Chemical Engineering October 2018 - 58

Engineering Practice
Calculate the Wetted Surface
Area of Pressure Vessels
This article provides a comparative study of two approaches to protect ASME semielliptical
pressure tanks from overpressure in the event of a fire
Babak Firoozi
Oilcor, Inc.
C
alculating the wetted surface
area is a crucial step
to protect American Society
of Mechanical Engineers'
(ASME) pressure vessels
from overpressure in the event of
a fire. The historical approach relies
on an analytical approximation,
using a linear equation to calculate
partial surface area of 2:1 semielliptical
(SE) heads that has been
published [1]. This article presents a
rigorous numeric analytical method
and compares partial surface area
calculations of 2:1 SE heads using
both methods.
Pressure relief from fire
The loss of fluids from enclosed
ASME pressure vessels as a result
of overpressure due to fire is a
major safety concern at chemical
process industries (CPI) facilities.
Such an event can not only lead to
worker injury and damage to mechanical
assets, but has the potential
for catastrophic losses to the
facility, the surrounding community
and the environment, as well. Fire
is often the cause of the greatest
relief load through a pressure safety
valve (PSV), and thus becomes a
critical aspect of appropriately sizing
NOMENCLATURE
SE Semi-elliptical
S Surface area
R Radius
D Diameter
V Volume
h Liquid level, 0 to D
dh Differential of liquid level for each i
i
hi
a1 Semimajor axis at hi
All dimensions are in consistent units
58
h
ai+1
ai
ai+1
ai
dh
2:1 SE head elevation view elliptical xy-planes
2:1 SE head plan view elliptical xy-planes
FIGURE 1. This figure shows the cross-section view of the SE heads of horizontal pressure vessels, in
both elevation view (left) and plan view (right)
FIGURE 2. In the event of a fire, the fluids inside a partially filled ASME pressure vessel with 2:1 SE heads
will absorb heat through the wetted surface, which is shown here in a darker shade of blue
the PSV.
Fluids in a vessel absorb the heat
Number of xy-planes, from 0 to n
Liquid level at i, hi = dh*i
of a fire through the wetted surface
area (Figure 2). The fluid's increase
in volume due to vaporization then
reaches a pressure that exceeds the
pressure capacity of the fixed vessel
volume. The expanded fluid must be
relieved through the PSV to avoid
rupturing the pressure vessel.
Per American Petroleum Inst.
(API) Standard 521, the head absorption
from fire is calculated by
Q = C1AWS
0.82, in which C1 is a
constant and Aws is the wetted surface
area [2]. The absorbed energy
across the wetted surface area proSurface
area calculations
Heads of ASME pressure vessels
are typically in the shape of an oblate
spheroid at a ratio of 2:1 (Figures
1 and 2). An analytic approximation
for wetted surface area of both 2:1
SE heads has been presented as
S=2.168Dh.
The shape of ellipsoids is well defined
by the general equation
x2/a2+y2/b2+z2/c2 = 1
and its total surface area is defined
by Knud Thomsen's formula [1]:
CHEMICAL ENGINEERING WWW.CHEMENGONLINE.COM
OCTOBER 2018
vides heat required to boil the liquid.

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Chemical Engineering October 2018

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