The Rw Problem

Three Routes to One Water

Every saturation in this chapter starts from the resistivity of the formation water, $R_w$, and the book has already found it three ways. Section 1.6 took it from the water leg, the wet sand below the oil-water contact, where the log is its own wet line: 173 half feet of the main sand, 6213.5 to 6300 ft, all give 0.040 ohm.m. Section 2.2 took it from the water's salinity and temperature, and Section 3.5 from the SP. On Ogbon-1 the three agree, because the well was built from one $R_w$ and its resistivity, its SP and its salinity were all computed from it. A real well gives no such agreement, and this section is about choosing among the routes when they differ and about what the difference costs. Figure 7.5 gives each route the input that can go wrong in it, and shows what the $R_w$ it then returns does to the saturation and the net pay. The errors it offers are the figure's own, chosen to show each route's weakness; none is the measured error of a real well.

What Each Route Needs

The water leg needs a wet sand that is clean and a porosity. In the AAPG Wiki's account of the Archie method, "This zone must be 100% water saturated and must not contain any clay or shale." It needs no sample and no temperature: the resistivity of a wet sand already is the water's at the formation's own temperature. Ogbon-1's main sand is 8 % shale by its gamma ray, so by that wording it is not clean; the well's resistivity was built clean, which is why its water leg is exact (Chapter 8 takes up shaly sands). Its weak input is the matrix density behind the porosity. The leg's $R_w$ is $R_t\,\phi^m/a$, so with $m = 2$ it goes as the square of the porosity: a matrix density 0.05 g/cc too high reads every porosity too high and gives 0.047 ohm.m, 1.17 times the well's; 0.05 g/cc too low gives 0.033 ohm.m, 0.83 times.

Salinity and temperature needs a sample and a temperature. The AAPG Wiki calls a sample of the formation water, with its resistivity measured, the most direct way, but says that "formation water samples, if available, are invariably contaminated by mud filtrate", which is the fresher water, so a contaminated sample reads too resistive. Ogbon-1's water would have 122,000 ppm at the 122 °F that Section 2.2 gives it. A sample half as salty, 61,000 ppm, reads 0.070 ohm.m, 1.76 times the well's, not twice, because the resistivity of a brine does not double when its salt halves (Section 2.2); one twice as salty, 244,000 ppm, reads 0.024 ohm.m, 0.61 times. The temperature matters as well, through Arps's rule: a temperature taken 20 °F too high gives 0.035 ohm.m, 0.87 times the well's, and one taken 20 °F too low gives 0.047 ohm.m, 1.18 times.

The SP needs a thick, clean sand, and a temperature for both $K$ and the filtrate. The AAPG Wiki says the method assumes "that the beds are clay free" and "does not give correct estimations of Rw in hydrocarbon-bearing zones"; Ogbon-1's SP does not know what fills the bed, and a real sand is not so forgiving (Section 3.5). Left as it stands, the shaly oil sand's deflection, with 22 % of the bed shale, gives 0.066 ohm.m, 1.66 times the well's, because shale shrinks the deflection and a smaller deflection looks like a fresher water; the upper oil sand, 6 % shale, gives 0.046 ohm.m, 1.15 times. Allowing for the shale (Section 3.5) returns 0.040 ohm.m in both. A temperature error moves this route the same way it moves the salinity route: 0.035 ohm.m, 0.88 times, for a temperature taken 20 °F too high, and 0.049 ohm.m, 1.21 times, for one taken 20 °F too low. The figure runs the salinity route at the 122 °F of Section 2.2 and the SP route at the 75.2 °F where the well's $K$ of 71 belongs (Section 3.5), because Ogbon-1 has no formation temperature of its own; a temperature error is measured from the one its section used.

What an Error Costs

Whichever route is taken, the $R_w$ goes into Archie's equation (Section 7.1), and with $n = 2$ the saturation goes as its square root. An $R_w$ twice the right one reads 1.41 times the water: the pay of the upper oil sand, 19 % water, reads 27 %. One half the right one reads 0.71 times: 13 %. The net pay moves less evenly. Section 1.6 found that a wet line drawn with twice the water leg's $R_w$ takes the net pay from 277.0 to 256.0 ft, 21.0 ft less, and one drawn with half takes it to 290.0 ft, 13.0 ft more, because the saturation in the transition zone climbs more steeply toward the contact than it falls away from it. Plate (b) draws that for every $R_w$ from 0.015 to 0.10 ohm.m, and the routes make the same bargain with their own errors. The sample half as salty takes the upper sand to 25 % water, the net pay to 261.0 ft, 16.0 ft less, and the hydrocarbon column from 38.1 to 32.4 ft; the sample twice as salty adds only 10.0 ft. The shaly sand's deflection left in the SP takes the net pay to 263.0 ft, 14.0 ft less. In the main sand, plate (c), the error is a shift of where the pay ends: 6190.5 ft in the well, 6174.5 ft with the half-salt sample.

Choosing Among the Routes

The AAPG Wiki says "It is quite common and good practice to determine Rw with more than one method, if possible, to check for consistency and reliability." The figure's third readout is that check, and where the routes differ the pattern says which input to doubt. A wrong temperature moves the salinity route and the SP route together and leaves the water leg alone; a wrong matrix density moves only the leg; a contaminated sample moves only the salinity route; shale left in the deflection moves only the SP. The wiki adds that where the methods differ "the values obtained can be averaged". An average takes the wrong route's error with it: the three routes with the half-salt sample read 0.040, 0.070 and 0.040 ohm.m, which average 0.050 ohm.m, 1.25 times the well's. So find the input that is wrong first, and where it cannot be found, take the route whose input is best known: a water leg exists only where the well has a clean wet sand, which Ogbon-1 has. Ogbon-1 offers no such doubt, since it was built forward from 0.040 ohm.m, and a real well has no truth to check against; the only check is the agreement of independent routes.

References

• AAPG Wiki. Water resistivity determination. wiki.aapg.org/Water_resistivity_determination.