Integrating Model Uncertainty in Probabilistic Decline-Curve Analysis for Unconventional-Oil-Production Forecasting

Abstract

Summary Decline-curve analysis (DCA) for unconventional plays requires a model that can capture the characteristics of different flow regimes. Thus, various models have been proposed. Traditionally, in probabilistic DCA, an analyst chooses a single model that is believed to best fit the data. However, several models might fit the data almost equally well, and the one that best fits the data might not best represent the flow characteristics. Therefore, uncertainty remains regarding which is the “best” model. This work aims to integrate model uncertainty in probabilistic DCA for unconventional plays. Instead of identifying a single “best” model, we propose to regard any model as potentially good, with goodness characterized by a probability. The probability of a model being good is interpreted as a measure of the relative truthfulness of this model compared with the other models. This probability is subsequently used to weight the model forecast. Bayes' law is used to assess the model probabilities for given data. Multiple samples of the model-parameter values are obtained using maximum likelihood estimation (MLE) with Monte Carlo simulation. Thus, the unique probabilistic forecasts of each individual model are aggregated into a single probabilistic forecast, which incorporates model uncertainty along with the intrinsic uncertainty (i.e., the measurement errors) in the given data. We demonstrate and conclude that using the proposed approach can mitigate over/underestimates resulting from using a single decline-curve model for forecasting. The proposed approach performs well in propagating model uncertainty to uncertainty in production forecasting; that is, we determine a forecast that represents uncertainty given multiple possible models conditioned to the data. The field data show that no one model is the most probable to be good for all wells. The novelties of this work are that probability is used to describe the goodness of a model; a Bayesian approach is used to integrate the model uncertainty in probabilistic DCA; the approach is applied to actual field data to identify the most-probable model given the data; and we demonstrate the value of using this approach to consider multiple models in probabilistic DCA for unconventional plays.