Pore-Scale Mixing and the Evolution of Hydrodynamic Dispersion in Porous Media

<p>Transport of dissolved substances through porous media is determined by the complexity of the pore space and diffusive mass transfer within and between pores. The interplay of diffusive pore-scale mixing and spatial flow variability are key for the understanding of transport and reaction phenomena in porous media. We study the interplay of pore-scale mixing and network-scale advection through heterogeneous porous media, and its role for the evolution and asymptotic behavior of hydrodynamic dispersion. In a Lagrangian framework, we identify three fundamental mechanisms of pore-scale mixing that determine large scale particle motion: (i) The smoothing of intra-pore velocity contrasts, (ii) the increase of the tortuosity of particle paths, and (iii) the setting of a maximum time for particle transitions. Based on these mechanisms, we derive an upscaled approach that predicts anomalous and normal hydrodynamic dispersion based on the characteristic pore length, Eulerian velocity distribution and P&#233;clet number. The theoretical developments are supported and validated by direct numerical flow and transport simulations in a three-dimensional digitized Berea sandstone sample obtained using X-Ray microtomography. Solute breakthrough curves, are characterized by an intermediate power-law behavior and exponential cut-off, which reflect pore-scale velocity variability and intra-pore solute mixing. Similarly, dispersion evolves from molecular diffusion at early times to asymptotic hydrodynamics dispersion via an intermediate superdiffusive regime. The theory captures the full evolution form anomalous to normal transport behavior at different P&#233;clet numbers as well as the P&#233;clet-dependence of asymptotic dispersion. It sheds light on hydrodynamic dispersion behaviors as a consequence of the interaction between pore-scale mixing and Eulerian flow variability.&#160;</p>

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Suitability of 2D modelling to evaluate flow properties in 3D porous media

10.5194/egusphere-egu21-8710 ◽

2021 ◽

Author(s):

Ester Marafini ◽

Michele La Rocca ◽

Aldo Fiori ◽

Ilenia Battiato ◽

Pietro Prestininzi

Keyword(s):

Porous Media ◽

Lattice Boltzmann Model ◽

Flow In Porous Media ◽

Hydrodynamic Dispersion ◽

Assessment Procedure ◽

Pore Scale ◽

Flows In Porous Media ◽

2D Modelling ◽

3D Flows ◽

2D And 3D

<p>Limitations stemming from the employment of 2D models to investigate the properties of 3D flows in porous media are generally overlooked. In this study, the extent to which 2D modelling can be employed for the representation of genuinely 3D flows in porous media is quantified. To this scope, Representative Elementary Volume (REV) sizes of 2D and 3D media sharing the same porosity are compared. The spatial stationarity of several Quantities of Interest (QoIs) namely, porosity, permeability, mean and variance of velocity, is numerically evaluated. In order to extend conclusions to transport phenomena, the analysis of the velocity variance, which is closely associated to the hydrodynamic dispersion process, is included. Porous media adopted in this study are composed by spheres and disks in 3D and 2D domains respectively, where both 2D and 3D geometries are characterized by random locations. Specifically, for 3D random packings creation, a sphere packing generator program is used. Pore scale flow is simulated by means of the Lattice Boltzmann Model (LBM): the LBM is employed as a numerical flow solver to reproduce the Darcy's experiment through the aforementioned domains. The LBM represents a powerful tool to model flow in porous media and it is able to accurately predict flow paths, permeability and hydraulic conductivity. Hydraulic QoIs are analysed at steady state conditions. To this purpose, the flow velocity field is used to inspect stationarity. The quantitative approaches adopted in the REV assessment procedure allow one to determine the residual variability of the quantity associated to the REV and consequently the level of accuracy that the modeller wants to achieve with respect to the QoIs. Such criteria show that REV estimations through 2D models are much larger than their 3D counterparts. In conclusion, pore scale LBM simulations highlight that the 2D approach leads to inconsistent results, due to the profound difference between 2D and 3D porous flows.</p>

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Impact of Synthetic Porous Medium Geometric Properties on Solute Transport Using Direct 3D Pore-Scale Simulations

Geofluids ◽

10.1155/2019/6810467 ◽

2019 ◽

Vol 2019 ◽

pp. 1-13

Author(s):

Paolo Roberto Di Palma ◽

Nicolas Guyennon ◽

Andrea Parmigiani ◽

Christian Huber ◽

Falk Heβe ◽

...

Keyword(s):

Porous Medium ◽

Porous Media ◽

Effective Diffusion ◽

Volume Averaging ◽

Transport Processes ◽

Hydrodynamic Dispersion ◽

Pore Scale ◽

Geometric Properties ◽

Advection Diffusion ◽

The Impact

Transport processes in porous media have been traditionally studied through the parameterization of macroscale properties, by means of volume-averaging or upscaling methods over a representative elementary volume. The possibility of upscaling results from pore-scale simulations, to obtain volume-averaging properties useful for practical purpose, can enhance the understanding of transport effects that manifest at larger scales. Several studies have been carried out to investigate the impact of the geometric properties of porous media on transport processes for solute species. However, the range of pore-scale geometric properties, which can be investigated, is usually limited to the number of samples acquired from microcomputed tomography images of real porous media. The present study takes advantage of synthetic porous medium generation to propose a systematic analysis of the relationships between geometric features of the porous media and transport processes through direct simulations of fluid flow and advection-diffusion of a non-reactive solute. Numerical simulations are performed with the lattice Boltzmann method on synthetic media generated with a geostatistically based approach. Our findings suggest that the advective transport is primarily affected by the specific surface area and the mean curvature of the porous medium, while the effective diffusion coefficient scales as the inverse of the tortuosity squared. Finally, the possibility of estimating the hydrodynamic dispersion coefficient knowing only the geometric properties of porous media and the applied pressure gradient has been tested, within the range of tested porous media, against advection-diffusion simulations at low Reynolds (<10-1) and Peclet numbers ranging from 101 to 10-2.

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Pore-Scale Experimental Study of Boiling in Porous Media

Proceedings of the 15th International Heat Transfer Conference ◽

10.1615/ihtc15.pbl.009914 ◽

2014 ◽

Cited By ~ 3

Author(s):

Paul SAPIN ◽

Paul Duru ◽

Florian Fichot ◽

Marc Prat ◽

Michel Quintard

Keyword(s):

Experimental Study ◽

Porous Media ◽

Pore Scale

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PORE-SCALE SIMULATION OF ICE MELTING PROCESS IN POROUS MEDIA

10.1615/tfec2017.prm.017991 ◽

2017 ◽

Author(s):

Pu He ◽

Li Chen ◽

Yu-Tong Mu ◽

Wen-Quan Tao

Keyword(s):

Porous Media ◽

Melting Process ◽

Pore Scale ◽

Ice Melting

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Dissolution of Microscale Energetic Residues in Saturated Porous Media: Visualization and Quantification at the Pore-Scale by Spectral Confocal Microscopy

Environmental Science & Technology ◽

10.1021/es201649k ◽

2011 ◽

Vol 45 (19) ◽

pp. 8352-8358 ◽

Cited By ~ 5

Author(s):

Chao Wang ◽

Volha Lazouskaya ◽

Mark E. Fuller ◽

Jeffrey L. Caplan ◽

Charles E. Schaefer ◽

...

Keyword(s):

Porous Media ◽

Confocal Microscopy ◽

Saturated Porous Media ◽

Pore Scale

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Thermodynamics of porous media

Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences ◽

10.1098/rspa.1993.0143 ◽

1993 ◽

Vol 443 (1917) ◽

pp. 247-255 ◽

Cited By ~ 29

Keyword(s):

Porous Media ◽

Elastic Energy ◽

Pore Scale ◽

Equilibrium Thermodynamics ◽

Energy Potential ◽

Macroscopic Variable ◽

Strain Tensors

Equilibrium thermodynamics for porous media is considered with special emphasis on its basis in pore-scale thermodynamics. It is shown that porosity, the new purely macroscopic variable, enters the relations on the same footing as mass densities and the strain tensors. Biot’s use of elastic energy potential, which lies at the foundation of his theory of poroelasticity, is examined in light of the results obtained here.

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