Effective-Medium Resistivity Models for Calculating Water Saturation in Shaly Sands
Charles R. Berg: ResDip Systems

Abstract: A saturation equation is derived from effective-medium theory (the Hanai-Bruggeman equation) for calculating water saturation from resistivity and porosity measure- ments. That saturation equation is then incorporated into dispersed-clay and laminated-shale models. The five basic variables needed for the saturation formula include whole-rock porosity, true formation resistivity, water resistivity, cementation exponent, and grain resistivity. In the dispersed-clay model, whole-rock porosity, true formation resistivity, and water resistivity are calculated by standard log-analysis methods. Next, cementation exponent and grain resistivity are calculated for the whole rock. These five variables are then used in the saturation equation to calculate whole-rock saturation that is, in turn, used to calculate effective saturation. Intermediate variables used in calculation include clay volume and effective porosity in addition to sand and shale counterparts for porosity, cementation exponent, and grain resistivity.
In the laminated-shale model, shale resistivity is subtracted from the whole-rock properties by resistors-in-parallel treatment and effective saturation is then calculated directly from the saturation equation using only sand input variables. The shaly sand models are proved accurate and stable by calculations on some published log data, including low-resistivity, low-contrast examples. Saturations can be determined from standard log suites. The variables used are calculated in a straightforward manner, while the calculation sequence is flexible to allow for unusual conditions such as nonclay microporosity.