Droplet Size Distribution of Crude Oil Emulsions - Stochastic Differential Equations and Bayesian Modelling

Water-in-oil emulsions (WOE) are two-phase colloidal systems formed during crude oil production and spills. The high viscosity and stability of WOEs imply challenges during their clean-up and removal. Such emulsions are difficult to disaggregate due to a combination of chemical and physical factors. Ultrasound spectrometry can be used to characterise the WOE physical properties, providing access to, e.g. the droplet size distribution (DSD), density and viscosity. The DSD has been identified as a significant property impacting emulsion stability. This study focuses on the data post-acquisition stage modelling the droplet size growth as a stochastic process. Geometric Brownian motion (GBM) and Itô stochastic differential equations (SDEs) are used. Bayesian inference is introduced as a tool aiding in conditions of poor sample quality. The obtained model could predict emulsion separation indicated by a sufficiently large mean and standard deviation of the droplet growth process. It could be used for emulsions of different chemical compositions, including with added dispersants, allowing to characterise their impact on the WOE stability over time.