Prediction of the Formation of Water-in-Oil Emulsions - Mathematical Modelling and Numerical Simulation of Oil Pollution Problems - page 71

Table 3.5 Viscosity
increases from starting oil and
typical water content

Viscosity increase on
First day Week Year

Entrained 1.9 1.9 2.1

Meso-stable 7.2 11 32

Stable 405 1054 991

Unstable 0.99 1.0 1.0

Typical water content
First day

Week Year

Entrained 44.5 27.5 6

Meso-stable 64.3 30 6

Stable 81 78 70

Unstable 6.1 6 5

3.5.4 Model II

The differences between the equations shown above and those for model II include:

1. The Gaussian expansion is simplified to one term expansion and one term com-
pression.
2. Three terms are not rationalized in the same manner as above, this includes den-
sity, viscosity and asphaltene/resin ratio. These are felt to be already continuous
functions and thus can be used as such.
3. The input values are also used directly as well as the Gaussian expansion.

The first step to procedure 2 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: not transformed—just take the exponential, abbreviated Den,

Viscosity: not transformed—just take the natural log, abbreviated Visc,

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.
(3.11)

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.

(3.12)