Classic identifiability analysis of flow barriers in incompressible single-phase flow reveals that it is not possible to identify the location and permeability of low-permeable barriers from production data (well bore pressures and rates), and that only averaged reservoir properties in-between wells can be identified. We extend the classic analysis by including compressibility effects. We use two approaches: 1) a twin-experiment with synthetic production data for use with a time-domain parameter estimation technique, and 2) a transfer function formalism in the form of bilaterally coupled four-ports allowing for an analysis in the frequency domain. We investigate the identifiability, from noisy production data, of the location and the magnitude of a low-permeable barrier to slightly-compressible flow in a one-dimensional configuration. We use an unregularized adjoint-based optimization scheme for the numerical time-domain estimation, using various levels of sensor noise, and confirm the results using the semi-analytical transfer function approach. Both the numerical and semi-analytical results show that it is possible to identify the location and the magnitude of the permeability in the barrier from noise-free data. By introducing increasingly higher noise levels the identifiability gradually deteriorates, but the location of the barrier remains identifiable for much higher noise levels than the permeability. The shape of the objective function surface, in normalized variables, indeed indicates a much higher sensitivity of the well data to the location of the barrier than to its magnitude. These theoretical results appear to support the empirical finding that unregularized gradient-based history matching in large reservoir models, which is well known to be a severely ill-posed problem, occasionally leads to useful results in the form of model parameter updates having unrealistic magnitudes but indicating the correct location of model deficiencies.

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