Formation Resistivity Factor

The formation resistivity factor, FR, is the ratio of the resistivity of a porous medium that is completely saturated with an ionic brine solution divided by the resistivity of the brine:

where Ro is the resistivity (ability to impede the flow electric current) of a brinesaturated rock sample in ohm-m, R, is the resistivity of the saturating brine in ohm-m, and FR is dimensionless. The formation resistivity factor, which is always greater than one, is a hnction of the porosity of the rock (amount of brine), pore structure, and pore size distribution. Other variables that affect formation factor include composition of the rock and confining pressure (overburden). Archie [42] proposed an empirical fornula that indicated a pa-law dependence of F, on porosity

where t$ is porosity and m is a constant (commonly called the cementation factor) related to the pore geometry. The constant, m, was the slope obtained from a plot of FR vs. porosity on log-log paper. For consolidated, shale free sandstones, the value of m ranged from 1.8 to 2. For clean, unconsolidated sands, m was found to be 1.3, and Archie speculated that m might vary from 1.3 to 2 for loosely or partly consolidated sands. Fquations 5-45 and 5-46 were also combined by Archie to give:

so that a reasonable estimate of F, or Ro can be made if the slope, m, is obtained. Several other correlations [43-551, mostly empirical, between formation factor and porosity have been reported in the literature and these are summarized in Table 5-7. From an analysis of about 30 sandstone cores from a number of different reservoirs throughout the United States, Winsauer et al. [45] presented what is now known as the Humble relation:

Results of a logging study in the Brown Dolomite formation, in which the resistivity of the mud filtrate was the same as the connate water, were used by Owen [48] to establish a relationship between the true formation factor and porosity. Shown in Figure 5-29 are the rerationships obtained with the equations of Archie, Winsauer, et al., and Tixier.