Research On Wave Propagation Characteristics And Relevant Problems In Two-phase Porous Media

Two-phase porous media are ubiquitous among the engineering materials in nature, and most of the oil reservoir, surface layer, and coastal soil on earth, which are of sufficient economic importance, are fluid saturated two-phase porous media. Therefore, it is of great practical values to conduct study on two-phase porous media. Since the establishment of Biot’s theory in1950s, subjects involving the theory and wave propagation in two-phase porous media have been widely studied, but there are still a lot of limitations in the previous researches. Two-phase porous media are most fundamental among the multi-phase porous media, and the theory of multi-phase porous media is key for wave analysis. Consequently, conducting research on the wave propagation characteristics and relevant problems in two-phase porous media is of theoretical significance, and lays firm foundation for the wave analysis in more complicated multi-phase porous media, such as unsaturated porous media and double-porosity porous media.Firstly, Biot’s theory and modified Biot’s theory, which have been widely applied for wave analysis in two-phase porous media, were fully compared. Thereinto, the relation between the stresses in the above two theories was analyzed, and various expressions of each elastic coefficient in Biot’s theory, such as A, R, Q and N, were derived. Besides, a reliable method was put forward to judge the accurate meaning of the pore pressure donation and its positive direction, and the parameters which are easily misunderstood got clarified.Next, considering the modulus-porosity-Poisson’s ratio relation, the theoretical solution of the body waves in two-phase porous media was derived. The effects of the compressibility of the solid grain, porosity, Poisson’s ratio and fluid viscosity on the propagation velocity and attenuation of the three kinds of body waves, namely, P1, P2and S waves, were numerically investigated, respectively. Moreover, by degeneration analysis, the numerical results above were compared with those in the case of neglecting the modulus-porosity-Poisson’s ratio relation.Then, the theoretical solution of the Rayleigh waves in two-phase poroelastic half-space was rigorously deduced in detail, and the secular equations under four different boundaries, namely, stress-free permeable boundary, stress-free impermeable boundary, rigid permeable boundary, and rigid impermeable boundary, were obtained. The dispersion and attenuation characteristics of the Rayleigh wave under each of the above boundaries were numerically analyzed. Additionally, comparison was made about the theoretical solutions of the Rayleigh waves obtained under two different potential functions corresponding to the case of considering two kinds of compressional waves (P1and P2waves) and the case of considering a kind of compressional wave (PI or P2wave). By numerical calculation, the Rayleigh wave propagation characteristics in the following three cases were discussed:(1) the case of considering P1and P2waves,(2) the case of considering P1wave, and (3) the case of considering P2wave.The theoretical solution of the Love wave in the case of a two-phase poroelastic layer overlaying a two-phase poroelastic half-space was rigorously deduced in detail, and the dispersive equation was obtained. Thereinto, some parameters, of which the expressions were ususlly given directly in the previous researches, were derived, and their accurate meanings got clarified as well. By degeneration analysis, the Love waves in the following three cases with different layers were theoretically discussed:(1) an elastic solid layer overlaying a two-phase porous half-space,(2) a two-phase porous layer overlaying an elastic solid half-space, and (3) an elastic solid layer overlaying a elastic solid half-space. Based on the above analysis, the propagation characteristics of the Love wave in elastic solids were numerically investigated.Finally, theoretical analysis was made about the two kinds of propagation velocities defined by different expressions in the previous researches, and taking two-phase porous medium as an example, the dispersion characteristics of the body waves corresponding to the above two different propagation velocities were numerically discussed. Moreover, the theoretical solutions of the Rayleigh waves in two-phase poroelastic half-space and elastic solid half-space were compared, through which the similarity in form and the difference in essence between them were pointed out. To validate the above analysis, the ratios between the propagation velocities of Rayleigh wave and body waves in two-phase poroelastic half-space with different boundaries were numerically analyzed.