Abstract
Data-driven models are an attractive alternative to reservoir simulation in workflows where full field-scale simulations may be computationally prohibitive [3,4]. One example is the forecasting and schedule optimization of waterflooding scenarios, where numerous function evaluations that correspond to a time consuming simulation may be required. Data-driven models must be calibrated to produce a satisfactory forecast, similar to the history matching of conventional simulation models. However, a lot of data is needed to produce a model capable of giving accurate forecasts for the flow distribution between the injectors and producers. Mature fields may have sufficient data to calibrate a purely data-driven model, but fields with limited historical data available require a different approach that can compensate for the lack of data.
Herein, under the assumption that a detailed reservoir simulation model exists, we use flow diagnostics [1] to obtain volumetric information about reservoir partioning and inter-well communication between injectors and producers. This enables us to quickly set up a data-driven model composed of a network of 1D inter-well communication models. This network of models is organized in a 2D Cartesian model, in which each row corresponds to one of the 1D flow paths that represent part of the corresponding 3D volume that is intersected by a certain well pair [3].
The initial data-driven model, before calibration, produces a good forecast for production data. The calibration process of the model is based on adjoint formulations, and the implementation is based on the automatic differentiation framework in MRST [2]. Several numerical examples will be presented, pointing out the advantages and limitations of this new methodology. To summarize, the main contributions of this methodology are:
A good forecast is obtained by an initial data-driven models (before calibration).
A simpler and very efficient calibration process is obtained by using gradient information obtained by solving the adjoint system.
A combination of flow diagnostic, adjoint methods, and automatic differentiation is used to build data-driven models for optimizing waterflooding.
[1] Olav Møyner, Stein Krogstad, and Knut-Andreas Lie. The application of flow diagnostics for reservoir management. SPE-Journal-April2015
[2] Knut-Andreas Lie. An Introduction to Reservoir Simulation Using MATLAB/GNU Octave: UserGuide for the MATLAB Reservoir Simulation Toolbox (MRST). Cambridge University Press, Jul 2019
[3] Zhenyu Guo and Albert C. Reynolds. INSIM-FT in three-dimensions with gravity. Journal-of-Computational Physics, 2019
[4] Guotong Ren, Jincong He, Zhenzhen Wang, Rami M. Younis, and Xian-Huan Wen. Implementation of physics-based data-driven models with a commercial simulator. SPE Reservoir-Simulation-Conference, 2019
Herein, under the assumption that a detailed reservoir simulation model exists, we use flow diagnostics [1] to obtain volumetric information about reservoir partioning and inter-well communication between injectors and producers. This enables us to quickly set up a data-driven model composed of a network of 1D inter-well communication models. This network of models is organized in a 2D Cartesian model, in which each row corresponds to one of the 1D flow paths that represent part of the corresponding 3D volume that is intersected by a certain well pair [3].
The initial data-driven model, before calibration, produces a good forecast for production data. The calibration process of the model is based on adjoint formulations, and the implementation is based on the automatic differentiation framework in MRST [2]. Several numerical examples will be presented, pointing out the advantages and limitations of this new methodology. To summarize, the main contributions of this methodology are:
A good forecast is obtained by an initial data-driven models (before calibration).
A simpler and very efficient calibration process is obtained by using gradient information obtained by solving the adjoint system.
A combination of flow diagnostic, adjoint methods, and automatic differentiation is used to build data-driven models for optimizing waterflooding.
[1] Olav Møyner, Stein Krogstad, and Knut-Andreas Lie. The application of flow diagnostics for reservoir management. SPE-Journal-April2015
[2] Knut-Andreas Lie. An Introduction to Reservoir Simulation Using MATLAB/GNU Octave: UserGuide for the MATLAB Reservoir Simulation Toolbox (MRST). Cambridge University Press, Jul 2019
[3] Zhenyu Guo and Albert C. Reynolds. INSIM-FT in three-dimensions with gravity. Journal-of-Computational Physics, 2019
[4] Guotong Ren, Jincong He, Zhenzhen Wang, Rami M. Younis, and Xian-Huan Wen. Implementation of physics-based data-driven models with a commercial simulator. SPE Reservoir-Simulation-Conference, 2019
