Upscaling solute transport in porous media in the presence of an irreversible bimolecular reaction

Porta, Giovanni; Riva, Mònica; Guadagnini, Alberto

doi:10.1016/j.advwatres.2011.09.004

Cited by 58 publications

(47 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Dynamic changes in reaction rate in a beadpack were predicted accurately and shown to be affected not only by incomplete mixing as it had been demonstrated before experimentally (Raje and Kapoor 2000;Gramling et al 2002;Jose and Cirpka 2004;Rolle et al 2009;Edery et al 2015) and numerically (Edery et al 2010;Bolster et al 2010;Dentz et al 2011;Ding et al 2013;Hochstetler and Kitanidis 2013), but also as a result of early-time pre-asymptotic spreading (Alhashmi et al 2015). The characterization of the pre-asymptotic behavior through a continuum-scale model has been recently discussed by Porta et al (2016), based on previous work by Porta et al (2012).…”

Section: Introductionmentioning

confidence: 74%

“…The model is based on an empirical relationship that was used as a calibrating parameter to find the effective reaction rate based on the ADRE. The validity of ADRE model on the basis of theoretical upscaling has been discussed elsewhere (Porta et al 2012). Using different methods, at the Darcy scale, Edery et al (2009Edery et al ( , 2010 accurately reproduced the experimental data of Gramling et al (2002) based on a continuous-time random walk (CTRW) model.…”

Section: Introductionmentioning

confidence: 77%

See 1 more Smart Citation

The Impact of Pore Structure Heterogeneity, Transport, and Reaction Conditions on Fluid–Fluid Reaction Rate Studied on Images of Pore Space

2016

View full text Add to dashboard Cite

We perform direct numerical simulation using a pore-scale fluid-fluid reactive transport model (Alhashmi et al. in J Contam Hydrol 179:171-181, 2015. doi:10.1016/j. jconhyd.2015 to investigate the impact of pore structure heterogeneity on the effective reaction rate in different porous media. We simulate flow, transport, and reaction in three pore-scale images: a beadpack, Bentheimer sandstone, and Doddington sandstone for a range of transport and reaction conditions. We compute the reaction rate, velocity distributions, and dispersion coefficient comparing them with the results for non-reactive transport. The rate of reaction is a subtle combination of the amount of mixing and spreading that cannot be predicted from the non-reactive dispersion coefficient. We demonstrate how the flow field heterogeneity affects the effective reaction rate. Dependent on the intrinsic flow field heterogeneity characteristic and the flow rate, reaction may: (a) occur throughout the zones where both resident and injected particles exist (for low Péclet number and a homogeneous flow field), (b) preferentially occur at the trailing edge of the plume (for high Péclet number and a homogeneous flow field), or (c) be disfavored in slow-moving zones (for high Péclet number and a heterogeneous flow field).

show abstract

Section: Introductionmentioning

confidence: 74%

Section: Introductionmentioning

confidence: 77%

The Impact of Pore Structure Heterogeneity, Transport, and Reaction Conditions on Fluid–Fluid Reaction Rate Studied on Images of Pore Space

2016

View full text Add to dashboard Cite

show abstract

“…Hence, its solution tends asymptotically toward a steady state condition, i.e., a steady closure of the system is valid only for long enough times. The relevance of the transient stage on the solution depends (in general) on the geometry of the problem at the level of the unit cell and on the P eclet number in each subregion as suggested in Porta et al [2012]. Here, we retain the transient effects in the formulation of the closure problems associated with both mobile and immobile regions.…”

Section: Closure Systemmentioning

confidence: 99%

“…These provide the link between small-scale variation of velocity and concentrations and volume averaged quantities. While steady-state closure approximations are generally assumed to hold, here we rely on an unsteady (time-dependent) closure following Moyne [1997], Chastanet and Wood [2008], Porta et al [2012], and Wood and Valdès-Parada [2012]. An unsteady closure formulation allows to (a) retrieve closed form equations explicitly embedding nonlocal temporal behavior and (b) include these in the final upscaled equations through time convolutions.…”

Section: Introductionmentioning

confidence: 99%

Upscaling solute transport in porous media from the pore scale to dual‐ and multicontinuum formulations

Porta

Chaynikov

Riva

et al. 2013

Water Resources Research

View full text Add to dashboard Cite

[1] We provide pore to Darcy-scale theoretical upscaling of solute transport in porous media and discuss the key theoretical elements underlying double-and multirate mass transfer formulations which are typically adopted to interpret laboratory-and/or field-scale transport experiments. We model pore-scale transport by considering advective and diffusive processes. The resulting mass balance equation is subject to volume averaging relying on an unsteady closure. This leads to a nonlocal in time continuum-scale twoequation transport model, which we compare against existing double-and multirate mass transfer formulations. Coefficients appearing in our upscaled model are expressed as functions of time and pore-scale geometry and velocity distribution. We analyze in detail the scenario associated with two-dimensional flow in a plane channel and discuss the temporal dynamics and the associated asymptotic behavior of the different effective coefficients appearing in the upscaled system of equations. The relative influence of the terms included in the continuum-scale model is quantitatively assessed.Citation: Porta, G., S. Chaynikov, M. Riva, and A. Guadagnini (2013), Upscaling solute transport in porous media from the pore scale to dual-and multicontinuum formulations, Water Resour.

show abstract

“…For mass transport through a straight tube, previous studies using series expansion methods showed that dynamic D increases monotonically from the molecular diffusion coefficient to the value specified by Taylor's theory at either steady or transient flow [9,10]. Here we applied the volume averaging method (VAM) with Green's function to derive the closed-form of dynamic D. The VAM was extensively used for upscaling properties of media from pore-scale to continuum scale [11][12][13][14]. This paper presents the theoretical development for the dynamic D with Hagen-Poiseuille flow to characterize non-Fickian and Fickian transport without time (or spatial) scale limitations when Peclet number (Pe) is reasonably high.…”

Section: Introductionmentioning

confidence: 99%

Closed-form expression for the dynamic dispersion coefficient in Hagen-Poiseuille flow

Wang¹,

Cardenas²

2017

Preprint

View full text Add to dashboard Cite

Abstract:We present an exact expression for the upscaled dynamic dispersion coefficient (D) for one-dimensional transport by Hagen-Poiseuille flow which is the basis for modeling transport in porous media idealized as capillary tubes. The theoretical model is validated by comparing the breakthrough curves (BTCs) from a 1D advection-dispersion model with dynamic D to that from direct numerical solutions utilizing a 2D advection-diffusion model. Both Taylor dispersion theory and our new theory are good predictors of D at lower Peclet Number (Pe) regime, but gradually fail to capture most parts of BTCs as Pe increases. However, our model generally predicts the mixing and spreading of solutes better than Taylor's theory since it covers all transport regimes from molecular diffusion, through anomalous transport, and to Taylor dispersion. The model accurately predicts D based on the early part of BTCs even at relatively high Pe regime (~62) where the Taylor's theory fails. Furthermore, the model allows for calculation of the time scale that separates Fickian from non-Fickian transport. Therefore, our model can readily be used to calculate dispersion through short tubes of arbitrary radii such as the pore throats in a pore network model.

show abstract

Upscaling solute transport in porous media in the presence of an irreversible bimolecular reaction

Cited by 58 publications

References 25 publications

The Impact of Pore Structure Heterogeneity, Transport, and Reaction Conditions on Fluid–Fluid Reaction Rate Studied on Images of Pore Space

The Impact of Pore Structure Heterogeneity, Transport, and Reaction Conditions on Fluid–Fluid Reaction Rate Studied on Images of Pore Space

Upscaling solute transport in porous media from the pore scale to dual‐ and multicontinuum formulations

Closed-form expression for the dynamic dispersion coefficient in Hagen-Poiseuille flow

Contact Info

Product

Resources

About