Dynamic Streaming Currents From Seismic Point Sources In Homogeneous Poroelastic Media

Abstract

In a porous medium saturated with a fluid electrolyte, mechanical and electromagnetic disturbances are coupled. The coupling is electrokinetic in nature since it is due to an excess of electrolyte ions that exist in an electric double layer near the grain surfaces within the material. Mechanically-induced streaming currents generated by point sources in homogeneous, isotropic porous media are presented. The electrically-induced streaming current is shown to be second-order in the electrokinetic coupling coefficient and can be neglected. This decouples the mechanical behavior from the electromagnetic behavior with respect to the induced fluxes and simplifies the analysis of the relative fluid flow and dynamic streaming current. We used Biot theory to calculate the amount of induced relative flow by the solution to Green's function. The transport coefficients-conductivity, dynamic permeability, and the electrokinetic coupling coefficient-and their sensitivity with respect to porosity, dc permeability, and frequency changes are evaluated. Conductivity decreases with increasing dc permeability. It has a k[subscript 0][superscript -1/2] dependence when grain surface conductances are more important than the bulk fluid phase conductivity. Stationary phase relative flow and streaming current solutions are calculated for an explosive and vertical point source acting on the bulk and a volume injection source acting on the fluid. The streaming currents are induced both by P and S waves. The streaming current decreases with increasing fluid conductivity. This is consistent with the decrease of the diffuse double layer thickness and ζ-potential. The porosity effect on the streaming current induced by S waves is different from the currents induced by the P waves. The porosity affects the bulk moduli of the solid. Its effect, combined with the frame bulk modulus and compressibility of the saturating fluid, determines the streaming current amplitude induced by a P wave versus porosity. The increase in streaming current amplitude induced by S waves with increasing porosity is due to the decrease of the shear frame modulus with increasing porosity. The streaming current behavior with respect to dc permeability is found to differ for sources applied to the elastic frame and volume injection sources.United States. Dept. of Energy (Grant DE-FG0293ER14322)Massachusetts Institute of Technology. Borehole Acoustics and Logging Consortiu