Page 225 - Introduction to Petroleum Engineering

212 UPSTREAM FACILITIES
thin‐walled cylindrical pressure vessel with internal pressure p, thickness t, and inner
radius r is
ic
pp r
a ic (11.13)
h t
with p equal to local atmospheric pressure. The axial force on the ends of a closed
a
cylindrical tank produces axial stress, which is directed along the longitudinal axis of
the cylinder. The axial stress σ of a thin‐walled cylindrical pressure vessel with
a
internal pressure p, thickness t, and inner radius r is
ic
pp r
a ic (11.14)
a t 2

The axial stress is half of the hoop stress.
The surface (tangential) stress of a spherical pressure vessel is the same in all
directions because of the spherical symmetry of the tank. The surface stress σ of a
s
thin‐walled spherical pressure vessel with internal pressure p, thickness t, and inner
radius r is
is
pp r
a is (11.15)
s t 2
Equations 11.13–11.15 can be used to estimate the maximum operating pressure
for thin‐walled pressure vessels. The maximum stress should equal the maximum
safe operating stress for the vessel wall. Steel pressure vessels are often designed
for a maximum stress of 20 000 psi. That specification can vary with the alloy and
the manufacturer. The maximum working pressure for a separator should be on the
nameplate for the vessel.

Example 11.5 Separator Tank
A separator tank with inner radius of 20 in. is fabricated from 0.25‐in.‐thick steel.
For an internal pressure of 250 psig, determine the hoop and axial stress in psi.
Answer
Solve using Equation 11.13. Note that 250 psig equals the difference between
internal pressure and ambient, or local atmospheric, pressure:

pp r ic 250 psi 20 in.
a
h 20000 psi
t 025 in.
.
Depending on the alloy, 250 psig may be the maximum safe operating pressure
for the vessel.