Scientific seminar “Modeling of a propagation of fractions loaded with viscous fluid pressure”

8 June 12:00 MSK

To describe the initial stage of hydraulic fracturing, a three-dimensional model of curvilinear crack propagation is proposed, describing the main processes: fluid movement in the crack, deformation and destruction of the rock. The simulation is based on the numerical solution of two-dimensional equations of fluid motion in a narrow channel (lubrication equations) and three-dimensional elastic equilibrium equations, for which the methods of finite and boundary elements are applied, respectively. The complexity of the numerical solution of the equations is due to the change in the areas in which they are applicable, with the growth of the crack and the strong influence of the problems on each other. The position of the boundaries of the regions is determined based on the Stefan condition and a new implicit criterion for choosing the direction of propagation. To obtain a joint solution, a set of methods for solving systems of nonlinear equations based on modifications of the relaxation and Newton methods is proposed and implemented.

A hierarchy of models of cracks propagating under the influence of fluid pressure is created, in which each of the processes occurring can be described using a number of simplifying approximations, which allows you to choose the level of detail of the description and the amount of computing resources required. Based on the models implemented in the form of a software package that are included in the hierarchy, a number of problems on the propagation of cracks are solved.

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