Shaly-Sand Models on the Ogbon-1 Well

Chapter 8, Shaly-Sand Saturation Models

Learning objectives

  • Run the Simandoux, Indonesia, Waxman-Smits and Dual-Water models half foot by half foot down Ogbon-1
  • Say why each model reads less water than the truth on a well built as clean Archie, and measure the over-correction
  • Count what the over-correction adds to the net pay and the hydrocarbon column
  • Use the water leg, where the answer is known, to see the over-correction
  • Say when a shaly-sand model does its job: a rock whose clay conducts, and a law that matches it

Back on the Well

Section 8.1 showed why a shaly sand needs more than Archie's equation: the clay carries current in parallel with the formation water, the resistivity falls, and the clean equation reads too much water. Sections 8.2 to 8.5 built four ways to take the clay out: the Simandoux equation (Simandoux, 1963), the Indonesia equation (Poupon and Leveaux, 1971), Waxman-Smits (Waxman and Smits, 1968) and the Dual-Water model (Clavier, Coates and Dumanoir, 1984). This section runs all four down Ogbon-1, the book's well, with the functions the chapter used, and reads each against the truth the well was built from. Figure 8.6 draws it: (a) the density porosity and the shale volume, (b) the water saturation of the model you choose, against the truth and against the clean equation, and (c) how far each model lies from the truth. The depth marker reads one half foot, and the other two controls are the model and the rock.

At 5982 ft, in the shaly oil sand, the shale volume is 22 % and the porosity 18.0 %.The resistivity is 32.5 ohm.m, built as clean Archie, so clean Archie reads 20 %water, the truth. Simandoux reads 13 % water, 6.5 points under the truth, anover-correction: the well has no clay conduction for the model to remove. Over thewhole well Simandoux finds 280.0 ft of net pay and a column of 40.3 ft, 3.0 ft morethan the built pay and 2.2 ft more than the built column; in the shaly oil sand itaverages 12.8 % water against the built 19.6 %.(a) Porosity, shale volume0501005800590060006100620063006400Porosity, shale volume (%)Depth (ft)contact(b) Water saturation050100Water saturation (%)(c) Departure from the truth−100+10Model minus truth (points of Sw)Key: the density porosity (black) and the shale volume (black, dashed) in (a), with the 40 % shalecutoff dashed; in (b) the water saturation of the chosen model (Simandoux, teal), shaded where itdeparts from the truth, with the truth the well was built from (black dots, a dot every 5 ft) and cleanArchie (grey, dotted); in (c) every model minus the truth, Simandoux teal, Indonesia green, Waxman-Smitsred, Dual-Water black dashed and clean Archie grey dotted, left of the zero line under the truth. Thelong dashed line is the oil-water contact and the dotted line the depth read.The readings at 5982 ftWater here 13 % (built with 20 %; 6.5 points under the truth). Pay-average water 19 % (by pore volume21 %; built with 23 %). Hydrocarbon column 40.3 ft (2.2 ft more than the built column). Net pay in thewell 280.0 ft (3.0 ft more than the built pay). Shaly oil sand, water 12.8 % (built with 19.6 %;6.8 points under the truth).

The Well Was Built Clean

Section 7.6 made a point that this section cannot avoid. Ogbon-1's deep resistivity was computed as clean Archie in every bed, the shaly oil sand included, so the well has no clay conduction in it. In the shaly oil sand, 5946 to 6018 ft, where the gamma-ray shale volume averages 21.8 % (the well was built with 21.9 %), clean Archie reads 19.6 % water, which is the truth. A shaly-sand model takes a clay conduction out of a resistivity; here there is none to take out, so each model reads less water than the truth. Averaged over the shaly oil sand the Simandoux equation reads 12.8 %, the Indonesia equation 16.3 %, Waxman-Smits 13.9 % and the Dual-Water model 14.8 %: 6.8, 3.3, 5.7 and 4.8 points under the truth. At 5982 ft, in plate (c), the built water is 20 % and the four models read 13, 16, 14 and 15 %. This is an over-correction, and it is not an improvement. The models are not wrong; they are being asked about a rock that does not have the property they were built for.

What the Over-Correction Costs

Less water is more oil, so the error is not harmless. The well's own numbers, those of Section 7.6, are 277.0 ft of net pay, 23 % pay-average water and a hydrocarbon column of 38.1 ft. With the Simandoux equation the well holds 280.0 ft of pay, 19 % water and a column of 40.3 ft, 2.2 ft more than the truth; the Indonesia equation gives 279.0 ft, 21 % and 39.2 ft; Waxman-Smits 278.0 ft, 20 % and 39.6 ft; and the Dual-Water model 278.0 ft, 21 % and 39.4 ft. The extra pay is all at the foot of the main sand, where the saturation crosses the 50 % cutoff of Section 13.1. At 7758 barrels an acre-foot the Simandoux column is 17 thousand reservoir barrels an acre more than the well holds, on the 296 thousand it does hold.

The Water Leg Gives It Away

On a real well there is no truth to compare with, but Ogbon-1 has a place where the answer is known: the main sand below the oil-water contact, 6213.1 ft, is all water, and clean Archie reads it 100 %. Averaged over its 173 half feet the Simandoux equation reads 95 % water, the Indonesia equation 96 %, Waxman-Smits 99 % and the Dual-Water model 99 %. Each reads a little oil in rock that holds none, the same over-correction as in the shaly sand, made plain.

Letting the Clay Conduct

The second control of Figure 8.6 swaps Ogbon-1 for a what-if rock with the same porosity, shale volume and true water saturation, but whose clay conducts, by the forward law behind the Simandoux equation,

1Rt=ϕm Swna Rw (1−Vsh)+Vsh SwRsh\dfrac{1}{R_t} = \dfrac{\phi^{m}\,S_w^{n}}{a\,R_w\,(1 - V_{sh})} + \dfrac{V_{sh}\,S_w}{R_{sh}}

At 5982 ft its resistivity falls from 32.5 ohm.m to 16.9 ohm.m, and now it is the clean equation that is wrong: it reads 27 % water against the truth's 20 %, 7.5 points over, and averages 27.6 % across the shaly oil sand. The Simandoux equation reads the truth, 19.6 % on average, because it is the inverse of the law the rock conducts by. The other three miss, by up to 6.1 points for Indonesia, 5.7 for Waxman-Smits and 6.3 for Dual-Water, because their laws differ from that one. The what-if rock is the figure's own construction, and it is a Simandoux rock, so these misses are not a ranking of the models. They show what a law the rock does not follow costs. With the clay conducting, clean Archie finds 274.0 ft of pay and a 35.8 ft column, 2.3 ft less than the truth: on a real shaly sand the clean equation errs the other way.

Inputs a Log Does Not Carry

Waxman-Smits and the Dual-Water model need more than a shale volume and a shale resistivity. PetroWiki: "Qv is the cation-exchange capacity (CEC) per unit PV" (Water saturation determination), and it is measured on core, which Ogbon-1 does not have. The figure therefore makes two assumptions of its own. It takes the Qv that gives the clay the same conductance the shale line gives it in the Simandoux equation, so that the Waxman-Smits term is the same size and only the sand term differs; that is the chapter's one way of setting Qv on the well, and Section 8.4's readout on Ogbon-1 takes it too. And it takes the Dual-Water model's bound water as the shale's pore space carried into the sand by the shale volume, using the shale porosity read from the well's shale beds, 9.8 %, and the bound-water resistivity of a shale that is all bound water, 0.0213 ohm.m, against 0.040 ohm.m for the free water. Where a half foot's log holds less water than the bound water its clay is given, the free water is set to 0 rather than printed negative: 29 half feet as built, all in the shaly oil sand. These choices set how far Waxman-Smits and the Dual-Water model sit from the Simandoux equation in the figure; a real evaluation takes them from core.

Choosing, and Closing

As the shale volume goes to zero every one of the models reduces to Archie's equation, so in clean rock the choice does not matter. In a shaly sand it does. The Simandoux and Indonesia equations need only a shale volume and a shale resistivity; Waxman-Smits needs the clay's exchange capacity and the Dual-Water model a description of its bound water. Whatever the data allow, the rock decides which law fits, and this well shows what happens when none does: at 5982 ft the four models differ by 3.3 points among themselves, and all four sit under the truth. So the choice is checked against core or a known result, and the spread among the models is carried as an uncertainty, not hidden by booking whichever gives the most oil. With saturation settled, in clean sand and shaly sand alike, the course turns to the third property the logs do not read directly, permeability.

References

  • Waxman, M. H. and Smits, L. J. M. (1968). Electrical conductivities in oil-bearing shaly sands. SPE Journal, June 1968, 107-122. SPE-1863-A. doi:10.2118/1863-A.
  • Clavier, C., Coates, G. and Dumanoir, J. (1984). Theoretical and experimental bases for the dual-water model for interpretation of shaly sands. SPE Journal, 24(2), 153-168. SPE-6859-PA. doi:10.2118/6859-PA.
  • Simandoux, P. (1963). Dielectric measurements on porous media, application to the measurement of water saturations: study of the behaviour of argillaceous formations. Revue de l'Institut Français du Pétrole, 18 (Supplementary Issue), 193-215.
  • Poupon, A. and Leveaux, J. (1971). Evaluation of water saturation in shaly formations. SPWLA 12th Annual Logging Symposium, Dallas, paper SPWLA-1971-O.
  • PetroWiki. Water saturation determination. petrowiki.spe.org/Water_saturation_determination.

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