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Mathematical model for mineral reserves evaluation

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Category: Geology

Last Updated on 29 July 2014

Published on 17 October 2013

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Authors:

M.G. Lustiuk, Dr. Sci. (Tech.), Professor, Private Higher Educational Institution “European University”, Rivne, Ukraine

V.M. Diakon, Cand. Sci. (Phys.-Math.), Associate Professor, Private Higher Educational Institution “European University”, Rivne, Ukraine

M.L. Petrina, Private Higher Educational Institution “European University”, Senior Instructor of the Department of Mathematical Sciences and Information Systems, Rivne, Ukraine

A.A. Rachkovska Private Higher Educational Institution “European University”, Lecturer of the Department of Mathematical Sciences and Information Systems, Rivne, Ukraine

Abstract:

Purpose. To develop the model and computation algorithm for evaluation of reserves of amber using orthogonal grid schemes of deposits.

Methodology. We have applied the methods of mathematical statistics and modeling. The choice of the weight function that provides minimal variance of the mean estimator is a complex mathematical problem.

Findings. The problem of estimation of the reserves of the mineral dispersed within a deposit of rectangular form with staggered wells has been formulated and solved. The algorithm of conformal mapping has been developed.

Originality. To estimate the amber reserves we have applied one of the mathematical modeling methods, namely the finite difference method and numerical conformal mapping. This is related to the problem of numerical conformal mapping of a simply connected plane polygon into the parametric rectangle.

Practical value. The method of constructing grids using numerical conformal mappings can be applied to the reserves evaluation problems in case of mineral deposits of curvilinear form, which often occur in practice. 

References:

1. Власюк А.П. Основи сучасного візуально-подвій ного програмування. Програмування в середовищі Delphi / Власюк А.П., Прищепа О.В. – Рівне: НУВГП, 2008. – 496 с.

Vlasiuk, A.P. and Pryshchepa, O.V. (2008), Osnovy suchasnoho vizualnopodviinoho prohramuvannia. Prohramuvannia v seredovyshchi Delphi [Fundamentals of Modern Visual Doble Programming. Programming in Delphi], NUVGP, Rivne, Ukraine.

2. Власюк А.П. Математичне і комп’ютерне моделювання оцінки запасів сипучих корисних копалин та процесу їх видобутку / А.П. Власюк, М.Г. Лустюк // Abstracts of International Conference “Problems of decision making under uncertainties” (PDMU-2005), Berdyansk. – 2005. – С. 107–109.

Vlasiuk, A.P. and Lustiuk, M.G. (2005), “Mathematical and computer modeling evaluation of bulk minerals and process their output”, Abstracts of International Conference “Problems of decision making under uncertainties” (PDMU-2005), Berdyansk, Ukraine.

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