mole balance for chemical reaction engineering (design equations for reactors) lec 3 week 3
TRANSCRIPT
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Mole balance for chemical reaction engineering
(Design Equations for reactors)Lec 3 week 3
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The General Mole Balance Equation
• To perform a mole balance on any system, the system boundaries must first be specified. The volume enclosed by these boundaries is referred to as the system volume.
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where Nj , represents the number of moles of species j in the system at time t.
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• The rate of generation of species j is expressed as The product of the reaction term and can be written in more
familiar terms, GA = rA V
• V is volume of the system. • Note that the units for this relation are consistent:
• If GA (and hence rA) varies with position in the system volume, we can take this into account by evaluating this term at several locations. Then GA1 = rA1 V1,
volumetimevolume
mass
time
mass
.
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• Summing the reactions over the entire volume yields:
• As (that is, as we decrease the size of these cubes and increase their number) then
which gives
k
iiAi
k
iAiA VrGG
11
k
V
AA dVrG
0V
we now replace G in equation (1) to get :
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• From this general mole balance equation we can develop the design equations for the various types of industrial reactors: batch, semi-batch. and continuous- flow.
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Types of Reactors• Batch
– No flow of material in or out of reactor– Changes with time
• Fed- Batch (semi batch)– Either an inflow or an outflow of material but not both– Changes with time
• Continuous– Flow in and out of reactor– Continuous Stirred Tank Reactor (CSTR)– Plug Flow Reactor (PFR)– Steady State Operation ( no change with time)
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General Mole Balance in terms of number of moles
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Batch reactor mole balance• Generalized Design Equation
for Reactors
• No flow into or out of the reactor, then, FA = FA0 = 0
• Good mixing, constant volume
Vrdt
dNA
A
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Batch Reactor
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Batch Reactor
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Fed Batch Reactor
• Reactor Design Equation
• No outflow FA = 0
• Good Mixing rA dV term out of the integral
dt
dNdVrFF A
V
AAA 0
dt
dNVrF A
AA 0
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CSTR• General Reactor Design Equation
• Assume Steady State
• Well Mixed • So or
dt
dNdVrFF A
V
AAA 0
0dt
dN A
A
V
A VrdVr
00 AAA VrFFA
AA
r
FFV
0
Continuous Stirred Tank Reactor
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CSTR
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Tubular Reactor (Plug Flow Reactor) (PFR)• Tubular Reactor• Pipe through which
fluid flows and reacts. • Poor mixing • Difficult to control
temperature variations. • An advantage is the
simplicity of construction
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PFR Design Equation• Design Equation
• Examine a small volume element (V) with length y and the same radius as the entire pipe.
• If the element is small, then spatial variations in rA are negligible, and
dt
dNdVrFF A
V
AAA 0
VrdVr A
V
A
Flow of A into Element
Flow of A out of Element
Assumption of “good mixing” applies only to the small volume element
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• If volume element is very small, then assume steady state with no changes in the concentration of A.
• Simplify design equation to:
• rA is a function of position y, down the length of the pipe and reactant concentration
• take the limit where the size of a volume element becomes infinitesimally small
0dt
dN A
0 VryyFyF AAA
AA
v
rdV
dF
lim
0
This is the Design Equation for a PFR
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• take the limit where the size of a volume element becomes infinitesimally small
• or because y A = V,
• This is the Design Equation for a PFR• Bioapplications - Sometimes hollow fiber
reactor analysis is simplified to a PFR
AA
v
rdV
dF
lim
0
AA r
dV
dF
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Plug Flow Reactor Mole Balance
PFR:
The integral form is:
V dFAr
AFA 0
FA
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
PBR
The integral form to find the catalyst weight is:
W dFA
r AFA 0
FA
FA0 FA r AdW dNA
dt
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Reactor Mole Balance Summary