Presence Of Pore System Research Articles

Attenuation of an external signal in a thermoelastic material with triple porosity in local thermal non-equilibrium

This work aims to highlight, by a series of spatial estimates, the effect of the presence of pore system and local thermal non-equilibrium properties in a triple porosity material matrix on the transmission depth of a thermo-mechanical signal. Two kind of spatial behaviors are established, for which the spatial response obeys a linear first-order differential inequality with two kind different coefficients: one is time independent and the other is time dependent. The first differential inequality furnishes some exponential decaying spatial estimates with uniform in time exponent and such estimates are recommended to be used for appropriately large values of the time variable. While the second first-order differential inequality furnishes some exponential decaying spatial estimates with time dependent exponent, thus showing a rapid spatial decrease of the solution for appropriate short values of time. These results are compared with their counterparts without mechanical effects, that is for purely pore system or local thermal non-equilibrium effects theories: this is done for appropriate short and large values of the time variable.

Thermoelastic waves in double porosity materials

The focus of this paper is on the propagation of thermoelastic waves with assigned wavelength within the context of theory of thermoelasticity for materials with double porosity. It is shown that there exist two shear waves that are undamped in time, non-dispersive and that are unaltered by the presence of pore system or by thermal effects. Furthermore, there also exist other four longitudinal wave solutions that are dispersive and damped in time: one longitudinal quasi-elastic wave and two quasi-pore modes and one quasi-thermal mode. The dispersion relation is explicitly established like a fifth degree algebraic equation with real coefficients and hence it always allows some real roots, thus predicting existence of some standing waves. A numerical analysis for Berea sandstone shows that the speed of propagation of the longitudinal quasi-elastic wave is larger than the wave speed for its counterpart from the classical elastic model or that in the double porosity elastic model. The propagation of the Rayleigh surface waves is addressed and the corresponding secular equation is explicitly established. As an illustrative example it is used Berea sandstone when the secular equation is solved by means of the graphical method to prove that the Rayleigh surface wave problem admits a solution.

On certain boundary-value problems for the equations of seepage of a liquid in fissured rocks

The focus of this paper is on the propagation of thermoelastic waves with assigned wavelength within the context of theory of thermoelasticity for materials with double porosity. It is shown that there exist two shear waves that are undamped in time, non-dispersive and that are unaltered by the presence of pore system or by thermal effects. Furthermore, there also exist other four longitudinal wave solutions that are dispersive and damped in time: one longitudinal quasi-elastic wave and two quasi-pore modes and one quasi-thermal mode. The dispersion relation is explicitly established like a fifth degree algebraic equation with real coefficients and hence it always allows some real roots, thus predicting existence of some standing waves. A numerical analysis for Berea sandstone shows that the speed of propagation of the longitudinal quasi-elastic wave is larger than the wave speed for its counterpart from the classical elastic model or that in the double porosity elastic model. The propagation of the Rayleigh surface waves is addressed and the corresponding secular equation is explicitly established. As an illustrative example it is used Berea sandstone when the secular equation is solved by means of the graphical method to prove that the Rayleigh surface wave problem admits a solution.