Аннотация:It is widely known that the determination of technological parameters, for which the wellbore
maintains its stability, and risk assessment during drilling are one of the most important
problems in geomechanics of hydrocarbon fields. When drilling, in general, a bit and mud
generates a pressure on the rock, thereby deforming it and redistributing the stresses
(superposition of generally finite strains), causing the reaction of the rock on the applied
impact. This may lead to the formation and development of localized zones of plastic shear
bands. Different rock’s properties and their evolution during deformation should be taken into
account to correctly simulate this process. In addition, the rock is usually prestressed, which is
defined by the components of the generally anisotropic initial stress tensor. Real rocks are
characterized by the presence of pores and a fluid that saturates them and the possibility of
nonlinear inelastic deformation with the accumulation of plastic deformations and their
localizations leading to the corresponding variations of dynamic porosity and permeability.
The paper presents mathematical models and numerical algorithms that can be used to solve
the problems of a wellbore stability in a poroelastoplastic formulation under small and finite
strains. A generalization of the classical Biot’s model to the poroelastoplastic medium is
considered in order to simulate a shear banding phenomena taking place around the borehole
drilled in the prestressed solid leading to the change in the pore pressure in the surrounding
rock as well as a redistribution of stresses and accumulated plastic strains. An isoparametric
spectral element method is applied to discretize a geometric model and equations in space on
curvilinear unstructured meshes of high order, which allows to precisely describe a curvilinear
shape of the borehole on a relatively coarse mesh. CUDA technology is used to parallelize the
implemented algorithm on the massively parallel graphics-processing unit. Several model
examples of the borehole stability problem are presented and numerical results are analyzed.
The research for this article was performed in Schmidt Institute of Physics of the Earth of the Russian
Academy of Sciences and was financially supported by Russian Science Foundation (project No. 19-
77-10062) in the part related to the development of mathematical models and numerical modeling and
was performed in Lomonosov Moscow State University and was supported by the grant of the President
of the Russian Federation for young scientists - doctors of sciences MD-208.2021.1.1 in the part related
to the development of numerical algorithms for problem solving and their parallel implementation on
massively parallel high performance computing systems.