The degree of mixing in continuous flow systems

Zwietering, Th.N.

doi:10.1016/0009-2509(59)80068-3

Cited by 417 publications

(171 citation statements)

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“…Although the reentry or accumulation of solute particles at the lower boundary is not physically realistic for advective flow, this phenomenon permits analytical solutions (8) and (9) to exhibit mean residence times unaffected by dispersion. This is unconditionally correct for closed systems [Danckwerts, 1953;Zwietering, 1959] or equivalently for column experiments where solute particles do not flow upstream and hence cannot reenter the domain once they have exited through the lower boundary.…”

Section: It Is Easily Verified That Substitution Of (2) Into (1) Yielmentioning

confidence: 99%

Boundary effects on solute transport in finite soil columns

Schwartz¹,

McInnes²,

Juo³

et al. 1999

Water Resources Research

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Abstract. This study investigates the influence of inlet and outlet disturbances and formulated boundary conditions on the estimation of the dispersion coefficient and retardation factor for short soil columns. Unsaturated miscible displacement experiments utilizing a Br-tracer were carried out on undisturbed columns of a fine-textured Ultisol. Solutions were applied using either a fritted plate or an array of dispensing tips that produced droplets at a prescribed flow rate. One-and two-layer analytical solutions of the advective-dispersive equation were fitted to effluent concentrations using nonlinear least squares parameter optimization. Comparison of two-layer simulations with experimental data indicated that the analytical solution with a semi-infinite interface boundary best approximated effluent concentrations under the conditions of this study. This solution corresponds to a continuous flux concentration and a macroscopically discontinuous resident concentration at the interface between the soil and porous plates. Parameter estimates were not significantly different with respect to the application method used at the inlet. This may be attributed to a less uniform distribution of solution onto the soil surface by the drip apparatus and/or by the presence of stagnant regions within the inlet reservoir and hence increased dispersion within the inlet platen apparatus. Two-layer simulations indicated that the dispersion coefficient was underestimated by 14-27% when the influence of the inlet and outlet apparatus were not included in the fitted solution of the advective-dispersive equation. In addition, use of one-layer analytical solutions caused the retardation factor to be overestimated by no more than the fractional increase in pore volume imparted by the platen apparatus. IntroductionStudies of solute transport are often limited to the analysis of breakthrough curves over relatively short longitudinal distances. For instance, soil vertical heterogeneity complicates the analysis of transport, and a complete description of the mechanisms often requires that each soil horizon be examined separately. In modeling the data obtained, one uses a mechanistic model with appropriate boundary and initial conditions to fit experimental breakthrough curves and quantify model parameters. When dispersivity is large in comparison to the distance from the inlet to the sampling point, the boundary conditions . Second, the use of reactive media with a wide range in particle size may introduce a certain degree of local nonequilibrium at high pore water velocities. Parker [1984] has shown that the analytical solution that prescribes a finite boundary at both the inlet and outlet fails to describe measured concentrations in the extreme case where local equilibrium between pore regions is not attained. In this paper we are principally concerned with slow pore water velocities where such effects are of minor importance, and hence the one-region advective-dispersive equation (ADE) should provide a good description to experimental...

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Section: It Is Easily Verified That Substitution Of (2) Into (1) Yielmentioning

confidence: 99%

Boundary effects on solute transport in finite soil columns

Schwartz¹,

McInnes²,

Juo³

et al. 1999

Water Resources Research

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“…The influence of the mixing in the reactive flows behaviour is widely reported in the literature, in particular in the processes that involve NO x [8,9]. The fundamental but simplified approach here considered is based on the description of the mixing process after Zwietering [10]. Comparison between experimental and calculated conversions.…”

Section: Resultsmentioning

confidence: 99%

Innovative technique for the control of NO_xformed in combustion processes

Verdone¹,

Scarsella²,

Liuzzo³

et al. 2010

WIT Transactions on Ecology and the Environment

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NO x formed in combustion processes is mainly constituted by nitrogen monoxide (NO) while nitrogen dioxide (NO 2 ) accounts for marginal concentration only. However, being NO 2 characterized by higher water solubility and equilibrium constant in the neutralization reaction operated with basic reactants, it is easily removed via dry or wet processes. On this basis an innovative process alternative to the conventional DeNO x SCR and SNCR can be envisaged, where the oxidation of NO to NO 2 makes the successive abatement of the oxidized fraction relatively easier. The scope of the work is the study of the oxidation of NO to NO 2 , considered as the controlling step of the proposed process, operated with hydrogen peroxide (H 2 O 2 ). A mathematical model of the oxidation has been developed in the Chemkin v. 3.7 environment, describing the gas phase kinetics in the energy recovery section of a generic combustion process through the Miller and Bowman (1989) kinetic mechanism. The base model has been improved with the introduction of the oxidation steps induced by the injection of hydrogen peroxide drawn from the literature. The NO oxidation reaction was investigated in a temperature range of 250-700°C, with a 20% excess of oxidizing agent with respect to the NO/oxidizer oxidation reaction stoichiometry. The experimental maximum conversion results are less than the calculated one of about 20%. The results of the model have been validated through experimental runs conducted in a bench scale pilot plant.

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“…Jetting leads to fluid elements that have a very short residence time and cause high values of E(t) at t > 0 s. Recirculation leads to fluid elements spending more time in the reactor, yielding middle values of E(t) as elements exit at t ∼ t. Stagnation (dead zones) at the inlet of the reactor cause fluid elements to remain entrained in the reactor for a long time before exiting the reactor at ∼ 2-3 × t at low values of E(t), leading to a long tail in the E curve. These three effects together lead to an E curve that looks similar to that of a CSTR, but mixing in CSTRs is dominated by recirculation, meaning that the local concentration of tracer at the exit is identical to all other locations in the reactor (Zwietering, 1959). Therefore, while tracer tests give a general idea about contacting patterns, CFD visualizes the hydrodynamics, and help model the reactor.…”

Section: Discussionmentioning

confidence: 99%

Assessing the degree of plug flow in oxidation flow reactors (OFRs): a study on a potential aerosol mass (PAM) reactor

Mitroo

Sun

Combest³

et al. 2018

Atmos. Meas. Tech.

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Abstract. Oxidation flow reactors (OFRs) have been developed to achieve high degrees of oxidant exposures over relatively short space times (defined as the ratio of reactor volume to the volumetric flow rate). While, due to their increased use, attention has been paid to their ability to replicate realistic tropospheric reactions by modeling the chemistry inside the reactor, there is a desire to customize flow patterns. This work demonstrates the importance of decoupling tracer signal of the reactor from that of the tubing when experimentally obtaining these flow patterns. We modeled the residence time distributions (RTDs) inside the Washington University Potential Aerosol Mass (WU-PAM) reactor, an OFR, for a simple set of configurations by applying the tankin-series (TIS) model, a one-parameter model, to a deconvolution algorithm. The value of the parameter, N, is close to unity for every case except one having the highest space time. Combined, the results suggest that volumetric flow rate affects mixing patterns more than use of our internals. We selected results from the simplest case, at 78 s space time with one inlet and one outlet, absent of baffles and spargers, and compared the experimental F curve to that of a computational fluid dynamics (CFD) simulation. The F curves, which represent the cumulative time spent in the reactor by flowing material, match reasonably well. We value that the use of a small aspect ratio reactor such as the WU-PAM reduces wall interactions; however sudden apertures introduce disturbances in the flow, and suggest applying the methodology of tracer testing described in this work to investigate RTDs in OFRs to observe the effect of modified inlets, outlets and use of internals prior to application (e.g., field deployment vs. laboratory study).

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The degree of mixing in continuous flow systems

Cited by 417 publications

References 1 publication

Boundary effects on solute transport in finite soil columns

Boundary effects on solute transport in finite soil columns

Innovative technique for the control of NO_xformed in combustion processes

Assessing the degree of plug flow in oxidation flow reactors (OFRs): a study on a potential aerosol mass (PAM) reactor

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The degree of mixing in continuous flow systems

Cited by 417 publications

References 1 publication

Boundary effects on solute transport in finite soil columns

Boundary effects on solute transport in finite soil columns

Innovative technique for the control of NOxformed in combustion processes

Assessing the degree of plug flow in oxidation flow reactors (OFRs): a study on a potential aerosol mass (PAM) reactor

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Product

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About

Innovative technique for the control of NO_xformed in combustion processes