[學習]反應工程基礎程易chpt14-fixedbedrea

1、Summary of Chapter 13,The concentration profile for a first-order reaction occurring in a spherical catalyst pellet is where ?1 is the Thiele modulus. For a first-order reactionThe internal effectiveness fact

2、or and overall effectiveness factor.,1,Summary (cont’d),For large values of the Thiele modulus for an n order reaction,For internal diffusion control, the me reaction order is related to the measured reaction order b

3、y The true and apparent activation energies are related by,2,Summary (cont’d),The Weisz-Prater Parameter The Weisz-Prater criterion dictates that: If CWP>1, internal diffusion limitations pre

4、sentMears Criteria for Neglecting External Diffusion and Heat Transfer,3,4,Chapter 14Fixed-Bed Reactor,Department of Chemical EngineeringTiefeng Wangwangtf@tsinghua.edu.cn,Contents,Introduction of fixed-bed reactorA

5、diabatic fixed bed reactorFixed-bed reactor with heating or coolingModel of the fixed-bed reactor,5,14.1 Types of the fixed bed reactor,6,7,Fixed-bed reactors for methanol synthesis,8,多段冷激式反應器,列管式合成反應器,徑向反應器,9,Fluidize

6、d bed reactor,10,Selection of the reactor type,11,Reactor type preferred as a function of on stream time of the catalyst between two regenerations (van Swaaij et al., Chem. Eng. J., 2002, 90: 25–45),Characters of the fix

7、ed-bed reactor,In passing through fixed beds, gases approximate plug flow. If efficient contacting in a reactor is of primary importance, then the fixed bed is favored.Effective temperature control of large fixed beds c

8、an be difficult because such systems are characterized by a low heat conductivity. If operations are to be restricted within a narrow temperature range, then the fluidized bed is favored.Fixed beds cannot use very small

9、 sizes of catalyst because of plugging and high-pressure drop, whereas fluidized beds are well able to use small-size particles.If the catalyst has to be treated (regenerated) frequently because it deactivates rapidly,

10、then the liquid-like fluidized state allows it to be pumped easily from unit to unit.There is no catalyst attrition in the fixed-bed reactor.,12,Temperature profile of the fixed bed reactor,13,Exothermic reaction,Hot sp

11、ot,14.2 Pressure Drop in the Packed Bed Reactor,In liquid phase, effect of pressure drop can be ignored.In gas phase, for an ideal gas, the concentration of reacting species i isFor isothermal operation:,14,where,

12、See Section 4.5,Analyze the following second order gas phase reaction that occurs isothermally in a PBR2A → B+C  Mole balance (must use differential form),Rate law,Stoichiometry,Combine,   &

13、#160;                Need to find (P/P0) as a function of W (or V if you have a PFR).,15,Pressure drop in a packed bed,P/P0 = f(Volume, V) or f(cat

14、alyst weight, W)Majority gas phase reactions happened in a packed bed of catalyst particles. Equation used to calculate pressure drop is the Ergun Eqn.:,16,,Ergun Equation,17,,ρb= bulk densityρc= solid catalyst density

15、 ? = porosity (void fraction),Pressure drop in reactor,For single reaction:For isothermal operation, T=T0 with ε = 0;,18,,This Eqn. is for multiple reactions and reaction in a membrane reactor.,Reaction with pressu

16、re drop,19,,,,,,,,,1.0,(a),(b),(d),(c),(e),Effect of pressure drop on P (a), CA (b), -rA (c), X (d), and ? (e),Reaction with pressure drop,20,A?B, 2nd order isothermal reaction,Rate law:,Stoichiometry: Gas phase isotherm

17、al reaction with ε=0,Mole balance:,Combining :,Separating variables:,Integrating with limits X=0 when W=0 and substituting for FA0=CA0?0 yields:,21,Solving for conversion gives:,Solving for catalyst weight, we have:,22,1

18、4.3 Adiabatic fixed-bed reactor,23,Dependence of -rA on T,In a general form,,For irreversible reaction: T? -rA ?,For first-order reactions:,For reversible exothermic reactions: -rA has a maximum, and E-&g

19、t;E+,With fixed conversion,24,14.3.1 Equilibrium temperature and optimum temperature,when -rA=0, the temperature is the equilibrium temperature Tewhen -rA gets its maximum, the temperature is the optimum, Topt,For ea

20、ch conversion x:,Te is obtained by setting,Topt is obtained by setting,25,,,,Curves of Te and Topt for reversible exothermic reactions,The relationship between the equilibrium and optimum temperatures:,For a specific con

21、version, the same reaction rate corresponds to two temperatures, one smaller than Topt, and the other larger than Topt,26,14.3.2 Adiabatic tubular reactor,,Energy balance for adiabatic operation of PFR,,Differential mol

22、e balance:,,Almost always we will use an ODE solver,Femlab? Matlab?,Eq. (8-30)Fogler,TR: reference T,Adiabatic temperature and equilibrium conversion,28,Exothermic reactions,,,,T0,T01,Xe,,Energy balance,,,Adiabatic temp

23、.,Equilibrium,,T01>T0,,For 1st-order reaction,Make Xe~T curve,,Mean heat capacity:,The elementary reversible gas-phase reaction,Pressure drop neglectedPure A enters,Mole balance,,,Rate law,with,,,Stoichiometry,,Combi

24、ne,,,Energy balance,,If pure A enters and if ?Cp=0, then,,,Optimum operating temperature for exothermic reversible reaction,Why is there a maximum in the rate of reaction with respect to conversion (hence with respect to

25、 temperature and reactor volume) for an adiabatic reactor?,Rate Law:,Curve A: Reaction rate slow, conversion dictated by rate of reaction and reactor volume. As temperature increases rate increases and therefore conversi

26、on increases.Curve B: Reaction rate very rapid. Virtual equilibrium reached in reaction conversion dictated by equilibrium conversion.,For fixed volume of catalyst, there is an Topt,in to give maximum XFor fixed conv

27、ersion, there is an Topt,in to use minimum volume of catalyst If Vcat,1>Vcat,2, Topt,in,1<Topt,in,2,Fixed Volume Exothermic Reactor,Optimum feed temperature for exothermic reversible reaction,,in,14.3.3 Staged ad

28、iabatic packed bed reactors,33,Optimization of the operations of staged packed bed,34,,,,,,,,,T0,T1’, x1,x1,T1,x3,To get the minimum, the following conditions should be fulfilled:,T2’, x2,x2,T2,,優(yōu)化變量,Ti為i-1級入口溫度,xi為 i 級出

29、口轉化率,以上條件的物理含義：第 i 級出口反應速率與第 i+1級反應速率相等第 i 級入口溫度是第 i 級出口轉換率的最優(yōu)溫度,35,Two-stage adiabatic packed bed reactors,36,Optimum two-stage packed bed reactor.,The optimization of operations reduces to minimizing the total amount

30、 of catalyst needed to achieve a given conversion.,Three variables:(1) the incoming temperature Ta(2) the amount of catalyst used in the first stage(3) the amount of inter-coolingProceduresGuess Ta.Move along the a

31、diabatic line until the following condition is satisfied:Cool to point c which has the same rate of reaction as point b; thusMove along the adiabatic from point c until the criterion of Eq. 1 is satisfied, giving

32、point d.Repeat until point d is at the desired final conversion.,37,,,,Eq. 1,Cold shot cooling multistage fixed-bed reactor,38,Optimum two-stage mixed flow reactor set up,39,Infinite recycle for staged packed beds,Optim

33、um two-stage packed bed reactor with recycle,40,The conversions shown represent a recycle ratio R = 1 in both stages.,14.4 Fixed-bed reactor with heating or cooling,Heat transfer in the fixed-bed reactorHeat transfer be

34、tween the particle and fluidEffective heat conductance of the bedHeat transfer between the bed and wall,41,42,14.4.1 Heat transfer between the particle and fluid,,Heat flux:,For forced convection, the heat transfer coe

35、fficient is normally correlated in terms of three dimensionless groups:,am is the surface area per unit weight of catalyst? is a factor related to the catalyst shape,14.4.2 Effective thermal conductivity of packed bed,T

36、he principle mechanisms of heat transfer in packed beds are as follows:Conduction through the gas and solid phasesRadiation between particles combined with conductionConvective flow of fluid elements,43,ktd is the tur

37、bulent diffusion thermal conductivitykt,f is the thermal conductivity of the fluidkte is the effective thermal conductivity of the bedkr is the radiation conductivity,(1) Conduction through the gas and solid particl

38、es,44,,45,(2) Radiant heat transfer,The radial flux between two surfaces is:,hr is the radial heat transfer coefficient?b is the bed voidage,Radiation between particles and conduction though the solid are accounted for

39、in the model of Schotte:,For 3-mm catalyst particles in air, kr is about 1.2kt,f at 300oC and 2.0kt,f at 500oC.,(3) Convective flow of fluid elements,46,,,Taking the Peclet number as 10, then,,14.4.3 Heat transfer betwee

40、n bed and wall,47,Tm: The average bed temperatureTR:The temperature that would be reached by extending the parabola to the wall.Tw:The wall temperatureTc:The temperature in the center.,Which temperature difference

41、 is used to calculate the heat transfer rate?,14.4.3 Heat transfer between bed and wall,48,一維模型：,二維模型：,The average bed temperature (Tm) is used to calculate the temperature difference, and the heat transfer coefficient i

42、s h0,The bed temperature at the boundary layer (TR) is used to calculate the temperature difference, and the heat transfer coefficient used is hw.,Using the overall heat transfer coefficient (U),where,,To relate kte to h

43、b, the bed geometry and shape of the temperature profile are needed.If q, the rate of heat generation per unit volume of bed, is assumed to be independent of the bed radius, a heat balance for a unit length of cylindric

44、al bed is:,49,The total heat generated is equated to the heat conducted from the bed, using the driving force (Tm-TR),,,hb的定義式,熱量平衡,,,50,Integration leads to:,As a result:,According to the definition of Tm, there is:,51,

45、In summary, the heat transfer rate can be calculated based on different driving force (?T), but the corresponding heat transfer coefficient must be properly used (hb, h0, hw, hj, U).,14.5 Design equation for the packed b

46、ed reactor,52,Assumptions:(1) Plug flow(2) Overall heat transfer coefficient is U,Molar balance:,Energy balance:,Boundary conditions:,自換熱固定床反應器,53,Iso-thermal reactor:,The reaction rate:,Tm is the temperature of the co

47、oling/heating fluid,54,Adiabatic packed bed:,Adiabatic temperature increase is:,,55,Non-isothermal and non-adiabatic fixed bed:,,The numerical schemes:,,（1）,,（2）,Iteration: 2?1?2?1 ... ... until convergence,56,Typical r

48、esults:,14.6 2D model of the packed bed reactor,57,In – Out + Generation = Accumulation,2D model of the packed bed reactor (cont’d),58,Molar balance:,Energy balance:,kte,r is the bed effective c

49、onductivity in the radial directionkte,z is the bed effective conductivity in the axial direction,Er is the bed effective diffusion coefficient in the radial directionEz is the bed effective diffusion coefficient in th

50、e axial direction,59,If Ez, Er, cp, u, kte,z and kte,r are constant:,Boundary conditions:,60,If EZ and kez are further neglected:,Boundary conditions:,61,偏微分方程的差分離散及求解,一、差分原理,y = f(x)在xi+1和xi?1Taylor展開：,這里的增量取負值。,從而得精度為0

51、(?x)的兩個一階差商：,一個精度為0(?x2)的一階差商：,及一個精度為0(?x2)的二階差商：,62,二、顯式差分格式,坐標離散：,最終得到迭代公式：,變量離散：,利用L’Hopitol法則修正軸心：,優(yōu)點是可以順序迭代，不需聯(lián)立求解；缺點是收斂性差。,離散邊界條件：,63,三、隱式差分格式,Crank-Nicholson法（在軸向格點中間對變量離散）：,最終得到迭代公式：,優(yōu)點是收斂性好；缺點是需要聯(lián)立求解代數(shù)方程組。,鄰二甲苯氧

52、化制鄰苯二甲酸酐,64,A: o-xylene (鄰二甲苯)B: phthalic anhydride (鄰苯二甲酸酐)C: CO+CO2,65,Design equations:,Boundary conditions:,66,Modeling Using Femlab,Start FEMLAB and select modelsDefine constants and expressionsGeometryPhysics