Abstract
Rock texture and structure play an important role in the formation of the rock physical properties, and also carry information about their genesis. The paper deals with the simulation of geometric shapes of various structures and textures of rocks by the finite-element method (FEM). It is carried out by programmed detailing of the element properties and their spatial location in the simulated object. When programming structures, it is also possible to set the physical properties of various parts of the model, grids, initial and boundary conditions, which can be changed in accordance with the scenarios for numerical experiments. In this study, on the basis of FEM, simulation of various structures and textures of rocks with inclusions and disruptions was implemented in COMSOL Multiphysics in conjunction with Matlab. Such structures are used to conduct computer generated simulations to determine physical properties of geomaterials and study the effect on them of agents of various physical nature. The building of several models was considered: a rock specimen with inclusions in the form of ellipses of equal dimensions with different orientations; a sandstone specimen containing inclusions with high modulus of elasticity in cement matrix when deforming; a limestone specimen with fractures filled with oil and saline water when determining its specific electrical resistance. As an example of a fractured structure analysis, the influence of the filler on the electrical resistance of the limestone specimen containing a system of thin elliptical predominantly horizontal fractures was considered. The change in the lines of current flow at different ratios between the matrix and the fracture filler conductivities and their effect on the effective (averaged) conductivity of the rock specimen was clearly demonstrated. The lower conductivity of the fracture filler leads to increasing the length and decreasing the cross-section of the current flow lines that, in turn, leads to significant decrease in the conductivity of the fractured rock specimen. The higher filler conductivity results in a slight increase in the conductivity of the fractured specimen compared to that of the homogeneous isotropic specimen. The resulting structures can be used for numerical experiments to study physical properties of rocks.
Highlights
Аннотация Текстура и структура горных пород играют существенную роль в формировании их физических свойств, а также несут информацию о генезисе
It is possible to set the physical properties of various parts of the model, grids, initial and boundary conditions, which can be changed in accordance with the scenarios for numerical experiments
On the basis of finite-element method (FEM), simulation of various structures and textures of rocks with inclusions and disruptions was implemented in COMSOL Multiphysics in conjunction with Matlab
Summary
Приведенный код соответствует построению структуры в пространстве 2D, аналогично могут быть осуществлены построения и в пространстве 3D. Демонстрационный пример Результат построения структуры в соответствии с приведенным выше кодом представлен на рис. 1. В данном случае случайным образом задавались наклоны эллипсов, а их размеры и положение не менялись. Границ изменения их размеров, угла наклона, положения, можно получать структуры, соответствующие различным типам горных пород. Полученные структуры могут быть использованы для проведения численных экспериментов по исследованию физических свойств пород. Построение структуры образца песчаника и моделирование его испытания при одноосном сжатии. Рассмотрим моделирование образца песчаника размером 32×32×64 мм в виде прямоугольной призмы с квадратным основанием. Полуоси зерен имеют размеры: большая от 1.8 до 2.9 мм и меньшая от 1.3 до 2.1 мм. Углы ориентации главной оси эллипсов ±90о от горизонтального направления. Модуль упругости E и коэффициент Пуассона ν, приведены в табл. 1
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