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Abstract

Summary

Numerical simulation of multiphase flow in porous media is of paramount importance to understand, predict and manage subsurface reservoirs with applications to hydrocarbon recovery, geothermal energy resources, CO2 geological sequestration, groundwater sources and magma reservoirs. However, the numerical solution of the governing equations is very challenging due to the non-linear nature of the problem and the strong coupling between the different equations. Newton methods have been traditionally used to solve the non-linear system of equations, although, the Picard iterative method has been gaining ground in recent years. The Picard method is attractive because the multiphysics problem can be subdivided and each subproblem solved separately, which gives wide flexibility and extensibility.

Rapid convergence of the non-linear solver is of vital importance as it strongly affects the overall computational time. Therefore, a great deal of effort has been put on obtaining robust and stable convergence rates. At the same time, machine learning (ML) is gaining more and more attention with revolutionary results in areas such as computer vision, self-driving cars and natural language processing. The success of ML in different fields has inspired recent applications in reservoir engineering and geosciences. Here, we present a Picard non-linear solver with convergence parameters dynamically controlled by ML. The ML is trained based on the parameters of the reservoir model scaled to a dimensionless space. In the approach reported here, data for the ML training is generated using simulation results obtained for multiphase flow in a two-layered reservoir model which captures many of the flow features observed in models of natural reservoirs. The presented method significantly reduces the computational effort required by the non-linear solver as it can adjust itself to the complexity/physics of the system. We demonstrate its efficiency under a variety of numerical tests cases, including gravity, capillary pressure and extremely heterogeneous models.

Technical contributions:

  • –  Significantly reduces the computational cost of the non-linear solver.
  • –  The ML model is trained very efficiently based on a two-layered reservoir model and dimensionless numbers.
  • –  Enables us to carry out large-scale and/or physically demanding numerical simulations.
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/content/papers/10.3997/2214-4609.202035127
2020-09-14
2024-04-25

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Non-Linear Solver Optimisation for Multiphase Porous Media Flow Based on Machine Learning
Conference Proceedings 2020, 1 (2020); https://doi.org/10.3997/2214-4609.202035127
/content/papers/10.3997/2214-4609.202035127
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