Lecture # Chemical Reaction Engineering Youn-Woo Lee School of Chemical and Biological Engineering Seoul National University 155-741, 599 Gwanangro, Gwanak-gu, Seoul, Korea ywlee@snu.ac.kr http://sfpl.snu.ac.kr
第 2 章 Conversion and Reactor Sizing Reaction Engineering 1 反應工學 I Seoul National University
개요. 제1장에서는반응이일어나는영역 ( 반응기 ) 에서일반몰수지식 (GMBE) 을유도하였고이를 4가지이상적인반응기에적용하여각반응기에대하여설계방정식을유도하였다. 제2장에서는어떻게이런반응기들의크기를구하고개념적으로어떻게배열하는지보여줄것이다. 이번단원에서는 전화율 (X) 을정의하고, 4종류의이상적인반응기의설계방정식들을전화율 X의항으로다시쓰며, 일단반응속도와전화율사이의관계가주어진경우 ( 즉, -r =f(x)) 에 Levenspiel Plot을그려보고, Levenspiel plot으로부터반응기의크기를구해보고, 어떻게 CSTR과 PR의크기를비교하는지보여주고, 어떻게반응기들을직렬로최적배열하는지보여줄것이다. 더욱이, 반응속도와전화율사이의관계가주어진경우에, CSTR 과 PR 의크기를 구할수있고직렬로배열된반응기들의총괄전화율과각각의반응기부피들을 계산할수있을것이다. Seoul National University
ollow the Reaction Design lgorithm ollow the Yellow Brick Road
Isothermal Reaction Design lgorithm
Objectives fter completing Chapter 2, reader will be able to: Define conversion. 편리한전화율사용! 왜전화율을사용하려고 X=.5일때반응기크기하는가? X=.9 일때반응시간은? Write the mole balances in terms of conversion for a batch reactor, CSTR, PR, and PBR. Size reactors either alone or in series once given the molar flow rate of, and the rate of reaction, - r, as a function of conversion, X. Seoul National University
2.1 Definition of Conversion Consider the general equation a bb cc dd (2-1) Choose as our basis of calculation (The basis of calculation is most always the limiting reactant ) b a B C Questions - How can we quantify how far a reaction has progressed? - How many moles of C are formed for every mole consumed? The convenient way to answer these question is to define conversion. c a d a D (2-2) X mole of reacted mole of fed Seoul National University
2.2 Batch Design Equations In most batch reactors, the longer a reactant is in the reactor, the more reactant is converted to product the reactant is exhausted. Consequently, in batch system, the conversion X is a function of reaction time the reactants spend in the reactor. If N is the number of moles of initially in the reactor, then the total number of moles of that have reached after a time t is [N X] mole of mole of consumed fed mole of consumed moles of reacted mole of fed N X (2-) The number of moles of that remain in the reactor after a time t, N,canbe express in terms of N and X: moles of moles of moles of that in reactor initially fed to have been consumed at time t reactor at t by chemical reaction N N N X (2-4) Seoul National University
2.2 Batch Design Equations The mole balance on species for a batch system dn dt r V (1-5) The number of moles of in the reactor after a conversion X N N (1 N X N X ) (2-4) In term of conversion by differentiating equation dn dt N dx dt The design equation for a batch reactor in differential form is The differential form for a batch reactor N dx dt r V (2-5) Seoul National University
2.2 Batch Design Equations The design equation for a batch reactor in differential form dn dt r V (2-5) Write the mole balances in terms of conversion 회분식반응기의설계방정식 N dx dt r V (2-6) Seoul National University
2.2 Batch Design Equations The design equation for a batch reactor in differential form dn dt r V Constant volume, V=V 1 V dn dt 1 V dn dt d N / V dt dc dt r r dc dt (2-7) Seoul National University
2.2 Batch Design Equations The design equation for a batch reactor in differential form dn dt r V (2-5) N dx dt r V (2-6) The differential forms of the batch reactor mole balances, Eqs (2-5) and (2-6), are often used in the interpretation of reaction rate data (Chapter 7) and for reactors with heat effects (Chapter 11-1), respectively. Seoul National University
2.2 Batch Design Equations Batch reactors are frequently used in industry for both gas-phase and liquid-phase reactions. The lab bomb calorimeter reactor is widely used for obtaining reaction rate data. Liquid-phase reactions are frequently carried out in batch reactors when small-scale production is desired or operating difficulties rule out the use of continuous flow systems. Seoul National University
or constant-volume batch reactor, V=V 1 V dn dt d N dt / V dc dt r C N V or the most common batch reactors where volume is not predetermined function of time, the time necessary to achieve a conversion X is The integral form for a batch reactor t N X t dx r V (2-7) Seoul National University
2. Design Equations for low Reactors If is the molar flow rate of species fed to a system at steady state, the molar rate at which species is reacting within the entire system will be X. X moles of time fed moles of reacted moles of fed X moles of reacted time Seoul National University
2. Design Equations for low Reactors The molar flow rate molar flow rate molar rate at which at which is consumed fed to the system within the system X molar flow rate at which leaves the system Rearranging gives 1 X (2-8) Seoul National University
2..1 CSTR or Backmix Reactor - The design equation for a CSTR V r (2-11) b B a c a C d a D - conversion of flow system - Combining (2-12) with (2-11) X (2-12) V X r exit (2-1) design equation for a CSTR Equation to determine the CSTR volume necessary to achieve a specified conversion X. Since the exit composition from the reactor is identical to the composition inside the reactor, the rate of reaction is evaluated at the exit condition. Seoul National University
2..2 Tubular low Reactor (PR) - General mole balance equation d dv r (1-12) - conversion of flow system - The differential form of the design equation X (2-12) dx dv r (2-15) - Volume to achieve a specified conversion X V X dx r (2-16) Seoul National University
2.. Packed-Bed Reactor (PBR) - General mole balance equation - conversion of flow system d dw r ' X (1-15) - The differential form of the design equation with P dx dw r ' (2-17) -The catalyst weight W to achieve a specified conversion X with P= W X dx ' r (2-18) Seoul National University
Summary of Design Equation N t N X t dx r V Design equation for a batch reactor V X r exit Design equation for a CSTR X dx r Design equation V for a PR X dx ' r Design equation W for a PBR 공통점? Seoul National University
Summary of Design Equation t N X t dx r V Reaction time ~ N ~ X V X r exit ~ 1/r V Reactor volume V X dx r (Catalyst weight) ~ W X dx ' r ~ X ~ 1/r Seoul National University
ollow the Reaction Design lgorithm ollow the Yellow Brick Road
Isothermal Reaction Design lgorithm
2.4 pplications of the design equation for continuous-flow reactor The rate of disappear of, -r, is almost always a function of the concentrations of the various species present. When a single reaction is occurring, each of the concentrations can be expressed as a function of the conversion x; consequently, -r, can be expressed as a function of X. V X dx r or a first-order reaction : r kc kc 1 X Seoul National University
How to use the raw data of chemical reaction rate? Consider the isothermal gas-phase isomerization B The laboratory measurements give the chemical reaction rate as a function of conversion. (at T=5K, 8.2atm) raw data.5.4 Greatest rate -r (mol/m s)..2 Smallest rate.1...2.4.6.8 1. Conversion, X Seoul National University
Levenspiel Plot - rate data convert reciprocal rates, 1/- r - plot of 1/- r as a function of X 25 Small rate 1/-r (m s/mol) 2 15 1 Greatest rate 5..2.4.6.8 1. Conversion, X Seoul National University
Levenspiel Plot - plot of [ /- r ] as a function of [X] 12 Table 2-1 /-r (m ) 8 6 4 2..2.4.6.8 1. Conversion ig. 2-2 Seoul National University
Reactor Size Given r as a function of conversion. Constructing a Levenspiel plot. r Here we plot either or as a function of X. 1 r r or vs. X, the volume of a CSTR and the volume of a PR can be represented as the shaded areas in the Levenspiel plots. Seoul National University
Example 2-1 Sizing a CSTR The reaction described by the data in Table 2- (below) B is to be carried out in a CSTR. Species enters the reactor at a molar flow rate of.4 mol/s. (a) Using the data in Table 2-, or ig. 2-1, calculate the volume necessary to achieve 8% conversion in a CSTR. (b) Shade the area in ig. 2-2 that would give the CSTR volume necessary to achieve 8% conversion. Table 2- Seoul National University
Example 2-1 Sizing a CSTR Calculate the volume necessary to achieve 8% conversion in a CSTR (a) V r X exit mol (.4 )(.8)(2 s m s ) mol 6.4m 12 (b) 64l =.4 mol/s.6m 1.5m 1 EXIT In CSTR, C, T, P, and X of the effluent stream are identical to that of the fluid within the reactor, because perfect mixing is assumed. /-r (m ) 8 6 4 2 V CSTR = 8 x.8 = 6.4 m..2.4.6.8 1. Conversion Seoul National University
Example 2-1 Sizing a CSTR The volume necessary to achieve 8% conversion in a CSTR is 6.4m. =.4 mol/s =.4 mol/s.6m 2.1m 1.5m 2.1m It s a large CSTR, but this is a gas-phase reaction, and CSTRs are normally not used for gas-phase reaction, and CSTRs are used primarily for liquid-phase reactions. Seoul National University
Example 2-2 Sizing a PR Calculate the volume necessary to achieve 8% conversion in a PR. We shall use the five point quadrature formula (-2) in ppendix.4..4 mol / s V X.8 dx r X r( X ).2 r 4 ( X.2) r 2 ( X.4) 4 r( X.6).2.89 4(1.) 2(2.5) 4(.54) (8.) m (2.47m ) 2.165m r ( X.8) V = 2.165 m = 2165 dm Seoul National University
Example 2-2 Sizing a PR Calculate the volume necessary to achieve 8% conversion in a PR Graphic Method 12 V X.8 r dx = area under the curve between X= and X=.8 = 2165 dm (2.165 m ) (see appropriate shaded area in ig. E2-.1) /-r (m ) 1 8 6 4 2 V PR =2.165 m..2.4.6.8 1. Conversion Seoul National University
Example 2-2 Sizing a PR Sketch the profile of r and X down the length of the reactor. Solution s we proceed down the reactor and more and more of reactant is consumed, the concentration of reactant decreases, as does the rate of disappearance of. However, the conversion increases as more and more reactant is converted to product. Simpson s rule (ppendix.4 Eq. -21) X=.2, X=.1 V X.2.1 dx r X r( X ).1.89 4(1.8) 1. m (6.54m ).218m 218dm r 4 ( X.1) r ( X.2) Seoul National University
Example 2-2 Sizing a PR Sketch the profile of r and X down the length of the reactor. Solution Simpson s rule (ppendix.4 Eq. -21) X=.4, X=.2 V X.4.2 dx r X r( X ).2.89 4(1.) 2.5 m (8.26m ).551m 551dm r 4 ( X.2) r ( X.4) Seoul National University
Example 2-2 Sizing a PR Sketch the profile of r and X down the length of the reactor. Solution Simpson s rule (ppendix.4 Eq. -21) X=.6, X=. V X.6. dx r X r ( X ) r..89 4(1.625).54 m (1.9m ) 1.9m 19dm 4 ( X.) r ( X.6) Seoul National University
Example 2-2 Sizing a PR Sketch the profile of r and X down the length of the reactor. Solution Simpson s rule (ppendix.4 Eq. -21) X=.8, X=.4 V X.8.4 dx r X r ( X ).4.89 4(2.5) 8. m (17.9m ) 2.279m 2279dm r 4 ( X.4) r ( X.8) Seoul National University
Example 2-2 Sizing a PR Sketch the profile of r and X down the length of the reactor. X.2.4.6.8 -r (mol/m s).45..195.11.5 V (dm ) 218 551 19 2279 Seoul National University
Example 2-2 Sizing a PR Sketch the profile of r and X down the length of the reactor. V=19 L X=.6 V=2165 L X=.8 V=551 L X=.4 1..8 V=218 L X.6.4 X=.2.2. 5 1 15 2 25 V (dm ) 반응기를따라내려감에따라서전화율은증가한다. Seoul National University
Example 2-2 Sizing a PR Sketch the profile of r and X down the length of the reactor..5.4 -r (mol/m s).2..1...5.2 1..4 1.5.6 2..8 2.5 1. V (m X ) 반응기를따라내려감에따라서전화율은증가하는한편반응속도 r 는감소한다. Seoul National University
Example 2- Comparing CSTR and PR Sizes Calculate the volume necessary to achieve 8% conversion in a CSTR and a PR.4 mol / s 12 1 V=2.2 m V=6.4 m /-r (m ) 8 6 4 2..2.4.6.8 1. Conversion or isothermal reaction of greater than zero order, the PR will always require a smaller volume than the CSTR to achieve. 차보다더큰차수의등온반응의경우에, 동일한전화율과동일한반응조건들 ( 온도, 유량등 ) 에대해서 CSTR 부피가 PR 부피보다일반적으로더크다. Seoul National University
Example 2- Comparing CSTR and PR Sizes.5 V=2.2 dm The isothermal CSTR volume is usually greater than the PR volume is that the CSTR is always operating at the lowest reaction rate (-r =.5). -r.4..2 The PR start at the higher rate at the entrance and gradually decreases to the exit rate, thereby requiring less volume because the volume is inversely proportional to the rate..1...2.4.6.8 1. X V=6.4 dm Seoul National University
Lecture #4 Chemical Reaction Engineering Youn-Woo Lee School of Chemical and Biological Engineering Seoul National University 155-741, 599 Gwanangro, Gwanak-gu, Seoul, Korea ywlee@snu.ac.kr http://sfpl.snu.ac.kr
ollow the Reaction Design lgorithm ollow the Yellow Brick Road
Isothermal Reaction Design lgorithm
Define conversion 2.5 Reactors in series The conversion X defined as the total number of moles of that have reacted up to that point per mole of fed to the first reactor. (assumption : no side stream withdrawn and the feed stream enters only the first reactor in the series) X i total moles moles of of reacted up to point fed to first reactor i
PR-CSTR-PR in series X 1 X= V 1 1 X 2 X V 2 2 V The relationships between conversion and molar flow rate 1 = - X 1 2 = - X 2 = - X where X 2 total moles of moles of reacted up to point fed to first reactor 2 similar definitions exist for X 1 and X
Reactor 1: V 1 X 1 dx r Reactor : X= V 1 X 1 1 V X dx X 2 r -r X 2 2 V 2 X V Reactor 2 : in out gen. 1 2 r2v 2 -r 2 -r 1 = - X 1 2 = - X 2 V 2 ( X r 2 2 X 1 ) -r 2 is evaluated at X 2 for the CSTR In this series arrangement = - X
our different schemes of reactors in series Two CSTRs in series X 1 =.4 e X 2 =.8 Two PRs in series X 1 =.4 e X 2 =.8 a PR and CSTR in series X 1 =.5 e X 2 =.8 a CSTR and PR in series X 1 =.5 e X 2 =.8
2.5.1 Two CSTRs in series X 1 =.4 -r 1 e X 2 =.8 -r 2 Reactor 1 V 1 1 r 1 X 1 (2-21) Reactor 2 V 2 ( X 2 r 2 X 1 ) (2-24)
Example 2-5: Two CSTRs in Series What is the volume of each of two CSTR reactors? X 1 =.4 e X 2 =.8 X [ o /-r ] (m )..1.2.4.6.7.8.89 1.9 1. 2.5.54 5.6 8. Reactor 1 [ o /-r ] x=.4 =2.5 m V 1 =([ o /-r ] x=.4 )(X 1 -X )=(2.5)(.4-)=.82 m Reactor 2 [ o /-r ] x=.8 =8. m V 1 =([ o /-r ] x=.8 )(X 2 -X 1 )=(8.)(.8-.4)=.2 m
Example 2-4: Two CSTRs in Series Therefore, V 1 + V 2 =.82 +.2 = 4.2 m What is the reactor volume to achieve 8% conversion in a single CSTR? [ o /-r ] x=.8 = 8. m V 1 = ([ o /-r ] x=.8 ) (X 1 -X ) = (8.)(.8-) = 6.4 m The sum of the two CSTR reactor volumes (4.2 m )in series is less than the volume of one CSTR (6.4 m )to achieve the same conversion (X=.8)
Example 2-4 One CSTR vs Two CSTRs The sum of the two CSTR reactor volumes (4.2 m ) in series is less than the volume of one CSTR (6.4 m ) to achieve the same conversion (X=.8) O /-r [m ] 12 1 8 6.2 m V 1 =.82 m X 1 =.4 e X 2 =.8 4 2.82 m..2.4.6.8 1. Conversion, X V 1 =.2 m V total = 4.2 m 12 1 O /-r [m ] 8 6 4 6.4 m X=.8 2..2.4.6.8 1. Conversion, X V total = 6.4 m
pproximating a PR pproximating a PR with a number of small, equal-volume CSTRs of V i in series 1 2 4 5 1 2 4 5 Then, compare the volume of all the CSTRs with the volume of one plug-flow reactor for the same conversion, say 8%
We can model a PR as a number of CSTRs in series 1 2 4 5 1 2 4 5 Modeling of a PR with a large number of CSTRs in series. 8 V 5 r 6 4 2 V 1 V 2 V V 4.5.5.65.74.8 X s we make the volume of each CSTR smaller and increase the number of CSTRs, the total volume of the CSTRs and the PR will become identical!
1 1 X r dx V 2 1 2 X X r dx V 2.5.2 Two PRs in series Reactor 1 Reactor 2 e X 2 =.8 1 X 1 =.4 2 1 1 2 X X X X total r dx r dx r dx V
Two PRs in Series -r X V = V + V = 1 dx + Total 1 2 X2 dx = -r X2 X 1 -r 12 1 8 O /-r [m ] 6 4 2 V 1 V 2..2.4.6.8 1. Conversion, X
Sizing PR in Series What is the volume of each of two reactors? Molar flow rate of is.4 mol/s X 1 =.4 X [ o /-r ] (m )..1.2.4.6.7.8.89 1.9 1. 2.5.54 5.6 8. e X 2 =.8 Reactor 1 By applying Simpson s rule in ppendix.4 (Text page 6),.2 V 1 = [.89+4(1.)+2.5] =.551 m =551 dm Reactor 2 ( ) By applying Simpson s rule in ppendix.4 (Text page 6), (.2 V ) 2 = [2.5+4(.54)+8.] =1.614 m =1614 dm Therefore, V 1 + V 2 =.551 m + 1.614 m =2.165 m < 4.2 m (Two CSTR in Series)
2.5. Combination of CSTR and PR in Series n industrial example of reactors in series for using dimerization of propylene into isohexane CH 2 CH -CH=CH 2 CH C=CH-CH 2 -CH X= 1 X 1 V 1 2 X 2 X V 2 V
2.5. Combination of CSTR and PR in Series CSTR 1 V 1 ( X 1 r 1 X ) X= 1 X 1 V 1 2 X 2 X CSTR 2 V 2 PR V ( X X X r 2 r 2 2 X dx 1 ) O /-r [m ] 12 1 8 6 4 2 V 2 V 1 V 2 V..2.4.6.8 1. Conversion, X V
Dimersol G unit (Two CSTR and one PR in series) Institute rançais du Petrόle Process Dimerization propylene into isohexanes
Plug-flow reactor for Dimersol process The finishing reactor ( the snake ) to comply with LPG specification in the US (less than 5% olefins)
Description of Dimersol Process The Dimersol process is used to dimerize light olefins such as ethylene, propylene and butylene. The process typically begins with the pretreatment of the propane /propylene or butane/butene feed prior to entering the reactor section of the process. Pretreatment can include the use of molecular sieve dryers, sand filters, etc. to remove water and/or H 2 S. Water in the feed stream can deactivate the catalysts used in the Dimersol process. fter drying the feed is combined with a liquid nickel carboxylate/ethyl aluminum dichloride (EDC) catalyst prior to entering the first of a series of three reactors.
Description of Dimersol Process The first two are continuous stirred tank reactors and the third is a plug-flow tubular reactor. The reactor feed is converted to the process product, dimate, primarily in the first reactor, and additional conversion is achieved in the last two reactors. The final reactor effluent consists of dimate product, unreacted C /C 4 s, and liquid catalyst. Immediately following the last reactor, the liquid catalyst is removed from the reactor effluent by treating the reactor effluent with caustic, subsequent water washing, and filtering to remove solids.
Description of Dimersol Process Spent caustic residuals are typically reused or reclaimed on- or off-site, and as a result, do not constitute solid wastes. fter filtering, the product stream enters a "Dimersol stabilizer," a distillation unit that removes unreacted LPG from the dimate product. In some cases, the product stream is also further treated by drying. LPG from the stabilizer overhead is typically sent to another unit of the refinery for further processing. The dimate product from the bottom of the stabilizer is sent to storage or product blending.
LC 1252 catalyst pplication : C or C4 Olefins Dimerization (Dimersol ) Type : nickel carboxylate/ethyl aluminum dichloride (EDC) Shape : Liquid Catalyst LC 1252 catalyst is used in the Dimersol process licensed by xens. High octane value motor gasoline is obtained from olefinic C cuts from CCs or steam crackers. Oligomerization of C or C 4 olefins produces, with high selectivity, hexenes, heptenes and higher olefins up to dodecenes
Dimersol G Process 25 plants,,,mt/year C H 6 (l) [C H 6 ] 2 H o 298 =-89.1 kj/mol (-21. kcal/mol) C 67% C = % LPG Unreacted C = T=57 o C P=17bar X 1 =.7 X 2 =.9 X =.97 5% max. propylene in propane (US LPG specification as a fuel) NaOH NH Dimersol stabilizer Isohexane bp=6 o C
Weak acid process for producing dinitrotoluene EP 9 6 2, IR PRODUCTS 1998 Dinitrotoluene is an important intermediate in producing toluenediisocyanate based polyurethanes.
TNT plant in Hiroshima, Japan TNT Production Plant EP 9 6 2, IR PRODUCTS 1998
Isothermal vs. diabatic 12 2.5 O /-r [m ] 1 8 6 4 Isothermal /-r (m ) 2. 1.5 1. diabatic 2.5..2.4.6.8 1. Conversion, X...1.2..4.5.6.7 Conversion, X
Example 2-5: n diabatic Liquid-Phase Isomerization Calculate the volume of each of the three reactors for an entering molar flow rate n-butane of 5 kmol/hr. Isomerization of butane n-c 4 H 1 i-c 4 H 1 X..2.4.6.65 -r (kmol/m -h) 9 5 59 8 25 X= 1 X 1 =.2 2 X 2 =.6 V 1 V 2 r 1 X =.65 V r
Example 2-5 o = 5 kmol/h X..2.4.6.65 -r (kmol/m -h) 9 5 59 8 25 [ o /-r ](m ) 1.28.94.85 1.2 2. (a) CSTR 1 (X 1 =.2) ( X 1 X ) V1 X 1 (.94 m )(.2). 188 r1 r1 m (b) PR (X 2 =.6) V 2.6.2.2 r dx X r X.2 4.94 4(.85 ) 1.2.8 m r X.4 r X.6 (c) CSTR 2 (X =.65) V X X 2 ) (2m )(.65.6). 1 r ( m
Example 2-5 2.5 2. /-r (m ) 1.5 1. V =.1 m.5 V 1 =.188 m V 2 =.8 m...1.2..4.5.6.7 Conversion, X
Comparing CSTR and PR Sizes 12.4 mol / s 12 1 1 /-r (m ) 8 6 4 2..2.4.6.8 1. V=6.4 dm > V=2.2 dm /-r (m ) 8 6 4 2..2.4.6.8 1. Conversion Conversion or isothermal reaction of greater than zero order, the PR will always require a smaller volume than the CSTR to achieve. 2.5 2.5 2. 2. /-r (m ) 1.5 1. < /-r (m ) 1.5 1..5...1.2..4.5.6.7 V=.188 m V=.27 m.5...1.2..4.5.6.7 Conversion, X Conversion, X or adabatic reaction, the CSTR may require a smaller volume than the PR to achieve.
Which reactor should go first to give the highest overall conversion? Which arrangement is best? It depends. X 1 e X 2 그때그때달라요 X 1 e X 2 X 1 e X 2 X 1 e X 2
n diabatic Liquid-Phase Isomerization X 1 =.4 X 1 =.4 e X 2 =.65 e X 2 =.65 2.5 2.5 2. 2. /-r /-r 1.5 1.5 (m ) 1. (m ) 1..5.5...1.2..4.5.6.7 Conversion, X Best arrangement...1.2..4.5.6.7 Conversion, X Worst arrangement
Laboratory and ull-scale operating conditions must be identical. -If we know the molar flow rate to the reactor and the reaction rate as a function of conversion, then we can calculate the reactor volume necessary to achieve a specific conversion. -However, the rate does not depend on conversion alone. It is also affected by the initial concentrations of the reactants, the temperature, and the pressure. -Consequently, the experimental data obtained in the laboratory are useful only in the design of full-scale reactors that are to be operated at the same conditions as the laboratory experiments (T, P, C ). -This conditional relationship is generally true; i.e., to use laboratory data directly for sizing reactors, the laboratory and full-scale operating conditions must be identical. -Usually, such circumstances are seldom encountered and we must revert to the methods described in Chapter to obtain r as a function of X. Seoul National University
To size flow reactor, only need -r =ƒ(x), It is important to understand that if the rate of reaction is available or can be obtained solely as a function of conversion, -r =ƒ(x), or if it can be generated by some intermediate calculations, one can design a variety of reactor or a combination of reactors. In Chapter, we show how we obtain the relationship between reaction rate and conversion from rate law and reaction stoichiometry. Seoul National University
2.6. Space time Space-time : The time necessary to process one reactor volume of fluid based on entrance conditions. lso called the holding time or mean residence time. V v time reactor required to volume of at specified process one feed measured condition time space-time of 2 min means that every 2 min one reactor volume of feed at specified condition is being treated by the reactor. V v v X dx r C X dx r
Space time The time necessary to process one reactor volume of fluid based on entrance conditions. lso called the holding time or mean residence time. a b 2m 2m Consider the tubular reactor, which is 2m long and.2 m in volume. The dashed line represents.2 m of fluid directly upstream of the reactor. The time it takes for this fluid to enter the reactor completely is the space time. or example, if the volumetric flow rate were.1 m /s, it would take the upstream volume shown by the dash lines a time V.2m.1m 2 s / s To enter the reactor. It take 2s for the fluid at point a tomovepoint b
Space time In the absence of dispersion, which is discussed in Chapter 14, the space time is equal to the mean residence time in the reactor, t m. This time is the average time the molecules spend in the reactor.
Table 2-4 Typical Space time for industrial reactor Reactor type Production capacity Batch 15 min ~ 2 h ew kg/day ~ 1, tons/year CSTR 1 min ~ 4 h 1 ~,, tons/year Tubular.5 s ~ 1 h 5 ~ 5,, tons/year Table 2-5 shows space times for six industrial reactions and reactors. (page 67)
Space velocity Definition of Space-velocity SV v V of reactor volumes of specified condition which treated in unit volume 1 1 number feed at can be time space-velocity of 5 hr -1 means that five reactor volumes of feed at specified condition are being fed into the reactor per hour. Difference in the definitions of SV and - space time : the entering volumetric flow rate is measured at the entrance condition - space velocity : other conditions are often used
LHSV and GHSV LHSV ( liquid hourly space velocity) -v is frequently measured as that of a liquid at 6 or 75, even though the feed to the reactor may be a vapor at some higher temperature. GHSV ( gas hourly space velocity) -v is normally measured at standard temperature and pressure (STP). LHSV v liquid V GHSV v V STP
Example 2-6 Reactor Space Times and Space Velocity Calculate the space time and space velocity for each of the reactors in Examples 2-2 and 2- rom Examples 2-2, v =.2 m /s, Volume of CSTR=6.4m V 6.4m 1 1 1 2 s.89 h; SV 1.125 h.2 m / s.89 h rom Examples 2-, v =.2 m /s, Volume of PR=2.165m V 2.165 m 1 1 1 18 s. h; SV.h.2 m / s. h
To summarized these last examples. In the design of reactors that are to be operated at conditions (e.g., temperature and initial concentration) identical to those at which the reaction rate data were obtained, we can size (determine the reactor volume) both CSTRs and PRs alone or in various combinations. In principle, it may be possible to scale up a laboratory-bench or pilot-plant reaction system solely from knowledge of r as a function of X or C. However, for most reactor systems in industry, a scale-up process cannot be achieved in this manner because knowledge of r solely as a function of X is seldom, if ever, available under identical conditions. Seoul National University
To summarized these last examples. In Chapter, we shall see how we can obtain -r =ƒ(x) from information obtained either in the laboratory or from the literature. This relationship will be developed in a two-step process. In Step 1, we will find the rate law that gives the rate as a function of concentration and in Step 2, we will find the concentrations as a function of conversion. Combining Step 1 and 2 in Chapter, we obtain -r =ƒ(x). Seoul National University
Homework # 1. P2-5 C 2. P2-7 B. P2-1 B 4. P2-1 Due date: one week