Algorithm of Mathematical Modeling of Layered Block Medium with Combined Hierarchical Inclusions for Acoustic Monitoring, Taking into Account Convective Mixing in Fluid-Saturated Inclusions

International Journal of Geoinformatics and Geological Science

© 2019 by SSRG - IJGGS Journal

Volume 6 Issue 1

Year of Publication : 2019

Authors : Olga Hachay, Yurie Khachay, Andrey Khachay

10.14445/23939206/IJGGS-V6I1P105

How to Cite?

Olga Hachay, Yurie Khachay, Andrey Khachay, "Algorithm of Mathematical Modeling of Layered Block Medium with Combined Hierarchical Inclusions for Acoustic Monitoring, Taking into Account Convective Mixing in Fluid-Saturated Inclusions," SSRG International Journal of Geoinformatics and Geological Science, vol. 6,  no. 1, pp. 21-27, 2019. Crossref, https://doi.org/10.14445/23939206/IJGGS-V6I1P105

Abstract:

Background: A new method of modeling acoustic monitoring of a layered-block elastic medium with several inclusions of various physical-mechanical and phase hierarchical structures has been developed. Methods: An iterative process of solving a direct problem for the case of three hierarchical inclusions of l, m, s ranks based on the use of 2D-integro differential equations has been developed. Results: The degree of hierarchy of inclusions is determined by the values of their ranks, which may be different. Hierarchical inclusions are located in different layers one above the other: the upper anomalously stressed, the second-fluid-saturated and the third anomalously dense. The degree of filling with inclusions of each rank is different for all three hierarchical inclusions. At the same time, the question of dynamic processes in fluid-saturated hierarchical inclusions related to convective mixing of a single-component fluid is investigated. Conclusions: The simulation results can be used when conducting monitoring studies of fluid return control of oil fields. The results can help explain the excessive water flooding of oil reservoirs.

Keywords:

hierarchical environment, acoustic field, iterative algorithm integral-differential equations, direct problem, free convection effects, oscillatory perturbations in a fluid-saturated inclusion.

References:

[1] I. Prangishvilli, F.Paschenko, B. Busigin, System laws and regularities in electrodynamics, nature and society, Nauka, Publ.: Moscow, Russia, 2001.
[2] G.Kocharjan, A.Spivak, Dynamics of deformation of block massive, IKZ “Akademkniga”: Moscow, Russia, 2003.
[3] M.Khasanov, G.Bulgakova, Nonlinear and noneqiulibrium effects in rheological complex environments, Institute of computer research: Moscow, Izhevsk, Russia, 2003.
[4] O.A.Khachay, A.Y. Khachay, On the integration of seismic and electromagnetic active methods for mapping and monitoring the state of two-dimensional heterogeneities in an N-layer medium, Vestnik SSSU. Series «Computer technologies, management, radio electronics », 2011, No.2 (219).
[5] O.A.Khachay, A.Y.Khachay, Modeling of electromagnetic and seismic fields in hierarchically heterogeneous media. Vestnik of SSSU, series "Computational mathematics and informatics", 2013, V.2, No.2.
[6] O.A.Khachay, A.Y. Khachay, Reflection of noneqiulibrium two-phase filtration processes in oil saturated hierarchical
media in active wave geophysical monitoring data, Mining information and analytical bulletin, 2014, No.4.
[7] O.A. Khachay, O.Y. Khachay, A.Y. Khachay, Integration of acoustic, gravitational, and geomechanical fields in hierarchical environments, Mining information and analytical bulletin, 2017, No.4.
[8] A.Y. Khachay, Algorithm for solving the direct dynamic seismic problem when excited by a horizontal point force located in an arbitrary layer of an n-layer elastic isotropic medium. In Informatics and mathematical modeling. USSU: Ekaterinburg, Russia, 2006.
[9] A.Y. Khachay, Algorithm for solving the direct dynamic seismic problem when excited by a vertical point force located in an arbitrary layer of an n-layer elastic isotropic medium. In Informatics and mathematical modeling. USSU: Ekaterinburg, Russia, 2006.
[10] G. Gershuni, E. Zhukhovitskiy, Convective stability of incompressible fluid, Nauka, Main editors of Phys. and Math. Literature: Moscow, Russia, 1972.
[11] V.V. Dryagin, The use of caused acoustic emission collectors for the detection and extraction of hydrocarbons. Georesources, 2018, V.20, No.3, Part2. DOI: https://doi.org./10/18599/grs.2018.3.134-140.
[12] Y. Khachay, M. Mindubaev, Effect of convective transport in porous media on the conductions of organic matter maturation and generation of hydrocarbons in trap rocks complexes. Energy Procedia, 2016, No. 74.