It is not trivial to devise a universally accepted metric to assess the convergence of a Monte Carlo process. For the case of reservoir model, there is no "true" solution to compare against, so there is no choice but to reach statistical convergence if one wants to compute the expected value, standard deviation, quantiles, and so forth. Although we are lacking a reliable metric to assess convergence, looking at logarithmic plots can provide an estimate of how close one may be to a converged value. We call "eyeball test". The assertion that from looking at the log plot, the variation is reduced enough to confidently use the results the main objective of this work is to illustrate the potential issues of relying on non-converged Monte Carlo Simulation to estimate quantities such as the Original Hydrocarbon in place (OHIP) in the context of reservoir simulation. We will show that even in a limited-uncertainty setup, the quantiles, and the moments of OHIP as will also illustrate that the converged quantiles accurately represent the uncertainty of the system and can be used as a reduced order model for sensitivity studies.
The current work illustrates the convergence properties of a Monte Carlo Simulation used to quantify the geological uncertainty of probabilistic estimation of OHIP. We investigate the convergence behavior of Monte Carlo Simulation on 3D reservoirs model using
Two options for monitoring and stopping Monte Carlo Simulation :
Post processing calculation (settlement of Statistical Moment)
Automatic Realtime monitoring (Specific Error Bound)
The distributions of the moments and quantiles of the OHIP from10,000 realizations of a geological model are presented in the form of their Cumulative Density Functions. Stability of the computed moments is assessed by plotting the sample moments of the target variable evaluated at specific points as a function of the number of Monte Carlo Simulation performed. Our results suggest that the improvement in the quality of the results is significant and well worth the extra effort. For sensitivity studies, running large ensembles is still intractable but yields set of quantiles that can be used as a Reduced Order Model. The conclusions we draw are applicable to a wide range of similar 3D reservoir model. The sensitivity of Monte Carlo Simulation to the number of realizations used is often overlooked. Even though convergence studies are rare and convergence criteria hard to estimate, uncertainty quantification using Monte Carlo Simulation is an increasingly important part of static modeling workflows