1. ALL RELATED EQUATIONS
Reaction Stoichiometry
A→B+2C
Mole Balances (Differential Form in Packed Bed Reactor)
d FA
=− r A
dW
d FB
=rA
dW
d FC
=2 r A
dW
Reaction Rate Expression
Since the reaction is elementary:
r A = k CA
Arrhenius form using activation parameter E/R:
E/ R E/R
k = k 450 . exp [ −
450 T
Gas Concentration Expression
Total molar flow:
F T = F A + FB + F C
Ideal gas concentration of A:
y P 0 FA
CA = .
RT FT
Conversion Definition
F A 0 − FA
X=
FA0
Energy Balance (Differential Form)
Denominator (heat capacity of mixture):
Cp , tot = FA CpA + FB CpB + F C CpC
Case A: Adiabatic Reactor
, dT − Δ Hr . r A
=
dW Cp ,tot
Case B: With Heat Exchanger (Cooling)
dT − Δ Hr . r A − U ( T − T )
= a a
dW Cp ,tot
Pressure Drop Equation (Ergun-based relationship in PBR)
Gas expansion factor:
ϵ=2
Pressure ratio:
P
y=
P0
Differential pressure drop equation:
dy 1+ ϵ X
=− α .
dW 2y
Initial Conditions (at W=0)
FA(0)=100 mol/min
FB(0)=0
FC(0)=0
T(0)=450 K
y(0)=1
These equations describe the full dynamic reactor model used for simulation of the
packed bed reactor under adiabatic and cooled operation conditions.
2. CODE FOR SIMULATION
{Parameters}
FA0=100
T0=450
y0=1
CpA=140
CpB=80
CpC=30
P0=10
E_R=5000
k450=1.3
Ua=15
Ta=350
alpha=0.008
eps=2
dH=-60000
R=0.08206
{Differential equations}
d(FA)/dW = -rA
d(FB)/dW = rA
d(FC)/dW = 2*rA
Reaction Stoichiometry
A→B+2C
Mole Balances (Differential Form in Packed Bed Reactor)
d FA
=− r A
dW
d FB
=rA
dW
d FC
=2 r A
dW
Reaction Rate Expression
Since the reaction is elementary:
r A = k CA
Arrhenius form using activation parameter E/R:
E/ R E/R
k = k 450 . exp [ −
450 T
Gas Concentration Expression
Total molar flow:
F T = F A + FB + F C
Ideal gas concentration of A:
y P 0 FA
CA = .
RT FT
Conversion Definition
F A 0 − FA
X=
FA0
Energy Balance (Differential Form)
Denominator (heat capacity of mixture):
Cp , tot = FA CpA + FB CpB + F C CpC
Case A: Adiabatic Reactor
, dT − Δ Hr . r A
=
dW Cp ,tot
Case B: With Heat Exchanger (Cooling)
dT − Δ Hr . r A − U ( T − T )
= a a
dW Cp ,tot
Pressure Drop Equation (Ergun-based relationship in PBR)
Gas expansion factor:
ϵ=2
Pressure ratio:
P
y=
P0
Differential pressure drop equation:
dy 1+ ϵ X
=− α .
dW 2y
Initial Conditions (at W=0)
FA(0)=100 mol/min
FB(0)=0
FC(0)=0
T(0)=450 K
y(0)=1
These equations describe the full dynamic reactor model used for simulation of the
packed bed reactor under adiabatic and cooled operation conditions.
2. CODE FOR SIMULATION
{Parameters}
FA0=100
T0=450
y0=1
CpA=140
CpB=80
CpC=30
P0=10
E_R=5000
k450=1.3
Ua=15
Ta=350
alpha=0.008
eps=2
dH=-60000
R=0.08206
{Differential equations}
d(FA)/dW = -rA
d(FB)/dW = rA
d(FC)/dW = 2*rA
