An efficient multigrid-DEIM semi-reduced-order model for simulation of single-phase compressible flow in porous media
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ORIGINAL PAPER
An efficient multigrid‑DEIM semi‑reduced‑order model for simulation of single‑phase compressible flow in porous media Jing‑Fa Li1 · Bo Yu1 · Dao‑Bing Wang1 · Shu‑Yu Sun2 · Dong‑Liang Sun1 Received: 2 July 2020 © The Author(s) 2020
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 reducedorder 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%. Keywords Compressible flow · Porous media · Multigrid method · Discrete empirical interpolation method · Peng– Robinson equation of state
1 Introduction As a kind of primary energy, petroleum plays a significant role in industrial production and daily life. According to BP Energy Outlook (BP 2019), the proportion of oil and gas consumption in total energy consumption will continue to grow from 2020 to 2040 although the new energy gains increasing attention in recent years. With the development of computer technology and the progress of calculation Edited by Xiu-Qiu Peng * Bo Yu [email protected] 1
School of Mechanical Engineering, Beijing Key Laboratory of Pipeline Critical Technology and Equipment for Deepwater Oil and Gas Development, Beijing Institute of Petrochemical Technology, Beijing 102617, China
Division of Physical Science and Engineering, King Abdullah University of Science and Technology, Thuwal 23955‑6900, Saudi Arabia
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methods, numerical simulation has become one of the important auxiliary tools for petroleum exploration and production. For example, the reservoir simulation can quantitatively provide the flow state and variation of reservoir parameters during oil and gas production. With the inc
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