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1.
Rahman MM  Worch E 《Chemosphere》2005,61(10):1419-1426
While the pH effect on sorption equilibrium of weak acids on natural sorbents was investigated in a number of studies, less is known about the pH dependence of sorption kinetics. This paper investigates the impact of pH on sorption kinetics during the transport of some selected phenols through a sandy aquifer material. Breakthrough curves measured in column experiments were analyzed using a mass transfer based nonequilibrium model designated as dispersed flow, film and particle diffusion model (DF-FPDM). In this model, the rate limiting intraparticle diffusion is characterized by the mass transfer coefficient, kSaV, which can be determined from breakthrough curves by curve fitting. The experimental results indicate that the kSaV is pH-dependent and inversely correlated with the pH-dependent distribution coefficient, K(d,app). Regression equations are presented that may be used to estimate approximate values of intraparticle mass transfer coefficients on the basis of experimentally determined or LFER predicted distribution coefficients.  相似文献   

2.
The Eulerian atmospheric tracer transport model MATCH (Multiscale Atmospheric Transport and Chemistry model) has been extended with a Lagrangian particle model treating the initial dispersion of pollutants from point sources. The model has been implemented at the Swedish Meteorological and Hydrological Institute in an emergency response system for nuclear accidents and can be activated on short notice to provide forecast concentration and deposition fields.The model has been used to simulate the transport of the inert tracer released during the ETEX experiment and the transport and deposition of 137Cs from the Chernobyl accident. Visual inspection of the results as well as statistical analysis shows that the extent, time of arrival and duration of the tracer cloud, is in good agreement with the observations for both cases, with a tendency towards over-prediction for the first ETEX release. For the Chernobyl case the simulated deposition pattern over Scandinavia and over Europe as a whole agrees with observations when observed precipitation is used in the simulation. When model calculated precipitation is used, the quality of the simulation is reduced significantly and the model fails to predict major features of the observed deposition field.  相似文献   

3.
A plume model is presented describing the downwind transport of large particles (1–100 μm) under stable conditions. The model includes both vertical variations in wind speed and turbulence intensity as well as an algorithm for particle deposition at the surface. Model predictions compare favorably with the Hanford single and dual tracer experiments of crosswind integrated concentration (for particles: relative bias=−0.02 and 0.16, normalized mean square error=0.61 and 0.14, for the single and dual tracer experiments, respectively), whereas the US EPA's fugitive dust model consistently overestimates the observed concentrations at downwind distances beyond several hundred meters (for particles: relative bias=0.31 and 2.26, mean square error=0.42 and 1.71, respectively). For either plume model, the measured ratio of particle to gas concentration is consistently overestimated when using the deposition velocity algorithm of Sehmel and Hodgson (1978. DOE Report PNL-SA-6721, Pacific Northwest Laboratories, Richland, WA). In contrast, these same ratios are predicted with relatively little bias when using the algorithm of Kim et al. (2000. Atmospheric Environment 34 (15), 2387–2397).  相似文献   

4.
Stable colloidal particles can travel long distances in subsurface environments and carry particle-reactive contaminants with them to locations further than predicted by the conventional advective-dispersive transport equation. When such carriers exist in a saturated porous medium, the system can be idealized as consisting of three phases: an aqueous phase, a carrier phase, and a stationary solid matrix phase. However, when colloids are present in an unsaturated porous medium, the system representation should include one more phase, i.e. the air phase. In the work reported, a mathematical model was developed to describe the transport and fate of the colloidal particles and a non-volatile contaminant in unsaturated porous media. The model is based on mass balance equations in a four-phase porous medium. Colloid mass transfer mechanisms among aqueous, solid matrix, and air phases, and contaminant mass transfer between aqueous and colloid phases are represented by kinetic expressions. Governing equations are non-dimensionalized and solved to investigate colloid and contaminant transport in an unsaturated porous medium. A sensitivity analysis of the transport model was utilized to assess the effects of several parameters on model behavior. The colloid transport model matches successfully with experimental data of Wan and Wilson. The presence of air-water interface retards the colloid transport significantly counterbalancing the facilitating effect of colloids. However, the retardation of contaminant transport by colloids is highly dependent on the properties of the contaminant and the colloidal surface.  相似文献   

5.
A model-based interpretation of laboratory-scale experimental data is presented. Hydrolysis experiments carried out using thin glass tanks filled with glass beads to construct a hypothetical and inert, homogeneous porous medium were analysed using a 2D numerical model. A new empirical formula, based upon results for non-reactive (tracer) experiments is used to calculate transversal dispersivity values for a range of grain sizes and any flow velocities. Combined with effective diffusion coefficients calculated from Stokes-Einstein type equations, plume lengths arising from mixing between two solutes can be predicted accurately using numerical modelling techniques. Moreover, pH and ion concentration profiles lateral to the direction of flow of the mixing species can be determined at any given point downstream, without the need for result fitting. In our case, this approach does not lead to overpredictions of lateral mixing, as previously reported when using parameters derived from non-reactive tracer experiments to describe reactive solute transport. The theory is based on the assumption of medium homogeneity.  相似文献   

6.
The influence of physicochemical characteristics and motility on bacterial transport in groundwater were examined in flow-through columns. Four strains of bacteria isolated from a crystalline rock groundwater system were investigated, with carboxylate-modified and amidine-modified latex microspheres and bromide as reference tracers. The bacterial isolates included a gram-positive rod (ML1), a gram-negative motile rod (ML2), a nonmotile mutant of ML2 (ML2m), and a gram-positive coccoid (ML3). Experiments were repeated at two flow velocities, in a glass column packed with glass beads, and in another packed with iron-oxyhydroxide coated glass beads. Bacteria breakthrough curves were interpreted using a transport equation that incorporates a sorption model from microscopic observation of bacterial deposition in flow-cell experiments. The model predicts that bacterial desorption rate will decrease exponentially with the amount of time the cell is attached to the solid surface. Desorption kinetics appeared to influence transport at the lower flow rate, but were not discernable at the higher flow rate. Iron-oxyhydroxide coatings had a lower-than-expected effect on bacterial breakthrough and no effect on the microsphere recovery in the column experiments. Cell wall type and shape also had minor effects on breakthrough. Motility tended to increase the adsorption rate, and decrease the desorption rate. The transport model predicts that at field scale, desorption rate kinetics may be important to the prediction of bacteria transport rates.  相似文献   

7.
The mixing processes of the aerosol particles from an outdoor environment in a ventilated scale chamber were experimentally studied. The particles were classified into five groups by size: 0.3–0.5 μm, 0.5–1.0 μm, 1.0–3.0 μm, 3.0–5.0 μm and 5.0–10.0 μm. The developing process for the concentration of each particle group was measured in different kinds of flow fields.The results show that the flow field configuration can effectively influence the dispersion time rate of the particles at certain positions. The increase in particle diameter can decrease the dispersion time rate. When the gas flow velocity is high, the particle dispersion time rate is independent of particle size; but when the gas flow velocity is low, particle size can significantly affect the particle dispersion time rate because the turbulent diffusion becomes important in the air and particle transport. The uniformity of the particle concentration for certain positions in steady state tends to be controlled by the inflow velocity, flow field configuration and the particle diameters.  相似文献   

8.
The investigation of the migration of a high pH plume in a fractured shear zone is foreseen by a long-term experiment at the Grimsel rock laboratory. In order to characterise the initial conditions for the long-term experiment and to evaluate an optimal hydraulic in situ set-up, several dipole experiments with nonreacting tracers have been performed. The dipole experiments differ in geometry, pumping rates and orientation to the background water flow. Several single and double-porosity models have been applied to fit the results of these dipole tracer tests in order to extract values for some transport parameters and discriminate for certain transport processes. A two-dimensional porous medium approach was successfully used to fit tracer breakthrough curves measured for a dipole experiment. A model based on a one-dimensional dual porous medium approach was also successful, although the applied hydraulic dipole, with similar injection and extraction rates, suggests the existence of an extended two-dimensional flow field. For the two-dimensional porous medium approach, tracer breakthrough could only be fitted with a complex flow field geometry within the heterogeneous fractured shear zone. The heterogeneity was generated by heterogeneous porosity and hydraulic permeability distributions. Predictions for further dipole geometries and a sorbing tracer have been calculated by means of both models using the flow and transport parameters deduced from fits for a single dipole experiment. This allows for comparison with the measured breakthrough of sorbing tracers. The foreseen experiment with sorbing (radionuclide) tracers will help decide on the appropriate approach that should be used to describe such dipole experiments in this shear zone. Additionally, the migration and spreading of a solution with high pH has been calculated taking into account mineral dissolution and precipitation in a two-dimensional porous medium approach in order to estimate the amount and character of the mineral reactions induced by the interaction between the high pH solution and the rock.  相似文献   

9.
Subsurface solute transport through structured soil is studied by model interpretation of experimental breakthrough curves from tritium and phosphorus tracer tests in three intact soil monoliths. Similar geochemical conditions, with nearly neutral pH, were maintained in all the experiments. Observed transport differences for the same tracer are thus mainly due to differences in the physical transport process between the different monoliths. The modelling is based on a probabilistic Lagrangian approach that decouples physical and chemical mass transfer and transformation processes from pure and stochastic advection. Thereby, it enables explicit quantification of the physical transport process through preferential flow paths, honouring all independently available experimental information. Modelling of the tritium breakthrough curves yields a probability density function of non-reactive solute travel time that is coupled with a reaction model for linear, non-equilibrium sorption–desorption to describe the phosphorus transport. The tritium model results indicate that significant preferential flow occurs in all the experimental soil monoliths, ranging from 60–100% of the total water flow moving through only 25–40% of the total water content. In agreement with the fact that geochemical conditions were similar in all experiments, phosphorus model results yield consistent first-order kinetic parameter values for the sorption–desorption process in two of the three soil monoliths; phosphorus transport through the third monolith cannot be modelled because the apparent mean transport rate of phosphorus is anomalously rapid relative to the non-adsorptive tritium transport. The occurrence of preferential flow alters the whole shape of the phosphorus breakthrough curve, not least the peak mass flux and concentration values, and increases the transported phosphorus mass by 2–3 times relative to the estimated mass transport without preferential flow in the two modelled monoliths.  相似文献   

10.
Multiple factors may affect the scale-up of laboratory multi-tracer injection into structured porous media to the field. Under transient flow conditions and with multiscale heterogeneities in the field, previous attempts to scale-up laboratory experiments have not answered definitely the questions about the governing mechanisms and the spatial extent of the influence of small-scale mass transfer processes such as matrix diffusion. The objective of this research is to investigate the effects of multiscale heterogeneity, mechanistic and site model conceptualization, and source term density effect on elucidating and interpreting tracer movement in the field. Tracer release and monitoring information previously obtained in a field campaign of multiple, conservative tracer injection under natural hydraulic gradients at a low-level waste disposal site in eastern Tennessee, United States, is used for the research. A suite of two-pore-domain, or fracture-matrix, groundwater flow and transport models are calibrated and used to conduct model parameter and prediction uncertainty analyses. These efforts are facilitated by a novel nested Latin-hypercube sampling technique. Our results verify, at field scale, a multiple-pore-domain, multiscale mechanistic conceptual model that was used previously to interpret only laboratory observations. The results also suggest that, integrated over the entire field site, mass flux rates attributable to small-scale mass transfer are comparable to that of field-scale solute transport. The uncertainty analyses show that fracture spacing is the most important model parameter and model prediction uncertainty is relatively higher at the interface between the preferred flow path and its parent bedrock. The comparisons of site conceptual models indicate that the effect of matrix diffusion may be confined to the immediate neighborhood of the preferential flow path. Finally, because the relatively large amount of tracer needed for field studies, it is likely that source term density effect may exaggerate or obscure the effect of matrix diffusion on the movement of tracers from the preferred flow path into the bedrock.  相似文献   

11.
Correct interpretation of tracer test data is critical for understanding transport processes in the subsurface. This task can be greatly complicated by the presence of intraborehole flows in a highly dynamic flow environment. At a new tracer test site (Hanford IFRC) a dynamic flow field created by changes in the stage of the adjacent Columbia River, coupled with a heterogeneous hydraulic conductivity distribution, leads to considerable variations in vertical hydraulic gradients. These variations, in turn, create intraborehole flows in fully-screened (6.5m) observation wells with frequently alternating upward and downward movement. This phenomenon, in conjunction with a highly permeable aquifer formation and small horizontal hydraulic gradients, makes modeling analysis and model calibration a formidable challenge. Groundwater head data alone were insufficient to define the flow model boundary conditions, and the movement of the tracer was highly sensitive to the dynamics of the flow field. This study shows that model calibration can be significantly improved by explicitly considering (a) dynamic flow model boundary conditions and (b) intraborehole flow. The findings from this study underscore the difficulties in interpreting tracer tests and understanding solute transport under highly dynamic flow conditions.  相似文献   

12.
13.
Tracer experiments conducted using a flow field established by injecting water into one borehole and withdrawing water from another are often used to establish connections and investigate dispersion in fractured rock. As a result of uncertainty in the uniqueness of existing models used for interpretation, this method has not been widely used to investigate more general transport processes including matrix diffusion or advective solute exchange between mobile and immobile zones of fluid. To explore the utility of the injection-withdrawal method as a general investigative tool and with the intent to resolve the transport processes in a discrete fracture, two tracer experiments were conducted using the injection-withdrawal configuration. The experiments were conducted in a fracture which has a large aperture (>500 microm) and horizontally pervades a dolostone formation. One experiment was conducted in the direction of the hydraulic gradient and the other in the direction opposite to the natural gradient. Two tracers having significantly different values of the free-water diffusion coefficient were used. To interpret the experiments, a hybrid numerical-analytical model was developed which accounts for the arcuate shape of the flow field, advection-dispersion in the fracture, diffusion into the matrix adjacent to the fracture, and the presence of natural flow in the fracture. The model was verified by comparison to a fully analytical solution and to a well-known finite-element model. Interpretation of the tracer experiments showed that when only one tracer, advection-dispersion, and matrix diffusion are considered, non-unique results were obtained. However, by using multiple tracers and by accounting for the presence of natural flow in the fracture, unique interpretations were obtained in which a single value of matrix porosity was estimated from the results of both experiments. The estimate of porosity agrees well with independent measurements of porosity obtained from core samples. This suggests that: (i) the injection-withdrawal method is a viable tool for the investigation of general transport processes provided all relevant experimental conditions are considered and multiple conservative tracers are used; and (ii) for the conditions of the experiments conducted in this study, the dominant mechanism for exchange of solute between the fracture and surrounding medium is matrix diffusion.  相似文献   

14.
A column containing four concentric layers of progressively finer-grained glass beads (graded column) was used to study the transport of the bacteriophage T7 in water flowing parallel to layering through a fining-upwards (FU) sedimentary structure. By passing a pulse of T7, and a conservative solute tracer upwards through a column packed with a single bead size (uniform column), the capacity of each bead type to attenuate the bacteriophage was determined. Solute and bacteriophage responses were modelled using an analytical solution to the advection-dispersion equation, with first-order kinetic deposition simulating bacteriophage attenuation. Resulting deposition constants for different flow velocities indicated that filtration theory-determined values differed from experimentally determined values by less than 10%. In contrast, the responses of solute and bacteriophage tracers passing upwards through graded columns could not be reproduced with a single analytical solution. However, a flux-weighted summation of four one-dimensional advective-dispersive analytical terms approximated solute breakthrough curves. The prolonged tailing observed in the resulting curve resembled that typically generated from field-based tracer test data, reflecting the potential importance of textural heterogeneity in the transport of dissolved substances in groundwater. Moreover, bacteriophage deposition terms, determined from filtration theory, reproduced the T7 breakthrough curve once desorption and inactivation on grain surfaces were incorporated. To evaluate the effect of FU sequences on mass transport processes in more detail, bacteriophage passage through sequences resembling those sampled from a FU bed in a fluvioglacial gravel pit were carried out using an analogous approach to that employed in the laboratory. Both solute and bacteriophage breakthrough responses resembled those generated from field-based test data and in the graded column experiments. Comparisons with the results of simulations using averaged hydraulic conductivities show that simulations employing averaged parameters overestimate bacteriophage travel times and underestimate masses recovered and peak concentrations.  相似文献   

15.
The gel barrier formation by a gelling liquid (Colloidal Silica) injection in an unsaturated porous medium is investigated by developing a mathematical model and conducting numerical simulations. Gelation process is initiated by adding electrolytes such as NaCl, and the gel phase consisting of cross-linked colloidal silica particles grows as the gelation process proceeds. The mathematical model describing the transport and gelation of Colloidal Silica (CS) is based on coupled mass balance equations for the gel mixture (the sol phase plus the gel phase), gel phase (cross-linked colloidal silica particles plus water captured between cross-linked particles), and colloidal silica particles (discrete and cross-linked) and NaCl in the sol (suspension of discrete colloidal silica particles in water) and gel phases. The solutions in terms of volumetric fraction of the gel phase yield the gel mixture viscosity via the dependency on the volumetric fraction of gel phase. This dependency is determined from a kinetic gelation model with time-normalized viscosity curves. The proposed model is verified by comparing experimentally and numerically determined hydraulic conductivities of gel-treated soil columns at different CS injection volumes. The numerical experiments indicate that an impermeable gel layer is formed within the time period twice the gel-point in a one-dimensional flow system. At the same normalized time corresponding to twice the gel-point, the CS solutions with lower NaCl concentrations result in further migration and poor performance in plugging the pore space. The viscosity computation proposed in this study is compared with another method available in the literature. It is observed that the other method estimates the viscosity at the mixing zone higher than the one proposed by the authors. The proposed model can simulate realistic injection scenarios with various combinations of operating parameters such as NaCl concentration and NaCl mixing time, and thus providing guidelines in performing this technology on site.  相似文献   

16.
It is known that under unsaturated conditions, the transport of solutes can deviate from ideal advective-dispersive behaviour even for macroscopically homogeneous porous materials. Causes may include physical non-equilibrium, sorption kinetics, non-linear sorption, and the irregular distribution of sorption sites. We have performed laboratory experiments designed to identify the processes responsible for the non-ideality of radioactive Sr transport observed under unsaturated flow conditions in an Aeolian sandy deposit from the Chernobyl exclusion zone. Miscible displacement experiments were carried out at various water contents and corresponding flow rates in a laboratory model system. Results of our experiments have shown that breakthrough curves of a conservative tracer exhibit a higher degree of asymmetry when the water content decreases than at saturated water content and same Darcy velocity. It is possible that velocity variations caused by heterogeneities at the macroscopic scale are responsible for this situation. Another explanation is that molecular diffusion drives the solute mass transfer between mobile and immobile water regions, but the surface of contact between these water regions is small. At very low concentrations, representative of a radioactive Sr contamination of the pore water, sorption and physical disequilibrium dominate the radioactive Sr transport under unsaturated flow conditions. A sorption reaction is described by a cation exchange mechanism calibrated under fully saturated conditions. The sorption capacity, as well as the exchange coefficients are not affected by desaturation. The number of accessible exchange sites was calculated on the basis that the solid remained in contact with water and that the fraction of solid phase in contact with mobile water is numerically equal to the proportion of mobile water to total water content. That means that for this type of sandy soil, the nature of mineral phases is the same in advective and non-advective domains. So sorption reaction parameters can be estimated from more easily conducted saturated experiments, but hydrodynamic behaviour must be characterized by conservative tracer experiments under unsaturated flow conditions.  相似文献   

17.
Saturated-unsaturated flow in strictly layered sediments proceeds via conductors in parallel in the direction parallel to bedding, and via resistors in series in the direction perpendicular to bedding. On sufficiently small scales of space and time, flow in such media will be subject to approximate capillary equilibrium locally, which provides a basis for approximating the effective hydraulic conductivity of a composite multi-layer medium in terms of the conductivities of the individual layers. Equations for the hydraulic conductivity tensor in "composite medium approximation" (COMA) are given in a coordinate system aligned with bedding. Hydraulic conductivity parallel to bedding is generally larger than in the perpendicular direction. The anisotropy depends on the spread of the conductivity distribution, and tends to increase for dryer conditions. The COMA model was implemented in a multi-phase flow simulator and tested by comparison with high-resolution simulations in which all layering heterogeneity is resolved explicitly. Under favorable conditions, COMA is found to accurately represent sub-grid scale flow and transport processes, providing a practical method for simulating field-scale flow and transport in layered media. The approximation improves when layers are thinner, and when flow rates are smaller.  相似文献   

18.
The mass transfer rate from residual dense non-aqueous phase liquids (DNAPLs) to the mobile aqueous phase is an important parameter for the efficiency of surfactant-enhanced remediation through solubilization of this type of contamination. The mass transfer kinetics are highly dependent on the dimensionality of the system. In this study, irregularly shaped residual TCE saturations in two-dimensional saturated flow fields were flushed with a 2% polyoxyethylene sorbitan (20) monooleate (POESMO) solution until complete removal had been achieved. A numerical model was developed and used for the simulation of the various surfactant-flushing experiments with different initial saturation patterns and flow rates. Through optimization against in situ concentration and saturation data, a phenomenological power-law model for the relationship between the mass transfer rate from the DNAPL to the mobile aqueous phase on the one hand and the residual DNAPL saturation and the flow velocity on the other hand was derived. The obtained mass transfer rate parameters provide a reasonable fit to the experimental data, predicting the cleanup time and the general saturation and concentration pattern quite well but failing to predict the concentration curves at every individual sampling port. The obtained mass transfer rate model gives smaller values for the predicted mass transfer rate but shows a comparable dependence on water flow and saturation as in earlier published one-dimensional column experiments with identical characteristics for porous medium, DNAPL and surfactant. Mass transfer rate predictions were about one order of magnitude lower in the 2-D flow cell experiment than in 1-D column experiments. These results give an indication for the importance of dimensionality during surfactant remediation.  相似文献   

19.
A two-dimensional model for colloid transport in geochemically and physically heterogeneous porous media is presented. The model considers patchwise geochemical heterogeneity, which is suitable to describe the chemical variability of many surficial aquifers with ferric oxyhydroxide-coated porous matrix, as well as spatial variability of hydraulic conductivity, which results in heterogeneous flow field. The model is comprised of a transient fluid flow equation, a transient colloid transport equation, and an equation for the dynamics of colloid deposition and release. Numerical simulations were carried out with the model to investigate the colloid transport behavior in layered and randomly heterogeneous porous media. Results demonstrate that physical and geochemical heterogeneities markedly affect the colloid transport behavior. Layered physical or geochemical heterogeneity can result in distinct preferential flow paths of colloidal particles. Furthermore, the combined effect of layered physical and geochemical heterogeneity may result in enhanced or reduced preferential flow of colloids. Random distribution of physical heterogeneity (hydraulic conductivity) results in a random flow field and an irregularly distributed colloid concentration profile in the porous medium. Contrary to random physical heterogeneity, the effect of random patchwise geochemical heterogeneity on colloid transport behavior is not significant. It is mostly the mean value of geochemical heterogeneity rather than its distribution that governs the colloid transport behavior.  相似文献   

20.
We consider the dispersion and elution of colloids and dissolved nonsorbing tracers within saturated heterogeneous porous media. Since flow path geometry in natural systems is often ill-characterized macroscopic (mean) flow rates and dispersion tensors are utilized in order to account for the sub-model scale microscopic fluctuations in media structure (and the consequent hydrodynamic profile). Even for tracer migration and dispersal this issue is far from settled.Here we consider how colloid and tracer migration phenomena can be treated consistently. Theoretical calculations for model flow geometries yield two quantitative predictions for the transport of free (not yet captured) colloids with reference to a non-sorbing dissolved tracer within the same medium: the average migration velocity of the free colloids is higher than that of the tracer; and that the ratio of the equivalent hydrodynamic dispersion rates of colloids and tracer is dependent only upon properties of the colloids and the porous medium, it is independent of pathlengths and fluid flux, once length scales are large enough.The first of these is well known, since even in simple flow paths free colloids must stay more centre stream. The second, if validated suggests how solute and colloid dispersion may be dealt with consistently in macroscopic migration models. This is crucial since dispersion is usually ill-characterized and unaddressed by the experimental literature. In this paper we present evidence based upon an existing Drigg field injection test for the validity of these predictions.We show that starting from experimental data the fitted dispersion rates of both colloids and non-sorbing tracers increase with the measured elution rates (obeying slightly different rules for tracers and colloids); and that the ratio of colloid and nonsorbing tracer elution rates, and the ratio of colloid and nonsorbing tracer dispersion rates may be dependent upon properties of the colloids and the medium (not the flow regime).It is important to realize that even for unretarded species, an earlier peak in the breakthrough curve does not necessarily correspond to a faster mean elution rate, or vice versa. But rather that a colloid may elute faster but disperse less than an equivalent tracer. Hence its peak may be retarded compared to that of the tracer, even assuming no retardation. Hence one must consider a combination of mean elution rate and mean dispersion rate, and not rely on “peak times” to corroborate chromatographic effects. The importance of this lies in the fact that these processes are not independent and yet upscale differently. Thus realistic estimates of effective colloid dispersion rates should be upscaled in a way consistent with that adopted for tracers within the same system.  相似文献   

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