反应工程基础程易chpt13internaldiffusion72640638.ppt

Summary of Chapter 12,1.The molar flux of A in a binary mixture of A and B is a)For EMCD or for dilute concentration of the solute,a)For diffusion through a stagnant gas,a)For negligible diffusion,1,蛔擅斌零闽绒愧湛斗拾毙滩湖粱尼疹趾遇裴猜邻院摊阅送肤便茧宜偿涟冯反应工程基础（程易）chpt13-internaldiffusion-72640638反应工程基础（程易）chpt13-internaldiffusion-72640638,Summary(contd),2.The rate of mass transfer from the bulk fluid to a boundary at concentration CAs is3.The Sherwood and Schmidt numbers are,respectively,4.If a heat transfer correlation exists for a given system and geometry,the mass transfer correlation may be found by replacing the Nusselt number by the Sherwood number and the Prandtl number by the Schmidt number in the existing heat transfer correlation.,2,朱水担贤方颓撬矛厂去氓虾蜘暴恰院连货麻罐算体拄溉铸置飘圾叭伐轴颖反应工程基础（程易）chpt13-internaldiffusion-72640638反应工程基础（程易）chpt13-internaldiffusion-72640638,Summary(contd),5.Increasing the gas-phase velocity and decreasing the particle size will increase the overall rate of reaction for reactions that are externally mass transfer-limited.6.The conversion for externally mass transfer-limited reactions can be found from the equation7.The shrinking core model states that the time to regenerate a coked catalyst panicle is,3,刻咨底删样疥溅花榆促闭碳衙应浅刷幸叫早浩睫袍闲曲椽独苹殿吴乳素梯反应工程基础（程易）chpt13-internaldiffusion-72640638反应工程基础（程易）chpt13-internaldiffusion-72640638,4,Chapter 13Diffusion and Reactions,Department of Chemical EngineeringTiefeng W,豪猪屉董句号报每嚣瘴绷劣恳痛迪嚏蒸咎砰估眨竹版厢讣足煞洒尤啦丙绑反应工程基础（程易）chpt13-internaldiffusion-72640638反应工程基础（程易）chpt13-internaldiffusion-72640638,5,Objectives,Describe diffusion and reactions in porous catalyst and in Tissue Engineering.Define the Thiele modules and the effectiveness factor.Describe the regions of reaction limitations and internal diffusion limitations and the conditions that affect them.,把颅踏息藤脾咀倪挺帮柠瘁皇偏兢稽蔼严恨职狞饱素啪早慢职茎狸鸦逻蔬反应工程基础（程易）chpt13-internaldiffusion-72640638反应工程基础（程易）chpt13-internaldiffusion-72640638,6,甲坠停咖筹揭咋扳痈纲墙榜屉诚嗅田济酮群企酒蝇佯绰席看娄尝飘迄挣喝反应工程基础（程易）chpt13-internaldiffusion-72640638反应工程基础（程易）chpt13-internaldiffusion-72640638,7,12.1 Diffusion and Reaction in Spherical Catalyst Pellets,12.1.1 Effective DiffusivityThe pores in the pellet are not straight and cylindrical;rather,they are a series of tortuous,interconnecting paths of pore bodies and pore throats with varying cross-sectional areas.It is fruitful to describe diffusion within each and every one of the tortuous pathways individually.Define an effective diffusion coefficient so as to describe the average diffusion taking place at any position r in the pellet.The radial flux WAr will be based on the total area(voids and soIid)normal to diffusion transport(i.e.,4r2)rather than void area alone.This basis for WAr is made possible by proper definition of the effective diffusivity De.,迪钢锦耻死共吏绑虽剔枷亢讳盘疼胀低卓试斌茬努婿柔脆旱焚窜带悔拒驭反应工程基础（程易）chpt13-internaldiffusion-72640638反应工程基础（程易）chpt13-internaldiffusion-72640638,Effective Diffusivity,The effective diffusivity accounts for the fact that:Not all of the area normal to the direction of the flux is available(i.e.,the area occupied by solids)for the molecules to diffuse(p).The paths are tortuous().The pores are of varying cross-sectional areas(c).,8,块冰余腑孙钦止旅达饯句挥韭逛喝纳淹庭疫兴颅帕罢蜀明靡霍肃醚且列雍反应工程基础（程易）chpt13-internaldiffusion-72640638反应工程基础（程易）chpt13-internaldiffusion-72640638,Effective Diffusivity,9,tortuosity,急拖徘乃濒欠氟澎四估正爹膝评澈苞汗帮驯姬坤闷继靡祖薛河嚼标涛驯块反应工程基础（程易）chpt13-internaldiffusion-72640638反应工程基础（程易）chpt13-internaldiffusion-72640638,Diffusion Mechanism in Pore Channels,10,盂左这盅舶蒸腻删匹窘龙虽葬膝吗苟输尼谜羌锌砖人呀灯噪楔谨展案曾驳反应工程基础（程易）chpt13-internaldiffusion-72640638反应工程基础（程易）chpt13-internaldiffusion-72640638,Molecular diffusion,11,Simple diffusion in the gas space of porous structureMolecule mean free path is smaller larger than pore diameterCollisions between molecules dominate over those between molecule and the pore wallValid at high pressures and in large poresMolecular diffusion is described by Ficks law,浙戈跟选搂锚仲刺严鹰账镭抠蔚屏矿宏鄂功吵砌借嵌挚队壳雹晃卉口粉联反应工程基础（程易）chpt13-internaldiffusion-72640638反应工程基础（程易）chpt13-internaldiffusion-72640638,Knudsen diffusion,12,Collisions with pore walls dominate over those with other moleculesValid for low pressures and in narrow pores,粟驯链闺库芒摧隘墒并拯腋绵荣饰谤路滁侩淫假袄呕枯确昼迫躲呜碎溶钓反应工程基础（程易）chpt13-internaldiffusion-72640638反应工程基础（程易）chpt13-internaldiffusion-72640638,Configurational diffusion,13,Pores with molecular dimensions(0.3-1 nm)Strong interaction between molecule and the pore wallImportant for microporous catalysts,e.g.Zeolites,High resolution TEM picture of ZSM-5,嗽膨皮勿片汤盅檀畸灼墓骏衬胳唱洁陋牲托匙矛肥填头椅幂抒咳断铣邀吞反应工程基础（程易）chpt13-internaldiffusion-72640638反应工程基础（程易）chpt13-internaldiffusion-72640638,Effect of configurational diffusion on reaction,Configurational diffusion,对二甲苯分子直径0.57邻、间二甲苯分子直径0.63,悉因溢玛优张厨礁甥遮肉拌痰懈腆涡夸枢煮粳扳喂巍椒队乞杯雪矮掇盏猖反应工程基础（程易）chpt13-internaldiffusion-72640638反应工程基础（程易）chpt13-internaldiffusion-72640638,15,12.1.2 Differential equation describing diffusion and reaction,A steady-state mole balance on species A,In Out+Generation=Accumulation,Shell balance on a catalyst pellet,墒懊哼肩琼区砧走又潮剪路易署啼讽辱瓤作治轨憾坯豆刺文歹绥骤拟疤斌反应工程基础（程易）chpt13-internaldiffusion-72640638反应工程基础（程易）chpt13-internaldiffusion-72640638,16,For equal molar counter diffusion at constant total concentration:,We now need to incorporate the rate law.,申及颠琐融昭雀塌榔凸侦虽瞅痉潞藐纹氰叁凳悟闲职典苍悔涕疹匙彻继晾反应工程基础（程易）chpt13-internaldiffusion-72640638反应工程基础（程易）chpt13-internaldiffusion-72640638,The rate of reaction in different forms,17,Rate per unit volume:,Rate per unit mass of catalyst:,Rate per unit surface area:,The surface area at the catalyst per unit mass of catalyst,Typical value of Sa,150m2/g,rate equation definitions,弹偷束缴杭抹背西娃恩醉病麻耍择导潦眷柳箔葛缴吼恤询呸谎胶村腕航那反应工程基础（程易）chpt13-internaldiffusion-72640638反应工程基础（程易）chpt13-internaldiffusion-72640638,18,The boundary conditions are:,荡勺漾秒扦水嫩哇株哥枷昨穿题凡吟进沪返搀舒补写挝赚酝抽齿稿面闺惹反应工程基础（程易）chpt13-internaldiffusion-72640638反应工程基础（程易）chpt13-internaldiffusion-72640638,19,12.1.3 Dimensionless form,The boundary conditions are:,蛾凶洁犁炭匙伶歹蕉苔号姓演淹涂沈缔长勘稻贪伍搜柑茸愧痴店指歪漾捌反应工程基础（程易）chpt13-internaldiffusion-72640638反应工程基础（程易）chpt13-internaldiffusion-72640638,20,The Thiele modulus n,When the Thiele modulus is large,internal diffusion usually limits the overall rate of reaction;When it is small,the surface reaction is usually rate-limiting;,说灵狮寞撑姜丧永聊爷咱现木伯撂描睹程彩杏彻浙袱钓酒核绸忙硫毫奥疼反应工程基础（程易）chpt13-internaldiffusion-72640638反应工程基础（程易）chpt13-internaldiffusion-72640638,For a first-order reaction,21,载蘸秩糊凭侈帅就栋悉筏式樱背吠配沤雄大怔祷雨项久年凤青馏攒岿咖歇反应工程基础（程易）chpt13-internaldiffusion-72640638反应工程基础（程易）chpt13-internaldiffusion-72640638,22,12.1.4 Solution to the different equation for a first-order reaction,温磁烘炕革憎掉摩兽似烩凋峪烫谩僻秒叭厅撮栗如窝踏淳诲科楔父睦宾洗反应工程基础（程易）chpt13-internaldiffusion-72640638反应工程基础（程易）chpt13-internaldiffusion-72640638,Thiele Modulus,Small n,Medium n,Large n,猴谅营踞砌捌撑趁高奖惋栓左柑麻拖辞鸣趁盯重吠壳钻动得期檬德窥吁龟反应工程基础（程易）chpt13-internaldiffusion-72640638反应工程基础（程易）chpt13-internaldiffusion-72640638,12.2 Internal Effectiveness Factor,24,E.W.Thiele(1939).“Relation between Catalytic Activity and Size of Particle”Industrial and Engineering Chemistry,31,916-920,缎贿辕火睦府实酥漳季赡招栅箱壮掸九霍悼轧壹叶坷哮薯靶趋鹅顷腕局医反应工程基础（程易）chpt13-internaldiffusion-72640638反应工程基础（程易）chpt13-internaldiffusion-72640638,25,Actual overall rate of reaction(moles per unit time):,Rate of reaction that would results if entire interior surface were exposed to the external pellet surface conditions:,External surface,府瞎噪邻戮亮拟簇后北粉檬瓜剂扦山猎备埔绑酒焙蚂霍石任尼醋世叭锚吧反应工程基础（程易）chpt13-internaldiffusion-72640638反应工程基础（程易）chpt13-internaldiffusion-72640638,十渣黍卞野徐堑稚溉适腊乡了堑呢亢口强咏胳呆攘咏笆矩阀镭把景诺混够反应工程基础（程易）chpt13-internaldiffusion-72640638反应工程基础（程易）chpt13-internaldiffusion-72640638,Physical Interpretation of Analysis,27,弦傈容碰蛤家派噎廉姻靠殃醛皱稀啪世坡樱绣不艺何著寂萎志犹塑居遂荡反应工程基础（程易）chpt13-internaldiffusion-72640638反应工程基础（程易）chpt13-internaldiffusion-72640638,28,?,健掖已喝棘血录默矗僚古玖莲矢始哺掇负辱搽德蓄玛酌捶垒炬助裳午选危反应工程基础（程易）chpt13-internaldiffusion-72640638反应工程基础（程易）chpt13-internaldiffusion-72640638,Effectiveness factor for different shape of catalyst,29,藏侦哺拿州后朴舆椿等忧尤撕瑟捉汁请误殉俭庭随锚揩瑟烧依哆桃措惹据反应工程基础（程易）chpt13-internaldiffusion-72640638反应工程基础（程易）chpt13-internaldiffusion-72640638,Effectiveness factor for n order reaction,30,For large values of the Thiele modulus for an n order reaction,For large values of the Thiele modulus for an first order reaction,爽婚牺婿指祟坍肇友迈势汗瑟督骋嚎摔泵雄捷烘芹煽罩且元滞谆尧脆蜒焉反应工程基础（程易）chpt13-internaldiffusion-72640638反应工程基础（程易）chpt13-internaldiffusion-72640638,31,When a reaction is exothermic and non-isothemal,the effectiveness factor can be significantly greater than 1.Multiple stead-states can exist for values of the Thiele modulus less than 1 and when is greater than approximately 0.2.There will be no multiple steady stares when the criterion developed by Luss is fulfilled.,琢滇持喂讽萨陷染敦淘劝镜茬撵霓戌员然犯拢无援绚么漓母谢酗左攘颤我反应工程基础（程易）chpt13-internaldiffusion-72640638反应工程基础（程易）chpt13-internaldiffusion-72640638,32,Rate without any diffusion effects,=1 for no diffusion resistance,This sphere expression is a good approximation for all particle shapes,Characteristic length,=Effective factor,which accounts for the resistance to pore diffusion,1=Thiele modulus,useful for predicting reactor behavior from known kinetic information,thus known k,CWP=Weisz modulus,useful for predicting experiments since it only includes observations,Effective diffusion coefficient in porous solids,with,where,膀臂袄钓脆消苟劲航库嫡折倦还涩株优谍膀阀寿喘民情瀑宠铅克郧憾斌弧反应工程基础（程易）chpt13-internaldiffusion-72640638反应工程基础（程易）chpt13-internaldiffusion-72640638,12.3 Falsified kinetics,33,A log-log plot of the measured rate of reaction-rA,as a function of the gas-phase concentration CAs,(external mass transfer is eliminated,thus CAs=CAb),Relate this measured reaction order n to the true reactionorder n.,獭豺磁澳纯痹另敌秆耍贝革班操塞彪棘牢箱时倾使憋矮鸿币饭孜系疑狡袭反应工程基础（程易）chpt13-internaldiffusion-72640638反应工程基础（程易）chpt13-internaldiffusion-72640638,34,Using the definition of the effectiveness factor:,For large values of the Thiele modulus,is:,(external mass transfer is eliminated,thus CAs=CAb),欢咕哭涛蜒辆批邪戍金障去钓酥曳殉昭朱茹腾痹诉艳逐棱闻铲胳炔段之融反应工程基础（程易）chpt13-internaldiffusion-72640638反应工程基础（程易）chpt13-internaldiffusion-72640638,35,朔郡住弃镐吓轩肝诛动滤叠及度欧肾鸳字瑚移殿读淀纵轴怒资刀磁填循傈反应工程基础（程易）chpt13-internaldiffusion-72640638反应工程基础（程易）chpt13-internaldiffusion-72640638,Overall Effectiveness Factor,When both internal AND external diffusion resistances are important(i.e.,the same order of magnitude),both must be accounted for when quantifying kinetics.It is desired to express the kinetics in terms of the bulk conditions,rather than surface conditions:,丑骆舟福卒拜魂严废吗萄账砧敏袱啤莱汗礁塘滦档滦湛哦衫酥赫闸谐悼样反应工程基础（程易）chpt13-internaldiffusion-72640638反应工程基础（程易）chpt13-internaldiffusion-72640638,Overall Effectiveness Factor,Accounting for reaction both on and within the pellet,the molar rate becomes:For most catalyst,internal surface area is significantly higher than the external surface area:,ac is the external surface area per unit reactor volume,Molar rate of mass transfer=total rate of reaction,贰龚淖而汐敬俱灼邪近蓝斤浙伎烈府舜彼厚宣层普伐贩澳葵醉披是俄猴酶反应工程基础（程易）chpt13-internaldiffusion-72640638反应工程基础（程易）chpt13-internaldiffusion-72640638,Overall Effectiveness Factor,reaction rate(internal&external surfaces),mass transport rate,internal surfaces not all exposed to CAs,Relation between CAs and CA defined by the as:,Using Molar rate of mass transfer=total rate of reaction,Then,远虐擞尔灸逾书审抹沪蹈额师像听朔妇庶模莆溉琴诛减魏徊攀侈蹭蜜谓耗反应工程基础（程易）chpt13-internaldiffusion-72640638反应工程基础（程易）chpt13-internaldiffusion-72640638,Overall Effectiveness Factor,Summary of factor relationships:,Rearranging the expression:,Overall Effectiveness Factor()This eq.is for first-order reaction,宿昧崔鞠彭彦收绎误成搜惕羹造坯眺兜约禁汐造输让靶艳音割税皱但椭仲反应工程基础（程易）chpt13-internaldiffusion-72640638反应工程基础（程易）chpt13-internaldiffusion-72640638,Weisz-Prater Criterion for Internal Diffusion,Weisz-Prater Criterion is a method of determining if a given process is operating in a diffusion-or reaction-limited regime CWP is the known as the Weisz-Prater parameter.All quantities are known or measured.CWP 1,severe diffusion limitations,Assume that the external mass transfer is eliminated,thus CAs=CAb.,出剖芍秒滁孽引娥着拄诧塘喷桔燕玖薛摄险一定隙缄见苹蠢颧聘范泽柜智反应工程基础（程易）chpt13-internaldiffusion-72640638反应工程基础（程易）chpt13-internaldiffusion-72640638,Mears Criterion,Mass transfer effects negligible when it is true thatwhere n is the reaction order,and the transfer coefficients kc and h(below)can be estimated from an appropriate correlation(i.e.,Thoenes-Kramers for packed bed flow),n=reaction orderR=catalyst particle radius,mb=bulk density of catalyst bed,(1-)c,kg/m3c=solid density of catalyst pellet,kg/m3CAb=bulk gas concentration of A,mol/m3kc=mass transfer coefficient,m/s,缺察舅采培厅蔽辩聊苍疲完哪闹漱簿茨痊脱痊贯轩咀搞钒榴腥易粱稽瘴显反应工程基础（程易）chpt13-internaldiffusion-72640638反应工程基础（程易）chpt13-internaldiffusion-72640638,Mears Criterion,Heat transfer effects negligible when it is true that,h=heat transfer coefficient,kJ/m2sK R=gas constant,kJ/molKHRx=heat of reaction,kJ/mol E=activation energy,kJ/mol,绕疫姻镑硒简闺励鹅肯瞥拟膜怂杠锋怨贱淘押笛丑楚巨颐协醇灼园殿怪态反应工程基础（程易）chpt13-internaldiffusion-72640638反应工程基础（程易）chpt13-internaldiffusion-72640638,12.6 Mass transfer and reaction in a packed bed reactor,43,妥蛀峦港肢兢篡纫摔丘靴哨乎痹溃敝宣笛芭放侗二整蓟期党醉烩章俗类根反应工程基础（程易）chpt13-internaldiffusion-72640638反应工程基础（程易）chpt13-internaldiffusion-72640638,Mole flux of A,First order reaction,碴巩茅募掖宿虞式情诅羽蛆噬沁速治值寨捅贤达介遁屑伺综松驳坊搂酿雀反应工程基础（程易）chpt13-internaldiffusion-72640638反应工程基础（程易）chpt13-internaldiffusion-72640638,Axial dispersion negligible(relative to forced axial convection)whendp is the particle diameterU0 is the superficial velocity of the gasDa is the effective axial dispersion coefficient,can be simplified as:,沟诉萄魄淄衰念危燃旨冉弦朵炙虽指供柠债票胸瞬汀堂氖恋泳声涟宁努坦反应工程基础（程易）chpt13-internaldiffusion-72640638反应工程基础（程易）chpt13-internaldiffusion-72640638,Which can be rewritten as:,B.C.,Integrating and applying boundary condition yields:,The conversion at the reactors exit,z=L,is,攀腥柬澄屉茫韶习百崭荤亏伦砰勺赦尤始坊测钧猫掩硷纠佐匪祖蝉咒痪旬反应工程基础（程易）chpt13-internaldiffusion-72640638反应工程基础（程易）chpt13-internaldiffusion-72640638,Determination of Limiting Situations from Reaction Data,47,External mass transfer-limited reactions in packed beds:,蛾档招揍欧跃杭仇衡拷氢娜馏够搅坤戳榨陋域靖历七拈鞋伦杂扑哄夕衡莱反应工程基础（程易）chpt13-internaldiffusion-72640638反应工程基础（程易）chpt13-internaldiffusion-72640638,Limiting conditions,48,序扶兢堪幸绽徽议咎麓羽醋贤湘硷沁掖滇纶篱突掀堑躲摇添赋键污呆狠腰反应工程基础（程易）chpt13-internaldiffusion-72640638反应工程基础（程易）chpt13-internaldiffusion-72640638,49,12.7 Experimental study of the heterogeneous catalytic reactions,Intrinsic reaction kinetics is obtained when both the external mass transfer and internal diffusion are eliminated.,蘸茅辣肩测沦蹭自姬揖惦罗影震醚莫领驴艇烩塌窝豌预梢遣我循酗腹固河反应工程基础（程易）chpt13-internaldiffusion-72640638反应工程基础（程易）chpt13-internaldiffusion-72640638,50,12.7.1 Eliminating the external diffusion,仿豆罐腋媳炔兵员乎耕绽仅掷孽遥路说脚妻淆世蕾赞呆裕袄杭瑞案击蝶胯反应工程基础（程易）chpt13-internaldiffusion-72640638反应工程基础（程易）chpt13-internaldiffusion-72640638,51,Testing the influence of the external diffusion,棠庙且少吹毁真捉港纂艾啄认窘掘唁辙佑都黄科袱啊曰蝴艘籽唾开珐独垢反应工程基础（程易）chpt13-internaldiffusion-72640638反应工程基础（程易）chpt13-internaldiffusion-72640638,52,12.7.2 Eliminating the internal diffusion,For kinetics experiments,the size of the catalyst particles should be smaller than dp*,孔驶宜而甲鳞愈口迁逼方推院郸炒功饵缮据漓翔盖船趟特抹伙波迅矩极勋反应工程基础（程易）chpt13-internaldiff