Mathematical modeling of the destabilization of crude oil emulsions using population balance equation

In this work, the stability of water-in-crude oil emulsions generated in laboratory was investigated using a phenomenological mathematical model based on the population balance equation, considering different phenomena such as the binary coalescence of water droplets, the interfacial coalescence with the resolved water phase, the diffusion of the dispersed phase, and droplet settling. The resulting population balance equation (PBE) was a nonlinear hyperbolic integro-partial differential equation, which for our particular case required numerical techniques for resolution. The PBE was converted into a system of partial differential equations using Kumar's fixed-pivot technique. The spatial coordinate was discretized using the finite volume method and a first order upwind scheme, while the discretization of the time coordinate was based on a semi-implicit approach. On the basis of this algorithm, the mathematical model was solved against experimental results of water-in-crude oil emulsion destabilization runs, providing suited predictions of droplet size distribution profiles, and of both emulsified water and free-water volumes.