Title of the Paper: The Unusual Small Wave Velocities in Structured Bodies
and Instability of Pore or Cracked Media by Small Vibration
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Authors: Sibiriakov B.P., Prilous B.I.
Abstract: This paper studies properties of a continuum with structure. The characteristic size of the structure governs the fact that difference relations do not automatically transform into differential ones. It is impossible to distinguish an infinitesimal volume of a body, to which we could apply the major conservation laws, because the minimum representative volume of the body should contain at least a few elementary microstructures. This leads to motion equations of infinite order. Solutions of such equations include, along with sound waves, perturbations propagating with abnormally low velocities not bounded below. It is shown that in such media weak perturbations can increase or decrease without limit. Weak dispersion of structure sizes reduces the intensity of such increase and therefore stabilizes the medium, whereas unlimited growth of dispersion destabilizes it. The nonlinearity of the stress-strain curve is shown to cause a reduction of specific surface of a cracked medium, i.e. the medium undergoes fracture with the formation of a system of a small number of large cracks as though it ignores a large number of small cracks.
Keywords: specific surface, operator of continuity, equation of motion, structured media, catastrophes.
Title of the Paper: Hydrodynamics Problems for Distribution of the Phases in Oil-and-Gas Formation
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Authors: V.I. Pen’kovskii, N.K. Korsakova
Abstract: Developed method of oil and gas formation electromagnetic logging is based on representation of apparent resistivity as convolution of real resistivity field with frequency distribution for every sonde sensitivity on near-well zone, mathematical modeling of drilling mud filtrate penetration processes and interaction of mud filtrate with native water.
Hydrodynamics of drilling mud filtrate invasion into formation is defined by solution of Buckley-Leverett system of equations with observance of kinematic conditions for phase discontinuity. As result the displacement front locations and oil and gas mean-integral values of the saturations in drilling mud filtrate invasion region are obtained. Depending on formation saturations of immiscible phases different cases of mutual displacement oil, gas and water front locations are possible. The location of fronts affects essentially to character of resistivity distribution and logging reading. The interpretation of field data is reduced to solution of inverse problems so as definition of initial data for system of immiscible liquid and salt-exchange equations. The example of applying of the method is given.
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