Rapid Construction of High-Resolution Models Constrained to Dynamic Data

Distance-based techniques have recently emerged in the context of ensemble modeling, in particular for history matching, model selection and uncertainty quantification. Starting with an initial ensemble of model realizations, a distance between any two realizations is defined. The purpose of this distance is to introduce the purpose of modeling into the process of geological modeling, thereby potentially enhancing the efficiency of techniques such as history matching. If one wants to create new models that are constrained to dynamic data (history matching), the calculation of the distance requires flow simulation for every model in the initial ensemble. This can be very time consuming, especially for high-resolution models. In this paper, we present a multi-scale framework for ensemble modeling. We propose to construct new fine-scale, high resolution models constrained to dynamic data, while performing flow simulations on the associated, upscaled coarse-grid models. An error modeling procedure is used in the calculation of the distance to account for the error in the upscaling. We demonstrate the efficiency of the method on two examples, one where the upscaling error is small, and another where the upscaling error is significant. Results show that the error modeling procedure can accurately capture the error in upscaling, and can reproduce with sufficient accuracy the fine-grid behavior from coarse-grid simulations. As a consequence, an ensemble of fine-grid, high resolution models can be obtained which are constrained to dynamic data, but with a minimum of simulations at the fine scale.