Question 2 of 11: Invasion profiles — transition and annulus zones
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Notes on this paper
National Exams — December 2016. 98-Pet-B1, Well Logging and Formation Evaluation (every question is log-interpretation content, not gas-engineering material). 3-hour closed-book exam, 11 questions, all marked, calculators and attached graphs/formula sheet permitted.
Reference texts: Bassiouni, Theory, Measurement, and Interpretation of Well Logs (SPE Textbook Series Vol. 4); Asquith & Krygowski, Basic Well Log Analysis, 2nd ed.; Ellis & Singer, Well Logging for Earth Scientists, 2nd ed.; Schlumberger, Log Interpretation Charts.
Check: Q3, Q7, Q8, Q9(b), Q10 and Q11 are built on the paper's printed logs and attached charts. Values printed as annotations on the logs (Q11's SSP, PSP and GR labels) are used exactly as printed. Values read off a curve or a chart (Q9(b) and the Q8 chart check, Q10's track readings) are read from the printed figure and flagged inline with their precision. All arithmetic that follows is exact.
Question 2: Invasion profiles — transition and annulus zones (5 marks)
Fig. Q2 — Idealized resistivity-vs-radius invasion profiles. Left: transition (gradual step) profile. Right: annulus profile, with a local resistivity peak between the flushed and uninvaded zones.
(i) Transition profile. Resistivity moves gradually and monotonically from $R_{xo}$ (flushed zone, near-wellbore) out to $R_t$ (true, uninvaded formation resistivity) with no local maxima or minima — a smooth "step" rather than a sharp discontinuity. This is the profile expected where the mud-filtrate front mixes progressively with formation water/hydrocarbon over a finite annular thickness (moderate permeability, moderate mud-cake quality), so there is no single sharp invasion-front radius; resistivity tools of increasingly deep depth of investigation (SN, ILD/LLD) read a smoothly increasing sequence of apparent resistivities.
(ii) Annulus profile. Resistivity rises from $R_{xo}$, overshoots to a local peak resistivity higher than either $R_{xo}$ or $R_t$, then falls back down to $R_t$ farther from the wellbore. The annulus effect arises in a water-bearing sand invaded by fresh mud filtrate: filtrate moves faster than the connate-water bank it displaces (viscous fingering/piston-like advance), leaving a transient ring of largely un-displaced but freshened formation water — locally more resistive than either the flushed zone (filtrate-saturated) or the far, unaltered formation (original connate water) — immediately behind the invasion front. It is a transient feature that dissipates with time as the water bank equilibrates, and it is diagnostic of a water-bearing (not hydrocarbon-bearing) zone, since the mechanism requires a mobile connate-water bank ahead of the filtrate.
