Impedance loading an acoustic source in a borehole located in a fluid‐saturated porous medium

Abstract

Conventional sonic logging tools are destined mainly for the determination of elastic waves’ velocities. In this paper, we have considered a different type of sonic logging tool that is destined for the registration of parameters of reflected waves in a borehole. We have calculated the mechanical impedance loading an acoustic source located on the axis of a fluid‐filled borehole. The problem was solved for a borehole drilled in a poroelastic formation. The solution was obtained in the framework of the Biot theory of poroelasticity. We have considered two limiting cases with permeable and impermeable (mudcake at the boundary between the borehole and porous rock) borehole wall. We have obtained the frequency dependences of the mechanical impedance. It was shown that the acoustic system ‘logging tool – fluid‐filled borehole – porous rock’ presents several resonance frequencies. These resonances’ frequencies are close to the resonance frequencies of a liquid layer between two rigid cylinders with radii equal to the source and borehole radii. The mechanical impedance calculated at the resonance frequency depends on the porosity and permeability that allows one to use impedance measurements in the frequency range near the resonance to determine the filtration properties of highly permeable rocks (of order higher than 10 mD). We have calculated the mechanical impedance in the low‐frequency range. The results obtained have shown that the use of low‐frequency impedance measurements provides a good way to evaluate the permeability of porous media.