Computational methods for multiphase flow and reactive transport problems arising in subsurface contaminant remediation

Arbogast, Todd; Bryant, Steve; Dawson, Clint; Saaf, Fredrik; Wang, Chong; Wheeler, Mary F.

doi:10.1016/0377-0427(96)00015-5

Cited by 35 publications

(15 citation statements)

References 14 publications

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“…Because of the presence of the tensor K in Equation (15), this can be a challenging task, especially when the medium is highly heterogeneous. We address this issue by using mixed finite elements (MFEs), a method that has proved very effective for this kind of problems [36][37][38][39]. In particular, we use the lowest-order Raviart-Thomas .RT 0 / elements [1,40,41].…”

Section: A Mixed Finite Element Formulationmentioning

confidence: 99%

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An integro‐differential model for non‐Fickian tracer transport in porous media: validation and numerical simulation

Ferreira

Pinto

2015

Math Methods in App Sciences

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Communicated by J. Vigo-AguiarDiffusion processes have traditionally been modeled using the classical parabolic advection-diffusion equation. However, as in the case of tracer transport in porous media, significant discrepancies between experimental results and numerical simulations have been reported in the literature. Therefore, in order to describe such anomalous behavior, known as non-Fickian diffusion, some authors have replaced the parabolic model with the continuous time random walk model, which has been very effective. Integro-differential models (IDMs) have been also proposed to describe non-Fickian diffusion in porous media. In this paper, we introduce and test a particular type of IDM by fitting breakthrough curves resulting from laboratory tracer transport. Comparisons with the traditional advection-diffusion equation and the continuous time random walk are also presented. Moreover, we propose and numerically analyze a stable and accurate numerical procedure for the two-dimensional IDM composed by a integro-differential equation for the concentration and Darcy's law for flow. In space, it is based on the combination of mixed finite element and finite volume methods over an unstructured triangular mesh.where the total mass flux J is given by where J adv is the flux due to convective transport J adv D vu, and by assuming that the diffusion-dispersion mass flux J dis satisfies the so-called Fick's law,Equation (1), being of the parabolic type, induces a pathologic behavior in the concentration u, namely, it presents infinite speed of propagation, which has no physical meaning. Other limitations associated with the definition of D.v/ have also been reported [6][7][8].Regarding the use of such an equation to simulate tracer transport, several gaps have been observed when simulation results were compared with laboratory experiments. These observations have been extensively reviewed [9][10][11][12][13][14][15][16][17][18].Several approaches have been developed in order to overcome the limitations associated with Equation (1); we refer, for example, to [7] and [8]. A common approach consists of the introduction of a hyperbolic or non-Fickian correction term. A particular model of this type can be obtained by assuming that the diffusion-dispersion mass flux J dis satisfies the following differential equation:where is a delay parameter [19]. Note that the left-hand side of Equation (5) is a first-order approximation of the left-hand side of J dis .x, t C / D D.v/ru.x, t/, which means that the dispersion mass flux at the point x and time t C depends on the gradient of the concentration at the same point but at a delayed time. Equation (5) leads towith the kernel term K er .t/ D 1 e t , provided that J dis .0/ D 0. Combining the partition (4) with Equation (3), where J dis is given by Equation (6), we obtain the integro-differential equationMoreover, if we assume that the diffusion-dispersion mass flux has both a Fickian component J F , and a non-Fickian component J NF , defined byandThe intent of this section is...

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Section: A Mixed Finite Element Formulationmentioning

confidence: 99%

“…Here, we make use of the second-order Monotonic Upstream-centered Scheme for Conservation Laws (MUSCL), as described in [43]. Schemes that combine MFEs and higher-order Godunov methods, called Godunov-mixed methods, have been successfully applied in the simulation of Fickian transport in porous media [36,38,44].…”

Section: The Numerical Schemementioning

confidence: 99%

An integro‐differential model for non‐Fickian tracer transport in porous media: validation and numerical simulation

Ferreira

Pinto

2015

Math Methods in App Sciences

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“…To conclude this introduction, we should point out that the standard schemes in widespread use for modeling reactive transport in groundwater flow make use of operator-splitting techniques-see, for example, [8], [19], [7], [24], [2], [3], and [1]. That is, one solves alternately the equilibrium equation system R(u) = 0 and the transport equation.…”

Section: Introductionmentioning

confidence: 98%

“…These include the fact that the transport can occur at the incorrect speed unless the reaction rates are sufficiently fast, an O(Δt) error arises due to the splitting, and stability constraints determined by the velocity of the transport equation are possible. Nonetheless, splitting schemes are computationally attractive and form the basis for several software packages, notably PARSIM [1] and MINTRAN [19].…”

Section: Introductionmentioning

confidence: 99%

Analysis of Box Schemes for Reactive Flow Problems

Mitchell¹,

Morton²,

Spence³

2006

SIAM J. Sci. Comput.

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Key properties of the box scheme are shown to be advantageous for reactive flow problems. Unconditional stability and compact conservation are shown by a detailed modified equation analysis to enable the scheme to reflect exactly the "reduced speed," enhanced diffusion, and dispersion which are typical of such "hyperbolic conservation laws with relaxation." A novel modified equation analysis is also used to show how the spurious checkerboard mode behaves and can be controlled. Numerical experiments for some nonlinear one-dimensional problems and a two-dimensional problem demonstrate that the behavior of the scheme deduced from a simple model problem has general validity.

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“…It is designed to accurately simulate incompressible, single phase flow and reactive transport of chemical components through porous media (Arbogast et al, 1996). Parssim uses a logically rectangular cell-centered finite difference procedure to discretize the flow equation.…”

Section: Permeability Field Generationmentioning

confidence: 99%

Origin of Scale-Dependent Dispersivity and Its Implications For Miscible Gas Flooding

Bryant¹,

Johns²,

Lake³

et al. 2008

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Dispersive mixing has an important impact on the effectiveness of miscible floods.Simulations routinely assume Fickian dispersion, yet it is well established that dispersivity depends on the scale of measurement. This is one of the main reasons that a satisfactory method for design of field-scale miscible displacement processes is still not available.The main objective of this project was to improve the understanding of the fundamental mechanisms of dispersion and mixing, particularly at the pore scale. To this end, microsensors were developed and used in the laboratory to measure directly the solute concentrations at the scale of individual pores; the origin of hydrodynamic dispersion was evaluated from first principles of laminar flow and diffusion at the grain scale in simple but geometrically completely defined porous media; techniques to use flow reversal to distinguish the contribution to dispersion of convective spreading from that of true mixing; and the field scale impact of permeability heterogeneity on hydrodynamic dispersion was evaluated numerically.This project solved a long-standing problem in solute transport in porous media by quantifying the physical basis for the scaling of dispersion coefficient with the 1.2 power of flow velocity. The researchers also demonstrated that flow reversal uniquely enables a crucial separation of irreversible and reversible contributions to mixing. The interpretation of laboratory and field experiments that include flow reversal provides important insight. Other advances include the miniaturization of long-lasting microprobes for in-situ, pore-scale measurement of tracers, and a scheme to account properly in a reservoir simulator (grid-block scale) for the contributions of convective spreading due to reservoir heterogeneity and of mixing. 3 EXECUTIVE SUMMARYDispersive mixing has an important impact on the effectiveness of miscible floods.Despite decades of research into dispersion, it continues to present theoretical and conceptual challenges. Simulations of miscible transport processes generally assume Fickian representations of dispersion in which the dispersivity of the medium is considered constant. However, dispersivity is found to be dependent on the scale of measurement. A satisfactory method for accurate designing and performance prediction of field scale miscible displacement processes is yet to be developed.The main objective of this project was to perform experimental and computational studies to understand the basic mechanisms of dispersion and mixing at pore scale. The work covered four primary topics: development of microsensors to enable the direct measurement of the solute concentrations at the scale of individual pores; grain-scale evaluation of the origin of hydrodynamic from first principles of laminar flow and diffusion; theoretical evaluation of the effect of flow reversal as a means to distinguish the contribution convective spreading from that of true mixing to dispersion; and numerical evaluation of the field scale impact of permeab...

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Computational methods for multiphase flow and reactive transport problems arising in subsurface contaminant remediation

Cited by 35 publications

References 14 publications

An integro‐differential model for non‐Fickian tracer transport in porous media: validation and numerical simulation

An integro‐differential model for non‐Fickian tracer transport in porous media: validation and numerical simulation

Analysis of Box Schemes for Reactive Flow Problems

Origin of Scale-Dependent Dispersivity and Its Implications For Miscible Gas Flooding

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