Permeability Profiles From Acoustic Logging
Authors: Staal J.J. , Robinson J.D. 
Published: December 2007

Abstract
The dependence of the attenuation of acoustic wave trains on formation permeability was found in data from two cored Groningen field wells. The acoustic wave trains were recorded with a Schlumberger Bore Hole Compensated sonic tool opposite 300 m of Slochteren sandstone. The energy of the part of the wave train that corresponds in velocity to the Stoneley wave was measured in a time window from 1400 us to 2310 us after the time of the first arrival. The energy of the first 130 us of the wave train was used for normalisation.
Permeability profiles were prepared from core measurements and compared with logs of normalised energy. The range of permeability was 0.5 mD to 500 mD. As predicted by Rosenbaum, the permeability profile and the normalised energy profile were similar. profile and the normalised energy profile were similar. The range of normalised energy ratio was 0.04 to 3.5.

Introduction
A means to estimate permeability from a continuous wireline log has not been reported. With the original nuclear magnetism logging tool (NML) a capillary-pressure histogram could be obtained, from which the permeability was immediately calculable for a sandstone formation. However, the NML tool had to remain stationary at each depth at which a capillary-pressure histogram was desired.
In a theoretical study, J. H. Rosenbaum observed that the relative energy content of parts of acoustic wave trains, obtained with a source and receiver in a fluid-filled borehole, is dependent on the permeability of the formation. We sought to observe the effect predicted by Rosenbaum. In several cored Groningen predicted by Rosenbaum. In several cored Groningen gasfield wells acoustic wave trains were recorded opposite a Slochteren-sandstone formation. More data have been obtained from three Lake Maracaibo oil wells. A standard Schlumberger sonic probe was used, although it was known from Rosenbaum's study that this tool was not the most suitable for our purpose.
This paper contains our results to date on the relation of acoustic energy in various parts of the wave trains to the permeability profile known from core analysis.

SYNTHETIC WAVE TRAINS
In a theoretical study J.H. Rosenbaum investigated the propagation of acoustic pulses in a fluid-filled borehole surrounded by a porous formation. Wave propagation in the borehole was described by the propagation in the borehole was described by the acoustic wave equation; in the fluid-filled porous formation, Rosenbaum applied Blot's theory of wave propagations. Blot's theory is based on the conceptual propagations. Blot's theory is based on the conceptual model of a medium consisting of an elastic solid matrix and a viscous pore fluid. The relative motion between the pore fluid and the matrix results in energy dissipation.
Assuming a bandwidth-limited pressure pulse, generated by a centred ring source, Rosenbaum computed the wave train received by a centred ring detector. The boundary conditions at the borehole wall are controlled by the mud cake. The influence of the mud cake was described by a surface impedance function, which relates the acoustic fluid-flow velocity across the borehole wall to the acoustic pressure difference between the borehole fluid and the pore fluid. Since no information on the acoustic behaviour of mud cakes was available, only the limiting conditions of a sealed interface and of an open interface were investigated.
Rosenbaum compared energies in gated sections of the wave trains. He found that for the sealed interface maximum sensitivity to permeability was obtained in the interval between shear-wave arrival and direct-wave arrival. For the open interface the entire signal following the shear-wave arrival could be used. The compressional-wave arrival was found to be least sensitive, and could therefore serve for normalization.