On the calculation and interpretation of NMR relaxation time distributions

We analyzed NMR relaxation time data using a multi-exponential model. The inversion of NMR data using such a model is an ill-posed problem. The answer is often not unique and requires subjective judgement. We studied two methods of regularization. One uses norm smoothing based on an article by Butler et al. We found that optimal norm smoothing depends on the input of measurement errors. The second method uses curvature smoothing which minimizes variations in the second derivative. The latter is more effective for suppressing fluctuations in the relaxation time distribution, but doesn't directly account for data quality. We studied NMR T₁ data at full and partial saturations with desaturation pressures ranging from 15 to 400 psi (air/brine). As a general guideline, we found that the relaxation time cutoff which corresponds to irreducible water saturation is about 33 ms. For a limited number of samples, we found that the T₁ relaxation time distribution has very little dependence on the frequency from 200 down to 1 MHz. We also found that T₂ could be correlated to permeability.