The name is absent



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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