Theoretical simulation of electroacoustic borehole logging in a fluid-saturated porous formation

Abstract

Electroacoustic (E-A) logging describes the acoustic response to an electromagnetic (EM) source in a fluid-filled borehole surrounded by a porous medium. The E-A response is simulated by two different methods in this paper. In the coupled method, the EM field and the acoustic field are modeled using Pride's model, which couples Maxwell's equations and Biot's equations. In the uncoupled method, the EM field is uninfluenced by the converted acoustic field, resulting in separate acoustic formulation with an electrokinetic source term derived from the primary EM field. The difference of the transient full waveforms between the above two methods is remarkably small for all examples, thus confirming the validity of using the computationally simpler uncoupled method. It is shown from the simulated waveforms that an EM-accompanying acoustic field is coupled to the EM field and appears with an apparent phase velocity of the EM wave in the formation. Acoustic waves with the conventional acoustic velocities are also seen in the converted full waveforms. For the sandstone models used in this paper, when permeability is less than 1 Darcy, the E-A Stoneley wave amplitude increases with porosity, which is different from that in conventional acoustic-to-acoustic logging.

Finite element modeling of SHTE and PSVTM electroseismics

“…As such, the flow driven electric current L(− ∇ p f + ω 2 ρ f u s ) is very small compared to the conduction current σE, and can be neglected in Maxwell's equations. The same assumption was made by Guan and Hu (2008) when studying the acoustic response induced by an applied electric dipole, and the obtained numerical results backing it can be found in Hu et al (2007). (e) As in this work interest lies in electroseismics, F (s) = F ( f ) = 0.…”

A new numerical technique for simulating the coupled seismic and electromagnetic waves in layered porous media

“…Haartsen and Pride (1997) used the so-called global matrix method whereas Garambois and Dietrich (2002) proposed an extension of the generalized reflection and transmission coefficients method (abbreviated as generalized R/T coefficients method in the following context), which was originally developed by Kennett (1983). For well logging exploration case, some analytical and numerical methods were performed to describe the electroacoustic waves in borehole in porous media (Hu et al, 2003(Hu et al, , 2007. The above algorithms were implemented in the frequency domain.…”

Moment tensors of a dislocation in a porous medium

“…F can be expressed as F ¼ /f þ ð1 À /Þf s , where f s is the average force density exerted on the solid grain; q ¼ /q f þ ð1 À /Þq s is the bulk density, where q f is the pore fluid density, and q s is the solid grain density; g is the fluid viscosity; jðxÞ is the dynamic permeability (JOHNSON et al 1987;HU et al 2007). The elastic moduli H, G, C, and M can be written as:…”