Efficient reservoir models are more desirable for fast-paced reservoir management. Moreover, due to the complexity of flow underground, it is also essential to capture the fundamental physics for model reliability. Although they are fast, pure data-driven models frequently have issues associated with interpretability, physical consistency, and ability to forecast. On the other hand, we have used full-physics simulation models to mimic and investigate hydrocarbon systems for over several decades. However, considering its infrequent model updates related to high model complexity, it is a big challenge to manage reservoirs using full-physics models in short cycles. The objective here is to propose an approach that blends reservoir physics with data-driven models to fit in the framework of dynamic reservoir management.

We propose to use a reservoir graph network (RGNet) modeling approach based on a diffusive time-of-flight (DTOF) concept to simulate reservoir behaviors. By assimilating field observation data (such as pressure and rates), an RGNet model can be used for future predictions, scenario studies, and well-control optimizations. By discretizing DTOF of a 3D system with multiple wells, RGNet simplifies the system into a graph network represented by a set of 1D grid blocks that significantly reduces the system complexity and run time. RGNet can also handle multiple flow problems with various types of physics. In this work, we propose to use two methods to develop reliable and parsimonious models scalable to large-scale systems. In addition, we propose a more robust method to assimilate pressure data.

We applied the proposed approach to a synthetic and a field example. Two different history-matching algorithms, the ensemble smoother with multiple data assimilation (ES-MDA) and an adjoint-based method, are compared. While ES-MDA provides the capability for uncertainty analysis, an adjoint-based method generally requires fewer simulation runs to generate a posterior model. With the proposed methods for generating interwell connections, RGNet model calibration can be achieved without system redundancy and spurious long-distance well connectivity. Also, by using a more stable pressure-matching technique, we show that pressure data are better matched and reservoir volume is accurately characterized.

RGNet provides a novel hybrid physics and data-driven reservoir modeling method to fit in closed-loop reservoir management (CLRM). As RGNet models are combined with fundamental flowing physics, the calibrated model parameters are easy to interpret and understand. An RGNet model runs with far less computational cost than required by a full-physics model, which allows it to be a more practical solution to history match, predict, and optimize real assets.

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