Step 1: The Streaming Potential Coefficient
Applying a pressure gradient ΔP [Pa] to a porous rock sample induces the fluid in the pore space to flow. A local convection current originates from the movement of some of the ions in the electrolyte; this current is counterbalanced by a conduction current, thus ensuring the electro-neutrality of the medium. This ohmic current creates a potential difference ΔV [V], called the streaming potential.
In the case of laboratory experiments, it is possible to measure both the applied ΔP and the measured ΔV.
The ratio between these quantities is called the streaming potential coefficient, or SPC, often noted C.
Step 2: The Electrical Double Layer
The model of the Electrical Double Layer (EDL) was proposed to explain the mechanisms giving rise to the streaming coefficient. It describes the way ions are organized in the pore fluid and along the mineral grains, at the microscopic scale.
The figure shows a simplified EDL model. Between the negatively charged grain and the free electrolyte are a series of intermediate layers.
The Stern layer contains positive ions (cations) adsorbed along the mineral grain. As the cations in the Stern layer do not compensate the negative surface charges, a diffuse layer exists, where cations outnumber the negative ions (anions). This excess of positive charges decreases exponentially until cations and anions are balanced in the free electrolyte. As a result, the electrical potential increases until it reaches 0 in the free electrolyte.
Step 3: The seismoelectric theory of Pride (1994)
In order to describe the conversion mechanisms between seismic and electromagnetic waves, Pride combined Maxwell's equations with Biot's equations for poroelasticity describing the propagation of seismic waves throughout a saturated porous medium. These two subsets of equations are linked through the two coupling equations given here.
Pride derived that L12=L21, i.e. the seismoelectric coupling equals the electro-seismic coupling. This is called the Onsager reciprocity and was already verified for electrokinetic and electro-osmotic phenomena. One can therefore write: L12=L21=L.
This coupling coefficient L(ω) can be written as the product of a static term L0 with a frequency-dependent term.
