This
guarantees that the response falls back to the Archie equation
when Vsh = 0.0. Thus: Where: CONDh
and CONDi both equal 0.0 so these two terms disappear. 1/F is
equal to (PHIe^M)/A, CONDsh equals 1/ RSH, and CONDw is equal
to 1/RW@FT. For the Simandoux equation, 1/Fsh is set equal to
Vsh/2. Various authors have proposed other assumptions for the
term 1/Fsh, so several forms of this equation are in use. When N = 2.0, this can be solved for Sw by using the standard quadratic equation solution. The first term is the standard Archie equation for the non-shale portion of the matrix, and the second term is a correction factor for the shale fraction. The Simandoux equation is one of the most popular and successful equations in common use which includes a shale correction for the saturation calculation.
4: THEN C = (1 - Vsh) * A * (RW@FT) / (PHIe ^ M) 5: D = C * Vsh / (2 * RSH) 6: E = C / RESD 7: Sws = ((D ^ 2 + E) ^ 0.5 - D) ^ (2 / N) 8: OTHERWISE Sws = 1.0 Where:
1. Simandoux, P., 1963, Dielectric measurements in porous media and application to shaly formation: Revue de L’Institut Français du Pétrole, v. 18, Supplementary Issue, p. 193–215. 2. Evaluation of Water Saturation in Shaly Formations A. Poupon, J. Leveaux, SPWLA, 1971. There are various versions of the Simandouc equation: the original, modified , and Indonesian. For a clear review of these, click HERE. For other variations, see Schlumberger Log Interpretation Principals / Applications, pages 8-15 and 8-16, 1989. Page numbers may vary in other editions. The Simandoux equation requires a three chart solution, given below. Because of their complexity, charts are not recommended.
There are many variations of the Simandoux equation. This version seems to work well in all areas of the world; in all environments.
for carbonates A = 1.00 M = 2.00 N = 2.00 (Archie Equation as first published) for sandstone A = 0.62 M = 2.15 N = 2.00 (Humble Equation) A = 0.81 M = 2.00 N = 2.00 (Tixier Equation - simplified version of Humble Equation) Asquith (1980 page 67) quoted other authors, giving values for A and M, with N = 2.0, showing the wide range of possible values: Average sands A = 1.45 M = 1.54 Shaly sands A = 1.65 M = 1.33 Calcareous sands A = 1.45 M = 1.70 Carbonates A = 0.85 M = 2.14 Pliocene sands S.Cal. A = 2.45 M = 1.08 Miocene LA/TX A = 1.97 M = 1.29 Clean granular A = 1.00 M = 2.05 - PHIe
RSH = 4.0 ohm-m PHIe = 0.11 RESD = 1.0 ohm-m A = 0.62 M = 2.15 N = 2.00 RW@FT = 0.015 ohm-m C = (1 - 0.33) * 0.62 * 0.015 / (0.11 ^ 2.15) = 0.717 D = 0.717 * 0.33 / (2 * 4.0) = 0.0296 E = 0.717 / 1.0 = 0.717 Sws = ((0.0296 ^ 2 + 0.717) ^ 0.5 - 0.0296) ^ (2 / 2.0) = 0.81 This
compares with an Sw of 1.03 for the Archie method. |
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