Implementation of Physics-Based Data-Driven Models With a Commercial Simulator

Abstract

The use of full-physics models in close-loop reservoir management can be computationally prohibitive as a large number of simulation runs are required for history matching and optimization. In this paper we propose the use of a physics-based data-driven model to accelerate reservoir management and we describe how it could be implemented with a commercial simulator. In the proposed model, the reservoir is modeled as a network of 1D flow paths connecting perforations at different wells. These flow paths are discretized and the properties at each grid block along each flow path are derived from history matching of production data. To simulate flow in this network model through a commercial simulator with all the physics, an equivalent 2D Cartesian model is set up in which each row corresponds to one of the 1D flow paths. Finally, the history matching is performed with ensemble smoother with multiple data assimilation (ESMDA). The proposed network model is tested on both waterflood and steamflood problems. It is demonstrated that the proposed model matches with well-level production history (including pressure and phase flow rate) well. The calibrated ensemble from ESMDA also provided a satisfactory probabilistic forecast of future production that almost always envelops the true solutions. This indicates that the proposed model, after calibrated with production data, is accurate enough for production forecast and optimization. In addition, the use of commercial simulator in the network model provided flexibility to account for complex physics, as demonstrated by the successfully application to the steamflood problem. Compared with traditional workflow that goes through the full cycle of geological modelling, history matching and probabilistic forecasting, the proposed network model only requires production data and can be built within hours. The resulted network model also runs much faster than a full-physics as it typically has much less grid blocks. We expect the proposed method to be most useful for mature fields when abundant of production data is available. As far as we know, this is first time a physics-based data-driven model is implemented with a commercial simulator. The use of commercial simulator makes it easy to extend the model for complex reservoir such as thermal or compositional reservoirs.

Deep reinforcement learning for optimal well control in subsurface systems with uncertain geology

“…There are a number of directions for future work in this area. The computations required for training could be accelerated through use of deep learning [12] or flow network [56] surrogate models, and the use of such treatments should be investigated. The incorporation of practical constraints, including limits on the shifts in well settings from control step to control step, should be incorporated.…”

Data-driven modelling with coarse-grid network models

“…The right plot shows the network graph as a circular ring. Nodes marked with P or I contain well perforations; the remaining are reservoir nodes smoother with multiple data assimilation (EsMDA) [35], as employed in studies such as [25], exhibit similar convergence properties to the Gauss-Newton method employed herein but require simulating an ensemble of models, resulting in additional computational costs. Ensemble-based methods, however, offer the advantage of estimating model output uncertainty, assuming proper understanding of model input uncertainties.…”

“…The family of interwell numerical simulation models (INSIM) focus on the dynamic behavior and interactions between multiple wells and use analytical or semi-analytical methods to evolve pressures and fluid compositions within each interwell connection [18][19][20][21][22]. A more general approach, referred to by different authors as StellNet/GPSNet/FlowNet, is to use standard finite-volume methods to represent the interwell connections and also allow direct fluid communication among different flow paths without going through the wells [23][24][25][26][27][28][29]. Compared with these interwell models, CGNet gives a richer network that has more free parameters per grid cell and a larger set of network paths connecting each pair of wells.…”

“…We show that surprisingly accurate network models can be developed using grids with a few tens or hundreds of cells. Compared with similar interwell network models (e.g., Ren et al, 2019, 10.2118, a typical CGNet model has fewer computational cells but a richer connection graph and more tunable parameters. In our experience, CGNet models therefore calibrate better and are simpler to set up to reflect known fluid contacts, etc.…”

Discrete Well Affinity Data-Driven Proxy Model for Production Forecast

“…There are many data-driven approaches available in the industry, including the statistical data-driven model proposed by Jansen and Kelkar (1997); reduced-order models (Cardoso et al 2009); the capacitance/resistance model (Albertoni and Lake 2003;Yousef et al 2005;Holanda et al 2018); the flow-network model (Lerlertpakdee et al 2014;Ren et al 2019;Borregales et al 2020;Kiaerr et al 2020) where a complex 3D flow is represented as a set of 1D finite-difference reservoir models; the interwell numerical-simulation model (Zhao et al 2015(Zhao et al , 2020 and the interwell numerical simulation model with front-tracking for 3D multilayer reservoirs (Guo and Reynolds 2019), which applies a new Riemann solver derived from a convex-hull method that helps to solve the Buckley-Leverett problem with gravity and allows for the inclusion of wells with arbitrary trajectories with multiple perforations; and many other alternative methods that rely on artificial intelligence (Mohaghegh 2009) and data fitting (Zubarev 2009). All of these approaches have specific advantages and limitations.…”