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Chapter 3

least-square fit of the experimental data for R, using d_gv, σ, Dcp and к as fitting
parameters. Detailed procedure is as follows:

1) Estimating initial values of geometric volume-based mean diameter d_gv
and geometric standard deviation σ; signal attenuation fraction κ₀i∣, ∕<emu∣
and κ_wat_e∣∙; diffusivity of continuous oil phase Dcp.

2) Using Eq. [3.9] with Dcp and D_waier to calculate attenuation R_0i∣ and R_wate∣∙;
using Eqs. [3.12], [3.16] and [3.17] to calculate attenuation R_emu∣; using Eq.
[3.23] to calculate total attenuation of the emulsion R.

3) Performing least-square fitting of the experimental data R_exp for R until
norm of the difference ∣∣R_e×p-^ll is smaller than tolerance to get fitted
values of all the parameters in step 1 ).

If combined with NMR CPMG T₂ distribution measurement, drop size
distribution and surface relaxivity of water in diluted bitumen p can be obtained ^[5].
In this case, fitting parameters are surface relaxivity p and phase signal
attenuation fraction κ. R_emui is calculated by drop size distribution, which is
obtained from T₂ distribution and surface relaxivity. Total signal attenuation of the
emulsion R is the weighted combination of phase signal attenuation with
attenuation fraction κ. Detailed procedure is as follows:

1) Getting T₂ distribution of water drops via CPMG measurement; estimating

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