History Matching in Low-Dimensional Connectivity-Vector Space

History matching is a high-dimensional and severely non-linear optimization problem, often requiring some form of dimensionality reduction. In addition, the history-matched models should honor prior geologic information often integrated within geostatistical algorithms. Traditional optimization methods that can handle these problems are, however, time-consuming and highly-dependent upon the initial realization. In this study, we generated a large set of equi-probable realizations that honor prior information (training image) by means of multiple-point geostatistical simulations. A history-matched model is obtained by searching amongst the set of initial realizations. In order to do this, we assigned each realization its proper connectivity vector. A connectivity vector is calculated by means of TOF (time-of-flight) between an injector and a producer. The connectivity vector is directly related to the production history of existing producers in the field. It provides two main advantages to rearrange the set of realizations into connectivity-vector space. First, the new space is very low-dimensional (the number of producers) while the set of realizations originally exists in extremely high-dimensional space (the number of grid-blocks). Secondly, in the new space, the objective function changes very smoothly with distance, which means that we can apply various optimization methods (neighborhood algorithm, gradient-based method, etc) more efficiently.