Mathematical analysis and numerical simulation of multi-phase multi-component flow in heterogeneous porous media

Geiger, Sebastian; Schmid, Karen Sophie; Zaretskiy, Yan

doi:10.1016/j.cocis.2012.01.003

Cited by 27 publications

(13 citation statements)

References 78 publications

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“…An open-source MATLAB implementation offering a flexible discretization which can be used in more complex structures has also been developed [56]. A good review of recent efforts to develop either semianalytical solutions for one-dimensional (1D) verification or novel numerical schemes for solving the governing equations efficiently is provided by Geiger, Schmid, and Zaretskiy [38].…”

mentioning

confidence: 99%

An $h$-Adaptive Operator Splitting Method for Two-Phase Flow in 3D Heterogeneous Porous Media

Chueh¹,

Djilali²,

Bangerth³

2013

SIAM J. Sci. Comput.

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Abstract. The simulation of multiphase flow in porous media is a ubiquitous problem in a wide variety of fields, such as fuel cell modeling, oil reservoir simulation, magma dynamics, and tumor modeling. However, it is computationally expensive. This paper presents an interconnected set of algorithms which we show can accelerate computations by more than two orders of magnitude compared to traditional techniques, yet retains the high accuracy necessary for practical applications. Specifically, we base our approach on a new adaptive operator splitting technique driven by an a posteriori criterion to separate the flow from the transport equations, adaptive meshing to reduce the size of the discretized problem, efficient block preconditioned solver techniques for fast solution of the discrete equations, and a recently developed artificial diffusion strategy to stabilize the numerical solution of the transport equation. We demonstrate the accuracy and efficiency of our approach using numerical experiments in one, two, and three dimensions using a program that is made available as part of a large open source library.

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mentioning

confidence: 99%

An $h$-Adaptive Operator Splitting Method for Two-Phase Flow in 3D Heterogeneous Porous Media

Chueh¹,

Djilali²,

Bangerth³

2013

SIAM J. Sci. Comput.

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“…Lax's stability conditions for discontinuities of system (1-3) project onto those for the auxiliary system (7) [13]. Now let's introduce diffusion with corresponding Peclet number 1/ d into system (1-3) (see [2,5] for detailed derivations). The system (1-3) becomes hyperbolic for  c = t = d =0.…”

Section: Solution Of the Auxiliary Problemmentioning

confidence: 99%

“…Therefore, the transformation (5) splits the systems with diffusion too. The splitting method (5) can be extended to three-dimensional flows in the case where the total mobility of two phases is constant. Introduction of a linear co-ordinate along the stream-lines splits the three-dimensional system into one-dimensional system (1-3) and a Laplace equation for a real pressure distribution (see the corresponding derivations in [2,23]).…”

Section: General Applicationsmentioning

confidence: 99%

“…Therefore, analytical solutions for (1-3) are very useful in reservoir simulation, particularly in three-dimensional stream-line and front-tracking models [1,3]. Matched asymptotic expansion solutions and also recently developed semi-analytical methods for the system (1-3) with dissipation and non-equilibrium ( c ,  t 0) allow for significant acceleration of numerical computations [4,5].…”

Section: Introductionmentioning

confidence: 99%

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Splitting in systems of PDEs for two-phase multicomponent flow in porous media

Borazjani

Roberts

Bedrikovetsky

2016

Applied Mathematics Letters

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The paper investigates the system of PDEs for two-phase n-component flow in porous media consisting of hyperbolic terms for advective transport, parabolic terms of dissipative effects and relaxation nonequilibrium equations. We found that for several dissipative and non-equilibrium systems, using the streamfunction as a free variable instead of time separates the general (n+1)×(n+1) system into an n×n auxiliary system and one scalar lifting equation. In numerous cases, where the auxiliary system allows for exact solution, the general flow problem is reduced to numerical or semi-analytical solution of one lifting equation.

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“…Models have been developed that provide detailed representations of pore structures and resolve bubble transport at the subpore level (µm), but due to their high computational demands these models are of limited use in addressing plot and field‐scale (1–100 m) questions relating to longer time scales of days to months. At present, coarser‐scale models can provide large‐scale predictions (1–100 m) of bubble movement and ebullition over long time periods (1–25 year) [ Amos and Mayer , ], but predictive uncertainty is high because the modeled spatial resolutions do not permit a detailed description of a porous medium and exclude important structural features (e.g., fractures, poorly permeable layers) that significantly alter bubble transport [ Thomson and Johnson , ; Geiger et al ., ; Helmig et al ., ]. Therefore, a major theoretical and computational challenge is to model bubble movement and ebullition at large spatiotemporal scales (≥1 m and >month), but to represent explicitly the spatial heterogeneity of the porous medium in order to reduce model uncertainty.…”

Section: Introductionmentioning

confidence: 99%

Testing a simple model of gas bubble dynamics in porous media

Ramírez

Baird

Coulthard

et al. 2015

Water Resources Research

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Bubble dynamics in porous media are of great importance in industrial and natural systems. Of particular significance is the impact that bubble-related emissions (ebullition) of greenhouse gases from porous media could have on global climate (e.g., wetland methane emissions). Thus, predictions of future changes in bubble storage, movement, and ebullition from porous media are needed. Methods exist to predict ebullition using numerical models, but all existing models are limited in scale (spatial and temporal) by high computational demands or represent porous media simplistically. A suitable model is needed to simulate ebullition at scales beyond individual pores or relatively small collections (<10 24 m 3 ) of connected pores. Here we present a cellular automaton model of bubbles in porous media that addresses this need. The model is computationally efficient, and could be applied over large spatial and temporal extent without sacrificing fine-scale detail. We test this cellular automaton model against a physical model and find a good correspondence in bubble storage, bubble size, and ebullition between both models. It was found that porous media heterogeneity alone can have a strong effect on ebullition. Furthermore, results from both models suggest that the frequency distributions of number of ebullition events per time and the magnitude of bubble loss are strongly right skewed, which partly explains the difficulty in interpreting ebullition events from natural systems.

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Mathematical analysis and numerical simulation of multi-phase multi-component flow in heterogeneous porous media

Cited by 27 publications

References 78 publications

An $h$-Adaptive Operator Splitting Method for Two-Phase Flow in 3D Heterogeneous Porous Media

An $h$-Adaptive Operator Splitting Method for Two-Phase Flow in 3D Heterogeneous Porous Media

Splitting in systems of PDEs for two-phase multicomponent flow in porous media

Testing a simple model of gas bubble dynamics in porous media

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