A Review of Proxy Modeling Highlighting Applications for Reservoir Engineering

Numerical models can be used for many purposes in oil and gas engineering, such as production optimization and forecasting, uncertainty analysis, history matching, and risk assessment. However, subsurface problems are complex and non-linear, and making reliable decisions in reservoir management requires substantial computational effort. Proxy models have gained much attention in recent years. They are advanced non-linear interpolation tables that can approximate complex models and alleviate computational effort. Proxy models are constructed by running high-fidelity models to gather the necessary data to create the proxy model. Once constructed, they can be a great choice for different tasks such as uncertainty analysis, optimization, forecasting, etc. The application of proxy modeling in oil and gas has had an increasing trend in recent years, and there is no consensus rule on the correct choice of proxy model. As a result, it is crucial to better understand the advantages and disadvantages of various proxy models. The existing work in the literature does not comprehensively cover all proxy model types, and there is a considerable requirement for fulfilling the existing gaps in summarizing the classification techniques with their applications. We propose a novel categorization method covering all proxy model types. This review paper provides a more comprehensive guideline on comparing and developing a proxy model compared to the existing literature. Furthermore, we point out the advantages of smart proxy models (SPM) compared to traditional proxy models (TPM) and suggest how we may further improve SPM accuracy where the literature is limited. This review paper first introduces proxy models and shows how they are classified in the literature. Then, it explains that the current classifications cannot cover all types of proxy models and proposes a novel categorization based on various development strategies. This new categorization includes four groups multi-fidelity models (MFM), reduced-order models (ROM), TPM, and SPM. MFMs are constructed based on simplifying physics assumptions (e.g., coarser discretization), and ROMs are based on dimensional reduction (i.e., neglecting irrelevant parameters). Developing these two models requires an in-depth knowledge of the problem. In contrast, TPMs and novel SPMs require less effort. In other words, they do not solve the complex underlying mathematical equations of the problem; instead, they decouple the mathematical equations into a numeric dataset and train statistical/AI-driven models on the dataset. Nevertheless, SPMs implement feature engineering techniques (i.e., generating new parameters) for its development and can capture the complexities within the reservoir, such as the constraints and characteristics of the grids. The newly introduced parameters can help find the hidden patterns within the parameters, which eventually increase the accuracy of SPMs compared to the TPMs. This review highlights the superiority of SPM over traditional statistical/AI-based proxy models. Finally, the application of various proxy models in the oil and gas industry, especially in subsurface modeling with a set of real examples, is presented. The introduced guideline in this review aids the researchers in obtaining valuable information on the current state of PM problems in the oil and gas industry.