nach oben

Mathematical Models and Computer Simulations

Erschienen in:

01.03.2020

Dimp-Hydro Solver for Direct Numerical Simulation of Fluid Microflows within Pore Space of Core Samples

verfasst von: V. A. Balashov, E. B. Savenkov, B. N. Chetverushkin

Erschienen in: Mathematical Models and Computer Simulations | Ausgabe 2/2020

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config

KI-gestützte Suche

Aus

Abstract

The paper is devoted to a description of the DiMP-Hydro software package being developed at the Keldysh Institute of Applied Mathematics (Russian Academy of Sciences). It is intended to simulate microflows of single- and two-phase viscous compressible fluids with different rheology in spatial voxel domains. Such geometric models are relevant due to the development and widespread use of computer microtomography methods. One of the main areas of the application of this software package is the simulation of microflows within pore spaces of core (rock) samples. The simulation results can be used to determine the macroscopic properties of core samples (for instance, absolute permeability) and features of displacement processes at the micro level, which is one of main tasks of digital rock technology. The used mathematical models, numerical algorithms, and the software package are described. To describe the fluid dynamics, the regularized Navier–Stokes (for single-phase flows) and Navier–Stokes–Cahn–Hillard equations (for two-phase flows) are used. The regularization is based on the quasi-hydrodynamic approach, which is physically justified and makes it possible to use explicit stable numerical algorithms that are relatively simple to implement. The software package is parallel and focused on the use of high-performance computing systems. The results of the use of DiMP-Hydro to simulate microflows of fluid (including two-phase fluid) and gas (including moderately rarefied gas) in the pore space of core samples are presented.

Vorheriger Artikel Difference Schemes of Consistent Approximation of the Stress-Strain State and Energy Balance of a Medium

Nächster Artikel Difference Scheme with a Symmetry Analyzer for Equations of Gas Dynamics

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

M. J. Blunt, B. Bijeljic, H. Dong, O. Gharbi, S. Iglauer, P. Mostaghimi, A. Paluszny, and C. Pentland, “Pore-scale imaging and modelling,” Adv. Water Res. 51, 197–216 (2013).CrossRef

M. J. Blunt, Multiphase Flow in Permeable Media: A Pore-Scale Perspective (Cambridge Univ. Press, Cambridge, 2017).CrossRef

C. F. Berg, O. Lopez, and H. Berland, “Industrial applications of digital rock technology,” J. Pet. Sci. Eng. 157, 131–147 (2017).CrossRef

A. Raoof, H. M. Nick, S. M. Hassanizadeh, and C. J. Spiers, “PoreFlow: a complex pore-network model for simulation of reactive transport in variably saturated porous media,” Comput. Geosci. 61, 160–174 (2013).CrossRef

L. Algive, S. Bekri, and O. Vizika, “Pore-network modeling dedicated to the determination of the petrophysical-property changes in the presence of reactive fluid,” SPE J. 15, 618–633 (2010).CrossRef

M. J. Blunt, “Flow in porous media and pore-network models and multiphase flow,” Curr. Opin. Colloid Interface Sci. 6, 197–207 (2001).CrossRef

F. O. Alpak, F. Gray, N. Saxena, J. Dietderich, R. Hofmann, and S. Berg, “A distributed parallel multiple-relaxation-time lattice Boltzmann method on general-purpose graphics processing units for the rapid and scalable computation of absolute permeability from high-resolution 3D micro-CT images,” Comput. Geosci. 22, 815–832 (2018).MathSciNetMATHCrossRef

Q. Kang, P. C. Lichtner, and D. R. Janecky, “Lattice Boltzmann method for reacting flows in porous media,” Adv. Appl. Math. Mech. 2, 545–563 (2010).MathSciNetCrossRef

X. He and L. S. Luo, “Theory of the lattice Boltzmann method: from the Boltzmann equation to the lattice Boltzmann equation,” Phys. Rev. E 56, 6811–6817 (1997).CrossRef

10.

W. Yong, W. Zhao, and L. Luo, “Theory of the Lattice Boltzmann method: derivation of macroscopic equations via the Maxwell iteration,” Phys. Rev. E 93, 033310 (2016).MathSciNetCrossRef

11.

S. Chen and G. D. Doolen, “Lattice Boltzmann method for fluid flows,” Ann. Rev. Fluid Mech. 30, 329–364 (1998).MathSciNetMATHCrossRef

12.

H. W. Zheng, C. Shu, and Y. T. Chew, “A lattice Boltzmann model for multiphase flows with large density ratio,” J. Comput. Phys. 218, 353–371 (2006).MathSciNetMATHCrossRef

13.

E. Aurell and M. Do-Quang, “An inventory of Lattice Boltzmann models of multiphase flows,” arXiv:cond-mat/0105372v1 [cond-mat.soft]

14.

S. Succi, The Lattice Bolzmann Equation for Fluid Dynamics and Beyond (Clarendon, Oxford, 2001).MATH

15.

M. C. Sukop and D. T. Thorne, Lattice Boltzmann Modeling: An Introduction for Geoscientists and Engineers, 2nd ed. (Springer, Berlin, Heidelberg, 2006), p. 172.CrossRef

16.

X. Shan and G. Doolen, “Multicomponent Lattice-Boltzmann model with interparticle interaction,” J. Stat. Phys. 81, 379–393 (1995).MATHCrossRef

17.

D. M. Anderson and G. B. McFadden, A Diffuse-Inreface Description of Fluid Systems (Natl. Inst. Standards Technolol., Gaithersburg, 1996), p. 35.CrossRef

18.

D. M. Anderson, G. B. McFadden, and A. A. Wheeler, “Diffuse-interface methods in fluid mechanics,” Ann. Rev. Fluid Mech. 30, 139–165 (1998).MathSciNetMATHCrossRef

19.

K. Kim, “Phase-field models for multi-component fluid flows,” Commun. Comput. Phys. 12, 613–661 (2012).MathSciNetMATHCrossRef

20.

R. Mauri, Multiphase Microfluidics: The Diffuse Interface Model, Vol. 538 of CISM Courses and Lectures (Springer, Wien, 2012), p. 176.

21.

S. Groß, “Numerical methods for three-dimensional incompressible two-phase flow problems,” Dissertation (RWTH Aachen, 2008).

22.

S. Gross and A. Reusken, Numerical Methods for Two-Phase Incompressible Flows (Springer, Berlin, Heidelberg, 2011), p. 482.MATHCrossRef

23.

A. Smolianski, “Numerical modeling of two-fluid interfacial flows,” Dissertation (Univ. of Jyväskylä, 2001).

24.

C. Gunde, B. Bera, and S. K. Mitra, “Investigation of water and CO2 (carbon dioxide) flooding using micro-CT (micro-computed tomography) images of Berea sandstone core using finite element simulations,” Energy 35, 5209–5216 (2010).CrossRef

25.

Q. Zhu, Q. Zhou, and X. Li, “Numerical simulation of displacement characteristics of CO2 injected in pore-scale porous media,” J. Rock Mech. Geotech. Eng. 8, 87–92 (2016).CrossRef

26.

A. Q. Raeini, M. J. Blunt, and B. Bijeljic, “Modelling two-phase flow in porous media at the pore scale using the volume-of-fluid method,” J. Comput. Phys. 231, 5653–5668 (2012).MathSciNetCrossRef

27.

J. Maes and C. Soulaine, “A new compressive scheme to simulate species transfer across fluid interfaces using the volume-of-fluid method,” Chem. Eng. Sci. 190, 405–418 (2018).CrossRef

28.

M. Shams, A. Q. Raeini, M. J. Blunt, and B. Bijeljic, “A numerical model of two-phase flow at the micro-scale using the volume-of-fluid method,” J. Comput. Phys. 357, 159–182 (2018).MathSciNetMATHCrossRef

29.

O. Yu. Dinariev, N. V. Evseev, and A. Yu. Demianov, Introduction to the Density Functional Method in Hydrodynamics (Fizmatlit, Moscow, 2014) [in Russian].

30.

R. T. Armstrong, S. Berg, O. Dinariev, N. Evseev, D. Klemin, D. Koroteev, and S. Safonov, “Modeling of pore-scale two-phase phenomena using density functional hydrodynamics,” Transp. Porous Media 112, 577–607 (2016).MathSciNetCrossRef

31.

http://www.slb.com/services/characterization/reservoir/core_pvt_lab/coreflow.aspx. Accessed Sept. 26, 2018.

32.

Yu. V. Sheretov, Continuous Media Dynamics with Spatiotemporal Averaging (RKhD, Izhevsk, Moscow, 2009) [in Russian].

33.

B. N. Chetverushkin, Kinetic Schemes and Quasi-Gasdynamic System of Equations (MAKS Press, Moscow, 2004; CIMNE, Barcelona, 2008).

34.

T. G. Elizarova, Quasi-Gas Dynamic Equations (Nauchnyi Mir, Moscow, 2007; Springer, Berlin, Heidelberg, 2009), p. 286.

35.

V. A. Balashov and E. B. Savenkov, “Quasi-hydrodynamic model of multiphase fluid flows taking into account phase interaction,” J. Appl. Mech. Tech. Phys. 59, 434–444 (2018).MathSciNetMATHCrossRef

36.

V. A. Balashov and E. B. Savenkov, “Quasihydrodynamic equations for diffuse interface type multiphase flow model with surface effects,” KIAM Preprint No. 75 (Keldysh Inst. Appl. Math., Moscow, 2015), pp. 1–37.

37.

J. Dvorkin, N. Derzhi, E. Diaz, and Q. Fang, “Relevance of computational rock physics,” Geophysics 76 (5), E141–E153 (2011).CrossRef

38.

Imperial College London. http://www.imperial.ac.uk/earth-science/research/research-groups/perm/research/pore-scale-modelling/micro-ct-images-and-networks/. Accessed Sept. 26, 2018.

39.

R. Ierusalimschy, L. Henrique de Figueiredo, and W. C. Filho, “Lua - an extensible extension language,” Software-Pract. Experience 26, 635–652 (1996).

40.

R. Ierusalimschy, Programming in Lua (Lua.Org, 2016).

41.

R. L. Graham, T. S. Woodall, and J. M. Squyres, “Open MPI: a flexible high performance MPI,” in Proceedings of the 6th Annual International Conference on Parallel Processing and Applied Mathematics, Poznan, Poland, September2005.

42.

V. A. Balashov and E. B. Savenkov, “Application of quasihydrodynamic equation for direct numerical simulation of flow in core samples,” KIAM Preprint No. 84 (Keldysh Inst. Appl. Math., Moscow, 2015), pp. 1–20.

43.

V. A. Balashov and E. B. Savenkov, “Direct pore-scale ow simulation using quasi-hydrodynamic equations,” Dokl. Phys. 61, 192–194 (2016).CrossRef

44.

V. A. Balashov and V. E. Borisov, “Numerical algorithm for 3D moderately rarefied gas flows simulation within domains with voxel geometry,” KIAM Preprint No. 99 (Keldysh Inst. Appl. Math., Moscow, 2017), pp. 1–24.

45.

V. A. Balashov, “Direct numerical simulation of moderately rarefied gas flow within core samples,” Mat. Model. 30 (9), 3–20 (2018).MathSciNet

46.

V. Balashov, A. Zlotnik, and E. Savenkov, “Numerical method for 3D two-component isothermal compressible flows with application to digital rock physics,” Russ. J. Numer. Anal. Math. Model. 34 (1), 1–13 (2019).MathSciNetMATHCrossRef

47.

V. A. Balashov and E. B. Savenkov, “Numerical simulation of two-dimensional two-phase fluid flows accounting for wettability with quasi-hydrodynamic equations,” KIAM Preprint No. 131 (Keldysh Inst. Appl. Math., Moscow, 2018), pp. 1–18.

48.

V. Balashov, A. Zlotnik, and E. Savenkov, “Analysis of a regularized model for the isothermal two-component mixture with the diffuse interface,” Russ. J. Numer. Anal. Math. Model. 32, 347–358 (2017).MathSciNetMATHCrossRef

49.

V. A. Balashov, A. A. Zlotnik, and E. B. Savenkov, “Numerical algorithm for simulation of three-dimensional two-phase flows with surface effects within domains with voxel geometry,” KIAM Preprint No. 91 (Keldysh Inst. Appl. Math., Moscow, 2017), pp. 1–28.

50.

J. W. Cahn and J. E. Hilliard, “Free energy of a nonuniform system. I. Interfacial free energy,” J. Chem. Phys. 28, 258–267 (1958).MATHCrossRef

51.

A. Novick-Cohen and L. A. Segel, “Nonlinear aspects of the Cahn-Hilliard equation,” Phys. D (Amsterdam, Neth.) 10, 277–298 (1984).

52.

O. Wodo and B. Ganapathysubramanian, “Computationally efficient solution to the Cahn-Hilliard equation: adaptive implicit time schemes, mesh sensitivity analysis and the 3D isoperimetric problem,” J. Comput. Phys. 230, 6037–6060 (2011).MathSciNetMATHCrossRef

53.

M. I. M. Copetti and C. M. Elliott, “Numerical analysis of the Cahn-Hilliard equation with a logarithmic free energy,” Numer. Math. 63, 39–65 (1992).MathSciNetMATHCrossRef

54.

G. Tierra and F. Guillén-González, “Numerical methods for solving the Cahn-Hilliard equation and its applicability to related energy-based models,” Arch. Comput. Methods Eng. 22, 269–289 (2015).MathSciNetMATHCrossRef

55.

J. Liu, “Thermodynamically consistent modeling and simulation of multiphase flows,” PhD Dissertation (Univ. Texas, Austin, 2014).

56.

A. Carlson, M. Do-Quang, and G. Amberg, “Modelling of dynamic wetting far from equillibrium,” Phys. Fluids 21, 121701 (2009).MATHCrossRef

57.

G. Karypis and V. Kumar, “A fast and high quality multilevel scheme for partitioning irregular graphs,” SIAM J. Sci. Comput. 20, 359–392 (1998).MathSciNetMATHCrossRef

58.

W. Schroeder, K. Martin, and B. Lorensen, The Visualization Toolkit, 4th ed. (Kitware, New York, 2006).

59.

H. Dong and M. J. Blunt, “Pore-network extraction from micro-computerized-tomography images,” Phys. Rev. E 80, 036307 (2009).CrossRef

60.

W. Degruyter, A. Burgisser, O. Bachmann, and O. Malaspinas, “Synchrotron X-ray microtomography and lattice Boltzmann simulations of gas flow through volcanic pumices,” Geosphere 6, 470–481 (2010).CrossRef

61.

Palabos: Parallel Lattice Boltzmann Solver. http://www.palabos.org/.

62.

J. G. Heid, J. J. McMahon, R. F. Nielsen, and S. T. Yuster, “Study of the permeability of rocks to homogeneous fluids,” in Drilling and Production Practice (Am. Pet. Inst., 1950), pp. 230–244.

63.

W. Tanikawa and T. Shimamoto, “Comparison of Klinkenberg-corrected gas permeability and water permeability in sedimentary rocks,” Int. J. Rock Mech. Mining Sci. 46, 229–238 (2009).CrossRef

64.

F. O. Jones and W. W. Owens, “A laboratory study of low-permeability gas sands,” J. Pet. Technol. 32 (9) (1980).

Titel: Dimp-Hydro Solver for Direct Numerical Simulation of Fluid Microflows within Pore Space of Core Samples
verfasst von: V. A. Balashov
E. B. Savenkov
B. N. Chetverushkin
Publikationsdatum: 01.03.2020
Verlag: Pleiades Publishing
Erschienen in: Mathematical Models and Computer Simulations / Ausgabe 2/2020
Print ISSN: 2070-0482
Elektronische ISSN: 2070-0490
DOI: https://doi.org/10.1134/S2070048220020027

Springer Professional

Abstract

Bitte loggen Sie sich ein, um Zugang zu Ihrer Lizenz zu erhalten.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Springer Professional "Wirtschaft"

Weitere Artikel der Ausgabe 2/2020

Difference Scheme with a Symmetry Analyzer for Equations of Gas Dynamics

Hysteretic Converters with Stochastic Parameters

Graphs for the Replicator Equations and the “Tragedy of the Exhaustion of the Common Resource”

Methods of Solving the Theoretic Game Models for Coordinating Interests in Regulating the Fishery Industry

Modeling Position Selection by Individuals during Informational Warfare with a Two-Component Agenda

Molecular Dynamic Calculation of Macroparameters of Technical Gases by the Example of Argon, Nitrogen, Hydrogen, and Methane