Permeability Identification from Pressure Observations: Some Foundations for Multiscale Regularization

The interrelation (denoted SNS) between sensitivity, nonlinearity and scale, associated with the inverse problem of permeability (fluid conductivity) identification from fluid pressure observations in porous-media flow, is considered. The family of models considered includes both single-phase and two-phase flows, with applications to groundwater flow/primary recovery in petroleum reservoirs and to water flooding of petroleum reservoirs, respectively. SNS is important for regularization of both of these ill-posed inverse problems, but so far, SNS has been shown to exist only for single-phase flow. Several multiscale/multiresolution estimation techniques, explicitly or implicitly based on SNS, have, however, been developed and applied to practical permeability estimation both for single- and two-phase flows. In this paper, SNS is shown to exist for one-dimensional, two-phase flow. Moreover, very similar approaches are applied to show the existence of SNS both for single- and two-phase flows. To convey some ...