A high-order, fully coupled, upwind, compact discontinuous Galerkin method for modeling of viscous fingering in compressible porous media

Huang, Hao; Scovazzi, Guglielmo

doi:10.1016/j.cma.2013.04.010

Cited by 21 publications

(18 citation statements)

References 42 publications

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“…Similar to the case of the upwind-biased SIPG method described in Section 4.1.6, it is possible to bias upwind the DG method described in the previous section. We will describe next, instead, an upwind-biased version of a compact DG (or, CDG) method [222], proposed by Scovazzi, Huang and co-authors [158,157]. This work has connections to the formulation presented in [216] and also to the local DG formulations (LDG) described in [223].…”

Section: Upwind-biased Compact Discontinuous Galerkin Methodsmentioning

confidence: 99%

“…With this definition of the lifting operators, we obtain an upwind version of the compact discontinuous Galerkin (CDG, [222]) formulation, which we can term upwind CDG or U-CDG [158,157]. While the CDG method is a variant of the LDG method, the U-CDG can also be interpreted as an upwind variant of the method proposed in [216], and for this reason, it does not fit the canonical definition of the LDG method [223,212].…”

Section: Upwind-biased Compact Discontinuous Galerkin Methodsmentioning

confidence: 99%

“…This is because, as opposed to the case of a stable physical system, in an unstable flow there is a natural tendency for slight differences and discrepancies between solutions to grow uncontrollably over time. Grid orientation effects can become more severe in multi-dimensional problems with large mobility ratios and heterogeneous coefficients, as discussed in [156,157,158,159,160,144].…”

Section: Grid Dependence and Grid Orientation Effects In Numerical Comentioning

confidence: 99%

“…The simplest possible strategy to satisfy the DSC principle, is to use the exact same discretization strategy for both (18) and (19), as suggested in [157,158], and demonstrated in the case of an upwind-biased discontinuous Galerkin method. In that case, it was found that it becomes essential, in order to preserve the DSC principle, to use upwind bias in the discrete Laplace-like operators in the flow equation, since they are obtained as the sum of convective operators in the transport equations.…”

Section: Discrete Sum Compatibility Principle Between the Flow And Trmentioning

confidence: 99%

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Analytical and variational numerical methods for unstable miscible displacement flows in porous media

Scovazzi

Wheeler

Mikelić

et al. 2017

Journal of Computational Physics

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International audienceThe miscible displacement of one fluid by another in a porous medium has received considerable attention in sub-surface, environmental and petroleum engineering applications. When a fluid of higher mobility displaces another of lower mobility, unstable patterns-referred to as viscous fingering-may arise. Their physical and mathematical study has been the object of numerous investigations over the past century. The objective of this paper is to present a review of these contributions with particular emphasis on variational methods. These algorithms are tailored to real field applications thanks to their advanced features: handling of general complex geometries, robustness in the presence of rough tensor coefficients, low sensitivity to mesh orientation in advection dominated scenarios, and provable convergence with fully unstructured grids. This paper is dedicated to the memory of Dr. Jim Douglas Jr., for his seminal contributions to miscible displacement and variational numerical methods

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Section: Upwind-biased Compact Discontinuous Galerkin Methodsmentioning

confidence: 99%

Section: Upwind-biased Compact Discontinuous Galerkin Methodsmentioning

confidence: 99%

Section: Grid Dependence and Grid Orientation Effects In Numerical Comentioning

confidence: 99%

Section: Discrete Sum Compatibility Principle Between the Flow And Trmentioning

confidence: 99%

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Analytical and variational numerical methods for unstable miscible displacement flows in porous media

Scovazzi

Wheeler

Mikelić

et al. 2017

Journal of Computational Physics

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“…generalized the Todd and Longstaff (1972) model to two-phase flow. A few more recent studies presented experiments of heavy oil displacement by solvent (Cuthiell et al, 2006), higher-order finite element simulations of viscous fingering in single-phase flow (Scovazzi et al, 2013a;Huang and Scovazzi, 2013;Scovazzi et al, 2013b;Gerstenberger et al, 2013), and experiments and stability analyses for forced imbibition (Sharma et al, 2012).…”

Section: Introductionmentioning

confidence: 99%

Viscous and gravitational fingering in multiphase compositional and compressible flow

Moortgat

2016

Advances in Water Resources

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Viscous and gravitational fingering refer to flow instabilities in porous media that are triggered by adverse mobility or density ratios, respectively. These instabilities have been studied extensively in the past for 1) single-phase flow (e.g., contaminant transport in groundwater, first-contact-miscible displacement of oil by gas in hydrocarbon production), and 2) multi-phase immiscible and incompressible flow (e.g., water-alternating-gas (WAG) injection in oil reservoirs). Fingering in multiphase compositional and compressible flow has received much less attention, perhaps due to its high computational complexity. However, many important subsurface processes involve multiple phases that exchange species. Examples are carbon sequestration in saline aquifers and enhanced oil recovery (EOR) by gas or WAG injection below the minimum miscibility pressure. In multiphase flow, relative permeabilities affect the mobility contrast for a given viscosity ratio. Phase behavior can also change local fluid properties, which can either enhance or mitigate viscous and gravitational instabilities. This work presents a detailed study of fingering behavior in compositional multiphase flow in two and three dimensions and considers the effects of 1) Fickian diffusion, 2) mechanical dispersion, 3) flow rates, 4) domain size and geometry, 5) formation heterogeneities, 6) gravity, and 7) relative permeabilities. Results show that fingering in compositional multiphase flow is profoundly different from miscible conditions and upscaling techniques used for the latter case are unlikely to be generalizable to the former.

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A DG Method for the Simulation of CO2 Storage in Saline Aquifer

Rivière

Yang

2018

Association for Women in Mathematics Series

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A high-order, fully coupled, upwind, compact discontinuous Galerkin method for modeling of viscous fingering in compressible porous media

Cited by 21 publications

References 42 publications

Analytical and variational numerical methods for unstable miscible displacement flows in porous media

Analytical and variational numerical methods for unstable miscible displacement flows in porous media

Viscous and gravitational fingering in multiphase compositional and compressible flow

A DG Method for the Simulation of CO2 Storage in Saline Aquifer

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