Appendix A
amplitude of magnetic gradient pulse g (G1 in script).
For monodisperse emulsion with geometric mean drop size dg and standard
deviation σg, most of the droplets have sizes in the range of one standard
deviation [dg∕e×p(σg), dg*e×p(σg)], if lognormal distribution is assumed. For a set of
parameters Δ, δ and g, the measurable minimum and maximum drop sizes in
NMR restricted diffusion measurement can be calculated based on Eqs. [3.29]
and [3.30]. Parameters for NMR restricted diffusion measurement are chosen that
the drop size range [dg∕e×p(σg), dg*exp(σg)] is within the measurable drop size
range [cfmin> C4nax]∙
In NMR restricted diffusion measurement for all diluted bitumen samples,
parameters are: diffusion time Δ 500 ms, gradient pulse duration δ 3 ms, range of
magnetic gradient g 0 - 40 G∕cm. The measurable drop size range is 4 μm - 72 μm.
For instance, emulsion sample 1 in chapter 3 has geometric mean drop size 14
μm and standard deviation 0.4. Drop size in the range of one standard deviation is
9 μm - 21 μm, which is within the measurable drop size range 4 μm - 72 μm.
Thereby correct drop size distribution can be obtained by NMR restricted diffusion
measurement using above parameters.
Ifthe emulsion is polydispersed, more than one set of parameters and multi-
exponential data fitting are required. Details of parameters selection and data
197
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