Diffusion limited mixing in heterogeneous porous media

2021 ◽  
Author(s):  
Mayumi Hamada ◽  
Pietro de Anna
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Flow Field ◽  
Fast Diffusion ◽  
Pore Scale ◽  
Mixing Processes ◽  
Local Flow ◽  
Gaussian Shape ◽  
Diffusion Limited ◽  
The Impact

<p><span><span>A pore-scale description of the transport and mixing processes is particularly relevant when looking at biological and chemical reactions. For instance, a microbial population growth is controlled by local concentrations of nutrients and oxygen, and chemical reaction are driven by molecular-scale concentration gradients. The heterogeneous flow field typically found in porous media results from the contrast of velocities that deforms and elongates the mixing fronts between solutes that often evolves through a lamella-like topology. For continuous Darcy type flow field a novel framework that describes the statistical distribution of concentration being transported was recently developed (Le Borgne et al., JFM 2015). In this model, concentrations in each lamella are distributed as a Gaussian-like profile which experiences diffusion in the transverse direction while the lamella is elongated by advection along the local flow direction. The evolving concentration field is described as the superposition of each lamella. We hypothesize that this novel view, while perfectly predicting the distribution of concentration for Darcy scale mixing processes, will breakdown when the processes description is at the pore scale. Indeed the presence of solid and impermeable boundaries prevents lamella concentration to diffuse freely according to the a Gaussian shape, and therefore changes the mixing front profile, the lamella superposition and elongation rules. P</span></span><span><span>revious work (Hamada et al, PRF, 2020) demonstrated that </span></span><span><span>the presence of solid boundaries leads to an enhanced diffusion and thus fast homogenization of concentrations. </span></span><span><span>In a purely diffusive process the local mixing time is reduced by a factor of ten with respect to the </span></span><span><span>continuous case and concentration gradient are dissipated exponentially fast while a </span></span><span><span>power law decrease </span></span><span><span>is </span></span><span><span>observed in continuous medium.</span></span><span><span> To investigate the impact of these mechanisms on mixing we developed a</span></span><span><span>n experimental set-up to visualize and quantify the displacement of a conservative tracer in a synthetic porous medium. The designed apparatus allows to obtain high resolution concentration measurement</span></span><span><span>s</span></span><span><span> at the pore scale. We show that the resulting mixing measures, computed in terms of concentration probability density function and dilution index values, diverge </span></span><span><span>qualitatively and quantitatively from what happens in a continuous domain. These observations suggest </span></span><span><span>that description of pore-scale diffusion-limited mixing requires model that takes into account the confined nature of porous medium, </span></span><span><span>otherwise we will tend to overestimate concentration value and neglect the fast diffusion dynamic taking place at microscopic level.</span></span></p>

scholarly journals Upscaling Mixing-Controlled Reactions in Unsaturated Porous Media

2021 ◽  
Author(s):  
Lazaro J. Perez ◽  
Alexandre Puyguiraud ◽  
Juan J. Hidalgo ◽  
Joaquín Jiménez-Martínez ◽  
Rishi Parashar ◽  
...  
Keyword(s):  
Experimental Data ◽  
Porous Media ◽  
Flow Field ◽  
Particle Tracking ◽  
Water Phase ◽  
Pore Scale ◽  
Unsaturated Porous Media ◽  
Reactive Mixing ◽  
The Impact ◽  
Random Walk Particle Tracking

AbstractWe study mixing-controlled chemical reactions in unsaturated porous media from a pore-scale perspective. The spatial heterogeneity induced by the presence of two immiscible phases, here water and air, in the pore space generates complex flow patterns that dominate reactive mixing across scales. To assess the impact of different macroscopic saturation states (the fraction of pore volume occupied by water) on mixing-controlled chemical reactions, we consider a fast irreversible reaction between two initially segregated dissolved species that mix as one solution displaces the other in the heterogeneous flow field of the water phase. We use the pore-scale geometry and water distributions from the laboratory experiments reported by Jiménez-Martínez et al. (Geophys. Res. Lett. 42: 5316–5324, 2015). We analyze reactive mixing in three complementary ways. Firstly, we post-process experimentally observed spatially distributed concentration data; secondly, we perform numerical simulations of flow and reactive transport in the heterogeneous water phase, and thirdly, we use an upscaled mixing model. The first approach relies on an exact algebraic map between conservative and reactive species for an instantaneous irreversible bimolecular reaction that allows to estimate reactive mixing based on experimental conservative transport data. The second approach is based on reactive random walk particle tracking simulations in the numerically determined flow field in the water phase. The third approach uses a dispersive lamella approach that accounts for the impact of flow heterogeneity on mixing in terms of effective dispersion coefficients, which are estimated from both experimental data and numerical random walk particle tracking simulations. We observe a significant increase in reactive mixing for decreasing saturation, which is caused by the stronger heterogeneity of the water phase and thus of the flow field. This is consistently observed in the experimental data and the direct numerical simulations. The dispersive lamella model, parameterized by the effective interface width, provides robust estimates of the evolution of the product mass obtained from the experimental and numerical data.

scholarly journals Influence of Grain Size Transition on Flow and Solute Transport through 3D Layered Porous Media

Lithosphere ◽  
2021 ◽  
Vol 2021 (Special 5) ◽  
Author(s):  
Zhi Dou ◽  
Xueyi Zhang ◽  
Jinguo Wang ◽  
Zhou Chen ◽  
Yunbo Wei ◽  
...  
Keyword(s):  
Grain Size ◽  
Porous Medium ◽  
Porous Media ◽  
Flow Field ◽  
Solute Transport ◽  
Transition Zone ◽  
Significant Influence ◽  
Local Flow ◽  
Layered Porous Media ◽  
Distribution Of Flow

Abstract Soils and other geologic porous media often have contrasting grain size layers associated with a grain size transition zone between layers. However, this transition zone is generally simplified to a plane of zero thickness for modeling assumption, and its influence has always been neglected in previous studies. In this study, an approach combining a deposition process and a random packing process was developed to generate 3D porous media without and with consideration of the transition zone. The direct numerical models for solving the flow and concentration fields were implemented to investigate the influence of the grain size transition on flow and solute transport. Our results showed that although the transition zone occupied 13.6% of the entire layered porous medium, it had little influence on the distribution of flow velocity at the scale of the entire layered porous medium. However, the transition zone had a significant influence on the local flow field, which was associated with the increased spatial variability of velocity and the varied distribution of flow velocity. This varied local flow field could increase the solute residence time and delay the breakthrough time for solute transport. Although using both the advection-dispersion equation (ADE) and the mobile and immobile (MIM) models to fit the breakthrough curves (BTCs) for solute transport through layered porous media resulted in trivial errors, the ADE model failed to capture the influence induced by the local flow field, especially the influence of the transition zone. In contrast, the MIM model was shown to be able to capture the influence of the transition on solute transport. It was found that the mass transfer rate α, a parameter of the MIM model, was significantly improved by the presence of the transition zone, while it decreased as the transition zone fraction increased. Our study emphasized that the transition zone can vary the local flow field at the pore scale, while it has little influence on the hydraulic properties (e.g., hydraulic conductivity) of the macroscale flow field. However, the local flow field varied by the transition zone has a significant influence on solute transport.

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

Geofluids ◽  
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.

The impact of porosity on organic matter cycling in a two-dimensional porous medium 

2021 ◽  
Author(s):  
Hanbang Zou ◽  
Pelle Ohlsson ◽  
Edith Hammer
Keyword(s):  
Porous Medium ◽  
Organic Matter ◽  
Carbon Sequestration ◽  
Soil Carbon ◽  
Pore Network ◽  
Pore Scale ◽  
Decomposition Of Organic Matter ◽  
Organic Matter Cycling ◽  
The Impact

&lt;p&gt;Carbon sequestration has been a popular research topic in recent years as the rapid elevation of carbon emission has significantly impacted our climate. Apart from carbon capture and storage in e.g. oil reservoirs, soil carbon sequestration offers a long term and safe solution for the environment and human beings. The net soil carbon budget is determined by the balance between terrestrial ecosystem sink and sources of respiration to atmospheric carbon dioxide. Carbon can be long term stored as organic matters in the soil whereas it can be released from the decomposition of organic matter. The complex pore networks in the soil are believed to be able to &quot;protect&quot; microbial-derived organic matter from decomposition. Therefore, it is important to understand how soil structure impacts organic matter cycling at the pore scale. However, there are limited experimental studies on understanding the mechanism of physical stabilization of organic matter. Hence, my project plan is to create a heterogeneous microfluidic porous microenvironment to mimic the complex soil pore network which allows us to investigate the ability of organisms to access spaces starting from an initial ecophysiological precondition to changes of spatial accessibility mediated by interactions with the microbial community.&lt;/p&gt;&lt;p&gt;Microfluidics is a powerful tool that enables studies of fundamental physics, rapid measurements and real-time visualisation in a complex spatial microstructure that can be designed and controlled. Many complex processes can now be visualized enabled by the development of microfluidics and photolithography, such as microbial dynamics in pore-scale soil systems and pore network modification mimicking different soil environments &amp;#8211; earlier considered impossible to achieve experimentally. The microfluidic channel used in this project contains a random distribution of cylindrical pillars of different sizes so as to mimic the variations found in real soil. The randomness in the design creates various spatial availability for microbes (preferential flow paths with dead-end or continuous flow) as an invasion of liquids proceeds into the pore with the lowest capillary entry pressure. In order to study the impact of different porosity in isolation of varying heterogeneity of the porous medium, different pore size chips that use the same randomly generated pore network is created. Those chips have the same location of the pillars, but the relative size of each pillar is scaled. The experiments will be carried out using sterile cultures of fluorescent bacteria, fungi and protists, synthetic communities of combinations of these, or a whole soil community inoculum. We will quantify the consumption of organic matter from the different areas via fluorescent substrates, and the bio-/necromass produced. We hypothesise that lower porosity will reduce the net decomposition of organic matter as the narrower pore throat limits the access, and that net decomposition rate at the main preferential path will be higher than inside branches&lt;/p&gt;

Pore-scale study of effects of surface roughness on the transport of interfacial reactive tracers during primary drainage process

2021 ◽  
Author(s):  
Huhao Gao ◽  
Alexandru Tatomir ◽  
Nikolaos Karadimitriou ◽  
Holger Steeb ◽  
Martin Sauter
Keyword(s):  
Surface Roughness ◽  
Porous Media ◽  
Reactive Transport ◽  
Capillary Condensation ◽  
Field Method ◽  
Phase Field Method ◽  
Pore Scale ◽  
Water Films ◽  
Mobile Mass ◽  
The Impact

&lt;p&gt;Porous media surface roughness strongly influences the transport of solutes during drainage, due to the formation of thick water films (capillary condensation) on the porous media surface. In the case of interfacial-reacted, water-based solutes, these water films increase both the production of the solute, due to the increased number of fluid-fluid interfaces, and the loss of the solute by the retention in the stagnant water films. The retention of the solute in flowing water is described by a mobile mass retention term. This study applies the pore-scale direct simulation with the phase-field method based continuous solute transport (PFM-CST) model on the kinetic interfacial sensitive (KIS) tracer reactive transport during primary drainage in a 2D slit with a wall with variable fractal geometries. The capillary-associated moving interface is found to be larger for rough surfaces than smoother ones. The results confirm that the impact of roughness regarding the film-associated interfacial area can be partly, or totally masked, in a drained slit. It is found that the mobile mass retention term is increased with larger volumes of capillary condensed water films. To conclude, it is also found that the surface roughness factor has a non-monotonic relationship with the overall production rate of solute mass in moving water.&lt;/p&gt;

scholarly journals Confinement and activity regulate bacterial motion in porous media

Soft Matter ◽  
2019 ◽  
Vol 15 (48) ◽  
pp. 9920-9930 ◽  
Author(s):  
Tapomoy Bhattacharjee ◽  
Sujit S. Datta
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Bacterial Motility ◽  
Cellular Activity ◽  
Direct Visualization ◽  
Pore Scale ◽  
Active Matter

Direct visualization reveals how bacterial motility in a porous medium is regulated by pore-scale confinement and cellular activity, yielding fundamental insights into the behavior of active matter under confinement.

scholarly journals Wettability control on multiphase flow in patterned microfluidics

2016 ◽  
Vol 113 (37) ◽  
pp. 10251-10256 ◽  
Author(s):  
Benzhong Zhao ◽  
Christopher W. MacMinn ◽  
Ruben Juanes
Keyword(s):  
Porous Media ◽  
Multiphase Flow ◽  
Contact Angles ◽  
Flow In Porous Media ◽  
Wetting Transition ◽  
Pore Scale ◽  
Displacement Efficiency ◽  
Pore Filling ◽  
Wide Range ◽  
The Impact

Multiphase flow in porous media is important in many natural and industrial processes, including geologic CO2 sequestration, enhanced oil recovery, and water infiltration into soil. Although it is well known that the wetting properties of porous media can vary drastically depending on the type of media and pore fluids, the effect of wettability on multiphase flow continues to challenge our microscopic and macroscopic descriptions. Here, we study the impact of wettability on viscously unfavorable fluid–fluid displacement in disordered media by means of high-resolution imaging in microfluidic flow cells patterned with vertical posts. By systematically varying the wettability of the flow cell over a wide range of contact angles, we find that increasing the substrate’s affinity to the invading fluid results in more efficient displacement of the defending fluid up to a critical wetting transition, beyond which the trend is reversed. We identify the pore-scale mechanisms—cooperative pore filling (increasing displacement efficiency) and corner flow (decreasing displacement efficiency)—responsible for this macroscale behavior, and show that they rely on the inherent 3D nature of interfacial flows, even in quasi-2D media. Our results demonstrate the powerful control of wettability on multiphase flow in porous media, and show that the markedly different invasion protocols that emerge—from pore filling to postbridging—are determined by physical mechanisms that are missing from current pore-scale and continuum-scale descriptions.

scholarly journals A homogenised model for flow, transport and sorption in a heterogeneous porous medium

2021 ◽  
Vol 932 ◽  
Author(s):  
L.C. Auton ◽  
S. Pramanik ◽  
M.P. Dalwadi ◽  
C.W. MacMinn ◽  
I.M. Griffiths
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Multiple Scales ◽  
Effective Diffusivity ◽  
Rectangular Lattice ◽  
Mathematical Framework ◽  
Anisotropic Flow ◽  
Flow And Transport ◽  
Soft Porous Media ◽  
The Impact

A major challenge in flow through porous media is to better understand the link between microstructure and macroscale flow and transport. For idealised microstructures, the mathematical framework of homogenisation theory can be used for this purpose. Here, we consider a two-dimensional microstructure comprising an array of obstacles of smooth but arbitrary shape, the size and spacing of which can vary along the length of the porous medium. We use homogenisation via the method of multiple scales to systematically upscale a novel problem involving cells of varying area to obtain effective continuum equations for macroscale flow and transport. The equations are characterised by the local porosity, a local anisotropic flow permeability, an effective local anisotropic solute diffusivity and an effective local adsorption rate. These macroscale properties depend non-trivially on the two degrees of microstructural geometric freedom in our problem: obstacle size and obstacle spacing. We exploit this dependence to construct and compare scenarios where the same porosity profile results from different combinations of obstacle size and spacing. We focus on a simple example geometry comprising circular obstacles on a rectangular lattice, for which we numerically determine the macroscale permeability and effective diffusivity. We investigate scenarios where the porosity is spatially uniform but the permeability and diffusivity are not. Our results may be useful in the design of filters or for studying the impact of deformation on transport in soft porous media.

Comparison of Competing Invasion-Percolation Models for Simulation of Multiphase Flow in Porous Media 

2021 ◽  
Author(s):  
Ishani Banerjee ◽  
Anneli Guthke ◽  
Kevin Mumford ◽  
Wolfgang Nowak
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Gas Flow ◽  
Flow Regimes ◽  
Flow In Porous Media ◽  
Invasion Percolation ◽  
Pore Scale ◽  
Discontinuous Flow ◽  
Model Version ◽  
Water Saturated

&lt;p&gt;Invasion-Percolation (IP) models are used to simulate multiphase flow in porous media across various scales (from pore-scale IP to Macro-IP). Numerous variations of IP models have emerged; here we are interested in simulating gas flow in a water-saturated porous medium. Gas flow in porous media occurs either as a continuous or as a discontinuous flow, depending on the rate of flow and the nature of the porous medium. A particular IP model version may be well suited for predictions in a specific gas flow regime, but not applicable to other regimes. Our research aims to compare various macro-scale versions of IP models existing in the literature and rank their performance in relevant gas flow regimes.&lt;/p&gt;&lt;p&gt;We test the performance of Macro-IP models on a range of gas-injection rates in water-saturated sand experiments, including both continuous and discontinuous flow regimes. The experimental data is obtained as a time series of images using the light transmission technique. To represent pore-scale heterogeneities of sand, we let each model version run on several random realizations of the initial entry pressure field. As a metric for ranking the models, we introduce a diffused version of the so-called Jaccard index (adapted from image analysis and object recognition). We average this metric over time and over all realizations per model version to evaluate each model&amp;#8217;s overall performance. This metric may also be used to calibrate model parameters such as gas saturation.&amp;#160;&lt;/p&gt;&lt;p&gt;Our proposed approach evaluates the performance of competing IP model versions in different gas-flow regimes objectively and quantitatively, and thus provides guidance on their applicability under specific conditions. Moreover, our comparison method is not limited to gas-water phase systems in porous media but generalizes to any modelling situation accompanied by spatially and temporally highly resolved data.&lt;/p&gt;

Impact of chaotic mixing on reactive transport: experiment in porous media at high Pe and Da

2021 ◽  
Author(s):  
Hugo Sanquer ◽  
Joris Heyman ◽  
Tanguy Le Borgne ◽  
Khalil Hanna
Keyword(s):  
Porous Media ◽  
Reactive Transport ◽  
3D Imaging ◽  
Fluid Phase ◽  
Reaction Rates ◽  
Transport Processes ◽  
Chaotic Mixing ◽  
Pore Scale ◽  
Chemical Gradients ◽  
The Impact

&lt;p&gt;Solute transport in porous media plays a key role in a range of chemical and biological processes, including contaminant degradation, precipitation, dissolution and microbiological dynamics. Increasing evidences have shown that the conventional complete mixing assumption at the pore scale can lead to a strong overestimation of reaction rates. Recent 3D imaging experiments of mixing in porous media suggest that these pore scale chemical gradients may be sustained by chaotic mixing dynamics. However, the consequences of such chaotic mixing on reactive processes are unknown.&lt;/p&gt;&lt;p&gt;In this work, we use reactive transport experiments coupled to 3D imaging to investigate the impact of micro-scale chaotic flows on mixing-limited reactions in the fluid phase. &amp;#160;We use optical index matching and laser-induced fluorescence to characterize the pore scale distribution of reactive product concentration for a range of Peclet and Damkh&amp;#246;ler numbers. We use these measurements to develop a reactive lamellar theory that quantifies the impact of pore scale chemical gradients induced by chaotic mixing on effective reaction rates. These results provide new perspectives for upscaling reactive transport processes in porous media.&lt;/p&gt;

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