure 6.4
B.
Postweld Heat Treatment Requirements
Welding heat changes the crystal structure and grain size of the weld heat
affected zone (HAZ). Postweld heat treatment (PWHT) may be necessary
to restore the material structure to the required properties. The need for
PWHT for these metallurgical reasons depends on the materials involved
and the service conditions that they are exposed to. PWHT requirements
for these metallurgical or process reasons are not included in the ASME
Code. They must be specified by the user based on the service and
materials involved.
As the weld metal and HAZ cool from the very high welding temperatures,
the thermal contraction that occurs in the locally heated area is resisted by
the cooler base metal that surrounds it. This resistance results in residual
stresses that remain in the structure. For thicker plates, these residual
stresses must be removed by PWHT. PWHT requirements based on
stress relief considerations are contained in the ASME Code, Section VIII.
146
The ASME Code contains the temperature and hold time requirements
when PWHT is needed for stress relief considerations. These ASME
Code PWHT requirements are based on material type and thickness, as
specified in Paragraph UCS-56 for carbon and low-alloy steels. The
ASME Code specifies the minimum PWHT temperature and the minimum
holding time at temperature based on the material P-No. and thickness.
Acceptable PWHT procedures are also specified to ensure that adequate
stress relief will occur. Heatup and cooldown rates must be controlled
within specified limits in order to avoid excessive local thermal stresses
during PWHT.
147
VII.
Inspection and Testing
A.
Inspection
Overall inspection of completed pressure vessels includes an examination
of the following:
•
Base material specification and quality
•
Welds
•
Dimensional requirements
•
Equipment documentation
The most common defects for which welds are examined are as follows:
•
Poor weld shape due to part misalignment.
•
Cracks in welds or HAZ of the base metal.
•
Pinholes on the weld surface.
•
Slag inclusions or porosity in the form of voids.
•
Incomplete fusion between weld beads or between the weld and the
base metal.
•
Lack of penetration or an insufficient extent of penetration of the weld
metal into the joints.
•
Undercut, an intermittent or continuous groove that is located adjacent
to the weld and that is left unfilled by weld metal.
Several of these common weld defects are illustrated in Figure 7.1.
148
Between Weld Bead and Base Metal
Between Adjacent Passes
Lack of Fusion
Incomplete Filling at Root on One Side Only
Incomplete Filling at Root
Incomplete Penetration
External Undercut
Internal Undercut
Undercut
Typical Weld Defects
Figure 7.1
The presence of defects reduces the strength of the weld below that
required by the design calculations, reduces the overall strength of the
fabrication, and increases the risk of failure. Weld inspection must be
performed in a manner that will detect unacceptable defects while not
damaging the vessel material. This type of inspection is called
nondestructive examination, or NDE.
The five primary weld NDE methods are as follows:
•
Radiographic examination (RT)
•
Visual Inspection (VT)
•
Liquid penetrant examination (PT)
•
Magnetic particle test (MT)
149
•
Ultrasonic examination (UT)
The choice of which weld examination method or methods to use depends
on the weld quality required of the joint, the position of the weld, the
material to be joined, and the particular defects that are most likely to
occur. These weld NDE methods are briefly discussed in the paragraphs
that follow. Figure 7.2 summarizes the types of NDE, the defects typically
found by each, and the advantages and limitations of each process.
NDE TYPE
DEFECTS
DETECTED
ADVANTAGES
LIMITATIONS
Radiographic
Gas pockets, slag
inclusions, incomplete
penetration, cracks
Produces permanent
Expensive.
record.
Not practical for
Detects small flaws.
complex shapes.
Most effective for buttwelded joints.
Visual
Porosity holes, slag
inclusions, weld
undercuts,
overlapping
Helps pinpoint areas
for additional NDE.
Can only detect what
is clearly visible.
Liquid Penetrant
Weld surface-type
defects: cracks,
seams, porosity, folds,
pits, inclusions,
shrinkage
Used for ferrous and
nonferrous materials.
Simple and less
expensive than RT,
MT, or UT.
Can only detect
surface imperfections.
Magnetic Particle
Cracks, porosity, lack
of fusion
Flaws up to ¼ in.
beneath surface can
be detected.
Cannot be used on
nonferrous materials.
Ultrasonic
Subsurface flaws:
laminations, slag
inclusions
Can be used for thick
plates, welds,
castings, forgings.
May be used for
welds where RT not
practical.
Equipment must be
constantly calibrated.
Summary of NDE types
Figure 7.2
150
1.0
Radiographic Examination (RT)
The most important NDE method is radiographic examination. In
radiographic examination, a ray is emitted from a controllable
source, penetrates a test specimen, and leaves an image on a strip
of film that is mounted behind the test specimen. This is illustrated
in Figure 7.3.
X-Ray Tube
X-Ray
Film
Test Specimen
Typical RT Setup
Figure 7.3
2.0
Visual Inspection (VT)
A thorough visual inspection is usually satisfactory for minor
structural welds. All weld surfaces that will be examined by more
extensive means are first subject to VT. VT provides an overall
impression of weld quality and helps to locate areas where
additional NDE should be performed.
3.0
Liquid Penetrant Examination (PT)
A liquid penetrant examination involves applying a penetrant which
contains a fluorescent or visible dye to mark potential defect areas.
The liquid penetrates into defects by capillary action. Then, by using
151
a developing procedure, the liquid bleeds out through a capillary
action at surface flaws and makes them visible.
4.0
Magnetic Particle Test (MT)
MT examination is based on the magnetic lines of flux (or force
lines) that can be generated within a test piece. These force lines
are parallel if no defects are present. If there is a defect, a small
break in the force lines appears at the defect location. In MT
examination, iron powder is applied to the surface and then the test
piece is magnetized. If there are no defects, the iron powder is
aligned in straight lines along the North-South magnetic flux lines. If
there is a defect, the iron powder alignment is disturbed and flows
around the defect.
5.0
Ultrasonic Examination (UT)
In UT examination, sound waves are generated by a power source
and applied to the test piece through a transducer. Figure 7.4
shows a pulse echo ultrasonic examination system. The sound
waves pass through the test piece and are reflected back to the
transducer either from the far side of the test piece or from a flaw
that is located at an intermediate position within the test piece. By
careful calibration, the UT operator knows if a flaw has been
detected and knows its location and its size.
B.
Pressure Testing
All pressure vessels that are designed to ASME Code requirements must
be pressure tested after fabrication and inspection to demonstrate their
structural integrity before they are placed into operation. The pressure
test is made at a pressure that is higher than the design pressure. This
excess pressure provides a safety margin since the vessel component
stress levels during the test will be higher than those that will occur during
operation. The objective of the pressure test is to bring the vessel to a
high enough internal pressure, under controlled conditions, to demonstrate
its mechanical integrity. Successful completion of the pressure test
signifies that the vessel is acceptable for operation.
152
Cathode Ray Tube (CRT)
A
C
Read Out
B
Base Line
Input-Output
Generator
Cable
Transducer
A
Couplant
Test Specimen
B
C
Flaw
Pulse Echo UT System
Figure 7.4
Pressure tests are typically made using water as the test medium because
of the relative safety of water compared to a pneumatic test. The ASME
Code permits a pneumatic pressure test as an alternative to a hydrostatic
test under certain circumstances. However, a pneumatic test should only
be considered on an exception basis due to the increased safety risks
involved.
Since the hydrostatic test will almost always be used, only the hydrostatic
test will be discussed here. Refer to the ASME Code for pneumatic test
requirements.
The standard hydrotest pressure at the top of the vessel is calculated as
follows:
PT = 1.5P (Ratio)
153
Where:
PT
=
Hydrotest pressure at the top of the vessel, psig
P
=
Vessel MAWP (use vessel design pressure if
the MAWP was not determined), psig
Ratio =
The lowest ratio of the allowable stress at the
test temperature to that at the design
temperature for the vessel materials used.
The following points must also be considered:
•
Hydrotest pressures must be calculated for the shop test with the
vessel in the horizontal position, for the field test with the vessel in the
final position and with uncorroded component thicknesses, and for the
field test with the vessel in the final position and with corroded
component thicknesses.
•
The calculated shop hydrotest pressure cannot exceed the test
pressure of the flanged connections.
•
During the pressure test, the stress at any section of the vessel cannot
exceed 90% of the material minimum specified yield strength (MSYS),
based on use of the design weld joint efficiency (E).
•
Vessels also must typically be designed to permit a hydrotest in the
field at a wind velocity that is typically 25-35% of the design wind
velocity for the site.
During a field hydrotest, water at a specific gravity of 1.0 is used, and the
vessel is filled to the top. The larger specific gravity and fill height of
hydrotest water results in a higher weight and hydrostatic head load than
occurs during normal operation. Therefore, thicker plates are sometimes
required for lower sections of a tall tower than would be required for the
operational loads.
154
VIII. Summary
This course provided an overview of pressure vessel mechanical design
requirements. It summarized the main components of pressure vessels and
discussed the scope of the ASME Code Section VIII, structure of Division 1,
materials of construction, design requirements and considerations, fabrication,
inspection and testing. Participants now have a good overall understanding of
pressure vessel mechanical design requirements, are prepared to use this
knowledge in their jobs, and have sufficient prerequisite information to take more
detailed pressure vessel courses.
155
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