Bayesian deconvolution of oil well test data using Gaussian processes

J. Andrés Christen, Bruno Sansó, Mario Santana-Cibrian and Jorge X. Velasco-Hernández

Journal of Applied Statistics, 2016, vol. 43, issue 4, 721-737

Abstract: We use Bayesian methods to infer an unobserved function that is convolved with a known kernel. Our method is based on the assumption that the function of interest is a Gaussian process and, assuming a particular correlation structure, the resulting convolution is also a Gaussian process. This fact is used to obtain inferences regarding the unobserved process, effectively providing a deconvolution method. We apply the methodology to the problem of estimating the parameters of an oil reservoir from well-test pressure data. Here, the unknown process describes the structure of the well. Applications to data from Mexican oil wells show very accurate results.

Date: 2016
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DOI: 10.1080/02664763.2015.1077374

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