Design Equations 3
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Transcript of Design Equations 3
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Ch E 441: Chemical Kineticsand Reaction Engineering
Mole Balances in Reacting Systems & Reactor Design EquationsDavid A. Rockstraw, Ph.D., P.E.New Mexico State UniversityChemical Engineering
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Objectives• Describe photos of real reactors. • Define the rate of chemical reaction. • Apply a general mole balance to
– a batch reactor, – a continuous stirred tank reactor (CSTR), – a plug flow reactor (PFR), and – a packed bed reactor (PBR).
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Industrial Reactors
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Industrial Reactors
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Industrial Reactors
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Spherical Reactors
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Industrial Reactors
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Industrial Reactors
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Industrial Reactors
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Industrial Reactors
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Industrial Reactors
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Industrial Reactors
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Industrial Reactors
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Packed Bed ReactorPacked Bed Reactor in use for a Fisher-Tropsch synthesis reaction at Sasol Limited Chemical.
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Moving Bed ReactorThis photo is of a catalytic cracker moving bed reactor. Only the disengager section of the reactor is visible in the picture - the reaction section is hidden behind the stair structure beneath the disengager.
The cracker is used for the catalytic cracking of gas oil into light aromatics and straight chain hydrocarbons, which are then separated in the distillation tower to the right of the photo.
The white unit to the left of the cat cracker is the catalyst regenerator,where coke deposits are burned off the catalyst. This is a highly exothermic operation, (1400°F), and so the boiler unit at the far left recovers the sensible heat of the regenerator exhaust to produce steam.
boilerdisengager
stillregenerator
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Straight ThroughTransport Reactor
Straight Through Transport Reactor (STTR) in use for a Fisher-Tropsch synthesis reaction at Sasol Limited Chemical.
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Industrial Reactors
Automotive Catalytic Converter
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Industrial Reactors
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Glass Lined Reactors
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General Reactor Construction
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Fluidized-Bed Reactor
Trickle-Bed Reactor
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Wetlands
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Chemical Vapor Deposition Reactor
reacting gas flows through annulus between outer edges of cylindrical wafers and the tube wall
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Laboratory CSTR/Batch Reactor
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Laboratory CSTR
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RC1e Reaction Calorimeter
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React IR 1000 (FTIR)
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Which of the following is probablyNOT a chemical reactor?
A. a pan of boiling water containing pastaB. a jar of medication in the bathroom cabinetC. a public swimming poolD. a cup of coffee with cream and sugarE. a cow’s stomach and contents
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Chemical Identity• A chemical species has reacted when it
has lost its chemical identity. The identity of a chemical species is determined by the kind, number, and configuration of that species' atoms.
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Loss of Chemical Identity• Decomposition; AB A + B• Combination; A + B AB• Isomerization; A B• single displacement (substitution);
A + BC AC + B• double displacement (metathesis);
AB + CD AD + CB
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Reaction Rate• The reaction rate 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 as the rate of appearance of a product.
• Reaction rates are associated with reaction stoichiometry, which describe molar relationships
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Reaction Rate• Consider species A: ☞ rA = rate of formation of A per unit vol
☞ -rA = rate of a disappearance of A per unit vol
☞ For a catalytic reaction, -rA' is the rate of disappearance of species A on a per mass of catalyst basis.
☞ NOTE: dCA/dt is not the rate of reaction
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Reaction Rate• Consider in general terms, species j…• The rate, rj is
– the rate of formation of species j per unit volume – a function of concentration, temperature, pressure,
and the type of catalyst (if any) – independent of the type of reaction system (batch,
plug flow, etc.) – an algebraic equation, not a differential equation
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Which reaction type characterizes the combusion of ethane?
2 C2H6 + 7 O2 4 CO2 + 6 H2O
A. combinationB. isomerizationC. decompositionD. single displacement E. double displacement
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Which statement is always false?
A.
B.
C.
D.
E.
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What are the units of reaction rate?
A. mass / length / time
B. moles / volume / time
C. moles / catalyst mass / time
D. both A and B
E. both B and C
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General Mole Balance Equation
GjGjFjo Fj
system within j of
onaccumulati of rate
system ofout j of
flow of rate
rxnby systemin j of
generation of rate
system into j of
flow of rate
dt
dNFGF j
jjjo where N is the moles of jin the system at time t.
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General Mole Balance Equation
GjGjFjo Fj
system within j of
onaccumulati of rate
system ofout j of
flow of rate
rxnby systemin j of
generation of rate
system into j of
flow of rate
dt
dNFGF j
jjjo VrG jj if all variables are spatially uniform
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General Mole Balance Equation• If rj varies with position in the system,
rj,1
V1
rj,2
V2
m
1iii,j
m
1ii,jj
11,j1,j
VrGG
VrG
0V ,m Let
V
jj dVrG
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General Mole Balance Equation
dt
dNFGF j
jjjo V
jj dVrG
dt
dNFdVrF j
j
V
jjo
GjGjFjo Fj
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GMBE Applied to Batch Reactors• For a batch reactor (no flows):
• GMBE reduces to:
0FF jo,j
dt
dNFdVrF j
j
V
jjo
dt
dNdVr jV
j
0 0
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GMBE Applied to Batch Reactors• Assuming perfect mixing:
dt
dNdVr jV
j dt
dNdVr jV
j
Vrdt
dNj
j Batch ReactorDesign EquationBatch ReactorDesign Equation
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GMBE Applied to Batch Reactors• For the simple reaction A products:
– In a constant volume reactor,
dt
dN
V
1r AA
dt
dC
dt
VNd
dt
dN
V
1r AAAA
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GMBE Applied to Batch Reactors• For the simple reaction A products:
– In a constant pressure reactor,
dt
VlndC
dt
dC
dt
dV
V
C
dt
dC
dt
VCd
V
1
dt
dN
V
1r
AAAA
AAA
dt
dN
V
1r AA
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Which is NOT a characteristic of an ideal batch reactor ?
A. Absence of concentration gradients (i.e., perfect mixing)
B. Steady state operationC. No material crosses system boundary
(i.e., no flows)D. Derivative with respect to time
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GMBE Applied to Flow Reactors• Continuous Stirred-Tank Reactor (CSTR):
reactants
products
dt
dNFdVrF j
j
V
jjo 0
steadystate
0FVrF jjjo perfectmixing
j
jjo
r
FFV
jj CF
volumetricflow rate
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GMBE Applied to Flow Reactors• Continuous Stirred-Tank Reactor (CSTR):
CSTRDesignEquation
CSTRDesignEquation
reactants
products j
jjo
r
FFV
dt
dNFdVrF j
j
V
jjo 0
steadystate
0FVrF jjjo perfectmixing
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Which is NOT a characteristic of an ideal CSTR?
A. Absence of concentration gradients (i.e., perfect mixing)
B. Steady state operationC. Material crosses system boundary
(i.e., flows in and out)D. Derivative with respect to time
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GMBE Applied to Flow Reactors• Tubular (Plug Flow) Reactor (PFR):
reactants products
yy+yy
VFj(y) Fj(y+y)
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GMBE Applied to Flow Reactors• Tubular (Plug Flow) Reactor (PFR):
dt
dNFdVrF j
j
V
jjo
0steadystate
0FVrF jjjo spatiallyuniform V
VFj(y) Fj(y+y)
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GMBE Applied to Flow Reactors• Tubular (Plug Flow) Reactor (PFR):
0yAryyFyF jjj uniformcross-section
dt
dNFdVrF j
j
V
jjo
0steadystate
0FVrF jjjo spatiallyuniform V
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GMBE Applied to Flow Reactors• Tubular (Plug Flow) Reactor (PFR):
jj r
dV
Fd
PFRDesignEquation
PFRDesignEquation
dy
dVrAr
dy
Fdjj
j
Ar
y
yF-yyFj
jj
dx
df
x
xf-xxflim
0x
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Which IS a characteristic of an ideal Plug Flow Reactor?
A. Absence of concentration gradients (i.e., perfect mixing)
B. Steady state operationC. Material crosses system boundary
(i.e., flows in and out)D. Derivative with respect to time
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GMBE Applied to Packed Bed Reactors• PBR used for fluid/solid catalytic reaction:
FAo FA
WW+WW
WFA(W) FA(W+W)
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GMBE Applied to Packed Bed Reactors• PBR used for fluid/solid catalytic reaction:
0WrWWFWF 'AA A
catalyst masscatalyst masstime
A molesWr '
A
dimensions of
generation term
WFA(W) FA(W+W)
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GMBE Applied to Packed Bed Reactors• PBR used for fluid/solid catalytic reaction:
'AA
rdW
Fd
PBRDesignEquation
PBRDesignEquation
'AAA
rW
WF-WWF
dx
df
x
xf-xxflim
0x
When pressure drop and catalyst decay canbe neglected, integral form can be used:
A
AoA
F
F 'A
r
FdW
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Which IS a characteristic of an ideal Packed Bed Reactor?
A. Absence of concentration gradients (i.e., perfect mixing)
B. Steady state operationC. No material crosses system boundary
(i.e., no flows)D. Derivative with respect to position
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Design Equation Summary
Batch Vrdt
dNA
A
CSTR
PFR
PBR 'AA
rdW
Fd A
AoA
F
F 'A
r
FdW
jj r
dV
Fd
j
jjo
r
FFV
A
Ao
F
FA
A
r
FdV
A
Ao
N
NA
A
Vr
Ndt
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Next Session• Define conversion and space time. • Write the mole balances in terms of conversion
for a batch reactor, CSTR, PFR, and PBR. • Size reactors either alone or in series once given
the molar flow rate of A, and the rate of reaction, -rA, as a function of conversion, X.