Isothermal Reactor DesignIsothermal Reactor Design

Dicky DermawanDicky Dermawanwww.dickydermawan.net78.net

dickydermawan@gmail.com

ITK-330 Chemical Reaction ITK-330 Chemical Reaction EngineeringEngineering

Algorithm for Isothermal Reactor DesignAlgorithm for Isothermal Reactor Design

Example of Application:Example of Application:First-order Gas Phase Reaction in PFRFirst-order Gas Phase Reaction in PFR

An Example: Effect of Reactor An Example: Effect of Reactor TypeType

The elementary gas phase reaction The elementary gas phase reaction 2 A + B 2 A + B C C

with rate constant k=10 Lwith rate constant k=10 L22/mol/mol22.s.stakes place in a CSTR at constant temperature (500 takes place in a CSTR at constant temperature (500

K) and constant pressure (16.4 atm). The feed is K) and constant pressure (16.4 atm). The feed is equal molar in A and B. The feed volumetric equal molar in A and B. The feed volumetric flow rate flow rate vvoo=25 L/s=25 L/s. In order to achieve 90% . In order to achieve 90% conversion:conversion:

a.a. Estimate the CSTR volumeEstimate the CSTR volumeb.b. What is the reactor volume if PFR is used?What is the reactor volume if PFR is used?c.c. How long would it take if the reaction is carried How long would it take if the reaction is carried

out in a constant volume batch reactor?out in a constant volume batch reactor?

P4-P4-55AA

P4-P4-77AA

General Guidelines for California Problems

In the past there have typically been six problems in a three hour segment of the California Professional Engineers Exam. Consequently one should be able to work each problem in 30 minutes or less. Many of these problems involve an intermediate calculation to determine the final answer.

1. Group unknown parameters/values on the same side of the equation example: [unknowns] = [knowns]

2. Look for a Case 1 and a Case 2 (usually two data points) to make intermediate calculations

3. Take ratios of Case 1 and Case 2 to cancel as many unknowns as possible

4. Carry all symbols to the end of the manipulation before evaluating, UNLESS THEY ARE ZERO

P4-11P4-11BB

P4-12P4-12B B Changing Feed RatioChanging Feed Ratio

P4-13P4-13B B Arranging Additional Arranging Additional ReactorReactor

L5-13: Scale Up L5-13: Scale Up ProblemProblem

(a)(a) The homogeneous gas reaction A The homogeneous gas reaction A 3 R follows 3 R follows second-order kinetics. For a feed rate of 4 msecond-order kinetics. For a feed rate of 4 m33/hr of /hr of pure A at 5 atm and 350pure A at 5 atm and 350ooC, an experimental C, an experimental reactor consisting of a 2.5 cm ID pipe 2 m long reactor consisting of a 2.5 cm ID pipe 2 m long gives 60% conversion of feed. A commercial plant gives 60% conversion of feed. A commercial plant is to treat 320 mis to treat 320 m33/hr of feed consisting of 50% A, /hr of feed consisting of 50% A, 50% inerts at 25 atm and 35050% inerts at 25 atm and 350ooC to obtain 80% C to obtain 80% conversion.conversion.How many 2-m lengths of 2.5 cm ID pipe are How many 2-m lengths of 2.5 cm ID pipe are required?required?Should they be placed in parallel or in series?Should they be placed in parallel or in series?Assume plug glow in the pipe, negligible pressure Assume plug glow in the pipe, negligible pressure drop, and ideal gas behaviordrop, and ideal gas behavior

L5-18: Scale Up & Laboratory L5-18: Scale Up & Laboratory ExperimentExperiment

Time, min 0 1 2 3 4 5 6 7V/V0 1 1.2 1.35 1.48 1.58 1.66 1.72 1.78

The homogeneous gas reaction A The homogeneous gas reaction A 2B is run at 100 2B is run at 100ooC at C at a constant pressure of 1 atm in an experimental a constant pressure of 1 atm in an experimental batch reactor. The data in below were obtained batch reactor. The data in below were obtained starting with pure A. starting with pure A.

What size plug flow reactor operated at 100What size plug flow reactor operated at 100ooC and 10 C and 10 atm would yield 90% conversion of A for a total atm would yield 90% conversion of A for a total feed rate of 10 mol/sec, the feed containing 40% feed rate of 10 mol/sec, the feed containing 40% inert?inert?

Time, min 8 9 10 11 12 13 14V/V0 1.82 1.86 1.88 1.91 1.92 1.94 1.95

P4-14P4-14C C Similarity: Adaptation, Scale Up Similarity: Adaptation, Scale Up etc.etc.

P4-15P4-15A A Similarity: Adaptation, Scale Similarity: Adaptation, Scale Up etc.Up etc.

P4-16P4-16B: B: Reactor NonidealityReactor Nonideality

Pressure DropPressure Dropin Packed Bed Reactorsin Packed Bed Reactors

Ergun:

X1F

F

0T

T

0T

T

0

00 F

F

T

T

P

P

T

0T0

0000 F

F

T

T

P

P

Catalyst weight:

Isothermal Fixed (i.e. Packed) Bed Isothermal Fixed (i.e. Packed) Bed Reactors DesignReactors Design

T

T

P

P

X1

X1CC 0

00AA

Performance equation:

Kinetics:

Stoichiometry:

Pressure drop:

T

1

T

1

R

Eexpkk

1

a1 Ar k AC

for small P: P/P0 = 1)X1(

P/P

P

T

T

2dW

dP

0

0

0

)X1(CC 0AA Gas liquid

0A

A

F

r

dW

dX

Combine:

)P,X(g)P,X(gdW

dP

)P,X(f )r(fdW

dXA

Thus…The combination results

in 2 simultaneous differential equations

Example for First Order Reaction

Introduction to Simultaneous Introduction to Simultaneous Ordinary Differential Equation Ordinary Differential Equation

SolverSolver

Polymat 5.0

P4-P4-1818BB

Example: PBR DesignExample: PBR Design

Reforming reactors are used to increase the octane Reforming reactors are used to increase the octane number of petroleum. In a reforming process 20.000 number of petroleum. In a reforming process 20.000 barrels of petroleum are to be processed per day. The barrels of petroleum are to be processed per day. The corresponding mass and molar feed rates are 44 kg/s corresponding mass and molar feed rates are 44 kg/s and 440 mol/s, respectively. In the reformer, and 440 mol/s, respectively. In the reformer, dehydrogenation reactions such as:dehydrogenation reactions such as:

Paraffin Paraffin Olefin + H Olefin + H22

occur. The reaction is first-order in paraffin with k’ = occur. The reaction is first-order in paraffin with k’ = 0.02 L/kg0.02 L/kgcatcat

..s. Assume that pure paraffin enters the s. Assume that pure paraffin enters the reactor at a pressure of 2000 kPa and the reactor at a pressure of 2000 kPa and the corresponding concentration of 0.32 mol/L. This corresponding concentration of 0.32 mol/L. This reaction is carried out in a tubular packed bed 2.4 m reaction is carried out in a tubular packed bed 2.4 m in diameter and 25 m in length containing 173870 kg in diameter and 25 m in length containing 173870 kg catalystcatalyst

PPBBRR DDeessiiggnn

The hydrodemethylation of toluene is to be carried out in a The hydrodemethylation of toluene is to be carried out in a packed bed reactor. Plot the conversion, pressure ratio packed bed reactor. Plot the conversion, pressure ratio

P/PP/P00, and the partial pressures of toluene, hydrogen, and , and the partial pressures of toluene, hydrogen, and

benzene as a function of catalyst weight. The molar feed benzene as a function of catalyst weight. The molar feed rate of toluene to the reactor is 50 mol/min and the reactor rate of toluene to the reactor is 50 mol/min and the reactor is operated at 40 atm and 640is operated at 40 atm and 640ooC. The feed consist of 30% C. The feed consist of 30% toluene, 45% hydrogen, and 25% inerts. Hydrogen is used toluene, 45% hydrogen, and 25% inerts. Hydrogen is used

in excess to help prevent coking. The pressure drop in excess to help prevent coking. The pressure drop parameter is 9.8parameter is 9.8xx1010-5-5 kg kg-1-1. Also determine the catalyst . Also determine the catalyst

weight in a CSTR with a bulk density of 400 kg/mweight in a CSTR with a bulk density of 400 kg/m33

atm/038.1Katm/39.1K

minkgatm

mol00087.0'k

PKPK1

PP'k'r

CHHCHCHHC

356

66

3563566666

3562356

CHHC

HCcat

2

CHHCCHHCHCHC

CHHCHCHHC

4662356

P4-19P4-19BB

ExercisesExercises

1. The first-order homogeneous gaseous decomposition A 2.5 R is carried out in an isothermal batch reactor at 2 atm with 20% inerts present, and the volume increases by 60% in 20 min. In a constant- volume reactor, find the time required to reach 8 atm if the initial pressure is 5 atm, 2 atm of which consist of inerts.

ExercisesExercises2. Kinetika reaksi dekomposisi zat A pada fasa larutan dipelajari

menggunakan indikator warna yang berubah saat konsentrasi A turun hingga kurang dari 0,1 mol/L. Umpan yang mengandung 0,6 mol A perliter dialirkan ke dalam tangki pertama dari dua reaktor tangki berpengaduk yang disusun secara seri, masing-masing bervolume 400 cm3. Perubahan warna terjadi dalam reaktor pertama pada keadaan tunak saat laju alirnya 10 cm3/menit. Perubahan yang sama baru terjadi di reaktor kedua pada keadaan tunak saat laju alir mencapai 50 cm3/menit. Larutan yang mengandung 0,8 mol A perliter direaksikan dalam susunan reaktor di atas. Berapa laju alir umpan agar dicapai konversi 95%?

ExercisesExercises

Design in Term of other than ConversionDesign in Term of other than Conversion

Vrdt

dNA

A

A

A0ACSTR r

FFV

AA r

dV

dF

In some instance it is more convenient to work in term ofNA, NB,… (batch) or FA, FB,… (continue) rather than conversion.

A0A rdV

dXF A

0ACSTR r

XFV

Vrdt

dXN A0A

Use Rather than

0T

T

F

FX1

0T

T

N

N or

or or

for each species involved

only for A

AB ra

br Ac r

a

cr

AD ra

dr

T

T

P

P

X1

XjCC 0

0

j0Aj

Θ

T

T

P

P

F

FCC 0

0T

j0Tj

1ab

ac

ad

Working in Terms of Molar Flow Working in Terms of Molar Flow Rates in a PFRRates in a PFR

The gas phase reaction:The gas phase reaction:A A 2 B 2 B

is carried out isothermally at 500 K & 10 atm without pressure is carried out isothermally at 500 K & 10 atm without pressure drop in a PFR and follows an elementary rate law.drop in a PFR and follows an elementary rate law.

Determine:Determine:a.a. Equilibrium conversionEquilibrium conversionb.b. The molar flow rates along the length of a 100 L reactor.The molar flow rates along the length of a 100 L reactor.c.c. Reactor volume required to achieve 95% of equilibrium Reactor volume required to achieve 95% of equilibrium

conversionconversion

Additional information:Additional information:kkAA = 2.7 min = 2.7 min-1-1

KKCC = 1.2 mol/L = 1.2 mol/LFFA0A0 = 10 mol/min = 10 mol/min

Illustration of Application:Illustration of Application:Semibatch ReactorsSemibatch Reactors

Vr00dt

dNA

A

VrFdt

dNA0B

B

Vrdt

dNA

C

Vrdt

dNA

D

Mole balances & stoichiometry:

Mass balances: 0dt

dV

C

DCBAA K

CCCCkrKinetics:

Illustration of Application:Illustration of Application:Semibatch ReactorsSemibatch Reactors

P4-26B

Illustration of Application:Illustration of Application:Unsteady State Operations -Unsteady State Operations -Semibatch ReactorsSemibatch Reactors

P4-27B

Illustration of Application:Illustration of Application:Membrane ReactorsMembrane Reactors

Mole balances & stoichiometry:

Mass transfer:

AA r

dV

dF

BB r

dV

dF

CCC Rr

dV

dF

CcCC CkR

C B A

HHCHC 266126

CBA rrr

Illustration of Application:Illustration of Application:Membrane ReactorsMembrane Reactors

P4-30B

Illustration of Application:Illustration of Application:Membrane ReactorsMembrane Reactors

P4-31C