Adjusting parameters in reservoir models by minimizing the discrepancy between the model's predictions and actual measurements is a popular approach known as history matching. One of the most effective techniques is gradient-based history matching. For reservoir models, the number of grid blocks and therefore, the size of the problem can become very large. In recent years, model-order reduction techniques aiming to replace large, complex dynamic systems with lower-dimension models have been incorporated into history matching. In both gradient-based history matching and model-reduced gradient-based history matching, first-order optimization methods are used in order to minimize the mismatch between simulated well-production data and observed production. In this work, we investigate the performance of some optimization methods on the minimization problem in model-reduced gradient-based history matching. The methods were tested on the history matching of a small reservoir model with synthetic measurements. Our results show that fast first-order techniques such as the spectral projected gradient method can compete with the popular quasi-Newton BFGS approach.


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