Prediction of the Formation of Water-in-Oil Emulsions - Mathematical Modelling and Numerical Simulation of Oil Pollution Problems - page 72

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 be-
comes the asphaltene content less 4. The value used in the equation is this trans-
formed value. If the value of the asphaltene content is zero, then set the value to 20.
(3.13)

A R or Asphaltene/Resin Ratio: not transformed For procedure 2, the class of the

resulting emulsion is then calculated as follows:

/

Stability = 5667 − 9520 · Den − 3 . 99 · Visc + 0 . 138 · Sst + 2 . 16 · Rst

− 0 . 395 · Ast + 17 . 9 · A / R + 224 · exp ( den ) + 2 . 88 e − 10 · exp ( Rst )

− 4 . 35 · exp ( A / R ) + 16823 · ln ( Den ) + 10 . 5 · ln ( Visc )

− . 671 · ln ( Sst ) + 0 . 147 · ln ( Rst ) + 0 . 107 · ln ( Ast ) + 1 . 62 · ln ( A / )

(3.14)

R

where:

Stability is the stability of the resulting water-in-oil type,
Den is the untransformed exponential of the density, abbreviated A here,
Visc is the untransformed natural logarithm (ln) of the viscosity, abbreviated B
here,
Sst is the transformed saturate content as calculated in Eq. ( 3.11 ), abbreviated C
here,
Rst is the transformed resin content as calculated in Eq. ( 3.12 ), abbreviated D ,
Ast is the transformed asphaltene content as calculated in Eq. ( 3.13 ), abbreviated E ,
A

R is the (untransformed) asphaltene/resin ratio, abbreviated F ,
Exponential den is the exponential of the exponential of density, abbreviated G ,
Exponential Rst is the exponential of the transformed resins, calculated inEq. ( 3.12 )
abbreviated,
Exponential of A

/

R , abbreviated I ,
Ln (natural logarithm) of the exponential of density, abbreviated J ,
Ln (natural logarithm) of the natural logarithm of viscosity, abbreviated K ,
Ln (natural logarithm) of the transformed saturates as calculated in Eq. ( 3.11 ),
abbreviated L ,
Ln (natural logarithm) of the transformed resins as calculated in Eq. ( 3.12 ), abbre-
viated M ,
Ln (natural logarithm) of the transformed asphaltenes as calculated in Eq. ( 3.13 ),
abbreviated N ,
Ln (natural logarithm) of the (untransformed) ( A

/

/ R ) ratio, abbreviated O .

A simplified version of the equation is then: