Oil-water mixing in pipes is common in the petroleum industry during the production, transportation, and processing of hydrocarbons. We present a model of oil-water dispersion describing the distribution of droplet concentrations in each cross section of the pipe using an advection-diffusion equation expressing the balance between turbulent diffusion and gravitational settling. In contrast to published models, the presented model incorporates the effects of droplet size distribution in a computationally efficient way. The model is coupled to a 1D steady-state three-phase flow framework and validated against experimental data for concentration profiles, pressure drop, cross-section averaged volume fractions, and flow pattern maps.
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