Equipment sizing

Author: Matt Nathal ^[2015]

Stewards: Jian Gong and Fengqi You

Vessel Specifications

A pressure vessel at a chemical plant.

The process requirements usually dictate specifications and parameters that the pressure vessel must fulfill. Some such requirements are:

• Min and Max design temperature
• Min and Max design pressure

Design Temperature

Maximum design temperature – highest mean metal temperature expected in operation plus a margin (typically 50°F).

Minimum design temperature – lowest mean metal temperature expected in operation minus a margin (typically 25°F).

Steps should be taken to account for potential failures of cooling/heating streams to prevent or minimize damage to equipment and injury to operators.

Design Pressure

Normal operating pressure – the expected pressure of the process.

Maximum operating pressure – the highest expected pressure, potentially during startup, shutdown, or emergencies.

Design pressure – the maximum operating pressure plus a margin. The margin is typically the greater of: 10% of max operating pressure or 25 psi.

The specified pressure is usually near the relief valve at the top of the vessel.

Vessel Geometry

Pressure Vessel Size and Shape

Typically pressure vessels are cylinders with at least a 2:1 ratio of height to width. 3:1 and 4:1 ratios are most common.

Pressure Vessel Orientation

Pressure vessels can be oriented either vertically or horizontally. Vertical vessels are more common because they use less land space and the smaller cross-sectional area of the vessel allows for easier mixing. Horizontal vessels are used when more phase separation is required because larger cross-sectional areas allow for less vertical velocities and therefore less entrainment. Settling tanks and flash vessels are typically horizontal for this reason. Horizontal vessels also allow easier cleaning, so heat exchangers are primarily horizontal.

Head Design

There are three different designs for the ends of the pressure vessel: hemispherical, ellipsoidal, and torispherical. Hemispherical heads are best for high pressure systems, they provide the largest internal volume of the three options, they are half the thickness of the shell, and are the most expensive to make and combine with the shell. Ellipsoidal heads are cheaper than hemispherical heads and provide less internal volume, they are the same thickness as the shell, and are most common for systems with greater than 15 bar. Torispherical heads are the cheapest of the three options, and are most commonly used when pressures do not exceed 15 bar.

Stresses and Strains

There are a variety of potential stresses on a pressure vessel that must be accounted for during design and construction:

• Internal and external pressure
• Weight of vessel
• Weight of contents
• Weight of internals (distillation trays, heating/cooling coils, packing supports)
• Weight of attached equipment
• Thermal expansion
• Cyclic loads caused by condition changes
• Friction loads
• Environmental loads (wind/snow/seismic)

Wall Thickness

There are two main stresses that can occur on the shell portion of the pressure vessel; hoop stress and longitudinal stress.

Hoop Stress:

Wall thickness $={\frac {PD}{2SE-1.2P}}$

Longitudinal Stress:

Wall thickness $={\frac {PD}{4SE+0.8P}}$

Where P is the pressure, D is the diameter, S is the max allowable stress, and E is the welded joint efficiency. The thicker of the two is chosen as the wall thickness. The minimum wall thickness (without considering corrosion allowances) is 1/16 inches.

Typically walls are much thicker. In high pressure vessels, internal pressure has the largest magnitude. In low pressure vessels, wall thickness is designed to resist vacuum.

Head thickness

Alternate equations govern the appropriate head thickness:

Hemispherical:

Thickness $={\frac {PD}{4SE-0.4P}}$

Ellipsoidal:

Thickness $={\frac {PD}{2SE-0.2P}}$

Torispherical:

Thickness $={\frac {0.885PRc}{SE-0.1P}}$

R_c is the crown radius.

Corrosion Allowance

A margin of wall thickness must be added to account for corrosion of the vessel over time. This margin is usually between 1/16” and 3/16”.

In heat exchangers where wall thickness can affect heat transfer, smaller margins are used.

Case Study

What is the wall thickness of a 304 stainless steel pressure vessel with a 5ft diameter, 400 psi design pressure, and 500F design temperature? Assume double-welded butt joints were used (E = 0.85).

First, the max allowable stress must be calculated. Using a table found in: ASME BPV Code Sec. VIII D.1, Sec. II Part D, the maximum allowable stress under these conditions is 12,900 psi. The hoop stress is calculated as follows:

$t={\frac {400(5)(12)}{2(129000)(0.85)-1.2(400)}}$ Failed to parse (syntax error): {\displaystyle t ≈ 1.12 inches }

The longitudinal stress is then calculated:

$t={\frac {400(5)(12)}{4(12900)(0.85)+0.8(400)}}$ Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle t ≈ 0.54 inches }

The larger of the two is hoop stress. Adding on the corrosion allowance and rounding to the nearest quarter inch gives a wall thickness of 1.25 inches.