Fingering regimes in unstable miscible displacements

Hamid, Saad; Muggeridge, Ann

doi:10.1063/1.5128338

Cited by 18 publications

(7 citation statements)

References 48 publications

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“…However, at late times as the single-finger exchange-flow decays, a pair of wider counter-propagating fingers manifest themselves along the boundaries (figure 3 e , f ). This is because, in contrast to the case with periodic boundaries, a half-wavelength mode is now permissible (Abdul Hamid & Muggeridge 2020). Since this mode is wider, it decays more slowly and is still unstable once the central propagating finger decays away.…”

Section: Limiting Casesmentioning

confidence: 99%

Horizontal miscible displacements through porous media: the interplay between viscous fingering and gravity segregation

2022

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We consider miscible displacements in two-dimensional homogeneous porous media where the displacing fluid is less viscous and has a different density than the displaced fluid. We find that the dynamics evolve through nine possible regimes depending on the viscosity ratio, strength of density variations and the strength of the background flow, as characterized by the Péclet number. At early times the interface is dominated by longitudinal diffusion before undergoing a transition to a slumping regime where vertical flow is important. At intermediate times, vertical flow and diffusion can be neglected and there are three different limiting solutions: a fingering limit; an injection-driven gravity-current limit; and a density-driven gravity-current limit. Finally at late times, transverse diffusion becomes important and there is a transition from an apparent shutdown regime to a viscously enhanced Taylor-slumping regime. In each of the regimes, the dominant scalings are identified and reduced-order models for the evolution of the concentration field are developed. Lastly, three case studies are considered to illustrate the dominant physical balances in the geophysically relevant setting of geological $\textrm {CO}_2$ storage.

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Section: Limiting Casesmentioning

confidence: 99%

Horizontal miscible displacements through porous media: the interplay between viscous fingering and gravity segregation

2022

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“…The numerical simulations were carried out for an R = 2.983 suggesting that the flow was unstable. The Peclet number was calculated using the methods described by (Abdul Hamid & Muggeridge, 2020;Brock & Orr Jr., 1991;Perkins & Johnston, 1963). Based on the fluid flowrates and dimensions of the reservoir models applied, the Peclet numbers of the flow displacements in all the models studied was obtained as Pe > 129.…”

Section: Andmentioning

confidence: 99%

The interactions of instabilities during miscible CO2 enhanced oil recovery: A numerical simulation study

Ogbeiwi¹,

Stephen²

2023

Preprint

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During field-scale simulations of miscible displacements, the effect of heterogeneity-induced channelling is always accounted for, while micro-scale physical instabilities like viscous fingering and molecular diffusion are ignored due to the computational costs of the required fine-grid simulations. Thus, the interplay between small- and macro-scale physical instabilities is not properly understood. In this study, we examined the interactions of the small- and macro-scale effects during miscible CO2 displacements using two-dimensional, inter-well scale, fine-grid models. Using the linear stability theory, we described the fingering behaviours of a set of homogeneous models which were perturbated initially to artificially seed different forms of fingers. We also attempted to identify the range of permeability variation in a set of heterogeneous models at which the effect of viscous fingering or physical diffusion diminishes, and the permeability heterogeneity dominates the process. Our results showed that in models with little or no heterogeneity, viscosity fingering, and physical diffusion exerted control on the dynamics of the flooding process. However, as the degree of heterogeneity increased, the influence of viscous fingering and diffusion diminished, with a corresponding increase in the influence of permeability heterogeneity/variation. Overall, during miscible displacements, oil recovery and CO2 storage were improved because of the interactions of diffusive forces, viscous fingering and/or reservoir heterogeneity.

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“…Viscous fingering is a type of flow instability where a low viscosity fluid displaces a high viscosity fluid. Typically, the interface between the two fluids is unstable, giving rise the so‐called Saffman–Taylor instability 27 (Figure 16). In our example, a low viscosity (

μ = 0.1

) fluid displaces a high viscosity (

μ = 1.0

) miscible fluid in a porous medium at a constant injection rate.…”

Section: Examplesmentioning

confidence: 99%

Non‐intrusive reduced order modeling: Geometrical framework, high‐order models, and a priori analysis of applicability

Kostorz

Muggeridge

Jackson

2021

Numerical Meth Engineering

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We present an intuitive geometrical framework for non‐intrusive model reduction. Based on simple low‐dimensional geometry that is easy to visualize and interpret, the approach enables one to predict model features a priori and explain them a posteriori. Two simple a priori methods for analyzing the suitability of non‐intrusive model reduction are consequently presented and discussed. As a natural consequence of the interpretation proposed a method extension is proposed, namely, higher‐order temporal discretization. It is also demonstrated that some generic properties of the physical system modeled such as periodicity or convergence towards a steady state are easily represented in the framework proposed. The approaches are illustrated using a number of representative test problems including a three‐dimensional case of the Saffman–Taylor instability and an example exhibiting a propagating discontinuity. It is shown that this property makes the underlying non‐intrusive reduced order modeling nonsmooth meaning it will provide a poor representation of the system dynamics.

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Fingering regimes in unstable miscible displacements

Cited by 18 publications

References 48 publications

Horizontal miscible displacements through porous media: the interplay between viscous fingering and gravity segregation

Horizontal miscible displacements through porous media: the interplay between viscous fingering and gravity segregation

The interactions of instabilities during miscible CO2 enhanced oil recovery: A numerical simulation study

Non‐intrusive reduced order modeling: Geometrical framework, high‐order models, and a priori analysis of applicability

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