Abstract

The paper discusses the use of finite element method for modeling the effective properties of rocks on the scale of core sample - a rock sample, extracted from the depths of the Earth using a special type of drilling. Estimation of the effective properties of the core sample is important for geomechanical modeling on a wellbore or a reservoir scale: the resulting effective properties are input data for such calculations. The estimation of core sample properties is performed numerically on the digital (voxel) model of the core sample, which is built using a CT-scan. After that, with the help of a specially developed software module on the voxel model a structured hexahedral mesh is built (each element of which corresponds to one voxel.). Effective properties are estimated at the representative volume element (RVE) of the core. The RVE is a fragment of the voxel model of the core sample, having a sufficiently large size so that its properties extend to the properties of the core in general. On a RVE in the form of a rectangular parallelepiped, six boundary problems of the theory of elasticity with various boundary conditions are solved, corresponding to three uniaxial tensions of the volume (along each of the coordinate axes) and three shifts (in each of the coordinate planes). The results of solving each boundary value problem are averaged over the volume, which gives effective (average) stress tensors. Since the core is at a great depth, it is subjected to considerable stress. Therefore, its mechanical properties under the ground and after extracting to the surface can be quite different. In this regard, the numerical modeling of the effective properties of the core sample must be carried out taking into account pre-loading. Preloading (as a pore pressure) is applied to a model for solving the above six elastic boundary problems. In addition, the seventh problem of the theory of elasticity is solved, in which the boundary of the core is tightly fixed, and the pore pressure is still applied. The results of solving the seventh problem solving are also averaged over the volume. All seven problems are solved taking into account geometric nonlinearity. As the effective stress tensors are calculated for the first six problems, an effective tensor is computed for the seventh problem. Then the effective elastic properties of the core sample are calculated as the dependence of the differences on the effective strain tensor. Calculations are performed using the finite element method with the help of a software module Fidesys Composite of CAE Fidesys. An effect of pore pressure on effective elastic modules of core sample is analyzed. The calculations are carried out for two types of cores: a sandstone (consisting of one mineral, porosity is 21%) and a limestone (consisting of three minerals, porosity 3%). It is shown that even with small porosity, the pore pressure significantly affects the effective elastic properties of the core sample. The dependence of effective properties on pore pressure is practically linear (the report shows the graphs of this dependence for both types of cores.). Thus, an importance of considering initial pre-loading of a core sample for its effective properties estimation is demonstrated. This work is supported by the Russian Science Foundation under grant 19-71-10008.