反应工程基础程易chapter9rtd283507575.ppt

Information needed to predict what a reactor can doReactorInputOutputPerformance equationRelates input to outputContacting pattern or how materials flow through and contact each other in the reactor Kinetics or how fast things happen. If very fast, then equilibrium tells what will leave the reactor. If not so fast, then the rate of chemical reaction, and maybe heat and mass transfer too, will determine what will happen.Fluidized Bed ReactorCase 1Case 2Case 3RTDs of gas and solidsGas RTDsSolids RTDsBi-modal RTDMixing in disc impeller systems Tilted configuration Structure in an eccentric stirred tank Concentric orbits in a 3-disc systemhttp://sol.rutgers.edu/~shinbrot/Group_Index.html高粘体系的液体高粘体系的液体混合现象混合现象Chapter 9 Distributions of Residence Times for Chemical ReactorsOverview•Nonideal reactors•Part-1: characterize (non)ideal reactorsResidence Time Distribution (RTD), E(t)Mean residence time, tmVariance, 2 Cumulative distribution function, F(t)•Part-2: predict conversion and exit concentrations based on RTDRTD not unique  modelsPart 1 Characterization and Diagnostics9.1 General characteristics•Two major uses of the RTD to characterize nonideal reactors1. To diagnose problems of reactors in operation2. To predict conversion or effluent concentration in existing/available reactors when a new reaction is used in the reactorExamples: Channeling Tank reactorDead zoneBypassingThe three concepts•RTD•Mixing•Model- To describe the deviations from the mixing patterns assumed in ideal reactors- To characterize the mixing in nonideal reactors9.1.1 RTD function•Residence time: the time the atoms spent in the reactor•Plug-flow reactor, batch reactorAll the atoms in the reactors have the same residence time•CSTRFeeds mixed immediately, but withdrawn continuously•“RTD”: some molecules leave quickly, others overstay their welcome.•RTD: a characteristic of the mixing that occurs in a chemical reactor 9.2 Measurement of the RTD•RTD is determined experimentally by injecting an inert chemical, molecule, or atom, called a tracer, into the reactor at some time t = 0 and then measuring the tracer concentration, C, in the effluent stream as a function of time•Tracer: nonreactive, easily detectable, similar physical properties to the fluid, no adsorption on the walls or surfaces, etc.•Pulse input and Step input阶跃注入脉冲注入9.2.1 Pulse input experimentReactorFeedInjectionDetectionEffluentCCtCCtttPulse injectionStep injectionStep responsePulse responseCCttPulse injectionPulse responseOnly flow carries tracer(No diffusion)E(t): resident time distribution functionhow much time different fluid elements have spent in the reactorC(t)tPulse responseE(t)tFraction of material leaving the reactor that has resided in the reactor for times between t1 and t2t1t2Problems using Pulse input:•“Pulse”: can be hard to obtain a reasonable pulse at the injection point•Long tails of the measured C(t) curveConvolution integral （卷积）Pulse Imperfect pulseStepA general description:Output concentration ~ Input concentrationInputEquivalent form9.2.2 Step tracer experimentCCttStep injectionStep responseStep injectionAdvantage of F(t): easier experimentsDrawbacks: differentiationerror large amount of tracer 9.3 Characteristics of the RTDE(t): exit-age distribution function, age distribution of the effluent stream i.e., the lengths of time various atoms spend at reaction conditions9.3.1 Integral relationshipsThe cumulative RTD function F(t)9.3.2 Mean residence timeThe first moment gives the average time the effluent molecules spent in the reactor.Space time or average residence time,  = V/In the absence to dispersion, for constant volumetric flow,  = 0 = tm9.3.3 Other moments of the RTDThe second moment about the mean is the varianceThe third moment, skewnessThe two parameters most commonly used to characterize the RTD are   and  2.9.3.4 Normalized RTD function, E(): represents the number of reactor volumes of fluid based on entrance conditions that have flowed through the reactor in time t.Why we use a normalized RTD?The flow performance inside reactors of different sizes can be compared directly.Example: all perfectly mixed CSTR: 9.3.5 Internal-age distribution, I(): represents the age of a molecule inside the reactorI( ): the fraction of material inside the reactor that has been inside the reactor for a period time between  and + CSTR:P633推导过程推导过程9.4 RTD in ideal reactors9.4.1 RTDs in batch and plug-flow reactorsPlug flow reactor:Properties of Dirac delta functionFor plug flowE(t)tOutF(t)t1.09.4.2 Single-CSTR RTDIn – Out = AccumulationFrom tracer experiment:E()F()1.01.09.4.3 Laminar flow reactorUThe minimum time the fluid may spend in the reactor:0.5E()0.5F()1PFRCSTRLFRNormalized RTD function for a laminar flow reactor9.5 Diagnostics and troubleshooting9.5.1 General comments9.5.2 Simple diagnostics and troubleshooting using the RTD for ideal reactorsA. The CSTR(a)Perfect operation (P)(b) Bypassing (BP)(c) Dead volume (DV)SummaryB. Tubular reactor(a) Perfect operation of PFR (P)(b) PFR with channeling (Bypassing, BP)(c) PFR with dead volume (DV)Summary9.5.3 PFR/CSTR series RTDCSTR + PFRPFR + CSTRRTD is not unique to a particular reactor sequence.CSTRPFRPFRCSTRE(t)tPFR1/CSTRExample: comparing second-order reaction systemsCSTR + PFRPFR + CSTRCSTRPFRPFRCSTR(1)(2)Part 2Predicting Conversion and Exit Concentration9.6 Reactor modeling using the RTDRTD + Model + Kinetic data Exit conversion and Exit concentrationModels for predicting conversion from RTD data1.Zero adjustable parametersa. Segregation modelb. Maximum mixedness model2. One adjustable parameter a. Tanks-in-series model b. Dispersion model3. Two adjustable parameters Real reactors modeled as combinations of ideal reactorsRTD: tells how long the various fluid elements have been in the reactor, but does not tell anything about the exchange of matter between the fluid elements (i.e., the mixing)Mixing of reacting species: one of the major factors controlling the behavior of chemical reactors. For first-order reactions, Conversion is independent of concentrationOnce the RTD is determined, the conversion can be predicted.For reactions other than first order, RTD is not sufficient.Model: to account for the mixing of molecules inside the reactorMacromixing: Produces a distribution of residence times without, however, specifying how molecules of different ages encounter one another in the reactor. Micromixing: Describes how molecules of different ages encounter one another in the reactor.Two extremes: (1)Complete segregation: All molecules of the same age group remain together as they travel through the reactor and are not mixed with any other age until they exit the reactor(2) Complete micromixing: Molecules of different age groups are completely mixed at the molecular level as soon as they enter the reactor.9.7 Zero-parameter models9.7.1 Segregation modelMixing of the globules of different ages occurs here. Mixing occurs at the latest possible moment. Each little batch reactor (globule) exiting the real reactor at different times will have a different conversion. (X1,X2,X3...)RTD + Model + Kinetic data Exit conversion and Exit concentrationMean conversion of those globules spending between time t and t+dt in the reactor=Conversion achieved in a globule after spending a time t in the reactorXFraction of globules that spend between t and t+dt in the reactorSegregation modelSummary: if we have the RTD, the reaction rate expression, then for a segregated flow situation (i.e., model), we have sufficient information to calculate the conversion. Consider a first-order reaction: For a batch reactor: For constant volume and with NA = NA0(1-X)solutionMean conversion for a first-order reactionExample: Applications of the segregation model for an ideal PFR, a CSTR, and a laminar flow reactor (first-order reaction)(1) PFR:Chapter 4(2) CSTR:Chapter 4(3) Laminar flow reactorHilder, M.H. Trans. IchemE 59 p143(1979) 9.7.2 Maximum mixedness modelSegregation model: mixing occurs at the latest possible point.Maximum mixedness model: mixing occurs at the earliest possible point.Segregation modelMaximum mixedness modelThe volume of fluid with a life expectancy between  and +The rate of generation of the substance A in this volume: Maximum mixedness gives the lower bound on conversion (X) when n>1.Mole balance9.7.3 Segregation vs. maximum mixedness predictionsIfthenO. Levenspiel, P358(a)(b)(c, d, e)9.8 Using software packagesRead CD.9.9 RTD and multiple reactionsFor multiple reactions use an ODE solver to couple the mole balance equations, dCi/dt=ri (where ri is the net rate of reaction). Segregation modelMaximum mixedness modelSummary1. E(t)dt: fraction of material exiting the reactor that has spent between time t and t+dt in the reactor.2. The mean residence time3. The variance about the mean residence time isis equal to the space time  for constant volumetric flow,  = 0 4. The cumulative distribution function F(t) gives the fraction of effluent material that has been in the reactor a time t or less:5. The RTD functions for an ideal reactor arePlug flowCSTRLaminar flow6. The dimensionless residence time is7. The internal-age distribution, [I(), ], gives the fraction of material inside the reactor that has been inside between a time  and a time +d8. Segregation modelFor multiple reactions9. Maximum mixedness: For multiple reactions。