Abstract
This work describes a methodology that evaluates the Discrete Latin Hypercube with Geostatistical Realizations (DLHG) sample size for complex models in the history matching under uncertainties process with application to the Norne Benchmark Case. The sample size affects the time demanded and results accuracy in a history matching process because a small sample size can yield inaccurate risk quantification and a high sample size can demand excessive time to reach good results. Both factors should be evaluated in order to improve the project's efficiency and to obtain reliable results. Such evaluation gains greater importance in complex reservoir models because the number of tests to determine the reservoir scenarios that match dynamic data can be high due to the level of complexity. The methodology presented in this work is divided in three steps. First, we evaluate the ability of DLHG to produce output cumulative distribution functions (CDF) that replicate a more exhaustive sampling technique (Monte Carlo) using the Kolmogorov-Smirnov test. The output is the misfit between observed and simulated production rates; then, we compare the influence and correlation matrices obtained with DLHG and Monte Carlo samples. The influence matrix shows the impact of the uncertainty variation on the outputs and the correlation matrix measures the strength of the dependence between the uncertainty attributes and outputs. Finally, we perform the stability test. The methodology was applied to the Norne benchmark case; a field located in the Norwegian Sea. The main characteristics of the methodology are: (1) it uses a statistical technique to compare the output CDFs from the reference and DLHG samples and (2) it evaluates the ability of the DLHG sample to identify the reservoir attributes that affect the history match results. We evaluated DLHG sample sizes of 20, 50, 100 and 200, and considered a MC sample size of 5,000 to the Norne benchmark case. The DLHG CDFs for the 100 sample size was able to accurately replicate the corresponding MC CDFs, however it did not replicated the behavior of the influence and correlation matrices. The DLHG sample size of 200 was able to reproduce the CDFs outputs, the influence and correlation matrices and it was considered stable. The study showed that even if the sample size is able to represent the CDFs outputs from a reference solution, the influence and correlation matrices should be evaluated. The methodology presented can be incorporated into usual history match routines.
