In order to develop a treater design procedure, the water droplet size to be used in the settling equation to achieve a given outlet water cut must be determined. As previously mentioned, it would be extremely rare to have laboratory data of the droplet size distribution for a given emulsion as it enters the coalescing section of the treater. Qualitatively, we would expect the minimum droplet size that must be removed for a given water cut to (1) increase with retention time in the coalescing section, (2) increase with temperature, which tends to excite the system, leading to more collisions of small droplets, and (3) increase with oil viscosity, which tends to inhibit the formation of small droplets from shearing that occurs in the system.
We have seen that, after an initial period, increasing the retention time has a small impact on the rate of growth of particles. Thus, for practically sized treaters with retention times of 10 to 30 minutes, retention time would not be expected to be a determinant variable. Intuitively, one would expect viscosity to have a much greater effect on coalescence than temperature.
Assuming that the minimum required size of droplets that must be settled is a function only of oil viscosity, equations have been developed correlating this droplet size and oil viscosity . The authors used data from three conventional treaters operating with 1% water cuts. Water droplet sizes were back-calculated using Equation 6-7. The calculated droplet sizes were correlated with oil viscosity, and the following equation resulted:
Using the same procedure, the following correlation for droplet size was developed for electrostatic treaters:
For viscosities below 3 cp, Equation 6-8 should be used. The two equations intersect at 3 cp, and electrostatic treaters would not be expected to operate less efficiently in this range. Additionally, the data from which the electrostatic treater droplet size correlation was developed did not include oil viscosities less than 7 cp.
The same authors also investigated the effect of water cut on minimum droplet size. Data from both conventional and electrostatic treaters over a range of water cuts were used to back-calculate an imputed droplet size as a function of water cut, resulting in the following equation:
As the volume of a sphere is proportional to the diameter cubed, Equation 6-10 indicates that the water cut is proportional to the droplet diameter cubed.
It must be stressed that the above equations should be used only in the absence of other data and experience. These proposed relationships are based only on limited experimental data.
An approximate sizing relationship, derived from Equations 6-13 and 6-14, is given in Figure 6-12 in terms of the flow rate of emulsion (given in bpd) flowing vertically through a horizontal cross-sectional area of one square foot. For a horizontal treater with vertical flow through the coalescing section, the flow area can be approximated as the diameter of the vessel times the length of the coalescing section.