Chapter 3
and oilfield emulsions[10]. This application is an extension of the usage of NMR
relaxation measurements for the determination of porosity in minerals and rocks.
If the fluid is confined in a planar, cylindrical or spherical cavity, the relaxation
can be written as [11]:
1 1 Z5X ro e1
-^=r--+ pU' [3'5]
12,i 12,bulk K
Here p is surface relaxivity. For the same water∕oil system, p keeps constant.
(S∕V)i is the surface to volume ratio of cavity /. For a sphere of radius ai, Eq. [3.4]
becomes:
113 11
- = ~ + P~, αi=3p∕(-~-) [3.6]
12,i 12,bulk ai 12,i 12,bulk
The number of protons present in a given volume of sample determines the
signal amplitude. For this reason, the fraction fi that is associated to each T2,∣
value renders a direct measurement of the fraction of droplets with the radius a∣.
Drop size distribution of emulsions can be obtained from T2 distribution. The
requirements for Eq. [3.5] are [5]:
1) Measurements are performed in the “fast diffusion” mode, that the
characteristic time scale tD for molecule diffusion should be much smaller
than that of surface relaxation t0. — = a∖lD « 1, => « 1. D is
p tp a] ID D
diffusivity of dispersed phase.
41
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