Number of cycles distribution in circulating systems

The characterization of certain circulating systems in terms of the number of cycles distribution (NCD) of the fluid during operation is considered. The theory of stochastic processes is used to obtain the NCD from the cycle time distribution (CTD) for the system. The case of the gamma distributed CTD is solved explicitly and the limiting distribution of the NCD as the operating time becomes large is considered. It is shown that for long operating times, the NCD converges to a normal distribution whose mean and variance depend only on the mean and the variance of the CTD.     

Measurement of residence time distribution in microfluidic systems

We present a method for measuring the residence time distribution (RTD) in microfluidic systems. A piezoelectrically actuated sample injector releases approximately 100 nl of tracer liquid into a microchannel of rectangular cross section. The spreading of the tracer pulse in pressure-driven microflows is monitored with fluorescence microscopy measurements. Residence time distributions are determined for single-phase liquid and segmented gas-liquid microflows, with the RTD being significantly narrower for the latter case. The selected flow conditions are relevant to synthesis in microreactors with residence times up to several minutes.     

Residence time distribution of sorbent particles in a circulating fluidised bed boiler

The residence time distribution of limestone sorbent particles has been studied in order to increase the understanding of the conditions for sulphur capture in fluidised bed boilers. Two methods were used. The ‘steady state method’ involves the study of residence time for various particle size fractions. The ‘transient method’ is based on the transient increase in the amount of sorbent carryover with the fly ash, following initial limestone addition to a fresh bed (i.e. a bed with little or no sorbent). For the boiler investigated both methods gave similar results, showing that the major fraction of the sorbent, 80–85%, had a residence time of one hour or more.     

Residence time distribution function for multi-stage systems with backmixing

The residence time distribution functions for multistage systems with backmixing are derived. The effect of backmixing on the system behavior is analyzed. In addition, an analytical expression for the probabilities for backmixing is given.     

The limiting residence time distribution of continuous recycle systems

The limiting residence time distribution (RTD) of continuous recycle systems as the recycle ratio approaches infinity is considered. It is shown that the RTD converges to the exponential distribution whenever the system does not consist of a “dead volume” at the limit. This limiting behavior is independent of the system configuration and flow patterns. Issues concerning the proper modeling approach and the mathematical formulation of the condition that the system has no “dead volume” are discussed in detail. Some examples illustrating the importance of selecting the proper modeling approach are also provided.     

On the residence time distribution for systems with open boundaries

Tracer tests cannot in general be used to determine the residence time distribution in systems with open boundaries. However the most commonly employed model for such systems, the diffusion model, turns out to be exceptional in this respect: its residence time distribution is derived and found to resemble closely the impulse response function.The general problem is then viewed with reference to the lifespan and drop-out distributions which, together with the residence time distribution, characterize flow through open boundaries. The familiar result for closed systems that the mean residence time is equal to the ratio of system hold-up to flow rate is shown to apply also for open systems.     

Fluidization behavior in a circulating slugging fluidized bed reactor. Part I: Residence time and residence time distribution of polyethylene solids

Square nosed slugging fluidization behavior in a circulating fluidized bed riser using a polyethylene powder with a very wide particle size distribution was studied. In square nosed slugging fluidization the extent of mixing of particles of different size depends on the riser diameter, gas velocity, hold up and solids flux in the riser. Depending on the operating conditions the particle residence time distribution of a riser in the slugging fluidization regime can vary from that of a plug flow reactor to that of a well-mixed system.Higher gas velocities cause shorter particle residence times because of a significant decrease in the hold-up of particles in the riser at higher gas velocities. A higher solids flux also shortens the average residence time. Both influences have been quantified for a given polyethylene-air system.Residence time and residence time distribution were determined for different particle size and the influence of gas velocity, solids flux, hold up and riser diameter was studied. When comparing data from segregation and residence time experiments it is clear that segregation data can predict the spread in residence time as a function of overall residence time, particle size and gas velocity. The differential velocity between small and large particles found in the segregation experiments can predict the spread in residence time as found in the residence time distribution experiments with a powder with a broad particle size distribution. Raining of particles through the slugs was studied as a function of plug length, gas velocity and pulse length. It was found that raining is not the determining mechanism for segregation of particles.     

Particle residence time distributions in circulating fluidised beds

This paper gives experimental measurements of the particle residence time distribution (RTD) made in the riser of a square cross section, cold model, circulating fluidised bed, using the fast response particle RTD technique developed by Harris et al. (Chem. Eng. J. 89 (2002a) 127). This technique depends upon all particles having phosphorescent properties. A small proportion of the particles become tracers when activated by a flash of light at the riser entry; the concentration of these phosphorescent particles can subsequently be detected by a photomultiplier. The influence of the solids circulation rate and superficial gas velocity on the RTD were investigated. The results presented are novel because (i) the experiments were performed in a system with closed boundaries and hence give the true residence time distribution in the riser and (ii) the measurement of the tracer concentration is exceedingly fast. The majority of previous studies have measured the RTD in risers with open boundaries, giving an erroneous measure of the RTD.Analysis of the results suggests that using pressure measurements in a riser to infer the solids inventory leads to erroneous estimates of the mean residence time. In particular, the results cast doubt on the assumption that friction and acceleration effects can be neglected when inferring the axial solids concentration profile from riser pressure measurements.An assessment of particle RTD models is also given. A stochastic particle RTD model was coupled to a riser hydrodynamic model incorporating the four main hydrodynamic regions observed in a fast-fluidised bed riser namely (i) the entrance region, (ii) a transition region, (iii) a core-annulus region and (iv) an exit region. This model successfully predicts the experimental residence time distributions.     

The residence time distribution and mixing of the gas phase in the riser of a circulating fluidized bed

CFBs are increasingly used for both gas-catalytic and gas-solid reactions. The conversion is a function of the gas hydrodynamics, subject of the present research.Available literature on the gas mixing in the riser of a CFB shows contradictory results: some investigators neglected back-mixing of gas, whereas others report a considerable amount of back-mixing in CFB risers. The present paper reports experimental findings obtained in a 0.1 m I.D. riser, for a wide range of combined superficial gas velocity (U) and solid circulation flux (G). The gas flow mode (plug vs. mixed) is strongly affected by the operating conditions, however with a dominant mode within a specific (U, G)-range. Sand was used as bed material. The superficial gas velocity was varied from 5.5 to 8.3 m/s, the solids circulation flux was between 40 and 170 kg/m² s. A tracer pulse response technique was used with a pulse of propane injected at the bottom and detected at the riser exit. The cumulative response curves, F(t), define (i) an average residence time (t₅₀) obtained for F(t) = 0.5; and (ii) the slope of the curves (a steeper one corresponding with more pronounced plug flow) and expressed in terms of a span, σ. These parameters (t₅₀ and σ) define the gas flow mode. A quantitative comparison of experimental results with literature RTD-models is inconclusive although the occurrence of both mixed flow and plug flow is evident, and (U, G)-dependent. The experimental results are expressed in empirical design equations, and the comparison of predicted and experimental results is fair: low values of σ determine the plug flow regimes, whereas back-mixing is more pronounced at higher value of σ. Experiments with similar systems might favor plug flow or mixing as function of the combined (U, G)-values. The introduction of the RTD-function in reaction rate equations can improve the prediction of the gas-conversion in a riser-reactor.     

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.     

Population balance and residence time distribution models for well-mixed reactor and regenerator systems

By the use of population balance and residence time distribution models, the activity distribution and average activities in well-mixed vessels and in reactor-regenerator system are evaluated and discussed. Both methods give a same formula to evaluate the activity distribution for the catalysts in a well-mixed vessel with inlet catalysts of uniform or distributed activity. When the entrance catalysts have distributed activity and experience nonlinear deactivation or regeneration, the average activity calculated by both of these two methods, which are believed to be correct approaches, is not the same as that obtained by the average activity method currently used. Only the population balance model can be used to find the activity distribution functions and average activities in a reactor-regenerator system, in which the catalysts experience nonlinear deactivation and regeneration. For first order independent deactivation and regeneration, the average activity in each vessel of this system can be directly obtained from the moment equations without inverse transformation. Some design considerations for such a system are also presented.     

Residence time distribution in continuous crystallisers

The theory of continuous crystallisation (especially of sucrose) in crystallisers connected in series, in which a suspension of growing crystals is fed forward through the system without backmixing, is presented, and the calculation of the minimum coefficient of variation that can be attained under stated conditions is described. Two cases specifically considered are: (1) stirred reactors of equal mean residence times connected in series, and (2) tubular reactors in which the residence time distribution is given by a Gaussian error function. Reduction of coefficients of variation either by connecting reactors in series or by extending a tubular reactor in the axial direction is considered. Series connexion is always superior to extension because it prevents backmixing at the points of connexion.     

A model for residence time distribution in multistage systems with cross-flow between active and dead regions

A three-parameter mathematical model is suggested for expressing the residence time distribution in multistage systems. It is assumed that a fraction of the feed short-circuits each stage which comprises of an active backmix region and a dead region with cross-flow of the material between the two regions. The mass balance differential equations are solved using Laplace transformation. The computed results for different values of the parameters are presented and the model is compared with the available experimental data.     

Residence time distribution in twin-screw extruders

Twin screw extruders are finding increased usage in reacting and devolatilizing applications. Using self-wiping profiles, the twin screws fulfill the requirement that there be no “dead” or “unmixed” zones. Agitator design must be chosen with care so that a reasonable balance can be obtained between forwarding rate, surface-generation rate, vapor passageway, power, and axial mixing. Techniques have been developed for measuring residence time distributions and characterizing axial flow behavior. The method also permits direct determination of the holdup in starved barrel applications. Data on residence time distribution are presented for 4-in. diameter twin screw equipment with a variety of rotor configurations.     

水平液固循环流化床颗粒分布状况的实验研究

为使水平液固循环流化床换热器更好地强化传热和防垢、除垢,管中颗粒的分布是关键,因此对卧式换热器前管箱进行改造,采用双进料口并在前管箱加入挡板,使得颗粒在管路中分布均匀。在实验中自行设计了一套水平多管液固循环流化床实验装置。采用CCD图像采集系统,获得了颗粒的运动及分布状况。研究表明:挡板的角度、颗粒密度等对颗粒分布性能都有较大影响。通过对实验结果的分析,得到了使固体颗粒在管束中分布效果较好的挡板角度以及较适宜颗粒分布的运行参数,以指导工程放大应用。     

Preparation of macromolecular tracers and their use for studying the residence time distribution of polymeric systems

In this study, an easy route was developed to incorporate antracene moieties in polymer chains. It consisted of copolymerizing the monomer of a polymer of interest with 3-isopropenyl-α, α'-dimethylbenzyl isocyanate (TMI) and then reacting the isocyanate-bearing polymer with 9-(methylamino-methyl)anthracene. Such an antracene-bearing polymer was then used as a tracer (macrotracer) to determine the RTD function of polymers in a twin screw extruder and compared with an antracene as a microtracer. As long as the tracers were well mixed with a polymer of interest and the resulting mixture had the same geometrical form as the polymer before they were charged to the flow stream, the differences between the microtracer and the macrotracer were not reflected in the measured RTD distribution. A variation in the feed rate (Q) or screw speed (N) changes both the RTD and the intensity of axial mixing. On the other hand, for a given but small Q/N, commonly called specific throughput, variations in Q and N change the RTD but not the intensity of axial mixing. When it is small, Q/N can be used as an operating parameter to separate the effect of the residence time from that of mixing for a small Q/N.     

Residence time distribution in a commercial twin-screw extruder

The residence time distribution of poly(vinyl chloride) (PVC) polymers in a counterrotating twin screw commercial extruder was determined and analyzed. The experimental technique involved the use of manganese dioxide as a tracer after being neutron activated and was injected into the extruder during normal operation without interrupting the poly(vinyl chloride) compound production. The experimental results enabled us to better understand the flow and mixing conditions in the extruder.