Continuous Reservoir Simulation Model Updating and Forecasting Using a Markov Chain Monte Carlo Method

摘要

Most reservoir simulation studies are conducted in a static context - at 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 unknown 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 MCMC in a real-time reservoir modeling application. The system operates in a continuous process of data acquisition, model calibration, forecasting, and uncertainty quantification. Since it operates continuously, over time 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. The system was validated on the PUNQ synthetic reservoir in a simulated years-long, continuous modeling scenario and yielded probabilistic forecasts that narrow with time. The continuous MCMC simulation approach 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 simulation study. It also provides a mechanism for calibrating uncertainty estimates over time.