Experimental and theoretical study of counter-current oil–water separation in wells with in-situ water injection

• Oil/water separation under counter-current flow condition is experimentally examined.
• Analytical models are developed to predict the critical water velocity for separation.
• Oil–water interfacial tension is the most important factor in the separation process.
• Oil and water viscosities should not be ignored in the counter-current flow.
• Increasing well size could increase the separation efficiency.

The study investigates a counter-current gravity separation in a downwards-flowing mixture of (up to 3%) oil in water. At much higher oil fraction, the separation is a basis for the conventional downhole oil–water separation (DOWS) where the whole oil and water separate in the well. In contrast, the counter-current separation of a very small oil content is needed in the new “downhole water loop” technique (DWL) prior to injecting the oil-free water in-situ. In the DWL triple-completed wells, the top completion produces oil and only trace of the oil contaminates the water drained by the lower “water sink” completion and is re-injected in-situ using the (third) bottom completion. A drift-flux concept was used to develop an empirical model for predicting the oil droplets raise velocity at different water flow velocities. The model was derived from experiments using seven different oils with a wide range of density, viscosity and interfacial tension values. The experiments monitored oil droplets ejected from a single perforation into the stream of water flowing downwards at various velocities. The results show that the oil–water interfacial tension is the most important factor in the separation process, as it controls the oil droplet size. This observation significantly simplifies the model by replacing the droplet size (most difficult to measure) with a correlation based on interfacial tension developed using the experimental results. The new model also considers the effect of oil viscosity that has been ignored in the co-current separation studies. (Our results reveal over 10% contribution of the viscosity effect to the counter-current separation process.) A practical finding in this study is the 0.33 ft/s (0.1 m/s) value of critical maximum water velocity for counter-current oil separation. In a real DWL well, this value corresponds to a point in the perforated well section above which separation takes place. It is also shown how oil separation could be predicted from a given water sink completion length and drainage–injection rate.