This paper presents the main aspects of fluid leakage through a hole in surface of a pipeline. In the general case, this problem has not yet been solved. In the classical theory of unsteady flows of a weakly compressible fluid in the pipe, the ascending its origins to the famous work of N. Zhukovsky "On the water hammer in water pipelines" (1899), is tacitly assumed that the pipeline is completely filled with liquid, so discharge wave spreads from the site of depressurization conduit in both directions. However, such an assumption in most practical cases is wrong. Profile of an oil pipeline usually has a large level difference, so the pressure in the propagating discharge wave may be reduced to elasticity of the saturated liquid vapor, which leads to the formation of steam-gas cavities inside pipe. Such cavities are insurmountable obstacles for the passage of pressure waves, so the transient process in the pipeline is developed in a different scenario than the one that is determined by the classical theory. The focus of the work is based on the fact that process of fluid leakage through a hole has transient character and is accompanied by the formation of voids in the pipeline, i.e. discontinuities liquid column due to the reduction of fluid pressure in some pipeline sections up to the value of elasticity of the saturated vapor. There are pipeline sections on which the fluid moves with full cross section but alternates with the pipeline sections in which the fluid moves with only partially filled cross section of the pipe. The pressure in these gravity flow sections is equal to elasticity of the saturated vapor. Thus, a complete solution to the problem of leakage of fluid through a hole is possible only on the basis of the general theory of transient processes taking into account the possibility of formation of voids and the gravity flow sections. The basic equations of the theory and examples of calculations are presented in this paper.

References

1. Truboprovodnyy transport nefti (Crude oil pipeline), edited by Vaynshtok

S.M., Moscow: Nedra-Biznestsentr Publ., 2004, Part 2, 621 p.

2. Lur’e M.V., Polyanskaya L.V., About a dangerous cause of the hydraulic

shock waves in relief crude- and refined oil product pipe-lines (In Russ.),

Neftyanoe khozyaystvo = Oil Industry, 2000, no. 8, pp. 66–68.

3. Lur’e M.V., Calculation method of transient phenomena in pipelines with

possible formation and disappearance of vapour-gas cavities (In Russ.),

Nauka i tekhnologii truboprovodnogo transporta nefti i nefteproduktov,

2011, no. 4, pp. 58–62.

4. Lur’e M.V., Matematicheskoe modelirovanie protsessov truboprovodnogo

transporta nefti, nefteproduktov i gaza (Mathematical modeling of oil

and gas pipeline transport), Moscow: Publ. of Gubkin Russian State University

of Oil and Gas, 2012, 456 p.

This paper presents the main aspects of fluid leakage through a hole in surface of a pipeline. In the general case, this problem has not yet been solved. In the classical theory of unsteady flows of a weakly compressible fluid in the pipe, the ascending its origins to the famous work of N. Zhukovsky "On the water hammer in water pipelines" (1899), is tacitly assumed that the pipeline is completely filled with liquid, so discharge wave spreads from the site of depressurization conduit in both directions. However, such an assumption in most practical cases is wrong. Profile of an oil pipeline usually has a large level difference, so the pressure in the propagating discharge wave may be reduced to elasticity of the saturated liquid vapor, which leads to the formation of steam-gas cavities inside pipe. Such cavities are insurmountable obstacles for the passage of pressure waves, so the transient process in the pipeline is developed in a different scenario than the one that is determined by the classical theory. The focus of the work is based on the fact that process of fluid leakage through a hole has transient character and is accompanied by the formation of voids in the pipeline, i.e. discontinuities liquid column due to the reduction of fluid pressure in some pipeline sections up to the value of elasticity of the saturated vapor. There are pipeline sections on which the fluid moves with full cross section but alternates with the pipeline sections in which the fluid moves with only partially filled cross section of the pipe. The pressure in these gravity flow sections is equal to elasticity of the saturated vapor. Thus, a complete solution to the problem of leakage of fluid through a hole is possible only on the basis of the general theory of transient processes taking into account the possibility of formation of voids and the gravity flow sections. The basic equations of the theory and examples of calculations are presented in this paper.

References

1. Truboprovodnyy transport nefti (Crude oil pipeline), edited by Vaynshtok

S.M., Moscow: Nedra-Biznestsentr Publ., 2004, Part 2, 621 p.

2. Lur’e M.V., Polyanskaya L.V., About a dangerous cause of the hydraulic

shock waves in relief crude- and refined oil product pipe-lines (In Russ.),

Neftyanoe khozyaystvo = Oil Industry, 2000, no. 8, pp. 66–68.

3. Lur’e M.V., Calculation method of transient phenomena in pipelines with

possible formation and disappearance of vapour-gas cavities (In Russ.),

Nauka i tekhnologii truboprovodnogo transporta nefti i nefteproduktov,

2011, no. 4, pp. 58–62.

4. Lur’e M.V., Matematicheskoe modelirovanie protsessov truboprovodnogo

transporta nefti, nefteproduktov i gaza (Mathematical modeling of oil

and gas pipeline transport), Moscow: Publ. of Gubkin Russian State University

of Oil and Gas, 2012, 456 p.