biotechnology
DESCRIPTION
biotechnologyTRANSCRIPT
Reactor Design
Lecture 4
Fall 2007
ChEE ABE 481a/581a
Mass Balance on Reactive System• In - out + gen - cons = accumulation
• A mass balance for the system is
• NA is the mass of “A” inside the system.
GARate of generation/consumption
FA0Rate of flow in
FARate of flow out
System
GARate of generation/consumption
FA0Rate of flow in
FARate of flow out
System
dt
dNGFF A
AAA 0
• The reaction term 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
• Summing the reactions over the entire volume yields:
• As (that is, as we decrease the size of these cubes and
increase their number)
• which gives
k
iiAi
k
iAiA VrGG
11
k
V
AA dVrG
0V
Generalized Design Equation for Reactors
• In - out + gen - cons = accumulation
dt
dNdVrFF A
V
AAA 0
Types of Reactors• Batch
– No flow of material in or out of reactor
– Changes with time
• Fed- 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
Batch Reactor• Generalized Design Equation for
Reactors
• No flow into or out of the reactor, then, FA = FA0 = 0
• Good mixing, constant volume
dt
dNdVrFF A
V
AA0A
V
AA dVr
dt
dN
Vrdt
dNA
A A
AA rdt
dC
dt
VNdor
Enzyme Batch Reactor(constant volume, well mixed)
• integrate from t = 0 to t = t, we obtain
Kmln (S0/S) + (S0 -S) = vmax t
• Batch reactors are often used in the early stage of development due to their ease of operation and analysis
SK
Sv
dt
dSr
M max
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
VCd
dt
dNVrF AA
AA
0
Fed Batch Continued• Convert the mass (NA) to concentration. Applying
integration by parts yields
• Since
• Then
• Rearranging
dt
dVC
dt
dCVVrF A
AAA 0
0AFdt
dV
00 AAA
AA FCdt
dCVVrF
V
FCr
V
F
dt
dC AAA
AA 00
Fed Batch Continued
• Or
• Used when there is substrate inhibition and for bioreactors with cells.
AAAA rC
V
F
dt
dC 10
Assumptions for a fed batch reactor include
Only
a fe
ed in
Eith
er a
feed
in o
r a...
Ste
ady
stat
e
2 a
nd 3
All
of the
above
0%
64%
7%
29%
0%
1. Only a feed in
2. Either a feed in or a removal stream
3. Steady state
4. 2 and 3
5. All of the above
Continuous Stirred Tank Reactor
• Assume rate of flow in = rate of flow out
• FA = v CA and FA0
= v CA0
• v = volumetric flow rate (volume/time)
CSTR - continued• 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
CSTR for Enzymes(Enzyme remains inside)
• Input - output + generation - consump = accumulation
• F - flow rate l/hr• S - substrate conc. • V- reactor volume • r - reaction rate• at Steady State dS/dt = 0
dt
dSvrVFSFS 0
CSTR - enzymes
rV = F(S0 - S)
or r = F/V(S0 - S) = D(S0 - S)
• D= dilution Rate (hr-1) = residence time (hr)
If
ThenSK
Svr
M max
SS
SvKS M
0
max
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.
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
• 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
• The volume of an element is the product of the length and cross-sectional area,
V = A y • Design Equation becomes:
0dt
dN A
0 VryyFyF AAA
A
AA Ary
yFyyF
• 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
y
Ardy
dF
lim
0
AA r
dV
dF