Determining Formation Water Resistivity From Chemical Analysis
Authors: Moore E.J. , Szasz S.E. , Whitney B.F. 
Published: December 2007

Abstract
An accurate value of formation water resistivity Rw is essential in calculating formation porosity and fluid saturation from electrical well logs. In the cases where Rw has not been measured directly, it must be obtained from other data, e.g., the SP curve. This paper deals with another approach: how to calculate Rw, from the chemical analysis of the formation water.
Introduction
It is known that the resistivity of aqueous solutions of pure salts depends on their concentration and on the temperature; the concentrations are given in MPL (mg of solute per liter of solution), or sometimes in ppm (mg of solute per kg of solution): MPL = ppm X specific gravity. Values for different pure salts are available in the literature, but not for solutions of mixtures which are of practical interest. The major component of the dissolved material in almost all formation waters being sodium chloride, it is customary to express the resistivity of formation waters in terms of equivalent sodium chloride concentration, i.e., the concentration of a solution of pure NaCl which has the same resistivity at a given temperature as that of the formation water under consideration. Thus, the problem of calculating Rw from the chemical analysis can also be stated as how to convert the other constituents of the solute into equivalent NaCl concentration. Salts dissolved in water are at least partly dissociated into ions, and do not conserve their identity. If known amounts of several salts are dissolved in water, the solution does not necessarily contain the same salts in the original proportion, but perhaps some other combination of the ions, along with free ions in solution. This is why the chemical analysis of formation waters is often given in terms of ion, as if all dissolved salts were completely dissociated. Our problem then boils down to how to convert the concentrations of the various ions to equivalent concentrations of Na+ and Cl. Dunlap and Hawthorne have proposed to convert the concentration of all other ions to equivalent Na+ and Cl-concentrations by means of constant multipliers; e.g., 0.95 for Ca++: 2.0 for Mg++; 0.27 for HCO-; 0.5 for SO--, etc. Their factors were based on measurements made at 68F on 26 formation water samples from the Texas Gulf Coast, ranging in concentration from 1,500 to 75,000 ppm. Dunlap method is widely used in electric log interpretation, and is often extrapolated beyond its original concentration range. A comparison of Rw, values calculated by this method and values actually measured on formation water samples has shown large discrepancies, especially at higher concentrations. Therefore, two new methods were developed at Sinclair Oil Corp's Tulsa Research Center to calculate equivalent sodium chloride concentration from the chemical analysis of formation water samples.
FUNDAMENTAL CONSIDERATIONS
The resistivity of a solution, or its reciprocal the conductivity, at a given temperature is determined by the charge, concentration and mobility of the ions actually present. Monovalent ions such as Na+ or Cl- always carry the same charge. Compounds of polyvalent ions, however, may show incomplete dissociation, e.g., NASO4- + Na+ instead of SO4-- + 2Na+. This happens especially in more concentrated solutions. Only very dilute solutions are completely dissociated, as assumed in the chemical analysis report. At higher concentration, the degree of dissociation depends not only on the nature and concentration of the particular salt under consideration but also on the nature and concentrations of the other solutes. Mobility of the ions depends on the viscosity of the solution. It also depends on the degree of hydration of the ions, which in turn is a function of the nature and the charge of the ions and also of the amount of free water available per ion, i.e., the total ionic concentration. The net effect is that the conductivity increases slower than proportional to the concentration, even if a solution contains only one salt such as NaCl, and is different for different salts (Fig. 1). Conductivity can even decline with a further increase in concentration, e.g., if additional salt is little dissociated but ties up some of the free water and/or causes an increase in viscosity. In solutions containing more than one salt, the contribution of one salt to the total conductivity depends not only on the fractional concentration of this same salt, but also on the concentration of all other solutes. A perfect method would give the conductivity or resistivity of a solution as a function of the concentrations of all solutes present. This is so complicated as to be impractical, and a simpler method must be found which is of acceptable accuracy.
JPT
P. 373ˆ