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1、Chapter 03 Ideal ReactorsBATCH REACTOR DESIGN1CONTINUOUS-FLOW REACTORS2PLUG-FLOW REACTORS33 ideal reactorsvStirred tanksvturbular or packed-bed reactorsv the criterion for ideality in tank reactors is that the liquid be perfectly mixed,which mans no gradients in temperature or concentration in the v
2、essel.vin plug-flow reactors,or PFRs,there are axial gradients of concentration and perhaps also axial gradients of temperature and pressure,but in the ideal PFR there is no axial diffusion or conduction.Batch Reactor DesignFirst-order reactions1Second-order reactions2Consecutive Reactions3Parallel
3、Reactions4Semibatch Reactions5First-order reactionsvFor an irreversible first-order reation of the type(3.2)First-order reactionsvThe result is often given in terms of the fraction converted:(3.3)Second-order reactions for a unimolecular second-order reation,(3.6)(3.5)(3.4)orSecond-order reactionsbi
4、molecular reationWhere R 1(3.7)Since and with A the limiting reactant. LetSecond-order reactions (3.8)Integration between limits gives(3.10)Second-order reactionsR=2.0Consecutive ReactionsThe rates of reaction depend on the concentration of B in the liquid phase, which is a function of gas solubilit
5、y, pressure, and agitation conditions.we are often concerned with the relative reaction rates and the selectivity, which do not depend on the concentration of B ,if the reaction orders are the same for both reactions. The reactions are treated as pseudo-first-order, and equations are developed for a
6、n ideal batch reactor with irreversible first-order kinetics:Consecutive Reactions(3.13)(3.12)The concentration of A falls exponentially, as was shown earlier in Eq. (3.2):(3.11)Consecutive ReactionsvThe material balance for product C isCombining these equations gives(3.15)(3.14)Consecutive Reaction
7、sIf no C is present at the start, integration of Eq. (3.15) gives The concentration of C goes through a maximum with time, can be found by differentiating Eq. (3.16) and setting the derivative to zero:(3.16)(3.17)Consecutive ReactionsThe concentration of D is obtained by a material balance:(3.18)(3.
8、19)(3.20)Consecutive Reactionsmaximum of 67% conversion of A is 86.5% and the selectivity is 77%.the conversion is 63% and the yield of C is 56% for aselectivity of 89%.Parallel ReactionsvSelectivity effects can also be important with parallel reactions having different reaction orders. Consider the
9、 case where the main reaction is first order to both reactants and the byproduct reaction is second order to one of the reactants:byproduct formationmain reactionParallel ReactionsvThe local or instantaneous selectivity is the ratio of to the total rate of consumption of A:(3.21)(3.22)Parallel React
10、ionsHigher selectivity could be achieved by decreasing theconcentration of A in the initial charge, but this would give a lower concentrationof C in the final product and increase separation costs.Semibatch ReactionsvThe reactor might be two-thirds to three-quarters full at the start, and the fluid
11、volume increases as A is added and no product withdrawn. vFigure 3.4 shows the calculated concentration curves for the same kinetics and as for Figure 3.3, with the feed of A at a slow, constant rate for 14 hoursSemibatch Reactionsthe initial selectivity is very high but decreases as decreases and i
12、ncreases slightly. After the feed is stopped, the selectivity again increasesCONTINUOUS-FLOW REACTORSReactors in Series2Temperature Optimization3CONTINUOUS-FLOW REACTORS1CONTINUOUS-FLOW REACTORSvOperating a stirred-tank reactor with continuous-flow of reactants and products (a CSTR) has some advanta
13、ges over batch operation. The reactor can make products 24 hours a day for weeks at a time, whereas for a typical cycle, the batch reactor is producing only about half the time. In the CSTR, temperature control is easier because the reaction rate is Constant, and the rate of heat release does not ch
14、ange with time, as it does in a batch reactor.CONTINUOUS-FLOW REACTORSvFinally, conversion and selectivity may vary from day to day with a batch reactor, and they are more likely to be constant with a CSTR and a good control system.vThe main disadvantage of continuous operation is that the reaction
15、rate is nearly always lower than the average rate for a batch reaction. In most cases, the batch reaction rate decreases as the conversion increases, and in the CSTR the reaction rate is the same as the final reaction rate in the batch reactor. For high conversions, the final rate may be several-fol
16、d lower than the average ratevand the average residence time in the CSTR must then be several-fold greater than the reaction time in a batch reactor.vThe average residence time in the CSTR is t =V/F. The ratio of CSTR residence time to batch residence time is readily derived for simple kinetic model
17、s. For a first order reaction in a CSTR, the steady-state material balance isCONTINUOUS-FLOW REACTORSIn terms of fraction converted, in - out(3.23)(3.24)(3.25)(3.26)(3.27)In-out = amount reactingCONTINUOUS-FLOW REACTORSorEquations (3.26), (3.27), and (3.28) are equivalent, and they are used when sol
18、ving for , t, or x. To compare the batch and CSTR times, the equation for a batch first-order reaction, Eq. (3.3) or Eq. (3.29), is used with Eq. (3.27):(3.28)(3.29)(3.30)CONTINUOUS-FLOW REACTORSCONTINUOUS-FLOW REACTORSCONTINUOUS-FLOW REACTORSFor the CSTR From Figure 3.5,or(3.31)(3.32)(3.33)(3.34)CO
19、NTINUOUS-FLOW REACTORSReactors in SeriesReactors in SeriesCSTR-1CSTR-2CSTRReactors in SeriesWhen the two reactors are used in series, the total volume is proportional to the sum of the rectangular area ebgf and cdhg in Figure 3.8. With several reactors in series, the total volume would approach that
20、 for a plugflow reactor.(3.36)(3.35)(3.37)(3.38)Reactors in SeriesWhen the reactors are equal in size and operate at the same temperature, theequation is(3.39)(3.40)Reactors in SeriesFor a very large number of tanks, the conversion approaches that for a plug-flow reactor or a batch reactor. With thr
21、ee tanks in series, the total time is 50% more than for plug flow if the desired conversion is 90% and for five tanks the time is only 25% greater.Reactors in Series It is easy to show that for a first-order reaction and two tanks, the volume should be equal:Taking, for example,:Any other combinatio
22、n with the same total time gives higher . Forexample, if and ;Temperature OptimizationvWhen a sequence of reactions produces a mixture of products, the selectivity for the main product is a major factor in choosing reaction conditions.v We have shown that the ratio of reactant concentrations and the
23、 conversion can affect the selectivity, particularly when the main and byproduct reactions have different reaction orders. When the reactions have different activation energies, the selectivity will also depend on the temperature. vIf the main reaction has the higher activation energy, raising the t
24、emperature will increase the selectivity and also decrease the time needed to reach the desired conversion. The best operating temperature cannot be chosen from just the kinetics but depends on other factors, such as the cost of supplying or removing heat, vaporization losses, corrosion rate, and sa
25、fety considerations.Temperature OptimizationvWhen the byproduct reaction has a higher activation energy than the main reaction, the selectivity is improved by reducing the temperature. However, this means a greater reaction time for a batch reactor or a larger reactor for a flow system. The temperat
26、ure chosen is again a compromise based on the reactor size, raw material costs, and the cost of product separation. vHowever, for an existing CSTR and a fixed feed rate, an optimum temperature can be defined as the temperature that gives the greatest yield of the main product. Increasing the tempera
27、ture increases the conversion but decreases the selectivity, so the yield goes through a maximum, as shown in the following example.Temperature OptimizationTemperature OptimizationTemperature OptimizationTemperature OptimizationPLUG-FLOW REACTORSHeterogeneous Reactions2Homogeneous Reactions1Adiabati
28、c Reactors3Optimum Reaction Temperature4Optimum Feed Temperature5PLUG-FLOW REACTORSvelements of the fluid are assumed to pass through the reactor with no mixingvall elements spend the same timev in the reactor.vWith a packed-bed reactor, the velocity profile is complex and changing with distance, as
29、 the fluid flows around and between the particles. However, when the bed depth is many times the particle diameter (L/dp 40), the residence time distribution of the fluid is quite narrow, and plug flow can be assumed.Homogeneous Reactions(3.41)To compare the equations for the PFR with a batch reacto
30、r, the molar feed rate is expressed as the volume feed rate F times the concentration of A:(3.42)Homogeneous Reactions(3.43)Equation (3.42) can then be presented using the space velocity SV or the space time , which is the reciprocal of the space velocity:wherevolumetric feed rate reactor volume(3.4
31、4)Heterogeneous ReactionsvFor a heterogeneous catalytic reaction in an ideal packed-bed reactor, the material balance is written for a differential mass of catalyst, dW. The basic equation for the conversion of the key reactant A is the same as for any type of reaction, or combination of reactions,
32、including reversible reactions.FororAB+COrHeterogeneous ReactionswhereMoles A fed/hr r=total moles A consumed/hr,kg W=mass of catalystIntegration of the rate equation gives the mass of catalyst needed per unit feed rate of A for a specified conversion.(3.46)Heterogeneous ReactionsvThe reactor volume
33、 is determined from the mass of catalyst and the bed density :(3.47)The dimensions of the reactor are not fixed by these equations, The reactor dimensions are selected to give reasonable proportions and a tolerable pressure drop. Often the mass velocity is chosen first, which gives the cross-section
34、al area, and the bed length is determined from the required volume. Heterogeneous ReactionsTo relate the conversion to the space velocity, the feed concentration and the bed density are introduced into Eq. (3.46):where(3.48)It is not really necessary to use the concept of space velocity in designing
35、 a reactor, since the mass of catalyst needed and the bed volume are determined directly from Eqs. 3.46 and 3.47. However, some patents and technical reports give the conversion as a function of space velocity and temperature rather than presenting fundamental kinetic data. To use such data, the spa
36、ce velocity must be carefully defined and interpreted.Heterogeneous ReactionsIn Eq. (3.48), the space velocity is defined using the volumetric flow rate at the entrance to the reactor, but it could be based on the volume of gas at standard conditions:Another definition is based on the void volume of
37、 the reactor 2, which corresponds toAlthough is closer to the gas residence time than is , there is noadvantage in using for alculations, and Eq. (3.50) incorrectly implies that raising would increase the conversion.(3.49)(3.50)Heterogeneous ReactionsOther terms that are used when feeding liquids to
38、 a reactor are the weight hourly space velocity (WHSV) and the liquid hourly space velocity (LHSV) 3. Both have units of but are defined differently:pounds of feed/hrpounds of catalyst=WHSVvolume of liquid/hrvolume of reactor=LHSVThe LHSV is sometimes used when feeding liquids that are vaporized in
39、a preheater before entering the reactor, and of course the LHSV is much lower than the SV based on the actual vapor flow to the reactor. Sometimes WHSV is based on the feed rate of one reactant rather than the total feed rateHeterogeneous ReactionsEven when the space velocity is clearly defined, the
40、re may be problems in scaleup or design. It might be thought that if temperature, pressure, and space velocity are kept constant on scaleup, the conversion will be constant. However, as Eq. (3.48) shows, a change in or may affect the conversion. A small-diameter laboratory reactor may have a lower b
41、ed density than a large reactor, in which case the large reactor might have a higher conversion for the same SV. Doubling would double r if the reaction is first order, and the conversion would not change; but for other orders the effects of would not cancel, and the conversion could change.Adiabati
42、c ReactorsvReactions on solid catalysts are often carried out in adiabatic reactors if there is little change in selectivity or the rate of catalyst aging with temperature. vThe reactor is generally a large-diameter cylindrical vessel containing one or more beds of catalytic particles supported on g
43、rids or heavy screens, as shown in Figure 3.12a. vAnother type of reactor has one or more annular beds of catalyst with radial flow of gas either inward or outward , as shown in Figure 3.12b.Adiabatic ReactorsAdiabatic ReactorsThe first step in reactor design is to calculate the equilibrium conversi
44、on as a function of temperature for a given pressure and feed ratio. For a bimolecular reversible reaction such as(3.54)Adiabatic ReactorsAt steady state, the energy released is equal to the increase in sensible heat of the feed stream, since there is no heat loss to the surroundings in an adiabatic
45、 reactor.The heat capacity of the catalyst and the reactor wall are not included in the heat balance, since once the steady-state temperature profile is established, the solids cannot store any more energy, and all the heat released must be absorbed by the flowing gas. From Eqs. (3.55) and (3.36),(3
46、.56)(3.55)Adiabatic Reactorssince, another form of Eq. (3.57) isAdiabatic ReactorsAdiabatic ReactorsIf a higher conversion is needed, the gases are cooled in an external exchanger and sent to a second bed. The temperature change in the second bed is proportional to the increase in conversion, and th
47、e slope is generally taken to be the same as for the first bed:(3.59)In some cases, three or four beds in series are used to get nearly complete conversion.Adiabatic ReactorsTaking 100 moles of feed as a basis, with mole fraction A, the heat balance can be written as(3.60)Adiabatic ReactorsThe tempe
48、rature pattern is then of the type shown in Figure 3.14 for a three-stage converter with two quenches. This type of converter is used for ICIs low-pressure methanol synthesis 6.send only part of the feed to the first stage and to use the rest of the feed to mix with and cool the hot gases between st
49、ages.Adiabatic ReactorsT but too high a feed temperature can lead to rapid catalyst fouling or greater formation of byproductsOptimum Reaction TemperatureOptimum Reaction TemperatureWhen both reactions have simple kinetics and follow the Arrhenius relationship, an equation for can be obtained. Consi
50、der the reactionOptimum Reaction TemperatureAt constant composition,(3.61)Optimum Reaction Temperaturetherefore(3.62)Optimum Reaction Temperature(3.63)Optimum Feed TemperatureThe amount of catalyst needed depends on the feed temperature and the conversionOptimum Feed TemperaturePRESSURE DROP IN PACKED BEDSThe pressure drop in a fixed bed can be calculated from the Ergun equation 10:(3.65) End!
