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Petrophysics laws as invariants of filtration model

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Abstract

In this paper the methods of Lie group analysis are used to investigate symmetry properties of differential equations that describe filtration of a two-phase liquid in a porousmedia. Lie algebra of operators of a group of equivalence transformations is calculated. Invariants with respect to a subgroup of the group of equivalence transformations are used for constructing the functional dependencies which define arbitrary parameters of the model. It is shown that one of the invariants of a subalgebra of operators of equivalence transformations is the Timur’s law, describing a relation between absolute permeability, porosity and residual water saturation.

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Authors and Affiliations

  1. Ufa State Aviation Technical University, Ufa, Russia

    V. A. Baikov, L. R. Galiakberova & I. S. Zheltova

  2. RN-UfaNIPIneft’, Ufa, Russia

    V. A. Baikov & V. G. Volkov

Authors
  1. V. A. Baikov
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  2. L. R. Galiakberova
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  3. V. G. Volkov
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  4. I. S. Zheltova
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Corresponding author

Correspondence to V. A. Baikov.

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Submitted by N.H. Ibragimov

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Baikov, V.A., Galiakberova, L.R., Volkov, V.G. et al. Petrophysics laws as invariants of filtration model. Lobachevskii J Math 31, 192–197 (2010). https://doi.org/10.1134/S1995080210020095

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  • DOI: https://doi.org/10.1134/S1995080210020095

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