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1、化 学 反 应 工 程Chapter 14 The Tanks-In-Series ModelThis model can be used whenever the dispersion model is used;and for not too large a deviation from plug flow both models give identical results,for all practical purposes.Which model you use depends on your mood(心情)and taste.The tanks-in-series model i
2、s simple,can be used with any kinetics,and it can be extended without too much difficulty to any arrangement of compartments,with or without recycle.化 学 反 应 工 程Figure 14.1 The tanks-in-series model 化 学 反 应 工 程14.1 PULSE RESPONSE EXPERIMENTS AND THE RTD Figure 14.1 shows the system we are considering
3、.We also define Then and at any particular time,from Eq.11 in Chapter 11Chapter 11 化 学 反 应 工 程For the first tank.Consider a steady flow m3/s of fluid into and out of the first of these ideal mixed flow units of volume V1.At time t=0 inject a pulse of tracer into the vessel which when evenly(均匀地)dist
4、ributed in the vessel(and it is)has a concentration C0(C0=M/V1).At any time t after the tracer is introduced make a material balance,thus 化 学 反 应 工 程Since the area under this C/C0 versus t curve is(check this if you wish)it allows you to find the E curve;so one may write N=1(1)That is to say,for a s
5、ingle mixed flow reactor,its E function is 化 学 反 应 工 程Separating gives a first-order differential equation,which when integrated gives N=2(2)For the second tank where C1 enters,C2 leaves,a material balance gives 化 学 反 应 工 程For the Nth tank.Integration for the 3rd,4th,Nth tank becomes more complicate
6、d so it is simpler to do all of this by Laplace transforms.The RTDs,means and variances,both in time and dimensionless time were first derived by MacMulin and Weber(1935)and are summarized by Eq.3.化 学 反 应 工 程化 学 反 应 工 程Figure 14.2 RTD curves for the tanks-in-series model,Eq.3.化 学 反 应 工 程14.2 CHEMICA
7、L CONVERSIONFirst-Order Reaction Chapter 6Chapter 6 develops the conversion equation.Thus for first-order reactions in one tankfor N tanks in series A comparison with plug flow performance is given in Fig.6.5.化 学 反 应 工 程Second-Order Reaction of a Microfluid,For a microfluid flowing through N tanks i
8、n series Eq.6.8 gives(10)and Fig.6.6 compares the performance to that for plug flow.化 学 反 应 工 程All Other Reaction Kinetics of Microfluids Either solve the mixed flow equation for tank after tank a rather tedious(乏味的)process,but no problem today with our handy(手边的)slave,the computer.Or else we could
9、use the graphical procedure shown in Fig.14.8.化 学 反 应 工 程Chemical Conversion of Macrofluids There is rare use for macrofluid equations for homogeneous reactions.However,if you do need them combine Eq.11.13 with Eq.3 for N tanks in series,to give These equations may not be of practical use for homoge
10、neous systems;however,they are of primary importance for heterogeneous systems,especially for G/S systems.化 学 反 应 工 程EXAMPLE 14.1 MODIFICATIONS TO A WINERYA small diameter pipe 32 m long runs from the fermentation room of a winery(葡萄酒厂)to the bottle filling cellar(酒窖,地窖).Sometimes red wine is pumped
11、 through the pipe,sometimes white,and whenever the switch(开关,切换)is made from one to the other a small amount of“house blend”rose is produced(8 bottles).Because of some construction in the winery the pipeline length will have to be increased to 50 m.For the same flow rate of wine,how many bottles of
12、rose may we now expect to get each time we switch the flow?化 学 反 应 工 程SOLUTION Figure E14.1 sketches the problem.Let the number of bottles,the spread,be related to.Figure E14.1 化 学 反 应 工 程But for small deviation from plug flow,from Eq.3 化 学 反 应 工 程EXAMPLE 14.2 A FABLE ON RIVER POLLUTIONLast spring o
13、ur office received complaints(投诉,控告)of a large fish kill along the Ohio river,indicating that someone had discharged(倾倒,卸货)highly toxic(有毒的)material into the river.Our water monitoring stations at Cincinnati and Portsmouth,Ohio(119 mile apart),report that a large slug(条,片,块)of phenol(苯酚)is moving do
14、wn the river,and we strongly suspect(怀疑)that this is the cause of the pollution.The slug took about 10.5 hours to pass the Portsmouth monitoring stations,and its concentration peaked at 8:00 A.M.Monday.About 26 hours later the slug peaked at Cincinnati,化 学 反 应 工 程SOLUTIONLet us first sketch what is
15、known,as shown in Fig.E14.2.To start,assume that a perfect pulse is injected.Then according to any reasonable flow model,either dispersion or tanks-in-series,we have Figure E14.2化 学 反 应 工 程or Dividing one by the other gives 化 学 反 应 工 程Comment.Since the dumping of the toxic phenol may not have occurr
16、ed instantaneously,any locating where L272 miles is suspect,or This solution assumes that different stretches of the Ohio River have the same flow and dispersion characteristics(reasonable),and that no suspect tributary(支流)joins the Ohio within 272 miles of Cincinnati.This is a poor assumption check a map for the location of Charleston,WV,on the Kanawah River.