ИСТИНА

The presentation will provide an overview of the problems of mathematical modeling of geomechanical processes occurring in rocks during the exploration and development of reservoirs [3, 4, 16]. These problems were solved using CAE Fidesys software [8, 11, 24], which allows solving static and dynamic problems of geomechanics and geophysics using finite (FEM) and spectral (SEM) element methods [9, 10, 23] of a variable approximation order in space at non-conformal unstructured meshes [17-21]. The mathematical formulation is based on the theory of repeated superposition of large deformations [13-15]. A numerical discretization of the posed boundary problems of interacting solids [12, 22, 23] is performed using a discontinuous spectral element method and multi-point contstraints [1, 2, 5-7] at non-matching mesh interfaces between interacting solid rock structures. Several industrial applications of the developed approach are considered. Seismic wave propagation in the heterogeneous media with initial geomechanical stresses is considered. A modelling of an induced anisotropy is performed by the superposition of dynamic deformations onto initial generally finite strains. Use of variable order spectral elements at non-conformal meshes allows one to simplify the process of unstructured mesh generation for the discretization of complex geological models and to set the local spatial order of the SEM discretization depending on the speed of seismic waves in geological structures, which significantly reduces the computational costs when conducting numerical modeling and lowers the requirements to the model preprocessing and mesh quality. Geomechanical simulation of the multistep drilling of the wellbore taking into account a historydependence of the strains due to the sequential origination of stress concentrators as well as mechanical properties change is presented. Using SEM, we simulated stresses and strains of the nearwell bore poroelastoplastic zone taking into account the dynamic change in the porepressure field of the saturating fluid. Assessment of deformation of the wellbore depending on the pressure of the drilling fluid inside it expands the possibilities of applying geomechanical modeling and allows one to clarify recommendations for the drilling parameters. The effect of the development of the plastic region is the cause of the non-uniform and, in real conditions, non-linear distribution of the mechanical and filtration-capacitive properties of the rock. Physical processes resulting from this effect, in turn, affect well productivity. A geomechanical model of the near-wellbore zone, built for a specific task, can reduce risks during drilling and trajectory, assess potentially promising areas for drilling and stimulation, and solve the problems of wellbore stability. The considered approach allows predicting in more detail the behavior of the rock during reservoir development, taking into account different stages of the field deformations. In particular, the redistribution of accumulated deformations during multistep loading and / or changes in the structure (topology) of the loaded body, as well as contact conditions of adhesion / sliding at the interlayer boundaries and bonded contacts are taken into account. The reported study was partially funded by Russian Science Foundation project № 19-77-10062 and by RFBR and Moscow city Government according to the research project № 19-38-70001.