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Durham University

Department of Mathematical Sciences


Publication details

Cumming, J A, Botsas, T, Jermyn, I H & Gringarten, A C (2020), Assessing the Non-Uniqueness of a Well Test Interpretation Model Using a Bayesian Approach, SPE Virtual Europec 2020. Society of Petroleum Engineers, SPE-200617-MS.

Author(s) from Durham


Objectives/Scope: A stable, single-well deconvolution algorithm has been introduced for well test analysis in the early 2000’s, that allows to obtain information about the reservoir system not always available from individual flow periods, for example the presence of heterogeneities and boundaries. One issue, recognised but largely ignored, is that of uncertainty in well test analysis results and non-uniqueness of the interpretation model. In a previous paper (SPE 164870), we assessed these with a Monte Carlo approach, where multiple deconvolutions were performed over the ranges of expected uncertainties affecting the data (Monte Carlo deconvolution).
Methods, Procedures, Process: In this paper, we use a non-linear Bayesian regression model based on models of reservoir behaviour in order to make inferences about the interpretation model. This allows us to include uncertainty for the measurements which are usually contaminated with large observational errors. We combine the likelihood with flexible probability distributions for the inputs (priors), and we use Markov Chain Monte Carlo algorithms in order to approximate the probability distribution of the result (posterior).
Results, Observations, Conclusions: We validate and illustrate the use of the algorithm by applying it to the same synthetic and field data sets as in SPE 164870, using a variety of tools to summarise and visualise the posterior distribution, and to carry out model selection.
Novel/Additive Information: The approach used in this paper has several advantages over Monte Carlo deconvolution: (1) it gives access to meaningful system parameters associated with the flow behaviour in the reservoir; (2) it makes it possible to incorporate prior knowledge in order to exclude non-physical results; and (3) it allows to quantify parameter uncertainty in a principled way by exploiting the advantages of the Bayesian approach.