Methods to mitigate loss of variance due to sampling errors in ensemble data assimilation with non-local model parameters.

Abstract Ensemble data assimilation methods are among the most successful techniques for assisted history matching. However, these methods suffer from sampling errors caused by the limited number of ensemble members employed in practical applications. A typical consequence of sampling errors is an excessive loss of ensemble variance. In practice, the posterior ensemble tends to underestimate the uncertainty range in the parameter values and production predictions. Distance-based localization is the standard method for mitigating sampling errors in ensemble data assimilation. A properly designed localization matrix works remarkably well to improve the estimate of gridblock properties such as porosity and permeability. However, field history-matching problems also include non-local model parameters, i.e., parameters with no spatial location. Examples of non-local parameters include relative permeability curves, fluid contacts, global property multipliers, among others. In these cases, we cannot use distance-based localization. This paper presents an investigation on several methods proposed in the literature that can be applied to non-local model parameters to mitigate erroneous loss of ensemble variance. We use a small synthetic history-matching problem to evaluate the performance of the methods. For this problem, we were able to compute a reference solution with a very large ensemble. We compare the methods mainly in terms of the preservation of the ensemble variance without compromising the ability of matching the observed data. We also analyse the robustness and difficulty to select proper configurations for each method. Highlights • Sampling errors due to limited ensemble size typically lead to excessive loss of posterior ensemble variance and, consequently, underestimation of uncertainty. • This paper presents an investigation on methods to mitigate loss of ensemble variance that can be applied to non-local model parameters. • The methods are compered in a small synthetic history matching problem. • All methods investigated were able to reduce the loss of variances, but in some cases, at a cost of a poor data match. [ABSTRACT FROM AUTHOR]