Chapter 3
R.
_ PΛp^da
^emul «о
ɪ Pvda
[3.16]
Here pv(a) is the volume-weighted distribution of sizes. Rsp(a) is determined
from Eq. [3.12].
The lognormal probability distribution function (p.d.f.), is the classic
assumption for the drop size distribution in absence of additional information,
because it is well known that sequential break-up processes yield such a
distribution [171, [18].
[ln(rf)-ln(⅛,)]
z ,ʌ 1 2σ2
[3.17]
PvW = /—j g
^2πdσ
dgv and σ are the geometric volume-based mean diameter and the width or
geometric standard deviation of the distribution, respectively.
For continuous oil phase, Eq. [3.9] is also valid. For an oil phase with the
effective diffusivity distribution p (Dcp), the equation for the attenuation is [5]:
Roil =
■bulk,C P(Dcp)dDcp
f PD(Dcp№cp)dDcp
[3.18]
If the emulsion is partially separated, Eq. [3.9] can also be applied for
separated bulk water, using bulk water diffusivity.
The maximum drop size that can be determined via PGSE is related to the
one-dimension root-mean-square displacement of spins undergoing free (Fickian)
48
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