Geostatistical techniques are increasingly being used for modeling reservoir heterogeneity and assessment of uncertainty in performance predictions. Although a large number of stochastic reservoir models or realizations may be generated, in practice only a small fraction can be considered for comprehensive flow simulations. This can be done through a ranking process. Several papers have been published in the literature on ranking of realizations. However, a consistent and generally applicable set of criteria for model ranking still remains unclear.

In this paper we propose a connectivity criterion based on the streamline time-of-flight and use this criterion to rank geostatistical realizations for detailed flow simulation purposes and risk assessment. Because time-of-flights reflect fluid front propagation at various times, the connectivity in the time-of-flight provides us with a direct measure of volumetric sweep efficiency for arbitrary heterogeneity and well configuration. We show that the proposed connectivity criterion exhibits strong correlation with waterflood recovery and thus, can be used for ranking stochastic reservoir models. Unlike permeability connectivity which is a static measure independent of the flow field, the time-of-flight connectivity rigorously accounts for the interaction between the flow field and the underlying heterogeneity.

Our proposed approach has been applied to synthetic as well as field examples. Synthetic examples are used to validate the sweep efficiency calculations using the streamline time-of-flight connectivity criterion by comparison with analytic solutions and published correlations. These examples also demonstrate the superiority and effectiveness of the ranking criterion over existing methods. The field example is from the North Robertson Unit, a low permeability carbonate reservoir in west Texas. Our example includes multiple patterns consisting of 27 producers and 15 injectors and illustrates the feasibility of the approach for large-scale field applications.


Geostatistical techniques can generate fine-scale description of reservoir properties that honor a variety of available data. The differences among multiple geostatistical realizations indicate the presence of uncertainty because of lack of information and sparsity of data. Quantifying this uncertainty in terms of reservoir performance forecast would require flow simulation of a large number of these plausible reservoir descriptions. The spread in the response derived from the flow simulations can provide a measure of uncertainty. However, this approach is not feasible in practice because of the computational costs associated with multiple detailed flow simulations. Therefore, ranking of stochastic reservoir models is an economical way of quantifying the impact of uncertainty in reservoir description on reservoir performance.

Several papers have been published in the literature on ranking of geostatistical realizations.1,2,3,4,6,17,18,19 Ballin et al.1 suggested the use of a fast simulator as a surrogate for a comprehensive flow simulator. Their approach then relied on identifying an appropriate quantile-preserving response parameter for ranking realizations. A single-phase tracer simulator was used as a fast simulator and various response parameters were examined. Others5,6 have used permeability connectivity for ranking purposes. The primary difficulty with this approach is that permeability connectivity is a static measure based on the heterogeneity only and does not account for the interactions between the flow field and heterogeneity. Any measure of connectivity should take into account the imposed flow field, that is, injector-producer configurations in order to be meaningful. Saad et al.4 proposed a ranking scheme based on the tracer production history. In particular, their results show that waterflood recovery correlated well with the first moment of the tracer response for a quarter five-spot pattern. However, generalization of the approach to multiple well conditions appears to deteriorate the correlation.

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