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

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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.