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## Reatores quimicos

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Catégorie :Category: mViewer GX Creator Lua TI-Nspire
Auteur Author: catotix
Type : Classeur 3.6
Page(s) : 33
Taille Size: 1.89 Mo MB
Mis en ligne Uploaded: 25/11/2021 - 13:56:00
Visibilité Visibility: Archive publique

### Description

The reaction ???? + ???? ↔ ???? + ???? takes place in a packed
bed reactor, assuming the pseudo-homogeneous ????
Curve 1 = −8.182
mechanism. Reagent A is fed at an initial concentration ????λ

of 4.85 M. The figure shows the concentration profiles in
two reactors with the same length at different feed
conditions. ????
Curve 2 = −3.25
????λ
a) Make the deduction of the condensated molar
balance equation to the reactor in terms of the Peclet
number and spatial time.
b) For each curve calculate the spatial time.
c) Calculate the catalyst weight in each reactor.

Boundary
conditions of
Danckwerts

SAERQ NOVA SST 21_22
a) The molar balance to the PBR with
axial dispersion and the kinetic law
are given at the exercise.
Kinetic law:

Condensed equation:

Dimensionless variables:

SAERQ NOVA SST 21_22
Condensed equation in terms of the Peclet
number Pe and spatial time .

SAERQ NOVA SST 21_22
b)
At the entry of the reactor:

λ=0

λ=0

SAERQ NOVA SST 21_22
SAERQ NOVA SST 21_22
c)

917
????????1 = ????????1 × ???? = ????1 × 0 = × 4.1 = 62.7 ????????3
60

8077
????????2 = ????????2 × ???? = ????2 × 0 = × 4.1 = 551.9 ????????3
60

SAERQ NOVA SST 21_22
62.7 35.2

551.9 309.6

SAERQ NOVA SST 21_22
EXERCISE
The reaction ???? ↔ ???? takes place in a 250 mL batch reactor, with 1 g
of a solid catalyst of spherical pellets. Figure shows the
concentration profiles at the beginning, middle and end of the
reaction, assuming the pseudo-homogeneous mechanism.
a) Make the deduction of the condensated molar balance
equation to the catalyst pellet and find the Thiele Modulus
expression.
b) Make the deduction of the Effectiveness factor expression in
terms of the conversion in the reactor.
c) Calculate the equilibrium constant value for the reaction.
d) Calculate the values of the observed kinetic constants for the 3
curves.
e) What is the reaction time needed for the conversion of 99% of
Xe.

Data: Intrinsic kinetic constant: k’=0.015 Lg-1mim-1; Pellets’
diameter: 1mm; Catalyst density: 0.32 g/cm3; De: 1x10-8 dm2/min.
a)

Kinetic law in any
point of the pellet.

Molar balance to
the spherical
pellet

Condensated equation:

???????? 2 = ???? 2 ????λ2

with
In terms of the conversion in the reactor
b)
Effectiveness
factor
Observed velocity

Applying the 1st Fick Law
Intrinsic velocity: =1, because the velocity is already in terms of the

Thiele Modulus
SAERQ NOVA SST_21_22
From the plot:
Tangents of the
curves for =1

SAERQ NOVA SST_21_22
c)
When the equilibrium is attained in the rA’=0
pellet:

For X=0:

SAERQ NOVA SST_21_22
d)

We calculate the effectiveness factor for the 3 curves.
k’ is the intrinsic kinetic constant.

X
k’obs
with:
X=0
X=0.495Xe
X=0.99Xe

SAERQ NOVA SST_21_22
Kinetic law
d)

Molar balance
• Molar balance to the batch
reactor
• In the reactor is always the
Condensated equation rAobs’

SAERQ NOVA SST_21_22
We already have the k’obs values for the conversions of the integration limits X=0 e
X=0.896 and for the intermedium value X=0.448, so we can use the SIMPSON RULE.
????
????/2
න ???? ???? ???????? = [???? 0 + 4 × ???? ????/2 + ???? ???? ]
3
0

SAERQ NOVA SST_21_22
k’obs

Simpson rule

SAERQ NOVA SST_21_22
Exercise #3_ Ergun Equation
The elementary reaction A↔ B in gaseous state is conducted in a packed bed reactor, at isothermal conditions, at strong
intraparticular diffusional limitations, loaded with cylindric pellets of a porous catalyst (10mm length and 3mm base
diameter). A is fed pure at a pressure of 10 atm and at a temperature of 573K, with a volumetric flow of 100 dm3/min.
Calculate:
a) The maximum length of the reactor, in which it is still possible to run.
b) The conversion that it is possible to obtain with a reactor with the same cross section but with length that corresponds
to 2% of the one calculated in a)
c) The pressure at the exit of the reactor at the conditions of b)

Data: De=1.02x10-6 m2/min; k’=0.17 dm3min-1g-1; =2.8 x 10-5 Pa.s; 0=3.2 kg/m3; C=1.3 g/cm3; bulk porosity: εb=0.40;
Reactor cross section diameter: D=20 cm.
Ergun Equation:
a)

Mass flow of A:

Mass velocity:

Effective cross section area- effectively where the flow passes.
Don´t forget that we are considering intense intraparticular diffusion limitations
We have to calculate the equivalent diameter of the pellet Dp:
Diameter of a spherical pellet with the same volume of the cylindric pellet

Volume of the cylindric pellet= Volume of a sphere

If the pellet is spherical just use its diameter
Calculate the Ergun equation parameter  0 and replace in  parameter:
Pressure drop variation (charge loss- Perda de carga)
ε=yA0 δ yA0=PA0/PT=1

ε==-1+1=0 Stoichiometry!
It is not porosity!!
It has analytical solution for =0
and isothermal conditions T=T0.
Integration between the entry of the
reactor and a point of coordinate z
(corresponds to a catalyst weight W)

????
????=
????????
At the entry of the
reactor P=P0, y=1

0≤y<1, P0>P
y=0 maximum pressure
drop conditons Bulk density= mass of catalyst
per volume of the reactor bed. b-bulk density (Wcat/VR)
????
????2 − 1
???? b=c(1-b)=catalyst density x c-catalyst density
න ???????????? = න ???????? = ???? catalyst fraction (Wcat/Vcat)
2 0
The maximum length of the reactor is when y=0 which corresponds to the total loss of
charge (pressure drop) in the column:
Molar balance to the reactor
b)

Kinetic law
The kinetic law will be given at the test.
obs For a tubular reactor, gaseous reaaction
???? (1−????) ???? ????
???????? = ????01+???????? ???? ????0
0

Pressure drop- Ergun equation

Condensing the three equations (3 in 1):
obs

obs

obs

(1 − ????)
obs

obs
The expression of  is Volume of the cylinder
given
× 0.01

2 x base area+ lateral area(2R x l)
Effectiveness factor

obs

For strong intraparticular
diffusion limitations
For 2% of the length from a)
c)
Exercise #4 Fluidization

A vertical tube with a cross section diameter of 120 cm equipped with a porous plaque at the
bottom, will be used for the fluidization of solid catalyst pellets (0.01 mm diameter). In rest, the
bulk presents a porosity of 6% and a height of 130 cm.
a) Calculate the catalyst weight.
b) What is the minimum volumetric flow of the feed, that ensures the fluidization of the bulk.
c) Calculate the bulk height at the conditions of minimum fluidization.

Data: =0.00011 poise; s=1.7 g/cm3; g=0.00107 g/cm3; =1
a) Volume fraction Bulk at rest conditions
of the catalyst

Volume
occupied by
the catalyst
b)
Porosity ...

### Archive contentsContenu de l'archive

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697.24 Ko KB Reatores_quimicos/01-10.tns
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167.56 Ko KB Reatores_quimicos/31-33.tns
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