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Friedrichs systems for systems of wave equations and shear waves in a three-dimensional elastic medium

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Journal of Applied Mechanics and Technical Physics Aims and scope

Abstract

This paper considers a two-dimensional hydraulic model which describes gas or oil flow to a horizontal well with hydraulic fractures and takes into account the reservoir geometry and fluid flow between the reservoir and the well. A computational algorithm is proposed, and calculations for gas and oil reservoirs are performed. A comparison of the calculation results and the solutions of the corresponding problems in a three-dimensional formulation show that the calculations using the approximate hydraulic model yield reasonably accurate results.

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References

  1. V. M. Gordienko, “Friedrichs system for the three-dimensional wave equation,” in: Differential Equations. Functional Spaces. Theory of Approximations, Abstracts of Int. Conf. Devoted to the 100th Birthday of Academician S. L. Sobolev, Inst. of Mathematics, Sib. Div., Russian Academy of Sci., Novosibirsk (2008), p. 126.

  2. V. M. Gordienko, “Application of quaternions to wave equation theory,” in: Mathematics in Applications, Conf. Devoted to 80th Birthday of Academician S. K. Godunov, Inst. of Mathematics, Sib. Div., Russian Academy of Sci., Novosibirsk (2009), pp. 90–91.

  3. V. B. Poruchikov, Methods of Dynamic Elasticity [in Russian] Nauka, Moscow (1986).

    Google Scholar 

  4. L. V. Ovsiannikov, Group Analysis of Differential Equations, Academic Press, New York (1982).

    MATH  Google Scholar 

  5. Y. A. Chirkunov, “Conditions of linear autonomy of the basic Lie algebra of the system of linear differential equations,” Dokl. Ross. Akad. Nauk, 426, No. 5, 605–607 (2009).

    MathSciNet  Google Scholar 

  6. S. K. Godunov, Equations of Mathematical Physics [in Russian] Nauka, Moscow (1971).

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Correspondence to Yu. A. Chirkunov.

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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 51, No. 6, pp. 121–132, November–December, 2010.

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Chirkunov, Y.A. Friedrichs systems for systems of wave equations and shear waves in a three-dimensional elastic medium. J Appl Mech Tech Phy 51, 877–886 (2010). https://doi.org/10.1007/s10808-010-0109-8

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  • DOI: https://doi.org/10.1007/s10808-010-0109-8

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