A Bayesian multi‐region radial composite reservoir model for deconvolution in well test analysis

Themistoklis Botsas, Jonathan A. Cumming and Ian H. Jermyn

Journal of the Royal Statistical Society Series C, 2022, vol. 71, issue 4, 951-968

Abstract: In petroleum well test analysis, deconvolution is used to obtain information about reservoir systems, for example the presence of heterogeneities and boundaries. This information is contained in the response function, which can be estimated by solving an inverse problem in the pressure and flow rate measurements. Our Bayesian approach to this problem is based upon a parametric physical model of reservoir behaviour, derived from the solution for fluid flow in a general class of reservoirs. This permits joint parametric Bayesian inference for both the reservoir parameters and the true pressure and rate values, which is essential due to the typical observational error levels. Using sets of flexible priors for the reservoir parameters to restrict the solution space to physical behaviours, samples from the posterior are generated using Markov Chain Monte Carlo. Summaries and visualisations of the posterior, response, and true pressure and rate values can be produced, interpreted, and model selection can be performed. The method is validated through a synthetic application, and applied to a field data set. The results are comparable to the state of the art solution, but through our method we gain access to system parameters, we can incorporate prior knowledge, and we can quantify parameter uncertainty.

Date: 2022
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