The name is absent

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--^{+ p}U'                        ^[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 a_i, Eq. [3.4]
becomes:

113    11

- = ~ + P~,     α_i=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 f_i 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 t_D for molecule diffusion should be much smaller
than that of surface relaxation t₀. — = ^a∖^lD « 1, =>     « 1. D is

^p t_p a] ID          D

diffusivity of dispersed phase.

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