Most reservoir-simulation studies are conducted in a static contextat a single point in time using a fixed set of historical data for history matching. Time and budget constraints usually result in significant reduction in the number of uncertain parameters and incomplete exploration of the parameter space, which results in underestimation of forecast uncertainty and less-than-optimal decision making. Markov Chain Monte Carlo (MCMC) methods have been used in static studies for rigorous exploration of the parameter space for quantification of forecast uncertainty, but these methods suffer from long burn-in times and many required runs for chain stabilization.
In this paper, we apply the MCMC in a real-time reservoirmodeling application. The system operates in a continuous process of data acquisition, model calibration, forecasting, and uncertainty quantification. The system was validated on the PUNQ (production forecasting with uncertainty quantification) synthetic reservoir in a simulated multiyear continuous-modeling scenario, and it yielded probabilistic forecasts that narrowed with time. Once the continuous MCMC simulation process has been established sufficiently, the continuous approach usually allows generation of a reasonable probabilistic forecast at a particular point in time with many fewer models than the traditional application of the MCMC method in a one-time, static simulation study starting at the same time.
Operating continuously over the many years of typical reservoir life, many more realizations can be run than with traditional approaches. This allows more-thorough investigation of the parameter space and more-complete quantification of forecast uncertainty. More importantly, the approach provides a mechanism for, and can thus encourage, calibration of uncertainty estimates over time. Greater investigation of the uncertain parameter space and calibration of uncertainty estimates by using a continuous modeling process should improve the reliability of probabilistic forecasts significantly.