Bayesian approaches to deconvolution in well test analysis

In petroleum well test analysis, deconvolution is used to obtain information about the reservoir system, for example the presence of heterogeneities and boundaries. This information is contained in the reservoir response function, which can be estimated by solving an inverse problem in the well pressure and flow rate measurements. We use a non-linear Bayesian regression model based on models of reservoir behaviour in order to make inferences about the response function. This allows us to include uncertainty for the independent variables, which is essential, since the measurements are usually contaminated with observational error. We combine the likelihood with a set of flexible priors for the response parameters, and we use Markov Chain Monte Carlo algorithms in order to approximate the posterior distribution. We validate and illustrate the use of the algorithm by applying it to synthetic and field data sets, using a variety of tools to summarise and visualise the posterior distribution, and to carry out model selection. The results are comparable in quality to the state of the art solution, but our method has several advantages: we gain access to meaningful system parameters associated with the flow behaviour in the reservoir; we can incorporate prior knowledge that excludes non-physical results; and we can quantify parameter uncertainty in a principled way by exploiting the advantages of the Bayesian approach.