Chemical Engineering January 2015 - 51

Engineering Practice
for material specification, the lower
bound of the recovery factor would
provide this estimate, as shown in
Equation (9).
for lowest recovery
(9)
In addition, in the evaluation and
development of the adiabatic-walltemperature
recovery factor, only
noncondensable gases have been
considered. It is conceivable that a
vapor stream may experience flowing
temperatures below its dewpoint,
thus possibly condensing
within the core stream. It is possible
that at the wall, the shearing work
and frictional heating is sufficiently
high to ensure that there are no liquid
droplets touching the wall, and
the flow behaves as an annular twophase
flow that can be treated as a
gas for practical purposes. On the
other hand, it is possible that the
condensed liquid droplets can contact
the wall, which may result in
additional cooling at the wall as the
liquid is vaporized. The evaluation
of the adiabatic wall temperature
for high-speed condensable vapor
flow remains as further work.
Application and examples
One of the direct applications of this
information would be the screening
of potential low-temperature
issues caused by low-flowing temperatures
in all-gas flow systems.
The recovery factor for these cases
can be determined as a function of
Pr at the reference temperature T*
as described by Eckert [3, 4], or perhaps
in the more detailed analysis
of Shapiro [5]. This recovery factor
can then be used to determine an
actual adiabatic wall temperature.
The recovery temperature should
then be compared to the minimum
design metal temperature (MDMT)
of the piping system for identification
of potential low-temperature
cases. In addition, any analysis that
is being performed involving heat
transfer between the fluid and the
pipe should be based on the effective
temperature differential between
the pipe wall temperature and this
adiabatic wall temperature.
A practical application of the adiArea
taBle
1. calculatIoN oF aDIaBatIc Wall temPerature
ft²
0.348
Volumetric flow
Mass flow
Density
Flowing enthalpy
Flowing entropy
Stagnation enthalpy
Stagnation temperature
Iteration
Wall temperature
Reference temperature
Specific heat capacity
Viscosity
Conductivity
Prandtl number
Recovery factor
Adiabatic wall temperature
°F
abatic wall temperature evaluation
can be found in natural-gas processing
facilities, where discharges from
pressure-relief or depressurization
valves may involve high-velocity
noncondensable gas. Evaluations of
discharge piping that are performed
assuming adiabatic flow yield flowing
temperatures and velocities.
These flowing conditions can be
used to determine the stagnation
enthalpy, and thus the stagnation
temperature, which can then be
used in the calculation of r.
Calculation example
As an example of wall-temperature
determination, consider the flow of
25,000 lb/h of methane at 400 ft/s
within an 8-in. Schedule 40 pipe
having a stream temperature of
-20°F. The following steps were performed,
using the equations defined
previously in this article, as well as
the properties of methane obtained
from the National Institute for
Standards and Technology's (NIST)
standard reference data program,
Refprop v. 9.0 [10]:
* Use the velocity and flowing enthalpy
to determine the stagnation
enthalpy per Equation (6)
* Perform an enthalpy-entropy
flash at the stagnation enthalpy
and flowing entropy to obtain the
stagnation temperature
* Iterate on the reference temperature
to obtain the specific heat
50 ChemiCal engineering www.Chemengonline.Com JanUarY 2015
ft³/h
lb/h
lb/ft³
Btu/lb
Btu/lb°R
Btu/lb
°F
500,000
25,000
0.05
341
1.49
344.125
-13.7
reference temperature iterations
1
°F
°F
Btu/lb°R
cP
Btu/h-ft°F
-13.7
-15.46
0.51185
0.00936
0.01576
0.736
0.903
-14.3
2
-14.3
-15.89
0.51177
0.00935
0.01574
0.736
0.903
-14.3
capacity at constant pressure,
viscosity and conductivity for use
in determining Pr
l
The stagnation temperature
is used as the adiabatic wall
temperature for the first step
in the iteration in this example,
but a better estimate can
be determined using an estimated
recovery factor of 0.88
and Equation (8)
l
The reference temperature is
calculated based on Equation
(5) at each step
l
The fluid properties are
re-evaluated at the reference
temperature and the
flowing entropy, and Pr is
recalculated
l
Calculate r based on Equations
(2), (3) or (9). Equation
(3) was used in this
particular example
l
Calculate an adiabatic wall
temperature based on Equation
(1)
l
Iteration is continued until
the solution converges on an
adiabatic wall temperature
In this case, an adiabatic wall temperature
of -14.3°F is calculated.
Table 1 gives a summary of the parameters
used in this example for
the iterative determination of the
adiabatic wall temperature. One will
find that by using an estimated recovery
factor of 0.88 to generate the
reference temperature from Equa
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Chemical Engineering January 2015

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