The propagation of borehole Stoneley waves has been shown to be sensitive to fluid mobility (the ratio of permeability to viscosity). When crossing a permeable formation Stoneley wave energy attenuates and slowness increases, a phenomenon that is well described by Biot's theory and one that has been verified in laboratory experiments.
However, as mobility effects on Stoneley waves are secondary and rather small, an accurate Stoneley wave propagation model as well as an optimal inversion technique is required to perform quantitative inversions of borehole log data. Effects of the mudcake on the borehole wall, which reduces pressure communication between the borehole fluid and the formation and thereby decreases Stoneley wave mobility effects, need to be included in the Stoneley wave propagation model. As such, an elastic membrane model was devised to include these effects in the Biot model. An inversion technique, which uses both slowness and attenuation of the Stoneley wave over a range of frequencies to evaluate mobility, is proposed to optimize the sensitivity of the inversion to formation mobility.
This paper describes the implementation of an interpretation methodology based on the above technique. The Stoneley wave propagation model employed is described with 13 parameters. The error analysis shows that the accurate determination of the fluid mobility requires that critical parameters, such as the mud slowness, mud attenuation and pore-fluid modulus be precisely determined. An interpretation procedure is proposed to determine these parameters with reasonable accuracy. The fluid mobility can then be determined without the need for external calibration with other mobility measurements. Finally, with knowledge of the saturating fluid viscosity, the intrinsic permeability of the rock can be derived.
When using the proposed methodology within the applicable measurement range limited. by Biot physics, the Stoneley wave can provide a continuous estimation of the formation permeability along a borehole wall. Core measurements are not required for calibration although they can be used for verification.
In addition to permeability estimation, the use of this technique has various related applications such as the optimal placement of wireline formation tests and perforation intervals. In the realm of earth science, other applications are expected to be developed as the use and interest in borehole measurements continues to grow.