Prediction of the Formation of Water-in-Oil Emulsions - Mathematical Modelling and Numerical Simulation of Oil Pollution Problems - page 75

requirement and are entrained and if not are marked as other. Those items in error
are shown as a coloured entry. In doing the screening for entrained types, it is noted
that only three oils were characterized incorrectly using the entrained screening for
a total error of 1.5%. This is an acceptable error rate.
Other items to note about Table 3.8 are that the oils are grouped by the water-
in-oil types and that the summary of certain properties is given under each type
as minimum, maximum and average. This aids in assessing the cut off points. The
assessment rules are given in a column of the table as well. The basic data on each
starting oil is given as well.
A second obvious cut-off screen is applied to those low-viscosity oils that do not
form a water-in-oil type. Such oils as gasoline, diesel fuel, very light crudes, will
never form a water-in-oil type. As shown in Table 3.8 , this screening results in a low
error rate of only 3.2%.
The third screening can be applied to those oils that have a very high viscosity
and do not form any type of water-in-oil type. This type is easily screened using only
the criteria of viscosity, that of viscosity 200,000mPaS. This results in a very high

accuracy rate and a very low error rate, but there are few candidates for this type of
oil. The third screening leaves the meso-stable and stable types. Several attempts to
separate these included:

>

• regression of density and viscosity with the stability index,

• separate regressions of density and viscosity with the stability index,

• simple screening by either density and viscosity,

•

Principle Components Analysis,

•

graphical procedures, and

• relationship to other parameters.

None of these resulted in a successful screening out of the meso-stable and stable
water-in-oil types. The difficulty of separating these two types has been noted in the
past [ 4 ]. It is noted, however, that the stable types have somewhat more scatter than
the meso-stable types. This can be used to provide a separation between the two.
The best separation was obtained using the scatter in the prediction of viscosity from
density. This is a fit of the equation:

2

ln visc = 270 − 235 . 3 · exp density + 51 . 7 · ( exp density ) (3.16)

Then taking the fact that the stables are more highly divergent then, the oil will form a
stable emulsion if the deviation from Eq. ( 3.1 ) is greater than 7.5%, and meso-stable
emulsion otherwise. This results in an error of about 31% as shown in Table 3.8 .The
screening is summarized in Table 3.9 .
While not excellent, this screening technique does provide a means of separating
the stable and meso-stable types using only density and viscosity as inputs.