Chapter 3
self-diffusion in isotropic, isothermal media during the diffusion time ∆pl:
<x≈√2(x2f2=2√DΔ [3.29]
Here <x2>ιz2 is root-mean-square displacement. D is diffusivity.
The minimum drop size dmi∏ that is measurable from PGSE data can be
expressed as 15j:
√ =(1752-r-?---)1/4, A = I-R (a = d ■ ∕2,δ=δ ) [3.30]
m'n v T2g3<^ / ’ sp× mm ’ max / p-,.wj
/ ð ½nax
Here δmaχ is the largest magnetic gradient duration can be used in the
measurement (usually δma× = 0.2Δ). Plausible values for Λ are 0.01 ≤λ ≤0.05.
3.3.3. Drop size determination of diluted bitumen emulsion
For diluted bitumen emulsion, the total attenuation for the emulsion can be
written as:
r = M 0iι (g > 0) +M emul (g > 0)+Mwater (g > 0) 1
Moil{g = ^ + Memul{g = Q') + Mwater{g = Q) L ∙ J
Subscripts emul, oil and water correspond to emulsified water, oil and bulk
water phases.
n τz^0,∕(g>°) R ^Mem,Ag>Q) R __ MwatAg > Q) Γ3 201
0i, Moil{g = oy emul Memul(g = oy waler Mwater(g = 0) l ■ j
Substituting Eq. [3.20] in Eq. [3.19],
r _ MqU (g — 0)Roil l Memul (g — 0)Remuι ɪ Mwater (g — Rwaler [321]
[∑J∏U [∑J∏U [∑Λ∕]srt '
49
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