Filtration-Capacitive Properties of the Periodic Porous Medium Rhombohedral Structure of the Skeleton of the Ball Segments

Tyumen State University Herald. Physical and Mathematical Modeling. Oil, Gas, Energy


Release:

2016, Vol. 2. №3

Title: 
Filtration-Capacitive Properties of the Periodic Porous Medium Rhombohedral Structure of the Skeleton of the Ball Segments


About the authors:

Dmitry E. Igoshin, Cand. Sci. (Phys-Math.), Senior Researcher, Tyumen Branch of the Khristianovich Institute of Theoretical and Applied Mechanics of the Siberian Branch of the Russian Academy of Sciences; Associate Professor, Department of Fundamental Mathematics and Mechanics, Department of Applied and Technical Physics, University of Tyumen; igoshinde@gmail.com

Nadezhda A. Khromova, Research Engineer, Tyumen Branch of Khristianovich Institute of Theoretical and Applied Mechanics of the Siberian Branch of the Russian Academy of Sciences; khromova.n.a@gmail.com

Abstract:

In the previous works the authors considered two-parameter models of periodic porous media. The unit cell size and a dimensionless parameter — the degree of the intersection of spheres — act as model parameters. In such models the porosity of the material is connected one-to-one with the permeability for a fixed unit cell size, i. e. graphically many points of the medium in the axes “porosity-permeability” are located on the curve. However, in real earth material the experimental values of porosity and permeability are located in these axes in a “cloud” even for a single lithology type material taken from a single well. In this regard, it is essential to develop a three-parameter model porous medium, for which the region values of the permeability will match better the experimental data. The aim of this article is the development of the previously reviewed models in the event of a broadcast angle different from a right angle. The model periodic structure based on the rhombohedral lattice system is considered as an example. For the described structure exact porosity and minimal luminal are obtained analytically. Permeability estimation is obtained taking into account the sinuous channels. It is shown that when θ = 90° permeability value agrees well with the corresponding value for the cubic simple structure, and at θ = 60° — with the appropriate value for the face-centered cubic structure.

References:

  1. Anderson J. D. 1995. Computational Fluid Dynamics: The Basics with Applications. McGraw-Hill Science.
  2. Gubaidullin A. A., Igoshin D. Ye., Khromova N. A. 2016. “Obobshchenie podkhoda Kozeni k opredeleniyu pronitsaemosti modelnykh poristykh sred iz tverdykh sharovykh segmentov” [The Generalization of the Kozeny Approach to Determining the Permeability of the Model Porous Media Made of Solid Spherical Segments]. Tyumen State University Herald. Physical and Mathematical Modeling. Oil, Gas, Energy, vol. 2, no 2, pp. 105–120. DOI: 10.21684/2411-7978-2016-2-2-105-120
  3. Gubaydullin A. A., Maksimov A. Yu. 2013. “Modelirovanie dinamiki kapli nefti v kapillyare s suzheniem” [Modeling the Dynamics of the Oil Droplets in the Capillary with the Restriction]. Tyumen State University Herald, no 7, pp. 71–77.
  4. Gubaydullin A. A., Maksimov A. Yu. 2015. “Sobstvennye chastoty prodolnyh kolebaniy kapli v suzhenii kapillyara” [Natural Frequencies of Longitudinal Oscillations of a Droplet in the Constriction of the Capillary Tube]. Tyumen State University Herald. Physical and Mathematical Modeling. Oil, Gas, Energy, vol. 1, no 2, pp. 85–91.
  5. Igoshin D. Ye. 2015. “Chislennoe opredelenie pronitsaemosti v srede periodicheskoy struktury, obrazovannoy razvetvlyayushchimisya kanalami” [Numerical Determination of Permeability in the Medium with a Periodic Structure Formed by Branching Channels]. Avtomatizatsiya, telemekhanizatsiya i svyaz v neftyanoi promyshlennosti, no 12, pp. 30–33.
  6. Igoshin D. Ye., Khromova N. A. 2015. “Osnovnye filtratsionnye svoystva poristoy sredy, obrazovannoy soobshchayushchimisya osesimmetrichnymi kanalami” [Main Filtration Properties of the Porous Medium Formed Communicating Axially Symmetric Channels]. Tyumen State University Herald. Physical and Mathematical Modeling. Oil, Gas, Energy, vol. 1, no 4, pp. 69–79.
  7. Igoshin D. Ye., Khromova N. A. 2016. “Gidravlicheskoe soprotivlenie izvilistykh kanalov” [Hydraulic Resistance of Tortuous Channels]. Proceedings in Cybernetics, no 3(23), pp. 8–17.
  8. Igoshin D. Ye., Maksimov A. Yu. 2015. “Chislennye i analiticheskie otsenki pronitsaemosti poristoy sredy, obrazovannoy kanalami, imeyushchimi vrashchatelnuyu simmetriyu” [Numerical and Analytical Assessment of the Permeability of a Porous Medium Formed by Channels Having Rotational Symmetry]. Tyumen State University Herald. Physical and Mathematical Modeling. Oil, Gas, Energy, vol. 1, no 3, pp. 112–121.
  9. Igoshin D. Ye., Nikonova O. A. 2015. “Pronitsaemost poristoy sredy periodicheskoy struktury s razvetvlyayushchimisya kanalami” [Permeability of the Porous Medium Periodic Structure with Branching Channels]. Tyumen State University Herald. Physical and Mathematical Modeling. Oil, Gas, Energy, vol. 1, no 2, pp. 131–141.
  10. Igoshin D. Ye., Nikonova O. A., Mostovoy P. Ya. 2014. “Modelirovanie poristoy sredy regulyarnymi upakovkami peresekayushchikhsya sfer” [Modeling Porous Medium Regular Packages Intersecting Spheres]. Tyumen State University Herald, no 7, pp. 34–42.
  11. Igoshin D. Ye., Saburov R. S. 2015. “Chislennoe issledovanie zavisimosti pronitsaemosti ot poristoy sredy, obrazovannoy kanalami regulyarnoy struktury” [Numerical Study Depending on the Permeability of the Porous Medium, Formed a Regular Structure of Channels]. Tyumen State University Herald. Physical and Mathematical Modeling. Oil, Gas, Energy, vol. 1, no 1, pp. 84–90.
  12. Ishkova Z. A., Kolunin V. S. 2016. “Opredelenie kapillyarnykh svoystv melkoporistoy sredy metodom nachala kristallizacii vody” [The Determination of Capillary Properties of Finely Porous Medium by the Water Crystallization Onset]. Tyumen State University Herald. Physical and Mathematical Modeling. Oil, Gas, Energy, vol. 2, no 1, pp. 19–25. DOI: 10.21684/2411-7978-2016-2-1-19-25
  13. Kislicyn A. A., Potapov A. G. 2015. “Issledovanie raspredeleniya por po razmeram v poristoy srede s pomoshhyu yadernogo magnitnogo rezonansa” [Study of Pore Size Distribution in Porous Medium by Nuclear Magnetic Resonance]. Tyumen State University Herald. Physical and Mathematical Modeling. Oil, Gas, Energy, vol. 1, no 3, pp. 52–59.
  14. Korn G., Korn T. 1974. Spravochnik po matematike [Mathematical Handbook]. Moscow: Nauka.
  15. Leybenzon L. S. 1947. Dvizhenie prirodnykh zhidkostey i gazov v poristoy srede [Movement of Natural Fluids in Porous Media]. Moscow: Gosudarstvennoe izdatelstvo tekhniko-teoreticheskoy literatury.
  16. Loytsyanskiy L. G. 2003. Mekhanika zhidkosti i gaza [Mechanics of Liquid and Gas]. Moscow: Drofa.
  17. Ministry of Energy of Russia. 2015. “Energeticheskaya strategiya Rossii na period do 2035 goda” [Energy Strategy of Russia for the period to 2035].
  18. Shabarov A. B., Shatalov A. V. 2016. “Poteri davleniya pri techenii vodoneftyanoy smesi v porovyh kanalah” [Pressure Drops in Water-Oil Mixture Flow in Porous Channels]. Tyumen State University Herald. Physical and Mathematical Modeling. Oil, Gas, Energy, vol. 2, no 2, pp. 50–72. DOI: 10.21684/2411-7978-2016-2-2-50-72
  19. Stepanov S. V., Shabarov A. B., Bembel G. S. 2016. “Vychislitelnaya tehnologiya dlya opredeleniya funktsii mezhfaznogo vzaimodeystviya na osnove modelirovaniya techeniya v kapillyarnom klastere” [Computer Technology for Determination of Interphase Interaction Function Based on Flow Simulation in Capillary Cluster]. Tyumen State University Herald. Physical and Mathematical Modeling. Oil, Gas, Energy, vol. 2, no 1, pp. 63–71. DOI: 10.21684/2411-7978-2016-2-1-63-71
  20. Succi S. 2001. The Lattice Boltzmann Equation for Fluid Dynamics and Beyond. Oxford University Press.
  21. Zagalskaya Y. G., Litvinskaya G. P., Egorov-Tismenko Y. K. 1986. Geometricheskaya kristallografiya [Geometrical crystallography]. Moscow: MGU.
  22. Zhizhimontov I. N., Malshakov A. V. 2016. “Metod rascheta koefficientov poristosti i pronicaemosti gornoy porody na osnove krivyh kapillyarnogo davleniya” [The Method of Determining the Coefficients of Porosity and Permeability of the Rock on the Basis of Capillary Pressure Curves]. Tyumen State University Herald. Physical and Mathematical Modeling. Oil, Gas, Energy, vol. 2, no 1, pp. 72–81. DOI: 10.21684/2411-7978-2016-2-1-72-81
  23. Zhuravlev A. S., Zhuravlev E. S. 2016. “Vliyanie neodnorodnostey filtracionno-emkostnyh parametrov na processy migracii i akkumulyacii uglevodorodov v estestvennyh geologicheskih sistemah” [The Heterogeneity Effect of Reservoir Properties on Migration and Accumulation of Hydrocarbons in Natural Geological Systems]. Tyumen State University Herald. Physical and Mathematical Modeling. Oil, Gas, Energy, vol. 2, no 1, pp. 101–109. DOI: 10.21684/2411-7978-2016-2-1-101-109