Development Of Proxy Models For Reservoir Simulation By Sparsity Promoting Methods And Machine Learning Techniques
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2018 European Association of Geoscientists and Engineers EAGE. All rights reserved. Learning from data has been a rich topic of research in many engineering disciplines. In particular, in reservoir engineering, data-driven methodologies have been applied successfully to infer interwell connections and flow patterns in the subsurface and in assisting field development plans, including, history matching and performance prediction phases, of conventional and unconventional reservoirs. Although real-time data acquisition and analysis are becoming routine in many workflows, there is still a disconnect with the traditional theoretical first laws principles, whereby conservation laws and phenomenological behavior are used to derive the underlying spatio-temporal evolution equations. In this work, 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. The solution is assumed sparse because we know there is only few terms are relevant for each governing equation. The sparse structure is invoked by two methods: sparse regression with hard threshold (SINDy) and sparse regression with soft threshold (LASSO). For each method to work properly without overfitting, unique ways have been developed for seeking a balance between accuracy and complexity of the model with either l1 or l2 norm penalty. In addition, the sparsity structure can be further fixed with the physical fact that flow term is only related with its adjacent cells. We apply the method to a two-dimensional single phase flow system. First, the time series data is generated from the simulator with recording points equally spread in space. Then a large library is built containing possible linear, nonlinear terms of the governing ODE equation and finally the combination of the terms is identified through a coefficient vector for each equation. Difference in each technique and detailed modification to the threshold tolerance and penalty factor will be discussed and compared. Extensions to the two-phase flow case is also underway and promising initial results will also be shown in this paper. The validation process is achieved by comparing the original single/two phase simulator results and the results solved from the identified ODE system by Newton iteration.
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ECMOR XVI - 16th European Conference on the Mathematics of Oil Recovery
