Simulation of the converted electric field during acoustoelectric logging

In acoustoelectric logging both the acoustic wave and the converted electric field are recorded when an acoustic transmitter emits acoustic waves. The existence of the electric field in the borehole is due to the electrokinetic effect in the porous formation and the boundary conditions on the borehole wall. This study presents a simplified yet highly accurate approach to simulate the full waveform of the converted electric field during acoustoelectric well logging. We simplify Pride's equations by ignoring the influence of the converted electric field on the propagation of acoustic wave. After formulating the acoustic field in the porous formation based on Biot's theory, and by quasi-static approximation of the electric field, we are able to deduce the electric field expressions from the simplified Pride equations. We calculate the full waveforms of the converted electric field for acoustoelectric logging in a consolidated sandstone formation saturated by low molarity water. The fastest wave component is the radiating electromagnetic wave that arrives every receiver on the borehole axis almost simultaneously. The other wave components are stationary electric fields that accompany the compressional, shear, and Stoneley waves respectively. When the center frequency is 6kHz and the offset is 3 meters the compressional wave has the largest conversion efficiency while the Stoneley wave has the largest accompanying electric field strength.