Modeling droplet dispersion in a vertical turbulent tubing flow

- A model of droplet dispersion in a vertical production tubing is developed.
- An advection-diffusion-population balance equation is solved.
- Model performance is illustrated by computations of water in oil dispersion.

Usually, during oil production, water and oil flow simultaneously in the wellbore. When water holdup in the borehole is small, water droplets may be dispersed into bulk oil making water breakthrough detection a challenging task. In this paper, a comprehensive engineering model of droplet dispersion is presented.Dispersion of droplets in a long vertical turbulent tubing flow is modeled by an Advection-Diffusion-Population Balance equation. The Prandtl Mixing-Length model of turbulence is used to describe the velocity profile across a tubing. The turbulence energy dissipation rate distribution across a pipe is calculated by an analytical equation. The fixed pivot method is employed for calculation of the population balance term of the governing equation. Droplet fragmentation is modeled using a recently developed droplet breakup model (Eskin et al., 2017). It is assumed that volume concentration of a dispersed phase does not exceed 10%. A computational code developed allows tracking evolution of droplet size distribution along a tubing. Model performance is illustrated by computations of the water in oil dispersion process. Effects of oil/water interfacial tension, well production rate and oil viscosity on dispersion are demonstrated.