An investigation of the exponent m in Archie's equation : comparing a numerical modeling approach with laboratory data

Archie’s equation is used routinely in estimating the water saturation of reservoirs, or for estimating a value for the reservoir water resistivity in the water leg. We consider experimental results from the laboratory for a range of samples exhibiting various grain-shapes, and mixtures of differently-shaped grains. These are combined with a numerical modeling approach, considering 3D flow of electric current around ‘typical’ grain shapes and is extended and applied to spheres and ellipsoids. Numerical modelling, considering a single, spherical grain, led to values of Archie’s ‘m’ parameter in excellent agreement with those obtained for large numbers of sand-sized glass spheres deposited and compacted in the laboratory. Similarly, for platy grains their orientation relative to the direction of flow of electric current is shown to be critical, in line with the efficiency concept proposed by Herrick and Kennedy (1993). Existing results for two-component mixtures of differently-shaped grains, namely: quartz sands, glass spheres and shell fragments are considered. Predictions made of Archie’s ‘m’ parameter for such mixtures, on the basis of their proportion and laboratory-determined values of ‘m’ for each component, matched laboratory derived values, suggesting the prospect of predicting Archie’s ‘m’ parameter on the basis of grain properties (e.g. shape) alone. Each individual sample, including these mixtures, obeyed Archie’s equation. Samples having differently shaped grains, however, when plotted together were better-described by Winsauer’s equation, although the values of ‘m’ derived from Archie and Winsauer’s equations were quite different. Our approach is applied to estimating m from a knowledge of the grains themselves, even though a sample may be highly disturbed and has been applied to sediment-hosted methane hydrate from the Cascadia Margin. Improving the possibilities for reservoir characterization in loose sands and sediment hosted methane hydrates.