Mathematical modeling of pyroxene-magnetite crystalline shales elastic and acoustic properties
Keywords:mathematical modeling, anisotropy, acoustic, elastic properties, crystalline shales, magnetite, quartz, pyroxene
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.
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