Understanding unsaturated flow behaviors in fractured rocks is essential for various applications. A fundamental process in this regard is flow splitting at fracture intersections. However, the impact of geometrical properties of fracture intersections on flow splitting is still unclear. This work investigates the combined influence of geometry (intersection angle, fracture apertures, and inclination angle), liquid droplet length, inertia, and dynamic wetting properties on liquid splitting dynamics at fracture intersections. A theoretical model of liquid splitting is developed, considering the factors mentioned above, and numerically solved to predict the flow splitting behavior. The model is validated against carefully-controlled visualized experiments. Our results reveal two distinct splitting behaviors, separated by a critical droplet length. These behaviors shift from a monotonic to a non-monotonic trend with decreasing inclination angle. A comprehensive analysis further clarifies the impacts of the key factors on the splitting ratio, which is defined as the percentage of liquid volume entering the branch fracture. The splitting ratio decreases with increasing inclination angle, indicating a decrease in the gravitational effect on the branch fracture, which is directly proportional to the intersection angle. A non-monotonic relationship exists between the splitting ratio and the aperture ratio of the branch fracture to the main fracture. The results show that as the intersection angle decreases, the splitting ratio increases. Additionally, the influence of dynamic contact angles decreases with increasing intersection angle. These findings enhance our understanding of the impact of geometry on flow dynamics at fracture intersections. The proposed model provides a foundation for simulating and predicting unsaturated flow in complex fractured networks.

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Keywords: Fracture rock, Fracture intersection, Unsaturated flow, Intersection angle