Most hydrocarbon fields have been operating for long enough to have significant production history. To quantify uncertainty in future yields it is essential to have a workflow that includes reservoir uncertainties in a way that respects the history. This starts with a simulation model, or more generally a forward model, that has been parameterised by uncertain input parameters with prior distributions. Proxy models can then be created to approximate chosen simulation outputs for all valid parameter combinations, based on a relatively small number of simulator runs. Each combination can be appropriately "weighted", using Bayesian methods, on the basis of the production history. This generates a probability distribution over the range of all possible history matches. Using the proxy models and Markov Chain Monte Carlo techniques it is possible to sample correctly from this probability.

Prediction uncertainty can now be calculated using two related and complementary mechanisms. The first is to take a moderately small sample (say 100) of parameter combinations to create a posterior ensemble of simulation runs. The prediction uncertainty can then be calculated directly from the ensemble of runs. The second is to create new proxy models which approximate the prediction responses of interest. The complementary benefits of the two approaches are discussed in this paper.

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