Modeling of acoustic logging in poroelastic media using spectral element methodстатья
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Дата последнего поиска статьи во внешних источниках: 4 июня 2021 г.
Аннотация:The paper discusses an application of the isoparametric spectral element method (SEM) for the numerical
solving of problems of full-wave modeling in heterogeneous regions of complex curvilinear shape with sharply changing
material parameters (including discontinuous). In particular a problem of the wave propagation in a borehole surrounded
by a poroelastic fluid saturated medium is considered. The mathematical model is described by non-stationary Biot’s
system of partial differential equations. Different types of boundary conditions between borehole fluid and porous solid
are presented. Special consideration is devoted to the numerical calculation of the convolution integral describing a
friction force between saturating fluid and a skeleton. An iterative procedure based on the Prony series is suggested. High
order isoparametric spectral element was used both to discretize a computational domain’s curvilinear geometry
(containing circular shape borehole) and model’s equations posed on it. Results of numerical solving an acoustic logging
problem in a poroelastic medium are presented. A difference between high and low-frequency approximations of the
friction force as well as an influence of different types of boundary conditions are analyzed.