Obtaining T1-T2 distribution functions from 1-dimensional T1 and T2 measurements : The pseudo 2-D relaxation model

• We present the pseudo 2-D relaxation model (P2DRM), a method to estimate multidimensional probability distributions of material parameters from independent 1-D measurements. We illustrate its use on 1-D T1 and T2 relaxation measurements of saturated rock and evaluate it on both simulated and experimental T1-T2 correlation measurement data sets. Results were in excellent agreement with the actual, known 2-D distribution in the case of the simulated data set. In both the simulated and experimental case, the functional relationships between T1 and T2 were in good agreement with the T1-T2 correlation maps from the 2-D inverse Laplace transform of the full 2-D data sets. When a 1-D CPMG experiment is combined with a rapid T1 measurement, the P2DRM provides a double-shot method for obtaining a T1-T2 relationship, with significantly decreased experimental time in comparison to the full T1-T2 correlation measurement.

Nyckelord

Heterogeneity

Inverse Laplace transform

Inverse-gamma distribution

Lognormal distribution

Multidimensional distribution function

Porous media

Relaxation correlation

T1

T2

Distribution functions

Inverse problems

Inverse transforms

Laplace transforms

Porous materials

Inverse gamma distribution

Log-normal distribution

Multidimensional distributions

Relaxation correlations

T₁

T₂

Probability distributions

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