Question 4 of 10: Transition and Annulus Invasion Profiles

Question 4: Transition and Annulus Invasion Profiles (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.

Given. The radial invasion picture of Question 3: mud cake at the wall, a flushed zone (R_xo, S_xo) next to the hole, and the undisturbed formation (R_t, S_w) beyond the reach of the filtrate. A fresh water-base mud is assumed, so R_mf > R_w.

Find. One resistivity-versus-radial-distance diagram for (i) a transition profile and one for (ii) an annulus profile, with a description of each.

Approach. Resistivity follows the fluid that fills the pores at each radius (Archie: R rises as the conductive water saturation falls or as the water becomes fresher). Draw how the filtrate and the formation fluids are distributed outward from the wall, then convert that distribution to resistivity. Both profiles share the same end points, R_xo at the wall and R_t far out; they differ in what happens between them.

i) Transition profile

In a transition profile the flushed zone does not end at a sharp front. Filtrate saturation falls gradually from S_xo at the edge of the flushed zone (diameter d_i) to the native S_w at the outer limit of invasion (diameter d_j). Between d_i and d_j the pore fluid is a mixture of filtrate and formation fluid in changing proportions, so resistivity grades continuously from R_xo to R_t with no local maximum or minimum. The diagram shows a water-bearing zone with fresh mud: R_xo > R_t and resistivity falls smoothly across the transition. In a hydrocarbon zone the same shape can run the other way (R_xo < R_t), but it stays monotonic. This is the most realistic description of ordinary invasion, and it is why a single "step" invasion diameter is only an approximation. Deep, medium and shallow resistivity tools each average a different part of the grade.

ii) Annulus profile

An annulus profile occurs only in hydrocarbon-bearing zones, typically oil or gas zones of good permeability and high hydrocarbon saturation. The invading filtrate displaces both the movable hydrocarbon and the movable formation water. Hydrocarbon has the higher relative mobility and moves ahead more easily, so formation water is banked into a ring just beyond the flushed zone. That ring, the annulus, has a HIGHER water saturation than the uninvaded zone, and it is filled with the saline formation water rather than fresh filtrate. Its resistivity R_an is therefore lower than both R_xo (fresh filtrate) and R_t (hydrocarbon). The profile is: R_xo high near the hole, a low-resistivity dip at the annulus, then a rise to the high R_t of the hydrocarbon zone.

The annulus is transient. The banked water disperses by diffusion and gravity within days to weeks, so it is seen mainly on logs run soon after drilling. When present it matters, because a deep induction tool sits in the low-resistivity ring. The deep reading is pulled down, R_t is underestimated and S_w is overestimated, and a productive zone can be passed over as wet. A medium-deep reading that is lower than the deep reading but inconsistent with a simple invasion correction is the usual clue.