BASIC DESIGN EQUATIONS FOR MULTIPHASE REACTORS

Starting Reference

1. P. A. Ramachandran and R. V. Chaudhari, Three-Phase Catalytic Reactors , Gordon and Breach Publishers, New York, (1983).

2. Nigam, K.D.P. and Schumpe, A., “Three-phase sparged reactors”, Topics in chemical engineering, 8, 11-112, 679 739, (1996) 3. Trambouze, P., H. Van Landeghem, J.-P. Wauquier, “Chemical Reactors: Design, Engineering, Operation”, Technip, (2004) 2

Objectives

1.

2.

3. 4.

5.

Review microkinetic and macrokinetic processes that occur in soluble and solid-catalyzed systems.

Review ideal flow patterns for homogeneous systems as a precursor for application to multiphase systems.

Derive basic reactor performance equations using ideal flow patterns for the various phases.

Introduce non-ideal fluid mixing models.

Illustrate concepts through use of case studies.

3

Types of Multiphase Reactions

• • Reaction Type Degree of Difficulty • Gas-liquid without catalyst • Gas-liquid with soluble catalyst Straightforward Gas-liquid with solid catalyst Gas-liquid-liquid with soluble or solid catalyst • Gas-liquid-liquid with soluble or solid catalyst

(two liquid phases)

Complex 4

Hierarchy of Multiphase Reactor Models

Model Type Empirical Implementation Straightforward Insight Very little Ideal Flow Patterns Phenomenological Volume-Averaged Conservation Laws Pointwise Conservation Laws Very Difficult or Impossible Significant 5

Macrokinetic Processes in Slurry Reactors Hydrodynamics of the multi-phase dispersion - Fluid holdups & holdup distribution - Fluid and particle specific interfacial areas - Bubble size & catalyst size distributions Fluid macromixing PDF’s of the various phases Fluid micromixing - Bubble coalescence & breakage - Catalyst particle agglomeration & attrition Heat transfer phenomena - Liquid evaporation & condensation - Fluid-to-wall, fluid-to-internal coils, etc.

Energy dissipation - Power input from variouis sources (e.g., stirrers, fluid fluid interactions,…) Reactor Model 6

Macrokinetic Processes in Fixed-Bed Reactors Hydrodynamics of the multi-phase flows - Flow regimes & pressure drop - Fluid holdups & holdup distribution - Fluid-fluid & fluid-particle specific interfacial areas - Fluid distribution Fluid macromixing PDF’s of the various phases Heat transfer phenomena - Liquid evaporation & condensation - Fluid-to-wall, fluid-to-internal coils, etc.

Energy dissipation - Pressure drop (e.g., stirrers, fluid fluid interactions,…) Reactor Model 7

Elements of the Reactor Model

Micro or Local Analysis Macro or Global Analysis • Gas - liquid mass transfer • Liquid - solid mass transfer • Interparticle and interphase mass transfer • Intraparticle and intraphase diffusion • Intraparticle and intraphase heat transfer • Catalyst particle wetting • Flow patterns for the gas, liquid, and solids • Hydrodynamics of the gas, liquid, and solids • Macro distributions of the gas, liquid and solid • Heat exchange • Other types of transport phenomena 8

Reactor Design Variables

Feed Q in T in C in Reactor Reactor = f Performance Process Variables Reaction Rates Q out T out C out Product Flow Patterns • Conversion • Selectivity • Activity • Flow rates • Kinetics • Macro • Inlet C & T • Transport • Micro • Heat exchange 9

Ideal Flow Patterns for Single-Phase Systems

Q (m 3 /s) Q (m 3 /s) a. Plug-Flow Q (m 3 /s) Q (m 3 /s) b. Backmixed Flow 10

Impulse Tracer Response

x(t) M T



t



t Q (m 3 /s) Reactor System y(t) t Q (m 3 /s) E ( t ) dt



y(t) M T / dt Q



Fraction of the outflow with a residence time between t and t + dt E(t) is the P.D.F. of the residence time distribution Tracer mass balance requirement: M T



Q

 

y(t) dt o 11

Q (m 3 /s) Fluid-Phase Mixing: Single Phase, Plug Flow 12

Fluid-Phase Mixing: Single Phase, Backmixed Q (m 3 /s) Mi = Mass of tracer injected (kmol) 13

Idealized Mixing Models for Multiphase Reactors

Model Gas-Phase Liquid Phase Solid-Phase Reactor Type 1 Plug-flow Plug-flow Fixed Trickle-Bed Flooded-Bed 2 Backmixed Backmixed Backmixed Mechanically agitated 3 Plug-Flow Backmixed Backmixed Bubble column Ebullated - bed Gas-Lift & Loop 14

Ideal Flow Patterns in Multiphase Reactors Example: Mechanically Agitated Reactors

or V R = v G 1 =



G + V L +



L



G



V r



G Q G + V C +



C



L



V r

( 1  

G

 

L

)

Q L

15

First Absolute Moment of the Tracer Response for Multiphase Systems

For a single mobile phase in contact with p stagnant phases:



1 = V 1 + p



j = 2 K 1j V j Q 1

For p mobile phases in contact with p - 1 mobile phases:

V 1 + p



j = 2 K 1j V j



1 = Q 1 + p



j = 2 K 1j Q j K 1j =

 

C j C 1

 

equil.

is the partition coefficient of the tracer between phase 1 and j 16

Relating the PDF to Reactor Performance

“For any system where the covariance of sojourn times is zero (i.e., when the tracer leaves and re-enters the flowing stream at the same spatial position), the PDF of sojourn times in the reaction environment can be obtained from the exit-age PDF for a non-adsorbing tracer that remains confined to the flowing phase external to other phases present in the system.

” For a first-order process:

1

X A =

 

e H p

(k c

H p (k c ) = pdf for the stagnant phase =



0



e (

k W W / ) t E ext Q 1 ) t ( t ) dt E ext ( t ) dt

0 17

Illustrations of Ideal-Mixing Models for Multiphase Reactors

Stirred tank Bubble Column



z

                             

z Trickle - Bed Flooded - Bed G • Batch catalyst L • Plug-flow of gas • Backmixed liquid & catalyst • Catalyst is fully wetted G L • Plug-flow of gas • Plug-flow of liquid • Fixed-bed of catalyst • Catalyst is fully wetted 18

Intrinsic Reaction Rates

Reaction Scheme: A (g) + vB (l)



C (l) 19

Gas Limiting and Plug-Flow of Liquid



z

Key Assumptions

1. Gaseous reactant is limiting 2. First-order reaction wrt dissolved gas 3. Constant gas-phase concentration 4. Plug-flow of liquid 5. Isothermal operation 6. Liquid is nonvolatile 7. Catalyst concentration is constant 8. Finite gas-liquid, liquid-solid, and intraparticle gradients G L 20

Gas Limiting and Plug flow of liquid

Constant gas phase concentration  valid for pure gas at high flow rate Relative distance from catalyst particle

Q l A l

(Net input by convection)

z



Q l A l z



dz

+

(Input by Gas Liquid Transport) 

k l a B



A *



A l



-

A r

(Loss by Liquid solid Transport)

dz- k s a p



A l



A s

= 0



A r dz=

0 Dividing by Ar.dz and taking limit dz  

(1) (2) (3) (4) 21

Gas Limiting and Plug flow of liquid 22

Gas Limiting and Plug flow of liquid

Solving the Model Equations

23

Concept of Reactor Efficiency



R



Rate of rxn in the Entire Reactor with Transport Effects Maximum Possible Rate 24

Conversion of Reactant B (in terms of Reactor Efficiency) 25

Gas Limiting and Backmixed Liquid

Stirred Tank

Key Assumptions

Bubble Column



z 1. Gaseous reactant is limiting 2. First-order reaction wrt dissolved gas 3. Constant gas-phase concentration 4. Liquid and catalyst are backmixed 5. Isothermal operation 6. Liquid is nonvolatile 7. Catalyst concentration is constant 8. Finite gas-liquid, liquid-solid, and intraparticle gradients G

                            

L 26

Gas Limiting and Backmixed Liquid

Relative distance from catalyst particle -Concentration of dissolved gas in the liquid bulk is constant [≠f(z)] [=A

l,0 ]

-Concentration of liquid reactant in the liquid bulk is constant [≠f(z)] [=B

l,0 ] A in liquid bulk

: Analysis is similar to the previous case

27

Gas Limiting and Backmixed Liquid A at the catalyst surface: For Reactant B:

(Net input by flow)

=

(Rate of rxn of B at the catalyst surface) (Note: No transport to gas since B is non-volatile)

28

Gas Limiting and Backmixed Liquid Solving the Model Equations 29

A

Flow Patterns Concepts for Multiphase Systems

A Single phase flow of gas or liquid with exchange between the mobile phase and stagnant phase.

Fixed beds, Trickle-beds, packed bubble columns

B Single phase flow of gas or liquid with exchange between a partially backmixed stagnant phase.

Semi-batch slurries, fluidized-beds, ebullated beds

B 30

C

Flow Patterns Concepts for Multiphase Systems

D C, D - Cocurrent or countercurrent two-phase flow with exchange between the phases and stagnant phase.

Trickle-beds, packed or empty bubble columns

E E - Exchange between two flowing phases, one of which has strong internal recirculation.

Empty bubble columns and fluidized beds

31

Axial Dispersion Model (Single Phase)

 

C t

 @ z = 0

D ax u

0  2

C



z

2

C

0 

u



C dz

 

uC



D ax



C



z R

Basis: Plug flow with superimposed “diffusional” transport in the direction of flow @ z = L 

C



z

 0 Let

η



z L Pe ax



uL D ax τ



L u τ

 

C t

 1

Pe ax

@  = 0   2

η C

2  

C d η C

0 

C

 1

Pe ax



C



η



τ R

@  = 1 

C



η

 0

32