Physics Constrained Data-Driven Technique for Reservoir Proxy Model and Model Order Reduction

In reservoir engineering, data-driven methodologies have been applied successfully to infer interwell connections and flow patterns in the subsurface, model order reduction of reservoir simulations, and in assisting field development plans, including, history matching and performance prediction phases, of conventional and unconventional reservoirs. In this work, we propose to utilize data driven methods for achieving two main objectives: (1) enhance model order reduction (MOR) techniques accounting for sparsity in the data; and (2) reservoir simulation proxy model development based solely on data. For the first objective, fast simulation algorithms based on reduced-order modeling have been developed in order to facilitate large-scale and complex computationally intensive reservoir simulation and optimization. Methods like proper orthogonal decomposition (POD) and Dynamic Mode Decomposition (DMD) have been successfully used to efficiently capture and predict the behavior of reservoir fluid flow. Non-intrusive techniques (e.g., DMD), are especially attractive as it is a data-driven approach that do not require code modifications (equation free). To achieve our first objective with the concept of sparsity in statistical learning, we further enhance the performance and reduce the dimension of standard DMD, by investigating sparse approximations of the snapshots. The method to achieve the second objective can further be classified into two categories: (1) building proxy model by system identification method; and (2) end to end production prediction with machine learning techniques. Although real-time data acquisition and analysis, are becoming routine in many workflows (such as in reservoir simulations), there is still a disconnect between raw data and the traditional theoretical first laws principles, whereby conservation laws and phenomenological behavior are used to derive the underlying spatio-temporal evolution equations. We propose to combine sparsity promoting methods and machine learning techniques to find the governing equation from the spatio-temporal data series from a reservoir simulator. The idea is to connect data with the physical interpretation of the dynamical system. We achieve this by identifying the nonlinear ODE system equations of our discretized reservoir system. In addition, as production prediction analysis has been the ultimate goal of many reservoir simulation/modeling, various types reservoir simulation has been developed to build efficient and accurate model to provide the most information about reserves and aid in decision making process. The other proxy model we developed is benefit from the evolution of machine learning technique and increasing availability of extensive amounts of historical data. A powerful technique called recurrent neural network (RNN) has been proved useful for modeling with sequence data. We apply RNN on analyzing control parameter data and synthetic historical production data for better reservoir characterization and prediction. All of the above mentioned MOR and proxy model development will be tested on single- and two-phase fluid flow reservoir simulation problem