Analytical Coupling of Scales — Transport of Water and Solutes in Porous Media (original) (raw)
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Low scale separation induces modification of apparent solute transport regime in porous media
Mechanics Research Communications
First order asymptotic homogenization allows to determine the effective behaviour of a porous medium by starting from the pore scale description, when there is a large separation between the pore scale and the macroscopic scale. When the scale ratio is âȂIJsmall but not too small,âȂİ additional terms need to be taken into account, which can be obtained by exploiting higher order equations in the asymptotic homogenization procedure. The aim of the present study is to derive second order models to describe solute transport in a macroscopically homogeneous porous medium at low scale separation. The three following macroscopic transport regimes are successively considered: pure diffusion with fluid at rest, predominant diffusion with fluid in motion and advection-diffusion. The results show that while the transport regime remains of diffusive type when the fluid is at rest, low scale separation induces modification of apparent transport regime when fluid is in motion. Indeed, predominant diffusion and advection-diffusion lead to the apparent regimes of advection-diffusion and of dispersion, respectively.
Pore-volume alteration measurements to evaluate scale formation during solid–fluid interactions
Mineralogical Magazine, 2014
Pore-volume changes in porous media during waterÀrock interaction can be studied using hydrological tracers. The tracers used here were amino G acid, napthionic acid and fluorescein at pH 3 and 6.5 in contact with basaltic glass, quartz and rhyolite. The experimental setup mimicked that of a hydrological tracer test where a fixed volume of tracer was injected into a flow-through column and the breakthrough curve monitored. The measured breakthrough tracer curves were compared to theoretical 1-D reactive transport simulations calculated using the PHREEQC program. In some cases the tracers were observed to behave ideally, whereas in others they clearly reacted with the solid surfaces. This implies that some common hydrological tracers used in groundwater hydrology may not be suitable under all conditions as they may react with the surrounding rocks in the groundwater system.
Scale Dependent Solute Dispersion in Porous Media
2003
Scale dependency of solute dispersion in porous media is one of the major striking issues in simulating larger scale aquifers. There are numerous studies dedicated to development of the simulation models that represent heterogeneous real world aquifers. In this paper we investigated the ability of a stochastic solute transport model (SSTM) of capturing the scale dependency. Initially, flow profiles were visually compared for different t10w lengths. Then a stochastic inverse method was used to estimate the corresponding dispersion coefficient (D) for each parameter combination of the stochastic model. The results reveal that SSTM is capable of simulating tlie scale effect of solute dispersion, and to some extent, they agree with the past literature. Dispersivity increases with the smaller t10w lengths, and the rate of increase decreases and tends to reach an asymptotic value for larger scales for similar parameters ofSSTM.
UPSCALING TRANSPORTOF ADSORBING SOLUTES IN POROUS MEDIA
Journal of Porous Media, 2010
Adsorption of solutes in porous media is commonly modeled as an equilibrium process. Indeed, one may safely assume that within the pore space, the concentration of adsorbed solute at a point on the grain surface is algebraically related to the concentration in the fluid next to the grain. The same, however, cannot be said about average concentrations. In fact, during solute transport, concentration gradients develop within the pore space, and these could potentially give rise to a scale-dependent adsorption process. The main objective of this research is to develop relationship between porescale adsorption coefficient and corresponding upscaled adsorption parameters. Two approaches are used: Theoretical averaging and numerical upscaling. In the averaging approach, equilibrium adsorption is assumed at the pore-scale and solute transport equations are averaged over REV. This leads to explicit expressions for macro-scale adsorption rate constants as a function of micro-scale parameters. In the numerical approach, first we simulate solute transport within a single tube undergoing equilibrium adsorption at the pore wall, and then flux averaged concentration breakthrough curves are obtained. These are used to determine the upscaled adsorption rate constants as functions of pore-scale hydraulic and adsorption parameters. Results of the two approaches agree very well.
Pore-scale modelling of transport phenomena in homogeneous porous media
1999
I wish to express my sincere gratitude to the people and organisations who inspired and assisted the development of this thesis. Many thanks to Prof Prieur du Plessis, my promoter, for his guidance, collaborative research approach and the interest he took in my work. He was supportive in many aspects concerning my dissertation and his motivation, friendly attitude and availability to discuss sections of this study at literally any time meant a lot to me. I, therefore, greatly acknowledge Prieur's judgement and leadership in the project. I would like to thank Prof J. LeGrand for inviting me to the Laboratoire de Genie de Procedes, IUT in Saint-Nazaire. He provided the opportunity to meet scientists in the same field and participate in laboratory experiments. I am also grateful to Dr Agnes Montillet for the numerous fruitful discussions we had during my visit to the IUT. She was very helpful in providing data obtained from her experiments and she generously shared her knowledge. Much of the credit for this dissertation must go to my wife, Lyndsey, who offered encouragement and support over the years. I would also like to thank Lyndsey for her perfectionistic approach in producing all of the figures in this dissertation. Finally, I would like to thank the FRD, the University of Stellenbosch and the Harry Crossley Fund for providing financial assistance. This enabled me to do three years full time research.
Raoof, A. and S.M. Hassanizadeh, Upscaling Transport of Adsorbing Solutes in Porous Media
Adsorption of solutes in porous media is commonly modeled as an equilibrium process. Indeed, one may safely assume that within the pore space, the concentration of adsorbed solute at a point on the grain surface is algebraically related to the concentration in the fluid next to the grain. The same, however, cannot be said about average concentrations. In fact, during solute transport, concentration gradients develop within the pore space, and these could potentially give rise to a scale-dependent adsorption process. The main objective of this research is to develop relationship between porescale adsorption coefficient and corresponding upscaled adsorption parameters. Two approaches are used: Theoretical averaging and numerical upscaling. In the averaging approach, equilibrium adsorption is assumed at the pore-scale and solute transport equations are averaged over REV. This leads to explicit expressions for macro-scale adsorption rate constants as a function of micro-scale parameters. In the numerical approach, first we simulate solute transport within a single tube undergoing equilibrium adsorption at the pore wall, and then flux averaged concentration breakthrough curves are obtained. These are used to determine the upscaled adsorption rate constants as functions of pore-scale hydraulic and adsorption parameters. Results of the two approaches agree very well.
Transport in Porous Media, 2010
A theory is developed providing a rational framework for spatial scaledependent fluid's flow and heat transfer, and mass of a component migrating with it through porous media. Introducing the assumption of a non-Brownian type motion and referring to asymptotic expansion in powers of a small defined parameter, we develop a novel approach associated with macroscopic balance equations obtained by averaging over a Representative Elementary Volume (REV). We prove that these equations can be decomposed into a primary part that refers to the REV length scale and a secondary part valid at a length scale smaller than that of the corresponding REV length. Further to our previous development, we obtain two general forms of the primary and secondary macroscopic balance equations. One is based on the assumption that the advective flux of the extensive quantity is dominant over that of the dispersive flux, whereas the other disregards this assumption. Moreover, we also introduce the primary and secondary macroscopic forms for the fluid heattransfer equation. Considering a Newtonian fluid, the resulting primary Navier-Stokes equation can vary from a nonlinear wave equation to a drag-dominant equation at the fluid-solid interface (Darcy's law). The secondary momentum balance equation describes a wave equation governing the concurrent propagation of the intensive momentum and the dispersive momentum flux, deviating from their corresponding average terms. The primary macroscopic fluid heat-transfer equation accounts for advective and dispersive heat fluxes and the secondary macroscopic heat-transfer equation involves the simultaneous advection of heat
Upscaling Transport of Adsorbing Solutes in Porous Media: Pore-Network Modeling
The main objec ve of this research was to enhance our understanding of and obtain quanta ve rela on between Darcy-scale adsorp on parameters and pore-scale fl ow and adsorp on parameters, using a three-dimensional mul direc onal pore-network model. This helps to scale up from a simplifi ed but reasonable representa on of microscopic physics to the scale of interest in prac cal applica ons. This upscaling is performed in two stages: (i) from local scale to the eff ec ve pore scale and (ii) from eff ec ve pore scale to the scale of a core. The fi rst stage of this upscaling from local scale to eff ec ve pore scale has been reported in an earlier manuscript. There, we found rela onships between local-scale parameters (such as equilibrium adsorp on coeffi cient, k d , and Peclet number, Pe) and eff ec ve parameters (such as a achment coeffi cient, k a , and detachment coeffi cient, k det). Here, we perform upscaling by means of a three-dimensional mul direc onal network model, which is composed of a large number of interconnected pore bodies (represented by spheres) and pore throats (represented by tubes). Upscaled transport parameters are obtained by fi ng the solu on of classical advec on –dispersion equa on with adsorp on to the average concentra on breakthrough curves at the outlet of the pore network. This procedure has resulted in rela onships for upscaled adsorp on parameters in terms of the microscale adsorp on coeffi cient and fl ow velocity. Abbrevia ons: LB, La ce –Boltzmann Transport of reac ve and adsorp ve solutes in soils and aquifers plays an important role in a variety of fi elds, including study of leaching of agrochemicals from soil surface to groundwater, uptake of soil nutrients by plant roots, and remediation of contaminated soils and aquifers.
Journal of Rock Mechanics and Geotechnical Engineering, 2016
In this paper, the behavior of breakthrough curves (BTCs) for reactive solute transport through stratified porous media is investigated. A physical laboratory model for layered porous media was constructed, in which thin layer of gravel was sandwiched in between two thick layers of natural soil. Gravel layer and natural soil layers were hydraulically connected as single porous continuum. A constant source of tracer was connected through gravel layer and elucidated at different sampling points in the direction of flow. Flexible multiprocess non-equilibrium (MPNE) transport equation with scale-dependent dispersivity function was used to simulate experimental BTCs of reactive solute transport through layered porous media. The values of equilibrium sorption coefficient and other input parameters were obtained experimentally. The simulation of BTC was performed using MPNE model with scale-dependent dispersivity. The simulation of different scale-dependent dispersivities was then compared and it was found that for field scale of estimation of dispersivity, asymptotic and exponential dispersivity functions performed better. In continuation to the comparison of simulated BTCs obtained using different models, spatial moment analysis of each aforesaid scale-dependent dispersivity model was also done. Spatial moment analysis provides the information related to mean solute mass, rate of mass travel, and mean plume dispersion. Linear and constant dispersivities showed higher variance as compared to asymptotic and exponential dispersion functions. This supports the field applicability of asymptotic and exponential dispersivity functions. The BTCs were also found to elucidate a nonzero concentration with time, which was clearly affected by physical non-equilibrium. In natural condition, such information is required in effective aquifer remediation process.
Evaluation of hydrodynamic scaling in porous media using finger dimensions
Water Resources Research, 1998
The use of dimensionless scaling is ubiquitous to hydrodynamic analysis, providing a powerful method of extending limited experimetnal results and generalizing theories. Miller and Miller [1956] contributed a scaling framework for immiscible fluid flow through porous media that relied on consistency of the contact angle between systems to be compared. It is common to assume that the effective contact angle will be zero in clean sand material where water is the wetting liquid. The well-documented unstable wetting process of fingered flow is used here as a diagnostic tool for the scaling relationships for infiltration into sandy media. Through comparison of finger cross sections produced using three liquids as well as various concentrations of anionic surfactant, it is shown that the zero contact angle assumption is very poor even for laboratory cleaned silica sand: Experimental results demonstrate effective contact angles approaching 60Њ. Scaling was effective for a given liquid between sands of differing particle size. These results suggest that caution should be exercised when applying scaling theory to initial wetting of porous media by liquids of differing gas-liquid interfacial tensions.