## No full-text available

To read the full-text of this research,

you can request a copy directly from the authors.

A new method for the representation of residence time variability in continuous flow systems is presented. The method is based on the use of the intensity function. The advantage of this method is that it allows a physical insight into the mixing processes within the system and enhances the interpretability of experimental curves. The phenomenon of stagnancy is discussed and defined operationally. Theoretical and practical examples are used to illustrate the usefulness of the concepts introduced.

To read the full-text of this research,

you can request a copy directly from the authors.

... Thus, it is indicated that BF gas RTD study should be carried out under the specific operational conditions. Residence time intensity function which allows a physical insight of residence time was derived and proposed by Naor and Shinnar (1963). It is a direct and useful parameter to predict and evaluate the stagnancy in different vessels, even in some cases where their residence time distribution show little difference. ...

... Residence time distribution can comprehensively characterize molecules flow patterns in reactors, and thus is expected that the key information can be derived from the density distribution curve. The second central moment method is widely used to calculate the variance of residence time distribution as this indicator can represent the molecules dispersion from ideal flow patterns (Buffham and Mason, 1993;Naor and Shinnar, 1963). The following equation is used to derive the variance of molecules' residence time distribution. ...

... The physical meaning of residence time intensity function is the probability of escape for molecules which have stayed for a period of t (Naor and Shinnar, 1963). Generally, for piston-type flow, the residence time intensity is infinity at the ''pulsing" time, while for complete mixing in a single vessel, the residence time intensity is always unity due to the total mixing effect. ...

Gas residence time distribution (RTD) is an effective and convenient indicator for evaluating the performance of complex multiphase chemical reactors including ironmaking blast furnaces (BFs). However, in the open literature, there lacks the systematic RTD research for BFs. In this study, an integrated mathematical model is developed for describing the gas RTD of a BF. The model combines a steady multi-fluid model for describing the in-furnace state of flow and thermo-chemical behavior of gas-solid-liquid phases and a transient model for describing the dynamic behavior of tracer materials. The results show that the gas flow field inside the BF is quite complex, resulting from many factors such as furnace geometry and coupled thermo-chemical behaviors of other phases. The tail of gas RTD curve resulted from the lagging phenomenon of tracer flow inside BFs, is captured. The gas RTD is discussed by using mean residence time, dispersion of molecules distribution, cumulative distribution function and residence time intensity function. Under the given BF conditions, mean residence time and space time of gas fluids are predicted as 13.5 s and 16.3 s, respectively. The existence of stagnant flow in the BF can be both derived and directly identified. Moreover, it is indicated the gas flow patterns in the BF are composed of piston-type flow, stagnant flow and limited mixing flow. This study provides a cost-effective tool for better understanding BF gas flow dynamics and optimizing BF operations.

... and F (t) may also be interpreted as probabilities [46]. F (t) is the probability of a single particle staying in the system for a time t or less and F (t) is the probability of the residence time exceeding t (notice the implicit assumption that both functions acquire values only in [0; 1]). ...

... Wang [53] mentions that mixing behaviour of a majority of the actual mixers deviates from the ideal mixer (exponential vessel). He argues that this deviation may be caused by non- Shinnar and Naor [46] have suggested the intensity function or escape probability density as a method of visualizing the features of RTD related to stagnancy. In the context of modelling based on Erlang and n-Hyperexponential distributions, stagnancy is generally associated with systems which total ‡ow may be decomposed into ‡ows connected in parallel and one of the components has a signi…cantly larger average residence time than the other. ...

... Thus any departure of (t) from constancy is an indication of ill-mixedness. Indeed, as Shinnar and Naor [46] indicate, a system with stagnancy is one in which the escape probability (or the intensity function) decreases in time over some interval. For example, imagine a system in which a considerable fraction of the particles moves in near plug ‡ow through it, whereas the remaining fraction is absorbed into a stagnant phase from which it is exuded later into the main stream. ...

In this report the concepts of heterogeneity and homogeneity are studied in the context of mixture of particulate materials. It is shown that the function of a mixer, defined as a chaos enhancer device, is to reduce the axial distributional heterogeneity of a mixture. In order to characterize this property, several different modelling techniques are reviewed. Based on these techniques several steady state models are developed and discussed.
A probabilistic approach to determination of residence time distribution (RTD) of a mixer is presented. Several possible RTD models and their physical significance are also explained. An outline of the most common experimental methods for determination of RTD is given. Moreover, it is shown that if the superposition condition is fulfilled, a continuous mixer can be modelled as a linear time invariant (LTI) system. In this context the RTD and the transfer function of the system should coincide.
It is demonstrated that the escape probability function of a mixer is a valuable tool in visualizing some of the general characteristics of a mixer. The mean residence time and variance reduction ratio are other quantities which can be used to measure the ability of a mixer in reducing axial distributional heterogeneity of a mixture. It is also demonstrated how results from queuing theory can be use to determine some of the features of the mean residence time of a mixer.
In case of steady state feeding, the ingoing axial heterogeneity can be modelled as a quasi-stationary stochastic process. The axial heterogeneity can be broken into two independent components, a deterministic and random component. An estimate of the variance of the random component can be found by studying small perturbations of the variogram functions of the input and output axial heterogeneity, around zero. This can also be used to show that the Danckwerts formula correctly describes the variance reduction ratio of a continuous mixer.
Each particle path in a mixer can be modelled by a random walk. It is shown that the dispersion model relates the statistics of these paths to the performance of the mixer.
This report is concluded by a sketch of the future plans for research on continuous mixing.

... As Shinnar and Naor (1963) have also noticed, the functions F (t) and F (t) may also be interpreted as probabilities. Therefore, F (t) can be considered as being the probability of a single particle staying in the system for a time t or less and F (t) the probability that the particle's residence time exceeds t. ...

... Little else exists in the literature on how to handle such complex models. Nonetheless, as Shinnar and Naor (1963) have pointed out, all actual distribution functions may be approximated by a theoretical model composed of a number of exponential and near plug ‡ow vessels connected in some network. This is of course mathematically equivalent to the statement that all well behaved functions can be approximated by some power series. ...

... These are evidently part of a reason for complicated modelling networks. Shinnar and Naor (1963) have suggested the intensity function or escape probability density as a method of visualizing the features of RTD related to stagnancy. In the context of modelling based on n-Erlang and n-Hyperexponential distributions, stagnancy is generally associated with systems in which total ‡ow may be decomposed into ‡ows connected in parallel where one of the components has a signi…cantly larger average residence time than the other. ...

A theoretical framework for sampling theory is developed. In this relation, concepts like mixture heterogeneity and representative samples are mathematically defined. Further, the relation between Gy's concepts of accuracy and reproducibility with mixture quality and the entropy of the sample distribution is established. Moreover, it is shown that within the developed framework, Lacey's conjecture is mathematically consistent. It is also shown that a consequence of the theory is the prediction of the number of key components of given size in random binary closed batch systems. It is also shown that this estimate is a function of microstructural properties of the mixture under study. Furthermore, this theory is used to develop a unifying approach to description of RTD of continuous systems. These results are further used to develop a model for RTD of a commercial twin screw extruder.
A new theoretical approach to the dynamics of the mixing processes is developed. In this context, the concept of heterogeneity landscape is introduced. It is argued that the valleys in the heterogeneity landscape correspond to different equilibrium states of the mixture. Further, it is shown that the valleys in the heterogeneity landscape can mathematically be described by heterogeneity equation and this would allow for classification of all the valleys. The characteristic function of the general solution to the heterogeneity equation is also determined. Moreover, it is shown that based on the mathematical model for the valleys, one can deduce that in the case of insufficient information about the mixture structure, the normal distribution, up to the second order; is the best distribution in describing the mixture structure.

... Although it is difficult to develop an analytical correlation between the observable geometric quantities, such as the distribution of hollow fibers, and the extent of bypass flow in a dialyzer shell, the presence of the flow maldistribution can be experimentally characterized by a relatively simple technique: the tracer dilution analysis [30,31]. This technique gives a macroscopic description of the flow distribution in a dialyzer. ...

... Exit age distribution functions of two dialyzers obtained from eqn. (31) are plotted in Fig. 10. The earlier appearance of the tracer (channeling) and the longer tail of the curve (hole up) are found for the loosely packed (55% packing) dialyzer. ...

Counter-current hollow fiber dialyzers were studied. Performance of loosely packed hollow fiber dialyzers deviated from the prediction based on ideal flow distribution while well packed dialyzers did not deviate. The flow maldistributions were characterized by tracer analysis. The behavior of dialyzers was simulated with a model based on bypass now.

... In the first case (ideal mixer: IM), all material elements inside the mixer at a given time have the same chance of exit; in the second (plug flow: PF), material flows like plug from inlet to outlet. In dimensionless terms, the RTD functions corresponding to these two ideal models are (Danckwerts, 1953;Naor and Shinnar, 1963 where t* = t/t AVG is the dimensionless time and e* has been normalized so that the area under it (the cumulative RTD) goes to 1 as t* goes to ¥ ; δ(ξ) is Dirac's delta function (a spike at ξ = 0). ...

... The two ideal models can be combined to form "mixed models", widely used to study backmixing in complex flow systems. One of the simplest is composed of N ideal mixers (IM) units in series, each with the same effective volume φV F /N, so the mean residence time in any one of them is t AVG / N. The dimensionless RTD of this tanks-in-series model (N´IM) is given by (Naor and Shinnar, 1963 for the N´IM model. The coefficient of dispersion can be taken as a good measure of the degree of backmixing. ...

... The chemical reaction engineering literature has dealt extensively with analytical, statistical, and computational dynamics models that can simulate the complex flow processes common to many types of flow reactors, both single and multiphase [see for example Levenspiel (1999) and Fogler (2006)]. So the issue of modeling biomass particle RTDs in flash pyrolysis is, in fact, a subset of a much more general problem that has received considerable attention for over 50 years [e.g., see Van de Vusse (1962) and Naor and Shinnar (1963)]. Many of the general modeling approaches developed for chemical reactors have been adapted for modeling particle RTDs in bubbling and circulating beds. ...

... in situ optical probe, can be modeled in various ways. [27][28][29][30][31] Without loss of generality, we demonstrate the applicability of our approach by modeling the normalized RVDs using simple empirical equations based on transfer functions that represent a series of perfect batch mixers. 32,33 A secondorder transfer function that corresponds to the mixing occurring in the screw and the die zones of the extruder was used. ...

Nanocomposites, with superior material properties, have promising potential applications in almost every field. The present work aims at developing a reproducible and continuous fabrication process to obtain the nanocomposites of aluminum nanoparticles that are uniformly dispersed in a polymer matrix and carbon nanotubes (CNTs) that are uni-directionally oriented in a polymer matrix. Due to its mixing potential, extrusion through a 28 mm Werner and Pfleiderer Twin Screw Extruder (TSE) was chosen to fabricate the nanocomposites. The aim of this research effort is to understand the nanoscale mixing characteristics of TSE using aluminum nanoparticles and CNTs, and to obtain the alignment of CNTs via extrusion through microchannels. Experimentally obtained residence time distributions of the mixing process were used to relate the mixing within the TSE to the microstructure of the extrudate. The microstructure of the nanocomposites has been characterized with scanning electron microscopy.

... Each particle that enters a continuous mixer spends a certain amount of time in the mixer. The duration of stay of each particle in the system, depending on the system parameters, follows a certain distribution that is known simply as the residence time distribution (RTD) of the mixer (Shinnar & Naor, 1963;Williams 145 & Rahman, 1971). The axial mixing capability of a mixer is often related to its RTD. ...

The concept of heterogeneity in relation to axial mixing in continuous mixers is investigated. The state of the mixture along the axial direction can be described by an axial heterogeneity function. It is shown that this function can be decomposed into two independent components. The first component describes the fluctuations caused by the feeding system. The second component is the fluctuations due to the particulate nature of the material. In addition, the second component, or the random component, can be modeled as a band-limited Gaussian white noise. Moreover, the variogram function is shown to be a useful tool in determining the variance of the random component. A linear time-invariant (LTI) model is proposed for continuous mixers. This model also implies that the Danckwerts-Weinekötter formula is applicable for the variance reduction ratio (VRR). However, it is shown that the Danckwerts formula for VRR is more appropriate for determination of mixer efficiency.

... Such a generalization was introduced in chemical engineering long ago, because of its importance in designing flow chemical reactors and in evaluating their performance. The significance of the random nature of residence time in a continuous flow system was pointed out by Danckwerts as early as in 1953, and this yielded to the introduction of the concept of a residence time distribution (besides Dankwerts [1953], see e.g., Naor and Shinnar [1963], Wolf and Resnick [1963], and Nauman [1969]). This approach and the subsequent developments are concerned to various dilution schemes other than the ideal mixing and do not usually consider the variability of the inflow/outflow; in other words, in the chemical engineering literature the random nature of the response variable (the concentration at the outlet) is caused by a source within the system (e.g., mechanism of micromixing/macromixing, shape of the chemical reactor, flow pattern, and so on). ...

Residence times of conservative pollutants in a lake or a reservoir are studied without the usual approximation of constant inflow/outflow. The effects of a random discharge flushing out a reservoir are investigated with the techniques of stochastic differential equations. Stochastic properties of the concentration in the reservoir are derived from stochastic properties of discharge (moments, autocorrelation function, and probability distribution function), and some approximations are analyzed. The major results are two simple and usable corrections for the residence time in two limiting cases: when autocorrelation time of discharge is much shorter than reservoir residence time and, at the opposite, when it is much longer.

A study on mixing–segregation phenomena in a gas fluidized bed of binary density system was performed by analysis of the residence time distribution and mixing degree. The effect of particle mixing on the residence time distribution and solid mixing was studied in a binary particle system with different densities. Residence time distribution curve and mean residence time of each particle were measured according to the flotsam particle size, mixing ratio and gas velocity in a gas fluidized bed (0.109m I.D., 1.8m height). The characteristics of residence time distribution and the deviation of mean residence time of each particle are consistent with previous mixing index based on the axial concentration of jetsam. From this study, mixing index of binary particle system with different densities should be considered by not only axial concentration distribution of jetsam particle but also characteristics of residence time distribution. This result suggests that the solid movement by fluidization gas is more important than solid axial dispersion.

A critical survey is given of the different models proposed for solids transport in gas-fluidized beds. It is shown that many of the models can fit the residence time distribution curve—the Ft-t curve—fairly well despite the fact that the physical behaviour of the bed is not recognized in these models. The intensity curve is recommended as a good tool for comparison of the models with the experiments.

The theory of residence-time distribution, RTD theory in short, is a cornerstone of chemical engineering science and practice, in general, and that of chemical reactor analysis and design, in particular. The creation of the modern, systematic RTD theory has been attributed to Danckwerts. As evident from his liberal adoption of terminologies of probability and statistics, he was apparently well aware of the stochastic nature of the process that gives rise to a residence-time distribution. While Danckwerts steered the development of the RTD theory essentially along the path of deterministic physics, obviously, the description of RTD is better couched in the statistical or stochastic parlance. Stochastic modeling visualizes the fluid in a flow system as being composed of discrete entities. This visualization reveals a greater insight into the underlying mechanism than deterministic modeling, thereby facilitating our understanding of the flow and mixing characteristic of the system. In the present work, an attempt has been made to derive a unified mathematical model of the RTD during process start-up by rigorously resorting to the theories and methodologies of stochastic processes. Specifically, the expressions for RTDs of molecules, fluid particles or any flowing entities passing through continuous flow systems have been derived from the stochastic population balance of these molecules, particles or entities. The resultant expressions are applicable to both unsteady-state and steady-state flow conditions.

Practical considerations lead to the use of small columns in preparative chromatography. In these applications extra column effects may overwhelm all broadening effects. The influence of the extra column effects on the band broadening and migration is demonstrated by simulation. The model assumes linearity of extra column effects. Consequently, these effects could be described by the convolution of the initial applied band width, an exponential decay and Gaussian broadening. An attempt has been made to discriminate between the column, pre- and postcolumn broadening.

According to Directive 2000/76/EC of the European parliament and of the council, of 4 December 2000, on the incineration of waste, plants for incineration of waste must raise gas temperature to 850°C, and in some cases 1100°C, for two seconds. Furthermore, the directive states that these properties shall be subjected to appropriate verification, in the form of measurements. How these measurements shall be performed, however, have not been clarified. Consequently, there is a need for a new method that is cost-effective and fairly simple to use in different furnace geometries, as well as generally applicable and available to consultant companies at a reasonable cost. The method proposed in this paper injects a pulse of helium into the furnace by using an injection lance, and then continuously samples the flue gas with a suction pyrometer to measure the temperature. The residence-time distribution is obtained by analysing the helium concentration in the sampled flue gas with a portable mass spectrometer as a function of time. We successfully tested this method in a 40 MW pulverised wood fired boiler at Kalmar Energi Värme AB, Kalmar, Sweden. The results indicate that it is sensitive to conditions influencing residence-time distribution and thus can be used to verify implementation of European Union requirements. Additional advantages of this method are that it is fairly inexpensive, simple, and can also be used to determine mixing-rate.

A study of drilling fluid flow in the annular space and drill pipe through residence time distribution (RTD) analysis of a tracer injected in impulse form while drilling an oil well is presented in this article. Two field trials were carried out in order to evaluate the technical feasibility and potential practical application of the RTD theory and the dispersion model. From the results it is possible to explain physically the flow behavior and its relation with parameters such as carrying capacity of the drilling fluid and hole cleaning conditions. The RTD analysis of tracer response indicates the presence of anomalous flow in both trials, characterized by two fluid volume fractions traveling with different velocities. The magnitude of these volume fractions concerns directly with the carrying capacity of the drilling fluid, hence, the hole cleaning conditions as is explained along the work. The dispersion number (RDN) as well as other distribution functions are suggested as a measure of the overall behavior of the fluid in a hole. This criterion is compared with empirical correlations employed in the industrial practice.

The classical Danckwerts-Zwietering treatment of segregation has been generalized to unsteady state flow reactors of arbitrary geometric shape. Basic equations which can be used to predict two limits of the extent of chemical reaction are developed from the population balance equation. It is shown that the residence time distribution uniquely determines the extreme of micromixing and the distribution can be determined from a series of standard tracer experiments. Nauman's treatment is confirmed but the restriction to stirred tank systems is removed in this study. Examples are given to illustrate the use of the theory. The segragation effect on a second order reaction is found to be small for both the isothermal and adiabatically cases. The effect on a biological growth process is very significant.

For processing on grooved-barrel extruders, a closer evaluation of the mixing mechanisms with respect to the thermal, mechanical, and rheological processes that take place in the screw channel is necessary if an estimate is to be made of the process behavior. A closer look is taken at longitudinal mixing. Two balance limits come into consideration here, first: the state of the solid material (e.g. (e.g., grain size distribution, property fluctuation in the raw material) that passes over the front edge of the hopper in the transport direction; the phase boundary between solid and molten material and the associated temperature differentials that prevail at the end of melting and which need to be smoothed out.

Es wird über die Untersuchung von Mischvorgängen in diskontinuierlich und kontinuierlich arbeitenden industriellen Anlagen berichtet. Diese Untersuchungen wurden mit Hilfe des radioaktiven Nuklids 24Na an einem Rührkessel zur Polykondensation, einer Mischtrommel und an einem kontinuierlich arbeitenden Schleudermischer durchgeführt.

Overload phenomena in GPC are investigated with samples of narrow polystyrenes and short but efficient columns packed with Styragel. Viscous fingering is shown to be a leading cause of peak skewing and broadening. A correlation is proposed to define a safe operating range in terms of sample concentration, volume, and the average intrinsic viscosity of the solute polymer.

The input-output thermal transient modelling of a multistage liquid-solid fluidized bed is proposed. This model is based on a flow modelling obtained from RTD measurements and a local heat transfer model. Experimental data are well represented by the model. Furthermore, sensitivity problems are studied and literature values of heat transfer coefficients are discussed.

The intellectual roots of residence time theory date back to 1908 and, thus, span the 100-year history of Industrial & Engineering Chemistry. The theory was created, developed, and extended by chemical engineers. It permeates chemical engineering in general and chemical reaction engineering in particular. It also has found widespread utility in the geosciences, environmental engineering, medicine, and biology. This paper provides an overview of the theory and gives some new results here and there.

The purpose of this report is to summarize the lecture given at the joint CAMURE-6 and ISMR-5 international symposium in Pune, India, in January 2007. The emphasis is on the pivotal role that reaction engineering has to play in addressing modern technological challenges. First the global challenges of reducing the environmental impact of our technologies are considered. Then the role of multiphase reaction engineering in enabling efficient transfer of molecular-scale discoveries to more benign and sustainable processes is outlined. Typical scale-up methodologies are introduced, and research needed for their further improvement is discussed. Examples of the importance of proper scale-up are provided.

A quantitative measure of stagnancy in a flow system is developed. It is based on a comparison of the mean residence time determined from extrapolated tracer washout experiments to the a priori value of the mean residence time that is calculated from the mass inventory and throughput. A distinction is made between absolute and relative stagnancy. Relatively stagnant material has such long residence times that its presence cannot be detected even by extrapolation of a washout experiment truncated at a particular time but would be detectable given a more prolonged experiment. Suitable extrapolation methods are based on asymptotic forms for the washout function. The primary method is appropriate to systems that are turbulent, that have substantial internal recycle, or that have significant mass transfer by diffusion. A secondary method is applicable to systems in laminar flow with negligible diffusion.

A theoretical framework is presented for the interpretation of tracer experiments in quasisteady-flow systems, where the inflow and outflow, as well as the internal flows, exhibit stationary fluctuations about fixed central values. The fluctuating throughout leads to the consideration of different types of sojourn time distribution of material in the system. These are discussed in detail, and related to different ways of carrying out tracer experiments on the system. The standard experiment, in which a known amount of tracer is injected quickly into the inlet and its concentration measured in the outlet, leads to none of these distributions.

Residence time distributions in flow systems are often determined by displacement experiments with tracer substances. During such experiments density changes are frequently introduced, which, though small, can affect the residence time distribution considerably.In order to analyse the significance of concentration gradients in vertical columns filled with glass spheres, experiments were carried out with aqueous solutions of KCl. During the experiments, which were performed at low Reynolds numbers, the response to a step change of the inlet concentration was measured conductometrically at the outlet of the column. Stepwise changes from a low to a high concentration and vice versa clearly revealed that density differences as small as 0.2 g/l resulted in different residence time functions. As the axial dispersion model was applied, various values of the Peclet number were also obtained.In order to reduce the density differences, small amounts of saccharose were added to the less concentrated electrolytic solution. The resulting gradual reduction of the density differences led to a corresponding decrease of the differences between the distribution functions and hence the Peclet numbers. When the densities of the two solutions were made equal according to this method, identical Peclet numbers were obtained. A further increase in the density of the weaker electrolyte by the addition of saccharose resulted in a “change of position” of the Peclet numbers in comparison with those for solutins free of saccharose.On the basis of the results, a method was developed for the determination of tracer-independent residence time distributions and Peclet numbers in columns of the type studied.

This chapter discusses the design of reactors that do not conform to the ideal models of reactors, such as the plug-flow reactor (PFR) and the perfectly stirred reactor operated in batch (IBR) or continuous (CSTR) modes; its attention is restricted to constant volume, single phase, isothermal reactors, which are operated in the steady state. The chapter provides an introduction to basic ideas and techniques. Some of the most common reasons for the behavior of real reactors departing from ideal predictions are partial bypassing, existence of relatively stagnant zones, channeling or the presence of diffusion, and turbulent eddies within the reactor. The Laplace transform and the concept of system transfer functions are extremely useful when designing nonideal reactors. While there may be initial difficulties associated with working in the Laplace domain, the benefits and ease of calculation which can result are so significant that Laplace transformed equations and transfer functions of reactor types are used frequently. The transfer function of a flow-mixing system may be used to predict the conversion of reactant, which will be achieved in that system when a reaction with first-order kinetics is occurring.

Testes com traçador para avaliar a distribuição de tempos de residência são usados em diversos tipos de circuitos em processos químicos e bioquímicos, porém são escassos em usinas de tratamento de minérios. Um ensaio com traçador foi utilizado para avaliar as características de um circuito industrial de moagem-classificação de uma usina de tratamento de minérios auríferos. LiCl foi injetado na forma de pulso e amostras de polpa foram coletadas em três pontos do circuito. As distribuições de tempos de residência foram determinadas usando as concentrações de Li na fase aquosa, dosada por absorção atômica. A análise das distribuições confirma a presença de reciclos no circuito, o que aumenta o tempo de residência médio. O tempo de residência global da fase líquida no circuito foi de 8,3 minutos. Esta distribuição ajustou-se bem com um modelo compartimentado, composto por seis reatores de mistura perfeita, dois divisores de fluxo e um reciclo.

Tracer methods are encountered in many areas of science and engineering. The diversity of their uses is illustrated by measurement of blood flow and capillary permeability of the microcirculation in medicine and by flow visualization in channels and around airplane wings in mechanical and aerospace engineering. Other applications are flow and transport measurements in rivers in hydrology, transport measurements of pollutants in soils in civil engineering, and measurements of spreading of plumes in the atmosphere in environmental engineering. Additional uses involve identification of reaction mechanisms of chemical and catalytic reactions, measurement of diffusion rates, etc. All these methods rely on perturbing the system under investigation and monitoring the system’s response to such perturbations. This response is then interpreted. Some conclusions can be obtained on a model-free basis, others are model dependent.

The characteristics of residence time distribution (RTD) of solid particles (Geldart B) with the pulse particle tracer approach in two cold rectangular bubbling fluidized beds (BFB) with continuous particle flow were experimentally investigated. The parameters tested were superficial gas velocity (U), feeding rate of particles (G s), particle bed height (H) and particle size (d p), and the used tracer was coal particles. The results showed that G s, H and dp were the major influential factors, while U affected little. The particle flow pattern in BFB reactor lied between those of the ideal plug flow reactor and completely stirred reactor (CSTR), it was close to the plug flow when the particle bed height was lower and G s, larger, whereas the flow was much closer to the full mixing flow of the CSTR at the higher particle bed height and smaller G s. The averaged residence time of particles was calculated as the value of 9%~18% below of the plug flow for the design of BFB based on the present experimental data.

A review is presented of reactor modeling as a tool in the hand of the designer and practitioner, and the role the academic can play in helping the practitioner to improve his skills. Emphasis is placed on methods and problems pertinent to deriving predictive models. The need for obtaining a proper synthesis between economics and statistical model building is discussed.

The present paper is a study of the interplay between kinetic parameters and different flow patterns and its effect on fractional conversions for second order reactions with arbitrary stoichiometry and arbitrary ratios between the initial concentrations of the reactants. The models studied are the normal, segregated and maximum-mixed axial dispersion and tanks-in-series models. The calculations required have been performed with the aid of digital simulation and the results are presented in diagrams making possible the determination of the fractional conversion for ten different models.

The composite algorithm derived in Part I is used to construct models from pulse responses of lumped and distributed systems, as well as an empirically measured residence time density. Along the way, salient points in the numerical implementation of the algorithm are indicated. In the present recursive procedure, the initial transient is predicted accurately by lower-order partial realizations; successive partial realizations involve progressively longer tails of the pulse response. The zeroth moment of the impulse response is used to advantage when realizations with no zeros are appropriate.

A cold model of a rotary holding furnace was studied using water and a kerosene-LIX® 973N organic mixture which are immiscible. The flow of the feed was found to behave similar to a gravity current where the feed preferentially moved along the liquid–liquid interface. Visual observation and residence time distribution obtained showed that the flow of the lighter feed mixture was similar to a laminar flow but with a preferential route along the wall with the outlet spout. In the commercial-scale rotary holding furnace, plug flow conditions are considered desirable while mixing or short-circuiting is considered undesirable. The flow in the cold model was fitted to a plug flow and three CSTRs all in series and a particular depth of the upper layer of organic was found where mixing with the bath fluid was a maximum. Air bubbling in the centre of the cold model showed that at low air flow rates, the air curtain acted to limit mixing but as the air flow rates increased, the increased circulation caused by the air flow increased mixing and negated the air curtain effect.

Es wird über Untersuchungen des Verweilzeitverhaltens der flüssigen Phase in einer kleintechnischen und in einer halblechnischen Hochdruckhydrieranlage berichtel. Die Messungen wurden mit Hilfe des radioaktiven Nuklids ⁸²Br in Form von Methylenbromid (CH2Br2) durchgeführt. Diskutiert werden Fragen der Selektivität von ablaufenden Reaktionen auf der Grundlage der gewonnenen Erkenntnisse über das Verweilzeitverhalten der flüssigen Phase.

A systematic study of liquid phase axial dispersion was conducted in glass columns (inner diameters, 1 cm and 1.6 cm), packed randomly with granular sand, by varying the fluid flow rate, particle size and bed height. Pulse and step response techniques, with KCl as an inert tracer, were used. The resultant data, covering the Reynolds number range from 1 to 50, are presented as plots of the Peclet number based on particle diameter against Reynolds number.Inert tracer experiments were also carried out in a column (inner diameter, 1.6 cm) packed with activated carbon granules, using different particle sizes, fluid flow rates and bed heights, in order to estimate the effective intraparticle diffusivity. We show that flow maldistribution produces pulse response curves with sharp, narrow peaks which, when compared with theoretical curves, result in small intraparticle diffusivities.We illustrate how the outer-phase transfer function can be obtained from the overall transfer function of the activated carbon bed and we compare it with the transfer function obtained directly using impermeable particles similar to the activated carbon granules.

Responses to a tracer dye have been measured in a laboratory scale stirred tank using fiber optics for water and aqueous polymer solutions. An empirica Short-circuiting becomes significant below a particular stirrer speed for a given system. The observable segregation decreases markedly as stirrer spee models are also evaluated and compared with those of the current study.RésuméA l'aide de la technique de l'optique des fibres et dans le cas de l'eau et de solutions aqueuses de polymères, on a étudié au laboratoire le de sortie lissées, et on présente des paramètres de mélangeage qui chiffrent l'importance de la ségregation et de la rétention du récipie mesure que la vitesse d'agitation croît, la diminution de la ségrégation est prononcée. Des courbes lissées et idéales de distribution de t certain nombre de modèles bien connus, et on les compare à ceux que l'on obtient dans le présent travail.ZusammenfassungAntwortfunktionen wurden durch farbigen Spurstoff in einem Laboratoriumsrührkessel durch die Anwendung von Glasfaseroptik und wässriger Polymer Entmischung und ‘Holdback’ angeben, wurden entwickelt. Der Kurzschluß wird unterhalb einer gegebenen Drehzahl des Rührers signifikant. Die beob denen Entmischung nachweisbar war. Halbempirische Parameter wurden aus einer Zahl gut bekannter Modelle ermittelt und mit denen der vorliegenden Arbeit

The cycle time distribution (CTD) within closed, continuously circulating systems is defined and related to the residence time distributions of flow regions which make up such systems. Examples of the application of the CTD are noted and experimental methods for determining CTDs for various systems are summarized.

Tracer experiments for studying transport processes in multiphase systems are discussed. Such experiments are useful in in vivo physiological studies of transport processes across membranes, in engineering studies of porous packed columns, and in chromatography. In all these processes, the main forward flow is in one continuous phase from which fluid diffuses into a stagnant outer phase (and back). A nondiffusible tracer is used to characterize the flow in the main phase (inside the capillaries of an organ or between the particles of a column), and diffusible tracers are used to study the transport through the interface (membrane or film) and in the outer phase (extravascular space or inside a porous particle). From the concentration history of the different tracers at the outlet, we can reconstruct sojourn time distributions in the different phases. The statistical properties and the relations between the distributions and their moments are discussed. Methods are given for estimating interfacial transport coefficients (or permeabilities) as well as the diffusion coefficients in the outer phase from the moments of the measured distributions. It is also shown that these relations simplify considerably the mathematical modelling of such systems.

A mathematical model for gas-fluidized beds is proposed that allows for a randomly fluctuating flow pattern. It is shown how mean first-order conversion is related to contact time distribution for arbitrary models of this type. A simplified version of the model is then studied, and it is found that the effect of fluctuating flow is similar to that of stagnancy in steady systems. This effect is inconsistent with the usual steady-state models, but it is shown that some published data on conversion in fluidized beds [6] exhibit this effect.RésuméOn propose un modèle mathématique pour des couches de gaz fluidisées permettant un courant présentant des fluctuations au hasard. On démontre la relation d'une conversion moyenne de premier ordre à la distribution des temps de contact, pour des modèles arbitraires de ce type. Une version simplifiée du modèle est ensuite étudiée et on trouve que l'effet du courant de fluctuation est similaire à celui de la stagnation dans les systèmes stables. Cet effet est contradictoire aux modèles habituels à l'état stable, mais l'on montre que certaines informations publiées sur la conversion des couches fluidisées [6] présentent cet effet.ZusammenfassungEs wird ein mathematisches Modell für durch Gas betätigte Wirbelschichten vorgeschlagen, das ein zufallsmässigen Schwankungen unterworfenes Strömungsbild in Betracht zieht. Die Beziehung der durchschnittlichen Umsetzung einer Reaktion erster Ordnung zur Verteilung der Berührungszeit für willkürlich gewählte Modelle dieser Art wird dann eine vereinfachte Version des Modells untersucht, und es wird festgestellt, dass der Effekt einer schwankenden Strömung ähnlich dem einer Stagnation in stationären Systemen ist. Dieser Effekt ist mit den üblichen Modellen des stationären Zustandes unvereinbar, doch wird gezeigt, dass verschiedene über die Umsetzung in Wirbelschichten gemachte Angaben [6] diesen Effekt aufzeigen.

A general method for calculating residence time distributions for systems with internal reflux is described. The method allows the derivation of the Laplace transform of any system composed of mixed vessels with both forward and backward flow between them. In particular, the properties of a linear cascade of mixed vessels with forward and backward flow between the vessels is discussed.RésuméUne méthode générale du calcul des répartitions du temps de résidence pour des systèmes ayant un reflux interne, est décrite. La méthode permet la dérivation de la transformation de Laplace de tout système composé de récipients mixtes ayant entre eux un courant dans les deux sens. En particulier, les propriétés d'une cascade linéaire de récipients mixtes avec courant dans les deux sens entre eux, est discuté.ZusammenfassungEine allgemeine Methode zur Berechnung der Verweilzeitverteilungen für Systeme mit innerem Rückfluss wird beschrieben. Die Methode gestattet die Ableitung der Laplace-Transformierten für jedes System, das sich aus Gefässen mit Vorwärts- und Rückwärtsfluss zwischen ihnen zusammensetzt. Im besonderen werden die Eigenschaften und das Verhalten einer Linearkaskade gemischter Gefässe mit Vorwärts- und Rückwärtsfluss zwischen den Gefässen besprochen.

The mixing plays a fundamental role in domains as fluid dynamics, chemical engineering, environmental studies and pharmacology.
Discrete and continuous time models, based on model categorification method have been developed. The residence time distributions,
RTD, for multi-scale imperfect mixing are expansions in terms of Meixner and Laguerre polynomials.
The resulting RTD are compared to different models of imperfect mixing.
Local anesthetic effects on membranes are presented in the general PSM framework.
The SDG solution for imperfect mixing is exposed.

IntroductionCharacteristic PropertiesGlobal Measuring TechniquesLocal Measuring TechniquesConclusions and Future TrendsReferences

Turbulent chemical reactors are modeled by networks of stirred tanks, with the stochastic nature of the mixing introduced by taking the interstage flows to be stationary Markov processes. Some general features of tracer experiments in these quasi-steady flows are discussed, together with their relation to residence time distributions. The statistics of tracer experiments are analyzed, and related on the one hand to the esti-mation of mixing parameters, and on the other hand to the forecast of average yield from the reactor system under first-order kinetics. The variability of the reactor performance and the general story of more complicated kinetic mechanisms are deferred for a later report.

ResearchGate has not been able to resolve any references for this publication.