Efficient history matching using a multiscale technique

It is demonstrated that a method for multiscale history matching can be used to improve efficiency and/or quality of the solution when achieving a fine-scale match as compared to history-matching directly on the fine scale. Starting from a given fine-scale realization, coarser models are generated using a global upscaling technique in which the coarse models are "history matched" with respect to the solution at the fine scale. Conditioning to dynamic data is performed by history matching a coarse model, and this model is then successively refined using a combination of downscaling and history matching until a model that matches dynamic data is obtained at the finest scale. Bias in predicted data because of upscaling errors may be taken into account. The advantage of this procedure is that the large-scale corrections are obtained using fast models that-combined with proper downscaling procedures-provide a better initial model for the final adjustment on the fine scale. Coarse-scale history matching also provides a regularization of the fine-scale match, making the process less dependent on a correct prior model. With the proposed methodology, a series of models with varying degrees of complexity-all being consistent with both static and dynamic data-may be generated without additional cost. Effects of including a priori information and different initial downscaling techniques, such as sampling or sequential Gaussian simulation with block kriging (SGSBK), are investigated using two synthetic reservoir models.