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Chemical Reaction Engineering

Dr. Yahia Alhamed

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What is reaction rate? It is the rate at which a species looses its

chemical identity per unit volume.The rate of a reaction can be expressed as:-

- The rate of disappearance of a reactant or - The rate of appearance of a product.

Kinetics and Reaction Rate

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Reaction RateConsider species A:

-rA = the rate of formation of species A per unit volume rB = the rate of formation of species B per unit volume

EXAMPLE: If B is being formed at 0.2 moles per decimeter cubed per second, ie, rB = 0.2 mole/dm3/s

Then A is disappearing at the same rate:-rA= 0.2 mole/dm3/sThe rate of formation (generation of A) is rA= -0.2 mole/dm3/s

YA1

Slide 3

YA1 Y A, 4/5/2008

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Reaction RateConsider species j: • rj is the rate of formation of species j per unit

volume [e.g. mol/dm3*s] • rj is a function of concentration, temperature,

pressure, and the type of catalyst (if any) • rj is independent of the type of reaction system

(batch, plug flow, etc.) • rj is an algebraic equation, not a differential

equation

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Rate Law Basics

• A rate law describes the behavior of a reaction. The rate of a reaction is a function of temperature (through the rate constant) and concentration.

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Reaction Rate for solid catalytic reactions

• For a catalytic reaction, we refer to -rA', which is the rate of disappearance of species A on a per mass of catalyst basis.

• -r'A = rA/bulk density of the catalyst (ρb)

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Rate Law Basics• A rate law describes the behavior of a reaction. The rate

of a reaction is a function of temperature (through the rate constant) and concentration.

• Power Law Modelk is the specific reaction rate (constant)

k is given by the Arrhenius Equation:

Where:E = activation energy (cal/mol)– R = gas constant (cal/mol*K)– T = temperature (K)– A = frequency factor (units of A, and k, depend on overall

reaction order)

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General Mole Balance

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Batch Reactor Mole Balance

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Constantly Stirred Tank Reactor Mole BalanceCSTR or MFR

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Plug Flow Reactor (PFR) Mole Balance

V =dF Ar

AFA 0

FA∫The integral form is:

This is the volume necessary to reduce the entering molar flow rate (mol/s) from FA0 to the exit molar flow rate of FA.

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Packed Bed Reactor Mole Balance

PBR

The integral form to find the catalyst weight is: W =dFA

′ r AFA 0

FA∫

FA0 − FA + ′ r AdW =dN A

dt∫

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Space time and space velocityFA0 = CAo vo

θ = is called space time (s) = V/vo

Space velocity = 1/θ, where;FA0 = Molar feed rate of key reactant A (mol/s)CAo= Concentration of key reactant A in the feed (mol/m3)vo=Volumetric flow rate of feed to the reactor (m3/s)V = volume of the reactor

For constant volume systems v = vo where v is volumetric flow rate leaving the reactor

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Reactor Mole Balance Summary

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Reactor Mole Balance Summary

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Reactor Mole Balance Summary

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Reactor Mole Balance Summary

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Reactor Mole Balance Summary

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Conversion

Consider the general reaction: aA + bB - cC + dDWe will choose A as bases of calculation (i.e. Key reactant)The limiting reactant is usually taken as the key reactant Then: A + (b/a)B (c/a)C + (d/a)DXA = moles reacted/moles fed

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Batch Reactor ConversiondN A

dt= r A V

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CSTR Conversion

Algebraic Form:

There is no differential or integral form for a CSTR.

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PFR Conversion

PFR dFAdV

= rA

FA = FA0 1− X( )

Differential Form:

Integral Form:

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Design Equations

V

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Reactor Sizing (CSTR)• Given -rA as a function of conversion, -rA=f(X), one can size any

type of reactor.• We do this by constructing a Levenspiel plot.• Here we plot either as a function of X.

• volume of a CSTR is:

FA0−rA

or 1−rA

V =FA0 X − 0( )− rA EXIT

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Reactor Sizing (PFR)

V PFR = F A 0

− r A0

X

∫ dX

For PFR th evolume of the reactor needed is given by the area under the curve

=area

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Summary

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Rate Law Basics

• A rate law describes the behavior of a reaction. The rate of a reaction is a function of temperature (through the rate constant) and concentration.

• Power Law Modelk is the specific reaction rate (constant)

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Examples of Rate Laws

62HCA

24262

kCrHHCHC

=−+→ ⎟

⎠⎞

⎜⎝⎛ −

−= T1

10001

mol82kcal

1e0.072sk

• First Order Reactions

(1) Homogeneous irreversible elementary gas phase reaction

with

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• First Order Reactions

(1) Homogeneous irreversible elementary gas phase reaction

with

(2) Homogeneous reversible elementary reaction

with and

Examples of Rate Laws

104104 HCiHCn −↔−

[ ]CiCnCn KCCkr44

−=−

⎥⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛ −

=360T

360T790631.1expk ⎥⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛ −

−=333T

333T830.33.03expKC

62HCA

24262

kCrHHCHC

=−+→ ⎟

⎠⎞

⎜⎝⎛ −

−= T1

10001

mol82kcal

1e0.072sk

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• First Order Reactions

(1) Homogeneous irreversible elementary gas phase reaction

with

(2) Homogeneous reversible elementary reaction

with and

• Second Order Reactions

(1) Homogeneous irreversible non-elementary reaction

with and

This is first order in ONCB, first order in ammonia and overall second order.

Examples of Rate Laws

104104 HCiHCn −↔−

[ ]CiCnCn KCCkr44

−=−

⎥⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛ −

=360T

360T790631.1expk ⎥⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛ −

−=333T

333T830.33.03expKC

62HCA

24262

kCrHHCHC

=−+→ ⎟

⎠⎞

⎜⎝⎛ −

−= T1

10001

mol82kcal

1e0.072sk

3NHONCBA CkCr =−

kmol.minm0.0017k

3

=molcal11273E = At 188˚C

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Examples of Rate Laws2323 NCNHBrCHNHCHCNBr +→+

23NHCHCNBrA CkCr =−s.mol

2.2dmk3

=with

• Second Order Reactions

(2) Homogeneous irreversible elementary reaction

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Examples of Rate Lawswith

2323 NCNHBrCHNHCHCNBr +→+

23NHCHCNBrA CkCr =−s.mol

2.2dmk3

=

• Second Order Reactions

(2) Homogeneous irreversible elementary reaction

This reaction is first order in CNBr, first order in CH3NH2 and overall second order.

(3) Heterogeneous catalytic reaction: The following reaction takes place over a solid catalyst: