Stability of miscible displacements in porous media: Radial source flow

Tan, Changhui; Homsy, G. M.

doi:10.1063/1.866289

Cited by 105 publications

(125 citation statements)

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“…Since the transport equation is linear and the discretizations are stable and consistent, the manifestation of the grid orientation effect must be attributed to the ill-posedness of the underlying physical model for high Peclet number flows (Tan and Homsy 1997). By this, we naturally do not mean that grid orientation effects are physical phenomena: the flow knows nothing of the computational grid.…”

Section: Model Problem and Equationsmentioning

confidence: 98%

“…Early-time and Near-wellSince perturbations and errors made in early-time and near-well flow are amplified as the simulation continues(Tan and Homsy 1997;Brand et al 1991), we seek to improve the robustness of numerical schemes by alleviating or reducing the numerical disturbances introduced near the injection well during the early stages of the injection process.…”

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confidence: 99%

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Grid Orientation Revisited: Near-well, Early-time Effects and Solution Coupling Methods

2007

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The grid orientation effect is a phenomenon which leads to the computation of fundamentally different solutions on grids oriented diagonal and parallel to the principal flow direction. Grid orientation remains an important consideration for many practical simulation studies, and renewed interest in gas injection processes motivates the revisiting of this classical problem. In this article, we show that there are aspects of the grid orientation effect that can be traced back directly to the treatment of early-time, near-well flow and therefore have a major impact on adverse mobility ratio displacements such as miscible or immiscible gas injection. The details of this effect mean that any uncertainty quantification study should account for the interaction of the near-well heterogeneity and the grid orientation effect. We also show how two possible methods-a well-sponge method and a local embedding technique-are able to produce a solution largely independent of grid orientation for single phase two-component miscible flow. Both methods are versatile in that they can be implemented on general grid topologies. They are illustrated on Cartesian grids for both the standard quarter five spot problem with two different grid orientations, and a problem with a single injection well and two producing wells at different angles to the grid lines. Our results show that it is possible to reduce grid-orientation effects for challenging adverse mobility ratio miscible displacements with only local treatments around the injection wells.

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Section: Model Problem and Equationsmentioning

confidence: 98%

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confidence: 99%

Grid Orientation Revisited: Near-well, Early-time Effects and Solution Coupling Methods

2007

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“…For porous media problems, this is important because most simulations are performed at scales that result in unstable displacements [32,38] and numerical errors can trigger these instabilities [8]. There have been many efforts to address this so-called grid orientation effect with multi-D schemes [5,10,15,25,36,41], but the methods proposed are either not monotone (positive for scalar, linear advection) for general flow fields or are not fully developed for multiphase flow.…”

Section: Introductionmentioning

confidence: 98%

“…Gravity and capillary forces can cause fluid phases to move against the direction of total flow, referred to as countercurrent flow, and introduce special challenges for flow simulation. Adverse viscosity differences can introduce physical fluid instabilities giving rise to viscous fingering [32,38]. These complications impose severe restrictions on the numerical methods used in practice.…”

Section: Introductionmentioning

confidence: 98%

Multidimensional upstream weighting for multiphase transport in porous media

2010

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Truly multidimensional methods for hyperbolic equations use flow-based information to determine the computational stencil, as opposed to applying one-dimensional methods dimension by dimension. By doing this, the numerical errors are less correlated with the underlying computational grid. This can be important for reducing bias in flow problems that are inherently unstable at simulation scale, such as in certain porous media problems. In this work, a monotone, multi-D framework for multiphase flow and transport in porous media is developed. A local coupling of the fluxes is introduced through the use of interaction regions, resulting in a compact stencil. A relaxed volume formulation of the coupled hyperbolic-elliptic system is used that allows for nonzero residuals in the pressure equation to be handled robustly. This formulation ensures nonnegative masses and saturations (volume fractions) that sum to one (Acs et al., SPE J 25(4):543-553, 1985). Though the focus of the paper is on immiscible flow, an extension of the methods to a class of more general scalar hyperbolic equations is also presented. Several test problems demonstrate that the truly multi-D schemes reduce biasing due to the computational grid.

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“…Much work has focused on characterizing miscible viscous fingering, including laboratory experiments [25][26][27], numerical simulations [28][29][30][31][32], and linear stability analyses to model the onset and growth of instabilities for rectilinear [33] and radial [34,35] geometries. Other studies have also focused on the effects of anisotropic dispersion [31,33,36], medium heterogeneity [32,[37][38][39][40], gravity [41][42][43][44][45][46], chemical reactions [3,[47][48][49], absorption [50], and flow configuration [51][52][53][54][55] on the viscous fingering instability.…”

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confidence: 99%

Interface evolution during radial miscible viscous fingering

2015

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We study experimentally the miscible radial displacement of a more viscous fluid by a less viscous one in a horizontal Hele-Shaw cell. For the range of tested injection rates and viscosity ratios we observe two regimes for the evolution of the fluid-fluid interface. At early times the interface length increases linearly with time, which is typical of the Saffman-Taylor instability for this radial configuration. However, as time increases, the interface growth slows down and scales as ∼t 1 2 , as one expects in a stable displacement, indicating that the overall flow instability has shut down. Surprisingly, the crossover time between these two regimes decreases with increasing injection rate. We propose a theoretical model that is consistent with our experimental results, explains the origin of this second regime, and predicts the scaling of the crossover time with injection rate and the mobility ratio. The key determinant of the observed scalings is the competition between advection and diffusion time scales at the displacement front, suggesting that our analysis can be applied to other interfacial-evolution problems such as the Rayleigh-Bénard-Darcy instability. A large number of natural and industrial flow processes depend on both the degree and the rate of mixing between fluids, such as chemical reactions [1][2][3][4], combustion [5], microbial activity [6], and enhanced oil recovery [7]. In such mixing-driven systems, the flow responsible for fluid displacement reflects the heterogeneity of the host medium structure [8][9][10][11] or the physical properties of the fluids, such as density [3,12,13] or viscosity [14,15]. Mixing takes place at the fluid-fluid interface and is determined by the combined action of molecular diffusion, which acts to reduce the local concentration gradients, and advection, which controls the interface dynamics [16][17][18][19][20][21]. Understanding the interface dynamics between two miscible fluids is therefore crucial to explaining and predicting the rate of mixing.When a less viscous fluid displaces a more viscous one, their interface is deformed and stretched by a hydrodynamical instability known as viscous fingering [15,22,23], and this results in complex interface dynamics [16,17,24]. Much work has focused on characterizing miscible viscous fingering, including laboratory experiments [25][26][27], numerical simulations [28][29][30][31][32], and linear stability analyses to model the onset and growth of instabilities for rectilinear [33] and radial [34,35] geometries. Other studies have also focused on the effects of anisotropic dispersion [31,33,36] [50], and flow configuration [51-55] on the viscous fingering instability. Despite the extensive work done, the effect of viscous fingering on mixing has only recently been investigated numerically for a rectilinear geometry [14,56]. While the dynamics of the interface between two miscible fluids is crucial to explain and predict the rate of mixing [1,16], a solid understanding of the temporal evolution of the viscously unstable fl...

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Stability of miscible displacements in porous media: Radial source flow

Cited by 105 publications

References 10 publications

Grid Orientation Revisited: Near-well, Early-time Effects and Solution Coupling Methods

Grid Orientation Revisited: Near-well, Early-time Effects and Solution Coupling Methods

Multidimensional upstream weighting for multiphase transport in porous media

Interface evolution during radial miscible viscous fingering

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