A Bayesian Framework for Addressing the Uncertainty in Production Forecasts of Tight-Oil Reservoirs Using a Physics-Based Two-Phase Flow Model

Abstract

Summary Extrapolation of history matched single-phase flow solutions is a common practice to forecast production from tight-oil reservoirs. Nonetheless, this approach (a) omits multiphase flow effects that exist below bubblepoint conditions and (b) has not included the quantification of the uncertainty of the estimated ultimate recovery (EUR). This work combines a new two-phase (oil and gas) flow solution within a Bayesian framework to address the uncertainty in the EUR. We illustrate the application of the procedure to tight-oil wells of west Texas. First, we combine the oil and the gas flow equations into a single dimensionless two-phase flow equation. The solution is a dimensionless flow rate model that can be easily scaled using two parameters: hydrocarbon pore volume and characteristic time. Second, this study generates the probabilistic production forecasts using a Bayesian approach in which the parameters of the model are treated as random variables. We construct parallel Markov chains of the parameters using an adaptative Metropolis-Hastings (M-H) Markov chain Monte Carlo (MCMC) for this purpose. Third, we evaluate the robustness of our inferences using posterior predictive checks (PPCs). Finally, we quantify the uncertainty in the EUR percentiles using the bootstrap method. The results of this research are as follows. First, this work shows that EUR estimates based on single-phase flow solutions will consistently underestimate the ultimate oil recovery factors in solution-gas drives where the reservoir pressure is less than the bubblepoint. The degree of underestimation will depend on the reservoir and flowing conditions as well as the fluid properties. Second, the application of parallel Markov chains using an adaptative M-H MCMC scheme that addresses the correlation between the model’s parameters solves the issues of mixing and autocorrelation of Markov chains and, thus, it speeds up speeding up the convergence of the Markov chains. Third, we generate replicated data from our posterior distributions to assess the robustness of our inferences (PPCs). Finally, we use hindcasting to calibrate and strengthen our inferences. To our knowledge, all these approaches are novel in EUR forecasting. Using a Bayesian framework with a low-dimensional (two-parameter) physics-based model provides a fast and reliable technique to quantify the uncertainty in production forecasts. In addition, the use of parallel chains with an adaptative M-H MCMC accelerates the rate of convergence and increases the robustness of the method.