Brown fields are fields with significant production history. Probabilistic forecasting for brown fields requires multiple history-matched models that are conditioned to available field production data. This paper presents a systematic and practical workflow to generate an ensemble of simulation models that is able to capture uncertainties in forecasts, while honoring the observed production data.

The proposed workflow employs the Bayes theorem to define a posterior Probability Density Function (PDF) that represents model forecast uncertainty by incorporating the misfit between simulation results and measured production data. Previous workflows use the Markov Chain Monte Carlo (MCMC) sampling method, which requires an extremely large number (thousands) of simulation runs. To alleviate this drawback, a Proxy-based Acceptance-Rejection (PAR) sampling method is developed in this study to generate representative simulation models that characterize the posterior PDF using hundreds of simulation runs. The proposed workflow can be summarized in five key steps:

  1. Run an initial set of reservoir simulations by simultaneously varying multiple uncertain parameters using an experimental design method.

  2. Construct a proxy function using a Radial-Basis Function (RBF) neural network to approximate the posterior PDF calculated from the initial set of simulation results.

  3. Sample the posterior PDF using the PAR sampling method and run an ensemble of new simulation models using the sample values.

  4. The new simulation results obtained in step 3 are added to the training datasets generated in step 1 to improve the accuracy of the proxy function. Steps 3 and 4 are repeated until a predefined stop criterion is satisfied.

  5. Filter all simulation runs generated in step 3 using appropriate tolerance criteria for various history-match quality indicators. The selected filtered cases constitute the final ensemble of simulation models that can be further used for uncertainty quantification in forecasting.

The proposed workflow is demonstrated on two reservoir simulation models:

  1. Synthetic case. The forecast uncertainty of the ninth SPE Comparative Solution Project (SPE9) simulation model is investigated with a synthetic production history and 32 uncertain parameters.

  2. Unconventional oil field case. The workflow is applied to an Eagle Ford shale oil well to determine P90 (conservative), P50 (most likely), and P10 (optimistic) cases of estimated ultimate recovery (EUR).

Results of the workflow are compared to those obtained using the Metropolis-Hasting MCMC sampling method. The comparison shows that the proposed workflow only requires 800 simulation runs to obtain results as accurate as the MCMC method with 8000 simulation runs. This translates into a 10- times speedup, which makes the proposed workflow practical for many real reservoir simulation studies.

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