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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. — = alD « 1, =>     « 1. D is

p tp a] ID          D

diffusivity of dispersed phase.

41



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