Multidimensional NMR inverse Laplace spectroscopy in petrophysics

The characterization of reservoir quality necessitates a good understanding of the pore scale physics of the reservoir, in particular permeability of the formation, wettability, and fluid saturations. Classical interpretation of 1D NMR logging data, a T ₂ relaxation response, uses a 1D inverse Laplace transform to derive a distribution of relaxation times from the magnetization decay, assuming weak coupling between pores and the fast diffusion limit, in which case the magnetization decay decouples into a sum of exponentials. The distribution is typically split into bound and free water by choosing an arbitrary cutoff, and permeability estimated by using a correlation involving the log mean relaxation time. More recently, 2D inverse Laplace experiments using T ₁ −T ₂ or T ₂ −D correlations were used to enable fluid typing in the case of partially saturated formations. While fluid typing is considerably more accurate using these 2D methods, mixed wettability and internal gradients can be significant obstacles. To overcome these difficulties, we present in this work higher dimensional measurements such that the relaxation is encoded for additional properties like diffusion or internal gradients (DG ² ₀ ), which enable a more precise characterization of the reservoir environment. In particular, we use pulsed field gradient NMR to encode for the effects of diffusion. Specialized timings further encode for T ₂ and internal gradient effects. 3D inverse Laplace algorithms are then used to calculate the correlation maps between T 2 − D − DG ² ₀ and T 2 − D − |G ₀ | of rock cores of varying characteristics. The analysis of higher-dimensional correlation maps has been shown to delineate between different fluids and characterize wettability. Potentially, projections of such delineated populations onto pore size distributions may provide estimates of absolute and relative permeability of the formation.