An Iterative Scheme to Construct Robust Proxy Models

Quantifying and understanding uncertainty in reservoir production forecasts is the key to robust reservoir management decisions. Monte-Carlo simulation is generally impractical because of the large number of subsurface realizations and the computationally intensive flow simulations. Response surface models have been introduced to improve the efficiency of the traditional asset development workflows: uncertainty assessment, history-matching and optimization of development plan. Linear regression techniques are the most popular methods to create the analytical response surfaces. However, the resulting proxies can be poor predictors of reservoir performance when strong non-linear effects are significant. We are proposing an iterative sampling strategy that is able to capture the non-linear behavior of the response and efficiently refine the proxy model. Thin-plate spline non-linear regression techniques have been selected to construct proxy models as they present a number of attractive properties. At each iteration, new combinations of parameters are rapidly evaluated with a score function and the best ones are selected for flow simulation. The benefit of the iterative scheme is demonstrated on a new field development and a mature asset with historical data. For a fixed computational cost, iterative response surfaces consistently provide better accuracy than traditional designs