Hypothesis & Motivation
Experimental data suggest a relationship between the macroscopic zeta potential measured on intact rock samples and the sample wettability. However, there is no pore-scale model to quantify this relationship.

Methods
We consider the simplest representation of a rock pore space: a bundle of capillary tubes of varying size. Equations describing mass and charge transfer through a single capillary are derived and the macroscopic zeta potential and wettability determined by integrating over capillaries. Model predictions are tested against measured data yielding a good match.

Findings
Mixed- and oil-wet models return a macro-scale zeta potential that is a combination of the micro-scale zeta potential of mineral-brine and oil-brine interfaces and the relationship between macro-scale zeta potential and water saturation exhibits hysteresis. The model predicts a similar relationship between zeta potential and wettability to that observed in experimental data but does not provide a perfect match. Fitting the model to experimental data allows the oil-brine zeta potential to be estimated at conditions where it cannot be measured directly. Results suggest that positive values of the oil-brine zeta potential may be more common than previously thought with implications for surface complexation models and the design of controlled salinity waterflooding of oil reservoirs.