Oil & Gas Validations
The separation of liquid-liquid dispersions is a problem encountered in many industrial situations. In the present case we consider a batch separator consisting of a vertical column containing a mixture of oil and water, as reported by Jeelani and Hartland, Ind. Eng. Chem. Res. 37, pp.547-554, 1998. Specifically the water is demineralized with density 996kg/m3 and viscosity 1mPa.s, while the dispersed phase consists of decane in paraffin oil having a density 837kg/m3 and viscosity 1.26mPa.s. The column height is 0.915m and the initial volume fraction of oil is 30% (foil=0.3) in the entire column.
FLOW-3D models this situation as a two-fluid mixture in which the two phases are allowed to flow relative to one another using a special “drift flux” model. The dispersed phase is assumed to be in the form of droplets having a specified diameter. The relative, or drift, velocity of the droplets is computed from a balance of buoyancy, gravity and viscous forces acting on a drop. This velocity it then modified with a Richardson-Zaki correlation that accounts for droplet-droplet effects in terms of the dispersed volume fraction. For all but very small volume fractions, the Richardson-Zaki correlation has been validated by many researchers to be an important contribution for accurate drift fluxes.
In the figure above, the bold lines are experimental data for the boundary heights of the top of the pure water region (Hs) collecting at the bottom of the separator (bottom lines in plot) and the bottom of the pure oil region (Hc) collecting at the top (top lines in the plot). In order for the oil drops to coalesce from a state of close packing to a state of pure oil it is necessary to switch the definition of the dispersed phase to be water instead of oil. This switch is done at the average volume fraction foil=0.5, so that the phase with the smallest volume fraction is treated as the dispersed phase.
Simulation results (open circles) are shown for a droplet diameter of 1.2e-3m. Excellent agreement with the experimental data is achieved at both early and late times.