Some three- and n-component waves in porous media

Abstract

Based on experimental results and self-consistent physical theory, a three-component description of nonlinear body waves in porous media is constructed. Applications of this result to two-component fluid flow in dynamic porous media and seismic wave propagation in multiphase porous media are presented. This description is important to petroleum reservoir simulation, groundwater hydrology, and seismic analysis of the earth. The two-body analogue of these results has been shown, in the past, to be inconsistent with the two-body linear models currently used by petroleum engineers and groundwater hydrologists. In seismic theory, simple linear models are generally used and much of the information obtained from the theory presented here is referred to as noise. The processes observed and described here have been patented and applied commercially to oil production and groundwater remediation. It is shown here that even if the correct nonlinear equations are used, three-component wave descriptions of porous media cannot be constructed solely from the equations of motion for the components. This is because of the introduction of the complexity of multiple scales into this nonlinear field theory. Information about the coupling between the components is required to obtain a physical description. It is observed that the fields must be coupled in phase and out of phase, and this result is consistent with the description of three- and n-body gravitational fields in Newtonian gravity and general relativity.