Prediction of the Formation of Water-in-Oil Emulsions - Mathematical Modelling and Numerical Simulation of Oil Pollution Problems - page 65

3.5.2 New Models
Several new models for the prediction of water-in-oil emulsions were recently
developed by the present author [ 4 ]. These models used empirical data to predict
the formation of emulsions using a continuous function and employing the physi-
cal and chemical properties of oil. The emulsification properties of more oils were
measured and the properties of some of the oils in the existing oil set have been
re-measured. This enables the models to be recalculated with sound data on over 400
discreet oil samples.
The basis of these models is the result of the knowledge demonstrated above—
namely that models are stabilized by asphaltenes, with the participation of resins.
Findings of this group and other groups show that the entire SARA (Saturates, Aro-
matic, Resins, and Asphaltene) distribution effects the formation of emulsions as the
prime stabilizers, asphaltenes and secondarily resins, are only available for emulsion
formation when the concentration of the saturates and aromatics are at a certain level
and when the density and viscosity are correct.
The approaches to model development were implemented and are detailed in
the literature [ 4 ]. One approach was to curve fit the physical and content data to a
stability index. Then this stability factor was used in turn to predict a class (stable,
meso-stable, entrained or unstable). The empirical data including oil content data,
viscosity, density and the resulting water-in-oil type stability were used to develop
mathematical correlation. The value for each parameter was correlated in a series of
models using DataFit (Oakdale Engineering) [ 8 ]. A two-step process is necessary
as DataFit is not able to calculate the specific mathematical function with more than
2 variables, due to the large number of possibilities. Thus, the functions (e.g., linear,
square, log) were calculated using a two-way regression ( TableCurve ,[ 11 ]) and
these functions were in turn used in developing a predictor model for emulsification.
The steps to produce the first models are summarized in earlier papers [ 4 ]. First the
parameters available were correlated one at a time with a stability index as the target
of the correlation. This new approach used a multi-regression program directly, using
various multi-functional transformations of the input oil property data. This allowed
the regression software to assign portions of the functions necessary to achieve the
highest correlation factor.
A transformation is needed to adjust the data to a singular increasing or decreasing
function. Regression methods will not respond correctly to a function that varies both
directly and inversely with the target parameter. Most parameters have an optimal
value with respect to class, that is the values have a peak function with respect to
stability or class. Arithmetic converts values in front of the peak to values behind
the peak, thus yielding a simple declining function. The optimal value of this manip-
ulation is found by using a peak function. This peak function fit is available from
TableCurve software.
The arithmetic to perform the transformation is: (1) if the initial value is less than
the peak value, then the adjusted value is the peak value less the initial value; (2) and
if the initial value is more than the peak value, the adjusted value is the initial value