Prediction of the Formation of Water-in-Oil Emulsions - Mathematical Modelling and Numerical Simulation of Oil Pollution Problems - page 68

Table 3.4 (continued)
Third step—parsing zeros from SARA numbers ∗∗
Resin content Rst Replace zero's at rationalization stage with

'20.1'

Asphaltene content Ast Replace zero's at rationalization stage with

'20.1'

Asphaltene/Resin ratio A/Rst Replace zero's at rationalization stage with

'0.01'

Fourth step—calculate Gaussian expansion steps
Viscosity cubed Vst 3 Cube the rationalized viscosity
Resin content cubed Rst 3 Cube the rationalized resin content
Asphaltene content cubed Ast 3 Cube the rationalized asphaltene content
Asphaltene/Resin ratio cubed A/Rst 3 Cube the rationalized asphaltene content
Natural log of viscosity lnVst Natural logarithm of rationalized viscosity
Natural log of resin content lnRst Natural logarithm of rationalized viscosity
Natural log of asphaltene/resin ratio lnA/Rst Natural logarithm of rationalized
asphaltene/resin ratio
Exponential of viscosity squared Exp 2 Vst (Exp(Vst)*Exp(Vst)
Exponential of A/Rst ratio square Exp 2 A/Rst (Exp(A/Rst)*Exp(A/Rst)
Log over square of density LogDst 2 (Log(Exp(Dst))/(Dst 2 )
Log over square of A/R ratio LogA/Rst 2 (Log(Exp(A/Rst))/(A/Rst 2 )
∗ This is an Excel-like statement, in this case reads: if the exponential of density is less than 2.5, the
standardized density becomes 2.5 less the exponential of density, if not the standardized density is
the exponential of density less 2.5
∗∗ Zeros must be purged from numbers as they cause problems in division and with logarithmic
expressions

3.5.3 Model I

The first step is to transform the input data so that it forms a continuous declining
or increasing function. It should be noted that the greater than can also be read as
greater or equal to.

Density: Take the exponential of the density. If the exponential of density is less
than 2.5, then the density parameter is 2.5 less the density and if it is greater than
2.5, it becomes the density less 2.5. The value used in the equation is this trans-
formed value. (3.1)

Viscosity: Take the natural logarithm (ln) of the viscosity. If the natural log of the
viscosity is less than 5.8, then the viscosity parameter is 5.8 less the viscosity natu-
ral log and if it is greater than 5.8, it becomes the natural log of viscosity less 5.8.
The value used in the equation is this transformed value. (3.2)