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Reactor Calculations The Continuous-flow, Stirred Tank Reactor CSTR
Lund University / Faculty of Engineering LTH / Department of Chemical Engineering / Per Warfvinge
Content
•! The continuous-flow, stirred tank reactor, CSTR
•! Properties
•! Mass balance equation
•! The residence time
•! Reactor calculations
–! Methodology
–! Example: 1st order irreversible reaction
–! Sequential solution
–! Simultanuous solution
•! Conversion
•! Remarks
Lund University / Faculty of Engineering LTH / Department of Chemical Engineering / Per Warfvinge
Continuous-flow, Stirred Tank Reactor
•! The CSTR:
–! Large scale chemical processes
–! Water treatement reactors
–! Lakes
•! Open with respect to matter and/or energy
•! Perfectly mixed:
–! No gradients with respect to concentration or temperature
–! There is no ”travel time” from the inlet point to any other point in the
reactor
Lund University / Faculty of Engineering LTH / Department of Chemical Engineering / Per Warfvinge
Mass balance for the CSTR
•! General, in molar quantities:
•! General, in process quantities:
•! Steady-state
Input + Prod = Output + Acc
Fin + Fprod = Fout +dN
dt
Fout
Fin
FprodN
Qincin + rV = Qoutc +d(cV )
dt
cin
c crV
Qin
Qout
Qcin + rV = Qccin
c c
rV
Lund University / Faculty of Engineering LTH / Department of Chemical Engineering / Per Warfvinge
The mean residence time
•! Since the content of the reactor is continuously renewed, we can define
a mean residence time as:
•! Steady-state mass balance:
! =V
Q
m3
m3/s= s
Qcin + rV = Qc
cin + r! = c
cin
cc! r
Lund University / Faculty of Engineering LTH / Department of Chemical Engineering / Per Warfvinge
CSTR reactor calculation methodology
1.! Determine the flow and mixing conditions in terms of an ideal reactor
model, and define the mass balance(s)
2.! Define the kinetic equation(s) and the kinetic coefficient(s)
3.! Combine the appropriate number of mass balances (for the reactor
model) with the kinetic equations to form the design equation
4.! Perform the calculation, analytically or numerically
Lund University / Faculty of Engineering LTH / Department of Chemical Engineering / Per Warfvinge
Example: 1st order irreversible reaction
•! Calculate the concentrations of A and B in the output flow of a steady-
state CSTR with the reaction:
•! System properties:
–! Input flow concentration of A: 3 mole/m3
–! Input flow concentration of B: 0.2 mole/m3
–! Volumetric input flow rate: 1.25 m3/min
–! Volumetric output flow rate: 1.25 m3/min
–! Reactor volume: 5 m3
–! Kinetic rate coefficient: 0.5 1/min
A !" B r = kcA
Lund University / Faculty of Engineering LTH / Department of Chemical Engineering / Per Warfvinge
Example
1.! Flow and mixing conditions
•! Reactor model: Steady-state CSTR
•! To mass balances needed are:
–! To calculate : Mass balance equation for A
–! To calculate : Mass balance equation for A and B
•! Mass balance equations:
r
Q
cA
cB
Q
cin,A
cin,B
cA
cB
V
cA
cB
!"
#
Qcin,A + rAV = QcA
Qcin,B + rBV = QcB
Lund University / Faculty of Engineering LTH / Department of Chemical Engineering / Per Warfvinge
Example
2.! Kinetic equation
•! 1st order with respect to :
3.! Combine mass balances with kinetic equations to the design equations:
r
Q
cA
cB
Q
cin,A
cin,B
cA
cB
VcA
r = kcA
rA = !kcA
rB = kcA
!"
#
Qcin,A ! kcAV = QcA
Qcin,B + kcAV = QcB
Lund University / Faculty of Engineering LTH / Department of Chemical Engineering / Per Warfvinge
Example
4.! Calculations
•! Two strategies
–! Sequential calculation: Solve for , then for
–! Simultanuous calculation for and
•! The seqential strategy works for A since the kinetic expression for the
formation of A only includes
cA
cA cB
r
Q
cA
cB
Q
cin,A
cin,B
cA
cB
V
cA
cB
Lund University / Faculty of Engineering LTH / Department of Chemical Engineering / Per Warfvinge
Example
•! Sequential solution, start with :
•! With numerical values:
•! And, since : cB = cin,B + kcA · !
cB = 0.2 + 0.5 · 0.667 · (5/1.25) = 1.553
cA
cA = 2 · 11 + 0.5 · (5/1.25)
= 0.667
Qcin,A ! kcAV = QcA
Qcin,A = (Q + kV )cA
cin,A = (1 + k!)cA
cA = cin,A · 11 + k!
Lund University / Faculty of Engineering LTH / Department of Chemical Engineering / Per Warfvinge
Example
•! Simultaneous solution:
•! With , it may be re-written as:
•! In matrix notation, this linear system of equations becomes:
!"
#Qcin,A ! kcAV = QcA
Qcin,B + kcAV = QcB
!(1 + k!)cA = cin,A
!k!cA + cB = cin,B
! = V/Q
AX = Y!1 + k! 0!k! 1
" !cA
cB
"=
!cin,A
cin,B
"X=A!1Y!"
!cA
cB
"=
!0.66671.5333
"
Lund University / Faculty of Engineering LTH / Department of Chemical Engineering / Per Warfvinge
Conversion
•! The conversion, with respect to a reactant component is:
•! For a steady-state reactor where :
•! For a reactant A that is converted according to :
X
X =Fin ! Fout
Fin=
Qincin !Qoutcout
Qincin
Qin = Qout
X =cin ! cout
cin= 1! cout
cin
X = 1! cout
cin= 1!
cin · 11+k!
cin!" X =
k!1 + k!
rA = !kcA
Lund University / Faculty of Engineering LTH / Department of Chemical Engineering / Per Warfvinge
Remarks
•! The mass balance is defined for the
whole reactor volume
•! The concentration in the output stream is
the same as the concentration in the reactor
•! Since the fact that the reactor operates with the output concentration of
reactans means the kinetic driving force is constant:
•! Real life advantages:
–! Long residence times in relation to reaction rate makes the reactor
stable
–! Heat may be added/removed through the reactor walls
rA = !kcA
Lund University / Faculty of Engineering LTH / Department of Chemical Engineering / Per Warfvinge
Content
•! The continuous-flow, stirred tank reactor, CSTR
•! Properties
•! Mass balance equation
•! The residence time
•! Reactor calculations
–! Methodology
–! Example: 1st order irreversible reaction
–! Sequential solution
–! Simultanuous solution
•! Conversion
•! Remarks
