Particle residence time distribution and axial dispersion coefficient in a pressurized circulating fluidized bed by using multiphase particle-in-cell simulation

The particle residence time distribution(RTD)and axial dispersion coefficient are key parameters for the design and operation of a pressurized circulating fluidized bed(PCFB).In this study,the effects of pressure(0.1-0.6 MPa),fluidizing gas velocity(2-7 m·s^(-1)),and solid circulation rate(10-90 kg·m^(-2)·s^(-1))on particle RTD and axial dispersion coefficient in a PCFB are numerically investigated based on the multiphase particle-in-cell(MP-PIC)method.The details of the gas-solid flow behaviors of PCFB are revealed.Based on the gas-solid flow pattern,the particles tend to move more orderly under elevated pressures.With an increase in either fluidizing gas velocity or solid circulation rate,the mean residence time of particles decreases while the axial dispersion coefficient increases.With an increase in pressure,the core-annulus flow is strengthened,which leads to a wider shape of the particle RTD curve and a larger mean particle residence time.The back-mixing of particles increases with increasing pressure,resulting in an increase in the axial dispersion coefficient.

Residence time distribution of high viscosity fluids falling film flow down outside of industrial-scale vertical wavy wall: Experimental investigation and CFD prediction

The flow behavior of gravity-driven falling film of non-conductive high viscosity polymer fluids on an industrial-scale vertical wavy wall was investigated in terms of film thickness and residence time distribution by numerical simulation and experiment.Falling film flow of high viscosity fluids was found to be steady on a vertical wavy wall in the presence of the large film thickness.The comparison between numerical simulation and experiment for the film thickness both in crest and trough of wavy wall showed good agreement.The simulation results of average residence time of falling film flow with different viscous fluids were also consistent with the experimental results.This work provides the initial insights of how to evaluate and optimize the falling film flow system of polymer fluid.

Distribution, residence time, autotrophic production, and heterotrophic removal of DOP in the Mirs Bay, northern South China Sea

The importance of dissolved organic phosphorus(DOP) as a potential nutrient source for primary producers in marine systems has been recognized for up to eight decades, but currently, the understanding of the biogeochemistry of DOP is in its infancy. In the present study, monthly data between 2000 and 2014 were used to analyze the temporal and spatial distributions of DOP in the Mir Bay, the northern South China Sea. The DOP residence time(TDOP) was also investigated using a simple regression analysis in combination with chlorophyll a(Chl a) measurements while excess DOP(ΔDOP), produced by the biogeochemical processes of autotrophic production and heterotrophic removal, was determined using a two-component mixing mass-balance model in combination with salinity measurements. The results showed that the DOP concentration was(0.017±0.010) mg/L higher in the surface-water compared with the bottom-water and higher in the inner Tolo Harbour and waters adjacent to Shatoujiao compared with the main zone of the bay. Although seasonal changes and annual variability in the DOP were small, the surface DOP concentration was higher in the wet season(April–September)than in the dry season(October–March) due to the impacts of seaward discharges and atmospheric deposition into the bay. Measurement and regression results showed that the DOP release rate from phytoplankton production was about 1.83(gP)/(gChl a) and the TDOP was about 7 d, which implied that the DOP cycle in the bay was rapid. The ΔDOP was calculated from the model to be about 0.000 mg/L in the main zone of the bay and about 0.002 mg/L in the inner Tolo Harbour and waters adjacent to Shaotoujiao, suggesting that the autotrophic production of DOP was almost balanced by the heterotrophic removal in the main zone of the bay and dominated in the inner Tolo Harbour and waters adjacent to Shaotoujiao. In conclusion, the Mirs Bay is very productive and fairly heterotrophic.

Modeling on Residence Time Distribution in Subsurface Flow Constructed Wetlands by Multi Flow Dispersion Model

As an important design factor for constructed wetlands,hydraulic retention time and its distribution will affect the treatment performance.Instantaneously injected sodium chloride tracers were used to obtain residence time distributions of the lab scale subsurface flow constructed wetland.Considering the presence of trailing and multiple peaks of the tracer breakthrough curve,the multi flow dispersion model(MFDM)was used to fit the experimental tracer breakthrough curves.According to the residual sum of squares and comparison between the experimental values and simulated values of the tracer concentration,MFDM could fit the residence time distribution(RTD)curve satisfactorily,the results of which also reflected the layered structure of wetland cells,thus to give reference for application of MFDM to the same kind of subsurface flow constructed wetlands.

RESIDENCE TIME DISTRIBUTION STUDIES WITH TRACER EXPERIMENTS:IMPULSE INJECTION VERSUS STEP CHANGE OF FEED

1 INTRODUCTIONThe popularly used axial dispersion model is mathematically expressed by aone-dimensional partial differential

ON THE RESPONSE FUNCTION AND RESIDENCE TIME DISTRIBUTION OF THE AXIAL DISPERSION MODEL FOR TUBULAR REACTORS

In view of confusion on the residence time distribution and transfer fucntions for dispersion models, the solution of the model subject to possible combinations of closed and open type boundaries at the ends of a chemical reactor is investigated systematically. In particular, some new results are obtained for the closed-open and open-closed types of reactors. It is found that the interchange of boundary conditions for these reactors is not immaterial. In several cases, caution is necessary to distinguish whether the transfer function is applied to the concentration or the flux. When the dispersive flux is notable, measurement techniques must be carefully selected to match the kind of transfer functions derived.

RESIDENCE TIME DISTRIBUTION IN AN OPEN REACTOR:EFFECT OF BACKGROUND REACTANT ON TRACER DISPERSION

A new approach is presented for deriving the residence time distribution(RTD)in open-type reactors with exclusion of residence in the fore section.Inasmuch as failure to predict the con-version of chemical reactions has been evidenced in many occasions,numerical solution of tracerdispersion in the presence of background concentration gradient of reactant is given to demonstratethe strong effect of background reactant on the true RTD a reactant molecule experiences.Withinthe error of computation,the conversion of a first-order chemical reaction under steady state is shownto be equal in both closed and open reactors,despite difference in relevant

THE RESIDENCE TIME DISTRIBUTION FOR MULTIFLOW SYSTEM

In this paper,the superposition rule of the residence time distribution functions for the general systemhaving multiple inlet and outlet streams has been described and proved rigorously.For the cascade ves-sels system where the processed material in separate stages may be nonideally mixed in various degrees andthe volumes of separate stages may not be equal,the overall residence time distribution function E(t)and eachE(t)of the flow systems have been derived.The applications of these results to various flow systems havebeen discussed.

Gas Residence Time Distributions in a Spouted Bed

In a spouted bed of 80mm in ID and 1700mm in height, the gas residence time distributions at different radial positions in both spout and annular area were measured with five different kinds of particles as spouting material, air as spouting gas, and hydrogen as tracer. The effects of superficial gas velocity, operating pressure, particle size and its category on gas residence time distribution were discussed. It was found that the gas velocity profile in spout was more uniform than that in annulus. It could be concluded that the gas flow in the spout could be treated as a plug-flow, while that in the annulus inhibited a strong non-ideal flow behavior. Increasing the superficial gas velocity and decreasing the operating pressure, the particle density and its size gave rise to spouting disturbance, thus the measured tracer concentrations vs. time curves fluctuated. The variances of residence time distribution curves could be taken as a measure of the gas fluctuation degree.

Numerical analysis on the transport properties and residence time distribution of ribbon biomass particles in a riser reactor based on CFD-DEM approach

A bended ribbon biomass particle model was developed to explore the dynamic transport properties inside a riser reactor.Residence time distribution(RTD)of the particles was analyzed by using the Eulerian-Lagrange method.The effects of sampling height,particle density,particle size and gas-to-solid mass ratio on RTD were investigated.The coupled Computational Fluid Dynamics and Discrete Element Method(CFD-DEM)model was verified firstly by experimental data on pressure drop and residence time distribution density function.The simulation results demonstrated that the ribbon biomass particles display a typical annular-core spatial distribution during transportation.The RTD of particles exhibit an approximate single-peaked normal distribution.The mean residence time(MRT)can reach up to 0.7 s when the particle density is 1200 kg/m^(3).Particle with higher density has longer mean residence time.The flow patterns are closer to plug flow if particle length over 12 mm.The particle flow pattern is not sensitive to changes in particle density and size,while the gas-to-material mass ratio has a significant impact on it.

Numerical simulation of flow field and residence time of nanoparticles in a 1000-ton industrial multi-jet combustion reactor

In this work,by establishing a three-dimensional physical model of a 1000-ton industrial multi-jet combustion reactor,a hexahedral structured grid was used to discretize the model.Combined with realizable k–εmodel,eddy-dissipation-concept,discrete-ordinate radiation model,hydrogen 19-step detailed reaction mechanism,air age user-defined-function,velocity field,temperature field,concentration field and gas arrival time in the reactor were numerically simulated.The Euler–Lagrange method combined with the discrete-phase-model was used to reveal the flow characteristics of particles in the reactor,and based on this,the effects of the reactor aspect ratios,central jet gas velocity and particle size on the flow field characteristics and particle back-mixing degree in the reactor were investigated.The results show that with the decrease of aspect ratio in the combustion reactors,the velocity and temperature attenuation in the reactor are intensified,the vortex phenomenon is aggravated,and the residence time distribution of nanoparticles is more dispersed.With the increase in the central jet gas velocities in reactors,the vortex lengthens along the axis,the turbulence intensity increases,and the residence time of particles decreases.The back-mixing degree and residence time of particles in the reactor also decrease with the increase in particle size.The simulation results can provide reference for the structural regulation of nanoparticles and the structural design of combustion reactor in the process of gas combustion synthesis.

An Estimation Method for Kill Probability Based on Random Residence Time Series

Relations between statistical residence time series and effective shooting are analyzed in accordance with the properties of the random residence time of maneuver targets crossing shot area in a given time. An estimation method for kill probability is proposed, which solves the probability of number of residence times satisfied effective shooting in given time. Some expressions and their approximate formulae of kill probability are derived, under known the distribution of residence time series. Theoretical analysis and simulation results show that this method is suitable for evaluating the hit ability of fire system for maneuver targets in random shooting.

Residence time distribution and heat/mass transfer performance of a millimeter scale butterfly-shaped reactor

A millimeter scale butterfly-shaped reactor was proposed based on sizing-up strategy and fabricated via femtosecond laser engraving. An improvement of mixing performance and residence time distribution was realized by means of contraction and expansion of the reaction channel. The liquid holdup was greatly increased through connection of multiple mixing units. Structure optimization of the reactor was carried out by computational fluid dynamics simulation, from which the effect of reactor internals on mixing and the influence of parallel branching structure on heat transfer were discussed. The UV–vis absorption spectroscopy was used to determine the residence time distribution in the reactor, and characteristic parameters such as skewness and dimensionless variance were obtained. Further, a chained stagnant flow model was proposed to precisely describe the trailing phenomenon caused by fluid stagnation and laminar flow in small scale reactors, which enables a better fit for the experimental results of the asymmetric residence time distribution. In addition, the heat transfer performance of the reactor was investigated, and the overall heat transfer coefficient was 110–600 W m^(-2)K-1in the flow rate range of 10–40 m L/min.

The Relationship Between Hysteresis and Liquid Flow Distribution in Trickle Beds

Experiments were conducted on a trickle bed with 0.283 m ID to eluddate the relation-ship between hysteretic phenomena and liquid distribution. The hysteresis of pressure drop and the variance of radial liquid distribution were observed simultaneously. Residence time dlstribu-tion (KTD), holdup and mean residence time (RT) of liquid phase were also found to demonmtrate hystereels of the same nature. RTD, liquid holdup and mean RT calculated with a simple model from the distribution of liquid flow rate show chaxacteristic consistant with the experlmeataJ data, suggesting that the hyteretic phenomena originate from the multiplicity and nonuniformity of liquid flow distribution.

Scale-up of bubbling fluidized beds with continuous particle flow based on particle-residence-time distribution

Few studies have investigated scale-up of the residence-time distribution （RTD） of particles in bubbling fluidized beds （BFBs） with continuous particle flow. Two approaches were investigated in this study： first, using well-known scaling laws that require changes in particle properties and gas velocity; second, using a simple approach keeping the same particles and gas velocity for different beds. Our theoretical analysis indicates it is possible to obtain similar RTDs in different BFBs with scaling laws if the plug-flow residence time （tpiug） is changed as m^0.5, where m is the scaling ratio of the bed; however, neither approach can ensure similar RTDs if tplug is kept invariant. To investigate RTD variations using two approaches without changing tplug, we performed experiments in three BFBs. The derivatives dE（θ）/dθ （where E（θ） is the dimensionless RTD density function and θ is the dimensionless time） in the early stage of the RTDs always varied with m 1, which was attributed to the fact that the particle movement in the early stage were mainly subject to dispersion. Using the simple approach, we obtained similar RTDs by separately treating the RTDs in the early and post-stages. This approach guarantees RTD similarity and provides basic rules for designing BFBs.

Onset velocity of circulating fluidization and particle residence time distribution:A CFD-DEM study

Until now, the onset velocity of circulating fluidization in liquid-solid fluidized beds has been defined by the turning point of the time required to empty a bed of particles as a function of the superfcial liquid velocity, and is reported to be only dependent on the liquid and particle properties. This study presents a new approach to calculate the onset velocity using CFD-DEM simulation of the particle residence time distribution （RTD）. The onset velocity is identified from the intersection of the fitted lines of the particle mean residence time as a function of superficial liquid velocity. Our results are in reasonable agreement with experimental data. The simulation indicates that the onset velocity is infuenced by the density and size of particles and weakly affected by riser height and diameter, A power-law function is proposed to correlate the mean particle residence time with the superficial liquid velocity. The collisional parameters have a minor effect on the mean residence time of particles and the onset velocity, but influence the particle RTD, showing some humps and trailing. The particle RTD is found to be related to the particle trajectories, which may indicate the complex flow structure and underlying mechanisms of the particle RTD.

Numerical Investigation of Residence Time Distribution for the Characterization of Groundwater Flow System in Three Dimensions

How to identify the nested structure of a three-dimensional(3D)hierarchical groundwater flow system is always a difficult problem puzzling hydrogeologists due to the multiple scales and complexity of the 3D flow field.The main objective of this study was to develop a quantitative method to partition the nested groundwater flow system into different hierarchies in three dimensions.A 3D numerical model with topography derived from the real geomatic data in Jinan,China was implemented to simulate groundwater flow and residence time at the regional scale while the recharge rate,anisotropic permeability and hydrothermal effect being set as climatic and hydrogeological variables in the simulations.The simulated groundwater residence time distribution showed a favorable consistency with the spatial distribution of flow fields.The probability density function of residence time with discontinuous segments indicated the discrete nature of time domain between different flow hierarchies,and it was used to partition the hierarchical flow system into shallow/intermediate/deep flow compartments.The changes in the groundwater flow system can be quantitatively depicted by the climatic and hydrogeological variables.This study provides new insights and an efficient way to analyze groundwater circulation and evolution in three dimensions from the perspective of time domain.

Residence time distribution and modeling of the liquid phase in an impinging stream reactor

Based on some experimental investigations of liquid phase residence time distribution(RTD)in an impinging stream reactor,a two-dimensional plug-flow dispersion model for predicting the liquid phase RTD in the reactor was proposed.The calculation results of the model can be in good agreement with the experimental RTD under different operating conditions.The axial liquid dispersion coefficient increases monotonously with the increasing liquid flux,but is almost independent of gas flux.As the liquid flux and the gas flux increase,the liquid dispersion coefficient of center-to-wall decreases.The axial liquid dispersion coefficient is much larger than that of center-to-wall,which indicates that the liquid RTD is dominated mainly by axial liquid dispersion in the impinging stream reactor.

Optimization of residence time distribution in RCDG and an assessment of its applicability in continuous manufacturing

Knowledge of residence time is a critical aspect in developing control and material diversion strategies for continuous manufacturing processes in pharmaceutical manufacturing.Dry granulation is a promising continuous granulation technique as it is fast and economical.In this study,a step-change method to determine residence time in roll compaction/dry granulation is introduced.The factors roll speed and rotational speed of the impeller in the powder inlet unit of the compactor were evaluated using a central composite circumscribed statistical design of experiments in order to optimize the residence time.The fill volume in the compactor was varied exemplarily.It was found that high roll speed,low rotational speed of the impeller and low fill volume in the compactor are beneficial to generate fast transition through the compactor.The impact of roll speed increase was estimated.It can be concluded that despite fast residence time in the process,high roll speed and its subsequent high material throughput can generate a large amount of material that has to be discarded if material diversion is required.