Three-dimensional modelling of streaming potential

The self-potential (SP) method responds to the electrokinetic phenomenon of streaming potential and has been applied to hydrogeologic and engineering investigations to aid in the evaluation of subsurface hydraulic conditions. To enable the study of variably saturated flow problems of complicated geometry, a 3-D finite volume algorithm is developed to evaluate the SP distribution resulting from subsurface fluid flow. The algorithm explicitly calculates the distribution of streaming current sources and solves for the SP given a model of hydraulic head and prescribed distributions of the streaming current cross-coupling conductivity and electrical conductivity. The forward solution is verified by comparing it with an analytical solution for a point source of flow and measured data taken at the surface of a homogeneous embankment. We apply the forward model to a synthetic pumping well example to illustrate that heterogeneous physical property distributions can result in significant charge accumulation. The sign and magnitude of this secondary charge is determined by the physical property and potential gradients at the interface, and can complicate the interpretation of SP data when a single primary flow source is assumed. The 3-D character of the SP response to seepage through an embankment and foundation is illustrated in a preliminary study of SP data collected at a dam site in British Columbia.