Forecast simulations of porous-media flow, e.g., within a petroleum reservoir, require that the spatially dependent fluid conductivity (the
permeability) is assigned a constant value within each grid cell. The amount of detail with which it is possible to infer this piecewise constant permeability function from spatially sparsely distributed fluid pressure and flow rate data, is, however, unknown. We use a multi-scale approach where the permeability resolution is gradually increased from coarse scales to finer scales during the estimation. The aim is to refine the parameterization only where it is warranted by the observed data, and thus identify the principal discontinuities and corresponding permeability values. A motivation for the approach, based on earlier work concerning an interrelation between coarse scale, high sensitivity and low nonlinearity for certain parameter estimation problems, will also be given.
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