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Use a new calibration method for gas pipelines

08.01.2011  |  Guemana, M.,  University of Boumerdes, AlgeriaAissani, S. ,  University of Boumerdes, AlgeriaHafaifa, A.,  University of Djelfa, Algeria

An advanced method improves calibrating orifice flowmeters while reducing maintenance costs

Keywords: [flowmeter] [custody transfer] [natural gas] [pipelines] [maintance] [calibration] [instrumentation]

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 high-volume natural gas pipeline system.


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 low-pressure 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 turbine-meter 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 venturi-necked sonic nozzles.10

The principle of gas flow measuring through the venturi-necked 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 in-situ conditions.

Sonic nozzle technology.

The sonic nozzle is a fluid-flow 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 stress-resistant, 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 sonic-device 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
  venturi-type 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 one-half the upstream pressure.


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:


Equation of dynamics:



Equation of energy:


Equation of state of ideal gas:

p / P = rT 

Note: For an ideal gas, the specific heat Cp at the constant pressure is given by the relation:


Using some transformations of fluid, we obtain the important relation of Hugoniot:11


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:


Two cases may arise, either:

1. dU = 0, and the velocity reaches a maximum and then decreases
2. M2 = 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.)

Mass-flow venturi nozzle.

The mass-flow venturi nozzle is passing through a slice where, Q = r Su in which a section of well-defined 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


Similarly, for an ideal gas, we have the following relation:


And replacing in Eq. 8, we get:


The application of this equation for the upstream section in which u = 0 and any section of the nozzle, gives us:


Given that the flow is isentropic, we will have speed in a section equalling:


This relationship gives the equations of fluid motion are often expressed in terms of Mach number, then Eq. 11 can be written as:


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:


Given that the flow is isentropic, we have:


By maintaining constant conditions, generating the mass flow is based on grouping Y = f (P / Pam).

Critical flow. From Eq. 13a, we see that maintaining constant upstream conditions implies that the flow depends only on the function:


In turn, this function depends only on (P / Pam = W) reaches a maximum when we have then:


This parameter is called the critical ratio of relaxation (Wcr), and the corresponding speed to this ratio is equal to:


Substituting Pam, ram 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:


Denotes the relaxation coefficient magnitude


and we write:


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 non-linearity.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 real-time 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 worst-case 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 gas-flow

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:



As the geometry of the venturi nozzle, we have adopted:


And u = 3°30’.

It takes time:



By giving values to the report Lt/dc, you can calculate the corresponding Wcr 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 Lt/dc are shown in Fig. 7.

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

  Fig. 7. Reports critical function of Lt/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.


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 real-time 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


1 Bignell, N., “Using small sonic nozzles as secondary flow standards,” Flow Measurement and Instrumentation, Elsevier, 2000, Vol. 11, No. 04, pp. 329–337.
2 Nakao, S. I., Y. Yokoi and M. Takamoto, “Development of a calibration facility for small mass flow rates of gas and the uncertainty of a sonic venturi transfer standard,” Flow Measurement and Instrumentation, Elsevier, 1996, Vol. 07, No. 02, pp. 77–83.
3 Hayakawa, M., Y. Ina, Y. Yokoi, M. Takamoto, S. Nakao, “Development of a transfer standard with sonic Venturi nozzles for small mass flow rates of gases,” Flow Measurement and Instrumentation, Elsevier, 2000, Vol. 11, No. 04, pp. 279–283.
4 Wright, P. H., “The application of sonic (critical flow) nozzles in the gas industry,” Flow Measurement and Instrumentation, Elsevier, 1993, Vol. 04, No. 02, pp. 67–71.
5 Zheng, Y., J. R. Pugh, D. McGlinchey and R. O. Ansell, “Simulation and experimental study of gas-to-particle heat transfer for non-invasive mass flow measurement,” Measurement, Elsevier, 2008, Vol. 41, No. 04, pp. 446–454.
6 Choi, Y. M., K. A. Park, J. T. Park, H. M. Choi and S. O. Park, “Interference effects of three sonic nozzles of different throat diameters in the same meter tube,” Flow Measurement and Instrumentation, Elsevier, 1999, Vol. 10, No. 03, pp. 175–181.
7 ISO 9300:2005: Measurement of gas flow by means of critical flow Venturi nozzles.
8 Chung Hu, C. and Win-Ti Lin, “Performance test of KOH-etched silicon sonic nozzles,” Flow Measurement and Instrumentation, Elsevier, 2009, Vol. 20, No. 03, pp. 122–126.
9 Bouam, A., R. Kadi and S. Aïssani, “Gas turbine performances improvement using steam injection in the combustion chamber under Sahara conditions,” Oil & Gas Science and Technology, Revue of IFP, 2008, Vol. 63, No. 02, pp. 251–261.
10 Guemana, M., S. Aissani and A. Bennani, “The compressibility effect on the counting gas method choice,” International Review of Mechanical Engineering, IREME, 2009, Vol. 03, No. 01, pp. 104–109.
11 Aissani, S. and E. Mikaelian, “Operational characteristics for gas pipelines in Algeria from 1976 to 1980,” Oil & Gas Science and Technology, Revue of IFP, 1982, Vol. 37, No. 06, pp. 847–852.
12 Mickan, B., R. Kramer and E. Von Lavante, “Determination of discharge coefficients of sonic nozzles with low uncertainty and without knowledge of throat diameter,” Proceedings of the International Conference on Flow Measurement, FLOMEKO’2004, Guilin, China, 2004.
13 Ishibashi, M., E. Von Lavante and M. Takamoto, “Quasi nonintrusive measurement of flow velocity field in a critical nozzle,” Proceedings of ASME FEDSM’00, Boston, 2000.
14 Kegel, T., C. Britton and R. Caron, “Measurement uncertainty considerations when using an array of critical flow venturies,” Proceedings of the 46th International Instrumentation Symposium, Instrument Society of America, 2000.
15 Park, K. A., Y. M. Choi, H. M. Choi, T. S. Cha and B. H. Yoon, “The evaluation of critical pressure ratio of sonic nozzles at low Reynolds numbers,” Flow Measurement and Instrumentation, Elsevier, 2001, Vol. 12, No. 01, pp. 37–41.
16 Lebrun, M., D. Vasiliu and N. Vasiliu, “Numerical simulation of the fluid control systems by AMESim,” Studies in Informatics and Control, SIC, 2009, Vol. 18, No. 2, pp. 111–118.
17 Szakonyi, L., “Investigation and control of a regional steam distribution network under two phase flow conditions,” Studies in Informatics and Control, SIC, 2009, Vol. 18, No. 2, pp. 119–126.
18 Ferrouk, M., S. Aissani, F. D’Auria, A. DelNevo and A. Bousbia Salah, “Assessment of 12 CHF prediction methods, for an axially non-uniform heat flux distribution, with the RELAP5 computer code,” Nuclear Engineering and Design, Elsevier, 2008, Vol. 238, No. 10, pp. 2718–2725.
19 Hafaifa, A., K. Laroussi and F. Laaouad, “Robust fuzzy fault detection and isolation approach applied to the surge in centrifugal compressor modeling and control,” Fuzzy Information and Engineering, Springer, 2010, Vol. 02, No. 01, pp. 49–73.
20 Hafaifa, A., F. Laaouad and K. Laroussi, “Fuzzy approach applied in fault detection and isolation to the compression system control,” Studies in Informatics and Control, SIC, 2010, Vol. 19, No. 01, pp. 17–26.
21 Hafaifa, A., F. Laaouad and K. Laroussi, “Fuzzy logic approach applied to the surge detection and isolation in centrifugal compressor,” Automatic Control and Computer Sciences, Springer, 2010, Vol. 44, No. 01, pp. 53–59.
22 Liu, S., Q. Chen, H. G. Wang, F. Jiang, I. Ismail and W. Q. Yang, “Electrical capacitance tomography for gas–solids flow measurement for circulating fluidized beds,” Flow Measurement and Instrumentation, Elsevier, 2005, Vol. 16, No. 2–3, pp. 135–144.
23 Myoung Lim, J., B. H. Yoon, S. Jang, H. M. Choi and K. A. Park, “Step-down procedure of sonic nozzle calibration at low Reynolds numbers,” Flow Measurement and Instrumentation, Elsevier, 2010, Vol. 21, No. 03, pp. 340–346.

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 co-authored 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 co-authored many scientific papers and research projects. 

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