Mathematical modeling of the flow in a pipeline with a leak

Pipeline leaks can lead to excessive economical loss as well as posing environmental hazards. Mathematical modeling of the flow in a pipeline with a leak can be used to evaluate the loss caused by a leak and provide a guide for pipeline operation as well as an aid for leak detection. The mathematical expressions describing the flow in a pipeline with a leak have been formulated. A new approach based on the analogy between pipeline and electric circuit has been proposed to solve these equations. In this approach, an equivalent circuit with a certain structure has been used to simulate the leaking pipeline and the flow characteristics of the pipeline end have been treated with approximation. The mathematical model of the pipeline with a leak has been developed with the solution of the equations. The model was verified by using an experimental gas pipeline and a real oil pipeline. The simulated results agreed well with the experimental recordings confirmed the accuracy of the models and the validity and efficiency of the proposed approach.

[1]  E. Benjamin Wylie,et al.  Fluid Transients in Systems , 1993 .

[2]  Lai Jian-bo.  Steady Leakage Calculation Models of Non-Isothermal Long Gas Pipeline , 2005 .

[3]  Dong Yuhua,et al.  Evaluation of gas release rate through holes in pipelines , 2002 .

[4]  A. Y. Allidina,et al.  Leak detection and location in gas pipelines , 1988 .

[5]  Josep Arnaldos,et al.  Mathematical modelling of accidental gas releases , 1998 .

[6]  H Mahgerefteh,et al.  A transient outflow model for pipeline puncture , 2003 .

[7]  Yehia A. Khulief,et al.  A non-linear multiple-model state estimation scheme for pipeline leak detection and isolation , 2002 .

[8]  Deng Song-sheng.  Study on the Leak in the Hydraulic Transient Simulation of the Pipeline , 2006 .

[9]  Haroun Mahgerefteh,et al.  Fast numerical simulation for full bore rupture of pressurized pipelines , 1999 .

[10]  Huo Chun-yong.  Estimation of accidental gas release flow rate in long transmission pipelines , 2004 .

[11]  Keith E. Holbert,et al.  Applying the equivalent pi circuit to the modeling of hydraulic pressurized lines , 2009, Math. Comput. Simul..

[12]  C. V. Kameswara Rao,et al.  On the analysis of pressure transients in pipelines carrying compressible fluids , 1993 .

[13]  Young Do Jo,et al.  A simple model for the release rate of hazardous gas from a hole on high-pressure pipelines. , 2003, Journal of hazardous materials.

[14]  H. C. Ti,et al.  Transient analysis of isothermal gas flow in pipeline network , 2000 .

[15]  H Mahgerefteh,et al.  Modelling outflow following rupture in pipeline networks , 2006 .

[16]  Wang Jianlin.  Modeling and Simulation of Leaking Gas Pipeline , 2011 .

[17]  Joseph B. Franzini,et al.  Fluid Mechanics with Engineering Applications. 6th Ed. By R. L.DAUGHERTY and J. B. FRANZINI. McGraw-Hill. 1965. 574 pp. $9.95 or 80s. Fluid Dynamics. By J. W. DAILY and D. R. F. HARLEMAN. Addison Wesley. 1966. 454 pp. $12.50 or 94s. , 1967, Journal of Fluid Mechanics.

[18]  Rolf Isermann,et al.  Leak detection methods for pipelines , 1984, Autom..

[19]  C. H. Tiley,et al.  Unsteady and transient flow of compressible fluids in pipelines—a review of theoretical and some experimental studies , 1987 .