Effects Of Hydrodynamic Dispersion Research Articles

Effect of hydrodynamic dispersion on spherical reaction front dynamics in porous media

Effect of hydrodynamic dispersion on spherical reaction front dynamics in porous media

Numerical Investigation of the Influence of Hydrodynamic Dispersion on Solutal Natural Convection

AbstractWe investigate numerically the effect of hydrodynamic dispersion on convective dissolution of carbon dioxide in saline aquifers. Solutions of the transport equations were used to describe the dissolution process in the aquifer and provide a systematic parametric analysis of the influence of dispersion on two important measures of convective dissolution, the wavenumber, and dissolution flux. The results suggest that dispersion decreases the dissolution rate and reduces the finger wavenumber. Based on the simulated results, new empirical scaling laws that predict the dissolution rate and wavenumber were developed. The application of the new laws to two storage sites shows that the currently available predictions overestimate the dissolution rates by ∼30%. We have identified some discrepancies between published scaling laws that were obtained for the dissolution rate. While most numerical studies identify a linear scaling, experimental investigations often suggest a sublinear behavior. Our findings resolve the controversy by suggesting that dispersion, which was not considered in these past numerical studies, is the reason for the apparent sublinear scaling.

Modelling challenges of volume-averaged combustion in inert porous media

In porous burners, the flame thickness can be smaller than the pore size, resulting in sharp and locally-anchored flame fronts. The presence of such steep gradients at the pore level is a major hurdle for the derivation of volume-averaged models, particularly for the highly non-linear reaction rates. With the intent to address the difficulties associated with volume-averaging for porous media combustion, this work makes use of 3D Pore-Level Direct Numerical Simulations including conjugate heat transfer and complex chemistry in burners of finite length. These detailed 3D simulations are compared to their 1D volume-averaged counterpart, with effective properties estimated directly on the computational domains and of identical thermo-chemical scheme. Discrepancies in terms of burning rate, profiles, and a priori analysis on the reaction rates are discussed. Various pore sizes and geometries are considered. At the pore level, it is shown that preheating, wrinkling and wall quenching are the three main factors driving the global burning rate. Importantly, hydrodynamic dispersion is shown to have an indirect role on combustion processes. From the observations of combustion at pore scale, a new closure for reaction rates based on a flamelet assumption is proposed. It accounts for flame wrinkling and eliminates the unwanted effect of hydrodynamic dispersion on burning rate.

Capillary flow of magnetic fluids with effect of hydrodynamic dispersion

A theoretical study is conducted on the influence of a shear-induced dispersion on the rheological response of a magnetic suspension. A capillary geometry is considered, in which a dilute ferrofluid flows under the action of a longitudinal applied magnetic field. The shear-induced dispersion is assumed to arise either due to particle roughness or non-sphericity (i.e., shape anisotropy). A new asymptotic solution for a suspension of rough spheres in the limit of weak flows is developed. The numerical results indicate that the dispersive flux by shear rate gradient produces a particle migration toward the center of the tube. In the case of smooth prolate spheroidal particles, the shape anisotropy may either intensify or reduce the viscous dissipation according to the non-dimensional physical parameters. For weak applied fields and weak shear rates, the relative viscosity presented a rising dependence with the aspect ratio. In contrast, at strong flows and/or large applied fields, the net result was a relative viscosity reduction in comparison with a suspension of spheres. The results provide useful insights into the rheology of ferrofluids in quadratic flows, especially to suspensions designed for biomedical applications, such as hyperthermia and magnetic drug targeting in the blood vessels.

Investigation of mineral trapping processes based on coherent front propagation theory: A dawsonite-rich natural CO2 reservoir as an example

After nearly 30 years of research on geological carbon storage, studies providing an in-depth conceptual understanding of mineral trapping processes are still scarce. Based on the reaction front propagation theory, this paper developed a set of concise mathematical models for front propagation and mineral trapping in quasi-2D-advection-diffusion-dispersion-reaction-kinetics systems in the coherent state and explored the nature of long-term mineral trapping processes and the effects of hydrodynamic dispersion on the front propagation. A criterion based on dawsonite volume fraction and front propagation distance was established to determine whether the mineral trapping rate is reaction- or transport-controlled for the coherent reaction fronts. Combined with the numerical simulation, the mantle-magmatic-sourced CO2 invasion, and long-term CO2 storage was investigated for the Hailar natural CO2 reservoir. The conclusions include: (1) The relative errors of the concise models for coherent front propagation speed and mineral trapping rate are 3-10% and 0.5-10%, respectively. (2) For the complete reaction stage, mineral trapping rates are always transport-controlled and are proportional to Darcy velocity, the difference of total dissolved carbon concentrations, and the correction coefficient for the hydrodynamic dispersion; when reaction controlling, the mineral trapping rate is proportional to front propagation distance and upstream dawsonite precipitation rate. (3) Specific results related to propagation speed, front width, hydrodynamic dispersion and mineral trapping rate caused by changing the rate constants of minerals and albite volume fraction were also obtained.

Dynamics of CO2 Density‐Driven Flow in Carbonate Aquifers: Effects of Dispersion and Geochemistry

AbstractThe dissolution of carbon‐dioxide (CO2) in deep saline aquifers is an important trapping mechanism in carbon storage. This process is triggered by unstable high‐density CO2 front, which later promotes density‐driven mixing, hydrodynamic dispersion of CO2, and favors the long‐term sequestration. In many former studies, effects of hydrodynamic dispersion and multispecies geochemical reactions have been ignored. This work elaborates the impacts of these simplifications on the dynamics of convective mixing by numerical simulations. Geochemical effects were studied by the implementation of rock‐fluid and fluid‐fluid interactions for a typical carbonate aquifer. Results show that accounting for the hydrodynamic dispersion decreases the convection onset time and increases the CO2 dissolution flux, which is more significant in larger dispersivities and Rayleigh numbers. Results indicate that carbonate geochemical reactions intense the long‐term overall efficiency of the process, while decrease the total amount of sequestered carbon in the diffusion‐dominated period. Results also reinforce the importance of realistic geochemical representation and importance of spatial and temporal dependence of the reactions pathway, subsequent to the finger development for more detailed simulation of the CO2 storage process.

Derivation of an effective dispersion model for electro-osmotic flow involving free boundaries in a thin strip

Since dispersion is one of the key parameters in solute transport, its accurate modeling is essential to avoid wrong predictions of flow and transport behavior. In this research, we derive new effective dispersion models which are valid also in evolving geometries. To this end, we consider reactive ion transport under dominate flow conditions (i.e. for high Peclet number) in a thin, potentially evolving strip. Electric charges and the induced electric potential (the zeta potential) give rise to electro-osmotic flow in addition to pressure-driven flow. At the pore-scale a mathematical model in terms of coupled partial differential equations is introduced. If applicable, the free boundary, i.e. the interface between an attached layer of immobile chemical species and the fluid is taken into account via the thickness of the layer. To this model, a formal limiting procedure is applied and the resulting upscaled models are investigated for dispersive effects. In doing so, we emphasize the cross-coupling effects of hydrodynamic dispersion (Taylor–Aris dispersion) and dispersion created by electro-osmotic flow. Moreover, we study the limit of small and large Debye length. Our results improve the understanding of fundamentals of flow and transport processes, since we can now explicitly calculate the dispersion coefficient even in evolving geometries. Further research may certainly address the situation of clogging by means of numerical studies. Finally, improved predictions of breakthrough curves as well as facilitated modeling of mixing and separation processes are possible.

Automatic Generation of Locally Refined Composite Grids for Efficient Solute Transport Modeling.

Widely used numerical models of solute transport processes in subsurface aquifers are limited to nonlocally refined rectangular, or logically rectangular, structured grids. This presents an unsuitable option to efficient numerical simulations maintaining an acceptable level of accuracy. Optimal selection of locally refined cells for efficient solute transport models is challenging to the current generation of numerical models. We present a novel and relatively simple to implement algorithm addressing these shortcomings. This method operates in four steps involving travel times simulations, a grid coarsening stage followed by a selective local grid refinement based on a cell-wise indicator, and a final postprocessing step. The refinement index is the sum of weighted logarithmic distributions of scaled forward and backward travel times. We calculate representative flow and transport properties at the two scales of the composite grid with a flow-based upscaling technique. We present two test problems to demonstrate the performances of this new gridding algorithm. We obtain the most important speedups for composite grids generated with the highest indicator thresholds. When hydrodynamic dispersion effects increase, we obtain less important speedups. An important outcome of this work is that grid design depends on nature and strength of the underlying flow and solute transport processes. Therefore, we suggest developing solute transport workflows integrating this grid generation algorithm as an integral component to build comprehensive and efficient groundwater models.

Evaluation of Natural Zeolite as a Material for Permeable Reactive Barrier for Remediation of Zinc-Contaminated Groundwater Based on Column Study

The permeable reactive barrier (PRB) filled with natural zeolite plays the role of a reactive treatment zone for remediation of contaminated groundwater. Based on column lab experiments, the volume of remediated solution, the distribution (Kd) and retardation (Rd) coefficients were evaluated, confirming successful removal and retention of zinc from contaminated groundwater. The effect of hydrodynamic dispersion on zinc capturing by zeolite in PRB was evaluated by the hydrodynamic dispersion coefficient (DL) and retarded hydrodynamic dispersion coefficient (DLR) using the Brigham method. For different assumed distances of the barrier, the simulation of one-dimensional zinc concentration profile from the point source through the barrier has been modeled by a simple analytical pulse model. The results show that the flow rate has the most significant effect on the concentration profile, peaks, and broadening of curves. The residence contact time (τ) corresponding to higher Kd and Rd as well as lower DL and DLR values outcomes the optimal range of 6.2–9.4 min. This interval corresponds to the experimental performance at the bed length of 8 and 12 cm and flow rate in the range of 6.38–9.57 PV/h. The calculated minimum thickness and longevity confirm the successful application of zeolite as a material in PRB for remediation of zinc contaminated groundwater.

Change in streamflow response in unregulated catchments in Sweden over the last century

AbstractA Fourier spectral analysis of daily discharge time series over the last century in 79 unregulated catchments in Sweden reveals a significant gradual steepening of the discharge power spectrum slope over time. Where historical meteorological observations are available (the 41 southernmost catchments), the results of our analyses indicate that local land use changes within the catchments have affected discharge power spectra to a greater extent than have changes in precipitation patterns. 1‐D distributed routing analysis based on current and historical maps and scenario modeling in the Törnestorp Catchment suggests that changes in stream network properties have led to increases in the hydraulic Péclet number ( ) and subsequent decreases in the discharge power spectrum over short periods. The analysis displays analytically how a change in stream network properties can result in changes in the power spectra, where the relative importance of the geomorphological and hydrodynamic dispersion effects determines the shape of the streamflow response. The lowering of the discharge power spectrum over short periods observed for many Swedish catchments is likely caused by increasing (a decrease in dispersion) over time, resulting in higher peak values, especially for rapid streamflow responses (i.e., over short periods), demonstrated empirically for the Törnestorp case study. The finding that the discharge power spectrum can change significantly over time highlights the need for hydrological models to account for the effect of the nonstationarity of parameters that result from temporal change caused by land use change and/or climate change that is due to anthropogenic or natural causes.

Effects of hydrodynamic dispersion on the stability of buoyancy-driven porous media convection in the presence of first order chemical reaction

Carbon dioxide (text {CO}_2) sequestration is one of several long-term solutions suggested to decrease the amount of greenhouse gases in the atmosphere. Among different methods of carbon dioxide sequestration, the dissolution of text {CO}_2 in deep saline aquifers is considered one of the most effective. A significant number of studies are currently being carried out to provide a good understanding of the physical mechanisms involved in this type of storage. The present work focuses on the hydrodynamic part of the problem: setting a model for carbon dioxide-loaded flows in an idealised two-dimensional geometry. It considers the impact of hydrodynamic dispersion in porous media on the development of convective instabilities. Particular attention is paid to the mathematical form of the dispersion tensor widely used in porous media studies, and a new type of bifurcation is investigated. We show that the analysis of bifurcations from the no-flow steady-state solution is a continuous but non-smooth problem, which is a key feature of the analysis. Although the problem is non-smooth, it is also shown that the basic behaviours of linear stability analysis are observed in its solution.

Effect of Hydrodynamic Dispersion in Denitrifying Wood-Chip Stormwater Biofilters

AbstractStormwater biofiltration systems can include a submerged layer containing a solid organic carbon substrate, such as wood chips, to promote biological denitrification. The objective of this research was to evaluate the effect of biofilter depth and dispersion on the performance of submerged wood-chip biofilters. Tracer and reactive column studies were performed on biofilters with varying depths (30, 45, and 60 cm), which were evaluated with stormwater at varying hydraulic retention times. The results from every tracer test (n=9) indicated that dispersion affected constituent transport. Shorter columns and/or higher hydraulic retention times resulted in dispersion dominated transport, which contributed to greater constituent bypass through the biofilters. Even though a wood-chip biofilter is considered a porous medium, dispersivity values in this layer were an order of magnitude larger than dispersivities of natural porous media (e.g., sand). These results provide evidence that less media volume is ...

Fully integrated modeling of surface‐subsurface solute transport and the effect of dispersion in tracer hydrograph separation

AbstractTracer hydrograph separation has been widely applied to identify streamflow components, often indicating that pre‐event water comprises a large proportion of stream water. Previous work using numerical modeling suggests that hydrodynamic mixing in the subsurface inflates the pre‐event water contribution to streamflow when derived from tracer‐based hydrograph separation. This study compares the effects of hydrodynamic dispersion, both within the subsurface and at the surface‐subsurface boundary, on the tracer‐based pre‐event water contribution to streamflow. Using a fully integrated surface‐subsurface code, we simulate two hypothetical 2‐D hillslopes with surface‐subsurface solute exchange represented by different solute transport conceptualizations (i.e., advective and dispersive conditions). Results show that when surface‐subsurface solute transport occurs via advection only, the pre‐event water contribution from the tracer‐based separation agrees well with the hydraulically determined value of pre‐event water from the numerical model, despite dispersion occurring within the subsurface. In this case, subsurface dispersion parameters have little impact on the tracer‐based separation results. However, the pre‐event water contribution from the tracer‐based separation is larger when dispersion at the surface‐subsurface boundary is considered. This work demonstrates that dispersion within the subsurface may not always be a significant factor in apparently large pre‐event water fluxes over a single rainfall event. Instead, dispersion at the surface‐subsurface boundary may increase estimates of pre‐event water contribution. This work also shows that solute transport in numerical models is highly sensitive to the representation of the surface‐subsurface interface. Hence, models of catchment‐scale solute dynamics require careful treatment and sensitivity testing of the surface‐subsurface interface to avoid misinterpretation of real‐world physical processes.

Solid Distribution in Clarifier Blanket: Numerical Modeling and Experimental Measurement

In this study, one-dimensional model for the solid distribution of flocculated suspensions in clarifier blanket is investigated by considering both up-flow velocity and hydrodynamic dispersion effects. The solution of the model equation predicts that the solid concentration will decrease remarkably along with the height of the blanket. And according to the characters of flocs, operational conditions such as up-flow flux, flocculent dosage and stirring speed affect the variation of SS. The following lab-scale experimental works with synthetic ferric-sludge flocculated with PAM confirm the numerical predictions. SS in various blanket heights under different PAM dosage was analyzed to recover the relationship between SS distribution and flocculant dosage. The results show that higher dosage of PAM will cause more dramatically SS variation due to the larger diameter of the agglomerated particles. The experiment also shows that up-flow flux has slight effect on the solid distribution inside the flocs blanket. Moreover, various stirring speeds within fitful range has no significant effect on the blanket. But too fast stirring will cause SS increasing at the top of the blanket due to the breakage of flocs.

Hydrodynamic dispersion within porous biofilms

Many microorganisms live within surface-associated consortia, termed biofilms, that can form intricate porous structures interspersed with a network of fluid channels. In such systems, transport phenomena, including flow and advection, regulate various aspects of cell behavior by controlling nutrient supply, evacuation of waste products, and permeation of antimicrobial agents. This study presents multiscale analysis of solute transport in these porous biofilms. We start our analysis with a channel-scale description of mass transport and use the method of volume averaging to derive a set of homogenized equations at the biofilm-scale in the case where the width of the channels is significantly smaller than the thickness of the biofilm. We show that solute transport may be described via two coupled partial differential equations or telegrapher's equations for the averaged concentrations. These models are particularly relevant for chemicals, such as some antimicrobial agents, that penetrate cell clusters very slowly. In most cases, especially for nutrients, solute penetration is faster, and transport can be described via an advection-dispersion equation. In this simpler case, the effective diffusion is characterized by a second-order tensor whose components depend on (1) the topology of the channels' network; (2) the solute's diffusion coefficients in the fluid and the cell clusters; (3) hydrodynamic dispersion effects; and (4) an additional dispersion term intrinsic to the two-phase configuration. Although solute transport in biofilms is commonly thought to be diffusion dominated, this analysis shows that hydrodynamic dispersion effects may significantly contribute to transport.

Transverse Hydrodynamic Dispersion Effects on Isotope Signals in Groundwater Chlorinated Solvents’ Plumes

The effects of transverse hydrodynamic dispersion on altering transformation-induced compound-specific isotope analysis (CSIA) signals within groundwater pollution plumes have been assessed with reactive transport modeling accommodating diffusion-induced isotope fractionation (DIF) and implementing different parameterizations of local transverse dispersion. The model reproduced previously published field data showing a negative carbon isotope pattern (-2 ‰) at the fringes of a nondegrading PCE plume. We extended the study to reactive transport scenarios considering vinyl chloride as a model compound and assessing, through a detailed sensitivity analysis, the coupled effects of transverse hydrodynamic dispersion (with and without DIF) and aerobic fringe degradation on the evolution of carbon and chloride isotope ratios. Transformation-induced positive isotope signals were increasingly attenuated with distance from the source and higher degradation rate. The effect of DIF on the overall isotope signal attenuation was greatest near the source and for low values of groundwater flow velocity, transverse dispersion coefficient, molecular weight, rate constant, and isotope fractionation factor, α, of the degradation reaction. Models disregarding DIF underestimate the actual α. The approximately twice larger DIF effect for chlorine than for carbon together with the low α for oxidation resulted in strong chlorine CSIA depletions for VC at the plume fringe.

The geomorphic structure of the runoff peak

Abstract. This paper develops a theoretical framework to investigate the core dependence of peak flows on the geomorphic properties of river basins. Based on the theory of transport by travel times, and simple hydrodynamic characterization of floods, this new framework invokes the linearity and invariance of the hydrologic response to provide analytical and semi-analytical expressions for peak flow, time to peak, and area contributing to the peak runoff. These results are obtained for the case of constant-intensity hyetograph using the Intensity-Duration-Frequency (IDF) curves to estimate extreme flow values as a function of the rainfall return period. Results show that, with constant-intensity hyetographs, the time-to-peak is greater than rainfall duration and usually shorter than the basin concentration time. Moreover, the critical storm duration is shown to be independent of rainfall return period as well as the area contributing to the flow peak. The same results are found when the effects of hydrodynamic dispersion are accounted for. Further, it is shown that, when the effects of hydrodynamic dispersion are negligible, the basin area contributing to the peak discharge does not depend on the channel velocity, but is a geomorphic propriety of the basin. As an example this framework is applied to three watersheds. In particular, the runoff peak, the critical rainfall durations and the time to peak are calculated for all links within a network to assess how they increase with basin area.

Relative Vulnerability of Public Supply Wells to VOC Contamination in Hydrologically Distinct Regional Aquifers

A process‐based methodology was used to compare the vulnerability of public supply wells tapping seven study areas in four hydrologically distinct regional aquifers to volatile organic compound (VOC) contamination. This method considers (1) contributing areas and travel times of groundwater flowpaths converging at individual supply wells, (2) the oxic and/or anoxic conditions encountered along each flowpath, and (3) the combined effects of hydrodynamic dispersion and contaminant‐ and oxic/anoxic‐specific biodegradation. Contributing areas and travel times were assessed using particle tracks generated from calibrated regional groundwater flow models. These results were then used to estimate VOC concentrations relative to an unspecified initial concentration (C/C0) at individual public supply wells. The results show that the vulnerability of public supply wells to VOC contamination varies widely between different regional aquifers. Low‐recharge rates, long travel times, and the predominantly oxic conditions characteristic of Basin and Range aquifers in the western United States leads to lower vulnerability to VOCs, particularly to petroleum hydrocarbons such as benzene and toluene. On the other hand, high recharge rates and short residence times characteristic of the glacial aquifers of the eastern United States leads to greater vulnerability to VOCs. These differences lead to distinct patterns of C/C0 values estimated for public supply wells characteristic of each aquifer, information that can be used by resource managers to develop monitoring plans based on relative vulnerability, to locate new public supply wells, or to make land‐use management decisions.

FLOW OF SUSPENSIONS IN TWO-DIMENSIONAL POROUS MEDIA WITH MOBILE AND IMMOBILE LIQUID ZONES

In this paper, flow of suspensions in a 2D porous medium is considered. The porous medium consist of two zones, one of them is saturated with a mobile, pure (without any solid particles) liquid and another one is saturated with an immobile liquid. The flow of suspensions occurs with colmatation and suffosion, longitudinal and across diffusion effects and in the immobile liquid zone only, diffusion transport of particles is observed. The problem is numerically solved and the influence of colmatation-suffosion, diffusion, hydrodynamic dispersion effects on filtration and mass transport characteristics is estimated. The fields of relative concentration of particles in both mobile and immobile liquid zones, porosity, permeability, and pressure gradient in the mobile liquid zone are determined for several values of diffusion, dispersion coefficients, and colmatation-suffosion intensity coefficients. Relative current, common, and total mass fluxes of solid particles through the common boundary of the mobile and immobile liquid zones are also determined. It is shown that the presence of immobile liquid zones in porous media considerably alter both the filtration and transport characteristics. Colmatation and suffosion effects in the zone with mobile liquid influence not only the filtration and transport characteristics of this zone, but also the diffusion particle transport from the zone with the mobile liquid into the zone with the immobile liquid. Results can be important in field data interpretation during water flooding in oil reservoirs, wastewater filtration, environment protection, etc.

Performance assessment of hanging funnel‐and‐gate structures designed by reverse particle tracking for capturing polluted groundwater

AbstractThe objective of this study was to evaluate the capability of partially penetrating (hanging) funnel‐and‐gate structures, designed using reverse flow trajectories, for capturing plumes of contaminated groundwater. Linear capture structures, comprised of two slurry cutoff walls on either side of a permeable gate, were positioned perpendicular to regional groundwater flow in a hypothetical unconfined aquifer. A four‐step approach was used for each of two simulated settings: (1) a numerical mass transport model generated a contaminant plume originating from a source area; (2) a particle‐tracking model projected groundwater flow paths upstream from a treatment gate; (3) the structure was widened and deepened until bounding path lines contained the plume; and (4) mass transport simulation tested the ability of the structure to capture the plume. Results of this study suggest that designing funnel‐and‐gate structures using reverse particle tracking may result in too small a structure to capture a contaminant plume. This practice generally ignores effects of hydrodynamic dispersion, which may enlarge plumes such that contaminants move beneath or around a capture structure. This bypassing effect may be considerable even for low values of dispersivity. Particle‐tracking approaches may also underestimate the amount of time required to reduce contaminant concentrations to acceptable levels. © 2007 Wiley Periodicals, Inc.