Question 4 of 10: Assumptions of Conventional Log-Interpretation Techniques

Question 4: Assumptions of Conventional Log-Interpretation Techniques (6 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.

"Conventional" (Archie-type) log interpretation — the resistivity-porosity-saturation workflow used throughout this paper — rests on six simplifying assumptions:

• 1. The formation is clean, granular, and intergranular-porous (no significant clay/shale, vugs, or fractures) so that Archie's law $R_t=aR_w/(\phi^mS_w^n)$ applies without a separate shale or dual-porosity correction.
• 2. The rock matrix and pore fluids are electrically non-conductive — all conduction is through the interconnected, continuous formation-water phase, so resistivity responds only to φ, S_w, and R_w.
• 3. Formation water resistivity R_w (and mud-filtrate resistivity R_mf) is uniform and known at the depth/temperature of interest, obtained either from a water sample, an SP calculation, or a nearby wet zone.
• 4. Invasion is radial and "piston-like" (a sharp, cylindrically symmetric front separating a uniformly filtrate-saturated flushed zone from the undisturbed formation), which is the geometric picture behind the R_xo/R_i/R_t profiles of Question 3.
• 5. The borehole is in gauge, mud-filled, and the tool is properly centralized (or decentralized, per its design) so that standard borehole/mudcake correction charts apply without an extra rugosity correction.
• 6. The bed is thick relative to the tool's vertical resolution (no unresolved thin-bed averaging) and the formation is macroscopically homogeneous and isotropic within the tool's depth of investigation.

The six assumptions are not independent wishes; they fall into two groups, and knowing which group a violation belongs to tells you what to do about it. Assumptions 1 and 2 are about the ROCK and, when they fail, the equation itself has to change: a shaly sand needs a dual-water, Waxman–Smits or V_sh-weighted form because the clay surface conducts in parallel with the pore water, and a vuggy or fractured carbonate needs a dual-porosity model because the conductive path is no longer the intergranular network Archie calibrated on. Assumptions 3 to 6 are about the MEASUREMENT and, when they fail, the equation stands but the numbers fed into it must be corrected first — an R_w carried to formation temperature, a borehole-size and mudcake correction from the tool charts, a bed-thickness (shoulder-bed) correction on the deep resistivity, and an invasion correction backed out of the two- or three-curve resistivity profile. This paper exercises both groups: Questions 8 and 9 apply shale corrections because assumption 1 fails in that well, while Question 7 relies on assumption 5 (an in-gauge hole) for the pad-contact density reading to be trustworthy at all.