Kara I. Numerical realization of the Boundary Integral Equations Method for analysis of wave processes in fluid-saturated porous media

Using as the basis the boundary integral equations method the new algorithm for analyzing of the vibrations and the stress-strain state of the porous fluid-saturated media with account of the time-changed dynamic force is developed. Peculiarities of numerical research of the elastic porous fluid-saturated media on the bases of the analytical literature review in the field of investigation are presented. The basis for modeling of the established harmonic vibrations processes of the poroelastic bodies are used Biot’s interrelations for the two-phased saturated media where the porous solid’s elements are belong to the first phase and the fluid’s elements – to the second phase. The primary interrelations, the boundary integral equations of the poroelastic theory and the fundamental solutions matrix are presented. The interrelations of the fundamental solutions generalized derivative for the three-dimensional harmonic poroelastisity are obtained. The formulas for the singular parts of the circular integrals calculation which comprised to the fundamental solutions using the expansion in a Maclaurin series are derived. The algorithm for the displacements and stresses calculation of the porous structures elements under the dynamic force is developed; the checking of the correctness and credibility of the received technique during the test problems solving is done. The software realization and approbation of the developed algorithm with the applied example were provided. The new results of the calculation of the dynamic stress-strain state of the underground reservoirs for the hydrocarbon storage warning elements after the burst in one of the reservoir were obtained; the influence of the porosity and the fluid filler to the quantities of the reservoirs boundary dots stress-strain state parameters was established.