Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Notes on this paper
National Examinations, 17-Pet-B1, Well Logging and Formation Evaluation — May 2019, 3 hours, closed book (Sharp or Casio approved calculators permitted), 10 questions, all marked. Every question on this paper is Well Logging & Formation Evaluation content, solved to the paper as printed. Every datum here was read from the paper: the Question 9 SP track prints "SSP −80 mV" and "PSP 47 mV", its gamma-ray track prints 28, 92 and 44 API against Zones B, C and A, and the attachments supply the gas-sand chart and SP departure chart used in Questions 7 and 10.
Reference texts: Bassiouni, Theory, Measurement, and Interpretation of Well Logs (SPE Textbook Series Vol. 4); Asquith & Krygowski, Basic Well Log Analysis, 2nd ed. (AAPG); Ellis & Singer, Well Logging for Earth Scientists, 2nd ed.; Schlumberger, Log Interpretation Charts / Log Interpretation Principles and Applications.
Question 1: Acoustic Properties of Rocks (8 marks)
(a) Compressional (Vp) and shear (Vs) wave velocities
The sonic tool records Vp directly (and Vs 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 Vp/Vs ratio (equivalently, dynamic Poisson's ratio) is diagnostic of lithology (carbonates plot with a higher Vp/Vs 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. Vs is essentially insensitive to pore fluid while Vp drops sharply when gas replaces liquid in the pore space, so a Vp/Vs (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, Vp 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.
