Pressure vessel

alt=A New Technology for Hydrogen Storage|thumb|A New Technology for Hydrogen Storage

upright=1.4|thumb|A welded steel pressure vessel constructed as a horizontal cylinder with domed ends. An access cover can be seen at one end, and a drain valve at the bottom centre.

A pressure vessel is a container designed to hold gases or liquids at a pressure substantially different from the ambient pressure.

Construction methods and materials may be chosen to suit the pressure application, and will depend on the size of the vessel, the contents, working pressure, mass constraints, and the number of items required.

Pressure vessels can be dangerous, and fatal accidents have occurred in the history of their development and operation. Consequently, pressure vessel design, manufacture, and operation are regulated by engineering authorities backed by legislation. For these reasons, the definition of a pressure vessel varies from country to country.

The design involves parameters such as maximum safe operating pressure and temperature, safety factor, corrosion allowance and minimum design temperature (for brittle fracture). Construction is tested using nondestructive testing, such as ultrasonic testing, radiography, and pressure tests. Hydrostatic pressure tests usually use water, but pneumatic tests use air or another gas. Hydrostatic testing is preferred, because it is a safer method, as much less energy is released if a fracture occurs during the test (water does not greatly increase its volume when rapid depressurisation occurs, unlike gases, which expand explosively). Mass or batch production products will often have a representative sample tested to destruction in controlled conditions for quality assurance. Pressure relief devices may be fitted if the overall safety of the system is sufficiently enhanced.

In most countries, vessels over a certain size and pressure must be built to a formal code. In the United States that code is the ASME Boiler and Pressure Vessel Code (BPVC). In Europe the code is the Pressure Equipment Directive. These vessels also require an authorised inspector to sign off on every new vessel constructed and each vessel has a nameplate with pertinent information about the vessel, such as maximum allowable working pressure, maximum temperature, minimum design metal temperature, what company manufactured it, the date, its registration number (through the National Board), and American Society of Mechanical Engineers's official stamp for pressure vessels (U-stamp). The nameplate makes the vessel traceable and officially an ASME Code vessel.

A special application is pressure vessels for human occupancy, for which more stringent safety rules apply.

Definition and scope

The ASME definition of a pressure vessel is a container designed to hold gases or liquids at a pressure substantially different from the ambient pressure.

The Australian and New Zealand standard "AS/NZS 1200:2000 Pressure equipment" defines a pressure vessel as a vessel subject to internal or external pressure, including connected components and accessories up to the connection to external piping.

This article may include information on pressure vessels in the broad sense, and is not restricted to any single definition.

Components

A pressure vessel comprises a shell, and usually one or more other components needed to pressurise, retain the pressure, depressurise, and provide access for maintenance and inspection. There may be other components and equipment provided to facilitate the intended use, and some of these may be considered parts of the pressure vessel, such as shell penetrations and their closures, and viewports and airlocks on a pressure vessel for human occupancy, as they affect the integrity and strength of the shell, are also part of the structure retaining the pressure. Pressure gauges and safety devices like pressure relief valves may also be deemed part of the pressure vessel. More complicated shapes have historically been much harder to analyze for safe operation and are usually far more difficult to construct.

File:Biogasholder and flare.JPG|Spherical gas container.

File:Ресивер хладагента FP-LR-100.png|Cylindrical pressure vessel.

File:Diffuser Head.jpg|Picture of the bottom of an aerosol spray can.

File:ABC Fire Extinguisher.jpg|Fire Extinguisher with rounded rectangle pressure vessel

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Theoretically, a spherical pressure vessel has approximately twice the strength of a cylindrical pressure vessel with the same wall thickness, and is the ideal shape to hold internal pressure.).

Scaling of stress in walls of vessel

Pressure vessels are held together against the gas pressure due to tensile forces within the walls of the container. The normal (tensile) stress in the walls of the container is proportional to the pressure and radius of the vessel and inversely proportional to the thickness of the walls. Therefore, pressure vessels are designed to have a thickness proportional to the radius of tank and the pressure of the tank and inversely proportional to the maximum allowed normal stress of the particular material used in the walls of the container.

Because (for a given pressure) the thickness of the walls scales with the radius of the tank, the mass of a tank (which scales as the length times radius times thickness of the wall for a cylindrical tank) scales with the volume of the gas held (which scales as length times radius squared). The exact formula varies with the tank shape but depends on the density, ρ, and maximum allowable stress σ of the material in addition to the pressure P and volume V of the vessel. (See below for the exact equations for the stress in the walls.)

Spherical vessel

For a sphere, the minimum mass of a pressure vessel is

:<math>M = {3 \over 2} P V {\rho \over \sigma}</math>,

where:

<math>M</math> is mass, (kg)
<math>P</math> is the pressure difference from ambient (the gauge pressure), (Pa)
<math>V</math> is volume, (m<sup>3</sup>)
<math>\rho</math> is the density of the pressure vessel material, (kg/m<sup>3</sup>)
<math>\sigma</math> is the maximum working stress that material can tolerate. (Pa)

Other shapes besides a sphere have constants larger than 3/2 (infinite cylinders take 2), although some tanks, such as non-spherical wound composite tanks can approach this.

Cylindrical vessel with hemispherical ends

This is sometimes called a "bullet" for its shape, although in geometric terms it is a capsule.

For a cylinder with hemispherical ends,

:<math>M = 2 \pi R^2 (R + W) P {\rho \over \sigma}</math>,

where

R is the Radius (m)
W is the middle cylinder width only, and the overall width is W + 2R (m)

Cylindrical vessel with semi-elliptical ends

In a vessel with an aspect ratio of middle cylinder width to radius of 2:1,

:<math>M = 6 \pi R^3 P {\rho \over \sigma}</math>.

Gas storage capacity

In looking at the first equation, the factor PV, in SI units, is in units of (pressurization) energy. For a stored gas, PV is proportional to the mass of gas at a given temperature, thus

:<math>M = {3 \over 2} nRT {\rho \over \sigma}</math>. (see gas law)

The other factors are constant for a given vessel shape and material. So we can see that there is no theoretical "efficiency of scale", in terms of the ratio of pressure vessel mass to pressurization energy, or of pressure vessel mass to stored gas mass. For storing gases, "tankage efficiency" is independent of pressure, at least for the same temperature.

So, for example, a typical design for a minimum mass tank to hold helium (as a pressurant gas) on a rocket would use a spherical chamber for a minimum shape constant, carbon fiber for best possible <math>\rho / \sigma</math>, and very cold helium for best possible <math>M / {pV}</math>.

Stress in thin-walled pressure vessels

Stress in a thin-walled pressure vessel in the shape of a sphere is

:<math>\sigma_\theta = \sigma_{\rm long} = \frac{pr}{2t}</math>,

where <math>\sigma_\theta</math> is hoop stress, or stress in the circumferential direction, <math>\sigma_{long}</math> is stress in the longitudinal direction, p is internal gauge pressure, r is the inner radius of the sphere, and t is thickness of the sphere wall. A vessel can be considered "thin-walled" if the diameter is at least 10 times (sometimes cited as 20 times) greater than the wall thickness.

thumb|Stress in the cylinder body of a pressure vessel.

Stress in a thin-walled pressure vessel in the shape of a cylinder is

:<math>\sigma_\theta = \frac{pr}{t}</math>,

:<math>\sigma_{\rm long} = \frac{pr}{2t}</math>,

where:

<math>\sigma_\theta</math> is hoop stress, or stress in the circumferential direction
<math>\sigma_{long}</math> is stress in the longitudinal direction
p is internal gauge pressure
r is the inner radius of the cylinder
t is thickness of the cylinder wall.

Almost all pressure vessel design standards contain variations of these two formulas with additional empirical terms to account for variation of stresses across thickness, quality control of welds and in-service corrosion allowances.

All formulae mentioned above assume uniform distribution of membrane stresses across thickness of shell but in reality, that is not the case. Deeper analysis is given by Lamé's theorem, which gives the distribution of stress in the walls of a thick-walled cylinder of a homogeneous and isotropic material. The formulae of pressure vessel design standards are extension of Lamé's theorem by putting some limit on ratio of inner radius and thickness.

For example, the ASME Boiler and Pressure Vessel Code (BPVC) (UG-27) formulas are:

Spherical shells: Thickness has to be less than 0.356 times inner radius

:<math>\sigma_\theta = \sigma_{\rm long} = \frac{p(r + 0.2t)}{2tE}</math>

Cylindrical shells: Thickness has to be less than 0.5 times inner radius

:<math>\sigma_\theta = \frac{p(r + 0.6t)}{tE}</math>

:<math>\sigma_{\rm long} = \frac{p(r - 0.4t)}{2tE}</math>

where E is the joint efficiency, and all others variables as stated above.

The factor of safety is often included in these formulas as well, in the case of the ASME BPVC this term is included in the material stress value when solving for pressure or thickness.

Shell penetrations

Also sometimes called hull penetrations, depending on context, shell penetrations are intentional breaks in the structural integrity of the shell, and are usually significant local stress-raisers, so they must be accounted for in the design so they do not become failure points. It is usually necessary to reinforce the shell in the immediate vicinity of such penetrations. Shell penetrations are necessary to provide a variety of functions, including passage of the contents from the outside to the inside and back out, and in special applications for transmission of electricity, light, and other services through the shell. The simplest case is gas cylinders, which need only a neck penetration threaded to fit a valve, while a submarine or spacecraft may have a large number of penetrations for a large number of functions.

Penetration thread

The screw thread used for high pressure vessel shell penetrations is subject to high loads and must not leak.

High pressure cylinders are produced with conical (tapered) threads and parallel threads. Two sizes of tapered threads have dominated the full metal cylinders in industrial use from in volume.

Pressure vessels may also be constructed from concrete (PCV) or other materials which are weak in tension. Cabling, wrapped around the vessel or within the wall or the vessel itself, provides the necessary tension to resist the internal pressure. A "leakproof steel thin membrane" lines the internal wall of the vessel. Such vessels can be assembled from modular pieces and so have "no inherent size limitations". There is also a high order of redundancy thanks to the large number of individual cables resisting the internal pressure.

The very small vessels used to make liquid butane fueled cigarette lighters are subjected to about 2 bar pressure, depending on ambient temperature. These vessels are often oval (1 x 2 cm ... 1.3 x 2.5 cm) in cross section but sometimes circular. The oval versions generally include one or two internal tension struts which appear to be baffles but which also provide additional cylinder strength. This geometry is relatively inefficient for supporting pressure loads.

Mass of a pressure vessel

For many pressure vessels, such as pressure hulls of submarines and deep submergence vessels, pressurised aircraft and spacecraft, and gas cylinders for self contained breathing apparatus, mass is a critical design constraint.

For an isotropic material, the necessary mass of a pressure vessel of a given size, shape and pressure rating for internal pressure will depend on the specific strength of the material at the working temperature. This may be affected by allowances for corrosion wastage and other damage and wear over the working life, other expected load conditions, and material characteristics under sustained load, variable temperature exposure, and fatigue loading conditions. For external pressure, buckling instability may be the critical load condition, and material stiffness and specific modulus will be critical material characteristics. Buckling is a major failure mode in submarine and submersible hulls. Modulus may also be a limiting factor where the geometry induces bending loads. For some materials and designs notch sensitivity may be an important factor.

Anisotropic materials

An advantage of composite materials for pressure vessel construction is the ability to align fibres in the directions where they will most efficiently support the loads, allowing less material to be used.

Manufacturing processes

Riveted

Riveting was the standard method of construction for boilers, compressed air receivers and other pressure vessels of iron or steel before gas and electrical welding of reliable quality became widespread. Sheets or plates which had been rolled and forged into shape, were then riveted together, often using butt straps along the joints, and caulked along the riveted seams by deforming the edges of the overlap with a blunt chisel to create a continuous line of high contact pressure along the joint. Hot riveting caused the rivets to contract on cooling, forming a tighter joint.

When rivets are installed hot they contract as they cool and generate a preload that compresses the butt straps and the shell together. The rivets deform plastically during cooling and preload stresses stabilise at approximately yield point.

Quality assurance includes welder qualification (coded welder) for manual welds, welding procedure specification, material specifications, and inspection and testing of the finished welds. Welds are first inspected visually, which can quickly identify many flaws like undercuts, overlaps and uneven surface height. Once the welds have passed visual inspection, they must also pass NDT tests appropriate for the specific pressure vessel, such as ultrasonic or x-ray inspection. Equipment to rotate the pressure vessel may be used to facilitate inspection, or it may be done by automated equipment. Radiographic testing can detect voids, internal cracks, porosity, slag inclusions, variations in material thickness, incomplete fusion or incomplete penetration, and other welding defects. Items which are mass produced may also undergo destructive mechanical tests of a representative sample of welds from each batch of products.

Advantages claimed for composite pressure vessels are relatively light weight, corrosion resistance, design flexibility and lower fabrication cost for some applictions.

Hoop wound fibre reinforcement is wound at an angle of nearly 90° to the cylinder axis.

Flexible composite pressure vessels

Low pressure hyperbaric stretchers have been made from fibre reinforced synthetic elastomer, which can be folded for storage. The ends are rigid dished shapes held in place by the internal pressure, and carry all of the penetrations.

Surface treatment and finishing

Surface treatment may include cleaning, deburring, and passivation to remove any impurities and improve corrosion resistance. The vessel may be finished with a paint system or other coatings to protect it from environmental conditions.

Certification

After completion, a pressure vessel is inspected to ensure that it complies with all the relevant standards, codes, and specifications, by designated and qualified inspectors, who check dimensional accuracy, weld quality, and structural integrity before issuing the certifications and documentation needed to comply with the relevant regulations. and the AIAA metallic pressure vessel standard, either require pressure vessel designs to be leak before burst, or require pressure vessels to meet more stringent requirements for fatigue and fracture if they are not shown to be leak before burst.

Testing and inspection

Hydrostatic test (filled with water) pressure is usually 1.5 times working pressure, but US DOT test pressure for scuba cylinders is 5/3 (1.67) times working pressure.

Operation standards

Pressure vessels are designed to operate safely at a specific pressure and temperature, technically referred to as the "Design Pressure" and "Design Temperature". A vessel that is inadequately designed to handle a high pressure constitutes a very significant safety hazard. Because of that, the design and certification of pressure vessels is governed by design codes such as the ASME Boiler and Pressure Vessel Code in North America, the Pressure Equipment Directive of the EU (PED), Japanese Industrial Standard (JIS), CSA B51 in Canada, Australian Standards in Australia and other international standards like Lloyd's, Germanischer Lloyd, Det Norske Veritas, Société Générale de Surveillance (SGS S.A.), Lloyd's Register Energy Nederland (formerly known as Stoomwezen) etc.

Note that where the pressure-volume product is part of a safety standard, any incompressible liquid in the vessel can be excluded as it does not contribute to the potential energy stored in the vessel, so only the volume of the compressible part such as gas is used.

List of standards

EN 13445: The current European Standard, harmonized with the Pressure Equipment Directive (Originally "97/23/EC", since 2014 "2014/68/EU"). Extensively used in Europe.
ASME Boiler and Pressure Vessel Code Section VIII: Rules for Construction of Pressure Vessels.
BS 5500: Former British Standard, replaced in the UK by BS EN 13445 but retained under the name PD 5500 for the design and construction of export equipment.
AD Merkblätter: German standard, harmonized with the Pressure Equipment Directive.
EN 286 (Parts 1 to 4): European standard for simple pressure vessels (air tanks), harmonized with Council Directive 87/404/EEC.
BS 4994: Specification for design and construction of vessels and tanks in reinforced plastics.
ASME PVHO: US standard for Pressure Vessels for Human Occupancy.
CODAP: French Code for Construction of Unfired Pressure Vessel.
AS/NZS 1200: Australian and New Zealand Standard for the requirements of Pressure equipment including Pressure Vessels, boilers and pressure piping.
AS 1210: Australian Standard for the design and construction of Pressure Vessels
AS/NZS 3788: Australian and New Zealand Standard for the inspection of pressure vessels
API 510.
ISO 11439: Compressed natural gas (CNG) cylinders
IS 2825–1969 (RE1977)_code_unfired_Pressure_vessels.
FRP tanks and vessels.
AIAA S-080-1998: AIAA Standard for Space Systems – Metallic Pressure Vessels, Pressurized Structures, and Pressure Components.
AIAA S-081A-2006: AIAA Standard for Space Systems – Composite Overwrapped Pressure Vessels (COPVs).
ECSS-E-ST-32-02C Rev.1: Space engineering – Structural design and verification of pressurized hardware
B51-09 Canadian Boiler, pressure vessel, and pressure piping code.
HSE guidelines for pressure systems.
Stoomwezen: Former pressure vessels code in the Netherlands, also known as RToD: Regels voor Toestellen onder Druk (Dutch Rules for Pressure Vessels).
SANS 10019:2021 South African National Standard: Transportable pressure receptacles for compressed, dissolved and liquefied gases - Basic design, manufacture, use and maintenance.
SANS 1825:2010 Edition 3: South African National Standard: Gas cylinder test stations ― General requirements for periodic inspection and testing of transportable refillable gas pressure receptacles. ISBN 978-0-626-23561-1

History

right|thumb|A pressure vessel from 1919, wrapped with high tensile steel banding and steel rods to secure the end caps.

The earliest documented design of pressure vessels was described in 1495 in the book by Leonardo da Vinci, the Codex Madrid I, in which containers of pressurized air were theorized to lift heavy weights underwater. The need for high pressure and temperature vessels for petroleum refineries and chemical plants gave rise to vessels joined with welding instead of rivets (which were unsuitable for the pressures and temperatures required) and in the 1920s and 1930s the BPVC included welding as an acceptable means of construction; welding is the main means of joining metal vessels today. which typically consist of an unpressurized water tank at an elevation higher than the point of use. Pressure at the point of use is the result of the hydrostatic pressure caused by the elevation difference. Gravity systems produce per foot of water head (elevation difference). A municipal water supply or pumped water is typically around .

Inline pump controllers or pressure-sensitive pumps.
In nuclear reactors, pressure vessels are primarily used to keep the coolant (water) liquid at high temperatures to increase Carnot efficiency. Other coolants can be kept at high temperatures with much less pressure, explaining the interest in molten salt reactors, lead cooled fast reactors and gas cooled reactors. However, the benefits of not needing a pressure vessel or one of less pressure are in part compensated by drawbacks unique to each alternative approach.

Notes

References

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Sources

A.C. Ugural, S.K. Fenster, Advanced Strength and Applied Elasticity, 4th ed.
E.P. Popov, Engineering Mechanics of Solids, 1st ed.
Megyesy, Eugene F. "Pressure Vessel Handbook, 14th Edition." PV Publishing, Inc. Oklahoma City, OK

External links

Use of pressure vessels in oil and gas industry
Basic formulas for thin walled pressure vessels, with examples
Educational Excel spreadsheets for ASME head, shell and nozzle designs
ASME boiler and pressure vessel website
Journal of Pressure Vessel Technology
EU Pressure Equipment Directive website
EU Simple Pressure Vessel Directive
EU classification
Pressure vessel attachments
Image of a carbon-fiber composite gas cylinder, showing construction details
Image of a carbon-fiber composite oxygen cylinder for an industrial breathing set