Stoneley Permeability
Stoneley permeability is the effective permeability of a formation derived from analysis of the Stoneley wave recorded on a borehole acoustic log. When a Stoneley wave propagates past a permeable interval, the oscillating pressure pulse drives fluid in and out of the pore throats at the borehole wall, dissipating acoustic energy and producing a measurable reduction in wave amplitude and an increase in slowness. Inversion of these amplitude and slowness changes using dynamic poroelastic theory yields a continuous permeability profile without requiring core samples or flow testing.
Physical Mechanism of Energy Dissipation
The fundamental physics underlying Stoneley permeability measurement derives from the coupling between acoustic pressure oscillations in the borehole fluid and fluid flow in the adjacent porous formation. As the Stoneley wave passes, the associated pressure gradient at the borehole wall is sufficient to drive pore fluid radially into and out of permeable intervals. This fluid exchange, governed by Darcy's law and the compressibility of the pore fluid, removes energy from the propagating wave. The Biot theory of poroelasticity predicts the amplitude decay and slowness increase as functions of formation permeability, porosity, fluid compressibility, and grain compressibility. Higher permeability allows more fluid exchange per unit time, producing greater attenuation. The effect is frequency-dependent: at the 1 to 3 kHz frequencies typical of wireline Stoneley waves, the measurement is most sensitive to permeabilities in the range of a few millidarcies to several hundred millidarcies, which encompasses the productive range of most sandstone and carbonate reservoirs.
Inversion Methodology
Converting raw Stoneley amplitude and slowness logs to permeability requires a model-based inversion. The most widely used approach applies the dynamic Biot model, which relates the complex Stoneley wave slowness and attenuation to formation properties. The inversion requires known or estimated inputs including porosity from a neutron-density log, fluid compressibility and viscosity from fluid sampling or a compositional model, and grain compressibility from mineralogy logs. With these inputs fixed, the Biot model is inverted iteratively at each depth level to find the permeability value that best reproduces the observed Stoneley slowness and amplitude. Processing software from Schlumberger (Optio, Techlog) and other vendors implements this workflow in the context of the full sonic waveform dataset. The output is a continuous permeability log at the centimeter-scale vertical resolution of the sonic receiver array, providing far more detail than widely spaced core plugs.
Comparison with Other Permeability Measurements
Stoneley permeability occupies a distinct position in the suite of formation permeability measurements available to reservoir engineers. Core plug permeability measured in a laboratory at ambient conditions represents a small volume of rock, is subject to alteration from coring and preservation, and requires upscaling to represent the wellbore interval. NMR permeability, estimated from relaxation time distributions using the SDR or Timur-Coates transforms, reflects pore geometry more than flow capacity and can overestimate or underestimate depending on pore type and wettability. DST and production test permeability integrates a larger drainage volume and captures effective reservoir flow capacity including fracture contribution, but is available at only a few depth intervals. Stoneley permeability provides a continuous, in-situ measurement that reflects the effective permeability at the borehole wall as seen by the Stoneley wave pressure pulse, which is sensitive to open fractures as well as matrix porosity. Where good core data exist, calibrating the Stoneley permeability inversion against core plug measurements substantially improves reliability.
Advantages and Limitations
The primary advantage of Stoneley permeability is its continuity. A single sonic log pass delivers permeability at every depth increment through the logged interval, capturing thin permeable beds, transition zones, and heterogeneous layering that sparse core coverage would miss. The measurement works in vertical and deviated wells without special equipment and is obtained as part of the standard acoustic logging program. It is non-destructive, requires no fluid samples to reach surface, and integrates naturally with other petrophysical logs in formation evaluation workflows. The principal limitations are its dependence on accurate borehole fluid properties and formation elastic parameters, which must be estimated if not measured directly. Borehole rugosity and mudcake can alter the Stoneley wave before it reaches the receivers, introducing uncertainty particularly in swelling shales or washed-out sections. The measurement also works best in consolidated sandstones and carbonates; in unconsolidated or very high-porosity formations, the Biot model assumptions may break down. Very low permeabilities below approximately 0.1 millidarcies and extremely high permeabilities above several hundred millidarcies also push against the sensitivity limits of the Stoneley wave approach.
Application in Formation Evaluation
Stoneley permeability logs are routinely used in exploration and development wells to rank reservoir intervals, design completion intervals, and model reservoir flow behavior. In carbonate reservoirs where matrix permeability is low but fracture permeability dominates, the Stoneley amplitude log often shows sharp attenuation spikes at fracture intersections, allowing fracture aperture and conductivity to be estimated in addition to matrix permeability. When combined with porosity, fluid saturation, and pressure data, the continuous Stoneley permeability profile is a key input to reservoir simulation models and net pay calculations. In deepwater wells where coring is expensive and DST testing is limited, Stoneley permeability can be the primary permeability dataset available before first production.
Key Takeaways
- Stoneley permeability is derived from the attenuation and slowness increase of the acoustic Stoneley wave as fluid exchange between the borehole and permeable formation dissipates wave energy.
- The Biot dynamic poroelastic model is inverted using known fluid and rock properties to convert raw Stoneley waveform data into a continuous permeability log at centimeter-scale vertical resolution.
- The measurement complements core plug and NMR permeability: it is continuous, in-situ, sensitive to both matrix and fracture permeability, and available without flow testing.
- Borehole condition, fluid property uncertainty, and formation consolidation state are the main sources of error and should be assessed before using Stoneley permeability in reserve calculations or completion design.