Original Theoretical Contribution to Droplet Dynamics in Oil-Water Emulsion Separation Systems under Oscillatory Flow Conditions Relevant to Subsea Processing in Nigeria

Subsea produced water separation technology represents a frontier in deepwater oil production, yet the behaviour of oil droplets in primary separators under oscillatory flow conditions generated by ocean wave-induced vessel motion has not been rigorously theorised for the composition ranges of Niger Delta produced water. This study makes an original theoretical contribution to understanding droplet dynamics in oil-water emulsion separation by developing a modified droplet trajectory model that incorporates the coupled effects of oscillatory accelerations, droplet size distribution evolution by coalescence and re-dispersion, non-Newtonian continuous phase behaviour, and surface-active agent adsorption kinetics at the oil-water interface. The theoretical model extends the existing Stokes sedimentation framework by incorporating an oscillatory buoyancy force term and a dynamic interfacial tension sub-model parameterised from surface tensiometry measurements on Niger Delta produced water-crude oil systems. Experimental validation was conducted using a purpose-built oscillatory flow separator cell capable of replicating the heave acceleration spectra measured on an FPSO operating in the Niger Delta. High-speed imaging was used to characterise droplet trajectories and coalescence events. The original model predicted droplet separation efficiency under oscillatory conditions within 8.3% of experimental measurements across all tested conditions, outperforming the unmodified Stokes model by a factor of 2.7 in accuracy. The theoretical framework provides a basis for designing optimised subsea separator geometries accounting for wave-induced motion in Niger Delta field applications, with implications for both separator sizing and demulsifier selection. Keywords: droplet dynamics, emulsion separation, oscillatory flow, subsea processing, Niger Delta