Rapid Compositional Simulation Using Model Order Reduction and Machine Learning Technique

Abstract

Fast and reliable reservoir simulation is a key for the successful decision making in integrated reservoir studies. Large and complex multiphase reservoir models usually require expensive computational infrastructure. Physics-based model order reduction (MOR) methods, especially snapshots-based methods such as the proper orthogonal decomposition (POD), have been introduced and applied especially for mitigating the computational cost of black oil models in workflows that require multiple calls of the reservoir simulator. However, only a limited number of methods have looked deeper at the effectiveness of these techniques to multiphase and compositional simulation where expensive flash and phase equilibrium calculations are added to the level of complexities associated with obtaining robust solutions. In this work, we develop coupled physics-based and artificial neural network (ANN)-based MOR techniques for rapid compositional simulations that accelerate calibrating of phase equilibrium during expensive computations. We base our framework on the so-called the POD-DEIM, which uses the discrete empirical interpolation method (DEIM) step to overcome the cost associated with the nonlinear terms. Rapid flash calculation can be accomplished by use of machine learning method such as ANN. The fully connected trained network yields reliable estimation for the solutions of the composition related variables. Therefore, the process for obtaining the solutions for the flash calculation is substituted without the expensive computation of Newton-Raphson iteration. In this study, we introduce a new formulation for the POD-DEIM method applied to a compositional simulator. The new formulation allows the tracking and approximation of each component individually as opposed to only pressures and saturations. We test the robustness of the POD-DEIM method integrated with the ANN-based rapid flash calculation to reduce the computational cost for multi-phase, multi-components 3D reservoir model. Our results show that the POD-DEIM technique enables us to approximate the conventional model with high levels of accuracy up to more than 99%. And it also enables a faster simulation due to the reduced order system. The reduced order modeling using the POD-DEIM reduces the CPU time of the compositional simulation by around 14% comparing to the fine scale model. Machine learning method makes the model get to the solutions much faster without a solver for the Newton-Raphson method. ANN-based MOR accelerates the flash calculation and the coupled the POD-DEIM and ANN technique reduces the CPU time of the compositional simulation by around 14.5% comparing to the fine scale model. When the rapid flash calculation using ANN is combined with the POD-DEIM, one can save the overall simulation time in both solving the system and calculating the EOS-based equilibrium equations.