Continuous Stirred Tank Reactors (CSTRs)

1 Chemical and Biological Reaction Engineering, Spring 2007 Prof. William H. Green Lecture 5: Continuous Stirred Tank Reactors (CSTRs) This lecture covers: Reactions in a perfectly Stirred tank. Steady State cstr . Continuous Stirred Tank Reactors (CSTRs) Continuous Plug Flow Reactor cstr Open system Steady State Well mixed Open system Steady State Continuous Batch Close system Well mixed Transient In terms of conversion, XA? Mole Balance on Component A In-Out+Production=Accumulation FF(steady state) Ao +ArAV=0 What volume do you need for a certain amount of conversion? FXV=AoA rAwhere rA is evaluated at the reactor concentration. This is the same as the exit concentration because the system is well mixed. For a liquid phase with constant P: FC=( =volumetric flow rate) AoAov00vFFAo VF==AAFAo XAF rAoAFigure 2. A batch reactor. Figure 1. A plug flow reactor, and Continuous Stirred tank reactor.

2 FCAA=v 0 VCX=AoA vr0 AV = average time a volume element of fluid stays in the reactor v0 Cite as: William Green, Jr., course materials for Chemical and Biological Reaction Engineering, Spring 2007. MIT OpenCourseWare ( ), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. AoAACXr = Consider: 1st Order Reaction Kinetics concentration or conversion? AArkC = convert rate law from CA to XA ()1 AAoACCX= ()1 AAorkCX = A ()()11reactor size in terms of conversion and rate constant AoAAAoAACXXkCXkX == rearrange to find how much conversion for a given reactor size 1 AkXk =+ average reactor residence time 1average time until reaction for a given molecule k We can now define a Damk hler number reaction rateis the reaction rate law at the feed conditionsflow, AoAoAorVDarF == For a liquid at constant pressure with 1st order kinetics: Dak = 1 ADaXDa =+ therefore: As Da , XA 1 As Da , XA 0 (molecule probably leaves before it can react) For a liquid at constant pressure with 2nd order kinetics: ()2221 AAAoArkCkCX == AoAoAACCXr == 2 AAoXkC()()2211 AAAoXXkCX= A solving for conversion: ()12142 AoAoAAokCkCXkC + += Chemical and Biological Reaction Engineering, Spring 2007 Lecture #5 Prof.

3 William H. Green Page 2 of 4 Cite as: William Green, Jr., course materials for Chemical and Biological Reaction Engineering, Spring 2007. MIT OpenCourseWare ( ), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. 2 AokCDa=AoVCAookCv = Thus, conversion can be put in terms of Da. ()12142 ADaDaXDa+ += How long does it take for a cstr to reach steady state? In-Out+Production=Accumulation AAoAAdNFFrVdt + = For a liquid at constant density this is: AAoAAdCCCrdt += non-dimensionalize AAAoCtCtC == AoAoAAoACCCkCC =AoC AdCdt P 11 DaAAdCkCdt ++ = () 11 AAdCDaCdt++= with initial conditions: 0, 0 ACt== we have the solution: () (1 )1 11 DatACeDa += + In nondimensional terms, it exponentially approaches a new steady state with a characteristic time 1Da +. Chemical and Biological Reaction Engineering, Spring 2007 Lecture #5 Prof. William H. Green Page 3 of 4 Cite as: William Green, Jr.

4 , course materials for Chemical and Biological Reaction Engineering, Spring 2007. MIT OpenCourseWare ( ), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. t AC 11Da+ 11Da+ Figure 3. Approach to steady state in a Continuous Stirred tank reactor ( cstr ). The time at which of the steady state concentration of CA is achieved is the htime: ln(2) 1+Da CSTRs in Series (Liquid and at constant pressure) alf CA0 CDa1 Da2 Figure 4. Two tanks in series. The output of the first tank is the input of the second tank. 1st order reaction kinetics CCA0A1= 1+Da1 For the second reactor iterate ()()CCA0A2= 11++Da12 DaIf the CSTRs are identical, ()CCAn=A0 1+Dan many CSTRs in series looks like a plug flow reactor. Chemical and Biological Reaction Engineering, Spring 2007 Lecture #5 Prof. William H. Green Page 4 of 4 Cite as: William Green, Jr., course materials for Chemical and Biological Reaction Engineering, Spring 2007.

5 MIT OpenCourseWare ( ), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. A2