Upscaling Diffusion and Nonlinear Reactive Mass Transport in Homogeneous Porous Media

Méndez, Helen Denise Lugo; Valdés‐Parada, Francisco J.; Porter, Mark L.; Wood, Brian D.; Ochoa‐Tapia, J. Alberto

doi:10.1007/s11242-015-0462-4

Cited by 31 publications

(20 citation statements)

References 59 publications

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“…Experiments studying the effects of soil structure on the dynamics of SOM mineralization (Killham et al, 1993;Stenger et al, 2002;Ruamps et al, 2011;Juarez et al, 2013;Negassa et al, 2015;Herbst et al, 2016) may introduce other types of heterogeneities that are not dealt with here. For example, samples with different pore networks (Ruamps et al, 2011) likely exhibit different water and air diffusive pathways, which in turn affect microbial respiration (Manzoni and Katul, 2014;Herbst et al, 2016;Koestel and Schlüter, 2019). When targeting experiments to test our upscaled equations, using data from previous studies is challenging because (i) spatial distributions of substrate and/or microbial C are not changed in a controlled manner and (ii) the scale at which physical treatments are performed is probably larger than the scale at which heterogeneity affects C dynamics.…”

Section: Linking Theory and Observationsmentioning

confidence: 99%

Dynamic upscaling of decomposition kinetics for carbon cycling models

et al. 2020

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Abstract. The distribution of organic substrates and microorganisms in soils is spatially heterogeneous at the microscale. Most soil carbon cycling models do not account for this microscale heterogeneity, which may affect predictions of carbon (C) fluxes and stocks. In this study, we hypothesize that the mean respiration rate R‾ at the soil core scale (i) is affected by the microscale spatial heterogeneity of substrate and microorganisms and (ii) depends upon the degree of this heterogeneity. To theoretically assess the effect of spatial heterogeneities on R‾, we contrast heterogeneous conditions with isolated patches of substrate and microorganisms versus spatially homogeneous conditions equivalent to those assumed in most soil C models. Moreover, we distinguish between biophysical heterogeneity, defined as the nonuniform spatial distribution of substrate and microorganisms, and full heterogeneity, defined as the nonuniform spatial distribution of substrate quality (or accessibility) in addition to biophysical heterogeneity. Four common formulations for decomposition kinetics (linear, multiplicative, Michaelis–Menten, and inverse Michaelis–Menten) are considered in a coupled substrate–microbial biomass model valid at the microscale. We start with a 2-D domain characterized by a heterogeneous substrate distribution and numerically simulate organic matter dynamics in each cell in the domain. To interpret the mean behavior of this spatially explicit system, we propose an analytical scale transition approach in which microscale heterogeneities affect R‾ through the second-order spatial moments (spatial variances and covariances). The model assuming homogeneous conditions was not able to capture the mean behavior of the heterogeneous system because the second-order moments cause R‾ to be higher or lower than in the homogeneous system, depending on the sign of these moments. This effect of spatial heterogeneities appears in the upscaled nonlinear decomposition formulations, whereas the upscaled linear decomposition model deviates from homogeneous conditions only when substrate quality is heterogeneous. Thus, this study highlights the inadequacy of applying at the macroscale the same decomposition formulations valid at the microscale and proposes a scale transition approach as a way forward to capture microscale dynamics in core-scale models.

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Section: Linking Theory and Observationsmentioning

confidence: 99%

Dynamic upscaling of decomposition kinetics for carbon cycling models

et al. 2020

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“…Finally, the simulated domain is small compared to an actual soil sample, but we regard the number of simulated grid cells (10 4 ) as representative of the range of variation occurring in larger, similarly idealized samples. In other studies, more complex micro-scale models based on nonlinear reactive and diffusive fluxes have been implemented (Monga et al, 2008;Nguyen-Ngoc et al, 2013;Monga et al, 2014); however, their spatial upscaling would require volume averaging of the coupled transport and reaction equations, making the problem mathematically intractable when aiming for analytical solutions (Whitaker, 1999;Valdés-Parada et al, 2009;Porter et al, 2011;Lugo-Méndez et al, 2015). The two pool micro-scale model with initial heterogeneous distributions of substrate and microorganisms as described in this study offers a simplified way of simulating reaction-diffusion systems.…”

Section: Limitations Of the Upscaling Approachmentioning

confidence: 99%

Dynamic upscaling of decomposition kinetics for carbon cycling models

Chakrawal¹,

Herrmann²,

Koestel³

et al. 2019

Preprint

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Abstract. The distribution of organic substrates and microorganism in soils is spatially heterogeneous at the micro-scale. Most soil carbon cycling models do not account for this micro-scale heterogeneity, which may affect predictions of carbon (C) fluxes and stocks. In this study, we hypothesize that the mean respiration rate R at the soil-core scale (i) is affected by the micro-scale spatial heterogeneity of substrate and microbes and (ii) depends upon the degree of this heterogeneity. To assess theoretically the effect of spatial heterogeneities on R, we contrast highly heterogeneous conditions with isolated patches of substrate and microbes versus spatially homogeneous conditions equivalent to those assumed in most soil C models. Moreover, we distinguish between biophysical heterogeneity, defined as the non-uniform spatial distribution of substrate and microbes, and full heterogeneity, defined as the non-uniform spatial distribution of substrate quality (or accessibility) in addition to biophysical heterogeneity. Three commonly used formulations for decomposition kinetics (linear, multiplicative and Michaelis-Menten) are considered in a coupled substrate-microbial biomass model valid at the micro-scale. We start with a 2D domain characterized by a heterogeneous substrate distribution and numerically simulate organic matter dynamics at each cell in the domain. To interpret the mean behavior of this spatially-explicit system, we propose an analytical scale transition approach in which micro-scale heterogeneities affect R through the second order spatial moments (spatial variances and covariances). It was not possible to capture the mean behavior of the heterogeneous system when the model assumed spatial homogeneity, because the second order moments cause the heterogeneous system to deviate from the behavior attained under homogeneous conditions. Consequently, R in the heterogeneous system can be higher or lower than the respiration of the homogeneous system, depending on the sign of the second order spatial moments. This effect of the spatial heterogeneities appears in the upscaled nonlinear decomposition formulations, whereas the upscaled linear decomposition model deviates from homogeneous conditions only when substrate quality is heterogeneous. Thus, this study highlights the inadequacy of applying at the macro-scale the same decomposition formulations valid at the micro-scale, and proposes a scale transition approach as a way forward to capture micro-scale dynamics in core-scale models.

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“…Another option, which has been used by numerous authors over the last two decades, consists of averaging microscopic descriptions of porous media, over either a Representative Elementary Volume or an arbitrary volume (e.g., associated with a measuring instrument), in order to obtain macroscopic variables ( Ayub and Bentsen, 1999 ; Lichtner and Kang, 2007a , b ; Golfier et al, 2009 ; Valdes-Parada et al, 2009 ; Wood, 2009 , 2010 ; Davit et al, 2010 ; Baveye, 2013a ; Lugo-Mendez et al, 2015 ). Davit et al (2013) have shown that in terms of outcome, this approach is equivalent to another popular upscaling method involving homogenization through multiscale asymptotics (e.g., Roose et al, 2016 ).…”

Section: Upscaling How?mentioning

confidence: 99%

Emergent Properties of Microbial Activity in Heterogeneous Soil Microenvironments: Different Research Approaches Are Slowly Converging, Yet Major Challenges Remain

et al. 2018

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Over the last 60 years, soil microbiologists have accumulated a wealth of experimental data showing that the bulk, macroscopic parameters (e.g., granulometry, pH, soil organic matter, and biomass contents) commonly used to characterize soils provide insufficient information to describe quantitatively the activity of soil microorganisms and some of its outcomes, like the emission of greenhouse gasses. Clearly, new, more appropriate macroscopic parameters are needed, which reflect better the spatial heterogeneity of soils at the microscale (i.e., the pore scale) that is commensurate with the habitat of many microorganisms. For a long time, spectroscopic and microscopic tools were lacking to quantify processes at that scale, but major technological advances over the last 15 years have made suitable equipment available to researchers. In this context, the objective of the present article is to review progress achieved to date in the significant research program that has ensued. This program can be rationalized as a sequence of steps, namely the quantification and modeling of the physical-, (bio)chemical-, and microbiological properties of soils, the integration of these different perspectives into a unified theory, its upscaling to the macroscopic scale, and, eventually, the development of new approaches to measure macroscopic soil characteristics. At this stage, significant progress has been achieved on the physical front, and to a lesser extent on the (bio)chemical one as well, both in terms of experiments and modeling. With regard to the microbial aspects, although a lot of work has been devoted to the modeling of bacterial and fungal activity in soils at the pore scale, the appropriateness of model assumptions cannot be readily assessed because of the scarcity of relevant experimental data. For significant progress to be made, it is crucial to make sure that research on the microbial components of soil systems does not keep lagging behind the work on the physical and (bio)chemical characteristics. Concerning the subsequent steps in the program, very little integration of the various disciplinary perspectives has occurred so far, and, as a result, researchers have not yet been able to tackle the scaling up to the macroscopic level. Many challenges, some of them daunting, remain on the path ahead. Fortunately, a number of these challenges may be resolved by brand new measuring equipment that will become commercially available in the very near future.

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Upscaling Diffusion and Nonlinear Reactive Mass Transport in Homogeneous Porous Media

Cited by 31 publications

References 59 publications

Dynamic upscaling of decomposition kinetics for carbon cycling models

Dynamic upscaling of decomposition kinetics for carbon cycling models

Dynamic upscaling of decomposition kinetics for carbon cycling models

Emergent Properties of Microbial Activity in Heterogeneous Soil Microenvironments: Different Research Approaches Are Slowly Converging, Yet Major Challenges Remain

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