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Comparison Of Reactors For Prediction Of Kinetics For A Reaction

3231 words - 13 pages

Comparison of reactors for prediction of kinetics for a reaction

Abstract
In this report, a Matlab model for simulating simultaneous oxidation of carbon monoxide and propylene in a fixed bed reactor. The model takes into account temperature variation and pressure drop down the reactor. The catalyst pellets are assumed to be isothermal; only the concentration variation is considered inside the pellet. Both external and internal diffusion is taken into account in the model. The results are then analyzed and some problems are noted. Then a new model is simulated to eliminate those problems. Also, a simpler isothermal case is also simulated for relative study.
Introduction
The reaction ...view middle of the document...

175cm. The length of the bed is 120m. These are represented by the following reactions:

1. CO + ½ O2 = CO2
2. C3H6 + 9/2 O2 = 3 CO2 + 3H2O

The rate equations for both the reactions are taken from Oh et al.:
r1=k1CcoCO21+KCOCco+KC3H6CC3H62

r2=k1CC3H6CO21+KCOCco+KC3H6CC3H62

The rate constants and adsorption constants are assumed to follow Arrhenius equation.

The assumptions considered in this model are as follows:
1. Particles are small compared to the length of reactor.
2. Plug flow in bed, no radial profiles.
3. Neglect axial diffusion in the bed.
4. Steady state.
5. Isothermal catalyst pellets
The various parameters and their values are given in the following table:

Parameter | Value |
Pressure | 2 atm |
Diameter of particle | 0.175 cm |
Tin | 550 K |
E1/R | 13108 |
E2/R | 15109 |
Eco/R | -409 |
Ec3h6 | 191 |
Ccof | 2% |
Co2f | 3% |
Cc3h6f | 0.05% |
k10 | 7.07E+19 |
kco | 8.10E+06 |
k20 | 1.47E+21 |
kc3h6 | 2.58E+08 |
Dco | 4.87E-02 |
Do2 | 4.69E-02 |
Dc3h6 | 4.87E-02 |
kmco | 3.90E+00 |
kmo2 | 4.07E+00 |
kmc3h6 | 3.90E+00 |

The mass transfer coefficients are taken from DeAcetis and Thodos.

Model equations:
All the modeling and simulation was done in Matlab.

The type of equations to describe a fixed bed reactor can be divided into 3 parts:
1. Equations for the reactor
2. Equations for the pellet
3. Coupling Equations
REACTOR EQUATIONS:
Mass balance:
dNjdV= Rj+AcUdCjdz

Heat Balance:
ρCpQdTdV= -∆HriRi+2RU0(Ta-T)

Pressure Drop across the reactor (Ergun’s equation):
dPdV=-1-ϵbDpϵb3QAc2 1501-ϵbμfDp+74ρQAc

For the reactor equations, we know the initial conditions (at the inlet of the reactor); hence those become boundary conditions.
Boundary conditions:
Nj=Nj,in at z=0
T=Tinat z=0
P=Pinat z=0
PELLET EQUATIONS:

The pellet is supposed to be isothermal, since the size of pellet is too small to show any significant temperature variations. Therefore, the only equation required for simulating the inside of the pellet is the mass balance.
Mass balance:
Dj1r2ddrr2dCjdr= -ΩRj'
where , overall effectiveness factor, is defined as the ratio of actual rate of reaction and rate of reaction if the entire surface was exposed to the bulk conditions. The value of overall effectiveness factor is derived from internal effectiveness factor, which in turn is derived from thiele modulus.
For the pellet, we have 2 boundary conditions:
Boundary conditions:
dCjdr=0 at r=0
DjdCjdr=kjmCjs-Cj at r=R

COUPLING EQUATION:
The final equation equates the production rate seen by the fluid phase Rj, to the rate of production inside the particles, which is where the reaction actually takes place.
Rj= -1-ϵb SpVp DjdCjdr at r=R

Global collocation method was used to integrate the differential equations. The value of all the required constants were obtained from credible sources on the internet and are given in Table 1.

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