Reactor Design Lectures Notes · 2018. 1. 19. · [Introduction to Chemical Reaction Engineering ]...

Dr. Farah Talib Al-Sudani

Third Year

Reactor Design Lectures Notes

Department of Chemical Engineering

University of Technology

[Introduction to Chemical Reaction Engineering ] | [Chapter-One]…..University of Technology-Chemical Engineering Department-Dr.Farah Al-Sudani

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Chemical kinetics is the study of chemical reaction rates and reaction mechanisms. The study of chemical reaction engineering (CRE) combines the study of chemical kinetics with the reactors in which the reactions occur. Chemical kinetics and reactor design are at the heart of producing almost all industrial chemicals. It is primarily a knowledge of chemical kinetics and reactor design that distinguishes the chemical engineer from other engineers. The selection of a reaction system that operates in the safest and most efficient manner can be the key to the economic success or failure of n chemical plant. Design of the reactor is no routine matter, and many alternatives can be proposed for a process. In searching for the optimum it is not just the cost of the reactor that must be minimized. One design may have low reactor cost, but the materials leaving the unit may be such that their treatment requires a much higher cost than alternative designs. Hence, the economics of the overall process must be considered. Reactor design uses information, knowledge, and experience from a variety of areas-thermodynamics, chemical kinetics, fluid mechanics, heat transfer, mass transfer, and economics. Chemical reaction engineering is the synthesis of all these factors with the aim of properly designing a chemical reactor. To find what a reactor is able to do we need to know the kinetics, the contacting pattern and the performance equation. We show this schematically in Figure (1).

Figure (1). Information needed to predict what a reactor can do. Much of this lectures deals with finding the expression to relate input to output for various kinetics and various contacting patterns, or

output = f [input, kinetics, contacting] ………………(1) This is called the performance equation. Why is this important? Because with this expression we can compare different designs and conditions, find which is best, and then scale up to larger units.

1.Introduction


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In Uchemical engineering U, chemical reactors are vessels designed to contain Uchemical reactionsU. The design of a chemical reactor deals with multiple aspects of Uchemical engineering U. Chemical engineers design reactors to maximize net present value for the given reaction. Designers ensure that the reaction proceeds with the highest efficiency towards the desired output product, producing the highest yield of product while requiring the least amount of money to purchase and operate. Normal operating expenses include energy input, energy removal, raw material costs, labor, etc.

There are a couple main basic vessel types:

A tank A pipe or tubular reactor (Ulaminar flow reactorU(LFR)) Both types can be used as continuous reactors or batch reactors. Most commonly, reactors are run at Usteady-state U, but can also be operated in a Utransient state U. When a reactor is first brought back into operation (after maintenance or inoperation) it would be considered to be in a transient state, where key process variables change with time. Both types of reactors may also accommodate one or more solids (UreagentsU, UcatalystU, or inert materials), but the reagents and products are typically liquids and gases.

There are three main basic models used to estimate the most important process variables of different chemical reactors:

UBatch ReactorU

UContinuous Stirred-Tank ReactorU U (CSTR)U

UPlug Flow ReactorU U (PFR)U

Key process variables include

Residence time (τ) , Volume (V) , Temperature (T) , Pressure (P) , Concentrations of chemical species (C1, C2, C3, ... Cn) ,Heat transfer coefficients (h, U)

Chemical reactions occurring in a reactor may be Uexothermic U, meaning giving off heat, or Uendothermic U, meaning absorbing heat. A chemical reactor vessel may have a cooling or heating jacket or cooling or heating coils (tubes) wrapped around the outside of its vessel wall to cool down or heat up the contents.

2.Type of Reactors.

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http://en.wikipedia.org/wiki/Chemical_reaction�






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http://en.wikipedia.org/wiki/Steady-state_(chemical_engineering)�

http://en.wikipedia.org/wiki/Transient_state_(chemical_engineering)�

http://en.wikipedia.org/wiki/Reagent�

http://en.wikipedia.org/wiki/Catalyst�

http://en.wikipedia.org/wiki/Batch_reactor�

http://en.wikipedia.org/wiki/Continuous_stirred-tank_reactor_model�

http://en.wikipedia.org/wiki/Plug_flow_reactor_model�

http://en.wikipedia.org/wiki/Exothermic�

http://en.wikipedia.org/wiki/Endothermic�


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2.1 Batch Reactor

Kinds of Phases Present

Usage Advantages Disadvantages

1. Gas phase

2.Liquid phase

3.Liquid Solid

1. Small scale production

2. Intermediate or one shot production

3.Testing new process that have not been fully developed

4.Manufacture of expensive products.

5.Pharmaceutical, Fermentation

1. High conversion per unit volume for one pass

2.Flexibility of operation-same reactor can produce one product one time and a different product the next

3. Easy to clean

1. High operating cost

2. Product quality more variable than with continuous operation

3.Difficalty of large scale production .

Figure(2) simple batch reactor .

•Batch ReactorType of Reactor

•Reactor is charged (i.e., filled) through the holes at the top ; while reaction is carried out.

• Nothing else is put in or taken out until the reaction is done; tank easily heated or cooled by jacket

Characteristics


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Semi-batch reactors operate much like Ubatch reactorsU in that they take place in a single stirred tank with similar equipment . It modified allow reactant addition and/or product removal in time. A semi-batch reactor, however, allows partial filling of reactants with the flexibility of adding more as time progresses. Semi-batch reactors are used primarily for liquid-phase reactions , two-phase reactions in which a gas usually is bubbled continuously through the liquid , and also for biological and polymerization reaction.

2.2. Continuous-Flow Reactors

2.2.1 Continuous-Stirred Tank Reactor CSTR



1. Gas phase 2. Liquid phase 3. Liquid Solid

1. When agitation is required 2. Series configurations for different concentration streams

1. Continuous operation 2. Good temperature control 3. Easily adapts to two phase runs 4. Simplicity of construction 5.Low operating (labor) cost 6. Easy to clean

1. Lowest conversion per unit volume, very large reactors are necessary to obtain high conversions 2. By-passing and channeling possible with poor agitation

•Continuous-Stirred Tank Reactor CSTRType of Reactor

•Run at steady state ,the flow rate in must equal the mass flow rate out, otherwise the tank will overflow or go empty (transient state).

• The feed assumes a uniform composition throughout the reactor, exit stream has the same composition as in the tank.

•The reaction rate associated with the final (output) concentration.

•Reactor equipped with an impeller to ensure proper mixing.•Dividing the volume of the tank by the average volumetric flow rate through the tank gives the residence time, or the average amount of time a discrete quantity of reagent spends inside the tank.

Characteristics

http://en.wikipedia.org/wiki/Batch_reactor�


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Some important aspects of the CSTR:

It is economically beneficial to operate several CSTRs in series. This allows, for example, the first CSTR to operate at a higher reagent concentration and therefore a higher reaction rate. In these cases, the sizes of the reactors may be varied in order to minimize the total Ucapital investmentU required to implement the process.

Figure (3) Flow sheet for the manufacture of nitrobenzene from benzene using a cascade of CSTR

http://en.wikipedia.org/wiki/Capital_investment�


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2.2.3. Tubular Reactor (PFR)



1. Primarily Gas Phase

1. Large Scale

2. Fast Reactions

3. Homogeneous Reactions

4. Heterogeneous Reactions

5. Continuous Production

6. High Temperature

1. High Conversion per Unit Volume

2. Low operating (labor) cost)

3.Good heat transfer

1. Undesired thermal gradients may exist

2. Difficult temperature control

3. Shutdown and cleaning may be expensive

4.Hot spot occur for exothermic reaction

• Tubular Reactor (PFR)Type of Reactor

•Consists of a long cylindrical tube or many short reactors in a tube bank.

•Operated at steady state.•The rate is very high at the inlet to the PFR. • No radial variation in reaction rate (concentration) and the reactor is referred to as a plug-fiow rcactor (PFR).

• Concentration changes with length down the reactor•As the concentrations of the reagents decrease and the concentration of the product(s) increases the reaction rate slows.

•A PFR typically has a higher efficiency than a CSTR of the same volume. That is, given the same space-time, a reaction will proceed to a higher percentage completion in a PFR than in a CSTR.

Characteristics


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• Other types of reactors:- Catalytic reactors(packed bed and Fluidized-bed Reactor

Kinds of Phases

Present Usage Advantages Disadvantages

1. Gas-Soli phase 2. Liquid-Solid phase 3. Gas-Liquid -Solid

Heterogeneous reaction

Most reaction gives the highest conversion per weight of catalyst of any catalytic reactor.

1. Difficulties with temperature control. 2. Catalyst is usually troublesome to replace 3. Channeling of the gas or liquid flow occurs, resulting in ineffective use of part of the reactor bed

Figure(4) Packed bed Reactors

• Paced bed Reactor (fixed-bed,PBR)Type of Reactor

• is essentially a tubular reactor that is packed with solid catalyst particles.Characteristics


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1. Gas-Solid phase 2. Liquid-Solid phase 3. Gas-Liquid –Solid phase

1.Heterogeneous reaction 2. reactor can handle large amounts of feed and solids

1.Good mixing 2. temperature is relatively uniform throughout 3. Catalyst can be continuously regenerated with the use of an auxiliary loop 4. good temperature control

1. Bed-fluid mechanics not well known 2. Severe agitation can result in catalyst destruction and dust formation 3. Uncertain scale-up

Figure(5) Fluidized-bed

Reactors

• Fluidized-bed ReactorType of Reactor

•Is analogous to the CSTR in that its contents.•Heterogeneous reactor, are well mixed. Characteristics


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it classify according to

Five traditional types of chemical reactions are

1. Decomposition reactions: single compound decomposes to two or more other substances,decomposition of calcium carbonate by heating it.

CaCO3(s) ---> CaO(s) + CO2(g)

2. Combination reactions (Synthesis reactions) 3. Single-replacement reactions (Displacement reactions):copper displaces silver

from an aqueous solution of silver nitrate is an example of a single-replacement reaction.

Cu(s) + 2 AgNO3(aq) ---> Cu(NO3)2(aq) + 2 Ag(s)

4. Double-replacement reactions (Metathesis reactions):Precipitation reactions are one type of double-replacement reaction. An example is

AgNO3(aq) + NaCl(aq) ---> AgCl(s) + NaNO3(aq)

5. Combustion reactions: substance reacts with oxygen,butane burns in air as follows.

2 C4H10(g) + 13 O2(g) ---> 8 CO2(g) + 10 H2O(l)

Also Oxidation-reduction reactions (Redox reactions).

phases involved:

o Homogeneous reaction : it takes place in one phase alone o Heterogeneous reaction : multiple phases, reaction usually occurs at the interface

between phases.

Direction of reaction o Irreversible Reaction: Proceeds in only one direction and continues in that

direction until the reactants are exhausted. Example : Heterogeneous reaction

Toluene-hydrogenation 𝐶𝐶6𝐻𝐻5𝐶𝐶𝐻𝐻3(𝐿𝐿) + 𝐻𝐻2(𝑔𝑔)𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐�⎯⎯⎯⎯� 𝐶𝐶6𝐻𝐻6(𝑔𝑔) + 𝐶𝐶𝐻𝐻4(𝑔𝑔)

3.Classification of Chemical Reaction


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Homogeneous reaction Decomposition N2O N2O (g)+2O2(g) →2 N2(g) + O2(g)

Water gas shift reaction H2O (g)+CO (g) →H2(g) + CO2(g)

o Reversible Reaction: Can proceed in either direction, depending on the concentrations of reactants and products present relative to the corresponding equilibrium concentration.

Example :

Homogeneous reaction

Ammonia synthesis 2𝑁𝑁2(𝑔𝑔) + 3𝐻𝐻2(𝑔𝑔) ⇔ 2𝑁𝑁𝐻𝐻3(𝑔𝑔)

Thermal cracking of ethane : 𝐶𝐶2𝐻𝐻6(𝑔𝑔) ⇔𝐶𝐶2𝐻𝐻4(𝑔𝑔) + 𝐻𝐻2(𝑔𝑔)

Heterogeneous reaction Ammonium chloride synthesis or decomposition

𝑁𝑁𝐻𝐻3(𝑔𝑔) + 𝐻𝐻𝐶𝐶𝐿𝐿(𝑔𝑔) ⇔ 𝑁𝑁𝐻𝐻4𝐶𝐶𝐿𝐿(𝑐𝑐)

[[[[Reaction Rate and Conceptes of Kinetics]Reaction Rate and Conceptes of Kinetics]Reaction Rate and Conceptes of Kinetics]Reaction Rate and Conceptes of Kinetics]

Reaction Rate and Conceptes of Kinetics]Reaction Rate and Conceptes of Kinetics]Reaction Rate and Conceptes of Kinetics]Reaction Rate and Conceptes of Kinetics][Chapter[Chapter[Chapter[Chapter----Two]…..Two]…..Two]…..Two]…..University of TechnologyUniversity of TechnologyUniversity of TechnologyUniversity of Technology----Chemical Engineering DepartmentChemical Engineering DepartmentChemical Engineering DepartmentChemical Engineering Department

Chemical Engineering DepartmentChemical Engineering DepartmentChemical Engineering DepartmentChemical Engineering Department----Dr.Farah AlDr.Farah AlDr.Farah AlDr.Farah Al----Sudani Sudani Sudani Sudani

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[[[[Reaction Rate and Conceptes of Kinetics]Reaction Rate and Conceptes of Kinetics]Reaction Rate and Conceptes of Kinetics]Reaction Rate and Conceptes of Kinetics][Chapter[Chapter[Chapter[Chapter----Two]…..Two]…..Two]…..Two]…..University of TechnologyUniversity of TechnologyUniversity of TechnologyUniversity of Technology----Chemical Engineering DepartmentChemical Engineering DepartmentChemical Engineering DepartmentChemical Engineering Department----Dr.Farah AlDr.Farah AlDr.Farah AlDr.Farah Al----Sudani Sudani Sudani Sudani

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In homogeneous reaction , the reaction rate (rA) is defined as the change in moles of component A(reactant consumed) or mole of product formed with respect to time per unit volume of reaction mixture.

In solid-catalyzed reactions, the reaction rate ( rA′ ) is defined as the change in

moles of component A with respect to time per unit reaction surface area or catalyst weight.

o rA = rate of formation of A per unit volume o -rA = rate of a disappearance of A per unit volume

Batch Reactor

−�� = − �� = �� disappear

�� × � homogeneousreaction…2a

−��%%%% = − ��& �

= �� disappear�� '(�� × � homogeneousreaction…2b

−��* = − ��+ � = �� disappear

',,��(''�-, × � heterogeneousreaction…2(

−��%% = − ��

. �= �� disappear

,��'( × � heterogeneousorhomogeneousreaction

…2d

−��%%% = − ��

�/ �= �� disappear�� 0''�-, × � heterogeneousreaction…2e

�� = +��*=.��%%=�/��%%%=�&��%%%%…………….3

The rate of reaction per unit weight catalyst, -rA, (e,g., -rA), and thi rate of reaction per unit volume, -rA, , are related through the bulk density ρ,(mass of solid /volume) of the catalyst particles in the fluid media:

1.Reaction Rate (Rate Law , 12


Tubular Flow Reactor

−

Where �*� is the molal rate of flow component A into the volume element

Rate of reaction r o a function of concentration, temperature, pressure, and the type of

catalyst (if any) o independent of the type of reaction system (batch, plug flow, etc.)

on the reaction chemistryo an algebraic equation, not a differential equation o Rate of reaction per unit weight of catalyst and rate of reaction per unit

volume is related the fluid media

Rate of reaction rA is(Concentration), and the material mean the temperature (random kineticmolecules), the light intensity within the system (this may affect the bond energy between atoms), the maonly need to consider the temperature

1. Stoichiometry.

• Consider the general reaction;

• on a “per mole of A basis”…

• where the Stoichiometric Coefficients

-rA= f {temperature dependent term,concetration dependent term}

= mole/m3.time

a

c

a

b,

2.Conceptes of Kinetics


Tubular Flow Reactor

−�� = − 34*536 ………………………….….4

is the molal rate of flow component A into the volume element

Rate of reaction rA is:

a function of concentration, temperature, pressure, and the type of catalyst (if any)

independent of the type of reaction system (batch, plug flow, etc.) on the reaction chemistry

an algebraic equation, not a differential equation Rate of reaction per unit weight of catalyst and rate of reaction per unit

volume is related through the bulk density of the catalyst particle in media

is an intensive quantity and depended on(Concentration), and the energy of the material (Temperaturethe material mean the temperature (random kinetic molecules), the light intensity within the system (this may affect the bond energy between atoms), the magnetic field intensity, etc. Ordinarilyonly need to consider the temperature

Consider the general reaction;

on a “per mole of A basis”…i.e assume A is the limiting reactant

where the Stoichiometric Coefficients ,

temperature dependent term,concetration dependent term}

.time

dDcCbBaA +→+

Da

dC

a

cB

a

bA

+

→

+

a

d,

2.Conceptes of Kinetics


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is the molal rate of flow component A into the volume element.

a function of concentration, temperature, pressure, and the type of

independent of the type of reaction system (batch, plug flow, etc.) but

Rate of reaction per unit weight of catalyst and rate of reaction per unit through the bulk density of the catalyst particle in

an intensive quantity and depended on composition Temperature) . Energy of

energy of the molecules), the light intensity within the system (this may affect the bond

gnetic field intensity, etc. Ordinarily we

limiting reactant :-

temperature dependent term,concetration dependent term}


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• Molecules are lost and formed by reaction , and mass conservation requires

that amounts of species are related by Stoichiometry as:-

1 mole of A and

a

b of B consumed , while mole of C and

a

d

mole of D formed or appear

Rate of reaction or disappearance of A =−�� 789:7;.=>7:

Rate of formation of C ?�@A = ?−��A 789:7;.=>7:

Rate of formation of D?�BA =

a

d ?−��A 789:

7;.=>7:

Also, Rate of formation of C ?�@A = C@3D ?�BA Rate of formation of D ?�BA = C3@D ?�@A

Then the reaction Stoichiometry ; E&5F =

E&GF =

&HF =

&IF

Examples (1),(2)

********************************************************************

2. Temperature – Dependent Term of a Reaction Rate Law.

Reaction Rate Contestant.

• Kinetic (reaction) Rate law?−��A gives relationship between reaction rate

and concentration (is an algebraic equation that relates ?−��A to species

concentrations)

−�� = �J K �'�� K L� �, (�L( L�'��L� K L� L �N 789:7;.=>7:

………………..5

a

c

a

c

( )[ ] ( )[ ]K,, BAAA CCfTkr ⋅=−

( )Tk A


• kA(T) is the reaction rate constant

– Strongly dependent on temperature

– Depends on whether

– NOT really a constant, but

• The rate constant

A ≡ Pre-exponential factor (frequency factor)

E ≡ Activation energy (J/mol)

R ≡ Gas constant (8.314 J/mol

T ≡ Absolute temperature

Activation Energy

Activation energy has been equated with minimum energy that must be

possessed by reacting molecules before the reaction will occur.

Figure(2.1)Activation energy for


reaction rate constant

trongly dependent on temperature

epends on whether or not a catalyst is present

NOT really a constant, but ≠ f(Ci)

rate constant is described by Arrhenius equation :-

……………………………6

………………………7

exponential factor (frequency factor)

ctivation energy (J/mol)

as constant (8.314 J/mol⋅K, 1.987 cal/mol ⋅K)

bsolute temperature (K)

Activation Energy



(2.1)Activation energy for exothermic and endothermic reaction.

( ) RTEA AeTk −=

( ) ( )

−=TR

EAk

1lnln


16

……………………………6

………………………7



exothermic and endothermic reaction.

Heat

Absorbed

Heat

Released


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At the same concentration but different two temperature Activation

Energy can be estimated as :

……………8

Figure (2.2) shows temperature dependency of the reaction rate

Example (4)

Example (5) =example 3.1 from elemental of chemical reaction

engineering , 4ed pag 95

*********************************************************************

( )( )

( )( )

−==

211

2

1

2 11

ln

ln

ln

ln

TTR

E

k

k

r

r


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3. Concentration – Dependent Term of a Reaction Rate Law.

……………….5

One of the most common general forms of this dependence is the product of concentrations of the individual reacting species, each of which is raised to a power .

Reaction Order.

– Elementary Reaction

A reaction order for which each specie is identical to its

Stoichiometric coefficient as shown :-

o a and b represent the reaction order with respect to the reactant

A and B respectively ,

over all reaction order( n ) = a + b

o Reaction rate constant, k will vary with the order of the reaction as

shown :-

( )[ ] ( )[ ]K,, BAAA CCfTkr ⋅=−

( )K,, BA CCf

dDcCbBaA +→+

bB

aAA CkCr =−


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A →→→→ products

Order Rate Equation Units

Zero

mol.V-1.s-1

First

s-1

Second

V.mol-1.s-1

Third

( V.mol-1 )2.s-1

nth order

(concentration)1-n.s-1

o Another example of elementary reaction ; reversible second

order :-

where Kc equilibrium constant

• All reversible reaction rate laws must reduce to the thermodynamic

relationship relating reacting species concentrations at equilibrium.

• At equilibrium, the net rate of reaction is zero for all species involved

in the reaction

Example (6)

krA =−

AA kCr =−

2AA kCr =−

3AA kCr =−

nAA kCr =−

210126612 HHCHC k +→←

k2

−=−

c

HDBB K

CCCkr 22

1

0=− ier

CBAA

A

k

k+↔

−

22AAA Ckr =−

CBAA CCkr −=Forward rate law

Backward or reverse rate law

CBAAAAAnetA CCkCkrrr −− +−=+= 2,

net rate law

CBAAAnetA CCkCkr −+−== 2, 0

CBAAA CCkCk −=2

CA

CB

A

A KC

CC

k

k ==−

2

Equilibrium condition

Equilibrium relationship

−=−

C

CBAAA K

CCCkr 2

Rate law in term Equilibrium relationship


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– Non-Elementary Reaction

Do not follow the Stoichiometric coefficients for the overall

reaction

Homogeneous Reactions : Gas-phase synthesis of phosgene,

n=5.5

Decomposition of nitrous oxide

n depended on CO2 concentration

Heterogeneous Reactions :

Heterogeneous reaction and corresponding rate law is the hydrodemethylation of toluene (T) to form benzene (B) and methane (M) carried out over a solid catalyst.

4. Molecularly Reaction.

The term molecularity refers to number of atoms, ions, or molecules

involved in the rate-limiting step of the reaction.

– Unimolecular – one reactant involved in reaction

– Bimolecular – two reactants must collide to react

– Termolecular – three reactants must interact for reaction to occur

22 COClClCO →+ 2/3

2ClCOCOCO CCkr =−

222 22 ONON +→

2

22

2 1 O

ONONON Ck

Ckr

′+=−

462.

2356 CHHCHCHHC cat +→+

TTPB

THT PKPK

PPkr

++=′−

12

2.. kPaskg

toluenemolk

cat

=


21

5. Conversion , yield and selectivity

conversion, X, is defined as the fraction (or percentage) of the more important or limiting reactant that is consumed. With two reactants A and B and a nearly Stoichiometric feed, conversions based on each reactant could be calculated. ……………………….8

yield, Y, is the amount of desired product produced relative to the amount that would have been formed if there were no byproducts and the main reaction went to completion

……9

6. Van't Hoff Equation.

Van't Hoff equation relates equilibrium composition to temperature:

……………..10

Van't Hoff equation can be integrated from 298K to any temperature T to

yield :

……….………11

Enthalpy change of reaction varies with temperature as:

( ) ( ) ∫ ∆+∆=∆T

T porr dTCTHTH

298298 ……..…………………..12

An approximate estimate of equilibrium constant at any time , ignore the second

term in equation 12, then equation 11 became :

……..13

For endothermic reactions, the equilibrium constant, Keq, increases with increasing temperature. While for exothermic reactions, Keq and Xeq decreases with increasing temperature.

fedA mole

reactedA mole=X

1.0 x product, of moles maximum

formedproduct of moles

==Y

( )dT

Kd

RT

H

dT

RTGd eqor

oR

ln/2 =∆=∆−

∫∆

+=T

req dT

RT

HKK

2982298lnln

−∆

−=298

11lnln 298

298 TR

HKK r

eq


Figure (2.3) show the equilibrium conversion as a function of temperature for an exothermic reac


the variation of the concentration equilibrium constant equilibrium conversion as a function of temperature for an exothermic reac


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equilibrium constant and equilibrium conversion as a function of temperature for an exothermic reaction.

[[[[Reactor Sizing and DesignReactor Sizing and DesignReactor Sizing and DesignReactor Sizing and Design]]]][Chapter[Chapter[Chapter[Chapter----FourFourFourFour]…]…]…]…

FourFourFourFour]…]…]…]…………………………………………………………………........University of TechnologyUniversity of TechnologyUniversity of TechnologyUniversity of Technology----Chemical Engineering DepartmentChemical Engineering DepartmentChemical Engineering DepartmentChemical Engineering Department


١


1. General Mole Balance Equation Mole balance on species j at any instance in time t ;

Fj0 = Entering molar flow rate of Fj = Exiting molar flow rate of

Gj = Rate(total rate)

rj = rate of generation(formation) of Nj = number of moles of

If rj varies with position in the system,

Then general mole balance:

From this general mole balance equation the various types of industrial rreactors.

+

ofsystem into j of

flow of rate

joF

2V∆

1V∆

1jr

2jr


General Mole Balance Equation

lance on species j at any instance in time t ;

…………..4.1

= Entering molar flow rate of species j (mol/time)= Exiting molar flow rate of species j (mol/time)

(total rate) of generation(formation) of species j (mol/time)V = Volume (e.g. m3)

= rate of generation(formation) of species j (mole/time= number of moles of species j inside the system Volume V (

varies with position in the system,

Then general mole balance:-

…………4.2

From this general mole balance equation we can develop the design equationsthe various types of industrial reactors: batch, semi-batch. and continuous

=

−

of

rate

system ofout j of

flow of rate

rxnby systemin j of

generation of rate

dt

dN j

jjjo =−+ FG

6V∆5V∆

4V∆

3V∆

3jr4jr 5jr

6jr

∑=

∆=

∆=∆

m

i

jj

jj

G

r

1

1,1,

G

G

m ∞→Let

∫=V

j rG

dt

dNdVr

j

j

V

jjo =−+ ∫ FF

VsystemVolumn


٢

(mol/time) (mol/time)

(mol/time)=rj .V

(mole/time.vol) inside the system Volume V (mole)

…………4.2

design equations for batch. and continuous-flow

system within j of

onaccumulati of rate

∑=

∆=

∆

m

i

iijij Vr

V

1

,,

1

0 , →∆∞ V

jdVr


o Operate under unsteady state o Neither inflow nor outflow of reactants or products

If the reaction mixture o Constant rate of reaction throughout

o Composition ≠ f o Composition =f (time)

o Temperature ≠ f o Temperature ≠ f

Mole Balance

REACTOR SIZING AND DESIGN

Batch Reactor

, =oj FF

dVrV

jjo + ∫F

dVrV

j∫


Operate under unsteady state either inflow nor outflow of reactants or products

mixture is perfectly mixed so: f reaction throughout the reactor volume f (Position)

(time)

f (Position)

f (time)

...............................4.3

REACTOR SIZING AND DESIGN

PART ONE

Batch Reactor

0=jF

dt

dNdV

j

j =− F

dt

dNdV

j=

Isothermal Operation


٣

ideal restrictions

[[[[Reactor Sizing and DesignReactor Sizing and DesignReactor Sizing and DesignReactor Sizing and Design]]]][Chapter[Chapter[Chapter[Chapter----FourFourFourFour]…]…]…]…………………………………………………………………........University of TechnologyUniversity of TechnologyUniversity of TechnologyUniversity of Technology----Chemical Engineering DepartmentChemical Engineering DepartmentChemical Engineering DepartmentChemical Engineering Department----Dr.Farah AlDr.Farah AlDr.Farah AlDr.Farah Al----Sudani Sudani Sudani Sudani

٤

………………………..4.4

Let's consider the isomerization of species A in a batch reactor

As the reaction proceeds. the number of moles of A decreases and the number of moles of B increases, as shown in Figure below

The time t necessary to reduce the initial number of moles NAo to a final number of mole NA can be estimated as : from equation 4.4 ………………4.4

integrating with limits that at :

t = 0 NA = NA0 ← stat of reaction and at t = t NA = NA reaction time (end of reaction ) we obtain

…………..4.5

•

=

=

fedmoles

reactedmolesmoles

A of

A of

0at t

fedinitially

A of

consumedor reacted

A of moles

BA →

dt

dNVr

j

j =

dt

dNVr A

A =

Vr

dNdt

A

A=

∫=0A

A

N

N A

A

Vr

dNt

[ ] [ ]XN A •=

0consumedor reacted

A of moles


٥

number of mole NA remain un-reacted after time t ,

Sub in equation 4.5 and 4.4

……….4.6 …4.7

Differential form Integral form Batch Reactor Design Equation Used in the Interpretation of m Lab Rate Data Space time or Mean Residence Time= is the time necessary to process one reactor mmmmmmmmmmmmmmmmmmm volume of fluid based on entrance conditions.

tB=t+tD

[ ] [ ] [ ] [ ]XNNN AAA •−= 00

−

=

=

consumedor reacted

A of moles

0at treactor the

tofedinitially

A of

ttime

at (remain)reacter in

A of moles moles

( )XNN AoA −= 1

Ao

AAo

N

NNX

−=

Vrdt

dXN AAo −=

Vrdt

dNA

A = ∫=0A

A

N

N A

A

Vr

dNt

( )XNN AoA −= 1

( )

∫ −=

tX

A

AoVr

dXNt

0


٦

At constant volume batch reactor

i.e constant density reaction mixture.

NAo = CAo * V → then; equations 4.4 and 4.5 become ( ) :

….……….4.8….(Reaction Time)

Evaluation of Reaction Time Graphically:

From equation 4.7 plot vs. X and evaluate the area under the curve

to estimate reaction time

X1 X X

Or

From equation 4.7 plot vs. CA and evaluate the area under the curve

to estimate reaction time

CA CA CAo

Example

dt

dCr A

A =−

∫ −=

A

Ao

C

CA

A

r

dCt

V

NC i

i =

Ar−

1

Ar−

1

Ar−

1( )

∫ −=

tX

A

AoVr

dXNt

0

AreaV

Nt Ao *=

Area

Area

Ar−

1 ∫ −=

A

Ao

C

CA

A

r

dCt

Areat =


٧

Evaluation of Reaction Time Numerically:

Need to size reactors or calculate reaction time

o For the reactions in which the rate depends only on the concentration of

one species then

First order and Irreversible :-

,

Second order and Irreversible :-

,

,

nth order and Irreversible :-

,

Example

BA →AA kCr =−

∫∫ −=−

=A

Ao

A

Ao

C

CA

AC

CA

A

C

dC

kkC

dCt

1

−=

Ao

A

C

C

kt ln.

1

kt

AoA eCC−=

2

AA kCr =−BA →

∫∫ −=−

=A

Ao

A

Ao

C

CA

AC

CA

A

C

dC

kkC

dCt

22

1

−−=

AoA CCkt

111

ktC

CC

Ao

AoA

+=

1

n

AA kCr =−BA →

( )11

1

1 +−+− −+−

=− n

Ao

n

A CCn

kt

( )[ ] nn

AoAoA tkCnCC −+−−+= 1

1111

)( AA Cfr =−

)(CAfrA =−


٨

Bimolecular Reactions

o when the rate law depends on more than one species , we must relate the

concentrations of the different species to eac2h other "as a function of

conversion ". This relationship is most easily established with

the aid of a Stoichiometric table.

In formulating our stoichiornetsic table, we shall take species A component as our basis of calculation (i.e.. limiting reactant) and then divide through by the stoichiometric coefficient of A , in order to put everything on a basis of "pet mole of A ".

Stoichiornetsic table presents the following information

o Column I: the particular species o Column 2: the number of moles of each species initially present o Column 3: the change in the number of moles brought about by reaction o Column 4: the number of moles remaining in the system at time t o Column 5: concentrations as a function of conversion of each species

• Consider the general reaction;

Stoichiometry set up of equations with A as basis

The rate law is :

Da

dC

a

cB

a

bA

+

⇔

+

−=−

C

d

D

c

Cb

B

a

AAAK

CCCCkr

)(XfrA =−


٩

Constant Volume (Constant Density)

liquid-phase and some of gas phase reaction system fall into this category.

Stoichiometric Table Batch System

Specie Initial Change Remaining Concentration

A NAo

-NAo X

NA = NAo(1 – X)

=AC ( )XCA −10

B NBo = NAo ΘΘΘΘB

-(b/a)NAo X

NB = NAo[ΘΘΘΘB –(b/a)X] =BC

−Θ X

a

bC BA0

C NCo = NAo ΘΘΘΘC

+(c/a)NAo X

NC = NAo[ΘΘΘΘC +(c/a)X] =CC

+Θ X

a

cC CA0

D NDo = NAo ΘΘΘΘD

+(d/a)NAo X

ND = NAo[ΘΘΘΘD +(d/a)X] =DC

+Θ X

a

dC DA0

I NI = NAo ΘΘΘΘ

NI = NAo ΘΘΘΘI

IoC

NTo = ΣΣΣΣNAo ΘΘΘΘi NT = NTo +δδδδNAoX

Where

ΘΘΘΘi = Nio/NAo = Cio/CAo= yio/yAo

δδδδ = (d/a) + (c/a) – (b/a) - 1

• Express table in terms of concentrations

– Concentration (batch):

Mole balance equation and the rate law are coupled and then solved

Example

V

NC i

i =

0VV =

( )( )

−Θ=

−Θ==

−=−

==

Xa

bCX

a

b

V

N

V

NC

XCV

XN

V

NC

BABAB

B

AAA

A

0

0

0

0

0

0 11

+Θ=

+Θ==

+Θ=

+Θ==

Xa

dCX

a

d

V

N

V

NC

Xa

cCX

a

c

V

N

V

NC

DADAD

D

CACAD

C

0

0

0

0

0

0


١٠

Variable Volume (Variable Density, but with Constant T and P )

Individual concentration can be determined by expressing the volume for

batch system as a function of conversion using the equation of state:

PV=ZNTRT………..at any time in the reaction

PoVo=ZoNToRTo……at any time =0;when reaction is initiated

Then,

=

0

0

00

0Z

Z

P

P

T

T

N

NVV

T

T………………….4.9

Change in the total number of moles during reaction in gas phase reaction system,

but with constant temperature and pressure, and the compressibility factor will not

change significantly during the course of the reaction ,

=

0

0

T

T

N

NVV

Where NT = NTo +δδδδNAoX

δδδδ = (d/a) + (c/a) – (b/a) – 1

= (change in total number of mole) / (mole of A reacted)

XN

N

N

N

T

Ao

T

T δ00

1+=

0T

Ao

AoN

Ny =

δδε Ao

T

Ao yN

N==

0

…………………………4.10a.

Then

XN

N

T

T ε+= 10

XN

NN

T

ToT

0

−=ε ………………….…………….4.10b


١١

At complete conversion i.e X=1 , NT= NTf ; therefore ,

0T

ToTf

N

NN −=ε ………………………………….4.11

= (change in total number of mole for complete conversion ) / (total moles fed)

Then the volume as a function of conversion :

( )XVV ε+= 10 …………………………………….4.12

Concentration at variable volume or density

Specie

=

V

NC A

A ( )V

XN A −=

10

( ))1(

10

XV

XN

o

A

ε+

−=

( ))1(

10

X

XCA

ε+

−=

=

V

NC B

B ( )

V

XN B (b/a)- B0 Θ=

( ))1(

(b/a)- B0

XV

XN

o

B

ε+

Θ=

( ))1(

(b/a)- B0

X

XCB

ε+

Θ=

=

V

NC C

C ( )

V

XNCo (c/a) C +Θ=

( ))1(

(c/a) C

XV

XN

o

Co

ε+

+Θ=

( ))1(

(c/a) C

X

XCCo

ε+

+Θ=

=

V

NC D

D ( )

V

XN D (d/a)- D0 Θ=

( ))1(

(d/a)- D0

XV

XN

o

D

ε+

Θ=

( ))1(

(d/a)- D0

X

XCD

ε+

Θ=

=

V

NC I

I V

N IAoΘ=

)1( XV

N

o

IAo

ε+

Θ=

)1( X

C IAo

ε+

Θ=

Example


١٢

Chemical reactors can liberate or absorb very large amounts of energy , and the handling of

this energy is a major concern in reaction engineering. It is important to estimate the

temperature increase or decrease in an adiabatic reactor in which no heat is add or

removed, and exothermic reactor and also the composition of the reaction mixture at any

time.

Energy Balance

+ =

( ) )( VrTH Ar −⋅∆− )( TTUAQ a −=& ∑

dt

dTCCV iip ,

T = reaction temperature K

Ta= wall temperature K

TR= reference temperature K

A = heat transfer area m2

Cpi = specific heat KJ/Kmol

U = overall heat transfer KJ/s.m2.K

rH∆ =enthalpy change in the reaction per mole of Areacting

The number of moles of species i at any X is = ( )XNN iiAi υ+Θ= 0

Then energy balance is :

( ) ∑

=−+−⋅∆−

dt

dTNCTTUAVrTH iipaAr ,)()(

………………….4.13

Energy and mole balance equations with the rate law are coupled and then solved

Non-Isothermal Operation

Heat Generated by

Reaction

Heat Addition and

Removal by wall

Heat Accumulated by

Reaction

( ) ( )dt

dTCpXCNTTUAVrTH ipiAaAr ∆+Θ=−+−⋅∆− ∑ ,0)()(


١٣

Mole balance equation

rH∆ is calculated as

( ) ( ) ∫ ∆+∆=∆T

TpR

o

rrR

dTCTHTH

The rate law is required as a function of temperature and composition

Variable Volume (Variable Density ,T and/or P)

"Variable T in non-isothermal"

The volume for batch system as a function of conversion as :-

=

0

0

00

0Z

Z

P

P

T

T

N

NVV

T

T

( )

+=

0

0

0

0 1Z

Z

P

P

T

TXVV ε

If the compressibility factor will not change significantly during the course of the

reaction Zo=Z

( )

+=

P

P

T

TXVV 0

0

0 1 ε

Concentration at variable volume (density , T and/or P )

Specie

=

V

NC A

A ( )V

XN A −10

( )

+

−

o

o

o

A

P

P

T

T

XV

XN

)1(

10

ε

( )

+

−

o

oA

P

P

T

T

X

XC

)1(

10

ε

=

V

NC B

B ( )

V

XN B (b/a)- B0 Θ

( )

+

Θ

o

o

o

B

P

P

T

T

XV

XN

)1(

(b/a)- B0

ε

( )

+

Θ

o

oB

P

P

T

T

X

XC

)1(

(b/a)- B0

ε

=

V

NC C

C ( )

V

XNCo (c/a) C +Θ

( )

+

+Θ

o

o

o

Co

P

P

T

T

XV

XN

)1(

(c/a) C

ε

( )

+

+Θ

o

oCo

P

P

T

T

X

XC

)1(

(c/a) C

ε

=

V

NC D

D ( )

V

XN D (d/a)- D0 Θ

( )

+

Θ

o

o

o

D

P

P

T

T

XV

XN

)1(

(d/a)- D0

ε

( )

+

Θ

o

oD

P

P

T

T

X

XC

)1(

(d/a)- D0

ε

=

V

NC I

I V

N IAoΘ

+

Θ

o

o

o

IAo

P

P

T

T

XV

N

)1( ε

+

Θ

o

oIAo

P

P

T

T

X

C

)1( ε

Example

Vrdt

dXN AAo −=


١٤

A batch reactor is usually well mixed, so that may neglect the special variation in

temperature and species concentration .

Batch reactors operated adiabatically are often used to determine the reaction orders, activation energies, and specific reaction rates of exothermic reactions by monitoring the temperature-time trajectories for different initial conditions.

In adiabatic operation of a batch reactor

0=Q&

( ) ( )dt

dTNCVrTH iipAr ∑=−⋅∆− ,)(

………………………….4.14

Energy and mole balance equations with the rate law are coupled and then

solved:

;Where To = initial temperature

Example

Adiabatic Operation of a Batch Reactor

( ) ( )dt

dTCpXCNVrTH ipiAAr ∆+Θ=−⋅∆− ∑ ,0)(

( )TH

TTCX

r

oipi

∆−

−Θ=∑

)(,

( )CpXC

XTHTT

ipi

ro

∆+Θ

∆−+=∑ ,


١٥

The highest conversion that can be achieved in reversible reactions is the equilibrium conversion XEB. For endothermic reactions, the equilibrium conversion increases with increasing temperature up to a maximum of 1.0. For exothermic reactions, the equilibrium conversion decreases with increasing temperature Figure ( ) show the variation of the concentration equilibrium constant as a function of temperature for an exothermic reaction the corresponding equilibrium conversion XEB as a function of temperature.

Figure ( ) show the variation of the concentration equilibrium constant and equilibrium conversion as a function of temperature for an exothermic reaction. To determine the maximum conversion that can be achieved in an exothermic reaction carried out adiabatically, we find the intersection of the equilibrium conversion as a function of temperature ,with temperature –conversion relationships from the energy balance

……………..4.15

Graphical solution of equilibriurn and energy balance equations to obtain the adiabatic temperature

and the adiabatic equilibriurn

conversion XEB.

Example

Equilibrium Conversion

( )TH

TTCX

r

oipi

EB∆−

−Θ=∑

)(,

Reactor Design Lectures Notes · 2018. 1. 19. · [Introduction to Chemical Reaction Engineering ]...

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