Prediction of the Formation of Water-in-Oil Emulsions - Mathematical Modelling and Numerical Simulation of Oil Pollution Problems - page 67

Table 3.3 Regression results for model I
Va r i a b l e

Va l u e Standard

error

t-ratio Prob(t) Input

variable

Math
applied

a 0.0126 0.09 0.14 0.88694 Saturates

b − 1.49 0.48 − 3.11 0.00239 Resins

c − 12.6 12.34 − 1.02 0.30914 A/R

d − 0.073 0.02 − 3.97 0.00013 ln viscosity Cubed

e 0.00193 0.00 2.08 0.0402 Resins Cubed

f 0.00016 0.00 0.22 0.82677 Asphaltenes Cubed

g − 4.23 14.21 − 0.30 0.76648 A/R Cubed

h − 0.59 0.77 − 0.77 0.44215 ln viscosity ln

i 1.59 1.03 1.55 0.12359 Resins ln

j 4.03 2.53 1.59 0.11479 A/R ln

k 3.73E-26 0.00 1.28 0.20272 ln viscosity Exp squared

l 1.21 7.02 0.17 0.8639 A/R Exp squared

m 0.022 0.01 1.59 0.11463 Exp density log/square x

n 0.11 0.13 0.83 0.40933 A/R log/square x

o 17.8 8.60 2.07 0.04066 Contant

Table 3.4 Summary of calculations for model I
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)
Density 2.5, 2.5lnV, expD2.5) ∗ Dst if(expD <

Viscosity Vst if(lnV < 5.8, 5.8lnV, LnV5.8)

Saturate content Sst if(S < 45, 45S, S45)

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

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

Asphaltene/Resin ratio A/Rst if(A/R < 0.6, 0.6A/R, A/R0.6)

(continued)