Droplet flow behavior and splitting dynamics at three-dimensional fracture intersections: A theoretical and experimental study

Abstract

Studying droplet behavior at intersections within three-dimensional fractured media is crucial for predicting fluid flow and solute transport. However, the relationship between droplet splitting at these intersections and macroscopic quantities like flow rate is still unclear. In this study, we developed and validated a theoretical model to describe droplet splitting in three-dimensional fractures using laboratory visualization experiments. Our findings show a strong alignment between the model’s predictions and the experimental data, indicating the model’s effectiveness in simulating real-world droplet behavior. We observed droplet behavior and transformation within a single three-dimensional fracture, noting that size is influenced by flow rate, aperture, contact angle, and inclination. Using these variables, we determined the capillary barrier size at intersections. We used our model to predict droplet splitting at intersections, defining three modes: Type I, full invasion of the horizontal fracture; Type II, partial invasion; and Type III, complete crossing of the fracture. Sensitivity analysis showed that droplet splitting shifts from Type I to Type II and stabilizes at Type III as the forward contact angle, flow rate, and inclination angle increase. Notably, there is a non-linear relationship between the splitting ratio and fracture aperture, especially during the Type I to Type II transition. Our findings improve understanding and contribute to more accurate predictions of unsaturated flow in fractured rock formations, impacting groundwater remediation, oil and gas production, and geothermal energy extraction.