Summary
Pressure-rate deconvolution is a technique used in well-test analysis to improve the interpretation of late-time reservoir behavior such as compartmentalization, pressure recharge, and pore volume (PV) estimation. However, the application is mostly restricted to single-well cases with low-noise buildup pressure data and accurate flow-rate histories. This limitation arises because the deconvolution solution is nonunique, and noisy pressure data increase the number of possible solutions, errors in the rate history produce erroneous superposition effects, and multiple wells require more complex parametrizations of the response function. These practical difficulties have limited the use of deconvolution for long-term pressure interpretation, and they are the main motivation for this work.
To address the nonuniqueness in deconvolution solutions, we use a Bayesian framework that weighs the available data according to their accuracy and incorporates prior reservoir knowledge to favor realistic solutions. This approach allows us to improve flow-rate history corrections by assimilating both buildup and flowing pressure data. We implement the Bayesian framework with the ensemble smoother with multiple data assimilation (ES-MDA) method. ES-MDA has a computational cost that is feasible for cases with long histories and multiple wells, and it does not require the computation of gradients, being simple to implement. To address the additional complexity of multiwell cases, we extend the investigation of a previous work (Kubota and Piccinini 2022), which proposed a new formulation for the response function. This formulation eliminates the need for curvature penalties and late-time constraints, producing smooth solutions and consistent late-time behavior for multiple wells. However, the original evaluation of this formulation was limited to drillstem tests and synthetic cases, and the issue of solution nonuniqueness was not addressed.
Our results indicate that long-term pressure data, with inclusion of flowing periods, can be deconvolved using the Kubota and Piccinini (2022) formulation for the response function and the ES-MDA framework for data assimilation. We apply the proposed methodology to three field cases in the Campos Basin and present the results for corrected flow-rate histories, investigated PVs, productivity indices, single-well deconvolved responses, as well as interference responses for a multiwell case. The results are compared with alternative estimates. Investigated PV is compared with volumetric estimates from geological models and material balance analysis, and deconvolved responses are compared with pressure buildups and the deconvolution obtained with a commercial software.