Compressible flow involves variation in the density with changes in pressure and temperature along the pipe length. This article revisits the conventional adiabatic pipe flow equation and finds a fundamental drawback in this equation. The corrected adiabatic pipe flow equation has fixed the fundamental error in the conventional adiabatic pipe flow equation where the average density estimation for the conventional adiabatic equation is lower than the lower bound of the average density based on isothermal temperature. However, both the conventional adiabatic equation and the corrected adiabatic equation result in an over prediction of mass flux due to a deficiency in the average density definition. The over prediction of mass flux is not significant if the pressure drop is less than 40%; however, the pressure drop is usually greater than 40% of the inlet pressure for most pressure relief system applications. The authors offer a novel adiabatic pipe flow equation based on insights presented in this work. The novel adiabatic pipe flow equation is the most suitable solution for the pressure relief system applications as well as any other common application since it better represents the nature of adiabatic flow in a pipe. The experimental data previously published is compared with the predictions to validate the new adiabatic pipe flow model.

References

1.
Yu
,
F. C.
, 1999, “Compressible Fluid Pressure Drop Calculation–Isothermal Versus Adiabatic,” Hydrocarbon Process., pp. 89–95.
2.
Hullender
,
D.
,
Woods
,
R.
, and
Huang
,
Y. W.
, 2010, “
Single Phase Compressible Steady Flow in Pipes
,”
ASME Trans. J. Fluids Eng.
,
32
, p.
014502
.
3.
Walters
,
T.
, 2000, “Gas-Flow Calculations: Don’t Choke,” Chem. Eng., pp. 70–76.
4.
Nouri-Borujerdi
,
A.
, and
Ziaei-Rad
,
M.
, 2009, “
Simulation of Compressible Flow in High Pressure Buried Gas Pipelines
,”
Int. J. Heat Mass Transfer
,
52
, pp.
5751
5758
.
5.
Kim
,
J. S.
, and
Dunsheath
,
H. J.
, 2010, “
A Homogeneous Equilibrium Model Improved for Pipe Flows
,”
Proceedings of World Congress on Engineering and Computer Science, International Association of Engineers, Hong Kong, Vol.
2
, pp.
733
738
.
6.
Crowl
,
D. A.
, and
Louvar
,
J. F.
, 1990,
Chemical Process Safety: Fundamentals With Applications
,
Prentice-Hall
,
Englewood Cliffs, NJ
, Chap. 4.
7.
Green
,
D.
, and
Perry
,
R. H.
, 2008,
Perry’s Chemical Engineers’ Handbook
,
McGraw-Hill
,
New York
, Chap. 6.
8.
McCabe
,
W. L.
, and
Smith
,
J. C.
, 1976,
Unit Operations of Chemical Engineering
,
McGraw-Hill
,
New York
, Chap. 6.
9.
Saad
,
M. A.
, 1985,
Compressible Fluid Flow
,
Prentice-Hall
,
Englewood Cliffs, NJ
, Chap. 5.
10.
Shapiro
,
A. H.
, 1953,
The Dynamics and Thermodynamics of Compressible Fluid Flow
,
The Ronald Press Company
,
New York
, Chap. 6.
11.
Keith
,
J. M.
, and
Crowl
,
D. A.
, 2005, “
Estimating Sonic Gas Flow Rates in Pipelines
,”
J. Loss Prev. Process Ind.
,
18
, pp.
55
62
.
12.
Abbas
,
Q.
,
Khan
,
M. M.
,
Sabir
,
R.
,
Khan
,
Y. M.
, and
Koreshi
,
Z. U.
, 2010, “
Numerical Simulation and Experimental Verification of Air Flow Through a Heated Pipe
,”
Int. J. Mechanical Mechatronics Eng.
,
10
(
2
), pp.
7
12
.
13.
Bhramara
,
P.
,
Sharma
,
V.
, and
Reddy
,
T. K. K.
, 2009, “
Prediction of Pressure Drop of Refrigerants for Two-Phase Flow Inside a Horizontal Tube Using CFD Analysis
,”
ARPN J. Eng. Appl. Sci.
,
4
(
9
), pp.
64
71
.
14.
Munkejord
,
S. T.
,
Molnvik
,
M. J.
,
Melheim
,
J. A.
,
Gran
,
I. R.
, and
Olsen
,
R.
, 2005, “
Prediction of Two- Phase Flows Using Simple Closure Relations in a 2D Two-Fluid Model
,”
Proceedings of the 4th International Conference on CFD in the Oil and Gas
, Metallurgical and Process Industries SINTEF/NTNU Trondheim, Norway.
15.
Crane
,
C.
, 1988, Flow of Fluids Through Valves, Fittings, and Pipe, Crane Technical Paper No. 410.
16.
Kern
,
R.
, 1975, “How to Size Piping and Components as Gas Expands at Flow Conditions,” Chem. Eng., pp. 125–132.
17.
ANSI/API Standard 521, 2007, Pressure-Relieving and Depressuring Systems, pp. 104–110.
18.
Page
,
R. T.
, 1935, “
Constant-Flow Orifice Meters of Low Capacity
,”
Ind. Eng. Chem.
,
7
(
5
), pp.
355
358
.
19.
Druett
,
H. A.
, 1955, “
The Construction of Critical Orifices Working With Small Pressure Differences and Their Use in Controlling Airflow
,”
Brit. J. Ind. Med.
,
12
, pp.
65
70
.
20.
Overcamp
,
T. J.
, 1985, “
A Theory of Critical Flow Through Hypodermic Needles
,”
Environ. Sci. Technol.
,
19
(
11
), pp.
1134
1136
.
21.
Fliegner
,
A.
, 1874,
“On the Flow of Atmospheric Air
,”
Proc. Inst. Civ. Engrs.
,
39
, pp.
370
375
.
22.
Huff
,
J. E.
, and
Shaw
,
K. R.
, 1982, “
Measurement of Flow Resistance of Rupture Disc Devices
,”
Plant/Oper. Prog.
,
11
(
3
), pp.
187
200
.
23.
Ekblom
,
A.
, and
Gullman-Strand
,
J.
, 1998, “
Experimental Study of Compressible Pipe Flow With Friction and Heat Addition
,” M.S. thesis, KTH, Stockholm, Sweden.
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