The name is absent

Chapter 3

the initial transverse magnetization, f∣ is the fraction of protons with relaxation time

T₂,,. T₂ distribution of the sample can be obtained using multi-exponential fitting to
the raw data of spin echoes, which was developed by Huang ^[6]. Fitting data to a
multi-exponential sum is an Illposed problem ^[7]. For this reason, a regularization
method is used to calculate the most representative T₂ distribution ^[8J.

3.2.2. Characterization of emulsions with CPMG measurement

In Eq. [3.2], f_i is proportional to the spin density of the fluids. Thus the volume
fraction φ_k of phase к is related to the T₂ distribution ^[9]:

∑(Z)_{1                               r},,₁

Й —                           [3 3]

^шк

HI is the hydrogen index, which is the ratio of proton density in the fluid and
that in water. In general, HI is about 1 for aqueous solutions, and 0.9 -1.0 for most
crude oils, except aromatic oils, which is 0.6-0.8. From Eq. [3.3], for water in oil
emulsion, the water fraction can be calculated as:

<P_dp=~^-----dps-------                    _[34]

[∑(Z)_α.∕tf∕c,]+[∑c‰∕tf⅛]

Here subscript DP is the dispersed water phase, subscript CP is the
continuous oil phase.

NMR CPMG measurement has been regarded as superior to all other
available techniques for the determination of water content in heavy oil, bitumen

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