Mexican Oil Institute

Mexico City, Mexico

Mexican Oil Institute

Mexico City, Mexico
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Kanaun S.,Mexican Oil Institute | Markov A.,Monterrey Institute of Technology
AIP Conference Proceedings | Year: 2017

An efficient numerical method for solution of static problems of elasticity for an infinite homogeneous medium containing inhomogeneities (cracks and inclusions) is developed. Finite number of heterogeneous inclusions and planar parallel cracks of arbitrary shapes is considered. The problem is reduced to a system of surface integral equations for crack opening vectors and volume integral equations for stress tensors inside the inclusions. For the numerical solution of these equations, a class of Gaussian approximating functions is used. The method based on these functions is mesh free. For such functions, the elements of the matrix of the discretized system are combinations of explicit analytical functions and five standard 1D-integrals that can be tabulated. Thus, the numerical integration is excluded from the construction of the matrix of the discretized problem. For regular node grids, the matrix of the discretized system has Toeplitz's properties, and Fast Fourier Transform technique can be used for calculation matrix-vector products of such matrices. © 2017 Author(s).


Kanaun S.,Mexican Oil Institute | Markov A.,Monterrey Institute of Technology
International Journal of Engineering Science | Year: 2014

An efficient numerical method for the 3D-problem of elasticity for a solid with multiple interacting cracks is developed. The problem is reduced to a system of 2D-integral equations for the crack opening vectors. Discretization of these equations is performed by Gaussian approximation functions centered at a set of nodes uniformly distributed on the crack surfaces; the procedure results in five standard 1D-integrals that can be tabulated. For planar cracks of arbitrary shapes, these integrals are calculated in closed analytical forms. The method is mesh free. Examples of various interacting, as well as intersecting, cracks are considered and compared with the solutions available in literature. © 2013 Elsevier Ltd. All rights reserved.


Kanaun S.,Technological Institute of Higher Education of Monterrey | Levin V.,Mexican Oil Institute
Solid Mechanics and its Applications | Year: 2013

The work is devoted to the effective field method and its application in the theory of heterogenous materials. For many years, various versions of the method have been used for the calculation of effective physical and mechanical properties of composite materials (the homogenization problem). In the historical survey, the most important steps of the development of the method are indicated starting from nineteenth century. The main attention is focused on the combination of the effective field and numerical methods that yields efficient numerical algorithms for the calculation of effective properties and detailed fields in periodic and random composite materials. Examples of the application of the method to prediction of conductive, elastic, and elasto-plastic properties of composites are presented. © Springer Science+Business Media Dordrecht 2013.


Kanaun S.,Mexican Oil Institute | Markov A.,Technological Institute of Higher Education of Monterrey | Babaii S.,Technological Institute of Higher Education of Monterrey
International Journal of Fracture | Year: 2013

The second boundary value problem of elasticity for 3D-bodies containing cracks is considered. Presentation of the solution in the form of the double layer potential reduces the problem to a system of 2D-integral equations which kernels are similar for the body boundary and crack surfaces. For discretization of these equations, Caussian approximation functions centered at a set of nodes homogeneously distributed on the body and crack surfaces are used. For such functions, calculation of the elements of the matrix of the discretized problem is reduced to five standard 1D-integrals that can be tabulated. For planar cracks, these integrals are calculated in closed analytical forms. The method is mesh free, and for its performing, only node coordinates and surface orientations at the nodes should be defined. Calculation of stress intensity factors at the crack edges in the framework of the method is discussed. Examples of an elliptical crack, a lens-shaped crack, and a spherical body subjected to concentrated and distributed surface forces are considered. Numerical results are compared with the solutions of other authors presented in the literature. Convergence of the method with respect to the node grid steps is analyzed. An efficient algorithm of the node grid generation is proposed. © 2013 Springer Science+Business Media Dordrecht.


Markov M.,Mexican Oil Institute | Markova I.,Mexican Oil Institute | Jarillo G.R.,Mexican Oil Institute
Geophysical Prospecting | Year: 2015

In the present work, the waveforms of reflected wave sonic log for open and cased boreholes are calculated. Calculations are performed for a borehole containing an acoustic multipole source (monopole, dipole, or quadrupole). A reflected wave is more efficiently excited at resonant frequencies. These frequencies for all source types are close to the frequencies of oscillations of a fluid column located in an absolutely rigid hollow cylinder. It is shown that the acoustic reverberation is controlled by the acoustic impedance of the rock Z = Vp ρs for fixed parameters of the borehole fluid, where Vp is the compressional wave velocity in the rock, and ρs is the rock density. This result is correct for all types of acoustic sources (monopole, dipole, or quadrupole). Methods of the waveform processing for determining parameters characterizing the reflected wave are discussed. © 2014 European Association of Geoscientists & Engineers.


Markova I.,Mexican Oil Institute | Ronquillo Jarillo G.,Mexican Oil Institute | Markov M.,Mexican Oil Institute | Gurevich B.,Curtin University Australia
Geophysical Journal International | Year: 2013

Most sedimentary rocks contain movable fluid in the pores. Hydrodynamic effects due towaveinduced oscillatory fluid flow can lead to significant changes of velocities and attenuations of elastic waves in these rocks. In this paper, we consider the influence of a squirt flow (local flow between the pores of different compressibility) on the sonic log response. The calculations are performed using a unified model describing the joint influence of squirt flow and Biot's global flow. The results show that the influence of the squirt flow increases with increase of a signal frequency. This influence is relatively small in the case of the Stoneley wave but it is significant in the case of P and S waves. © The Authors 2013. Published by Oxford University Press on behalf of The Royal Astronomical Society.

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