Monte Carlo simulation for uncertainty quantification in reservoir simulation: A convergence study

The present work illustrates the convergence properties of a Monte Carlo Simulation (MCS) used to quantify the geological uncertainty in a 3D, 3-phase reservoir simulation test case. Our reservoir model along with fluid and numerical properties was obtained from a major oil and gas company. We generate 10,000 realizations of a geological model and run a Black-Oil flow simulation using a commercial reservoir simulator and a synchronous parallel implementation. The distributions of the moments and quantiles of the Net Present Value (NPV) are presented in the form of their Cumulative Density Functions (CDF). We also show the distributions of the break even time (BET) and the probability of breaking even in order to see the effect of considering quantities that are different in nature. We use log-plots to assess the convergence of the results, and verify that the convergence of the quantities of interest follows a squared-root law in the number of realizations used. We quantify the relative error made on various quantities and illustrate that the use of a small ensemble can yield errors of hundreds of percents, and that lowering the error to a given precision (e.g. below ten percent) can require thousands of realizations. For decision making and profitability assessments, using large sets of realizations is now feasible due to the availability of fast, distributed architectures and the parallel nature of MCS. Our results suggest that the improvement in the quality of the results is significant and well worth the extra effort. For optimization and sensitivity studies, running large ensembles is still intractable but yields sets of quantiles that can be used as a Reduced Order Model (ROM). Setting up a test case using this dataset is under consideration, and could provide an interesting integrated setup for comparisons of uncertainty quantification (UQ) methods.