Mathematical-physical reappraisal of Archie's first equation on the basis of a statistical network model

Knowledge of the geometrical properties of porous rocks is crucial for the evaluation of their hydrocarbon potential. A major problem in quantitative formation evaluation is to provide a physical basis of Archie's equations first published in 1942, which are widely used in formation evaluation and are believed to reflect this knowledge empirically. Our study, a theoretical model-based approach, provides a physical basis of Archie's first equation (Archie I) and puts it up for scientific discussion. We employ the statistical network model theory of Schopper, and take sedimentation and favorable diagenetic conditions restricted to compaction into account. We find that compaction is a prominent geological feature that needs to be considered and quantified in order to establish a physical basis of Archie I. Our interpretation of Archie I - that it measures in relative terms - is in agreement with this finding, but not in line with the mainstream view, which interprets Archie I in absolute terms. Evidence suggests that compaction may also provide the overarching physical basis to address within-well integration of borehole-geophysical data (including resistivity data) as well as their integration across spatial scales from well-to-well and beyond. Although our more consistent understanding of Archie's first equation clearly helps to advance today's evaluation of resistivity logs, the gain in evaluating these logs is still not satisfactory.