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[a] Craft & Hawkins Department of Petroleum Engineering， Louisiana State University， Baton Rouge， Louisiana 70803， USA.
Corresponding author.
Received 18 December 2012； accepted 9 March 2013
Abstract
The use of pipelines is one of the most popular ways of delivering gas phases as shown by numerous examples in hydrocarbon transportation systems in Arctic regions， oil and gas production facilities in onshore and offshore wells， and municipal gas distribution systems in urban areas. A gas leak from pipelines can cause serious problems not only because of the financial losses associated but also its social and environmental impacts. Therefore， establishing an early leak detection model is vital to safe and secure operations of such pipeline systems.
A leak detection model for a single gas phase is presented in this study by using material balance and pressure traverse calculations. The comparison between two steady states， with and without leak，
NOMENCLATURE
INTRODUCTION
One of the applications most sensitive to hydrocarbon leak is perhaps offshore hydrocarbon production and transportation systems as observed in the 1989 Exxon Valdez Oil Spill and the 2010 BP Oil Spill due to their devastating social， environmental and economical impacts. During recent years， increasing deepwater hydrocarbon production has been receiving a great level of attention. Relatively large field sizes and high production rates of the offshore wells are two important characteristics of deepwater oil and gas development as illustrated by the average annual oil production in Figure 1 （Minerals Management Services [MMS]， 2009）. However， the inevitable use of complex drilling and production facilities and long subsea pipelines poses significant challenges in terms of technology and operation （Payne， 2007； Richardson et al.， 2008）.
Figure 1
Gulf of Mexico Oil and Gas Production History and Forecast （MMS， 2009）
A safe operation of natural gas and crude oil pipelines has also been an important issue in the remote geographical locations. Failure of pipeline systems has been reported in many different locations， including Alaska， China， Russia and Arctic area （Papadakis， 1999； Papadakis， Porter， & Wettig， 1999； Rosen & Schneyer， 2011； Simonoff， Restrepo， & Zimmerman， 2010； Wang & Carroll， 2007）. According to U.S. department of transportation’s Pipeline and Hazardous Materials Safety Administration （PHMSA， 2010）， 653 pipeline incidents were reported annually on average in the U.S. during 2005 through 2009， which resulted in an average of 456 millions of dollars per year of property damages. Pipeline leaks are one of the major concerns in the municipal transportation and distribution systems of natural gas as well as water supply， especially when those pipelines are located near the heavily populated urban areas. A recent major incident can be found from gas explosion in San Bruno， California on September 9， 2010 when a Pacific Gas & Electric natural gas pipeline exploded in a residential area and caused not just eight people’s death， six missing and sixty injured， but millions of dollars for repair and compensation （Berton， 2010； Hoeffel， Hennessy-Fiske， & Goffard， 2010）.
Many of the leak detection approaches can be classified into two different categories： hardware-based methods using optical fiber， acoustic sensors， chemical sensors and electrical sensors； and software-based methods using fully transient computer simulations and steady-state modeling techniques （Scott & Barrufet， 2003）. Because of the complexity of leak detection phenomena， it is typically believed that there is no single perfect solution–rather， a combination of different methods is highly recommended and preferred.
Recent leak detection modeling studies （Gajbhiye & Kam， 2008； Kam， 2010）， which focused on the change in system response by comparing two steady states （with and without leak） in flowlines with two-phase gas-liquid mixtures， show that the steady-state modeling has good potential as part of early warning system. Those modeling studies also show that an accurate estimation of leak coefficient （CD）， which defines how easily fluid can escape from the pipe through the leak， is critical in order to build a reliable leak detection model. Although the value of CD is regarded as the single-most important model parameter in leak detection modeling， it has not been investigated in large field-scale leak experiments so far.
A physical phenomenon similar to pipeline leak can be found in other applications such as flow through nozzles or chokes. The suggested empirical equations typically have a proportionality constant called discharge coefficient which is similar to leak coefficient in this study （Ashford & Pierce， 1975； Gilbert， 1954； Ros， 1960； Sachdeva， Schmidt， Brill， & Blais， 1986）. These studies show the magnitude of discharge coefficient depends on the design of nozzles and chokes （such as sizes and configurations）， the flow of interest （such as water， oil， gas， or air）， the range of flowrates passing through the system， and the surrounding conditions. For example， Ashford and Pierce （1975） show a range of 0.86-1.2 for gas-oil two-phase flow through an orifice. In both studies， the specific gravities of gas and oil were about 0.6 and 0.89 respectively， and the models were successfully compared with and verified by actual field data from an oil well. In the study of Guo， Al-Bemani， and Ghalambor （2002）， the multiphase choke flow model from Sachdeva et al. （1986） was tested with field data from 239 gas condensate wells in Southwest Louisiana. Their recommendation was a discharge-coefficient value of 0.78， if gas phase is dominant， and 1.53， if oil phase is dominant. By looking through the literature， similar studies for single gas-phase flow through nozzles， chokes and other constrictions can be spotted easily. Crane Company’s technical book （1957） has been used as a reference in many studies， showing the following observations： （i） for nozzle-type chokes， the discharge coefficient shows a range of 0.92 - 1.2 for Reynolds Number between 2×103 and 2×106； （ii） for orifice-type chokes， a range of 0.3-1.3 for Reynolds Number of 20-2×106； and （iii） interestingly， when Reynolds Number is above 10，000， the discharge coefficient increases with Reynolds Number for nozzle-type chokes， but decreases for orifice-type chokes. Morris （1996） shows a range of 0.67-0.95 for discharge coefficient of gas flow for most type of safety valves. Richardson， Saville， Fisher， Meredith， and Dix （2008） examined a single-phase natural gas flow through orifice with three different sizes of 8， 10 and 15 millimeter. Their results show a discharge-coefficient range of 0.86 - 0.94 for mass rates below 1 kg/s while almost constant at 0.9 for mass rates between 1-3 kg/s.
An important observation from the literature search is that many of these studies point out that the discharge coefficient is not a single fixed value， but in general is a function of flow conditions， more specifically， being linearly proportional to NRe-1/2 （Crane Company， 1957； Guo et al.， 2002； Ishibashi & Takamoto， 2000； Kim， Kim， & Park， 2006）.
By following the methodology presented by Gajbhiye and Kam （2008） and Kam （2010）， which compares the two steady states （one with leak， and the other without leak） and presents the level of disturbance of the system as a function of leak opening size and longitudinal leak location， this study aims to extract the range of leak coefficient （CD） from large field-size leak detection experiments with a single gas phase， and investigates its implication in leak detection modeling. The experimental data which this modeling study is made a fit to are from Scott and Yi （1998） which carried out field-scale flow tests in the Petroleum Engineering Research & Technology Transfer Laboratory （PERTT LAB） at Louisiana State University.
Our model assumes that the two boundary conditions are fixed inlet flowrate （qin； meaning the feed-in flow rate is known at the entrance of the pipeline） and fixed outlet pressure （pout； meaning the back-pressure at the outlet of the pipeline is kept constant）， and calculates the inlet pressure （pin） and the outlet flowrate （qout） in the absence and presence of leak. Therefore， the change in inlet pressure （Δpin） and the change in outlet flowrate （Δqout） serve as two leak detection indicators. It should be noted that deciding which variables should be fixed and which variables should be varied among those four parameters （pin， pout， qin， and qout） for modeling purpose is somewhat arbitrary， therefore the same methodology can be applied to the cases with different boundary conditions. 1. METHODOLOGY
The actual flowrate of gas phase in pipelines may vary significantly along the longitudinal distance， because many of gas-phase properties such as compressibility， density， and viscosity are sensitive to pressure and temperature. We assume that the pipeline of interest can be approximated by a one-dimensional system， represented by a number of calculation nodes， along which the properties of gas phase change as a function of pressure and temperature. The inlet of the pipeline is defined by input parameters， including pressure， temperature， and gas flow rate.
Suppose the pressure and temperature information is available at one node （let’s say， ith node）. This allows basic gas properties to be decided， for example， gas viscosity from the correlation developed by Lee， Gonzalez， and Eakin （1966） and gas compressibility suggested by Dranchuk and Abou-Kassem （1975）. Then， the total pressure gradient at that particular node， i， can be calculated by adding the contribution of three different components， i.e.，
2. RESULTS AND DISCUSSIONS
The large-scale experiments to which our model intends to fit have the following test conditions： methane as a gas phase； 9，460 ft （about 1.8 miles） long horizontal flow loops； 3.64 and 4.5 inch inner and outer diameter pipes； outlet pressure around 610 to 680 psia； injection gas flow rates around 1 to 6 MMscf/day； leak location in the middle of the pipeline； and three leak opening sizes with the diameters of 1/8， 1/4， and 3/8 inches. See Scott and Yi （1998） for more detailed information.
2.1 Response without Leak vs. Response with Leak
REFERENCES
[1] Arnold， K.， & Stewart， M. （1999）. Surface Production Operations （Volume 2）. Houston， Tx： Gulf Publishing Company.
[2] Ashford， F. E.， & Pierce， P. E. （1975）. Determining Multiphase Pressure Drops and Flow Capacities in Down-Hole Safety Valves. Journal of Petroleum Technology， 27（9）， 1145-1152.
[3] Berton， J. （2010）. San Bruno’s 8th Fatality from PG&E Blast. San Francisco Chronicle. Retrieved from http：//www.sfgate.com/cgi-bin/article.cgi？f=/c/a/2010/09/28/BAIQ1FKVE5.DTL&type=health
[4] Chen， N. H. （1979）. An Explicit Equation for Friction Factor in Pipe. Ind. Eng. Chem. Fundam.， 18（3）， 296-297.
[5] Crane Company. （1957）. Flow of Fluids Through Valves， Fittings， and Pipe （TP 410）. New York， N.Y.
[6] Danesh， A. （1998）. PVT and phase behaviour of petroleum reservoir fluids. Amsterdam： Elsevier. [7] Dranchuk， P. M.， & Abou-Kassem， J. H. （1975）. Calculation of z-Factors for Natural Gases Using Equations of State. Journal of Canadian Petroleum Technology， 14（3）， 34-36.
[8] Gajbhiye， R. N.， & Kam， S. I. （2008）. Leak Detection in Subsea Pipeline： a Mechanistic Modeling Approach with Fixed Pressure Boundaries. SPE Projects， Facilities， and Construction， 3（4）， 1–10.
[9] Guo， B.， Lyons， W. C.， & Ghalambor， A. （2007）. Petroleum Production Engineering， a Computer-Assisted Approach. Gulf Professional Publishing.
[10] Guo， B.， Al-Bemani， A. S.， & Ghalambor， A. （2002）. Applicability of Sachdeva’s Choke Flow Model in Southwest Louisiana Gas Condensate Wells. Paper Presented at the SPE Gas Technology Symposium， Calgary， Alberta.
[11] Gilbert， W. E. （1954）. Flowing and Gas-Lift Well Performance. Drill. & Prod. Practice， 126.
[12] Hoeffel， J.， Hennessy-Fiske， M.， & Goffard， C. （2010）. San Bruno Explosion Death Toll Climbs to Seven； Six are Missing. Los Angeles Times. Retrieved from http：//www.latimes.com/news/local/la-me-0912-san-bruno-explosion-20100912，0，251794.story
[13] Ishibashi， M.， & Takamoto， M. （2000）. Theoretical Discharge Coefficient of a Critical Circular-Arc Nozzle with Laminar Boundary Layer and Its Verification by Measurements Using Super-Accurate Nozzles. Flow Measurement and Instrumentation， 11（4）， 305-313.
[14] Kam， S. I. （2010）. Mechanistic Modeling of Pipeline Leak Detection at Fixed Inlet Rate. Journal of Petroleum Science and Engineering， 70（3）， 145-156.
[15] Kim， J. H.， Kim， H. D.， & Park， K. A. （2006）. Computational/Experimental Study of a Variable Critical Nozzle Flow. Flow Measurement and Instrumentation， 17， 81-86.
[16] Lee， A.， Gonzalez， M. H.， & Eakin， B. E. （1966）. The Viscosity of Natural Gases. Journal of Petroleum Technology， 18（8）， 997-1000.
[17] Minerals Management Services. （2009）. Gulf of Mexico oil and gas production forecast： 2009-2018 （OCS Report MMS 2009-012）. Retrieved from http：//www.gomr.boemre.gov/
[18] Moody， L. F. （1944）. Friction Factors for Pipe Flow. Transactions of the ASME， 66（8）， 671–684.
[19] Morris， S. D. （1996）. Choke Pressure in Pipeline Restrictions. Journal of Hazardous Materials， 50（1）， 65–69.
[20] Papadakis， G. A.， Porter， S.， & Wettig， J. （1999）. EU Initiative on the Control of Major Accident Hazards Arising from Pipelines. Journal of Loss Prevention in the Process Industries， 12（1）， 85-90.
[21] Papadakis， G. A. （1999）. Major Hazard Pipelines： a Comparative Study of Onshore Transmission Accidents. Journal of Loss Prevention in the Process Industries， 12（1）， 91-107. [22] Payne， M. L. （2007）. Deepwater Activity in the US Gulf of Mexico Continues to Drive Innovation and Technology. Exploration & Production： The Oil and Gas Review 2007 - OTC Edition.
[23] Richardson， S. M.， Saville， G.， Fisher， A.， Meredith， A. J.， & Dix， M. J. （2006）. Experimental Determination of Two-Phase Flow Rates of Hydrocarbons Through Restrictions. Process Safety and Environmental Protection， 84（1）， 40-53.
[24] Richardson， G. E.， Nixon， L. D.， Bohannon， C. M.， Kazanis， E. G.， Montgomery， T. M.， & Gravois， M. P. （2008）. Deepwater Gulf of Mexico 2008： America’s Offshore Energy Future. U.S. Dept. of the Interior， Minerals Management Service， Gulf of Mexico OCS Region， New Orleans， LA.
[25] Ros， N. C. J. （1960）. An Analysis of Critical Simultaneous Gas/Liquid Flow Through a Restriction and Its Application to Flowmetering. Applied Scientific Research， 9（1）， 374-388.
[26] Rosen， Y.， & Schneyer， J. （2011）. Alaska Pipeline Restart Unknown； Oil up， BP Dips. Reuters. Retrieved from http：//www.reuters.com/article/2011/01/10/us-oil-pipeline-alaska-idUSTRE7080H820110110
[27] Sachdeva， R.， Schmidt， Z.， Brill， J. P.， & Blais， R. M. （1986， October）. Two-Phase Flow Through Chokes. Paper Presented at the SPE Annual Technical Conference and Exhibition， New Orleans， Louisiana.
[28] Scott， S. L， & Barrufet， M. A. （2003）. Worldwide Assessment of Industry Leak Detection Capabilities for Single & Multiphase Pipelines （PB2011-104131）. Minerals Management Service.
[29] Scott， S. L.， & Yi， J. （1998）. Detection of Critical Flow Leaks in Deepwater Gas Flowlines. Paper Presented at the SPE Annual Technical Conference and Exhibition， New Orleans， LA.
[30] Simonoff， J. S.， Restrepo， C. E.， & Zimmerman， R. （2010）. Risk Management of Cost Consequences in Natural Gas Transmission and Distribution Infrastructures. Journal of Loss Prevention in the Process Industries， 23（2）， 269-279.
[31] U.S. Department of Transportation’s Pipeline and Hazardous Materials Safety Administration. （2010）. PHMSA significant incident files. Retrieved from www.phmsa.dot.gov
[32] Wang， S.， & Carroll， J. J. （2007）. Leak Detection for Gas and Liquid Pipelines by Transient Modeling. SPE Projects， Facilities & Construction， 2（2）， 1-9.
Corresponding author.
Received 18 December 2012； accepted 9 March 2013
Abstract
The use of pipelines is one of the most popular ways of delivering gas phases as shown by numerous examples in hydrocarbon transportation systems in Arctic regions， oil and gas production facilities in onshore and offshore wells， and municipal gas distribution systems in urban areas. A gas leak from pipelines can cause serious problems not only because of the financial losses associated but also its social and environmental impacts. Therefore， establishing an early leak detection model is vital to safe and secure operations of such pipeline systems.
A leak detection model for a single gas phase is presented in this study by using material balance and pressure traverse calculations. The comparison between two steady states， with and without leak，
NOMENCLATURE
INTRODUCTION
One of the applications most sensitive to hydrocarbon leak is perhaps offshore hydrocarbon production and transportation systems as observed in the 1989 Exxon Valdez Oil Spill and the 2010 BP Oil Spill due to their devastating social， environmental and economical impacts. During recent years， increasing deepwater hydrocarbon production has been receiving a great level of attention. Relatively large field sizes and high production rates of the offshore wells are two important characteristics of deepwater oil and gas development as illustrated by the average annual oil production in Figure 1 （Minerals Management Services [MMS]， 2009）. However， the inevitable use of complex drilling and production facilities and long subsea pipelines poses significant challenges in terms of technology and operation （Payne， 2007； Richardson et al.， 2008）.
Figure 1
Gulf of Mexico Oil and Gas Production History and Forecast （MMS， 2009）
A safe operation of natural gas and crude oil pipelines has also been an important issue in the remote geographical locations. Failure of pipeline systems has been reported in many different locations， including Alaska， China， Russia and Arctic area （Papadakis， 1999； Papadakis， Porter， & Wettig， 1999； Rosen & Schneyer， 2011； Simonoff， Restrepo， & Zimmerman， 2010； Wang & Carroll， 2007）. According to U.S. department of transportation’s Pipeline and Hazardous Materials Safety Administration （PHMSA， 2010）， 653 pipeline incidents were reported annually on average in the U.S. during 2005 through 2009， which resulted in an average of 456 millions of dollars per year of property damages. Pipeline leaks are one of the major concerns in the municipal transportation and distribution systems of natural gas as well as water supply， especially when those pipelines are located near the heavily populated urban areas. A recent major incident can be found from gas explosion in San Bruno， California on September 9， 2010 when a Pacific Gas & Electric natural gas pipeline exploded in a residential area and caused not just eight people’s death， six missing and sixty injured， but millions of dollars for repair and compensation （Berton， 2010； Hoeffel， Hennessy-Fiske， & Goffard， 2010）.
Many of the leak detection approaches can be classified into two different categories： hardware-based methods using optical fiber， acoustic sensors， chemical sensors and electrical sensors； and software-based methods using fully transient computer simulations and steady-state modeling techniques （Scott & Barrufet， 2003）. Because of the complexity of leak detection phenomena， it is typically believed that there is no single perfect solution–rather， a combination of different methods is highly recommended and preferred.
Recent leak detection modeling studies （Gajbhiye & Kam， 2008； Kam， 2010）， which focused on the change in system response by comparing two steady states （with and without leak） in flowlines with two-phase gas-liquid mixtures， show that the steady-state modeling has good potential as part of early warning system. Those modeling studies also show that an accurate estimation of leak coefficient （CD）， which defines how easily fluid can escape from the pipe through the leak， is critical in order to build a reliable leak detection model. Although the value of CD is regarded as the single-most important model parameter in leak detection modeling， it has not been investigated in large field-scale leak experiments so far.
A physical phenomenon similar to pipeline leak can be found in other applications such as flow through nozzles or chokes. The suggested empirical equations typically have a proportionality constant called discharge coefficient which is similar to leak coefficient in this study （Ashford & Pierce， 1975； Gilbert， 1954； Ros， 1960； Sachdeva， Schmidt， Brill， & Blais， 1986）. These studies show the magnitude of discharge coefficient depends on the design of nozzles and chokes （such as sizes and configurations）， the flow of interest （such as water， oil， gas， or air）， the range of flowrates passing through the system， and the surrounding conditions. For example， Ashford and Pierce （1975） show a range of 0.86-1.2 for gas-oil two-phase flow through an orifice. In both studies， the specific gravities of gas and oil were about 0.6 and 0.89 respectively， and the models were successfully compared with and verified by actual field data from an oil well. In the study of Guo， Al-Bemani， and Ghalambor （2002）， the multiphase choke flow model from Sachdeva et al. （1986） was tested with field data from 239 gas condensate wells in Southwest Louisiana. Their recommendation was a discharge-coefficient value of 0.78， if gas phase is dominant， and 1.53， if oil phase is dominant. By looking through the literature， similar studies for single gas-phase flow through nozzles， chokes and other constrictions can be spotted easily. Crane Company’s technical book （1957） has been used as a reference in many studies， showing the following observations： （i） for nozzle-type chokes， the discharge coefficient shows a range of 0.92 - 1.2 for Reynolds Number between 2×103 and 2×106； （ii） for orifice-type chokes， a range of 0.3-1.3 for Reynolds Number of 20-2×106； and （iii） interestingly， when Reynolds Number is above 10，000， the discharge coefficient increases with Reynolds Number for nozzle-type chokes， but decreases for orifice-type chokes. Morris （1996） shows a range of 0.67-0.95 for discharge coefficient of gas flow for most type of safety valves. Richardson， Saville， Fisher， Meredith， and Dix （2008） examined a single-phase natural gas flow through orifice with three different sizes of 8， 10 and 15 millimeter. Their results show a discharge-coefficient range of 0.86 - 0.94 for mass rates below 1 kg/s while almost constant at 0.9 for mass rates between 1-3 kg/s.
An important observation from the literature search is that many of these studies point out that the discharge coefficient is not a single fixed value， but in general is a function of flow conditions， more specifically， being linearly proportional to NRe-1/2 （Crane Company， 1957； Guo et al.， 2002； Ishibashi & Takamoto， 2000； Kim， Kim， & Park， 2006）.
By following the methodology presented by Gajbhiye and Kam （2008） and Kam （2010）， which compares the two steady states （one with leak， and the other without leak） and presents the level of disturbance of the system as a function of leak opening size and longitudinal leak location， this study aims to extract the range of leak coefficient （CD） from large field-size leak detection experiments with a single gas phase， and investigates its implication in leak detection modeling. The experimental data which this modeling study is made a fit to are from Scott and Yi （1998） which carried out field-scale flow tests in the Petroleum Engineering Research & Technology Transfer Laboratory （PERTT LAB） at Louisiana State University.
Our model assumes that the two boundary conditions are fixed inlet flowrate （qin； meaning the feed-in flow rate is known at the entrance of the pipeline） and fixed outlet pressure （pout； meaning the back-pressure at the outlet of the pipeline is kept constant）， and calculates the inlet pressure （pin） and the outlet flowrate （qout） in the absence and presence of leak. Therefore， the change in inlet pressure （Δpin） and the change in outlet flowrate （Δqout） serve as two leak detection indicators. It should be noted that deciding which variables should be fixed and which variables should be varied among those four parameters （pin， pout， qin， and qout） for modeling purpose is somewhat arbitrary， therefore the same methodology can be applied to the cases with different boundary conditions. 1. METHODOLOGY
The actual flowrate of gas phase in pipelines may vary significantly along the longitudinal distance， because many of gas-phase properties such as compressibility， density， and viscosity are sensitive to pressure and temperature. We assume that the pipeline of interest can be approximated by a one-dimensional system， represented by a number of calculation nodes， along which the properties of gas phase change as a function of pressure and temperature. The inlet of the pipeline is defined by input parameters， including pressure， temperature， and gas flow rate.
Suppose the pressure and temperature information is available at one node （let’s say， ith node）. This allows basic gas properties to be decided， for example， gas viscosity from the correlation developed by Lee， Gonzalez， and Eakin （1966） and gas compressibility suggested by Dranchuk and Abou-Kassem （1975）. Then， the total pressure gradient at that particular node， i， can be calculated by adding the contribution of three different components， i.e.，
2. RESULTS AND DISCUSSIONS
The large-scale experiments to which our model intends to fit have the following test conditions： methane as a gas phase； 9，460 ft （about 1.8 miles） long horizontal flow loops； 3.64 and 4.5 inch inner and outer diameter pipes； outlet pressure around 610 to 680 psia； injection gas flow rates around 1 to 6 MMscf/day； leak location in the middle of the pipeline； and three leak opening sizes with the diameters of 1/8， 1/4， and 3/8 inches. See Scott and Yi （1998） for more detailed information.
2.1 Response without Leak vs. Response with Leak
REFERENCES
[1] Arnold， K.， & Stewart， M. （1999）. Surface Production Operations （Volume 2）. Houston， Tx： Gulf Publishing Company.
[2] Ashford， F. E.， & Pierce， P. E. （1975）. Determining Multiphase Pressure Drops and Flow Capacities in Down-Hole Safety Valves. Journal of Petroleum Technology， 27（9）， 1145-1152.
[3] Berton， J. （2010）. San Bruno’s 8th Fatality from PG&E Blast. San Francisco Chronicle. Retrieved from http：//www.sfgate.com/cgi-bin/article.cgi？f=/c/a/2010/09/28/BAIQ1FKVE5.DTL&type=health
[4] Chen， N. H. （1979）. An Explicit Equation for Friction Factor in Pipe. Ind. Eng. Chem. Fundam.， 18（3）， 296-297.
[5] Crane Company. （1957）. Flow of Fluids Through Valves， Fittings， and Pipe （TP 410）. New York， N.Y.
[6] Danesh， A. （1998）. PVT and phase behaviour of petroleum reservoir fluids. Amsterdam： Elsevier. [7] Dranchuk， P. M.， & Abou-Kassem， J. H. （1975）. Calculation of z-Factors for Natural Gases Using Equations of State. Journal of Canadian Petroleum Technology， 14（3）， 34-36.
[8] Gajbhiye， R. N.， & Kam， S. I. （2008）. Leak Detection in Subsea Pipeline： a Mechanistic Modeling Approach with Fixed Pressure Boundaries. SPE Projects， Facilities， and Construction， 3（4）， 1–10.
[9] Guo， B.， Lyons， W. C.， & Ghalambor， A. （2007）. Petroleum Production Engineering， a Computer-Assisted Approach. Gulf Professional Publishing.
[10] Guo， B.， Al-Bemani， A. S.， & Ghalambor， A. （2002）. Applicability of Sachdeva’s Choke Flow Model in Southwest Louisiana Gas Condensate Wells. Paper Presented at the SPE Gas Technology Symposium， Calgary， Alberta.
[11] Gilbert， W. E. （1954）. Flowing and Gas-Lift Well Performance. Drill. & Prod. Practice， 126.
[12] Hoeffel， J.， Hennessy-Fiske， M.， & Goffard， C. （2010）. San Bruno Explosion Death Toll Climbs to Seven； Six are Missing. Los Angeles Times. Retrieved from http：//www.latimes.com/news/local/la-me-0912-san-bruno-explosion-20100912，0，251794.story
[13] Ishibashi， M.， & Takamoto， M. （2000）. Theoretical Discharge Coefficient of a Critical Circular-Arc Nozzle with Laminar Boundary Layer and Its Verification by Measurements Using Super-Accurate Nozzles. Flow Measurement and Instrumentation， 11（4）， 305-313.
[14] Kam， S. I. （2010）. Mechanistic Modeling of Pipeline Leak Detection at Fixed Inlet Rate. Journal of Petroleum Science and Engineering， 70（3）， 145-156.
[15] Kim， J. H.， Kim， H. D.， & Park， K. A. （2006）. Computational/Experimental Study of a Variable Critical Nozzle Flow. Flow Measurement and Instrumentation， 17， 81-86.
[16] Lee， A.， Gonzalez， M. H.， & Eakin， B. E. （1966）. The Viscosity of Natural Gases. Journal of Petroleum Technology， 18（8）， 997-1000.
[17] Minerals Management Services. （2009）. Gulf of Mexico oil and gas production forecast： 2009-2018 （OCS Report MMS 2009-012）. Retrieved from http：//www.gomr.boemre.gov/
[18] Moody， L. F. （1944）. Friction Factors for Pipe Flow. Transactions of the ASME， 66（8）， 671–684.
[19] Morris， S. D. （1996）. Choke Pressure in Pipeline Restrictions. Journal of Hazardous Materials， 50（1）， 65–69.
[20] Papadakis， G. A.， Porter， S.， & Wettig， J. （1999）. EU Initiative on the Control of Major Accident Hazards Arising from Pipelines. Journal of Loss Prevention in the Process Industries， 12（1）， 85-90.
[21] Papadakis， G. A. （1999）. Major Hazard Pipelines： a Comparative Study of Onshore Transmission Accidents. Journal of Loss Prevention in the Process Industries， 12（1）， 91-107. [22] Payne， M. L. （2007）. Deepwater Activity in the US Gulf of Mexico Continues to Drive Innovation and Technology. Exploration & Production： The Oil and Gas Review 2007 - OTC Edition.
[23] Richardson， S. M.， Saville， G.， Fisher， A.， Meredith， A. J.， & Dix， M. J. （2006）. Experimental Determination of Two-Phase Flow Rates of Hydrocarbons Through Restrictions. Process Safety and Environmental Protection， 84（1）， 40-53.
[24] Richardson， G. E.， Nixon， L. D.， Bohannon， C. M.， Kazanis， E. G.， Montgomery， T. M.， & Gravois， M. P. （2008）. Deepwater Gulf of Mexico 2008： America’s Offshore Energy Future. U.S. Dept. of the Interior， Minerals Management Service， Gulf of Mexico OCS Region， New Orleans， LA.
[25] Ros， N. C. J. （1960）. An Analysis of Critical Simultaneous Gas/Liquid Flow Through a Restriction and Its Application to Flowmetering. Applied Scientific Research， 9（1）， 374-388.
[26] Rosen， Y.， & Schneyer， J. （2011）. Alaska Pipeline Restart Unknown； Oil up， BP Dips. Reuters. Retrieved from http：//www.reuters.com/article/2011/01/10/us-oil-pipeline-alaska-idUSTRE7080H820110110
[27] Sachdeva， R.， Schmidt， Z.， Brill， J. P.， & Blais， R. M. （1986， October）. Two-Phase Flow Through Chokes. Paper Presented at the SPE Annual Technical Conference and Exhibition， New Orleans， Louisiana.
[28] Scott， S. L， & Barrufet， M. A. （2003）. Worldwide Assessment of Industry Leak Detection Capabilities for Single & Multiphase Pipelines （PB2011-104131）. Minerals Management Service.
[29] Scott， S. L.， & Yi， J. （1998）. Detection of Critical Flow Leaks in Deepwater Gas Flowlines. Paper Presented at the SPE Annual Technical Conference and Exhibition， New Orleans， LA.
[30] Simonoff， J. S.， Restrepo， C. E.， & Zimmerman， R. （2010）. Risk Management of Cost Consequences in Natural Gas Transmission and Distribution Infrastructures. Journal of Loss Prevention in the Process Industries， 23（2）， 269-279.
[31] U.S. Department of Transportation’s Pipeline and Hazardous Materials Safety Administration. （2010）. PHMSA significant incident files. Retrieved from www.phmsa.dot.gov
[32] Wang， S.， & Carroll， J. J. （2007）. Leak Detection for Gas and Liquid Pipelines by Transient Modeling. SPE Projects， Facilities & Construction， 2（2）， 1-9.