Question 1 of 10: Porosity Tools and Acoustic-Property Applications

Question 1: Porosity Tools and Acoustic-Property Applications (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) Three logging tools that measure porosity

• Sonic (acoustic) log. Measures the compressional-wave transit time Δt between a transmitter and a pair of receivers; converted to porosity through Wyllie's time-average relation, $\phi=(\Delta t-\Delta t_{ma})/(\Delta t_f-\Delta t_{ma})$ (the attachment formula), most reliable in consolidated, intergranular rock with no secondary (vuggy/fracture) porosity.
• Compensated Formation Density (FDC) log. A back-scattered-gamma-ray tool whose count rate is converted to bulk density ρ_b, then to porosity via $\phi_D=(\rho_{ma}-\rho_b)/(\rho_{ma}-\rho_f)$ — the same relation used in Questions 7 and 8; responds to total (matrix + fluid) porosity and is highly sensitive to the assumed matrix and fluid densities.
• Compensated Neutron Log (CNL). Counts thermal/epithermal neutrons after moderation by hydrogen in the pore fluid, reading an apparent porosity directly on a chosen lithology (matrix) scale; because it responds to the HYDROGEN INDEX of the pore fluid rather than to porosity itself, it under-reads badly in gas (Question 7) and over-reads in a shale interval bound water, so it is normally used together with the density log rather than alone.

(b)(i) 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, complementing the neutron-density gas crossover of Question 7.

(b)(ii) 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.