Mathematical simulation of minerals with polynomial interlination on the system deviated wells

Authors

Keywords:

mathematical model, interlineation, cores, inclined boreholes, polynomial interpolation

Abstract

This paper provides an overview of the new minerals distribution mathematical models construction 3D methods by 3 variables functions interlineation methods on a system of inclined boreholes. The problem of constructing minerals distribution spatial mathematical models for the case when the information about minerals distribution function f(x, y, z) is specified in the M inclined boreholes is considered. Methods of three-dimensional mathematical model construction with the use of functions interlineation on an inclined boreholes system, which are based on the use of limited fractionally rational auxiliary functions, are given. The method of minerals distribution modeling with the help of polynomial interlineants on inclined boreholes system placed both in the same plane and in an arbitrary manner is proposed. Experimental data are mineral resources distribution at every point of the boreholes system. The given mathematical model allows calculating an unknown mineral resources distribution between the boreholes.

Author Biographies

О. О. Литвин, Ukrainian Engineering and Pedagogical Academy

Candidate of Physical and Mathematical Sciences

Н. І. Штепа, Ukrainian Engineering and Pedagogical Academy

Candidate of Physical and Mathematical Sciences

C. І. Кулик, National Technical University "Kharkiv Polytechnic Institute"

Candidate of Physical and Mathematical Sciences

References

Isachenko C. H. Directional boreholes / C. H. Isachenko. – M: Nedra, 1987. (in Russian). 2. Lytvyn O. M. Mathematical modeling distribution of mineral resources with the help of interlineation functions of three variables / O. M. Lytvyn, N. I. Shtepa // Appr. Of the NAS of Ukraine. – 2009. – № 1. – P. 25–29. (in Ukraine). 3. Lytvyn O. M. Method evaluation of mineral resources on the basis of the analysis of the results of borehole drilling and generalized interlineation functions of 3 variables / O. M. Lytvyn, N. I. Shtepa // Collection of abstracts XLII scientific-practical conference UPA-December 15, 2008 Part Harku. – 2008. – P. 84. (in Ukraine). 4. Lytvyn O. M. On the mathematical modelling of the structure of Earth's crust using interlineation functions of three variables / O. M. Lytvyn, N. I. Shtepa // Proceedings of IV international school-seminar "Decision Theory". Uzhgorod: Uzh NU. 29 September – 4 October. 2008. – P. 105. (in Ukraine). 5. Lytvyn O. M. Mathematical modeling distribution of minerals resources with the help of interlineation functions of three variables / O. M. Lytvyn, N. I. Shtepa / Proceedings of the international Symposium problems of optimization of calculations (VET-XXXV): Crimea, PGT. Katsiveli, 24–29 September 2009. T.2; Kiev. – 2009. – P. 20–24. (in Ukraine). 6. Kalinin A., Drilling of inclined boreholes: Directory / A. Kalinin, N. A. Grigoryan, B. H. Sultanov // Ed. by A. G. Kalinina. – M: Nedra, 1990. – P. 348 (in Russian). 7. Lytvyn O. N. Interlineation functions: Teaching material / O. N. Lytvyn. – Kyiv: UMK VO, 1988. – 31 p. (in Russian). 8. Lytvyn O. M. Mathematical modeling distribution of mineral resources be interlineation and interflatation functions / O. O. Lytvyn, N. І. Shtepa. – Kyiv:Naukova dumka. 2011. – 211 p. (in Ukraine). 9. Lytvyn O. M. Interlineation functions and some of its applications / O. M. Lytvyn. – Kharkiv: Osnova, 2002. – 544 p. (in Ukraine). 10. Lytvyn O. M. Methods of calculations. Additional sections / O. M. Lytvyn. – Kyiv: Nauk. Dumka, 2005. – 331 p. (in Ukraine).

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Published

2014-09-11

Issue

Vol. 17 No. 2 (2014)

Section

Applied mathematics

License

Copyright (c) 2015 О. О. Литвин, Н. І. Штепа, C. І. Кулик, О. С. Чорна

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