Parameter Estimation for a Gas Lifting Oil Well Model Using Bayes' Rule and the Metropolis–Hastings Algorithm

Abstract

Oil well models are frequently used in the oil production process. Estimation of unknown parameters of these models has long been a question of great interest in the oil industry field. Data collected from an oil well system can be useful for identifying and characterizing the parameters in the corresponding model. In this article, we present a solution to estimate the parameters and uncertainty of a gas lifting oil well model by designing Bayesian inference and using the Metropolis-Hastings algorithm. To present and evaluate the estimation, the performance of the chains and the distributions of the parameters were shown, followed by posterior predictive distributions and sensitivity analysis. Compared with the conventional maximum likelihood estimation methods that tried to identify one optimum value for each parameter, more information of the parameters is obtained by using the proposed model. The insights gained from this study can benefit the optimization and advanced control for the oil well operation.