«Proceedings of Gubkin University»

ESTIMATION OF PERMEABILITY TENSOR BY NUMERICAL SIMULATION OF FLUID FLOW IN POROUS MEDIA DIGITAL MODEL

UDC: 519.87
DOI: -

Authors:

¹ Gubkin Russian State University of Oil and Gas

Keywords: computer microtomography, porous media digital model, full permeability tensor, numerical solution of Navier-Stokes equations.

Annotation:

On the basis of direct fluid flow simulation using a porous media digital model obtained from computer microtomography of the core sample an adaptive algorithm for the estimation of the full permeability tensor and its principle parametres is proposed. A sequential method for the estimation of parameters of the generalized nonstationary Darcy law and influence of its components on the filtration process is proposed. Applying the inverse interpolation method an algorithm for adaptation of one-parameter porous media digital model to the results of the laboratory core tests is presented.

Bibliography:

1. Арсеньев-Образцов С.С. Численное моделирование микротечений в пористой среде по результатам 3D компьютерной томографии//Сборник тезисов докладов IX Всероссийской научно-технической конференции „Актуальные проблемы развития нефтегазового комплекса России”, 30 января — 1 февраля 2012 г. — М.: Издательский центр РГУ нефти и газа имени И.М. Губкина, 2012. — Часть II. — 85 с.
2. Арсеньев-Образцов С.С. Моделирование двухфазного течения на компьютерной микромодели пористой среды//Сборник тезисов докладов X Всероссийской научно-технической конференции „Актуальные проблемы развития нефтегазового комплекса России”, 10–12 февраля 2014 г. — М.: Издательский центр РГУ нефти и газа имени И.М. Губкина, 2014. — 256 с.
3. Flannery B.P., Deckman H.W., Roberge W.G. and D’Amico K.L. Three-Dimensional X-ray Microtomography. Science, 1987, 237 (4821), p. 1439-1444.
4. Carman P.Z. Flow of Gases through Porous Media. Butterworths, London (1956).
5. Durlofsky L.J. Numerical calculation of equivalent grid block permeability tensors for heterogeneous porous media, 1991, Water Res. Res., v. 27, p. 699-708.
6. Kirkpatrick S. Percolation and conduction. Reviews of Modern Physics 45, no. 4 (1973), 574-588.
7. Pan C., Hilpert M., Miller C.T. Pore-scale modeling of saturated permeabilities in random sphere packings. Phys. Rev. E: Stat. Phys., Plasmas, Fluids. 64 (2001).
8. Acharya R.C., Van Der Zee, S.E.A.T.M Leijnse A. Porosity-permeability properties generated with a new 2-parameter 3D hydraulic pore-network model for consolidated and unconsolidated porous media. Adv. Water Res. 27, р. 707–723 (2004).
9. Lindquist W.B. Network flow model studies and 3D pore structure. Contemporary Mathematics, 295 (2002), р. 355-366.
10. Schena, G., Favretto, S. Pore space network characterization with sub-voxel definition. Transp. Porous Media. 70 (2), р. 181–190 (2007).
11. Succi S. The Lattice Boltzmann Equation: For Fluid Dynamics and Beyond. Series Numerical Mathematics and Scientific Computation. Oxford University Press, Oxford (2001).