Nonlinearly preconditioned constraint-preserving algorithms for subsurface three-phase flow with capillarity

Yang, Haijian; Li, Yiteng; Sun, Shuyu

doi:10.1016/j.cma.2020.113140

Cited by 8 publications

(6 citation statements)

References 56 publications

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“…In addition to that, we also notice that, as the time step size ∆t decreases, the average number of nonlinear and linear iterations become smaller, whereas the total computing time increases. This behavior is somehow expected for the fully implicit approach in a variety of applications [2,16,32,35,36].…”

Section: Robustness and Efficiency Of The Solvermentioning

confidence: 65%

Parallel multilevel restricted Schwarz preconditioners for implicit simulation of subsurface flows with Peng-Robinson equation of state

Yang

2020

Preprint

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Parallel algorithms and simulators with good scalabilities are particularly important for large-scale reservoir simulations on modern supercomputers with a large number of processors. In this paper, we introduce and study a family of highly scalable multilevel restricted additive Schwarz (RAS) methods for the fully implicit solution of subsurface flows with Peng-Robinson equation of state in two and three dimensions. With the use of a second-order fully implicit scheme, the proposed simulator is unconditionally stable with the relaxation of the time step size by the stability condition. The investigation then focuses on the development of several types of multilevel overlapping additive Schwarz methods for the preconditioning of the resultant linear system arising from the inexact Newton iteration, and some fast solver technologies are presented for the assurance of the multilevel approach efficiency and scalability. We numerically show that the proposed fully implicit framework is highly efficient for solving both standard benchmarks as well as realistic problems with several hundreds of millions of unknowns and scalable to 8192 processors on the Tianhe-2 supercomputer.

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Section: Robustness and Efficiency Of The Solvermentioning

confidence: 65%

Parallel multilevel restricted Schwarz preconditioners for implicit simulation of subsurface flows with Peng-Robinson equation of state

Yang

2020

Preprint

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“…Numerical simulation for subsurface flows has been extensively applied in industry, such as in the management of groundwater energy and waste pollutants, petroleum engineering, and exploitation of geothermal energy [1][2][3][4][5][6][7][8][9][10][11][12][13]. The main numerical methods in the simulation include the Fully Implicit scheme (FI) [14][15][16][17] and the IMplicit EXplicit scheme (IMEX) [18][19][20].…”

Section: Introductionmentioning

confidence: 99%

Improved IMPES Scheme for the Simulation of Incompressible Three-Phase Flows in Subsurface Porous Media

et al. 2021

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In this work, an improved IMplicit Pressure and Explicit Saturation (IMPES) scheme is proposed to solve the coupled partial differential equations to simulate the three-phase flows in subsurface porous media. This scheme is the first IMPES algorithm for the three-phase flow problem that is locally mass conservative for all phases. The key technique of this novel scheme relies on a new formulation of the discrete pressure equation. Different from the conventional scheme, the discrete pressure equation in this work is obtained by adding together the discrete conservation equations of all phases, thus ensuring the consistency of the pressure equation with the three saturation equations at the discrete level. This consistency is important, but unfortunately it is not satisfied in the conventional IMPES schemes. In this paper, we address and fix an undesired and well-known consequence of this inconsistency in the conventional IMPES in that the computed saturations are conservative only for two phases in three-phase flows, but not for all three phases. Compared with the standard IMPES scheme, the improved IMPES scheme has the following advantages: firstly, the mass conservation of all the phases is preserved both locally and globally; secondly, it is unbiased toward all phases, i.e., no reference phases need to be chosen; thirdly, the upwind scheme is applied to the saturation of all phases instead of only the referenced phases; fourthly, numerical stability is greatly improved because of phase-wise conservation and unbiased treatment. Numerical experiments are also carried out to demonstrate the strength of the improved IMPES scheme.

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“…Transport of a liquid occurs by diffusion, capillary absorption, and by filtration. Consequently, the derivation of mass-transfer relations in capillary-porous bodies (Kojic et al, 2017;Yang, Li, & Sun, 2020) on the basis of a molecular and molar transport mechanism involves great difficulties.…”

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confidence: 99%

Numerical analysis of vacuum drying of a porous body in the integrated domain

Amiri

Ayani

Ziółkowski

et al. 2022

J Food Process Engineering

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In the present study, the vacuum drying process of an apple slice is numerically modeled based on a control volume method. Transient two‐dimensional Navier–Stokes, energy, moisture, and Luikov equations are solved by numerical coding (Fortran) to simulate the simultaneous heat and mass transfer in the ambient and apple slice, respectively. The privilege of using Luikov's model is that the capillary forces are considered, and a differentiation between air, vapor, liquid, and solid is made. Luikov described the two phenomena associated with the transport of air, vapor, and liquids through the porous media as molecular transport and molar transport. The ambient pressure linearly reduced within a minute until it reached a constant value. One of the intellectually demanding preoccupations among researchers is how to simulate the sample and its surroundings with high accuracy of boundary conditions, which enables to avoid the use of empirical transfer coefficients. This study can be scrutinized from various dimensions, among which nonuse of boundary condition between a porous sample and its surroundings is the most conspicuous novelty. Results showed that although at 50 s, isothermal and iso‐moisture lines inside the sample are symmetric, they are not symmetric at 100, 200, and 400 s. In addition, at first minute, pump operation leads to vary the density of the isothermal and iso‐moisture lines around the sample, but at 100, 200, and 400 s, higher temperature and moisture gradients have been achieved at the right and top of the sample surface. Practical Applications Drying is the main technique of food preservation, so that it reduces the humidity of crops and is the most crucial procedure for safeguarding agricultural crops because it has a considerable impact on the condition of parched goods. In this study, some assumptions of drying including using empirical transfer coefficients between sample and its surrounding and vacuum drying under constant pressure have been eliminated. To achieve this goal, computational fluid dynamics (CFD), plays a crucial role to simulate the parameters inside the sample and its ambient without using boundary condition.

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Nonlinearly preconditioned constraint-preserving algorithms for subsurface three-phase flow with capillarity

Cited by 8 publications

References 56 publications

Parallel multilevel restricted Schwarz preconditioners for implicit simulation of subsurface flows with Peng-Robinson equation of state

Parallel multilevel restricted Schwarz preconditioners for implicit simulation of subsurface flows with Peng-Robinson equation of state

Improved IMPES Scheme for the Simulation of Incompressible Three-Phase Flows in Subsurface Porous Media

Numerical analysis of vacuum drying of a porous body in the integrated domain

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