Geodesic
On the double porosity model of fractured-porous reservoirs based on the hybrid overflow function
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 21 (2018) no. 2, pp. 155-169.

Voir la notice de l'article provenant de la source Math-Net.Ru

The paper considers a model of double porosity for a fractured porous medium using a combination of classical and gradient mass transfer functions among cracks and porous blocks in the case of a flow of a weakly compressible single-phase fluid. As compared to well-known models, such a mass transfer function allows one to take into account the anisotropic properties of filtration in a more general form. The results of numerical tests for two-dimensional and three-dimensional model problems are presented. The computational algorithm is based on the use of finite element approximation with respect to space and completely implicit approximations with respect to time. 
@article{SJVM_2018_21_2_a2,
     author = {A. V. Grigorev and Yu. M. Laevsky and P. G. Yakovlev},
     title = {On the double porosity model of fractured-porous reservoirs based on the hybrid overflow function},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {155--169},
     publisher = {mathdoc},
     volume = {21},
     number = {2},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2018_21_2_a2/}
}
TY  - JOUR
AU  - A. V. Grigorev
AU  - Yu. M. Laevsky
AU  - P. G. Yakovlev
TI  - On the double porosity model of fractured-porous reservoirs based on the hybrid overflow function
JO  - Sibirskij žurnal vyčislitelʹnoj matematiki
PY  - 2018
SP  - 155
EP  - 169
VL  - 21
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SJVM_2018_21_2_a2/
LA  - ru
ID  - SJVM_2018_21_2_a2
ER  - 
%0 Journal Article
%A A. V. Grigorev
%A Yu. M. Laevsky
%A P. G. Yakovlev
%T On the double porosity model of fractured-porous reservoirs based on the hybrid overflow function
%J Sibirskij žurnal vyčislitelʹnoj matematiki
%D 2018
%P 155-169
%V 21
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SJVM_2018_21_2_a2/
%G ru
%F SJVM_2018_21_2_a2
A. V. Grigorev; Yu. M. Laevsky; P. G. Yakovlev. On the double porosity model of fractured-porous reservoirs based on the hybrid overflow function. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 21 (2018) no. 2, pp. 155-169. http://geodesic.mathdoc.fr/item/SJVM_2018_21_2_a2/

[1] Barenblatt G. I., Zheltov Yu. P., Kochina I. N., “Ob osnovnykh predstavleniyakh teorii filtratsii v treschinovatykh sredakh”, Prikl. matematika i mekhanika, 24:5 (1960), 852–864 | Zbl

[2] Warren J. E., Root P. J., “The behavior of naturally fractured reservoirs”, Society of Petroleum Engineers Journal, 3:3 (1963), 245–255 | DOI

[3] Dmitriev N. M., Maksimov V. M., “Models of flow through fractured-porous anisotropic media”, Fluid Dynamics, 42:6 (2007), 937–942 | DOI | MR | Zbl

[4] Vabishchevich P. N., Grigoriev A. V., “Numerical modeling of fluid flow in anisotropic fractured porous media”, Numerical Analysis and Applications, 9:1 (2016), 45–56 | DOI | MR | Zbl

[5] Landau L. D., Lifshits E. M., Teoriya uprugosti. Kurs Teoreticheskoi Fiziki, v. VII, 4-e izd., ispr., Nauka, M., 1987

[6] Pruess K., Brief guide to the MINC-method for modeling flow and transport in fractured media, Earth Sciences Division, Lawrence Berkeley Laboratory, University of California, Berkeley, 1992

[7] Brenner S. C., Scott L. R., The Mathematical Theory of Finite Element Methods, Texts in Applied Mathematics, 15, 3rd ed., Springer, 2007 | MR

[8] Dupont T., Hoffman J., Johnson C. et all, The FEniCS project, Tech. Rep. 2003-21, Preprint, Chalmers Finite Element Center, Chalmers University of Technology, Goteborg, 2003

[9] Langtangen H. P., Logg A., Solving PDEs in Minutes, The FEniCS Tutorial, 1, Springer, 2016 | MR

[10] Geuzaine C., Remacle J.-F., “Gmsh: A 3-D finite element mesh generator with built-in pre- and post-processing facilities”, Int. J. for Numerical Methods in Engineering, 79:11 (2009), 1309–1331 | DOI | MR | Zbl

[11] SPE Comparative Solution Project, http://www.spe.org/web/csp/datasets/set02.htm

[12] Karypis G., Kumar V., “A parallel algorithm for multilevel graph partitioning and sparse matrix ordering”, J. of Parallel and Distributed Computing, 48:1 (1998), 71–95 | DOI | MR