document preview

The Waxman-Smits physical model for describing conductivity in shaly sand has been extended to allow for oil-bearing sand, and the required assumptions have been confirmed by laboratory measurements. A conclusion from the tests is that the effective concentration of clay-exchange cations increases in proportion to the decrease in water saturation. The temperature coefficients of electrical conductivity for a group of shaly sands were measured and these data were treated by the same model.

Introduction

Waxman and Smits have recently advanced a simple physical model describing shaly sand conductivities. physical model describing shaly sand conductivities. The model assumes: (1) a parallel conductance mechanism for free electrolyte and clay-exchange cation components, (2) an exchange cation mobility that increases to a maximum and constant value with increasing equilibrating electrolyte concentration, and (3) identical geometric conductivity constants applicable for the contributions of both the free electrolyte and the clay-exchange cation conductance to the sand conductivity. The general equation for water-saturated sands is then obtained: ..........................................(1)

with

..........................................(2)

Co and Cw are the specific conductances of the sand and equilibrating brine, respectively (mho cm). F* is the shaly sand formation resistivity factor, related to porosity (0) according to an Archie-type relation:

..........................................(3)

where m* is the porosity exponent. 1/F* is the slope of the straight-line portion of the Co vs Cw, curve. Qv is the effective concentration of clay-exchange cations (equiv/liter or meq/mi) and can be determined independently from the ratio of cation exchange capacity (meq per 100 gm of rock) per unit pore volume of rock (ml per 100 gm of rock). B represents the equivalent conductance of the clay counterions as a function of Cw with units of mho cm2 meq -1. lambda Na (or B max) is the maximum equivalent ionic conductance of the (sodium) exchange ions, and a and lambda are empirical constants. Waxman and Smits report values (Group 1 samples) of a = 0.83, = 0.02, and lambda Na = 38.3 cm2 equiv- 1 ohm-1 at 25 degrees C. Somewhat different values of the a, y, and lambda Na were reported by Waxman and Smits for another and considerably smaller set of shaly sand samples (Group 2). These were a = 0.6, lambda = 0.013, and lambda Na = 46.0 CM2 equiv-1 ohm-1 at 25 degrees C. Further work reported here (Table 2) supports the values obtained for the Group 1 samples. The Qv values calculated from conductivity data and a value of lambda Na = 38.3 cm2 equiv-1 ohm-1 agree within experimental error with Qv values determined by independent laboratory procedures for the new group of shaly sands used for this study.

JPT

P. 213