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# Residence time distribution

About: Residence time distribution is a research topic. Over the lifetime, 2472 publications have been published within this topic receiving 42777 citations.

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TL;DR: In this article, the authors proposed a method to predict the distribution of residence-times in large systems by using distribution-functions for residencetimes, which can be used to calculate the etficiencies of reactors and blenders.

Abstract: Summary--When a fluid flows through a vessel at a constant rate, either "piston-flow" or perfect mixing is usually assumed. In practice, many systems do not conform to either of these assumptions, so that calculations based on them may be inaccurate. It is explained how distribution-functions for residencetimes can be defined and measured for actual systems. Open and packed tubes are discussed as systems about which predictions can be made. The use of the distribution-functions is illustrated by showing how they can be used to calculate the etficiencies of reactors and blenders. It is shown how models may be used to predict the distribution of residence-times in large systems.

1,416 citations

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TL;DR: The use of segmented flow in capillaries, also known as Taylor flow, for reaction engineering purposes has soared in recent years as mentioned in this paper, with an emphasis on the underlying principles.

Abstract: The use of segmented flow in capillaries, also known as Taylor flow, for reaction engineering purposes has soared in recent years. On the one hand, Taylor flow has been used in honeycomb monolith catalyst supports. On the other hand, Taylor flow is the common flow pattern in multiphase microchannel reactors. This contribution reviews the fluid mechanical aspects of this flow pattern in quite general terms, with an emphasis on the underlying principles. From very simple analysis, design estimates for mass transfer, pressure drop and residence time distribution may be obtained with relative ease and—for multiphase reactors—surprising accuracy.

573 citations

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01 Jan 1983

TL;DR: In this article, the authors present a detailed discussion of the role of the heat effect on the performance of different types of chemical reactions in a cascade of tank and tubular reactions.

Abstract: Preface to the First Edition Preface to the Second Edition Preface to the Student Edition List of Symbols Chapter I Fundamentals of chemical reactor calculations 1.1 Introduction 1.2 The material, energy and economic balance - Material balance - Energy balance - Economic balance 1.3 Thermodynamic data: heat of reaction and chemical equilibrium - Heat of reaction - Chemical equilibrium 1.4 Conversion rate, chemical reaction rate and chemical reaction rate equations - Influence of temperature on kinetics - Influence of concentration on kinetics 1.5 The degree of conversion - Relation between conversion and concentration expressions 1.6 Selectivity and yield - Selectivity and yield in a reactor section with recycle of non-converted reactant 1.7 Classification of chemical reactors References Chapter II Model reactors: single reactions, isothermal single phase reactor calculations II.1 The well-mixed batch reactor II.2 The continuously operated ideal tubular reactor II.3 The continuously operated ideal tank reactor 11.4 The cascade of tank reactors II.5 The semi-continuous tank reactor II.6 The recycle reactor II.7 A comparison between the different model reactors - Batch versus continuous operation - Tubular reactor versus tank reactor II.8 Some examples of the influence of reactor design and operation on the economics of the process - The use of one of the reactants in excess - Recirculation of unconverted reactant - Maximum production rate and optimum load with intermittent operation References Chapter III Model reactors: multiple reactions, isothermal single phase reactors III.1 Fundamental concepts - Differential selectivity and selectivity ratio - The reaction path III.2 Parallel reactions - Parallel reactions with equal order rate equations - Parallel reactions with differing reaction order rate equations - A cascade of tank reactors III.3 The continuous cross flow reactor system III.4 Consecutive reactions - First order consecutive reactions in a plug flow reactor - First order consecutive reactions in a tank reactor - General discussion III.5 Combination reactions - Graphical methods - Optimum yield in a cascade of tank reactors - Algebraic methods III.6 Autocatalytic reactions - Single biochemical reactions - Multiple autocatalytic reactions References Chapter IV Residence time distribution and mixing in continuous flow reactors IV.1 The residence time distribution (RTD) - The E and the F diagram - The application of the RTD in practice IV.2 Experimental determination of the residence time distribution - Input functions IV.3 Residence time distribution in a continuous plug flow and in a continuous ideally stirred tank reactor. IV.4 Models for intermediate mixing - Model of a cascade of N equal ideally mixed tanks - The axially dispersed plug flow model IV.5 Conversion in reactors with intermediate mixing IV.6 Some data on the longitudinal dispersion in continuous flow systems - Flow through empty tubes - Packed beds - Fluidized beds - Mixing in gas-liquid reactors References Chapter V Influence of micromixing on chemical reactions V.1 Nature of the micromixing phenomena - Macro or gross overall mixing as characterized by the residence time distribution - The state of aggregation of the reacting fluid - The earliness of the mixing V.2 Boundaries to micromixing phenomena - The model tubular and tank reactors - Boundaries for micromixing for reactors with arbitrary RTDs V.3 Intermediate degree of micromixing in continuous stirred tank reactors - Formal models - Agglomeration models - Model for micromixing via exchange of mass between agglomerates and their average' environment, the IEM model V.4 Experimental results on micromixing in stirred vessels V.5 Concluding remarks on micromixing References Chapter VI The role of the heat effect in model reactors VI.1 The energy balance and heat of reaction VI.2 The well-mixed batch reactor - Batch versus semi-batch operation VI.3 The tubular reactor with external heat exchange - Maximum temperature with exothermic reactions para-metric sensitivity VI.4 The continuous tank reactor with heat exchange VI.5 Autothermal reactor operation - The tank reactor - An adiabatic tubular reactor with heat exchange between reactants and products - A multi-tube reactor with internal heat exchange between the reaction mixture and the feed - Determination of safe operating conditions VI.6 Maximum permissible reaction temperatures VI.7 The dynamic behaviour of model reactors - The autothermal tank reactor - Tubular reactor References Chapter VII Multiphase reactors, single reactions VII.1 The role of mass transfer VII.2 A qualitative discussion on mass transfer with homogeneous reaction - Concentration distribution in the reaction phase VII.3 General material balance for mass transfer with reaction VII.4 Mass transfer without reaction - Stagnant film model - Penetration models of Higbie and Danckwerts VII.5 Mass transfer with homogeneous irreversible first order reaction - Penetration models - Stagnant film model - General conclusion on mass transfer with homogeneous irreversible first order reaction - Applications VII.6 Mass transfer with homogeneous irreversible reaction of complex kinetics VII.7 Mass transfer with homogeneous irreversible reaction of order (1.1) with Al " 1 - Slow reaction - Fast reaction - Instantaneous reaction - General approximated solution VII.8 Mass transfer with irreversible homogeneous reaction of arbitrary kinetics with Al "1 VII.9 Mass transfer with irreversible reaction of order (1, 1) for a small Hinterland coefficient VII.10 Mass transfer with reversible homogeneous reactions VII.11 Reaction in a fluid-fluid system with simultaneous mass transfer to the non-reaction phase (desorption) VII.12 The influence of mass transfer on heterogeneous reactions - Heterogeneous reaction at an external surface - Reactions in porous solids VII.13 General criterion for absence of mass transport limitation VII.14 Heat effects in mass transfer with reaction - Mass transfer with reaction in series - Mass transfer with simultaneous reaction in a gas-liquid system - Mass transfer with simultaneous reaction in a porous pellet VII.15 Model reactors for studying mass transfer with chemical reaction in heterogeneous systems - Model reactors for gas-liquid reactions - Model reactors for liquid-liquid reactions - Model reactors for fluid-solid reactions. VII.16 Measurement techniques for mass transfer coefficients and specific contact areas in multi-phase reactors - Measurement of the specific contact area a - Measurement of the product kLa - Measurement of the product kGa - Measurement of mass transfer coefficients kL, kG VII.17 Numerical values of mass transfer coefficients and specific contact areas in multi-phase reactors - Fluid-solid reactors - Fluid-fluid (-solid) reactors References Chapter VIII Multi-phase reactors, multiple reactions VIII.1 Introduction VIII.2 Simultaneous mass transfer of two reactants A and A' with independent parallel reactions A P and A' X (Type I Selectivity) - Mass transfer and reaction in series - Mass transfer and reaction in parallel VIII.3 Mass transfer of one reactant (A) followed by two dependent parallel reactions A(+B) P A(+B,B') X (Type II Selectivity) - Mass transfer and reaction in series - Mass transfer and reaction in parallel VIII.4 Simultaneous mass transfer of two reactants (A and A') followed by dependent parallel reactions with a third reactant: A + B P, A' + B X - Complete mass transfer limitation in non-reaction phase - One reactant mass transfer limited in non-reaction phase - One reaction instantaneous - Both reactions instantaneous - No diffusion limitation of reactant originally present in reaction phase - More complex systems VIII.5 Simultaneous mass transfer of two reactants (A and A') which react with each other VIII.6 Mass transfer with consecutive reactions A P X (Type III Selectivity) - Mass transfer and reaction in series - Mass transfer and reaction in parallel VIII.7 Mass transfer with mixed consecutive parallel reactions - The system: A(1) A(2) A(2) + B(2) P(2) P(2) + B(2) X(2) - The system: A(1) A(2) A(2) + B(2) P(2) A(2) + P(2) X(2) - Complex systems References Chapter IX Heat effects in multi-phase reactors IX.1 Gas-liquid reactors - General - Column reactors - Bubble column reactors - Agitated gas-liquid reactors IX.2 Gas-solid reactors - Single particle behaviour - Catalytic gas-solid reactors - The moving bed gas-solid reactor - Thermal stability and dynamic behaviour of gas solid reactors IX.3 Gas-liquid-solid reactors References Chapter X The optimization of chemical reactors X.1 The object and means of optimization - The objective function - The optimization variables - Relation between technical and economic optima X.2 Optimization by means of temperature - The optimization of exothermic equilibrium reactions - Temperature optimization with complex reaction systems X.3 Some mathematical methods of optimization - Geometric programming - The Lagrange multiplier technique - Numerical search routines - Dynamic programming Pontryagin's maximum principle References Author index Subject Index

516 citations

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TL;DR: In this paper, the concepts of D anckwerts about the degrees of mixing and segregation are extended to the case of a continuous flow system with an arbitrary but known residence time distribution.

Abstract: The concepts of D anckwerts about the degrees of mixing and segregation are extended to the case of a continuous flow system with an arbitrary but known residence time distribution. For this purpose a life-expectation distribution is defined in addition to the age distribution. Further, a condition of maximum mixedness (minimum segregation) is defined for such a system. This condition, and the condition of complete segregation introduced by D anckwerts , are two opposite extremes. When the system is a reactor in which a chemical reaction of an arbitrary order takes place, the conversion can be calculated for both cases; thus two limits are obtained between which the conversion must lie.

379 citations

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TL;DR: In this article, the authors measured the hyporheic residence time distribution in a 2nd-order mountain stream at the H J Andrews Experimental Forest, Oregon, and found it to be a power-law over at least 15 orders of magnitude in time (15 hr to 35 d).

Abstract: [1] We measured the hyporheic residence time distribution in a 2nd-order mountain stream at the H J Andrews Experimental Forest, Oregon, and found it to be a power-law over at least 15 orders of magnitude in time (15 hr to 35 d) The residence time distribution has a very long tail which scales as t−128, and is poorly characterized by an exponential model Because of the small power-law exponent, efforts to characterize the mean hyporheic residence time (ts) in this system result in estimates that are scale invariant, increasing with the characteristic advection time within the stream channel (tad) The distribution implies the hyporheic zone has a very large range of exchange timescales, with significant quantities of water and solutes stored over time-scales very much longer than tad The hyporheic zone in such streams may contribute to short-time fractal scaling in time series of solute concentrations observed in small-watershed studies

307 citations