Conceptual Reactor Design, Multi-phase Reactors, Non-Isothermal Reactors

8/18/2019 Conceptual Reactor Design, Multi-phase Reactors, Non-Isothermal Reactors

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r k CFEEDa

=

Reactor Phase

< Higher concentrations of CFEED- Rapid reaction rate- reduce reactor volumes

• Gas-phase system is preferred< When high mass transfer rates are required

< When reactor temperature is above the critical temperature of the chemical

species

The choice of reactor phase is not available for multiphase systems

• Operation in the liquid phase is usually preferred

e.g. single reaction system : FEED

PRODUCT


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Gas-liquid and Liquid-liquid Reactors• Two phase reactions< Feed material is inherently in different phases at the inlet conditions.

< Two-phase behaviour is needed to remove an unwanted component from one of the phases or imporve the selectivity.

< It is necessary that the phases be intimately mixed.

- Provide effective mass transfer of the reactants between the phases

• Overall rate of reaction must take account of :< The mass tansfer resistance

< The resistance of the chemical reactions

• Reactor design for temperature control should consider simultaneously< mixing

< mass transfer

< reaction


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( )r k p p AG AG A AI= −

( )r k C C AL AL AI A= −

p H C AI A AI=

Two-film theory

GasFilm

Gas LiquidInterface

LiquidFilm

C A

C AI

P AI

P A

P AI = H AC AI

• Effect of mass transfer

< The rate of transfer of A through gas film:

< The rate of transfer of A through liquid film:

< Henry’s law

(assume equilibrium conditions at the interface)

where r G, r L : rate of transfer in the gas and liquid film (mol m-2

s-1

)k AG, k AL : mass transfer coefficient in the gas and liquid filmp A, p AI : partial pressure in the gas phase and at the interface (Pa)C A, C AI : concentration in the bulk of liquid phase and at the interface (mol m

-3)H A : Henry’s Law constant (Pa m

3 mol-1)

- Henry’s law constant must be determined experimentally


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( ) ( )r

k

H

k

p H C K p H C A

AG

A

AL

A A A AGL A A A=

+

− = −

1

1

1 1

K k

H

k AGL AG

A

AL

= +

r k Cr k C

FEED

a

FEED

a

1 1

2 2

1

2

=

=

< Assume steady state (r AG= r AL= r A)

• Effect of mass transfer (continued)

Overall masstransfer coefficient

Where

Gas film

resistance

Liquid film

resistance< Low solubility gases (H A is large) - k AG >> k AL/ H A : the mass transfer is liquid-film controlled

< High solubility gases (H A is small) - k AG r 2

FEED 6 PRODUCT

FEED 6 BYPRODUCT

• Mass transfer can influence the selectivity.


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• Effect of temperature< As temperature increases:

- Rate of reaction increases

- Solubility of the gas in the liquid decreases

- Rates of mass transfer increase

- Volatility of the liquid phase increases, decreasing the partial pressure of the dissolving gas

< The relative magnitude of mass tranfer enhancement and its consecutive effects depend on the

reaction system.

• Effect of chemical reaction< High reaction rate

- Reduce the liquid film resistance

- Effective increase in the overall mass tansfer coefficient

- The capacity of the liquid is increased.

< Low reaction rate

- When compared with pure physical absorption, the dissolving gas reacts and does not build up

in the bulk liquid to the same extent as pure physical absorption.

- The driving force for mass transfer is greater than that for physical absorption alone.

- Small effect on the overall mass transfer coefficient


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Contacting Patterns for Gas-liquid Reactors (I)

• (B) Co-current packed bed

< Poorer performance than the counter-current

type

< Effective when the flow of gas is much larger

than the flow of liquid - trickle-bed ractor

< Another method for co-current contact : feed

both phases to a pipe containing an in-line mixer G L

G L

G

L

G

L

• (A) Counter-current packed bed or

plate column

< Packing material or distillation trayscan be used to create interfacial area

G L

G L

G

L

G + L


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Contacting Patterns for Gas-liquid Reactors (II)

• (D) Bubble column< Induce a low gas-film mass transfer coefficient

and a high liquid-film mass transfer coefficient

< Ineffective for a reaction with a high viscosity

liquid

< Advantage over a packed bed

- The liquid hold-up per unit reactor volume is higher.

- The liquid contains a dispersed solid.

- A packed bed will become clogged.

G L

G L

Mixed-flowbehaviour

Plug-flowbehaviour

G

L

G

L

G L

G L

Mixed-flowbehaviour

Plug-flowbehaviour

G

L

G

L

• (C) Spray column< Induce a high gas-film mass transfer

coefficient and a low liquid-film mass

transfer coefficient

< Spray column is necessary when

- The liquid contains solids or solids are

formed in the reaction.

- The reaction has a tendency to foul a

packed bed.


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Contacting Patterns for Gas-liquid Reactors (III)

• Counter-current packed beds offer the largest mass transfer driving force and

agitated tanks the lowest

G L

G L

G

L

L

G

• (E) Agitated tanks< The gas is sparged through the liquid

< Low driving force

< When the liquid is viscous, a sparged agitated vessel allows good contactbetween the gas and the liquid.


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Liquid-liquid Reactors

• Liquid-liquid reactions< Much of the discussion for gas-liquid reactions also applies to liquid-liquid reactions.

< The reaction may occur in one phase or both phases simultaneously

• Mass transfer between two immisible liquids< Two liquid-film resistances exist

< One liquid must be dispersed in the other

< In most cases the liquid with the smaller liquid flowrate will be dispersed in the other

< Overall mass transfer coefficient depends on the physical properties of the liquids and the

interfacial area.

< Interfacial area is governed by the size of the liquid droplets and the volume fraction of the

dispersed phase.

• Dispersion of liquid

< External power input is required through an agitator or from pumping< The degree of dispersion depends on

- Power input

- Interfacial tension between the liquids and physical properties

< Too effective dispersion might lead to the formation of an emulsion.


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Contacting Patterns for Liquid-liquid Reactors (I)

• Counter-current packed bed or

plate column

LL HL

LL HL

HL

LL

HL

LL

• In-line static mixer < Suitable for reactions with

short residence time

< Dispersion is promoted by

repeatedly changing thedirection of flow locally

• Multi-stage agitated

contactor < A large number of stages

< Low back mixing

LL HL

LL HL

HL

LL

LL

HL

LL HL

LL HL

HL

HL

LL

LL

Plug-flow for both heavy and light phases


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Contacting Patterns for Liquid-liquid Reactors (II)• Spray column with light

liquid dispersed

< Multi-stage agitated tank and settler

- counter-current flow arrangement- cross-flow arrangement :

- useful if the reaction is limited

by chemical equilibrium

• Spray column with heavy

liquid dispersed

LL HL

LL HL

LL HL

LL HL

LL HL

LL HL

HL

LL

HL

LL

HL

LL

HL

LL

LL

HLHL

LL

Spray columns generallygive a lower driving force

• Agitated tank with settler


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< Air and fuel fluidize the solid particles and produce the high temperaturenecessary for the reaction.

Kilns

CaCO3 CaO + CO2 heat

• Reactions involving free-flowing solid, paste, and slurry

materials can be carried out in kilns.< Rotary kiln : rotation of cylinder shell

Example :

• Suitable for gas-solid non-catalytic reactions

< Static kiln : rotation of mechanical rake

CaF2 + H2SO4 2HF + CaSO4calcium flouride sulfuric acid hydrogen flouride calcium sulfate

Example :


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Reactor Configuration

from Optimisation of a Superstructure

So far, we have reviewed at length the factors influencing

the choice of reactor configuration and conditionsbased on the development of the CONCEPTUAL ISSUES.

- Another approach : Optimisation of Superstructure

• Superstructure< Includes all the structural features that might be candidates for the final design

< Contains redundunt features that need to be removed

• A combined structual and parameter optimisation carries out theevolution of the superstructure to the final design.


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Optimisation of Isothermal Reactors

Feed Product

• Multi-phase reactors by introducing

superstructure for each phase< Consider a plug-flow or mixed-flow reactor in

each phases and mass transfer between the

phases.

• A simple superstructure for a

homogenous reaction< Consider two options of using either a plug-

flow or mixed-flow reactor

Optimise for maximum yield,

maximum selectivity,minimum cost, etc

Feed 1 Product 1

Feed 2 Product 2

Mass Transfer

PHASE 1

PHASE 2

However, only conventional designs will result


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Novel Reactor Arrangements

Liquidfeed

Gas productGas feed

• Complex mixing patterns might lead to novel reactor arrangements or designs.

-

Liquid

Gas

Liquid

Gas

Liquid

Open up the possibilities of further design options in the superstructure.- we might obtain much better overall performance of the reactor.


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Mathematical Methods for

Superstructure Optimisation

• A more complex superstructure of reactor components allows series, parallel,

series-parrallel and parralled-series arrangements of plug-flow, semi plug-flow

and mixed-flow options.< Three compartments open up different arrangements of mixing patterns.

• A simple superstructure with plug-flow, semi-plug flow and mixed-flow options.

FEED

Complex arrangements

cannot be obtained.

A greater number of compartments- A greater number of possibilities


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Mathematical Methods for SuperstructureOptimisation

• Superstructure for two phase reactions with three reactor compartments in

each phase< The complexity should not increase unnecessarily by adding combinations of mixing patterns

and mass transfer between phases that can never be possible in a practical reactor.

< Mass transfer is only allowed with the corresponding shadow compartment.

FEED

PHASE 1

FEED

PHASE 2

Mass Transfer

Straightfoward to extend the superstructure to include multiple feeds and products


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Mathematical Methods for Superstructure Optimisation

• Optimisation of superstructure for reactor design< Highly non-linear equations: reaction kinetics, mass transfer and any hydrodynamic models

< A combined structural and parameter optimisation

< Resulting in a MINLP problem

• Can be solved by methods based on mathematical programming

< e.g. branch and bound algorithms< Such problems can be non-convex, so depending on the starting point, the algorithm can get trapped

in the neighbourhood of a local extremum

< Global optimisation methods exist, but are computationally intesive

• Stochastic optimisation (simulated annealing) has proved to be a relatively simple and reliable method.<

Stochastic optimisation reduces the chances of being trapped near a local optimum , thereforesolutions close to the global optimum can be obtained.

Simulationsimulate a specific structure

EvaluationObjectve function / Constraints

Simulated annealing Accept / Reject

Pertubation MovesNew features of design

-

There are usually a number of competitive solutions that areclose to the global optimum.


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( )[ ] ( )

( ) ( )

r y k k C k k C k C k C

r k r C

k e k e k

y

L L L L

L

MC A DC A C A Cl

Cl

T T

1 1 2 1 2 2 3

2 3 1

1

5 22

2

0 00176

3

4

12

4

12

4

12

2

2

3120 1880

1

0 00136

0 037

= + + + +

=

= = =

=

− −. ..

.

Cl2 + C4 A ö MC4 A + HCl

2Cl2 + C4 Aö

DC4 A + 2HClMC4 A - "-monochlorobutanoic acid, DC4 A - ","-dichlorobutanoic acid

Catalyst molar fraction

Salmi T, Paatero E, Fagerstolt K, Chem. Eng. Sci., 48(1993), pp.735-751.

Case Study: Synthesis of -Chlorocarboxylic Acids


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Feed and Reaction Conditions

!P = 10 bar

!Liquid feed: 13.3 kmoles of C4 A

!Gas feed: 100 kmoles of Cl2!Temperature bounds: 100 OC # T # 500 OC

Phase equilibria and mass transfer !HCl2 = HHCl = 211.76 bar

!a = 254.6 m2/m3 , gg = 0.5, *L = 10-4 m

!DCl2 = 6.66*10-9 m2/sec, DHCl = 8.45*10

-9 m2/sec

Film model for mass transfer

Salmi T, Paatero E, and Fagerstolt K, Chem. Eng. Sci., 48(1993), pp.735-751

Romanainen and Salmi T, Chem. Eng. Sci., 47(1992), pp.2493-2498

Problem Data


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Counter currentpacked bed

Mechanicallyagitated vessel

Bubble column

Yield = 69.5% Yield = 72.8%Yield = 74.4%

Conventional Designs


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Yield = 96.9%

Vol = 9.93m3

Liquid Feed

Gas Feed

Liquid Product

Gas Product

Liquid feed

Gas feed

Liquidproduct

Gasproduct

Gasfeed

Liquidproduct

LiquidGas

Gas product

Liquid product

Network model Reactor designs

Results


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Yield

69.5 %

74.4 %

72.8. %

96.9 %

Volume (m3)

16.1

12.0

12.2

9.9New design

Results and Comparison


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Non-isothermal Reactors

• Non-isothermal operation brings additional complexity to the superstructure

approach.< Temperature profiles used to identify the optimum temperature profile for reactors.

(a) Isothermal. (d) Asymptotic/exponential.

(f) Single peak maximum.(e) Asymptotic/exponential. (g) Single peak maximum.

(b) Monotonic increasing

(concave/convex).

(c) Monotonic increasing

(concave/convex).


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T L a a L a L( ) = + +0 1 22

• Optimisation of temperature profile

< The objective function is maximised or minimised by varying the shape of the temperature profile.

< Assume that heat can be added or removed wherever required at whatever

rate required so that the optimal temperature profile can be achieved.

< Optimum profile provides an ultimate target to aim for in the final design.

But it may not be achieved exactly due to practical issues.

- Sub-optimal performance

Where T = reactor temperature at point LL = dimensionless reactor length (0


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Cooling

Heating

• Superstructure allows heat to be transferred indirectly or directly

through intermediate feed injection.

• Optimisation of superstructure can be carried out reliably using

simulated annealing.

Conceptual Reactor Design, Multi-phase Reactors, Non-Isothermal Reactors

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