Abstract
Using borehole geophysics to map groundwater total dissolved solids (TDS) has become an important method for monitoring groundwater TDS in and around oil fields. This method typically uses a series of empirical relationships, including Archie's equation, to estimate TDS from deep-reading formation resistivity. The method also involves an equation that relates water resistivity to TDS and the temperature of the water; therefore, the method requires an understanding of the temperature field. In some oil fields, temperature follows the local geothermal gradient, which can be estimated using bottom-hole temperature measurements. However, in thermal oil fields, temperature perturbations arising from steam injection prevent accurate TDS calculations unless temperature is observed and modeled. Here, we present a new method of modeling the temporal and spatial structure of TDS that uses available borehole resistivity and porosity data along with temperature logs from nearby observation wells. This method uses a Gaussian process to jointly model non-collocated resistivity, porosity, temperature, and TDS observations. The model yields volume maps of all four quantities. We apply this method to the San Ardo Oil Field in Monterey County, California, a field that has undergone extensive thermal-enhanced oil recovery. This oil field has an unusual number of publicly available temperature logs spanning 2006 to 2019, allowing understanding of the temporal and spatial temperature structure during this time. We expect techniques developed here will apply to other thermal oil fields in the future.