Determination of permeability distributions using NMR velocity imaging

This study develops a methodology for determining the absolute permeability distribution in a porous media sample using velocity data obtained from NM R imaging experiments. An objective function describing the discrepancy bet ween observed and simulated data is reduced by iteratively updating the per meability. This parameter estimation scheme is based on an iterative method which uses optimal control theory to refine the estimates. Although this t heory is developed for both isotropic and anisotropic porous media, the per meability reconstructions examined in this paper are restricted to the isot ropic case. Synthetic data are used to investigate the impact of varying th e noise in the experimental data, the degree of parameterization, the relat ive weighting of the regularization term in the objective function, and the amount and type of data required to obtain a satisfactory permeability rec onstruction. These synthetic data are extracted from the solution of numeri cal experiments that have utilized an assumed permeability distribution. Th e methodology is also applied to data gathered in laboratory experiments fo r water flow in a sandstone sample.