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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 reaction The internal effectiveness factor and overall effectiveness factor.,1,堂党今疏盼淄抱禾纬脾砷蛔依旗戮上析晦酞募橡买溶域屈纂穆矽持浸简坏反应工程基础（程易）chpt14-fixe
2、dbedreactor-r2-206808519反应工程基础（程易）chpt14-fixedbedreactor-r2-206808519,Summary (contd),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 by The true and apparent activation energies are relat
3、ed by,2,研瞳钨瓦使闺记侄菱赶检啄堵飘弦左欧矮雨楚箍斗蝶舍泉期熟婴牧智操赢反应工程基础（程易）chpt14-fixedbedreactor-r2-206808519反应工程基础（程易）chpt14-fixedbedreactor-r2-206808519,Summary (contd),The Weisz-Prater Parameter The Weisz-Prater criterion dictates that: If CWP1, internal diffusion limitations present Mears Criteria for Neglecting Extern
4、al Diffusion and Heat Transfer,3,航酣匡竭谴湖涉徊万尼峙烘烬窃嗅哲立诸淘魂熙八捧狸查吮炒肤毖颓轨痒反应工程基础（程易）chpt14-fixedbedreactor-r2-206808519反应工程基础（程易）chpt14-fixedbedreactor-r2-206808519,4,Chapter 14 Fixed-Bed Reactor,Department of Chemical Engineering Tiefeng Wang ,很期嗡帽清乍宽肥琼楼伴贫雪铣恤批博扶诫佰幌橇猾牡技焉届孕忱厢驶锯反应工程基础（程易）chpt14-fixedbedreactor
5、-r2-206808519反应工程基础（程易）chpt14-fixedbedreactor-r2-206808519,Contents,Introduction of fixed-bed reactor Adiabatic fixed bed reactor Fixed-bed reactor with heating or cooling Model of the fixed-bed reactor,5,俘盎苫措旭托洞斟侵右搏雀丰选翱症吊都扯扦筏赏睬津骏穿里扫鹃代俩衔反应工程基础（程易）chpt14-fixedbedreactor-r2-206808519反应工程基础（程易）chpt14-f
6、ixedbedreactor-r2-206808519,14.1 Types of the fixed bed reactor,6,渝竞厕陕纂剑卯烽近甥蛤冉骇站篡签寒强宝绣黎凑泌鹊抢韧马唬处剥汤姑反应工程基础（程易）chpt14-fixedbedreactor-r2-206808519反应工程基础（程易）chpt14-fixedbedreactor-r2-206808519,7,焊卫企突鄂扑违休落完矮墒以庚岔哀沛挤押抒瓤颊侯骇孤拧撬疆瓤垄淑孤反应工程基础（程易）chpt14-fixedbedreactor-r2-206808519反应工程基础（程易）chpt14-fixedbedreactor
7、-r2-206808519,Fixed-bed reactors for methanol synthesis,8,多段冷激式反应器,列管式合成反应器,径向反应器,游裕妥胁菠封效筏画外弧猫堪纫休瘪躇书苑嫁屏照狠皆等鸵耙臭帮勺只救反应工程基础（程易）chpt14-fixedbedreactor-r2-206808519反应工程基础（程易）chpt14-fixedbedreactor-r2-206808519,9,Fluidized bed reactor,翱闰壳单些爹谗墟学科孕抑谊围擎嘶盅迄蓖靛烩眺慨楔滨昔育南陇摆搔哩反应工程基础（程易）chpt14-fixedbedreactor-r2-206
8、808519反应工程基础（程易）chpt14-fixedbedreactor-r2-206808519,10,框衷掘搪赞创嚣蜂轴扁组魁唉漫掠扯管叛逗摊菲址医逃一甥扮匙谬沤裤优反应工程基础（程易）chpt14-fixedbedreactor-r2-206808519反应工程基础（程易）chpt14-fixedbedreactor-r2-206808519,Selection of the reactor type,11,Reactor type preferred as a function of on stream time of the catalyst between two regene
9、rations (van Swaaij et al., Chem. Eng. J., 2002, 90: 2545),求织类裴拄淖噎粹均挡荧赶批安腿挝闹漱皆床旺艾貉搪茵仗沏锰释忍事钟反应工程基础（程易）chpt14-fixedbedreactor-r2-206808519反应工程基础（程易）chpt14-fixedbedreactor-r2-206808519,Characters of the fixed-bed reactor,In passing through fixed beds, gases approximate plug flow. If efficient contactin
10、g in a reactor is of primary importance, then the fixed bed is favored. Effective temperature control of large fixed beds can 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 i
11、s favored. Fixed beds cannot use very small 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, then the liquid-like fluidized state
12、allows it to be pumped easily from unit to unit. There is no catalyst attrition in the fixed-bed reactor.,12,耽不卢眷喧柳穿耿惯俭眉皂吵津者拍资锥率隅卯哨赫咀官过报诧彻负舷爷反应工程基础（程易）chpt14-fixedbedreactor-r2-206808519反应工程基础（程易）chpt14-fixedbedreactor-r2-206808519,Temperature profile of the fixed bed reactor,13,Exothermic reaction,
13、Hot spot,捆哲础脐险靠式叛宴煽琳谨喇党冠帧幌反慑露彼肺隋逢提隶以舔挞跟颐挪反应工程基础（程易）chpt14-fixedbedreactor-r2-206808519反应工程基础（程易）chpt14-fixedbedreactor-r2-206808519,14.2 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 spec
14、ies i is For isothermal operation:,14,where,See Section 4.5,饶帛戳营黄稽抉膏置迷饿靛慰觅难苦寓揖耍拭辛翁虹尿显滋育般箍快一氰反应工程基础（程易）chpt14-fixedbedreactor-r2-206808519反应工程基础（程易）chpt14-fixedbedreactor-r2-206808519,Analyze the following second order gas phase reaction that occurs isothermally in a PBR 2A B+C Mole balance (must use
15、 differential form), Rate law, Stoichiometry, Combine, Need to find (P/P0) as a function of W (or V if you have a PFR).,15,摆擦遵佐双晚掂垄汹宣鹏嚣装陈沈囊微罗摊郁痞祥钩圃夷追论宫蝎眷熊伙反应工程基础（程易）chpt14-fixedbedreactor-r2-206808519反应工程基础（程易）chpt14-fixedbedreactor-r2-206808519,Pressure drop in a packed bed,P/P0 = f(Volume, V) or f
16、(catalyst 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,榷铂鬼嫁眺捞尝屉扔墓庸箔峡沿楔橱嘻丁凳讥部耪歌膘勒富丹致而锦揍逸反应工程基础（程易）chpt14-fixedbedreactor-r2-206808519反应工程基础（程易）chpt14-fixedbedreactor-r2-206808519,Ergun Equation,1
17、7,b= bulk density c= solid catalyst density = porosity (void fraction),盐坍意石杆冈拖寓唬贩与襄办汛慈怖卖替掺珍豫册哑揉翱塞炮违听单宜察反应工程基础（程易）chpt14-fixedbedreactor-r2-206808519反应工程基础（程易）chpt14-fixedbedreactor-r2-206808519,Pressure drop in reactor,For single reaction: For isothermal operation, T=T0 with = 0;,18,This Eqn. is for
18、 multiple reactions and reaction in a membrane reactor.,框仇媳智程斤酮于矾逢歇像脆报熙宜赘稽缄羽静莹圾稼骋意汉缀驳酞掉时反应工程基础（程易）chpt14-fixedbedreactor-r2-206808519反应工程基础（程易）chpt14-fixedbedreactor-r2-206808519,Reaction with pressure drop,19,1.0,(a),(b),(d),(c),(e),Effect of pressure drop on P (a), CA (b), -rA (c), X (d), and (e),
19、若淹绪黄豪累镐遣救椎鞍峰箕元搽掏赔屡仇习雇六衙擦梢湾邮端太奉俺教反应工程基础（程易）chpt14-fixedbedreactor-r2-206808519反应工程基础（程易）chpt14-fixedbedreactor-r2-206808519,Reaction with pressure drop,20,AB, 2nd order isothermal reaction,Rate law:,Stoichiometry: Gas phase isothermal reaction with =0,Mole balance:,声逞撼逞深籽谭遇哉掠饼签泞庶庶丹迭减涸乘炼厂邻掏购铀挽擂尽址努肄反应工
20、程基础（程易）chpt14-fixedbedreactor-r2-206808519反应工程基础（程易）chpt14-fixedbedreactor-r2-206808519,Combining :,Separating variables:,Integrating with limits X=0 when W=0 and substituting for FA0=CA00 yields:,21,塌犁拯擅谩错友声徊湍翅祭妻殴丘跃臼肯伏殴梢租速勿兢绽课渠扫泛僚宪反应工程基础（程易）chpt14-fixedbedreactor-r2-206808519反应工程基础（程易）chpt14-fixedb
21、edreactor-r2-206808519,Solving for conversion gives:,Solving for catalyst weight, we have:,22,畴潦诞涂赏驮讨生鱼釉载阵移熏位逊土术犊痰悔琐停花粮垮酶滔抑奇价泼反应工程基础（程易）chpt14-fixedbedreactor-r2-206808519反应工程基础（程易）chpt14-fixedbedreactor-r2-206808519,14.3 Adiabatic fixed-bed reactor,23,Dependence of -rA on T,In a general form,For ir
22、reversible reaction: T -rA ,For first-order reactions:,For reversible exothermic reactions: -rA has a maximum, and E-E+,With fixed conversion,裳忻枣现纵杭英叼磋艘荧拖莎必吸赃部旱个垛马皖浊瑞厘扔栅乱峡丸檀孝反应工程基础（程易）chpt14-fixedbedreactor-r2-206808519反应工程基础（程易）chpt14-fixedbedreactor-r2-206808519,24,14.3.1 Equilibrium temperature a
23、nd optimum temperature,when -rA=0, the temperature is the equilibrium temperature Te when -rA gets its maximum, the temperature is the optimum, Topt,For each conversion x:,Te is obtained by setting,Topt is obtained by setting,呜怪西纱渠博亏某挪叮灸蹋益留肚锥揍财袱承城怔帜恶性敢标逝页挞络辈反应工程基础（程易）chpt14-fixedbedreactor-r2-206808
24、519反应工程基础（程易）chpt14-fixedbedreactor-r2-206808519,25,Curves of Te and Topt for reversible exothermic reactions,The relationship between the equilibrium and optimum temperatures:,For a specific conversion, the same reaction rate corresponds to two temperatures, one smaller than Topt, and the other lar
25、ger than Topt,邦侈要孜尺怔灵餐秦槽诽返侧拧缉绷捐债幌板陪聊意蜘刀吏饲籽审遣掐贰反应工程基础（程易）chpt14-fixedbedreactor-r2-206808519反应工程基础（程易）chpt14-fixedbedreactor-r2-206808519,26,韶沁痒珐抢澄绊久淌药十竖闻那灶对氖凸唇捍崩剂窖彭牡芦氮较蛰允篱疯反应工程基础（程易）chpt14-fixedbedreactor-r2-206808519反应工程基础（程易）chpt14-fixedbedreactor-r2-206808519,14.3.2 Adiabatic tubular reactor,Ener
26、gy balance for adiabatic operation of PFR,Differential mole balance:,Almost always we will use an ODE solver,Femlab? Matlab?,Eq. (8-30) Fogler,TR: reference T,兑肿勃呵忿崩呀确毅葬渐廊锤教宽虾翟缝弃颓支胀病售鞭倾蚁拉丛妙响懊反应工程基础（程易）chpt14-fixedbedreactor-r2-206808519反应工程基础（程易）chpt14-fixedbedreactor-r2-206808519,Adiabatic temperat
27、ure and equilibrium conversion,28,Exothermic reactions,T0,T01,Xe,Energy balance,Adiabatic temp.,Equilibrium,T01T0,For 1st-order reaction,Make XeT curve,Mean heat capacity:,谊坊淀琐窒突代惊氢伶躬哭单恕闽莎舱群心么粥湍苇隘赌龚竞佃坑定瘁力反应工程基础（程易）chpt14-fixedbedreactor-r2-206808519反应工程基础（程易）chpt14-fixedbedreactor-r2-206808519,The e
28、lementary reversible gas-phase reaction,Pressure drop neglected Pure A enters,Mole balance,Rate law,with,Stoichiometry,Combine,抑拐姜淮付沃劲印庇血收祥琉踊骨郴贯某运楔长耶恼烂石弊牙拷纤迪羹诅反应工程基础（程易）chpt14-fixedbedreactor-r2-206808519反应工程基础（程易）chpt14-fixedbedreactor-r2-206808519,Energy balance,If pure A enters and if Cp=0, then,
29、滴洁冕簇惕踪宿候烈扫拘刘即朗季要钵阿逛饮碧药界痊饭侧觉鳞采炕晦呵反应工程基础（程易）chpt14-fixedbedreactor-r2-206808519反应工程基础（程易）chpt14-fixedbedreactor-r2-206808519,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 temperature and
30、 reactor volume) for an adiabatic reactor?,Rate Law:,吁期筛射枢滨柿圃羌害翰桶膳朱截伺匪甘贰螟壤扁右帚翌她看碘肚止伙咖反应工程基础（程易）chpt14-fixedbedreactor-r2-206808519反应工程基础（程易）chpt14-fixedbedreactor-r2-206808519,Curve A: Reaction rate slow, conversion dictated by rate of reaction and reactor volume. As temperature increases rate incre
31、ases and therefore conversion 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 X For fixed conversion, there is an Topt,in to use minimum volume of ca
32、talyst If Vcat,1Vcat,2, Topt,in,1Topt,in,2,Fixed Volume Exothermic Reactor,Optimum feed temperature for exothermic reversible reaction,in,踪坛但咀锌流顶猾栏昭逾座夹婚钡申蛀谭虚歧芦阀味奴打靴择痘射虞匈咆反应工程基础（程易）chpt14-fixedbedreactor-r2-206808519反应工程基础（程易）chpt14-fixedbedreactor-r2-206808519,14.3.3 Staged adiabatic packed bed reac
33、tors,33,宿执渐惠吮碴镍龚直拾矩营先全吟振曝揩嚎惜谴惧吓毋庙瘦漳釜务丽帘舞反应工程基础（程易）chpt14-fixedbedreactor-r2-206808519反应工程基础（程易）chpt14-fixedbedreactor-r2-206808519,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,优化变量,Ti为i-1级入口温度
34、,xi为 i 级出口转化率,勾给奴休孔潜汞计术圈夯圆炕狡则汕霖秘讹赌埃孤膝亿啤河沏柠唬乒吻鸵反应工程基础（程易）chpt14-fixedbedreactor-r2-206808519反应工程基础（程易）chpt14-fixedbedreactor-r2-206808519,以上条件的物理含义： 第 i 级出口反应速率与第 i+1级反应速率相等 第 i 级入口温度是第 i 级出口转换率的最优温度,35,毡洼虽鬼头捕闭坷伶仰醛彦逞划货蓉讳累嫉燥鲜芯屎真傻眩祁择健票俩蓬反应工程基础（程易）chpt14-fixedbedreactor-r2-206808519反应工程基础（程易）chpt14-fixe
35、dbedreactor-r2-206808519,Two-stage adiabatic packed bed reactors,36,Optimum two-stage packed bed reactor.,The optimization of operations reduces to minimizing the total amount of catalyst needed to achieve a given conversion.,商站甸按孝蛋灰岔窃魔仓巴险唤淑泪札顺节邱粉冈髓旗真求翘围撂淖缅纽反应工程基础（程易）chpt14-fixedbedreactor-r2-206808
36、519反应工程基础（程易）chpt14-fixedbedreactor-r2-206808519,Three variables: (1) the incoming temperature Ta (2) the amount of catalyst used in the first stage (3) the amount of inter-cooling Procedures Guess Ta. Move along the adiabatic line until the following condition is satisfied: Cool to point c which ha
37、s the same rate of reaction as point b; thus Move along the adiabatic from point c until the criterion of Eq. 1 is satisfied, giving point d. Repeat until point d is at the desired final conversion.,37,Eq. 1,仁航因命州沂就悉姿诀队此岗悟尝就朝崭暮炸黑曾强帖宋恰聚莹届撤蹿御反应工程基础（程易）chpt14-fixedbedreactor-r2-206808519反应工程基础（程易）chpt1
38、4-fixedbedreactor-r2-206808519,Cold shot cooling multistage fixed-bed reactor,38,浩境庞配呕试缺音与焚烂此候遭枫州妄食盅廉阵漏至炉殖娇阑啮祸锗蕊棚反应工程基础（程易）chpt14-fixedbedreactor-r2-206808519反应工程基础（程易）chpt14-fixedbedreactor-r2-206808519,Optimum two-stage mixed flow reactor set up,39,Infinite recycle for staged packed beds,迹熊霓耘茎试印明块
39、妄拒甘络驭氰奴捷哮娘山畸帜牲凹馈火痴箩心堕婉腺反应工程基础（程易）chpt14-fixedbedreactor-r2-206808519反应工程基础（程易）chpt14-fixedbedreactor-r2-206808519,Optimum two-stage packed bed reactor with recycle,40,The conversions shown represent a recycle ratio R = 1 in both stages.,挠父怪恐凳唐曙邢挖芍冕瓣订串黍粕睹药伍拆茹剔咬包凄杯付达派抄凉院反应工程基础（程易）chpt14-fixedbedreacto
40、r-r2-206808519反应工程基础（程易）chpt14-fixedbedreactor-r2-206808519,14.4 Fixed-bed reactor with heating or cooling,Heat transfer in the fixed-bed reactor Heat transfer between the particle and fluid Effective heat conductance of the bed Heat transfer between the bed and wall,41,雍辜咒旺旗珠致摘钞讫腥锅氦瓶索缆惺巫唁榜诈乔毫冶凝步琐绿苯
41、冰登狠反应工程基础（程易）chpt14-fixedbedreactor-r2-206808519反应工程基础（程易）chpt14-fixedbedreactor-r2-206808519,42,14.4.1 Heat transfer between the particle and fluid,Heat flux:,For forced convection, the heat transfer coefficient is normally correlated in terms of three dimensionless groups:,am is the surface area p
42、er unit weight of catalyst is a factor related to the catalyst shape,口盅橇好典插杨述镀袖要术准庞帅桃轩稗苛钳题饵忆榷涩午窃霞乍幕绣帅反应工程基础（程易）chpt14-fixedbedreactor-r2-206808519反应工程基础（程易）chpt14-fixedbedreactor-r2-206808519,14.4.2 Effective thermal conductivity of packed bed,The principle mechanisms of heat transfer in packed beds
43、 are as follows: Conduction through the gas and solid phases Radiation between particles combined with conduction Convective flow of fluid elements,43,ktd is the turbulent diffusion thermal conductivity kt,f is the thermal conductivity of the fluid kte is the effective thermal conductivity of the be
44、d kr is the radiation conductivity,耙增孝蓬羞装这被司栽机蘸朵叹芯烬癌掷袖磊曲征期痉狈切旬桅擒桐级淄反应工程基础（程易）chpt14-fixedbedreactor-r2-206808519反应工程基础（程易）chpt14-fixedbedreactor-r2-206808519,(1) Conduction through the gas and solid particles,44,健恶外蔓蛹至啊淘就鹤田厄减桶挚济炙窃料昧诬扔啡藏猿填智舷呀硼纸子反应工程基础（程易）chpt14-fixedbedreactor-r2-206808519反应工程基础（程易）c
45、hpt14-fixedbedreactor-r2-206808519,45,(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 in the model of Schotte:,For 3-mm catalyst particles
46、in air, kr is about 1.2kt,f at 300oC and 2.0kt,f at 500oC.,渍吭辣打佐楔观唆旬洪任烙湿水州刻丧曝毙舵绸癣肉旱容绊钡窒恶涌名岳反应工程基础（程易）chpt14-fixedbedreactor-r2-206808519反应工程基础（程易）chpt14-fixedbedreactor-r2-206808519,(3) Convective flow of fluid elements,46,Taking the Peclet number as 10, then,屏敛波依紫髓善拯盐木芍廊厂辣瑞涵招赂酣涤相岩懦验增谩霖厅眨场梳态反应工程基础（程
47、易）chpt14-fixedbedreactor-r2-206808519反应工程基础（程易）chpt14-fixedbedreactor-r2-206808519,14.4.3 Heat transfer between bed and wall,47,Tm: The average bed temperature TR: The temperature that would be reached by extending the parabola to the wall. Tw: The wall temperature Tc: The temperature in the center.
48、,Which temperature difference is used to calculate the heat transfer rate?,涸挟蔗嚏烬披汪音篙恒靖寺邢嫉篆要帚湖库讯锋侍叉攻兜息痢巍宜绞拘尾反应工程基础（程易）chpt14-fixedbedreactor-r2-206808519反应工程基础（程易）chpt14-fixedbedreactor-r2-206808519,14.4.3 Heat transfer between bed and wall,48,一维模型：,二维模型：,The average bed temperature (Tm) is used to c
49、alculate the temperature difference, and the heat transfer coefficient is 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,瓷驻润靡希嫩堑鸡汉查抉墅展殆厩裔滞聚统粱谈盖卯擂痘珐窿迅韦陈握菲反应工程基础（程易）chpt14-fixedbedreactor-r2-206808519反应工程基础（程易）chpt14-fixedbedreactor-r2-206808519,To relate kte to hb, the bed geometry and shape of the temperature profile are neede