Methods and limitations of NMR data inversion for fluid typing

We introduce two NMR inversion methods within the framework of 1D NMR to extract fluid saturations by varying echo spacing and wait time. The first method connects the T2 distribution of each fluid with the overall apparent T2 distribution using a shift matrix. Each fluid's saturation and T2 distribution are extracted by minimizing the difference between the model T2 distributions and measured apparent T2 distributions. The second method relates a model T2 distribution of each fluid with CPMG echo trains using a global evolution matrix that governs the evolution of magnetization under T1, T2 relaxation, and diffusion. These methods will be useful whenever data are not sufficient for 2D NMR inversion. They are also much faster than 2D for fluid typing. We also point out an inherent limitation associated with NMR inversion methods for fluid typing. Whenever there is singularity in the inversion matrix caused by similar behavior of model function for different fluids, most inversion algorithms remove the solution space associated with the singularity and choose a solution vector of the minimum length. This results in equal proportions of different fluids in the final answer. If prior knowledge such as saturation or T2 shape of the oil is available, there are several methods to tailor the solution to our desired outcome. However, if there is no prior knowledge available, such ambiguity always exists irregardless of the inversion schemes.