Inversion-based Interpretation of Borehole Spontaneous Potential Measurements for Accurate Estimation of Water Resistivity in the Presence of Shoulder-Bed and Mud-Filtrate Invasion Effects

Electrical resistivity of formation water is a fundamental property used to quantify in situ water quality for human consumption or for assessment of hydrocarbon pore volume. Resistivity interpretation methods commonly used to quantify the electrical resistivity of formation water invoke rock porosity and fitting parameters that require additional and independent core measurements. Alternatively, the spontaneous potential (SP) log can be used to calculate water resistivity without knowledge of rock porosity in wells drilled with water-based mud. In combination with resistivity and gamma-ray logs, SP logs can be used to estimate water quality, apparent volumetric concentration of shale, and for qualitative assessments of permeability. However, SP logs often exhibit both shoulder-bed and mud-filtration effects; these effects need to be mitigated before using SP logs for calculation of water resistivity. We develop a new inversion-based method to simultaneously mitigate shoulder-bed and mud-filtrate invasion effects present in SP logs via fast numerical simulations based on Green functions. The interpretation method is implemented on SP logs acquired across aquifers with various degrees of complexity using noisy synthetic and field measurements to estimate equivalent NaCl concentration, radius of mud-filtrate invasion, and sodium macroscopic transport number. Interpretation results compare well to those obtained from resistivity and nuclear logs, provide estimates of uncertainty, and can incorporate a priori knowledge of aquifer petrophysical properties in the estimation.