Holdup and dispersion: tracer residence times, moments and inventory measurements

Buffham, B.A.; Mason, Geoffrey

doi:10.1016/0009-2509(93)80366-x

Cited by 32 publications

(11 citation statements)

References 17 publications

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“…One way to test robustness is to examine the sensitivity of fitted parameter values to perturbations in system conditions. For laboratory miscible-displacement experiments, this could involve, for example, changing the pore-water velocity or magnitude of the input pulse (e.g., De Lasa et al, 1986; Brusseau et al, 1989; Buffham and Mason, 1993; Young and Ball, 2000; Schnaar and Brusseau, 2013). The potential experiment-condition dependency of the continuous-distribution rate model has received minimal investigation to date.…”

Section: Introductionmentioning

confidence: 99%

Nonideal Transport of Contaminants in Heterogeneous Porous Media: 11. Testing the Experiment Condition Dependency of the Continuous Distribution Rate Model for Sorption–Desorption

Schnaar

Brusseau

2014

Water Air Soil Pollut

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A series of miscible-displacement experiments was conducted to examine the impact of experiment conditions (detection limit, input-pulse size, input concentration, pore-water velocity, contact time) on the performance of a mathematical solute–transport model incorporating nonlinear, rate-limited sorption/desorption described by a continuous-distribution reaction function. Effluent solute concentrations were monitored over a range of approximately seven orders of magnitude, allowing characterization of asymptotic tailing phenomenon. The model successfully simulated the extensive elution tailing observed for the measured data. Values for the mean desorption rate coefficient (ln k2) and the variance of ln k2 were obtained through calibration of the model to measured data. Similar parameter values were obtained for experiments with different input-pulse size, input concentration, pore-water velocity, contact time. This suggests that the model provided a robust representation of sorption-desorption for this system tested. The impact of analytical detection limit was examined by calibrating the model to subsets of the breakthrough curves wherein the extent of the elution tail was artificially reduced to mimic a poorer detection limit. The parameters varied as a function of the extent of elution tail used for the calibrations, indicating the importance of measuring as full an extent of the tail as possible.

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Section: Introductionmentioning

confidence: 99%

Nonideal Transport of Contaminants in Heterogeneous Porous Media: 11. Testing the Experiment Condition Dependency of the Continuous Distribution Rate Model for Sorption–Desorption

Schnaar

Brusseau

2014

Water Air Soil Pollut

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“…When the Bo number tends to infinity, the mixing conditions are similar to those of a plug-flow reactor, and the reactor can be considered as well mixed for low Bo numbers. The alternative approach of Buffham and Mason (165) states that the mixing characteristics of a piece of equipment should be expressed as the variance σ 2 of the distribution obtained by injection of a pulse of tracer without adopting any mechanistic model (165). The relationship between Bo and σ 2 depends on the reactor configuration (166).…”

Section: Liquid Mixingmentioning

confidence: 99%

Bioreactors: Airlift Reactors

Merchuk

Camacho

2010

Encyclopedia of Industrial Biotechnology

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ALRs are popular in modern bioprocess research and development and, in many cases, they have found industrial uses. The distinctive characteristics of ALRs are conferred by the fluid dynamics of the liquid‐gas or liquid gas‐solid mixtures: holdup, liquid velocity, and mixing in the riser, gas separator, and downcomer. Only a correct understanding of the interconnection of these regions can make possible the scale‐up of a laboratory device, to pilot or industrial size. Several correlations are available in the literature for the prediction of the fluid dynamic characteristics of the reactor and of the mass and heat transfer coefficients, and a selection is presented in this review. Significant progress has been made in the application of modern computational tools to the simulation and design of ALRs. In parallel, innovative and sophisticated methods have been applied to obtain a deeper insight into the mechanisms of fluid motion and the flow patterns in the reactor. However, no single research group has managed to cover all the variables over a wide range. The engineer confronting scale‐up or de novo design of an ALR must analyze the validity of the correlations and computation methods used for the calculations.

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“…For pulse inputs (Valocchi, 1985)

\begin{matrix} μ_{1}^{' i} = \frac{\int_{0}^{t_{F}} {tC}_{g}^{i} d t}{\int_{0}^{t_{F}} C_{g}^{i} d t} - \frac{t_{p}}{2} \end{matrix}

where μ ′ 1 is the mean travel time of the conservative ( i = c ) or partitioning ( i = p ) tracer, t F is the time the tracer measurements were terminated, and t p is the duration of the input pulse. For pulse inputs, the concentration of the tracer at t = t F was designated as the tracer detection limit, c d g For step inputs (Buffham and Mason, 1993),

\begin{matrix} μ_{1}^{' i} = \int_{0}^{t_{F}} true(1 - C_{g}^{i} true) d t \end{matrix}

The retardation factor and the water saturation were then calculated by

\begin{matrix} R = \frac{μ_{1}^{' p}}{μ_{1}^{' c}} \end{matrix}

\begin{matrix} S_{w} = \frac{1}{1 + \frac{1}{K_{H} true(R - 1 true)}} \end{matrix}

Spreading of the conservative tracer was influenced only by the Peclet number, since R = 1 and the second and third moments are only affected by Pe (Eq. [13] and [14]) Because of this and our focus on the influence of mass transfer limitations on measurement error, in the computational experiments discussed below we assumed the mean travel time of the conservative tracer was determined exactly, while the mean travel time of the partitioning tracer was computed using Eq.…”

Section: Mathematical Modelingmentioning

confidence: 99%

Water Saturation Measurements by Gas Tracers in Unsaturated Porous Media—Effect of Mass Transfer Limitations

Imhoff

2005

Vadose Zone Journal

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saturation in the vadose zone (Whitley et al., 1999; Dwarakanath et al., 1999;Nelson et al., 1999) and to Water saturation is a key parameter in studies of pollutant transport measure water saturation in lab-scale experimental sysin the vadose zone and an important factor controlling the rate of waste degradation in municipal solid waste landfills. The partitioning tems (Deeds et al., 1999a; Dwarakanath et al., 1999). interwell tracer test (PITT) has been suggested as a useful tool forRecently, this same technology has been used to meameasuring water saturation over large measurement volumes in both sure water in solid waste (Imhoff et al., 2003). systems. However, heterogeneous water distributions may result inDuring a field-scale PITT, injection and extraction mass transfer limitations, which can affect the accuracy of the measurewells are installed such that chemical tracers flow in the ments. In this study, we examined the influence of water saturation, zone of interest. This region typically contains mobile Henry's Law constant, injected tracer mass, tracer quantification limit, (e.g., air or water) and immobile (e.g., water and/or and local rates of mass transfer between air and water on PITT measure-NAPL) fluid phases. Partitioning tracers and a conserments. A single-region model was used to describe transport of gasvative tracer are injected simultaneously in the mobile phase tracers in a one-dimensional system and to investigate the effect phase into the injection well and later removed from of these factors on measurement error. To verify the conclusions drawn from this modeling exercise, laboratory-scale partitioning tracer tests the extraction well. Partitioning tracers partition into were conducted in four different sand packings. Finally, the results the immobile phases, retarding the transport of these from the mathematical modeling and laboratory experiments were tracers with respect to a conservative tracer. A compariused to suggest guidelines for minimizing measurement error in fieldson of partitioning and conservative tracer breakthrough scale PITTs for water saturation measurement.as the injected tracer mass decreased, and as the tracer Published

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Holdup and dispersion: tracer residence times, moments and inventory measurements

Cited by 32 publications

References 17 publications

Nonideal Transport of Contaminants in Heterogeneous Porous Media: 11. Testing the Experiment Condition Dependency of the Continuous Distribution Rate Model for Sorption–Desorption

Nonideal Transport of Contaminants in Heterogeneous Porous Media: 11. Testing the Experiment Condition Dependency of the Continuous Distribution Rate Model for Sorption–Desorption

Bioreactors: Airlift Reactors

Water Saturation Measurements by Gas Tracers in Unsaturated Porous Media—Effect of Mass Transfer Limitations

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