Bayesian Variable Pressure Decline-Curve Analysis for Shale Gas Wells

Decline-curve analysis (DCA) and production forecasting are usually performed from a deterministic standpoint (point estimation). This approach does not quantify the uncertainty of the model’s parameters and thus, the model’s estimated ultimate recovery (EUR). In addition, decline-curve models do not consider the variations in the bottomhole flowing pressure (BHP), which can greatly impact the accuracy of the model’s predictions. This work combines a new technique that incorporates variable BHP conditions into DCA models with Bayesian inference to improve the accuracy of production history-matches while quantifying the uncertainty of the model’s parameters and its future production prediction. We present the application of this workflow for shale gas wells. This work uses the constant-pressure solution of the pressure diffusivity equation for a compressible fluid as a decline-curve model. The solution is a dimensionless flow rate model that can be easily scaled using two parameters: the original gas in-place and a characteristic time. Next, we apply an optimization algorithm that provides a history-match to production data subject to variable BHP. Then, this work generates the probabilistic production history-matches and forecasts using Bayesian inference treating the model’s parameters as random variables. We use an adaptive Metropolis-Hastings (M-H) Markov chain Monte Carlo (MCMC) algorithm for this purpose. Finally, we illustrate the calibration of the inferences through production hindcasts. This work introduces a method to efficiently perform probabilistic production history-matches and forecasts using decline-curve models while accounting for variable BHP effects. The results of the algorithm are the distributions of the model’s parameters and EUR estimates. In addition, the adaptive M-H MCMC uses information of previous iterations to improve the efficiency of the proposal distribution to accelerate the convergence of the Markov chains. Finally, incorporating variable BHP conditions into the algorithm constrains the model’s parameters and EUR distributions more than probabilistic DCA without considering BHP variations. This paper illustrates a workflow that generates probabilistic history-matches and production forecasts for any decline-curve model while incorporating variable BHP conditions. The method provides fast production history-matches and forecasts of shale gas wells and more accurately than traditional DCA while quantifying the uncertainty in the model’s parameters and EUR estimates. The main contribution of this work is the illustration of a new method for probabilistic variable pressure DCA.