Upscaling of pore-scale mixing and reaction through effective dispersion coefficients

2021 ◽  
Author(s):  
Alexandre Puyguiraud ◽  
Lazaro Perez ◽  
Juan J. Hidalgo ◽  
Marco Dentz
Keyword(s):  
Green Function ◽  
Molecular Diffusion ◽  
Early Time ◽  
Hydrodynamic Dispersion ◽  
Pore Scale ◽  
Dispersion Coefficients ◽  
Incomplete Mixing ◽  
Effective Dispersion ◽  
Structure Heterogeneity ◽  
Field Heterogeneity

<p>We utilize effective dispersion coefficients to capture the evolution of the mixing interface between two initially segregated species due to the coupled effect of pore-scale heterogeneity and molecular diffusion. These effective dispersion coefficients are defined as the average spatial variance of the solute plume that evolves from a pointlike injection (the transport Green function). We numerically investigate the effective longitudinal dispersion coefficients in two porous media of different structure heterogeneity  and through different Péclet number regimes for each medium. We find that, as distance traveled increases (or time spent), the solute experiences the pore-scale velocity field heterogeneity due to advection and transverse diffusion, resulting in an evolution of the dispersion coefficients. They evolve from the value of molecular diffusion at early time, then undergo an advection dominated regime, to finally reach the value of hydrodynamic dispersion at late times. This means that, at times smaller than the characteristic diffusion time, the effective dispersion coefficients can be notably smaller than the hydrodynamic dispersion coefficient. Therefore, mismatches between pore-scale reaction data from experiment or simulations and Darcy scale predictions based on temporally constant hydrodynamic dispersion can be explained through these differences. We use the effective dispersion coefficients to approximate the transport Green function and to quantify the incomplete mixing occurring at the pore-scale. We evaluate the evolution of two initially segregated species via this methodology. The approach correctly predicts the amount of chemical reaction occuring in reactive bimolecular particle tracking simulations. These results shed light on the upscaling of pore-scale incomplete mixing and demonstrates that the effective dispersion is an accurate measure for the width of the mixing interface between two reactants. </p>

Pore-scale Mixing and the Evolution from Anomalous to Normal Hydrodynamic Dispersion

2021 ◽  
Author(s):  
Marco Dentz ◽  
Alexandre Puyguiraud ◽  
Philippe Gouze
Keyword(s):  
Porous Media ◽  
Large Scale ◽  
Molecular Diffusion ◽  
Pore Space ◽  
Breakthrough Curves ◽  
Heterogeneous Porous Media ◽  
Hydrodynamic Dispersion ◽  
Pore Scale ◽  
Sandstone Sample ◽  
Flow Variability

<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 Péclet 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 Péclet numbers as well as the Péclet-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. </p>

Impact of flow conditions on pore-scale solute mixing: experiments in heterogeneous 2D porous media

2021 ◽  
Author(s):  
Oshri Borgman ◽  
Turuban Régis ◽  
Baudouin Géraud ◽  
Le Borgne Tanguy ◽  
Méheust Yves
Keyword(s):  
Porous Media ◽  
Fluorescence Intensity ◽  
Dispersion Coefficient ◽  
Reaction Rates ◽  
Pore Scale ◽  
Flow Conditions ◽  
Dispersion Coefficients ◽  
Incomplete Mixing ◽  
The Mean ◽  
Solute Mixing

<p>Solute mixing mediated by flow in porous media plays a significant role in controlling reaction rates in subsurface environments. In many practical cases, incomplete mixing—inhomogeneous solute concentrations—occurs at the pore-scale, limiting local and thus upscaled reaction rates, and renders their prediction based on effective dispersion coefficients derived from dispersion models (or by assuming Taylor-Aris dispersion) inaccurate. We perform solute transport experiments in transparent, quasi-two-dimensional, soil analog models to investigate the relationships between pore-scale solute dispersion and mixing under different flow conditions. We use Fluorescein as a conservative tracer and record its fluorescence intensity in monochrome images at fixed time intervals. We convert the fluorescence intensity to solute concentration fields based on a calibration curve obtained with various homogeneous solute concentrations and subsequently compute concentration gradients. Our images provide evidence for incomplete mixing at the pore-scale and show strong gradients transverse to the overall flow direction. We fit the mean longitudinal concentration profile to an analytical solution of the advection-dispersion equation and compute the effective longitudinal dispersion coefficient. Based on the lamellar mixing theory, we also infer an effective diffusion coefficient relevant to the mean concentration gradient’s dynamics. By comparing these two diffusion/dispersion coefficients in saturated flow conditions, we show that while their values are similar at low Péclet, their scaling behaviors as a function of Péclet are different. Hence, as pointed out by several previous studies, modeling reactive transport processes requires accounting for a mixing behavior driven by a diffusive process that cannot entirely be described by the solute dispersion coefficient. We extend this work by varying the saturation degree in the experiments and our samples' structural heterogeneity to investigate how flow desaturation and porous medium structure impact solute mixing.</p>

Effective dispersion coefficients for the upscaling of pore-scale mixing and reaction

2020 ◽  
Vol 146 ◽  
pp. 103782
Author(s):  
Alexandre Puyguiraud ◽  
Lazaro J. Perez ◽  
Juan J. Hidalgo ◽  
Marco Dentz
Keyword(s):  
Pore Scale ◽  
Dispersion Coefficients ◽  
Effective Dispersion

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

2021 ◽  
Vol 126 (16) ◽  
Author(s):  
Alexandre Puyguiraud ◽  
Philippe Gouze ◽  
Marco Dentz
Keyword(s):  
Porous Media ◽  
Hydrodynamic Dispersion ◽  
Pore Scale

Gaseous dispersion in laminar flow through a circular tube

1965 ◽  
Vol 284 (1399) ◽  
pp. 540-550 ◽  
Keyword(s):  
Circular Tube ◽  
Dispersion Coefficient ◽  
Straight Tube ◽  
Laminar Regime ◽  
Thermal Conductivity Detector ◽  
Longitudinal Dispersion Coefficient ◽  
Dispersion Coefficients ◽  
Effective Dispersion ◽  
Flow Through ◽  
Gaseous Dispersion

The dispersion of a pulse of ethylene injected into nitrogen, flowing in the laminar régime through straight and curved tubes, has been investigated at pressures of 1.0 and 4.4 atm. From the study of the concentration profiles with a thermal conductivity detector (katharometer) it is found that the experimental results for gas velocities between 1.00 and 16.00 cm/s agree well with the analytical solution to this problem for a straight tube given by Sir Geoffrey Taylor and extended by Aris. In particular, at low velocities, the effective dispersion coefficients tend to the molecular diffusivities. The presence of a bend slightly reduces the effective longitudinal dispersion coefficient and the introduction of constrictions enhances it. Data are also given on a number of other gas pairs. It is concluded that measurements of dispersion provide an accurate and simple way of studying diffusion in gas mixtures.

Effect of non-uniform passive advection on A+B->C radial reaction-diffusion fronts 

2021 ◽  
Author(s):  
Alessandro Comolli ◽  
Anne De Wit ◽  
Fabian Brau
Keyword(s):  
Molecular Diffusion ◽  
Early Time ◽  
Reaction Diffusion ◽  
Transport Processes ◽  
Calcium Carbonate Precipitation ◽  
Atmospheric Reactions ◽  
Passive Advection ◽  
Reaction Fronts ◽  
Time Regime ◽  
Long Time

<p>The interplay between chemical and transport processes can give rise to complex reaction fronts dynamics, whose understanding is crucial in a wide variety of environmental, hydrological and biological processes, among others. An important class of reactions is A+B->C processes, where A and B are two initially segregated miscible reactants that produce C upon contact. Depending on the nature of the reactants and on the transport processes that they undergo, this class of reaction describes a broad set of phenomena, including combustion, atmospheric reactions, calcium carbonate precipitation and more. Due to the complexity of the coupled chemical-hydrodynamic systems, theoretical studies generally deal with the particular case of reactants undergoing passive advection and molecular diffusion. A restricted number of different geometries have been studied, including uniform rectilinear [1], 2D radial [2] and 3D spherical [3] fronts. By symmetry considerations, these systems are effectively 1D.</p><p>Here, we consider a 3D axis-symmetric confined system in which a reactant A is injected radially into a sea of B and both species are transported by diffusion and passive non-uniform advection. The advective field <em>v<sub>r</sub>(r,z)</em> describes a radial Poiseuille flow. We find that the front dynamics is defined by three distinct temporal regimes, which we characterize analytically and numerically. These are i) an early-time regime where the amount of mixing is small and the dynamics is transport-dominated, ii) a strongly non-linear transient regime and iii) a long-time regime that exhibits Taylor-like dispersion, for which the system dynamics is similar to the 2D radial case.</p><p>                                  <img src="https://contentmanager.copernicus.org/fileStorageProxy.php?f=gnp.ff5ab530bdff57321640161/sdaolpUECMynit/12UGE&app=m&a=0&c=360a1556c809484116c55812c8c06624&ct=x&pn=gnp.elif&d=1" alt="" width="299" height="299">                                                     <img src="https://contentmanager.copernicus.org/fileStorageProxy.php?f=gnp.671a6980bdff51231640161/sdaolpUECMynit/12UGE&app=m&a=0&c=c5a857c3fab835057e3af84001a91d15&ct=x&pn=gnp.elif&d=1" alt="" width="302" height="302"></p><p>                                                   Fig. 1: Concentration profile of the product C in the transient (left) and asymptotic (right) regimes.</p><p> </p><p>References:</p><p>[1] L. Gálfi, Z. Rácz, Phys. Rev. A 38, 3151 (1988);</p><p>[2] F. Brau, G. Schuszter, A. De Wit, Phys. Rev. Lett. 118, 134101 (2017);</p><p>[3] A. Comolli, A. De Wit, F. Brau, Phys. Rev. E, 100 (5), 052213 (2019).</p>

scholarly journals The Hydrodynamic Dispersion Characteristics of Coral Sands

2019 ◽  
Vol 7 (9) ◽  
pp. 291 ◽  
Author(s):  
Xiang Cui ◽  
Changqi Zhu ◽  
Mingjian Hu ◽  
Xinzhi Wang ◽  
Haifeng Liu
Keyword(s):  
Particle Size ◽  
Porous Media ◽  
Flow Velocity ◽  
Molecular Diffusion ◽  
Dispersion Coefficient ◽  
Hydrodynamic Dispersion ◽  
Dispersion Characteristics ◽  
Factors Affecting ◽  
Mechanical Dispersion ◽  
Freshwater Aquifers

Dispersion characteristics are important factors affecting groundwater solute transport in porous media. In marine environments, solute dispersion leads to the formation of freshwater aquifers under islands. In this study, a series of model tests were designed to explore the relationship between the dispersion characteristics of solute in calcareous sands and the particle size, degree of compactness, and gradation of porous media, with a discussion of the types of dispersion mechanisms in coral sands. It was found that the particle size of coral sands was an important parameter affecting the dispersion coefficient, with the dispersion coefficient increasing with particle size. Gradation was also an important factor affecting the dispersion coefficient of coral sands, with the dispersion coefficient increasing with increasing d10. The dispersion coefficient of coral sands decreased approximately linearly with increasing compactness. The rate of decrease was −0.7244 for single-grained coral sands of particle size 0.25–0.5 mm. When the solute concentrations and particle sizes increased, the limiting concentration gradients at equilibrium decreased. In this study, based on the relative weights of molecular diffusion versus mechanical dispersion under different flow velocity conditions, the dispersion mechanisms were classified into five types, and for each type, a corresponding flow velocity limit was derived.

Groundwater flow and solute transport in a laboratory-scale analogue of a decommissioned in-pit tailings management facility

2003 ◽  
Vol 40 (2) ◽  
pp. 326-341 ◽  
Author(s):  
Anthony CF West ◽  
Paul J Van Geel ◽  
Kenneth G Raven ◽  
Thanh Son Nguyen ◽  
Mahrez Ben Belfadhel ◽  
...  
Keyword(s):  
Groundwater Flow ◽  
Early Time ◽  
Solute Concentration ◽  
Laboratory Scale ◽  
Hydrodynamic Dispersion ◽  
Concentration Data ◽  
Advection Dispersion ◽  
Steady Rate ◽  
Tailings Management ◽  
Rate Controlled

A laboratory-scale analogue of an in-pit tailings management facility (TMF) was constructed using mortar sand, fluorescent-dye-containing ground silica, and filter gravel to represent fractured host rock, tailings, and a pervious surround, respectively. In a series of experiments, the performance of the analogue was observed through collection of hydraulic head, groundwater discharge, and solute concentration data. These data were found to be sufficient to validate numerical simulations of the experiments carried out using FRAC3DVS. The validation exercise indicated that adequate discretization of the tailings' periphery was critical to accurate simulation of early time solute release from the ground silica, while accurate simulation of groundwater flow and hydrodynamic dispersion adjacent to the ground silica was critical to accurate simulation of the down-gradient solute plumes. The validated model was used to predict how the analogue would have performed over its entire "contaminating lifespan." The results of the experiments and subsequent numerical modelling were used to support the argument that, assuming no dissolution of tailings solids, solute mass flux out of a decommissioned in-pit TMF would decrease asymptotically with time from a rate controlled by diffusion at the tailings' periphery towards a steady rate controlled by advection through their core.Key words: tailings, groundwater contamination, in-pit disposal, physical model, numerical model, advection-dispersion.

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