Question 1 of 10: Acoustic Properties of Rocks

Question 1: Acoustic Properties of Rocks (8 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

(a) Compressional (V_p) and shear (V_s) wave velocities

The sonic tool records V_p directly (and V_s with a dipole/array sonic), and the pair of velocities is one of the most widely used log measurements outside its original role of a seismic velocity survey:

• Sonic porosity. Wyllie's time-average relation, $\phi=(\Delta t-\Delta t_{ma})/(\Delta t_f-\Delta t_{ma})$ (the attachment formula), converts the compressional transit time directly into porosity in consolidated, intergranular rock.
• Lithology and mechanical-property (geomechanics) determination. The V_p/V_s ratio (equivalently, dynamic Poisson's ratio) is diagnostic of lithology (carbonates plot with a higher V_p/V_s than clean quartz sandstone) and feeds the dynamic elastic moduli (Young's modulus, shear modulus, bulk modulus) used for fracture-height/fracability modelling and sanding/wellbore-stability predictions.
• Fluid and gas detection. V_s is essentially insensitive to pore fluid while V_p drops sharply when gas replaces liquid in the pore space, so a V_p/V_s (or "shear-sonic") crossover is a direct, lithology-independent gas indicator, complementary to the neutron-density crossover used in Question 8.
• Seismic tie and synthetic seismogram generation. Combined with the density log, V_p gives acoustic impedance, letting the well be tied to surface seismic through a synthetic seismogram and calibrating time-depth conversion.

(b) Compressional and shear wave attenuation

Attenuation (amplitude loss per unit travel distance, expressed in dB/ft, or its inverse the quality factor Q) is far more sensitive than velocity to rock texture and fluid mobility:

• Fracture and permeability detection. Open, fluid-filled fractures and high intergranular permeability strongly attenuate both P- and S-waves (viscous fluid-flow and scattering losses), so an attenuation (or amplitude) log that spikes without an accompanying velocity change flags fractured or highly permeable intervals that a velocity-only reading would miss.
• Cement-bond and casing-integrity evaluation. In cased holes, the attenuation of the casing-arrival compressional wave is the basis of the cement bond log (CBL): a well-bonded cement sheath rapidly attenuates the casing signal, while a free (unbonded) pipe rings with very low attenuation.
• Gas and unconsolidated-rock flags. Even small amounts of free gas in the pore fluid disproportionately increase attenuation (far more than the corresponding velocity drop), and poorly consolidated/unconsolidated formations attenuate the shear arrival heavily — both used as auxiliary gas and rock-competency indicators alongside part (a).

(c) Amplitude of reflected waves

Where the sonic or borehole-acoustic tool records the AMPLITUDE of an arrival reflected from an interface (the borehole wall itself, or an internal casing/cement interface), rather than just its travel time:

• Cement bond and micro-annulus detection (CBL/VDL amplitude). The amplitude of the casing compressional arrival, calibrated against a free-pipe baseline, is read directly as percent bond; a full acoustic waveform (variable-density log, VDL) additionally distinguishes a true bonding defect from a pressure-induced micro-annulus.
• Borehole televiewer / fracture and breakout imaging. The amplitude (and travel time) of the acoustic pulse reflected from the borehole WALL itself, recorded azimuthally, images fractures, vugs, bedding, and stress-induced breakouts as low-amplitude ("dark") sinusoidal traces on the unrolled borehole image.
• Acoustic impedance contrast / reflection-coefficient work. Reflected-wave amplitude scales with the acoustic-impedance contrast across an interface, the same physics used (at seismic scale) to build synthetic seismograms and (at log scale) to flag hard streaks, vugs, or bed boundaries too thin for the primary travel-time curve to resolve cleanly.