Prediction of the Formation of Water-in-Oil Emulsions - Mathematical Modelling and Numerical Simulation of Oil Pollution Problems - page 74

Table 3.7 Summary of calculations for model II
Basic inputs

Symbol Units

Density D g/mL

Viscosity V mPa s

Saturate content S %

Resin content R %

Asphaltene content A %

First step-transformation Description
Density expD Take exponential of density
Viscosity lnV Take natural logarithm of viscosity
Asphaltene/Resin ratio A/R Divide asphaltene content by resin content
Second step—rationalization (converts units to simple declining or increasing functions)
Saturate content Sst if(S < 45, 45S, S45)

Resin content Rst if(R < 10, 10R, R10)

Asphaltene content Ast if(A < 4, 4A, A4)

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'

Fourth step—calculate Gaussian expansion steps
Exponential of density exp(Den) Exponential of the exponential of density
Exponential of resin content exp(Rst) Exponential of rationalized resin content
Exponential of A/R ratio exp(A/R) Exponential of A/R ratio
Natural logarithm of density ln(Den) Natural logarithm (ln) of the exponential of
density
Natural logarithm of viscosity ln(Visc) Natural logarithm (ln) of the natural logarithm
of viscosity
Natural logarithm of saturates ln(Sst) Natural logarithm (ln) of the rationalized
saturate content
Natural logarithm of resins ln(Rst) Natural logarithm (ln) of the rationalized resin
content
Natural logarithm of asphaltenes ln(Ast) Natural logarithm (ln) of the rationalized
asphaltene content
Natural logarithm of A/R ratio ln(A/R) Natural logarithm (ln) of the A/R ratio
∗ Zeros must be purged from numbers as they cause problems in division and with logarithmic
expressions

Entrained water-in-oil types show a unique character, that is they show a starting
oil density of greater than 0.96 g/mL, but less than 1.0 g/mL. Further, the starting oils
have a viscosity greater than 2300mPa s and less than 200,000mPa s. An example
of the screening process is shown in Table 3.8 . The screening (shown as screen
entrained) is applied to all the oils and they are marked as sent if they meet this