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>

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

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>

Chemotaxis under flow disorder shapes microbial dispersion in porous media 

2021 ◽  
Author(s):  
Pietro de Anna ◽  
Amir A. Pahlavan ◽  
Yutaka Yawata ◽  
Roman Stocker ◽  
Ruben Juanes
Keyword(s):  
Porous Media ◽  
Dispersion Coefficient ◽  
Pore Space ◽  
Low Flow ◽  
Pore Scale ◽  
Porous Rocks ◽  
Chemical Gradients ◽  
Deep Earth ◽  
Bacterium Bacillus Subtilis ◽  
Bacterium Bacillus

<div> <div> <div> <p>Natural soils are host to a high density and diversity of microorganisms, and even deep-earth porous rocks provide a habitat for active microbial communities. In these environ- ments, microbial transport by disordered flows is relevant for a broad range of natural and engineered processes, from biochemical cycling to remineralization and bioremediation. Yet, how bacteria are transported and distributed in the sub- surface as a result of the disordered flow and the associ- ated chemical gradients characteristic of porous media has remained poorly understood, in part because studies have so far focused on steady, macroscale chemical gradients. Here, we use a microfluidic model system that captures flow disorder and chemical gradients at the pore scale to quantify the transport and dispersion of the soil-dwelling bacterium Bacillus subtilis in porous media. We observe that chemotaxis strongly modulates the persistence of bacteria in low-flow regions of the pore space, resulting in a 100% increase in their dispersion coefficient. This effect stems directly from the strong pore-scale gradients created by flow disorder and demonstrates that the microscale interplay between bacterial behaviour and pore-scale disorder can impact the macroscale dynamics of biota in the subsurface.</p> </div> </div> </div>

Pore-Scale Simulations of Residual Trapping in Homogeneous and Heterogeneous Porous Media

2020 ◽  
Author(s):  
R.A.E. Nhunduru ◽  
K.L. Wlodarczyk ◽  
A. Jahanbakhsh ◽  
O. Shahrokhi ◽  
S. Garcia ◽  
...  
Keyword(s):  
Porous Media ◽  
Heterogeneous Porous Media ◽  
Pore Scale ◽  
Residual Trapping

Fundamentals of Transport Equation Formulation for Two-Phase Flow in Homogeneous and Heterogeneous Porous Media

1999 ◽  
Author(s):  
Michel Quintard ◽  
Stephen Whitaker
Keyword(s):  
Porous Media ◽  
Large Scale ◽  
Practical Importance ◽  
Volume Averaging ◽  
Heterogeneous Porous Media ◽  
Homogenization Theory ◽  
Length Scale ◽  
Two Phase ◽  
The Hierarchical Structure ◽  
Method Of Volume Averaging

Most porous media of practical importance are hierarchical in nature; that is, they are characterized by more than one length-scale. When these length-scales are disparate, the hierarchical structure can be analyzed by the method of volume averaging (Anderson and Jackson, 1967; Marie, 1967; Slattery, 1967; Whitaker, 1967). In this approach, macroscopic quantities at a given length-scale are defined in terms of a boundary value problem that describes the phenomena at a smaller length-scale, and information is filtered from one scale to another by a series of volume and area integrals. Other methods, such as ensemble averaging (Matheron, 1965; Dagan, 1989) or homogenization theory (Bensoussan et al, 1978; Sanchez-Palencia, 1980), have been used to study hierarchical systems, and developments specific to the problems under consideration in this chapter can be found in Bourgeat (1984), Auriault (1987), Amaziane and Bourgeat (1988), and Sáez et al. (1989). The transformation from the Darcy scale to the large scale is a recurrent problem in reservoir and aquifer engineering. A detailed description of reservoir properties is available through geostatistical analysis (Journel, 1996) on a fine grid with a length-scale much smaller than the scale of the blocks in the reservoir simulator. “Effective” or “pseudo” properties are assigned to the coarse grid blocks, while the forms of the large-scale equations are required to be the same as those used at the Darcy scale (Coats et al., 1967; Hearn, 1971; Jacks et al., 1972; Kyte and Berry, 1975; Dake, 1978; Killough and Foster, 1979; Yokoyama and Lake, 1981; Kortekaas, 1983; Thomas, 1983; Kossack et al., 1990). A detailed discussion of the comparison between the several approaches is beyond the scope of this chapter; however, one can read Bourgeat et al. (1988) for an introductory comparison between the method of volume averaging and the homogenization theory, and Ahmadi et al. (1993) for a discussion of the various classes of pseudofunction theories.

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.

Capillary-Dominated Fluid Displacement in Porous Media

2019 ◽  
Vol 51 (1) ◽  
pp. 429-449 ◽  
Author(s):  
Kamaljit Singh ◽  
Michael Jung ◽  
Martin Brinkmann ◽  
Ralf Seemann
Keyword(s):  
Porous Media ◽  
Pore Space ◽  
Contact Angles ◽  
Pore Scale ◽  
Fluid Displacement ◽  
Invasion Pattern ◽  
Theoretical Considerations ◽  
Displacement Processes ◽  
Synchrotron Microtomography ◽  
Relevant Material

Liquid invasion into a porous medium is a phenomenon of great importance in both nature and technology. Despite its enormous importance, there is a surprisingly sparse understanding of the processes occurring on the scale of individual pores and of how these processes determine the global invasion pattern. In particular, the exact influence of the wettability remains unclear besides the limiting cases of very small or very large contact angles of the invading fluid. Most quantitative pore-scale experiments and theoretical considerations have been conducted in effectively two-dimensional (2D) micromodels and Hele–Shaw geometries. Although these pioneering works helped to unravel some of the physical aspects of the displacement processes, the relevance of 2D models has not always been appreciated for natural porous media. With the availability of X-ray microtomography, 3D imaging has become a standard for exploring pore-scale processes in porous media. Applying advanced postprocessing routines and synchrotron microtomography, researchers can image even slow flow processes in real time and extract relevant material parameters like the contact angle from the interfaces in the pore space. These advances are expected to boost both theoretical and experimental understanding of pore-scale processes in natural porous media.

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