Choosing a Simple Stress-Conductivity Relationship for Shale

Abstract

A fitted stress-conductivity curve can describe a loading branch accurately while remaining unreliable outside the fitted interval. This note compares exponential and power-law forms using a deliberately synthetic calibration point. Both reproduce the selected point but diverge at higher stress, illustrating why goodness of fit alone does not establish extrapolation quality. A practical model-selection procedure is proposed that separates loading history, exposure, specimen identity, and validation.