basic design equations for multiphase reactors · 2018. 3. 20. · 3 objectives 1. review...

BASIC DESIGN EQUATIONS FOR MULTIPHASE REACTORS

2

Starting Reference

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

2. Nigam, K.D.P. and Schumpe, A., “Three-phase spargedreactors”, 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)

3

Objectives

1. Review microkinetic and macrokinetic processes thatoccur in soluble and solid-catalyzed systems.

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

3. Derive basic reactor performance equations using idealflow patterns for the various phases.

4. Introduce non-ideal fluid mixing models.

5. Illustrate concepts through use of case studies.

4

Types of Multiphase Reactions

• Gas-liquid without catalyst

• Gas-liquid with soluble catalyst

• Gas-liquid with solid catalyst

• Gas-liquid-liquid with soluble

or solid catalyst

• Gas-liquid-liquid with soluble

or solid catalyst (two liquid phases)

Straightforward

Complex

Reaction Type Degree of Difficulty

5

Hierarchy of Multiphase Reactor Models

Empirical

Ideal Flow Patterns

Phenomenological

Volume-Averaged

Conservation Laws

Pointwise Conservation

Laws

Straightforward

Implementation Insight

Very little

Very Difficult

or Impossible

Significant

Model Type

6

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

7

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

Macrokinetic Processes in Fixed-Bed Reactors

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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

9

Reactor Design Variables

Reactor Process Reaction Flow

= f

Performance Variables Rates Patterns

• Conversion • Flow rates • Kinetics • Macro

• Selectivity • Inlet C & T • Transport • Micro

• Activity • Heat exchange

Feed ReactorQin

Tin

Cin

Product

Qout

Tout

Cout

10

Ideal Flow Patterns

for Single-Phase Systems

Q (m3/s) Q (m3/s)

Q (m3/s) Q (m3/s)

a. Plug-Flow

b. Backmixed Flow

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Impulse Tracer Response

Q (m3/s) Q (m3/s)Reactor System

t

x(t) MT t

t

y(t)

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:

oT dt y(t) Q M

Q /M

dt y(t) dt )t(E

T

12

Fluid-Phase Mixing: Single Phase, Plug Flow

Q (m3/s)

13

Fluid-Phase Mixing: Single Phase, Backmixed

Q (m3/s)

Mi = Mass of tracer injected (kmol)

14

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

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Ideal Flow Patterns in Multiphase ReactorsExample: Mechanically Agitated Reactors

L

r G L

L

V

Q

( )1

G

r G

G

V

Q

VR = vG + VL + VC

1 = G + L + C

or

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First Absolute Moment of the

Tracer Response for Multiphase Systems

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

1 =

V1 + K1j Vj

j = 2

p

Q1

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

1 =

V1 + K1j Vj

j = 2

p

Q1 + K1j Qj

j = 2

p

K1j = C j

C1

equil.

is the partition coefficient of the tracer

between phase 1 and j

17

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:

0

H -A

pe = X - dt )t(E 1 extt )(k c

0

( -e = dt )t(E ext

t )Q/Wk 1W

Hp(kc) = pdf for the stagnant phase

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Illustrations of Ideal-Mixing Models

for Multiphase Reactors

z

G L• Plug-flow of gas

• Backmixed liquid & catalyst

• Batch catalyst

• Catalyst is fully wetted

z

G L• Plug-flow of gas

• Plug-flow of liquid

• Fixed-bed of catalyst

• Catalyst is fully wetted

Stirred tank

Bubble Column

Trickle - Bed

Flooded - Bed

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Intrinsic Reaction Rates

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

20

z

G L

Gas Limiting and Plug-Flow of Liquid

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

Key Assumptions

21

Gas Limiting and Plug flow of liquid

Constant gas phase concentration

valid for pure gas at high flow rate

Conce

ntr

ation o

r Axia

l H

eig

ht

Relative distance from catalyst particle

0dz= AAAadz- kAAAakAQAQ rslpsrl

*

Bldzzllzll

(Net input by convection)

(Input by Gas-Liquid Transport)

(Loss by Liquid-solid Transport)

+ - = 0 (1)

(2)

(3)

(4)

Dividing by Ar.dz and taking limit dz

22

Gas Limiting and Plug flow of liquid

23

Gas Limiting and Plug flow of liquid Solving the Model Equations

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Concept of Reactor Efficiency

RRate of rxn in the Entire Reactor with Transport Effects

Maximum Possible Rate

25

Conversion of Reactant B(in terms of Reactor Efficiency)

26

Gas Limiting and Backmixed Liquid

z

G L

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

Stirred Tank

Bubble Column

Key Assumptions

27

Gas Limiting and Backmixed LiquidConce

ntr

ation o

r Axia

l H

eig

ht

Relative distance from catalyst particle

-Concentration of dissolved gas in the liquid bulk is constant [≠f(z)] [=Al,0]-Concentration of liquid reactant in the liquid bulk is constant [≠f(z)] [=Bl,0]

A in liquid bulk: Analysis is similar to the previous case

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Gas Limiting and Backmixed LiquidA at the catalyst surface:

For Reactant B:

(Note: No transport to gas since B is non-volatile)

(Net input by flow)

(Rate of rxn of B at the catalyst surface)

=

29

Gas Limiting and Backmixed LiquidSolving the Model Equations

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Flow Patterns Concepts

for Multiphase Systems

A BA - 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

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Flow Patterns Concepts

for Multiphase Systems

C D EC, D - Cocurrent or

countercurrent two-phase

flow with exchange between

the phases and stagnant

phase.

Trickle-beds, packed or

empty bubble columns

E - Exchange between two

flowing phases, one of

which has strong internal

recirculation.

Empty bubble columns and

fluidized beds

32

Axial Dispersion Model (Single Phase)

Basis: Plug flow with superimposed “diffusional” transport in the

direction of flow

Rdz

Cu

z

CD

t

Cax

2

2

@ z = 0z

CDuCCu ax

00

@ z = L 0

z

C

Let

L

zη

ax

axD

uLPe

u

Lτ

Rτηd

C

η

C

Pet

Cτ

ax

2

21

@ = 0 η

C

PeCC

ax

10

@ = 1 0

η

C