Applicability regimes for macroscopic models of reactive transport in porous media

Battiato, Ilenia; Tartakovsky, Daniel M.

doi:10.1016/j.jconhyd.2010.05.005

Cited by 184 publications

(141 citation statements)

References 14 publications

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“…Battiato and Tartakovsky (2011) proposed the use of non-dimensional numbers in hydrological upscaling approaches and to provide quantitative measures of the validity of upscaling approximations. We now explore two nondimensional variables that make up the key components of our connectivity framework.…”

Section: Non-dimensional Numbersmentioning

confidence: 99%

“…One of the challenges for the prediction of material transfer through catchments is the high degree of heterogeneity (of source distributions, transport media and biogeochemical processes), and its dependence on scale. Dooge (1986) suggested that scaling issues were fundamental to the development of hydrological theory, specifically the development of scaling relations across catchment scales and up-scaling from small-scale processes (Battiato and Tartakovsky, 2011). Since that time there has been substantial research on small-scale process-based distributed model descriptions, however the application of these models to large catchments has at times been problematic and the preferred modes of investigation continue to vary across scales (Table 1).…”

Section: Introductionmentioning

confidence: 99%

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A generalized Damköhler number for classifying material processing in hydrological systems

Oldham

Farrow

Peiffer

2013

Hydrol. Earth Syst. Sci.

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Abstract. Assessing the potential for transfer of pollutants and nutrients across catchments is of primary importance under changing land use and climate. Over the past decade the connectivity/disconnectivity dynamic of a catchment has been related to its potential to export material; however, we continue to use multiple definitions of connectivity, and most have focused strongly on physical (hydrological or hydraulic) connectivity. In contrast, this paper constantly focuses on the dynamic balance between transport and material transformation, and defines material connectivity as the effective transfer of material between elements of the hydrological cycle. The concept of exposure timescales is developed and used to define three distinct regimes: (i) which is hydrologically connected and transport is dominated by advection; (ii) which is hydrologically connected and transport is dominated by diffusion; and (iii) which is materially isolated. The ratio of exposure timescales to material processing timescales is presented as the non-dimensional number, N E , where N E is reaction-specific and allows estimation of relevant spatial scales over which the reactions of interest take place. Case studies within each regime provide examples of how N E can be used to characterise systems according to their sensitivity to shifts in hydrology and gain insight into the biogeochemical processes that are signficant under the specified conditions. Finally, we explore the implications of the N E framework for improved water management, and for our understanding of biodiversity, resilience and chemical competitiveness under specified conditions.

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Section: Non-dimensional Numbersmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A generalized Damköhler number for classifying material processing in hydrological systems

Oldham

Farrow

Peiffer

2013

Hydrol. Earth Syst. Sci.

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“…We use the multiple-scale expansion technique 16,17 to derive effective continuum scale equations for average concentration Cðx; tÞ hcðx; tÞi. The method postulates that concentration exhibits both large-scale (across the porous material, denoted by the coordinate x) and small-scale (inside individual pores, denoted by the coordinate y) spatial variability, such that y ¼ À1 x with ( 1; the corresponding temporal scales are denoted, respectively, by t and s r ¼ Da t where Da is the Damk€ ohler number.…”

Section: Appendix B: Homogenization Of Transport Equationsmentioning

confidence: 99%

“…It depends only on the geometry of the unit cell. We represent its solution as 16,17 c 1 ðx; y; t; s r Þ ¼ vðyÞ Á r x c 0 ðx; t; s r Þ þ c 1 ðx; t; s r Þ: …”

Section: Appendix B: Homogenization Of Transport Equationsmentioning

confidence: 99%

“…14 This can be accomplished with a variety of upscaling techniques, including volume averaging 15 and homogenization via multiple-scale expansions. [16][17][18] We use the latter approach to predict anisotropic diffusion coefficients and effective adsorption rates for a class of nanoporous materials, 19 whose synthesis allows one to control their pore structure. It is worthwhile emphasizing that the use of various homogenization techniques to derive effective (continuum-or Darcy-scale) models of reactive transport in porous media (primarily subsurface environments) is not new.…”

Section: Introductionmentioning

confidence: 99%

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Design of nanoporous materials with optimal sorption capacity

Zhang

Urita

Moriguchi

et al. 2015

Journal of Applied Physics

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Modern technological advances have enabled one to manufacture nanoporous materials with a prescribed pore structure. This raises a possibility of using controllable pore-scale parameters (e.g., pore size and connectivity) to design materials with desired macroscopic properties (e.g., diffusion coefficient and adsorption capacity). By relating these two scales, the homogenization theory (or other upscaling techniques) provides a means of guiding the experimental design. To demonstrate this approach, we consider a class of nanoporous materials whose pore space consists of nanotunnels interconnected by nanotube bridges. Such hierarchical nanoporous carbons with mesopores and micropores have shown high specific electric double layer capacitances and high rate capability in an organic electrolyte. We express the anisotropic diffusion coefficient and adsorption coefficient of such materials in terms of the tunnels' properties (pore radius and inter-pore throat width) and their connectivity (spacing between the adjacent tunnels and nanotube-bridge density). Our analysis is applicable for solutes that undergo a nonequilibrium Langmuir adsorption reaction on the surfaces of fluid-filled pores, but other homogeneous and heterogeneous reactions can be handled in a similar fashion. The presented results can be used to guide the design of nanoporous materials with optimal permeability and sorption capacity. V C 2015 AIP Publishing LLC. [http://dx

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Hybrid modeling of heterogeneous geochemical reactions in fractured porous media

Roubinet

Tartakovsky

2013

Water Resour. Res.

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[1] Quantitative modeling of geochemical reactions at the Darcy scale is challenging due to their dependence on pore-scale characteristics that often cannot be averaged out. We propose a hybrid pore-scale/continuum-scale algorithm to bridge the gap between the porescale mechanisms of reactive transport and the Darcy-scale observations of their impact. These two scales are coupled by introducing extra nodes at the pore/continuum interfaces, in which the continuity of both concentrations and mass fluxes is enforced. Our algorithm is applicable to highly localized transport phenomena that can be adequately described by Darcy-scale equations in most of a computational domain except for small regions (e.g., reaction fronts) wherein pore-scale simulations are necessary. We employ the proposed hybrid algorithm to model transient reactive solute transport involving fracture cementation.

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Applicability regimes for macroscopic models of reactive transport in porous media

Cited by 184 publications

References 14 publications

A generalized Damköhler number for classifying material processing in hydrological systems

A generalized Damköhler number for classifying material processing in hydrological systems

Design of nanoporous materials with optimal sorption capacity

Hybrid modeling of heterogeneous geochemical reactions in fractured porous media

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