Automatic History Matching Using Covariance Localization in ES-MDA

Reservoir numerical simulation is a core tool in petroleum engineering, with history matching essential to predictive accuracy and development decisions. Conventional history-matching methods are often inefficient, labor-intensive, and computationally expensive. Although the ensemble smoother with multiple data assimilation (ES-MDA) can accelerate automatic history matching, practical use still suffers from filter divergence and spurious correlations. We propose a covariance-localized ES-MDA that limits long-range, dynamically irrelevant correlations during updates and apply it to the PUNQ benchmark. Compared with conventional ES-MDA, the localized variant, for production-parameter inversion, reduces fitting error by 21.23%, increases convergence speed by 25%, and improves stability; for model-parameter inversion, it yields estimates closer to the reference model, lowering parameter error by 4.78%. It also reduces cumulative post-iteration divergence by 91.72%, indicating stronger data-assimilation capability and better resistance to overfitting. Overall, the covariance-localized ES-MDA enhances the accuracy and stability of reservoir history matching and offers a practical route to efficient, reliable automatic calibration of reservoir models.