Solute Residence Time Distributions Research Articles

Hyporheic Flows in Stratified Sediments: Implications on Residence Time Distributions

AbstractThe fate of nutrients and contaminants in fluvial ecosystems is strongly affected by the mixing dynamics between surface water and groundwater within the hyporheic zone, depending on the combination of the sediment's hydraulic heterogeneity and dune morphology. This study examines the effects of hydraulic conductivity stratification on steady‐state, two‐dimensional, hyporheic flows and solute residence time distribution. First, we derive an integral transform‐based semi‐analytical solution for the flow field, capable of accounting for the effects of any functional shape of the vertically varying hydraulic conductivity. The solution considers the uneven distribution of pressure at the water‐sediment interface (i.e., the pumping process) dictated by the presence of dune morphology. We then simulate solute transport using particle tracking. Our modeling framework is validated against numerical and tracer data from flume experiments and used to explore the implication of hydraulic conductivity stratification on the statistics and pdf of the residence time. Finally, reduced‐order models are used to enlighten the dependence of key residence time statistics on the parameters characterizing the hydraulic conductivity stratification.

Modeling the Effect of Hyporheic Flow on Solute Residence Time Distributions in Surface Water

Understanding the dynamics of hyporheic flow is important for managing water resources, since this interfacial flow exchange affects the fate and transport of contaminants in rivers. This study numerically quantifies the effect of hyporheic exchange on solute residence times in surface water systems by simulating solute transport in unified turbulent open-channel and hyporheic zone systems. Interfacial hyporheic fluxes (qint) increase with increased Reynolds number (Re) that produces an enhanced bottom pressure gradient over the ripple bed. Heavy-tailed breakthrough curves emerge when hyporheic flow is considered in transport simulation. This reveals that hyporheic flow is a dominant driver of non-Fickian transport in surface water as this interfacial flow exchange delays solute transport with slow porewater flows. Furthermore, the increase in Re extends the longitudinal spreading of solute tracers because a higher surface flow velocity intensifies the magnitude of hyporheic flow and associated storage effects. This can be confirmed by the ratio of the maximum residence time to the peak arrival time that increases with the increase in Re, following a power-law relationship with both Re and qint.

Numerical simulations of the effect on twisted spacer filaments on biofouling and scaling in the feed channel of reverse osmosis membrane modules

Overcoming biofouling and scaling in membrane-based separation processes is significant as it affects the permeate quality. In the present study, the effect of biofouling (on membrane only, spacer only, membrane as well as spacer) and scaling on the velocity field, pressure variation, solute residence time distribution and water flux in the reverse osmosis feed channel consisting of twisted spacer filaments is presented using numerical simulations. The twisted spacer filaments caused fluid mixing, which enhanced membrane performance. The biofouling on spacer filaments and/or membrane surfaces and scaling resulted in a narrower effective area for fluid flow, thus causing fluid acceleration and higher pressure drop. The study of solute residence time distribution for biofouling revealed that the breakthrough time decreased with residence time due to fluid acceleration. The observations of solute tracer movement revealed that the solute advection pattern broadened when the feed time for the solute tracer was increased. An irregular and heterogeneous pattern of solute tracer movement was observed in the reverse osmosis feed channel with biofouling which enhanced the flow dispersion and acceleration. The effect of feed temperature on the biofouling pattern was also observed. Biofouling reduced with temperature because the increased feed temperature improved biomass mobility. The water flux in the computational domain containing spacer with scaling was higher compared to the computational domain containing spacer with biofouling because biofouling reduced the membrane porosity, diffusion coefficient and increased flow resistance. The present study concludes that the twisted spacer can effectively reduce biofouling and scaling with improved water flux in reverse osmosis membrane modules.

Computational fluid dynamic (CFD) simulation of a cuboid packed-bed chromatography device

Flow non-uniformity is a major problem with process chromatography columns which typically have small bed height to diameter ratios. In recent publications, we have proposed box-shaped or cuboid packed-bed devices as efficient alternative to process columns for carrying out high-resolution chromatographic separations. Cuboid packed-bed devices show superior performance in terms of number of theoretical plates, peak width, and peak resolution in multicomponent separations. This paper attempts to explain this based on computational fluid dynamic (CFD) simulations of a cuboid packed-bed device and its equivalent column, i.e. having the same bed height and area of cross-section, and packed with the same chromatographic media. The radial velocity in the column headers decreased very rapidly from the axis to the periphery resulting in significant variation in average velocity along the different flow paths within the column. By contrast, the velocity decreased linearly in the top channel and increased linearly in the bottom channel of a cuboid packed-bed device, resulting in significantly lower variation in the average velocity. Simulated flow-through peaks obtained with the cuboid packed-bed device using dextran as a macromolecular and sodium chloride as a low molecular weight tracer were significantly sharper and more symmetric. Experimental results were in good agreement with those obtained by simulation. Overall, the superior performance of the cuboid packed-bed device could be primarily attributed to the narrower solute residence time distribution resulting from greater flow uniformity.

An annular-flow, hollow-fiber membrane chromatography device for fast, high-resolution protein separation at low pressure

High-resolution protein separation is currently carried out using columns packed with ultrafine particulate chromatographic media which can only be operated at very high pressures. This restricts the flow rate and thereby the speed of separation. A membrane with ultrafine pores shares the same mass transport advantages as a bed of ultrafine particles. However, application of membrane chromatography has largely been restricted to low-resolution separation applications, primarily due to limitations associated with poorly designed devices. In this paper, we describe a novel annular-flow hollow-fiber membrane chromatography (AHMC) device, suitable for fast, high-resolution protein separation. The AHMC device was designed primarily from a fluidics perspective to ensure a narrow solute residence time distribution, a low dead-volume, and minimal fluid back-mixing. Using this device, it was possible to separate a ternary protein mixture in less than a minute, at less than 0.3 MPa backpressure. The high-resolution separation capability of AHMC was further demonstrated through its use for the separation of bovine serum albumin (BSA) dimer from the monomeric form of the protein. This was achieved in less than 3 min which was considerably faster than other reported techniques for protein aggregates separation.

Enhancing the efficiency of disc membrane chromatography modules by using a flow directing layer

Disc membrane chromatography modules are widely used for laboratory-scale protein separations. These have high radial to axial aspect ratios, with the inlet and the outlet being located at the centre. This results in a huge variability in flow path lengths. Also, the radial velocity in the feed side header decreases very significantly in an outward direction, while that in the permeate side header increases in an inward direction. Therefore, the flow paths closer to the axis of the membrane disc have higher average velocity compared to those closer to the periphery. Consequently, the solute residence time distribution within the disc membrane chromatography module is very large, which results in broad flow-through and eluted peaks and early breakthrough of bound solutes. In this paper, we discuss a simple but effective solution to this problem which involves the incorporation of a flow directing layer (FDL) within the membrane module. The FDL could be placed either in the front or at the rear of the membrane disc. The presence of FDL results in equalization of path lengths within the module, leading to narrowing of residence time distribution, and thereby improvement in separation efficiency. Modules housing strong cation exchange membrane discs having two different bed volumes of 0.4 mL (40 mm diameter) and 4.7 mL (60 mm diameter) were designed and fabricated in-house. The impact of using FDL on both the front side (F-FDL) and the rear side (R-FDL) was investigated. The separation efficiency of the membrane modules was assessed using salt tracer experiments, breakthrough protein binding, and ternary protein separation carried out in the bind-and-elute mode. The results confirmed that the use of the FDL significantly enhanced the separation efficiency. In addition to membrane chromatography, this approach of using an FDL could be extended to other membrane disc based modules such as in-line and syringe filters and membrane reactors.

Cuboid Packed-Beds as Chemical Reactors?

Columns are widely used as packed-bed or fixed-bed reactors in the chemical process industry. Packed columns are also used for carrying out chemical separation techniques such as adsorption, distillation, extraction and chromatography. A combination of the variability in flow path lengths, and the variability of velocity along these flow paths results in significant broadening in solute residence time distribution within columns, particularly in those having low bed height to diameter ratios. Therefore, wide packed-column reactors operate at low efficiencies. Also, for a column of a particular bed height, the ratio of heat transfer surface area to reactor volume varies inversely as the radius. Therefore, with wide columns, the available heat transfer area could become a limiting factor. In recent papers, box-shaped or cuboid packed-bed devices have been proposed as efficient alternatives to packed columns for carrying out chromatographic separations. In this paper, the use of cuboid packed-beds as reactors for carrying out chemical and biochemical reactions has been proposed. This proposition is primarily supported in terms of advantages resulting from superior system hydraulics and narrower residence time distributions. Other potential advantages, such as better heat transfer attributes, are speculated based on geometric considerations.

Biofilm growth in gravel bed streams controls solute residence time distributions

AbstractStreambed substrates harbor a rich biome responsible for biogeochemical processing in riverine waters. Beyond their biological role, the presence of benthic and hyporheic biofilms can play an important role in influencing large‐scale transport of solutes, even for conservative tracers. As biofilms grow and accumulate biomass, they actively interact with and influence surface and subsurface flow patterns. To explore this effect, we conducted experiments at the Notre Dame Linked Ecosystems Experimental Facility in four outdoor streams, each with different gravel beds. Over the course of 20 weeks we conducted transport experiments in each of these streams and observed different patterns in breakthrough curves as biofilms grew on the substrate. Biofilms played a major role in shaping the observed conservative transport patterns. Overall, while the presence of biofilms led to a decreased exchange rate between the fast (mobile) and slow (immobile) parts of the flow domain, water that was exchanged tended to be stored in the slow regions for longer times once biofilms had established. More specifically, we observed enhanced longitudinal dispersion in breakthrough curves as well as broader residence time distributions when biofilms were present. Biofilm colonization over time homogenized transport patterns across the four streams that were originally very distinct. These results indicate that stream biofilms exert a strong control on conservative solute transport in streams, a role that to date has not received enough attention.

Fractal patterns in riverbed morphology produce fractal scaling of water storage times

AbstractRiver topography is famously fractal, and the fractality of the sediment bed surface can produce scaling in solute residence time distributions. Empirical evidence showing the relationship between fractal bed topography and scaling of hyporheic travel times is still lacking. We performed experiments to make high‐resolution observations of streambed topography and solute transport over naturally formed sand bedforms in a large laboratory flume. We analyzed the results using both numerical and theoretical models. We found that fractal properties of the bed topography do indeed affect solute residence time distributions. Overall, our experimental, numerical, and theoretical results provide evidence for a coupling between the sand‐bed topography and the anomalous transport scaling in rivers. Larger bedforms induced greater hyporheic exchange and faster pore water turnover relative to smaller bedforms, suggesting that the structure of legacy morphology may be more important to solute and contaminant transport in streams and rivers than previously recognized.

Effects of solute breakthrough curve tail truncation on residence time estimates: A synthesis of solute tracer injection studies

Hydrologic transport and retention strongly affect biogeochemical processes that are critical to stream ecosystems. Tracer injection studies are often used to characterize solute transport and retention in stream reaches, but the range of processes accurately resolved with this approach is not clear. Solute residence time distributions depend on both in‐stream mixing and exchange with the hyporheic zone and the larger groundwater system. Observed in‐stream breakthrough curves have most commonly been modeled with in‐stream advection‐dispersion plus an exponential residence time distribution, but process‐based models suggest that hyporheic exchange is a fractal process, and that hyporheic residence time distributions are more appropriately characterized by power law tailing. We synthesized results from a variety of tracer‐injection studies to investigate the information content of tracer breakthrough curves. We found that breakthrough curve tails are often not well characterized in stream tracer experiments. The two main reasons for this are: 1) experimental truncation of breakthrough curves, which occurs when sampling ends before all tracer mass reaches the sampling location, and 2) sensitivity truncation of breakthrough curves, when tracer concentrations in the tail are too low to be detected reliably above background levels. Tail truncation reduces observed mass recovery and obscures assessment of breakthrough curve tailing and solute residence time. Failure to consider tail truncation leads to underestimation of hyporheic exchange and solute retention and to corresponding overestimation of hyporheic biogeochemical transformation rates. Based on these findings, we propose criteria for improved design of in‐stream tracer injection experiments to improve assessment of solute tailing behavior.

Zonal rate model for stacked membrane chromatography. I: Characterizing solute dispersion under flow-through conditions

Conventional models of both packed-bed and stacked-membrane chromatography typically attribute elution band broadening to non-idealities within the column. However, when the column length to diameter ratio is greatly reduced, as in stacked-membrane chromatography, variations in solute residence times within the feed-distribution (inlet) and eluent-collection (outlet) manifolds can also contribute to band broadening. We report on a new zonal rate model (ZRM) for stacked-membrane chromatography that improves on existing hold-up volume models that rely on one plug-flow reactor and one stirred-tank reactor in series to describe dispersion of solute during transport into and out of the column. The ZRM radially partitions the membrane stack and the hold-up volumes within the inlet and outlet manifolds into zones to better capture non-uniform flow distribution effects associated with the large column diameter to height ratio. Breakthrough curves from a scaled-down anion-exchange membrane chromatography module using ovalbumin as a model protein were collected at flow rates ranging from 1.5 to 20 mL min −1 under non-binding conditions and used to evaluate the ZRM as well as previous models. The ZRM was shown to be significantly more accurate in describing protein dispersion and breakthrough. The model was then used to decompose breakthrough data, where it was found that variations in solute residence time distributions within the inlet and outlet manifolds make the dominant contribution to solute dispersion over the recommended range of feed flow rates. The ZRM therefore identifies manifold design as a critical contributor to separation quality within stacked-membrane chromatography units.

Effect of channel size on solute residence time distributions in rivers

The effect of channel size on residence time distributions (RTDs) of solute in rivers is investigated in this paper using tracer test data and the variable residence time (VART) model. Specifically, the investigation focuses on the influence of shear dispersion and hyporheic exchange on the shape of solute RTD, and how these two transport processes prevail in larger and smaller streams, respectively, leading to distinct tails of RTD. Simulation results show that (1) RTDs are dispersion-dependent and thereby channel-size (scale) dependent. RTDs increasing longitudinal dispersion coefficient. Small streams with negligible dispersion coefficient may display various types of RTD from upward curving patterns to a straight line (power-law distributions) and further to downward curving lognormal distributions when plotted in log–log coordinates. Moderate-sized rivers are transitional in terms of RTDs and commonly exhibit lognormal and power-law RTDs; (2) the incorporation of water and solute losses/gains in the VART model can improve simulation results and make parameter values more reasonable; (3) the ratio of time to peak concentration to the minimum mean residence time is equal to the recovery ratio of tracer. The relation provides a simple method for determining the minimum mean residence time; and (4) the VART model is able to reproduce various RTDs observed in rivers with 3–4 fitting parameters while no user-specified RTD functions are needed.

Direct simulation of pore level Fickian dispersion scale for transport through dense cubic packed spheres with vortices

The transition from non‐Fickian to Fickian macroscale transport is explicitly demonstrated for an increasing array of three‐dimensional pores with vortices in between a lattice of cubic packed spheres by microscale finite element Navier‐Stokes flow and transport simulations. Solute residence time distribution begins with a power law for one pore but gradually and eventually transforms to an exponential distribution typical of classic dispersive transport after about ten pores. Parameter fitting of an analytical solution to the 1‐D advection‐dispersion equation using the simulated breakthrough curves leads to fitted pore velocities within 1% of actual values and an asymptotic fitted dispersion coefficient after a few pores. Therefore, after dozens of pores, bulk transport can be described by the advection‐dispersion equation. Persistent vortices in similarly structured porous media subjected to similar grain‐scale Reynolds and Peclet numbers may have minimal contribution to anomalous transport observed at larger scales.

Comparison of instantaneous and constant‐rate stream tracer experiments through non‐parametric analysis of residence time distributions

Artificial tracers are frequently employed to characterize solute residence times in stream systems and infer the nature of water retention. When the duration of tracer application is different between experiments, tracer breakthrough curves at downstream locations are difficult to compare directly. We explore methods for deriving stream solute residence time distributions (RTD) from tracer test data, allowing direct, non‐parametric comparison of results from experiments of different durations. Paired short‐ and long‐duration field experiments were performed using instantaneous and constant‐rate tracer releases, respectively. The experiments were conducted in two study reaches that were morphologically distinct in channel structure and substrate size. Frequency‐ and time domain deconvolution techniques were used to derive RTDs from the resulting tracer concentrations. Comparisons of results between experiments of different duration demonstrated few differences in hydrologic retention characteristics inferred from short‐ and long‐term tracer tests. Because non‐parametric RTD analysis does not presume any shape of the distribution, it is useful for comparisons across tracer experiments with variable inputs and for validations of fundamental transport model assumptions.

Predicting membrane flux decline from complex mixtures using flow-field flow fractionation measurements and semi-empirical theory

Flow-Field Flow Fractionation (FI-FFF) is an idealization of the cross flow membrane filtration process in that, (1) the filtration flux and crossflow velocity are constant from beginning to end of the device, (2) the process is a relatively well-defined laminar-flow hydrodynamic condition, and (3) the solutes are introduced as a pulse-input that spreads due to interactions with each other and the membrane in the dilute-solution limit. We have investigated the potential for relating FI-FFF measurements to membrane fouling. An advection-dispersion transport model was used to provide 'ideal' (defined as spherical, non-interacting solutes) solute residence time distributions (RTDs) for comparison with 'real' RTDs obtained experimentally at different cross-field velocities and solution ionic strength. An RTD moment analysis based on a particle diameter probability density function was used to extract "effective" characteristic properties, rather than uniquely defined characteristics, of the standard solute mixture. A semi-empirical unsteady-state, flux decline model was developed that uses solute property parameters. Three modes of flux decline are included: (1) concentration polarization, (2) cake buildup, and (3) adsorption on/in pores, We have used this model to test the hypothesis-that an analysis of a residence time distribution using FI-FFF can describe 'effective' solute properties or indices that can be related to membrane flux decline in crossflow membrane filtration. Constant flux filtration studies included the changes of transport hydrodynamics (solvent flux to solute back diffusion (J/k) ratios), solution ionic strength, and feed water composition for filtration using a regenerated cellulose ultrafiltration membrane. Tests of the modeling hypothesis were compared with experimental results from the filtration measurements using several correction parameters based on the mean and variance of the solute RTDs. The corrections used to modify the boundary layer mass transfer coefficient and the specific resistance of cake or adsorption layers demonstrated that RTD analysis is potentially useful technique to describe colloid properties but requires improvements.

A Dynamic Model for Radiotracer Determination of Solute Residence Time Distribution in Counter-Current Pulse Column Solvent Extraction Processes

A radiotracer method for the measurement of the mass holdup of a solute being processed in a counter-current pulse column using the average residence time distribution is presented and investigated by mathematical modelling. Typical solutions to the model for impulse tracer injections of the solute at the inlet show that while the number and volume of stages have a significant effect on the response of the system, the amount of backmixing has little effect, particularly for small systems. The system response to impulse tracer injections under various conditions was simulated with this model and model parameters were extracted from these simulated results by using a nonlinear least squares method to demonstrate the approach.