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In petroleum well test analysis, deconvolution is used to obtain informationabout the reservoir system. This information is contained in the responsefunction, which can be estimated by solving an inverse problem in the pressureand flow rate measurements. Our Bayesian approach to this problem is based upona parametric physical model of reservoir behaviour, derived from the solutionfor fluid flow in a general class of reservoirs. This permits joint parametricBayesian inference for both the reservoir parameters and the true pressure andrate values, which is essential due to the typical levels of observation error.Using a set of flexible priors for the reservoir parameters to restrict thesolution space to physical behaviours, samples from the posterior are generatedusing MCMC. Summaries and visualisations of the reservoir parameters'posterior, response, and true pressure and rate values can be produced,interpreted, and model selection can be performed. The method is validatedthrough a synthetic application, and applied to a field data set. The resultsare comparable to the state of the art solution, but through our method we gainaccess to system parameters, we can incorporate prior knowledge that excludesnon-physical results, and we can quantify parameter uncertainty.

A Bayesian approach to deconvolution in well test analysis