scholarly journals A POD Coupled Adaptive DEIM (POD-ADEIM) Reduced-Order Model for Incompressible Multiphase Flow in Porous Media

2019 ◽  
Vol 22 (3) ◽  
pp. 141-142
Author(s):  
Jingfa Li ◽  
Shuyu Sun ◽  
Bo Yu ◽  
Yang Liu ◽  
Tao Zhang
Keyword(s):  
Porous Media ◽  
Multiphase Flow ◽  
Reduced Order Model ◽  
Flow In Porous Media ◽  
Order Model ◽  
Reduced Order

scholarly journals An efficient multigrid-DEIM semi-reduced-order model for simulation of single-phase compressible flow in porous media

2020 ◽  
Author(s):  
Jing-Fa Li ◽  
Bo Yu ◽  
Dao-Bing Wang ◽  
Shu-Yu Sun ◽  
Dong-Liang Sun
Keyword(s):  
Porous Media ◽  
Equation Of State ◽  
Single Phase ◽  
Reduced Order Model ◽  
Flow In Porous Media ◽  
Order Model ◽  
Reduced Order ◽  
Proposed Model ◽  
Speed Up ◽  
Robinson Equation

Abstract In this paper, an efficient multigrid-DEIM semi-reduced-order model is developed to accelerate the simulation of unsteady single-phase compressible flow in porous media. The cornerstone of the proposed model is that the full approximate storage multigrid method is used to accelerate the solution of flow equation in original full-order space, and the discrete empirical interpolation method (DEIM) is applied to speed up the solution of Peng–Robinson equation of state in reduced-order subspace. The multigrid-DEIM semi-reduced-order model combines the computation both in full-order space and in reduced-order subspace, which not only preserves good prediction accuracy of full-order model, but also gains dramatic computational acceleration by multigrid and DEIM. Numerical performances including accuracy and acceleration of the proposed model are carefully evaluated by comparing with that of the standard semi-implicit method. In addition, the selection of interpolation points for constructing the low-dimensional subspace for solving the Peng–Robinson equation of state is demonstrated and carried out in detail. Comparison results indicate that the multigrid-DEIM semi-reduced-order model can speed up the simulation substantially at the same time preserve good computational accuracy with negligible errors. The general acceleration is up to 50–60 times faster than that of standard semi-implicit method in two-dimensional simulations, but the average relative errors of numerical results between these two methods only have the order of magnitude 10−4–10−6%.

Reduced-Order Modeling for Multiphase Flow Using a Physics-Based Deep Learning

2021 ◽  
Author(s):  
Thamer Alsulaimani ◽  
Mary Wheeler
Keyword(s):  
Deep Learning ◽  
Multiphase Flow ◽  
Loss Function ◽  
Dimensional Space ◽  
Mass Conservation ◽  
Reduced Order Model ◽  
High Dimensional ◽  
Order Model ◽  
High Dimensional Space ◽  
Reduced Order

Abstract Reservoir simulation is the most widely used tool for oil and gas production forecasting and reservoir management. Solving a large-scale system of nonlinear differential equations every timestep can be computationally expensive. In this work, we present a two-phase physics-constrained deep-learning reduced-order model as a surrogate model for subsurface flow production forecast. The implemented deep learning model is a physics-guided encoder-decoder, constructed based on the Embed-to-Control (E2C) framework. In our implementation, the E2C works in a way analogous to Proper Orthogonal Decomposition combined with Discrete Empirical Interpolation Method (POD-DEIM) or Trajectory Piece-Wise Linearization approach (POD-TPWL). The E2C-Reduced-order model (ROM) involves projecting the system from a high-dimensional space into a low-dimensional subspace using the encoder-decoder, approximating the progression of the system from one timestep to the next using a linear transition model, and finally projecting the system back to high-dimensional space using the encoder-decoder. To guarantee mass conservation, we adopt the Finite Elements Mixed Formulation in the neural network's loss function combined with the original data-based loss function. Training simulations are generated using a full-physics reservoir simulator (IPARS). High-fidelity pressure, velocity, and saturation solution snapshot at constant time intervals are taken as training input to the neural network. After training, the model is tested over large variations of well control settings. Accurate pressure and saturation solutions are predicted along with the injection and production well quantities using the proposed approach. Errors in the predicted quantities of interest are reduced with the increase in the number of training simulations used. Although it required a large number of training simulations for the offline (training) step, the model achieved a significant speedup in the online stage compared to the full physics model. Considering the overall computational cost, this ROM model is proper for cases when a large number of simulations are required like in the case of production optimization and uncertainty assessments. The proposed approach shows the capability of the deep-learning reduced-order model to accurately predict multiphase flow behavior such as well quantities, and global pressure and saturation fields. The model honors mass conservation and the underlying physics laws, which many existing approaches don't take into direct consideration.

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