Chemical engineering apparatus desisgn

Chemical Engineering
Apparatus Design
BY: ABEBE EDESSA
DIRE DAWA UNIVERSITY
INSTITUTE OF TECHNOLOGY
SCHOOL OF CHEMICAL AND BIO ENGINEERING ACADEMIC YEAR 2020

PRESSURE VESSELS
INTRODUCTION
▪ The pressure vessels (i.e. cylinders or tanks) are used to store
fluids under pressure.
▪ The pressure vessels are designed with great care because rupture
of a pressure vessel means an explosion which may cause loss of life
and property.
▪ The material of pressure vessels may be brittle such as cast iron,
or ductile such as mild steel.
By: ABEBE EDESSA
2
ACADEMIC YEAR 2020
SCHOOL OF CHEMICAL AND BIO ENGINEERING

They are used in a variety of industries like
▪Petroleum refining
▪Chemical
▪Power
▪Food & beverage
▪Pharmaceutical
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By: ABEBE EDESSA

Classification of Pressure Vessels
According to the dimensions:
The pressure vessels, according to their dimensions, may be
classified as thin shell or thick shell.
If the wall thickness of the shell (t) is less than 1/10 of the
diameter of the shell (d), then it is called a thin shell.
If the wall thickness of the shell is greater than 1/10 of the
diameter of the shell, then it is said to be a thick shell.
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By: ABEBE EDESSA

According to the end construction:
The pressure vessels, according to the end construction,
may be classified as open end or closed end.
A simple cylinder with a piston, such as cylinder of a press
is an example of an open end vessel, whereas a tank is an
example of a closed end vessel.
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By: ABEBE EDESSA

There are three main types of pressure vessels in general
❑Horizontal Pressure Vessels
❑Vertical Pressure Vessels
❑Spherical Pressure vessels
However there are some special types of Vessels like Regeneration
Tower, Reactors but these names are given according to their use
only.
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By: ABEBE EDESSA

HORIZONTAL PRESSURE VESSEL
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SCHOOL OF CHEMICAL AND BIO ENGINEERING By: ABEBE EDESSA

VERTICAL PRESSURE VESSEL
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By: ABEBE EDESSA

SPHERICAL PRESSURIZED STORAGE VESSEL
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MAIN COMPONENTS OF PRESSURE VESSEL
The main pressure vessel components are as follow:
✓ Shell
✓ Head
✓ Nozzle
✓ Support
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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
cylindrical, spherical and conical in shape.
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By: ABEBE EDESSA

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.
Heads can also be used inside a vessel. Heads are usually categorized
by their shapes. Ellipsoidal, Hemispherical, Torispherical, Conical,
Toriconical and flat are the common types of heads. Ellipsoidal (2:1)
would be the most common type of heads, which is used during the
designing of pressure vessels.
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By: ABEBE EDESSA

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Types of Heads
By: ABEBE EDESSA

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 or pressure gauges).
▪ Provide access to the vessel interior at manways.
▪ Provide for direct attachment of other equipment items, (e.g., a heat
exchanger or mixer).
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By: ABEBE EDESSA

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, and
earthquake loads.
Typical kinds of supports are as follow:
➢ Saddle
➢ Leg
➢ Skirt
➢ Lug
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By: ABEBE EDESSA

Saddle
Horizontal drums 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.
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By: ABEBE EDESSA

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A typical scheme of saddle support
By: ABEBE EDESSA

Leg
Small vertical drums 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. 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. 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 is typically used to help absorb wind
or earthquake loads
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By: ABEBE EDESSA

Skirt
Tall, vertical, cylindrical pressure vessels (e.g., the tower and reactor)
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. 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
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By: ABEBE EDESSA

Lug
Lugs that are welded to the pressure vessel shell and 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
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By: ABEBE EDESSA

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Typical Scheme of lug
By: ABEBE EDESSA

Thin Cylindrical Shell under Internal Pressure
The analysis of stresses induced in a thin cylindrical shell are made on
the following assumptions:
➢ The effect of curvature of the cylinder wall is neglected.
➢ The tensile stresses are uniformly distributed over the section of the
walls.
➢ The effect of the restraining action of the heads at the end of the
pressure vessel is neglected.
When a thin cylindrical shell is subjected to an internal pressure, it is
likely to fail in the following two ways:
➢ It may fail along the longitudinal section (i.e. circumferentially) splitting
the cylinder into two troughs, as shown in Fig. a.
➢ It may fail across the transverse section (i.e. longitudinally) splitting
the cylinder into two cylindrical shells, as shown in Fig. b.
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Failure of a cylindrical shell

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Circumferential or Hoop Stress
A tensile stress acting in a direction tangential to the circumference
is called circumferential or hoop stress. In other words, it is a
tensile stress on longitudinal section (or on the cylindrical walls).
INSTITUTE OF TECHNOLOGY By: ABEBE EDESSA

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Total force acting on longitudinal section
= 𝐼𝑛𝑡𝑒𝑛𝑠𝑖𝑡𝑦 𝑜𝑓 𝑝𝑟𝑒𝑠𝑠𝑢𝑟𝑒 × 𝑃𝑟𝑜𝑗𝑒𝑐𝑡𝑒𝑑 𝑎𝑟𝑒𝑎 = 𝑃 × 𝐷 × 𝑙 (i)
Total resisting force acting on the cylinder walls
= 𝜎 × 2𝑡 × 𝑙 (ii)
From equations (i) and (ii), we have
𝜎 × 2𝑡 × 𝑙 = 𝑝 × 𝐷 × 𝑙 or
𝜎 =
𝑃𝐷
2𝑡

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Longitudinal Stress
A tensile stress acting in the direction of the axis is called
longitudinal stress. In other words, it is a tensile stress acting on
the transverse or circumferential section Y-Y (or on the ends of the
vessel).
By: ABEBE EDESSA

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Total force acting on transverse section
= 𝐼𝑛𝑡𝑒𝑛𝑠𝑖𝑡𝑦 𝑜𝑓 𝑝𝑟𝑒𝑠𝑠𝑢𝑟𝑒 × 𝐶𝑟𝑜𝑠𝑠 𝑠𝑒𝑐𝑡𝑖𝑜𝑛𝑎𝑙 𝑎𝑟𝑒𝑎 = 𝑃 ×
𝜋
4
× 𝐷2
(i)
Total resisting force
= 𝜎 × 𝜋 × 𝐷 × 𝑙 (ii)
From equations (i) and (ii), we have
𝜎 =
𝑃𝐷
4𝑡

Thick Cylindrical Shell under Internal Pressure
When a cylindrical shell of a pressure vessel, hydraulic cylinder, gun
barrel and a pipe is subjected to a very high internal fluid pressure, then
the walls of the cylinder must be made extremely heavy or thick.
In thin cylindrical shells, we have assumed that the tensile stresses are
uniformly distributed over the section of the walls. But in the case of
thick wall cylinders, the stress over the section of the walls cannot be
assumed to be uniformly distributed. They develop both tangential and
radial stresses with values which are dependent upon the radius of the
element under consideration.
The distribution of stress in a thick cylindrical shell, the tangential
stress is maximum at the inner surface and minimum at the outer
surface of the shell. The radial stress is maximum at the inner surface
and zero at the outer surface of the shell.
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Stress distribution in thick cylindrical shells subjected to internal pressure

Lame’s equation.
Assuming that the longitudinal fibers of the cylindrical shell are
equally strained, Lame has shown that the tangential stress at any
radius x is:
and radial stress at any radius x
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By: ABEBE EDESSA

Since we are concerned with the internal pressure ( 𝑃𝑖 = 𝑃) only,
therefore substituting the value of external pressure, 𝑃𝑜 = 0.
Tangential stress at any radius x
Radial stress at any radius x
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The tangential stress is always a tensile stress whereas the radial
stress is a compressive stress. The tangential stress is maximum
at the inner surface of the shell (i.e. when x = ri ) and it is
minimum at the outer surface of the shell (i.e. when x = ro).
Substituting the value of x = ri and x = ro in equation (i), we find
that the maximum tangential stress at the inner surface of the
shell.
Minimum tangential stress at the outer surface of the shell
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The radial stress is maximum at the inner surface of the shell
and zero at the outer surface of the shell. Substituting the value
of x = ri and x = ro in equation (ii).
Maximum radial stress at the inner surface of the shell
Minimum radial stress at the outer surface of the shell
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By: ABEBE EDESSA

In designing a thick cylindrical shell of brittle material (e.g. cast iron,
hard steel and cast aluminum) with closed or open ends and in
accordance with the maximum normal stress theory failure, the
tangential stress induced in the cylinder wall
Since ro = ri + t, therefore substituting this value of ro in the above
expression:
The value of σt for brittle materials may be taken as 0.125 times the
ultimate tensile strength (σu).
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In case of cylinders made of ductile material, Lame’s equation is
modified according to maximum shear stress theory.
Maximum principal stress at the inner surface
Minimum principal stress at the outer surface
Maximum shear stress
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The value of shear stress (𝜏) is usually taken as one-half the
tensile stress (σt). Therefore the above expression may be
written as
From the above expression, if the internal pressure ( p) is
equal to or greater than the allowable working stress (σt or
τ), then no thickness of the cylinder wall will prevent failure.
Thus, it is impossible to design a cylinder to withstand fluid
pressure greater than the allowable working stress for a
given material.
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OPTIMUM VESSEL PROPORTIONS
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V =vessel volume, cu ft
P = internal pressure, PSlG
L=length, ft
D =diameter, ft
C =corrosion allowance, in.
F2 =vessel ratios
S =allowable stress, psi
E =joint efficiency

OPTIMUM VESSEL PROPORTIONS
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Method
1. Calculate F2.
2. From Figure determine L/D
ratio.
3. From the L/D ratio, calculate the
diameter, D.
4. Use D and V to calculate the
required length, L.
By: ABEBE EDESSA

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External pressure on cylindrical shells causes compressive forces that
could lead to buckling. The equations for the buckling of cylindrical
shells under external pressure are extremely cumbersome to use
directly in design (Jawad, 1994). However, these equations can be
simplified for design purposes by plotting them so that the minimum
buckling strain is expressed in terms of length, diameter and
thickness of the cylinder. These plots are utilized by the ASME.
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External pressure

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For an open-ended cylinder, the critical pressure to cause buckling Pc
is given by the following expression; Windenburg and Trilling (1934):

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External Pressure for Cylinders with 𝐷 𝑜/𝑡 ≥ 10
The ASME uses plots to express the lowest critical strain, A, in
terms of the ratios L/Do and Do/t of the cylinder. The designer
calculates the known quantities L/Do and Do/t and then uses the
figure to determine buckling strain. A. To correlate buckling strain
to allowable external pressure, the designer uses the stress-strain
diagram to obtain a B value.
The Allowable External Pressure
𝑷 = (𝟒/𝟑)(𝑩)(𝑫 𝒐/𝒕)
When A falls to the left of the curves, the value of P is determined
𝑷 = 𝟐𝑨𝑬/𝟑(𝑫 𝒐/𝒕)
E = Modulus of Elasticity

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External Pressure for Cylinders with 𝐷 𝑜/𝑡 < 10
When Do/t is less than 10, the allowable external pressure is taken
as the smaller of the values determined from the following two
equations:
𝑷 𝒂𝟏 = Τ𝟐. 𝟏𝟔𝟕 Τ𝑫 𝒐 𝒕 − 𝟎. 𝟎𝟖𝟑𝟑 𝑩
𝑷 𝒂𝟐 =
𝟐𝑺
Τ𝑫 𝒐 𝒕
Τ𝟏 − 𝟏 Τ𝑫 𝒐 𝒕
Where B is obtained as discussed above. For values of (Do/t) of less
than or equal to 4, the A value is calculated from
𝑨 = 𝟏. 𝟏/( Τ𝑫 𝒐 𝒕) 𝟐
For values of A greater than 0.10, use a value of 0.10

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External Pressure for Cylinders with 𝐷 𝑜/𝑡 < 10
The value of S is taken as the smaller of two times the allowable
tensile stress, or 0.9 times the yield stress of the material at the
design temperature.

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By: ABEBE EDESSA

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The major sources of dead weight loads are:
1. The vessel shell.
2. The vessel fittings: manways, nozzles.
3. Internal fittings: plates (plus the fluid on the plates);
heating and cooling coils.
4. External fittings: ladders, platforms, piping.
5. Auxiliary equipment which is not self-supported;
condensers, agitators.
6. Insulation.
7. The weight of liquid to fill the vessel
Weight loads

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Weight loads
The approximate weight of a cylindrical vessel with domed ends, and
uniform wall thickness, can be estimated from the following equation:
For a steel vessel

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Wind Loads (Tall Vessels)
The vessel under wind loading acts as a cantilever beam. For a
uniformly loaded cantilever the bending moment at any plane is
given by:
where x is the distance measured from the free end and w the
load per unit length (Newtons per meter run).

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Dynamic wind pressure
The load imposed on any structure by the action of the wind will
depend on the shape of the structure and the wind velocity.
By: ABEBE EDESSA

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A wind speed of 160 km/h (100 mph) can be used for preliminary
design studies; equivalent to a wind pressure of 1280 N/m2 (25
lb/ft2).
The loading per unit length of the column can be obtained from the
wind pressure by multiplying by the effective column diameter: the
outside diameter plus an allowance for the thermal insulation and
attachments, such as pipes and ladders.

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Stresses Analysis
Pressure stresses:
Dead weight stress: Bending stresses:
By: ABEBE EDESSA

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Chemical engineering apparatus desisgn

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