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Organic contaminants in ground water, such as those in landfill leachate or hydrocarbon spills, are of concern when they impact drinking water. Self potentials have been proposed as a rapid, simple and inexpensive method for mapping a plume from the ground surface as it is hypothesized they may be sensitive to gradients in the redox potential that develop around such plumes in some cases. We conducted self potential and resistivity surveys on two sites with hydrocarbon contaminant plumes in ground water and did not find a correlation between redox and self potentials, even after the electrical measurements were corrected for anthropogenic noise. To further explore the relationship between contaminant plumes and self potentials, we undertook modeling based on coupled fluxes. We used a finite element code and, as input, simulation results from a kinetic reactive transport model of a hypothetical hydrocarbon spill. Two types of source currents were tested. The first type is sources caused by diffusion, modeled using the Nernst-Plank equation. The diffusion model does not produce anomalies at the ground surface greater than 2 mV, which would be in the range of measurement error and within normal background variations in the field. The second type is sources caused by redox potential gradients, using an equation that assumes a transition zone where charge transfer is through a hypothetical electronic conductor, perhaps microbial nanowires or bioprecipitated minerals. For the case of the electronic conductor transition zone, the strength of the surface SP signal is affected by the electrical conductivity of the transition zone. The only scenarios that produced measureable self potential anomalies at the ground surface were those using the redox hypothesis with a transition zone that did not have very large electrical conductivity compared to background and strong Eh gradients.