Dispersed Plug Flow Research Articles

Residence time distribution measurements and flow modeling in a supercritical water oxidation reactor: Application of transfer function concept

Residence time distribution (RTD) measurements are carried out in a flow-through tubular supercritical water oxidation (SCWO) reactor using ex situ pulse response experiments. The experiments are performed from ambient to supercritical water conditions with a volumetric flow rate fixed at 1 ml/min. The transfer function concept is used to interpret tracer information and to elucidate hydrodynamic flow patterns inside the “hot zone” of the reactor vessel. The experimental RTD curves are modeled by an axially dispersed plug flow. At supercritical conditions, the studied tubular SCWO reactor can be characterized as a mixed flow system (with Péclet numbers of 1.4–2). The results also indicate the presence of fast preferential fluid flow in the reactor below 573 K and 10 MPa.

ION EXCHANGE COLUMN PERFORMANCE MODEL FOR SEPARATION OF ZR (IV) AND HF (IV) IN ELUTION PROCESS

A mathematical model of sorption of Zirconium and Hafnium cations mixture and elution of these ions from a cation exchange resin bed is developed. Sulfuric acid is selected as the eluent for selective separation of Zr and Hf in a packed bed of Dowex cation exchange resin. The column model is a dispersed plug flow model,and assumed to consist of randomly packed synthetic and spherical resin beads with constant diameter. The beads are assumed to be porous containing not only active sites on their solid structure but also solution-filled pores. The model incorporates mass transfer resistances including inter and intra-particle effects within the solid and fluid phases. Intra-particle diffusion is treated by employing pore diffusion model. The adsorption phenomena of the cations on the active sites is expressed by the equilibrium relationship characterized by a form of the extended Langmuir equation. The batch experiments are carried out in order to determine Langmuir parameters at equilibrium, and pore diffusivity at transitional conditions. These parameters are used in the dynamic model of adsorption and desorption of the mentioned cations. Unlike a number of earlier models the present mathematical model does not have assumptions such as the linearity of the sorption isotherms, uniform concentration profile in the resin particles and ideal plug liquid flow along the bed. It is found that the present model predicts the breakthrough and chromatographic curves with a fair degree of accuracy. It is concluded that the eluent acid concentration and flow rate of the liquid along the bed are the most two important variables which influence the efficiency of separation.

Modelling of the residence time distribution in micromixers

Abstract A technique for the measurement of the residence time distribution (RTD) in microfluidic devices is presented. The measurements were performed by an input–response technique monitoring a dye tracer concentration spectroscopically at the inlet and outlet of a microfluidic device. The measurement setup ensures the interchangeability of microfluidic devices and thus allows characterising of many different devices containing diverse mixing structures and microchannel geometries. Since the experimental method is based on an external stimulus the measured RTD data show deviations from the actual RTD of the microfluidic device. These deviations are caused by the connected capillaries and their contribution to the overall RTD of the whole system. Therefore, modelling of the RTD is necessary. Two different models were applied in this study. The first one is the well-known axially dispersed plug flow model which is often used for macroscopic reactors. Since this model was developed for plug flow processes, its applicability to the laminar flow regime of microfluidic devices is strongly limited. Therefore, another empirical model was developed and applied in order to consider a wider range of different microstructures and process parameters. The RTDs of three different micromixers were investigated in a specified range of flow rates and modelled with the empirical model. Based on these results the mixing performance and integral flow behaviour of the different reactors could be analysed and discussed.

An extended macroscopic model for solute dispersion in confined porous media

Abstract In the analysis of longitudinal dispersion data in a classical laboratory experiment, it is usually assumed that the dispersion of species undergoes Fickian behaviour with constant dispersivities. If the length and time scales of an experiment are not sufficient for a tracer to traverse the cylinder radius and sample the velocity variations, this could give rise to persisting non-Fickian transients that cannot be predicted by the conventional plug flow dispersion models. Such transients cause the deviation from the Gaussian concentration distribution predicted by the plug models. In this paper, some shortcomings of the Fickian model are examined and a more general non-Fickian macroscopic dispersion model is provided to give insight into some of the factors that contribute to the dispersion process. The analysis describes the transient development of the solute spread and some non-Fickian effects associated with it. The extended model provides a set of conditions under which the classical axial plug dispersion model can be applicable. The model results for tracer dispersion in cylindrical packed beds show that the longitudinal dispersion coefficient converges to its asymptotic value on a time-scale proportional to R 2 /〈 D T 〉 where R is the cylinder radius and 〈 D T 〉 represents the mean value of the radial dispersion coefficient D T ( r ) over the cross-section of the bed.

Hydraulic characteristics of biological filters.

Relationships between the removal efficiency and the hydraulic regimes of trickling filters were investigated. At low flow rates, where break-up of liquid jets occurs and drops form, completely mixed conditions prevail. For large hydraulic loadings effluent concentrations were calculated by means of a dispersed plug flow model. The ranges of validity of these models were studied theoretically. The effects of drop formation and breakage of liquid jets on the substrate utilization are expressed in terms of hydraulic and physical properties of the media and liquid.

Residence Time Distribution in Tubular Joule Effect Heaters with and without Geometric Modifications

AbstractIn the food industry, heat treatment of highly viscous fluids in continuous processes is becoming more and more common, and the process should perform as a homogenous thermal treatment, in order to ensure quality and safety of the final product. To improve treatment homogeneity, geometric modifications can be used even in the laminar regime, to induce flow perturbation and mixing. The objectives of this work include: (i) Investigation of the residence time distribution (RTD) for industrial indirect Joule effect heaters (JEH), with smooth (ST) and modified (MT) tubes, (ii) Demonstration and quantification of the efficiency of the geometrical modifications, and (iii) Proposition of a single semi‐empirical model including the flow regime (10 < Re < 2000) and tube diameters (18 and 23 mm). The results obtained confirm that the simple Dispersed Plug Flow (DPF) model is not adaptable to small Reynolds numbers. Further analysis demonstrates that certain geometrical modifications improve the treatment homogeneity by increasing the plug flow contribution and reducing the value of the reduced variance. These beneficial effects increase when the Reynolds number is increased, the nominal diameter is reduced, and modified tubes are used. The proposed model enables the prediction of the RTD in JEH with an accurate degree of confidence.

Adsorption process on fixed bed column in rich organic wastewater treatment experimental studies and numerical simulation

None axially dispersed plug flow model (NADPF) was applied to simulate adsorption process on fixed bed column. To determine model input parameters and verify the model, isotherm curve, solid diffusion coefficient (\(D_s\)) and breakthrough curve have been determined from experiment. Activated carbon SWW 210&220 was selected as the main adsorbent for research. Wastewater of Minhkhai Textile Company is the sample used in experiment study. According to isotherm function, textile wastewater is poorly adsorbed into SWW210&220. Kinetic data also show that diffusion step of textile wastewater is very slow (DS ~ 1.31*\(10^{-13}\) m\(^2\)/s). With textile wastewater, NADPF model can be used to simulate adsorption process.

Heat transfer of gas flow through a packed bed

This paper reports an experimental study of both the transient and steady-state heat transfer behaviour of a gas flowing through a packed bed under the constant wall temperature conditions. Effective thermal conductivities and convective heat transfer coefficient are derived based on the steady-state measurements and the two-dimensional axial dispersion plug flow (2DADPF) model. The results reveal a large temperature drop at the wall region and the temperature drop depends on the axial distance from the inlet. The 2DADPF model predicts the axial temperature distribution fairly well, but the prediction is poor for the radial temperature distribution. Length-dependent behaviour of the effective heat transfer parameters and non-uniform flow behaviour are proposed to be responsible. A comparison with previously published correlations and data in the literature shows that the relationships proposed by Bunnell et al. and Demirel et al. agree well with the measured effective radial thermal conductivity, whereas the wall–fluid heat transfer coefficient is better represented by the Li–Finlayson correlation.

Gas and solids mixing in a dynamically scaled fluid coker stripper

Gas mixing and solids mixing were studied in a geometrically and dynamically scaled cold model fluid coker stripper. Tracer gas (helium) was first injected into the stripper standpipe to quantify total gas entrainment into the underflow stream. Tracer gas was then injected into the upper reactor and lower stripper separately to investigate gas mixing in the stripper. The stripping efficiency was found to depend strongly on operating conditions (solids circulation rate, stripping gas velocity) as well as on the baffle configuration in the stripper. Unsteady state measurements were also obtained in an effort to understand gas dispersion in the stripper. The results show that gas mixing is most intensive in the stripper core. To study solids mixing and residence time distribution in the stripper, solid tracer particles impregnated with salt were injected into the reactor and detected at the top of the stripper and standpipe. The results indicate that axial dispersion of solids in the presence of the baffles could be represented by axially dispersed plug flow.

Dispersed plug flow model for upflow anaerobic sludge bed reactors with focus on granular sludge dynamics

A new approach to model upflow anaerobic sludge bed (UASB)-reactors, referred to as a one-dimensional dispersed plug flow model, was developed. This model focusses on the granular sludge dynamics along the reactor height, based on the balance between dispersion, sedimentation and convection using one-dimensional (with regard to reactor height) equations. A universal description of both the fluid hydrodynamics and granular sludge dynamics was elaborated by applying known physical laws and empirical relations derived from experimental observations. In addition, the developed model includes: (1) multiple-reaction stoichiometry, (2) microbial growth kinetics, (3) equilibrium chemistry in the liquid phase, (4) major solid-liquid-gas interactions, and (5) material balances for dissolved and solid components along the reactor height. The integrated model has been validated with a set of experimental data on the start-up, operation performance, sludge dynamics, and solute intermediate concentration profiles of a UASB reactor treating cheese whey [Yan et al. (1989) Biol Wastes 27:289-305; Yan et al. (1993) Biotechnol Bioeng 41:700-706]. A sensitivity analysis of the model, performed with regard to the seed sludge characteristics and the key model parameters, showed that the output of the dispersed plug flow model was most influenced by the sludge settleability characteristics and the growth properties (especially mu(m)) of both protein-degrading bacteria and acetotrophic methanogens.

A phenomenological model for the gas phase flow in high-aspect-ratio stirred vessels: the role of small bubbles in non-coalescent and moderately viscous liquids

A crucial issue in the characterisation of gas–liquid stirred systems is the choice of a suitable model to describe the fluid dynamic features of both the liquid and gas phases. In spite of increasing attention to CFD tools, semi-empirical models are still extremely useful to interpret experimental data and to provide an insight into the physics of these systems with an affordable effort. Two types of problems arise in connection with the use of a model like plug flow with dispersion (PFD) for describing the gas phase with viscous liquids and, to a more limited extent, non-coalescent systems: inaccurate K L a data (when measured with dynamic techniques) and unrealistic Peclet numbers (this last being the parameter of the PDF model). Both problems can be attributed to the assumption of a single, unstructured phase for the ensemble of the gas bubbles. In the present paper, a two gas fraction model was introduced and used to interpret the experimental gas RTD curves in low to moderately viscous solutions in vessels stirred with triple impellers of two types (Rushton turbines and BT-6 impellers). Water, sulphate (non-coalescent) and (moderately) viscous PVP solutions were used. Two fractions of the gas hold-up were considered: large bubbles, whose behaviour was described with the usual PFD model, and small bubbles that were considered as perfectly mixed. The main parameters of the model are the Peclet number of the large bubbles fraction and the volumetric fraction of the large bubbles. The model proved capable to interpret the experimental RTD curves of the gas phase obtained after a pulse disturbance at the inlet. A comparison of the estimated volume fractions of small-size gas bubbles with experimental transient hold-up measurements was also carried out and good agreement was obtained. This study suggests the existence of a critical bubble size, which discriminates between the mixed and the plug flow behaviour of the small and large bubbles. The action of an antifoam agent on the hold-up structure was also studied for a single condition.

Residence Time Distribution Characterization of the Flow Structure in Dissolved Air Flotation

A numerical and analytical investigation is performed on a dissolved air flotation (DAF) pilot tank by using the residence time distribution (RTD) of the conservative dye rhodamine measured with a fluorometer. The experiments are numerically analyzed with regard to the total volume of the DAF tank separation zone in order to detect differences between observed separation zone flow structures in previous studies. The mean hydraulic detention time, the variance, and the estimated number of completely mixed tanks (N-cstr) in a series model are calculated. The variance is found to relate to the flow structure and the N-cstr is used for characterizing the occurrence of a stratified flow structure, which is beneficial for particle separation by DAF. The result shows a significant difference in RTD depending on expected flow structure. Analytically, a conceptual model is defined by dividing the DAF tank into an upper and a lower layer. In the upper layer, the water flow is horizontal and in the lower the water flow is vertical. The hypothesis is that mixing of the tracer takes place in the upper layer and that there is no significant mixing in the lower layer. Two simple mixing models are evaluated for the upper layer; the completely mixed tanks in series model, characterized by the number of tanks, and the dispersed plug flow model, characterized by the Peclet number. The models show good agreement with the experiments when the stratified flow structure is expected, but less agreement when the flow deviates from the stratified flow structure. The dispersed plug flow model shows the best fit with the experiments. The completely mixed tanks in series model is less sensitive, generating greater changes to the modeled RTD curve, which makes it more difficult to fit the model to the experiments. (Less)

Removal of Chloride in the Kraft Chemical Recovery Cycle of Pulp Mills Using the Ion-Exchange Process

High levels of chloride in the kraft recovery cycle of pulp mills can cause serious problems, particularly in recovery boiler operation. The treatment of ash collected from the electrostatic precipitator (ESP) for chloride removal was investigated experimentally using the ion-exchange process based on an amphoteric resin (BIORAD AG 11 A8). Saturation and regeneration experiments in a fixed bed were carried out for different flow rates. Experimental adsorption results obtained in the saturation step were well predicted with a mathematical model that takes into account dispersed plug flow for the bulk liquid, external mass-transfer resistance, intraparticle mass transfer by pore diffusion, and instantaneous equilibrium of adsorption at the pore/wall interface. The equilibrium was modeled using an extended Langmuir−Freundlich isotherm for three components (Cl-, SO42-, and CO32-) based on single-component equilibrium data. The resin performance was tested during cyclic operation, in which a chloride removal e...

A new kinetic model for titanium dioxide mediated heterogeneous photocatalytic degradation of trichloroethylene in gas-phase

This paper focuses on the kinetics of photocatalytic removal and carbon mineralization of gaseous trichloroethylene (TCE) on near-UV irradiated TiO2 Degussa P25. Experiments were carried out in a flat-plate photoreactor at TCE inlet concentrations of 100–500ppmv, relative humidities (RH) of 0–62% and gas residence times of 2.5–60.3s. Gas residence time distribution (RTD) curves revealed an axial dispersed plug flow in the photoreactor with Peclet numbers above 59.4. For all experimental conditions, the carbon mineralization efficiency (5.1–73.0%) was lower than the removal efficiency (8.6–99.9%) and dichloroacetylchloride (DCAC) was detected as a gas-phase degradation product. TCE removal efficiencies increased with lower TCE inlet concentrations, lower RH and higher gas residence times. Evaluating different kinetic models by least squares analysis, it was shown that the Langmuir–Hinshelwood (LH) model could not give an adequate fitting to the experimental results. A new kinetic model, explicitly taking into account electron–hole pair reactions, was developed based on linear TCE adsorption–desorption equilibrium and first order reaction kinetics. The new kinetic model described the experimental results in a more accurate way, as exemplified by a more randomly distributed set of residuals and by a reduction of the sum of squares (SSQ) by a factor 1.7–8.5. The effect of TCE gas-phase concentration, RH and light intensity on adsorption–desorption kinetics, electron–hole concentrations and chemical conversion rates is discussed.

Flow Characterization of Moving and Stirred Bed Vacuum Pyrolysis Reactor from RTD Studies

Experiments were conducted in a moving and stirred bed vacuum pyrolysis reactor handling polydispersed softwood bark feedstock to study flow characteristics as functions of feed throughput, agitation speed, particle size and shape. A new idea of polydispersed fluorescent tracers was employed for the first time to investigate the residence time distribution (RTD), mean residence time and reactor hold-up. A single parameter dispersed plug flow model and an identical CSTRs-in-series model have been successfully used to fit the experimental data. Correlations are proposed for mean residence time, reactor hold-up, vessel dispersion number and number of identical CSTRs-in-series in terms of operating variable, for example feed throughput and agitation speed in the range of 20–70 kg hr–1 and 10–30 cm s–1, respectively.

Hydrodynamics of horizontal subsurface flow constructed wetlands

Constructed wetland hydrodynamics were modeled using mathematical tools generally employed in chemical engineering processes. The hydraulic residence time (HRT) distributions of the subsurface horizontal flow constructed wetland from Curienne (France) were estimated using the impulsion tracer method. A non-ideal flow wetland was first modeled by classical method: the dispersion plug flow model (DPFM), which gives a constant ratio to axial dispersion (the Peclet number Pe), and the stirred tanks in series model (STSM), which gives a number of stirred tank in series (NSTS). Six experimental HRTs were monitored to determine flow characteristics. Several periods were monitored to represent different seasons. It was found that evapotranspiration played a major role in summer by improving HRT.

Radial gas mixing in a fluidized bed using response surface methodology

Radial gas mixing in a fluidized bed was studied using response surface methodology (RSM), which enables effect examinations of parameters with a moderate number of experiments. All experiments were conducted in a 0.29-m ID fluidized-bed cold model. The gas dispersion process within the bed is described using the dispersed plug flow model. Pure carbon dioxide was used as the tracer gas, continuously injected into the center of the bed by a point source. The downstream radial tracer concentration profile was measured using a gas chromatograph. The radial gas dispersion coefficient, D r, was well correlated with operating parameters and the particle and gas properties: ( U− U mf)/ U mf, H s/ d b, φ d, and Ar, with a determination coefficient R 2 of 0.966. Effect test indicates that the dimensionless characteristic velocity, ( U− U mf)/ U mf, has the most significant influence on D r, while the static bed height to bed diameter ratio, H s/ d b, is less remarkable. The interactions of ( U− U mf)/ U mf with the distributor open-area ratio, φ d, and with the Archimedes number, Ar, both play important roles. An evolutive response surface model was proposed to describe the radial gas mixing in the bubbling/slugging fluidization regimes.

Dispersed plug flow model for steady-state laminar flow in a tube with a first order sink at the wall

Steady state, laminar flow transport in a tube with a first order sink at the wall involves two dimensions—radial and axial. In this paper, a novel iterative technique has been proposed for reducing such a two-dimensional model to an equivalent one-dimensional dispersed plug flow model. The latter yields an analytical expression for the equivalent axial dispersion and a simple, closed form, but approximate, analytical solution of the original two-dimensional problem. The operating range in which this analytical solution is useful has been investigated for a system with mass transfer at the wall.

Adsorption of Sulfur Dioxide from Pseudo Binary Mixtures on Hydrophobic Zeolites: Modeling of the Breakthrough Curves

The adsorption of SO2 from pseudo binary mixtures with water and CO2 on hydrophobic zeolites (MFI and MOR type) was investigated using the breakthrough curve method. The SO2 and water breakthrough curves were compared with theoretical ones based on an axially dispersed plug flow through the column and the linear driving force rate equation. In addition, different semi-predictive multi-component equilibrium equations were used for the breakthrough modeling: Langmuir 1, Langmuir 2 and Langmuir-Freundlich extended models. The overall mass transfer coefficients were derived by matching theoretical with experimental breakthrough curves for single component systems, i.e., water vapor or SO2 in a carrier gas. They were also predicted from a simplified bi-porous adsorbent model and compared with experimentally derived values. The presence of CO2 species in ternary mixtures with water vapor and SO2, even at relatively high concentrations of 9 vol%, had no significant effect on the breakthrough behavior of the other two species. For that reason the CO2 species was ignored in the analysis of the resulting pseudo binary mixtures. The breakthrough model was solved by finite element orthogonal collocation method using the commercial software gPROMS. Both extended Langmuir 1 and Langmuir 2 based models gave reasonable predictions of the water and SO2 breakthrough curves for pseudo binary mixtures involving a mordenite sample for all water concentration levels used in this study (up to 3.5 vol%). However, the same models were successfully used to predict SO2 breakthrough curves for a MFI sample only at low water concentrations, i.e., 1.5 vol%. At the higher water levels both models failed to describe equilibrium behavior in the MFI sample due to the introduction of multi-layer adsorption in the interstices between small MFI-26 crystals.

Alternative generation of H 2, CO and H 2, CO 2 mixtures from steam—carbon dioxide reforming of methane and the water gas shift with permeable (membrane) reactors

Replacing coal and oil with natural gas reduces greenhouse gas emissions without weakening economic development. Sorption enhanced steam methane reforming (SESMR) is an emerging process for an affordable transition towards cleaner energy systems, as it exploits natural gas coupled with in-situ CO2 capture to produce hydrogen. SESMR is performed on a steam reforming catalyst and a sorbent (cyclically regenerated by calcination) or, alternatively and more efficiently, on bi-functional Combined Sorbent-Catalyst Materials (CSCM). A double fluidized bed (reformer and oxyfuel combustor for calcination) with circulation of particulate material is anticipated for continuous SESMR at commercial scale. In this work, a Ni-CaO-mayenite CSCM was investigated in multicycle experimental tests under mild (pure N2, 850 °C) and severe (pure CO2, 925 °C) regeneration conditions, in thermogravimetric analysis for CO2-capture/regeneration and in an automated packed bed test rig for SESMR/calcination: the evolution of Ni and CaO functionalities as functions of cycle number was highlighted, also with the aid of scanning electron microscopy. Moreover, experimental results obtained with the hybrid material, collected under mild regeneration conditions, were used to simulate both CO2 sorption in TGA and packed bed SESMR multicycle tests: a Particle Grain Model (PGM) and an Axial Dispersion Plug Flow Reactor (ADPFR) model were integrated numerically, respectively. The same parameter values needed to characterize the material behaviour allowed a good fitting of both types of multicycle tests, thus demonstrating the possibility to use CO2-capture TGA data as a predictive tool for the CSCM performance in SESMR, provided that the catalytic activity is preserved.