Data-driven approach to dynamic uncertainty quantification of oil well production: Decline curve analysis and Hidden Markov Model

Abstract

The upstream oil and gas industry has already used decline curve analysis to forecast oil flow rates and estimate the ultimate recovery for decades. Despite its popularity, the applications are theoretically limited and could not handle irregular variations in oil well flow behavior. In other words, it is a method for predicting the general behavior of oil wells rather than providing reliable information in specifics. It is mostly irritated by subjective implementation and a single offer of a solution without uncertainty quantification.The Hidden Markov Model (HMM) was employed in this work for dynamic uncertainty quantification in oil well flow forecast and estimated ultimate recovery (EUR). It is performed by determining the set of appropriate decline curves along with the corresponding probabilities. HMM has three main parameters: the probability transition matrix (A), the emission probability matrix (B), and the prior distribution. All these parameters can be learned from data using the Baum-Welch algorithm. The trained HMM was utilized to generate the posterior. Accordingly, using HMM and learning from the data, a dynamic probabilistic decline curve analysis is conducted. It preserves the decline curve's strength of simplicity while also covering the flaws of subjectivity and lack of uncertainty quantification. The novelty of our study is that it focuses on dynamic uncertainty quantification of oil production forecasts using new observations and covers any regular or irregular (planed or naturally stochastic) variations of flow trends. We implemented the method in cases with the variation of the flow rate by choke opening and also a sharp decline in the late time, which are not covered by decline curve analysis and not proposed in previous studies. Dynamic predictions by HMM followed the variations in flow patterns obtained by the new observations. In addition, the calculated data-driven probability distribution of EUR acceptably covers the true values.