A probabilistic and statistical model of rock deformation

Abstract

A new approach to the study of strength characteristics of the rocks on the basis of probabilistic and statistical models of the deformation processes (models of dilatancy initiation processes) under conditions of uncertainty is presented. The main purpose of the study is to create geological and mathematical tools, which could be used to study the development of volumetric deformation (dilatancy, disintegration) of reservoirs at a constant tension, acting on the array. The information and analytical basis of the performed study consists of methods of mathematical statistics and probability theory and the sedimentary rocks research methods. The probabilistic-statistical approach is formed in the study of deformation processes of the productive stratum structure, taking into account the degree of heterogeneity of the reservoirs. The obtained analytical expressions allow us to determine the moment of the beginning of the volumetric deformation process (dilatancy, disintegration) in the rock, similar to the identification of the bifurcation point in the development of geological and dynamic systems