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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.
Closed loop reservoir management is challenged with building reliable and fast predictive reservoir models to make field decisions. Traditional numerical simulation models can be difficult to characterize, tedious to build and calibrate, and at times computationally prohibitive for short term decision cycles in field applications. On the other hand, pure data-driven methods often lack physical insights and have limited range of applicability. For operational scenarios such as short-term production forecasting, waterflood optimization, production control and understanding major reservoir mechanisms, it is desirable to use a reservoir modeling methodology that is easy to build, history match, compute and interpret.
In this work, we propose to use a hybrid and efficient reservoir graph network (RGNet) modeling approach based on time of flight concept that can be built using routinely measured field measurements (such as pressure and rates) and can be used for real-time forecasts, scenario modeling, production optimization and control.
We propose a gridding method based on discretized time of flight for multi-well scenario with interference. It simplifies the 3D reservoir flow problem into a graph network representation that can be solved with any commercial reservoir simulator, which enables the RGNet model to be readily applied for various types of fluid physics. The parameters in RGNet model are obtained through assimilating observed data. The RGNet model has a very compact model representation that requires significantly less complexity compared with full-physics 3D models, which leads to very fast simulation. The efficiency of RGNet makes it appealing for applications where many simulation runs are needed.
We applied the proposed approach on SPE benchmark reservoir simulation models for single well, multi-well with interference and injector-producer pairs. The calibrated models are used to quantify uncertainty for production forecasting. In all cases, the range of uncertainty is reduced effectively and efficiently with data assimilation. The posterior RGNet models are also shown to provide reasonable estimates of reservoir and well drainage volumes. By virtue of the reduced complexity, the modeling methodology is highly scalable while still retains physical interpretability (in terms of pore volume and transmissibility). We also discuss the potential applications of the method such as reservoir connectivity analysis and well control optimization.
The proposed reservoir graph network (RGNet) modeling approach provides a unique and sustainable way to combine advanced analytics and physics to develop an explainable dynamic reservoir model that can be effectively used to understand reservoir behavior and optimize performance. The lightweight model lends itself naturally to fast computation that are required for scenario analysis and optimization.
Closed-loop reservoir management (CLRM) consists of continuous application of history matching and optimization of model-predictive control to maximize production or reservoir net present value in any given period. Traditional field-scale implementation of CLRM by using a large number of reservoir models, in particular when uncertainty is accounted for, is computationally impractical. This presented machine-learning assisted workflow uses the Echo State Network (ESN) coupled with an empirical water fractional flow relationship as a proxy to replace time-consuming simulations and improve the computational efficiency of the CLRM. The ESN, under the paradigm of reservoir computing, provides a specific architecture and supervised learning principle for recurrent neural networks (RNN). ESNs, with randomly generated and invariant input weights and recurrent weights, greatly minimize the computational load and solve potential problems during typical backpropagation through time in traditional RNNs while it still obtains the benefits of RNNs to memorize temporal dependencies. Also, the linear readout layer makes the training much faster by using analytical Ridge Regression. Field level well control and production response data are fed into the workflow to obtain a trained ESN and fitted fractional flow relationship, which will represent/reproduce the dynamics of the reservoir under various well control scenarios. Further production optimization is directly applied on the matched models to maximize reservoir net present value. Optimized well control scenario is applied and further observation is obtained to update the models. History matching and production optimization are performed again in a closed-loop fashion. The aforementioned advantages make ESN a very powerful tool for CLRM with both history matching and production optimization quickly accomplished and make near-real-time CLRM possible. In the research, two case studies will be presented to prove the effectiveness of the proposed workflow.
Abstract We develop a new data-driven model for the assisted history matching of production data from a reservoir under waterflood. Although the model is developed from production data and requires no prior knowledge of rock property fields, it incorporates far more fundamental physics than that of the popular capacitance-resistance model (CRM). The new model also represents a substantial improvement on an interwell numerical simulation model (INSIM) which was presented previously in a paper co-authored by the last two authors of the current paper. The new model, which is referred to as INSIM-FT, eliminates the three deficiencies of the original INSIM data-driven model. (1) For some complex cases, e.g., when a producer is converted to an injector or when injected water from more than one injector passes through an intermediate well node, the INSIM procedure for calculation of water saturation degrades to an ad hoc calculation which introduces inaccuracies. Our new model uses an accurate front-tracking procedure to calculate water saturation, hence the name INSIM-FT. (2) The original INSIM formulation assumes relative permeabilities are known a priori which defeats the objective of finding a model without requiring knowledge of petrophysical properties; INSIM-FT estimates relative permeabilities by historymatching. (3) Unlike CRM, the original INSIM model does not provide a reasonable characterization of how water from an injector is allocated among producers and thus does not reliably identify large-scale geological features such as faults. INSIM-FT remedies this INSIM deficiency. The reliability of INSIM-FT for history-matching, future reservoir performance prediction and reservoir characterization is validated with two synthetic models, and its performance is compared with that of CRM. Finally, INSIM-FT is applied to a field case.
Summary Closed‐loop reservoir management (CLRM) consists of continuous application of history matching and optimization of model‐predictive control to maximize production or reservoir net present value (NPV) in any given period. Traditional field‐scale implementation of CLRM by using a large number of reservoir models, in particular when uncertainty is accounted for, is computationally impractical. This presented machine-learning-assisted workflow uses the echo state network (ESN) coupled with an empirical water fractional flow relationship as a proxy to replace time‐consuming simulations and improve the computational efficiency of the CLRM. The ESN, under the paradigm of reservoir computing, provides a specific architecture and supervised learning principle for recurrent neural networks (RNNs). ESNs, with randomly generated and invariant input weights and recurrent weights, greatly minimize the computational load and solve potential problems during typical backpropagation through time in traditional RNNs while it still obtains the benefits of RNNs to memorize temporal dependencies. Also, the linear readout layer makes the training much faster using analytical ridge regression. Field‐level well control and production‐response data are fed into the workflow to obtain a trained ESN and fitted fractional‐flow relationship, which will represent/reproduce the dynamics of the reservoir under various well‐control scenarios. Further production optimization is directly applied to the matched models to maximize reservoir NPV. The optimized well‐control scenario is applied, and further observation is obtained to update the models. History matching and production optimization are performed again in a closed‐loop fashion. The previously mentioned advantages make ESN a very powerful tool for CLRM, with both history matching and production optimization quickly accomplished, and make near‐real‐time CLRM possible. In this paper, two case studies will be presented to prove the effectiveness of the proposed workflow.