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-permeability barriers from production data (wellbore 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: a twin experiment with synthetic production data for use with a time-domain parameter-estimation technique, and 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-permeability barrier to slightly compressible flow in a 1D configuration. We use an unregularized adjoint-based optimization scheme for the numerical time-domain estimation, by use of various levels of sensor noise, and confirm the results by use of the semianalytical transfer-function approach. Both the numerical and semianalytical 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 with unrealistic magnitudes but indicating the correct location of model deficiencies.

SUMMARYIt is well known that parameter updating of large-scale numerical reservoir flow models (a.k.a. 'computer assisted history matching') is an ill-posed inverse problem. Typically the number of uncertain parameters in a reservoir flow model is very large whereas the available information for estimating these parameters is limited. The classic solution to this problem is to regularize the unknowns, e.g. by penalizing deviations from a prior model. Attempts to estimate all uncertain parameters from production data without regularization typically lead to unrealistically high parameter values and therefore to updated parameter fields that have little or no geological realism. However, it has been suggested that the application of unregularized reservoir parameter estimation may still add value, because it, sometimes, gives an indication of the location of significant missing features in the model. We investigated under which conditions this perceived added value might occur. We conducted several twin experiments and applied unregularized parameter estimation to update uncertain parameters in a simple two-dimensional reservoir model that contained a major deficiency in the form of a missing high or low permeability feature. We found that in case of low-permeability barriers or high-permeability streaks it is indeed sometimes possible to localize the position of the model deficiency. To further analyze this behavior we conducted onedimensional experiments using a transfer function formalism to characterize the identifiability of the location and magnitude of model deficiencies (flow barriers).