Investigation of local mixing and its influence on core scale mixing (dispersion)

textLocal displacement efficiency in miscible floods is significantly affected by mixing taking place in the medium. Laboratory experiments usually measure flow-averaged ("cup mixed") effluent concentration histories. The core-scale averaged mixing, termed as dispersion, is used to quantify mixing in flow through porous media. The dispersion coefficient has the contributions of convective spreading and diffusion lumped together. Despite decades of research there remain questions about the nature and origin of dispersion. The main objective of this research is to understand the basic physics of solute transport and mixing at the pore scale and to use this information to explain core-scale mixing behavior (dispersion). We use two different approaches to study the interaction between convective spreading and diffusion for a range of flow conditions and the influence of their interaction on dispersion. In the first approach, we perform a direct numerical simulation of pore scale solute transport (by solving the Navier Stokes and convection diffusion equations) in a surrogate pore space. The second approach tracks movement of solute particles through a network model that is physically representative of real granular material. The first approach is useful in direct visualization of mixing in pore space whereas the second approach helps quantify the effect of pore scale process on core scale mixing (dispersion). Mixing in porous media results from interaction between convective spreading and molecular diffusion. The converging-diverging flow around sand grains causes the solute front to stretch, split and rejoin. In this process the area of contact between regions of high and low solute concentrations increases by an order of magnitude. Diffusion tends to reduce local variations in solute concentration inside the pore body. If the fluid velocity is small, diffusion is able to homogenize the solute concentration inside each pore. On the other hand, in the limit of very large fluid velocity (or no diffusion) local mixing because of diffusion tends to zero and dispersion is entirely caused by convective spreading. Flow reversal provides insights about mixing mechanisms in flow through porous media. For purely convective transport, upon flow reversal solute particles retrace their path to the inlet. Convective spreading cancels and echo dispersion is zero. Diffusion, even though small in magnitude, causes local mixing and makes dispersion in porous media irreversible. Echo dispersion in porous media is far greater than diffusion and as large as forward (transmission) dispersion. In the second approach, we study dispersion in porous media by tracking movement of a swarm of solute particles through a physically representative network model. We developed deterministic rules to trace paths of solute particles through the network. These rules yield flow streamlines through the network comparable to those obtained from a full solution of Stokes' equation. In the absence of diffusion the paths of all solute particles are completely determined and reversible. We track the movement of solute particles on these paths to investigate dispersion caused by purely convective spreading at the pore scale. Then we superimpose diffusion and study its influence on dispersion. In this way we obtain for the first time an unequivocal assessment of the roles of convective spreading and diffusion in hydrodynamic dispersion through porous media. Alternative particle tracking algorithms that use a probabilistic choice of an out-flowing throat at a pore fail to quantify convective spreading accurately. For Fickian behavior of dispersion it is essential that all solute particles encounter a wide range of independent (and identically distributed) velocities. If plug flow occurs in the pore throats a solute particle can encounter a wide range of independent velocities because of velocity differences in pore throats and randomness of pore structure. Plug flow leads to a purely convective spreading that is asymptotically Fickian. Diffusion superimposed on plug flow acts independently of convective spreading causing dispersion to be simply the sum of convective spreading and diffusion. In plug flow hydrodynamic dispersion varies linearly with the pore-scale Peclet number. For a more realistic parabolic velocity profile in pore throats particles near the solid surface of the medium do not have independent velocities. Now purely convective spreading is non-Fickian. When diffusion is non-zero, solute particles can move away from the low velocity region near the solid surface into the main flow stream and subsequently dispersion again becomes asymptotically Fickian. Now dispersion is the result of an interaction between convection and diffusion and it results in a weak nonlinear dependence of dispersion on Peclet number. The dispersion coefficients predicted by particle tracking through the network are in excellent agreement with the literature experimental data. We conclude that the essential phenomena giving rise to hydrodynamic dispersion observed in porous media are (i) stream splitting of the solute front at every pore, thus causing independence of particle velocities purely by convection, (ii) a velocity gradient within throats and (iii) diffusion. Taylor's dispersion in a capillary tube accounts for only the second and third of these phenomena, yielding a quadratic dependence of dispersion on Peclet number. Plug flow in the bonds of a physically representative network accounts for the only the first and third phenomena, resulting in a linear dependence of dispersion upon Peclet number.Petroleum and Geosystems Engineerin

Biofilms in porous media: development of macroscopic transport equations via volume averaging with closure for local mass equilibrium conditions

In this work, we upscale a pore-scale description of mass transport in a porous medium containing biofilm to develop the relevant Darcy-scale equations. We begin with the pore-scale descriptions of mass transport, interphase mass transfer, and biologically-mediated reactions; these processes are then upscaled using the method of volume averaging to obtain the macroscale mass balance equations. We focus on the case of local mass equilibrium conditions where the averaged concentrations in the fluid and biological phases can be assumed to be proportional and for which a one-equation macroscopic model may be developed. We predict the effective dispersion tensor by a closure scheme that is solved for the cases of both simple and complex unit cells. The domain of validity of the approach is clearly identified, both theoretically and numerically, and unitless groupings indicating the domain of validity are reported

Activity of comets: Gas Transport in the Near-Surface Porous Layers of a Cometary Nucleus

The gas transport through non-volatile random porous media is investigated numerically. We extend our previous research of the transport of molecules inside the uppermost layer of a cometary surface (Skorov and Rickmann, 1995; Skorov et al. 2001). We assess the validity of the simplified capillary model and its assumptions to simulate the gas flux trough the porous dust mantle as it has been applied in cometary physics. A new microphysical computational model for molecular transport in random porous media formed by packed spheres is presented. The main transport characteristics such as the mean free path distribution and the permeability are calculated for a wide range of model parameters and compared with those obtained by more idealized models. The focus in this comparison is on limitations inherent in the capillary model. Finally a practical way is suggested to adjust the algebraic Clausing formula taking into consideration the nonlinear dependence of permeability on layer porosity. The retrieved dependence allows us to accurately calculate the permeability of layers whose thickness and porosity vary in the range of values expected for the near-surface regions of a cometary nucleus.Comment: 25 pages, 9 figure

Challenges in imaging and predictive modeling of rhizosphere processes

Background Plant-soil interaction is central to human food production and ecosystem function. Thus, it is essential to not only understand, but also to develop predictive mathematical models which can be used to assess how climate and soil management practices will affect these interactions. Scope In this paper we review the current developments in structural and chemical imaging of rhizosphere processes within the context of multiscale mathematical image based modeling. We outline areas that need more research and areas which would benefit from more detailed understanding. Conclusions We conclude that the combination of structural and chemical imaging with modeling is an incredibly powerful tool which is fundamental for understanding how plant roots interact with soil. We emphasize the need for more researchers to be attracted to this area that is so fertile for future discoveries. Finally, model building must go hand in hand with experiments. In particular, there is a real need to integrate rhizosphere structural and chemical imaging with modeling for better understanding of the rhizosphere processes leading to models which explicitly account for pore scale processes

Influence of solid phase thermal conductivity on species separation rate in packed thermogravitational columns: A direct numerical simulation model

n this work, a direct numerical simulation model has been proposed to study the influence of porous matrix thermal properties on the separation rate in a model of packed thermogravitational column saturated by a binary mixture. The coupled flow, heat and mass dimensionless equations and boundary conditions have been derived in pore-scale and then solved over a vertical column containing fluid and solid phases. The results show that the separation rate is changed significantly by the conductivity ratio of the solid/fluid phases. The classical maximum separation at optimal Rayleigh number increases by decreasing the solid thermal conductivity. We obtained that the influence of the solid thermal conductivity for small Rayleigh number is not considerable but for intermediate Rayleigh number the separation rate initially decreases with increasing the thermal conductivity ratio and then reaches an asymptote. As the Rayleigh number increases, convection dominates and the effect of thermal conductivity ratio on separation rate becomes completely inversed

Investigation of suitability of the method of volume averaging for the study of heat transfer in superconducting accelerator magnet cooled by superfluid helium.

In the field of applied superconductivity, there is a growing need to better understand heat transfers in superconducting accelerator magnets. Depending on the engineering point of view looked at, either 0-D, 1-D, 2D or 3D modeling may be needed. Because of the size of these magnets, alone or coupled together, it is yet, impossible to study this numerically for computational reasons alone without simplification in the description of the geometry and the physics. The main idea of this study is to consider the interior of a superconducting accelerator magnet as a porous medium and to apply methods used in the field of por-ous media physics to obtain the equations that model heat transfers of a superconducting accelerator magnet in different configurations (steady-state, beam losses, quench, etc.) with minimal compromises to the physics and geometry. Since the interior of a superconducting magnet is made of coils, collars and yoke filled with liquid helium, creating channels that interconnect the helium inside the magnet, an upscaling method provides models that describe heat transfer at the magnet scale and are suitable for numerical studies. This paper presents concisely the method and an example of application for super-conducting accelerator magnet cooled by superfluid helium in the steady-state regime in considering the thermal point of view

Nuclear magnetic resonance cryoporometry

Nuclear Magnetic Resonance (NMR) cryoporometry is a technique for non-destructively determining pore size distributions in porous media through the observation of the depressed melting point of a confined liquid. It is suitable for measuring pore diameters in the range 2 nm-1 mu m, depending on the absorbate. Whilst NMR cryoporometry is a perturbative measurement, the results are independent of spin interactions at the pore surface and so can offer direct measurements of pore volume as a function of pore diameter. Pore size distributions obtained with NMR cryoporometry have been shown to compare favourably with those from other methods such as gas adsorption, DSC thermoporosimetry, and SANS. The applications of NMR cryoporometry include studies of silica gels, bones, cements, rocks and many other porous materials. It is also possible to adapt the basic experiment to provide structural resolution in spatially-dependent pore size distributions, or behavioural information about the confined liquid