A novel calibration approach can save on maintenance costs for industrial gas
pipeline systems. A new intelligent measurement technique for
gas flow uses a sonic nozzle sensor. A case history examines
the application and test validity for such measurement technology on a highvolume natural
gas pipeline system.
Background.
There has been increased interest by nozzle manufactures to
design nozzles that will effectively reduce the volume flow in
gas compression systems.^{1} Compressible flow dynamics
are a critical aspect of many engineering applications in
processes and equipment, such as expansion processes, high and
lowpressure nozzles, valves and
compressors.^{2–4} This study is focused on
measuring the mass flowrate of a compressible fluid through a
convergent divergent nozzle with respect to inlet and outlet
pressures.
Gas flowmeters must operate properly and
reliably because the measurement data constitute not
only the basis for billing quantities of delivered gas, but
also for rational exploitation of the pipeline network. With
pipeline transport of natural gas, small measurement errors can
have serious consequences.^{5} When using gas
flowmeters in commercial transactions, it is necessary to
ensure correct metering, as prescribed by competent
authorities. Each meter must be properly certified and
calibrated to the operating conditions.^{6,7}
In connection with the increasing demand of natural gas as a
primary energy supply and connected higher demands on
measurement and test rig technology, sonic nozzles, which are
already established in the low pressure area get more important
also for high pressure.^{8}
Sonic nozzles are recommended in many
engineering applications—for example, in the turbinemeter
standard for meter calibration, etc.^{9} This article
examines the performance for onsite calibration of a sonic
nozzle sensor installed in a gas pipeline system. The
regulation of the sonic nozzle sensor during the periodic
checks, measuring instruments is compared to the standards to
verify their performance; these calibrations are generally
performed onsite.
For a gas pipeline system, onsite calibration is generally
difficult because it requires providing a headline to install a
standard meter and the flexibility to impose flowrates that
correspond to the points defined by the rules. In practice,
these sensors are calibrated in the workshop facilities, which are approved by
the competent authorities. Among these calibrations, we can
also use the venturinecked sonic nozzles.^{10}
The principle of gas flow measuring through the
venturinecked sonic nozzle is based on the determination of
the pressure ratio between the upstream and downstream and the
necked section of the nozzle. The accuracy of the flow
determination is about 0.5%, which is appreciable. The aim of
our work is the study of an installation using the benefits of
sonic nozzles mounted in parallel to determine the gas flow,
which is transported by the pipeline under insitu
conditions.
Sonic nozzle technology.
The sonic nozzle is a fluidflow measurement device used in
many industrial applications, and it is based on the principle
that gas flow accelerates to a critical velocity at the nozzle
throat.^{6,10–12} At critical velocity, the mass
flowrate of gas flowing through the nozzle is the maximum
possible for the existing upstream conditions.^{13}
Because it has no mobile parts, it is very stable and
stressresistant, and it can be used repeatedly, with very low
maintenance. Due to their high
repeatability and reproducibility, sonic nozzles are considered
to be very precise. Sonic devices operate on the principle that
as fluid flows through the meter, the fluid accelerates as it
approaches the throat. As the differential pressure increases,
the velocity at the throat increases. When the velocity of the
fluid reaches the speed of sound, it is considered choked,
sonic or critical.^{14} Once the flow has reached the
critical state, increasing the differential pressure will not
affect the fluid flowrate.^{15} Several components are
important to a sonicdevice metering system; upstream and
downstream piping, pressure sensors, temperature sensors and
flow computers.^{10,16} Measurement solutions are shown
in Fig. 1.

Fig.
1. Measurement solutions for a
venturitype nozzle. 
The sonic nozzle is similar to a subsonic variable head type
flowmeter in which a constriction is present in the flow
stream.^{7} As the gas flows through the converging
section of the nozzle, the inlet pressure is converted to
velocity, which reaches a maximum at the throat. When the fluid
velocity reaches the speed of sound at the throat, the flowrate
will vary linearly with the inlet pressure and will not be
affected by downstream pressure fluctuations.^{13} The
pressure drop across the nozzle must be sufficient to maintain
sonic flow at the throat. Normally, sonic flow occurs when the
downstream pressure is not greater than onehalf the upstream
pressure.
Example.
Assume that the flow is permanent, one dimensional,
compressible and isentropic for an ideal gas in a venturi
nozzle. The general equations of fluid motion in a net current
can be written as:
Differential equation of continuity:
(1)
Equation of dynamics:
(2)
Equation of energy:
(3)
Equation of state of ideal gas:
(4)
Note: For an ideal gas, the specific heat
C_{p} at the constant pressure is given by the
relation:
Using some transformations of fluid, we obtain the important
relation of Hugoniot:^{11}
(5)
Where u / a = M is the local Mach
number.^{17}
Analyzing this equation to the main sections of the nozzle
gives us:
• In the convergent nozzle, when ds < 0,
then du > 0 and the speed increases, subsonic
flow.
• At the neck ds = 0 so:
(6)
Two cases may arise, either:
1. dU = 0, and the velocity reaches a maximum
and then decreases
2. M^{2} = 1 and the velocity becomes
sonic at the neck.
• Finally, in the divergent part, ds >
0. In this case there, are two outlets. If M < 1,
then du < 0 and the velocity decreases, subsonic
flow.
Eq. 6 shows that in given piping with an isentropic flow,
the fluid velocity cannot be equal to sound (M = 1),
except at the neck of the venturi nozzle. (In this piping
section, the area has a maximum or minimum.)
Massflow venturi nozzle.
The massflow venturi nozzle is passing through a slice
where, Q = r Su in which a section of
welldefined and constant to calculate the flow simply
determine with good precision the values r and u. By
integrating the thermodynamic Eq. 3, we have the equation of
Zeuner:^{11,12}
(7)
Similarly, for an ideal gas, we have the following
relation:
(8)
And replacing in Eq. 8, we get:
(9)
The application of this equation for the upstream section in
which u = 0 and any section of the nozzle, gives
us:
(10)
Given that the flow is isentropic, we will have speed in a
section equalling:
(11)
This relationship gives the equations of fluid motion are
often expressed in terms of Mach number, then Eq. 11 can be
written as:
(12)
Eq. 12 is very important; it can be used to determine
critical parameters of the flow. And, finally, by substituting
u in Eq.10, we have:
(13)
Given that the flow is isentropic, we have:
(13a)
By maintaining constant conditions, generating the mass flow
is based on grouping Y = f (P / P_{am}).
Critical flow. From Eq. 13a, we see that maintaining
constant upstream conditions implies that the flow depends only
on the function:
(14)
In turn, this function depends only on (P /
P_{am} = W) reaches a maximum when we have
then:
(15)
This parameter is called the critical ratio of relaxation
(W_{cr}), and the corresponding speed to this
ratio is equal to:
(16)
Substituting P_{am,}
r_{am} the values of dependent parameters
collar, we have finally:
which is the speed of sound in the neck of the venturi
nozzle and the mass flow will be:
(17)
Denotes the relaxation coefficient magnitude
and we write:
(18)
Thus, we see that the mass flow of a sonic flow depends only
on parameters upstream of the venturi nozzle. This value
represents a maximum possible flow nozzle. For example, assume
the characteristics of the critical state of a nozzle without a
diverging natural gas (g = 1.22):
Flow computers.
Flow computers are electronic devices that can use various
process measurements to calculate flow. The flow computers have
been applied to solve various linearization and compensation
equations that were previously done using other
methods.^{16, 18–21} They are especially
convenient to operators who need standalone devices to be
configured and that are able to add, subtract, multiply,
divide, drop out, square root, linearize, totalize, solve for
exponents, algorithms, etc.
In this application, the sonic nozzle in a gas compression
system may be calibrated to measure accurately when it is
operated at a particular pressure and temperature. The flow
computers can make corrections for Reynolds number effects and
changing fluid density, as well as, remove
nonlinearity.^{22,23} Because the gas can be
compressed, measurement error will occur when the sonic nozzle
is operated at a different pressure and temperature.
When provided with the raw flow, operating pressure, and
operating temperature measurements, a flow computer can be used
to mathematically correct the raw flow measurement to account
for realtime changes in operating pressure and temperature.
The gas flow measurement and control in gas pipeline systems
using intelligent sonic nozzle sensor proposed is shown in Fig.
2.

Fig.
2. Gas flow measurement and control
in gas pipeline system using an intelligent
sonic nozzle sensor. 
The flow computer provides the intelligence and the controls
necessary to run the proving process and to calculate the
correct sonic nozzle flowrates. The prover uses modern
electronics and a sophisticated computer technology, as shown in Fig. 3. This
flow computer can be applied when the measurement error, due to
actual operating conditions, becomes large enough to be
unacceptable in the application. The measurement error can be
estimated by calculating the worstcase operating
conditions.
The calculations presented here are for nozzles carrying a
liquid as described in ISO 3500. The ISO equations are
used in the calculations.

Fig.
3. Computers used in gasflow
measurements. 
Results and discussion.
The experimental test setup is shown schematically in Figs.
4 and 5; two flow venturi venturis (FVs) are installed upstream
of the chamber in the gas pipeline. They are identified as FV01
and FV02. The objective of adding the third FV is to isolate
the source of any observed variance in the test chamber of the
sonic nozzle in parallel montage. This is accomplished by
comparing the results of any two FVs relative to the third.
Determining the variance contributed by the multiple FV chamber
in parallel montage compared to that contributed by a single
unit is of particular interest.

Fig.
4. Experimental test. 

Fig.
5. Experimental test. 
Venturi nozzle test.
According to the assumption of isentropic flow, the sonic
and subsonic elsewhere neck, leaving the continuity equation at
the neck and out of the venturi nozzle, was obtained for Eq.
14:
(19)
As the geometry of the venturi nozzle, we have
adopted:
And u = 3°30’.
It takes time:
(20)
By giving values to the report L_{t}/dc,
you can calculate the corresponding W_{cr}
report. The results obtained for the reports critical function
of the angle of divergence are shown in Fig. 6. The results for
the critical function of L_{t}/dc are shown in
Fig. 7.

Fig.
6. Reports critical function of the
angle
of divergence. 

Fig.
7. Reports critical function of
L_{t}/dc. 
Other tests results investigated in the examined gas pipeline
system are presented in this section. The influence of the
compressibility factor on the rate flow, for the pressure and
temperature, in the intelligent sonic nozzle sensor is shown in
Figs. 8 and 9.

Fig.
8. Influence of the compressibility
factor on the flowrate for the temperature. 

Fig.
9. Influence of the compressibility
factor on the flowrate for the pressure. 
Conclusion.
To savings on maintenance costs for pipeline
systems, the flow venturi sonic nozzle can be used as a single
unit in gas pipeline, or several units can be installed in
parallel within a chamber. It is more complicated than the flow
venturi sonic nozzle limiting orifice, but it has better
performance because the divergent section of the sonic nozzle
can recover some pressure. Using venturi nozzle collar sonic
requires knowledge of critical reports. The great advantage of
these nozzles is determining flow measurements with great
precision that makes them indispensable as regulators and
stabilizers of flow during the calibration of the other
measuring means. The design parameters of the sonic nozzle were
optimized with a flow computer to determine the mathematically
correct raw flow measurement to account for realtime changes
in operating pressure and temperature. With this method, this
optimized design enables a constant flowrate control to be
attained with a substantial reduction in the gas pipeline
capacity requirements and cost. HP
LITERATURE
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The authors 


Mouloud
Guemana received a graduate engineer degree in
mechanical engineering from the National Institute of
Hydrocarbons and Chemistry INH, of Boumerdes, Algeria, in
1998. After little time spent in the industry, he joined
the physical laboratory of genius of hydrocarbons where
he worked with the measurements for large natural gas
pipelines. From May 1999 to January 2003, he was an
associated postdoctoral researcher the University of
Boumerdes, and became an associate professor beginning in
2004. He has authored coauthored many technical and
research papers. His research interests include
optimization of measuring equipment the transport of
natural gas. 

Prof.
Slimane Aissani earned a graduate degree in
mechanical engineering de cycle, from the National
Institute of Hydrocarbons and Chemistry INH in 1976. He
received his PhD in 1986 from the University Pierre and
Marie Curie Paris VI, France. In 1988–2002, he was a
researcher and the president of the scientific company.
In 1999–2005, he became the director of the Research
Laboratory and Development in Genius Physiques of
Hydrocarbons. Dr. Aissani was responsible for post
graduation at the University of Boumerdes, Algeria. He
has broad interests in optimization flow measurement for
natural gas transmission, thermal coupling, improved
performance of energy systems and various environmental subjects. He has
supervised several master students and authored many
technical papers. 


Dr. Ahmed Hafaifa is a graduate
engineer from the National Institute of Hydrocarbons
and Chemistry INH, of Boumerdes, Algeria, in 1999. From
May 1999 to June 2002, he was a postdoctoral research
associate at the University of Boumerdes, doing
research on robust control and fuzzy control of
compression systems in collaboration with the
Department of Electrical Control of DJELFA, Algeria. He
became an associate professor beginning in July 2003 to
the present. He is currently with the Industrial
Automation and Diagnosis Systems Laboratory, Science
and Technology Faculty,
University of Djelfa. Dr. Hafaifa has authored and
coauthored many scientific papers and research projects.
