Transient streaming potential measurement on fluid-saturated porous rocks: an experimental verification of Biot's slow wave in the quasi-static limit

Abstract

The time behavior of the streaming potential is identical to that of differential pressure when local laminar flow is maintained and electromagnetic relaxation is not important. The time evolution of the streaming potential waveform resulting from the application of a pressure pulse to one face of a cylindrical water-saturated core is found to depend on the elastic properties of the fluid and rock frame and on the porosity and permeability of the core. The analysis of this quasi-static flow based on Biot's soil consolidation work (1941) is completely equivalent to that obtained from Biot's slow wave model (1956) in the limit of zero frequency. Both analyses result in a homogeneous diffusion equation in pore pressure (and streaming potential) where the diffusivity is expressed in terms of the bulk moduli of the fluid and solid constituents, bulk and shear moduli of the solid frame, fluid viscosity, porosity, and permeability. The predicted streaming potential transient response is in excellent agreement with experimental observations, permitting, for example, the extraction of core permeability. Models assuming an incompressible frame are shown to be grossly inadequate in describing the temporal features of quasi-static flow.

Theory of dynamic permeability and tortuosity in fluid-saturated porous media

“…The elastodynamic properties of porous media are interesting in part because of the possibility of macroscopic relative motion between the fluid and the solid constituents. These effects are of prime importance in understanding fourth sound in a superfluid/superleak system (Johnson 1980), pressure diffusion through porous media (Chandler & Johnson 1981 ;Chandler 1981), slow waves and the consolidation transition , elastodynamics of gels (Johnson 1982) as well as the acoustic properties of 'ordinary ' porous media saturated with 'ordinary fluids . These properties are discussed in a review of recent work (Johnson 1984).…”