chemical reaction engineering - kau · 2008-04-05 · 2 what is reaction rate? it is the rate at...
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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
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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: