An alternative proxy for history matching using proxy-for-data approach and reduced order modeling

• Improved the proxy quality of history matching mismatch functions with the PFD approach.
• Reduced-order models introduced to tackle problems with large numbers of data points.
• Consistent improvement in proxy quality observed in both synthetic and field cases.

Response surface methods are commonly used in history matching process to approximate the functional relationship between the input parameters and the aggregated mismatch. The quality of the proxy (accuracy in prediction) degrades as the nonlinearity of the response surface increases. However, commonly-used definitions of aggregated mismatch, such as root mean squared error (RMSE) or mean absolute error (MAE), are highly nonlinear. As a result, the quality of the proxy for aggregated mismatch can be unsatisfying in many cases.In this work, we propose the proxy-for-data (PFD) approach, in which one proxy is built for each observation data point and then the data values predicted by those proxies are used to calculate the aggregated mismatch. Because proxies are constructed for the data themselves rather than for the aggregated mismatch, the nonlinearity of the aggregated mismatch definition will not affect the quality of the proxy. It is shown in multiple test cases that the new approach could potentially improve proxy quality for different types of proxies and different aggregated mismatch definitions. For cases with a large amount of observation data points, we also show that the use of reduced-order modeling can efficiently reduce the number of proxies needed and achieve similar improvement. The new approach is successfully applied to both synthetic and field examples and both examples show improved proxy quality.