Mathematical modeling of pyroxene-magnetite crystalline shales elastic and acoustic properties

Authors

  • I. Bezrodna Taras Shevchenko National University of Kyiv, Institute of Geology, Ukraine
  • D. Bezrodny Taras Shevchenko National University of Kyiv, Institute of Geology, Ukraine
  • V. Svystov Taras Shevchenko National University of Kyiv, Institute of Geology, Ukraine

DOI:

https://doi.org/10.24028/gzh.v43i5.244082

Keywords:

mathematical modeling, anisotropy, acoustic, elastic properties, crystalline shales, magnetite, quartz, pyroxene

Abstract

The analysis of the results of mathematical modeling of the influence of the format, mineral concentration and fracture of metamorphic crystalline shales of the Pishcha iron ore structure is presented.

The aim of this work is to analyze the influence of mineral composition, types, orientation and concentration of mineral inclusions and microcracks on the acoustic and elastic properties of a group of samples of “quartz-magnetite-pyroxene” crystalline shales of Pishchans’ka iron ore structure.

Based on the method of conditional moments, mathematical modeling of the influence of the format, orientation and content of mineral grains, as well as the concentration and format of cracking on the acoustic and elastic properties of rocks of the Pishchans`ka iron ore structure was performed. According to the obtained data, a weak effect of changes in the content of rock-forming minerals and a significant effect of different types of fractures on the value of elastic and acoustic anisotropy (10-40%) was proved.

Elastic constants of models with layered and chaotic orientation of structural-textural elements are calculated. It is established that most models, as well as basic samples have a rhombic type of acoustic symmetry. When comparing the stereoprojections of the anisotropy parameters of real samples with the stereoprojections obtained during modeling, the authors found that in most samples there is a double system of cracking: chaotic and directed in the area of shale.

The results of mathematical modeling showed that for models with ordered crack orientation, the change in the format and concentration of voids is a defining characteristic. This effect is significantly smaller for models with a chaotic arrangement of structural elements.

It is proved that models with a combined (layered and chaotically oriented) type of fracture are the closest to real samples. The authors show that this technique allows you to create and operate models close to the real geological environment.

References

Aleksandrov, K. S., Prodayvoda, G. T. (2000). Anisotropy of elastic properties of minerals and rocks. Novosibirsk: Publishing house of the SB RAS, 354 p. (in Russian).

Aleksandrov, P. N., & Krizsky, V. N. (2018). Mathematical modeling of effective elastic parameters. Vestnik YUUrGU. Seriya «Matematicheskoye modelirovaniye i programirovaniye», 11(2), 5—13. https://doi.org/10.14529/ mmp180201.

Bayuk, I. O., Postnikov, O. V., Ryzhkov, V. I., & Ivanov, I. S. (2012). Modelling anisotropic effective elastic properties of carbonate reservoir rocks of a complex structure. Tekhnologii seysmorazvedki, (3), 42—55 (in Russian).

Bezrodna, I., Bezrodnyi, D., & Holiaka, R. (2016). Mathematical modeling of influence of the mineral composition and porosity on elastic anisotropic parameters of complex sedimentary rocks of Volyn-Podillya area. Visnyk Kyyivskoho natsionalnoho universytetu imeni Tarasa Shevchenka. Heolohiya, (2), 27—32 (in Ukrainian).

Bezrodnaya, I. N., Bezrodny, D. A., & Kozionova, O. A. (2019). Mathematical modeling of acoustic and elastic anisotropy of shale reservoir rocks of the Dnieper-Donetsk depression. Visnyk Kharkivskoho natsionalnoho universytetu imeni V. N. Karazina. Seriya: Heolohiya. Heohrafiya. Ekolohiya, (50), 42—53. https://doi.org/ 10.26565/2410-7360-2019-50-03 (in Russian).

Bezrodnaya, I. N., Bezrodny, D. A., & Prodayvoda, G. T. (2018). Mathematical modeling of elastic anisotropy of reservoir rocks. Lambert Academic Publishing, 193 p. (in Russian).

Bezrodny, D. A. (2008). Elastic anisotropy of metamorphic rocks of Kryvbas and its use for solving problems of tectonofacial analysis. Doctor¢s thesis. Kyiv, 250 p. (in Ukrainian).

Prodayvoda, G. T., Vyzhva, S. A., Bezrodny, D. A., & Bezrodna, I. M. (2011). Acoustic texture analysis of tectonofacies of metamorphic rocks of Kryvyi Rih. Kyiv: Kyiv University Publishing and Printing Center, 368 p. (in Ukrainian).

Khoroshun, L. P. (1972). Elastic properties of materials reinforced with unidirectional short fibers. Prikladnaya matematika, VIII(12), 86—92 (in Russian).

Khoroshun, L.P. (2017). Effective elastic properties of granular stochastic composite materials with defects at the interface between the com¬ponents. Prikladnaya matematika, 3(5), 108¬—121 (in Russian).

Bezrodnyi, D., Svystov, V., & Bezrodna, I., (2019). Comparative analysis of results of an acoustic anisotropy invesigations of rock samples of Pishchans`ka iron-ore structure. Conference Proceedings, Monitoring 2019, Nov. 2019 (Vol. 2019, pp. 15). https://doi.org/10.3997/2214-4609.201903207.

Boerset, K., Berland, H., Nordahl, K., & Rustad, A. (2009). Multiscale Modelling of Elastic Parameters. Amsterdam: European Association of Geoscientists & Engineers. doi:doi.org/10.3997/2214-4609.201400553.

Hashin, Z., & Shtrikman, S. (1962). On some variational principles in anisotropic and non homogeneous elasticity. Journal of the Mechanics and Physics of Solids, 10(4), 335—342. https://doi.org/10.1016/0022-5096(62)90004-2.

Hashin, Z., & Shtrikman, S. (1963). A variational approach to the theory of the elastic behavior of multiphase materials. Journal of the Mechanics and Physics of Solids, 11(2), 127—140. https://doi.org/10.1016/0022-5096(63)90060-7.

Hill, R. (1965). A self-consistent mechanics of composite materials. Journal of the Mechanics and Physics of Solids, 13(4), 213—222. https://doi.org/10.1016/0022-5096(65)90010-4.

O’Connell, R., & Budiansky, B. (1974). Seismic velocities in dry and saturated cracked solids. Journal of Geophysical Research, 79(35), 5412—5426. https://doi.org/10.1029/JB079i035p05412.

Reuss, A. (1929). Berechnung Der Fließgrenze Von Mischkristallen auf Grundder Plastizität Bedingung für Einkristalle. Journal of Applied Mathematics and Mechanics, 9(1), 49—58. https://doi.org/10.1002/zamm. 19290090104.

Voight, W. (1928). Lehrbuch der Kristallphysik (mit Ausschluss der Kristalloptik). Berlin: Berlin Teubern.

Walpole, L. (2001). An elastic singularity in a bounded region: volume change and related effects. Journal of the Mechanics and Physics of Solids, 49(3), 551—569. https://doi.org/10.1016/S0022-5096(00)00044-2.

Walpole, L. (1969). On the overall elastic moduli of composite materials. Journal of the Mechanics and Physics of Solids, 17(4), 235—251. https://doi.org/10.1016/0022-5096(69)90014-3.

Published

2021-11-24

How to Cite

Bezrodna, I. ., Bezrodny, D. ., & Svystov, V. . (2021). Mathematical modeling of pyroxene-magnetite crystalline shales elastic and acoustic properties. Geofizicheskiy Zhurnal, 43(5), 208–218. https://doi.org/10.24028/gzh.v43i5.244082

Issue

Section

Articles