  In petroleum well test analysis, deconvolution is used to obtain information
about the reservoir system. 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 levels of observation error.
Using a set of flexible priors for the reservoir parameters to restrict the
solution space to physical behaviours, samples from the posterior are generated
using 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 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 that excludes
non-physical results, and we can quantify parameter uncertainty.
