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Department of Chemical Engineering

Reaction Engineering II Heterogeneous and Multiphase Reactor Design

Lecture Script V 4.5 16 May 2014

Lecturer: Dr. Clemens Brechtelsbauer

Script compiled by Dr. Klaus Hellgardt with additions by Dr. Clemens Brechtelsbauer based on a course by Dr. Esat Alpay

Page 1 of 91

Course Aims The course focuses on heterogeneous and multi-phase reactors. Through understanding the underlying physics of the different reactor types, the student will be equipped to carry out reactor design tasks for conventional and novel reactors in a systematic way. Particular focus is on teaching a generally applicable problem solution approach, which is of relevance to the 4th year design project as well as professional practice.

Course Structure The course consists of the following components:

    

Fundamentals of transport processes in heterogeneous reactors Fixed bed catalytic reactors Fluidised bed reactors Gas-liquid and gas-liquid-solid reactors Non-catalytic fluid-solid reactors

Learning Outcomes By the end of the course students should be able to:    



Establish and follow a selection process to determine the most appropriate reactor type for a specific process Apply a general problem solving approach to design heterogeneous and multi-phase reactors Carry out reactor sizing calculations to the level of detail required Identify critical parameters affecting the performance of heterogeneous and multi-phase reactors Estimate the margin for and level of error in their calculations

Further Reading To fully appreciate the subject, further study of the following references is strongly recommended: 1. Gilbert F. Froment, Kenneth B. Bischoff, Chemical Reactor Analysis and Design, 2nd Edition, John Wiley & Sons, 1990 2. H. Scott Fogler, Elements of Chemical Reaction Engineering, 2nd Edition, Prentice-Hall, 1992 3. Octave Levenspiel, Chemical Reaction Engineering, 3rd Edition John Wiley & Sons, 1999 The course is essentially based on [1], which is the primary reference. However, [2] and [3] provide good alternative perspectives, particularly if you want to build your understanding. Beware though of the differences in notation! Page 2 of 91

Reaction Engineering II: Course Overview 1

Introduction to Heterogeneous and Multiphase Reactors ..................................................................... 4

2

Transport Processes in Heterogeneous Catalysis ................................................................................... 6 2.1 Interfacial Gradient Effects .................................................................................................................. 6 2.1.1 Reactions at Catalyst Surface ....................................................................................................... 6 2.1.2 Attaining Values of km ................................................................................................................ 8 2.1.3 Concentration (Partial Pressure) Differences across the External Film ..................................... 10 2.1.4 Temperature Differences across the External Film .................................................................... 11 2.1.5 Mass Transfer on Metallic Surfaces........................................................................................... 12 2.2 Intraparticle Gradient Effects ............................................................................................................. 14 2.2.1 Catalyst Internal Structure ......................................................................................................... 14 2.2.2 Pore Diffusion ............................................................................................................................ 14 2.2.3 Reaction and Diffusion within a Catalyst Pellet ........................................................................ 18 2.2.4 Temperature Gradients within a Catalyst Pellet......................................................................... 27 2.3 Combined Interfacial (External) and Intraparticle (Internal) Resistances ......................................... 30

3

Fixed Bed Catalytic Reactor (FBCR) Design........................................................................................ 31 3.1 Pseudo-Homogeneous PFR and Axially Dispersed PFR Models ...................................................... 31 3.1.1 PFR Model ................................................................................................................................. 31 3.1.2 Axially Dispersed PFR Model ................................................................................................... 33 3.2 Heterogeneous Models....................................................................................................................... 36 3.2.1 Use of Effectiveness Factor ....................................................................................................... 36 3.2.2 Use of Intraparticle Diffusion Equations ................................................................................... 37 3.3 2D Models.......................................................................................................................................... 38

4

Fluidised Bed Reactors ........................................................................................................................... 40 4.1 Overview of Fluidisation Principles .................................................................................................. 40 4.2 Overview of Key Applications .......................................................................................................... 48 4.3 Modelling of Fluidised Bed Reactors: Non-Transport....................................................................... 50 4.3.1 Two-Phase Models..................................................................................................................... 50 4.3.2 Three-Phase (Hydrodynamic) Models ....................................................................................... 54 4.4 Modelling of Transport (Riser) Reactors ........................................................................................... 56

5

Multiphase Reactors ............................................................................................................................... 58 5.1 Background ........................................................................................................................................ 58 5.2 Review of Two-Film Theory ............................................................................................................. 60 5.3 General Design Models for Multiphase Reactors .............................................................................. 65 5.3.1 Gas & Liquid Phases Completely Mixed ................................................................................... 65 5.3.2 Gas & Liquid Phases in Plug Flow ............................................................................................ 69 5.3.3 Gas Phase in Plug Flow, Liquid Phase Completely Mixed........................................................ 70 5.3.4 Effective Diffusion Model ......................................................................................................... 70 5.4 Simplifications to Multiphase Design Models ................................................................................... 71 5.4.1 Instantaneous Reactions ............................................................................................................. 71 5.4.2 Very Fast Reactions ................................................................................................................... 71 5.4.3 Slow Reactions........................................................................................................................... 71 5.4.4 Solid Catalyzed Reactions ......................................................................................................... 72 5.4.5 Resistances in Series Approximation: Gas-Liquid-Solid Reactions .......................................... 72 5.4.6 Resistances in Series Approximation: Gas-Liquid Reactions .................................................... 74 5.5 Factors in Selecting a Gas-Liquid Contactor ..................................................................................... 77

6

Non-Catalytic Fluid-Solid Reactions ..................................................................................................... 78 6.1 Total Particle Dissolution................................................................................................................... 79 6.2 Shrinking Core Model........................................................................................................................ 81 6.3 Reactor Design ................................................................................................................................... 85 6.3.1 Plug Flow of Solids.................................................................................................................... 86 6.3.2 Mixed Flow of Solids................................................................................................................. 87

7

Notation .................................................................................................................................................... 88 Page 3 of 91

1 Introduction to Heterogeneous and Multiphase Reactors 

Reaction Engineering I: material and energy balances for ideal PFR, CSTR, and batch reactors



Pseudo-homogeneous assumption: Mass transfer & heat transfer resistances between different phases are neglected, such that reactor contents can be treated as a single phase. Useful for preliminary design or truly homogeneous systems.



Heterogeneous model used when temperature (T) and composition (C) need to be distinguished between the phases.



Real reactors may involve multiple phases (i.e. multiphase reactors), which will often need to be considered as heterogeneous. However, the phrase “multiphase reactors” is usually used for systems involving fluid-fluid interactions, i.e. gas-liquid and liquid-liquid systems.



For systems involving solids, two general cases exist: (i) Solid as porous catalyst pellet Solid not consumed in reaction but its physical and chemical nature may change. E.g. (1) Pore blocking due to deposits of carbonaceous by-products of reaction, i.e. coking. (2) Metal particles (the active catalyst) may coalesce at high temperatures, reducing the overall surface area for reaction and hence the rate constant, i.e. sintering. sintering

(ii) Solids as non-catalyst E.g. (1) Dissolution of solid through reaction with a fluid (2) Burning off of coke in a catalyst pellet for its regeneration 

Most practical (and common) utilisation of solid catalysts is in a fixed bed catalytic reactor (FBCR), i.e. a tubular reactor packed with catalyst, through which the fluid reaction species flow. Advantages of FBCR: - No solids handling - Little solids attrition - High surface area through use of porous catalysts - Plug flow operation can be approached - No separation of catalyst from reaction products needed Disadvantages of FBCR: - Pressure drop - Complex (e.g. multitubular) arrangement for reactions requiring high heat-exchange duties - Large down-time for catalysts which deactivate rapidly Page 4 of 91



Where disadvantages of FBCR are prohibitive, reactors involving the fluidisation of the catalyst, or the flow (transport) of the catalyst in some way, are employed. Such operation enables better heat transfer between the fluid-solid and the fluid and heatexchange surface, and provides a means for the continuous removal of catalyst for regeneration, and feed of fresh catalyst.



The general performance equation to design heterogeneous and multiphase reactors is quite complex: Output = f(input, material balance, equilibrium, kinetics, flow & contacting pattern, phase aggregation)

Hence we always search for simplifying approximations! 



To model our reactors, we will use the rate of consumption rA (or rate of reaction for short). It is a positive number! Unless otherwise stated, we will also use the convention of positive stoichiometric coefficients, e.g. r r r r (1-1) a A + b B  c C + d D, with a, b, c, d > 0 so that A  B  C  D a b c d All reactor models use approximations, modifications or combinations of the ideal cases: batch, PFR, differential reactor and CSTR. Therefore, it is important to know these reactor design equations: Batch Reactor rA  

1 dnA V dt

(1-2) 

Integral Reactor PFR dn rA   A dV (1-3)

Differential Reactor nA  n A0 rA   V (1-4)

CSTR

rAexit 

n A0  n exit A

V (1-5)

To design a reactor, knowledge of the rate of reaction is key. For heterogeneous and multiphase reactors, the rate of reaction can be expressed in many different ways. We have to use the rate which is most convenient for our design, as we can always convert one into the other:  mol   mol   mol  dn A      r V r m r  '    2   Asurfa ce A reactor A cata lyst A   3 S  dt     kgcata lyst  s   msurfa ce s   mreactor  s  (1-6)



The choice of a reactor for a specific application depends on the reaction rate, the catalyst stability and product distribution considerations. The selectivity of the process is a key factor for selecting the desired mixing environment we require for our process.



Regardless of the problem type, the general solution approach to design heterogeneous and multiphase reactors remains the same: 1. Assemble all relevant physico-chemical data for the process. 2. Quantify the relationship between intrinsic and mass transfer rate. 3. Draw a model sketch. 4. Define the balance equations, model parameters and boundary conditions. 5. Look for model simplification opportunities, taking into account step (2.) above. 6. Solve the model by combining equations to arrive at XA = f(t or ). 7. Use this equation to determine the expected conversion for a given reactor volume or calculate the reactor volume for a desired conversion. Page 5 of 91

2 Transport Processes in Heterogeneous Catalysis 2.1 Interfacial Gradient Effects 2.1.1 Reactions at Catalyst Surface (CA at solid surface) CSAs

active centres

CAs

CA

(CA in solid)

NA FLUID

externalfilm

SOLID

l z



0

First-order reaction A  B: S

S

rAS  k SC AS mol rASS : m2S  s kS :

C SAS :

(2-1)

m 3f m2S  s mol

m 3f

at z = 0

At steady-state: rASS  N A ( rA )

(2-2)

where S N A  k mC (C A  C AS )

(2-3)

kmC :

m3f m 2S  s Page 6 of 91

or:

NA   k my  ( y  y S )  A AS     NA k mP   (PA  PASS )    k C  k P  k  mC mP my      kS C ASS  k m C (C A  C ASS )  C SA S 

kmC k S  k mC

 CA

Substitute this back into (2-1):

rA  k 0C A 1 1 1   where k0 km C k S

(2-4) (2-5)

k0: overall rate constant Limiting cases: (i) k mC  k S (rapid mass transfer), then:

k0  k S and C SAS  CA i.e. overall process is reaction rate controlled. (ii) k S  k mC (rapid reaction), then: k0  k mC

and C SAS  0

i.e. overall process is diffusion controlled. 

Second-order reaction 2A  B: We are using similar procedure to above, but equation (2-1) is replaced with:

rASS  k S (C ASS )

2

(2-6)

gives

rA  kmC (  ( 2 1) 1/ 2 )C A with   1

(2-7)

km C 2k S C A

i.e. neither 1st nor 2nd order concentration dependence. Limiting cases: (i) k mC  k S  rA  kS C 2A (ii) k S  k mC  rA  kmC C A Page 7 of 91



Mass transfer can thus lead to difficulties in experimentally determining rate coefficients and orders! However, we can work under conditions where we have either reaction or diffusion controlled process. i.e. - k mC  k S or - k S  k mC (in this case should reduce T or increase fluid turbulence/mixing)



For complex reactions, analytical solution is not usually possible.

2.1.2 Attaining Values of km Usually correlations in handbooks define the mass transfer coefficient under conditions of equimolar counter-diffusion, k0m 

How is k0m related to km? (i) Equimolar counter-diffusion (ECD): N A   N B  N  y  CD dyA N A T A AB dz But there is no net total molar flow: N T  N A  N B  0 dy  N A  CD AB A dz l

yA

0

yAS

 NA  dz  CDAB

 dy

0

A

(Also k mC  Note:

(2-10)

CD AB l

k m0y  k my

(2-11)

for km y C

(2-9)

S

CD AB ( yA  y ASS )  N A  l

But k m y 

(2-8)



ECD DAB ) l

DAB (diffusion coefficient or diffusivity) is ~10-9 m2/s in liquids, ~10-8 – 10-6 m2/s in porous media, and ~10-5 – 10-4 m2/s in gases.

(ii) For reaction in which total moles are not conserved, e.g.:

a A  bB b  NA a equimolar counter-diffusion cannot be used.  N B  

Page 8 of 91

(2-12)

Substitute (2-12) into (2-9) and rearrange: yA l dy A  NA  dz  CD AB  b 0 ySAS 1  (1  )y a A

 N A  kmy ( y A  y ASS ) where:

km y  y fA 

km0 y

(2-13a)

y fA (1   A y A )  (1   A y ASS )

‘film factor’ (2-13b)  1  Ay A   ln   1   A y SA  S   ( b a) A  ‘stoichiometric coefficient correction factor’ (with a, b > 0) (2-13c) a see Reaction Engineering I for  A  0, 

0 y fA  1 and kmy  kmy

For the general reaction: aA  bB  ...  rR  sS  ...

Equations (2-13a) and (2-13b) are applicable but

A  

( r  s  ...)  ( a  b  ...) a

(with a, b, ..., r, s, ... > 0)

A common method for predicting k0m is through the use of the jD factor. 2 k0 M j D  m m  Sc 3 G  g  Mm : average molecular mass    mol   g  G: mass flux  2   m  s  viscous effects Sc: Schmidt number    f  D diffusion effects where

: f: D:

Note:

(2-14)

viscosity fluid density molecular diffusivity

Sc is ~1 for most gases, and ~103 for common liquids. 0

0

k0m can be taken as k m y or k m f , as long as it is remembered that:

k0m  kmy  y f A  kmP  P  y f A  kmP  Pf A

( P f A is referred to as pressure film factor.)

Page 9 of 91



In addition to (2-14), a second relationship for jD is available from charts or correlations (see e.g. Froment/Bischoff, p. 129) e.g. for flow in a bed packed with spherical particles and  b = 0.37: jD = 1.66 Re-0.51 for Re < 190 jD = 0.983 Re-0.41 for Re > 190 G  d p inertial effects  Re   viscous effects Thus, given (2-14) and a suitable correlation, we can solve for k0m and thus k m y if y f A is given (see chapter 2.1.3)



Similar correlations...