Prediction of the Formation of Water-in-Oil Emulsions - Mathematical Modelling and Numerical Simulation of Oil Pollution Problems - page 69

Saturate Content: If the saturate content is less than 45, then the saturate content
parameter is 45 less the saturate content and if it is greater than 45, it becomes the
saturate content less 45. The value used in the equation is this transformed value.
(3.3)

Resin Content: If the resin content is less than 10, then the resin content parameter
is 10 less the resin content and if it is greater than 10, it becomes the resin content
less 10. The value used in the equation is this transformed value. If the value of
the resins is zero, then set this value to 20. (3.4)

Asphaltene Content: If the asphaltene content is less than 4, then the asphaltene
content parameter is 4 less the asphaltene content and if it is greater than 4, it
becomes the asphaltene content less 4. The value used in the equation is this
transformed value. If the value of the asphaltene content is zero, then set the
value to 20. (3.5)

A/R or Asphaltene/Resin Ratio: The A/R is taken as the direct value of the asphal-
tene content in percent (untransformed) divided by the resin content in percent
(again untransformed). If A/R is less than 0.6, then the A/R parameter is 0.6 less
the A/R and if it is greater than 0.6, it becomes the A/R less 0.6.
The value used in the equation is this transformed value. (3.6)

The class of the resulting emulsion is then calculated as follows:

Stability = 17 . 8 + 0 . 013 · Sst − 1 . 49 · Rst − 12 . 6 · A / Rst − 0 . 073 · Vst 3

+ 0 . 0019 · Rst 3 + 0 . 00016 · Ast 3 − 4 . 23 · A / Rst 3 − 0 . 59 · ln ( Vst )

+ 1 . 59 · ln ( Rst ) + 4 . 028 · ln ( A / Rst ) + 3 . 72 X 10 − 26 · Exp ( Vst ) 2 (3.7)

+ 1 . 207 · Exp ( A / Rst ) 2 + 0 . 022 · ( LogDst / Dst 2 )

+ 0 . 11 · ( LogA / Rst / A / Rst 2 )

where:
Stability is the stability of the resulting water-in-oil type,
Sst is the transformed saturate content as calculated in Eq. ( 3.3 ), abbreviated A
here,
Rst is the transformed resin content as calculated in Eq. ( 3.4 ), abbreviated B ,
A/Rst is the transformed asphaltene/resin ratio as calculated in ( 3.6 ), abbreviated C ,
Vst3 is the cube of the transformed ln viscosity as calculated in ( 3.2 ), abbreviated D ,
Rst3 is the cube of the transformed resin content as calculated in Eq. ( 3.4 ), abbre-
viated E ,