Propagation Of Pore Pressure Wave In Water-Saturated Rock

The pores in the rock contain oil or water, strictly speaking, the rock is a two-phase medium. The pores of the oil or water and the rock matrix are interaction and coupling, so the study is more difficult. At present, the classical model is the Biot theory, but the theory is very complicated both in derivation and application. In seismic wave exploration and rock mechanics, the observed wave is mainly in the solid medium, and the wave in the small pore is difficult to be observed directly, so the model can be used to study the seismic wave.This paper uses Lagrange analysis method, mainly studies two kinds of situations. The first is that the confining pressure is zero, which will lead to the diffusion wave equation. On the basis of academician Chen Yong’s model, we revised some over simplified formulas to establish a more rigorous and realistic model for the propagation of pore fluid pressure wave. Emphasis is on the relationship between the P wave and the solid matrix, and the physical parameters such as rock porosity and permeability.The other is the non-zero confining pressure, which is the innovation of this paper. We first derive the three-dimensional pore pressure wave equation. In practice, seismic body wave propagation in rock by P or S wave can be approximated as 1 dimensional plane wave.Therefore,we ignore the Poisson effect, the three-dimensional pore pressure wave equation is simplified to 1 dimensional wave equation. Our solution is divided into three kinds, one is assuming the confining pressure is a plane wave, derives the corresponding pore pressure wave; the second is that confining pressure is an impulse function, is derived from the corresponding pore pressure wave; the third is the confining pressure is a square wave, and derives the corresponding pore pressure wave. The characteristics of the solution can be seen (1) the pore pressure wave and the P wave are symbiotic; (2) the amplitude is small and there is a phase difference. This is due to the flow of viscous fluid in the pores. The three solutions are not in violation of the conservation of energy.