Permeability on the Ogbon-1 Well

A Permeability Log

Section 9.2 set out Timur's equation, which turns a porosity and an irreducible water saturation into a permeability:

with $\phi$ and $S_{wi}$ in per cent and $k$ in mD. Figure 9.6 runs it down every half foot of Ogbon-1, the book's well, in the 386 ft of net reservoir that the book's cutoffs leave ($V_{sh} \le 40\%$ and $\phi \ge 8\%$), using the density porosity of Section 4.2 and the Archie water saturation of Section 7.6. Ogbon-1's own permeability is this equation with an irreducible water saturation of 18 %, applied in its net reservoir when the well was built: the 410, 109, 6.6 and 704 mD of the pay in its four beds that Section 1.4 quotes. It is a model and not a core measurement, so the figure can ask one clean question: what does Timur's equation return when it is given a different water?

The Log's Water Is Not the Irreducible Water

Timur (1968) measured the irreducible water saturation on cores with a centrifuge (PetroWiki): it is the water a rock holds back. A log reads the water that is there. In a tall oil column the two are close, but PetroWiki is plain about the rest: "within the transition zone, only part of the water is irreducible (Swi); the remainder is movable", and so "a log-based estimate of saturation immediately above the oil/water contact will overestimate Swi." Because the water stands under a square in Timur's equation, too much water is too little permeability. For the same rock, the estimate over the well's permeability is

whatever the porosity, because the porosity cancels.

Ogbon-1 shows each case. In the upper oil sand the log reads 19 % water at 5890 ft, 1 point over the well's 18 %, so Timur gives 387 mD against the well's 425 mD, 1.1 times too low. The main sand does not come as close: its pay is the foot of a short column, its top 114 ft above the free-water level (Section 11.3), and the lowest water in it is 26.6 %, at 6136 ft. Its pay averages 198 mD by the log's water against the well's 704 mD, 3.6 times too low. Below the oil-water contact, 6213.1 ft, the log reads 100 % water and the estimate at 6230 ft is 22 mD against the well's 670 mD, 31 times too low, in a rock whose porosity is 25.7 %, as at 6150 ft (25.6 %), and whose permeability is as high (670 mD against 655 mD). Run on the log's water, 164 ft of the 386 ft of net reservoir is wrong by more than 2 times (a yardstick of the figure's own), and the geometric mean in the pay is 66 mD against the well's 101 mD.

Give It the Right Water

With one irreducible water saturation of 18 % for every foot, the estimate lies on the well's permeability: 655 mD at 6150 ft, 670 mD at 6230 ft, and 704 mD across the main sand's pay. That match is exact only because Ogbon-1 was built with this equation and this water. Timur's equation is an empirical relationship, fitted to 155 sandstone samples from three oil fields (PetroWiki), so on a real well even the right water would not return a core's permeability exactly. The tight limestone lies outside those sandstones: the well applies the equation to it too, so its 6.6 mD is the well's, built the same way, and not a limestone measurement.

A wrong value does not show itself. At 12 % every foot of the well reads 2.3 times too high; at 30 %, 2.8 times too low. The permeability goes as the inverse square of the water, and the ratio is the same from the top of the log to the bottom, so no feature of the log gives the mistake away. The right water has to come from somewhere other than the log's saturation: the capillary-pressure curve of Chapter 11, which says how much water a rock holds at each height, or the bound fluid that nuclear magnetic resonance measures (Section 9.5 and Chapter 10).

Onward

Porosity, water saturation and now permeability are all in hand, each with the assumption that bounds it. Section 10.1 turns to nuclear magnetic resonance, a tool that listens to the pore fluids themselves.

References

• PetroWiki (SPE). Estimating permeability based on surface area and water saturation. https://petrowiki.spe.org/Estimating_permeability_based_on_surface_area_and_water_saturation
• Timur, A. (1968). An investigation of permeability, porosity, and residual water saturation relationships. SPWLA 9th Annual Logging Symposium, paper J.