Drexel University Chemical and Biological Engineering Department

Philadelphia, PA, December 4th 2014.

Bianca Silva Cordeiro

Chemical Kinetics and Reactor Design CHE 424

Prof. Dr. Jason Baxter

1. Introduction

A packed bed reactor needs to produce between 100 and 150 MM gallons/year of Cyclohexane with 99.9% weight total of purity. The heterogeneous gas phase hydrogenation of Benzene using a Ni/SiO2 catalyst produces Cyclohexane. The aromatic feed consists of 250 MM gallons/year of 99% weight total of Benzene. However, in a Benzene feed there is presence of Toluene, which represents 1% weight total of the feed in. Due to this presence, Methylcyclohexane is also produced. Therefore, two reactions take place independently, they are:

Figure 1 Hydrogenation of Benzene (1) and Toluene (2)

The present project was designed with the goal of an annual cyclohexane production rate between 100 and 150 MM gallons/year, and knowing that, Hydrogen is available with 85%mol purity with impurities of Propane, Methane and Nitrogen using one packed bed reactor.

The algebra showed that a feed of 250 MM gallons/year of Benzene + Toluene was too much, because only a small part of it reacted. For this reason, it was decided to use a feed of 200 MM gallons/year.

The approach used to find the desired production rate of cyclohexane was by using Excel spreadsheets. As it was required, the RK4 method was used to determine the mass necessary of catalyst for the process.

2. Methods

The rate equation in which these two reactions are based on have a similar form and can be expressed as a turnover frequency (TOF) [1]:

Where TOF is the number of molecules of the aromatic hydrocarbon reactant reacted per Ni catalyst site per second, k0 is the pre-exponential factor, Eapp is the apparent activation energy, and Pmaromatic and Pnhydrogen are the partial pressures (in atm) of the aromatic hydrocarbon reactant and hydrogen, respectively. The m and n exponents are the apparent individual orders of reaction and are temperature dependent (T in K) as given by:

Depending on the temperature range, the rate coefficient parameters k0 and Eapp vary because of a shift in kinetic behavior:

First, as the information gives only weight total percentage, it is necessary that this percentage to be converted to molar fraction, since the feed is a gas phase:

Using a mass basis of 100g, convert 99% and 0.01% weight total into molar %. 0.99 100 = 99 0.01 100 = 1

Divide the mass found before by the molecular weight to find the number of moles it represents:

99

78.11/= 1.26744349

1

92.14/= 0.01085305

Divide the number of moles of each specie for the sum of them to find a molar %:

1.2674439

1.278296399= 0.991509755

0.01085305

1.278296399= 0.008490245

Multiply the molar % by the volume total of the Feed in:

0.991509755 200

= 198.301951

0.008490245 200

= 2.122561269

It is important that we have the knowledge of the feed in molar flux instead of volumetric, because only with these values the stoichiometric table can be constructed.

Convert the Feed from MM Gallon/year to mole/year multiplying this value by the density of the species and dividing by its molecular weight:

198.301951

78.11

3317.939206

=

8423426165

2122561269

92.14

3281.59897

=

75595776.81

Knowing this, the molar flow rate of Hydrogen can be estimated. The stoichiometry of the hydrogenation of benzene reaction (Figure 1) shows that it is needed at least three times of Hydrogen more in the feed for the reaction to occur. Also, the second reaction consumes the Hydrogen too. For this reason, a feed of four times the feed of Benzene plus four times the feed of Toluene was chosen as the feed of Hydrogen

= 4 8423426165

+ 4

75595776.81

=33996087768

The feed of Hydrogen found above corresponds to 85% Hydrogen, 10% Methane, 4.5% Propane and 0.5% Nitrogen. So the pure Hydrogen fed can be found by:

(85%) =33996087768

0.85 =

28896.6746

= 33996087768

0.1 =

3399608777

= 33996087768

0.045 =

1529823950

=33996087768

0.05 =

169678055.7

Which gives a total feed:

=42419513933

The chosen conversion for Benzene was of 0.5. The excess of Hydrogen in the feed will consume almost all the Toluene and convert it into Methylcyclohexane. Knowing this, it is possible to build a stoichiometric table (Table 1), that follows:

Table 1 Stoichiometric Table

Stoichiometric Table

Species Feed in(mol/year) Feed out(mol/year)

Benzene 8423426165 FB0 -0.5*FB0 = 5054055699

Hydrogen (85% pure) 28845269475 18555728212 = FH0-3*1 -*2

Cyclohexane 0 1 = FC = FB0 FB =

3369370466

Toluene 60476621.45 FT0 - 2 = 0.00000001

Methylcyclohexane 0 2 = 60476621.45

Methane 3393561115 3393561115

Propane 1527102502 1527102502

Nitrogen 169678055.7 169678055.7

Total 42419513933 32129972671 = Fs0 - 3*1 -

3*2

Where i is the extent of reaction for each reaction.

The next step is to use the TOF equation to find out in what temperature should the reactor be running. However, to find the TOF it is needed the partial pressures of the species. Considering that the mixture of gas phase is an ideal mixture, because it is formed by ideal gases, the partial pressure can be calculated by the simply product between the molar fraction (molar feed out of each species divided by the total molar feed out) and the total pressure of the reactor:

=

1

Where i is the correspondent to certain species.

Which results in the Table 2 that follows:

Table 2 Partial Pressures

Pressure ( atm)

P reactor 1

Pbenzene 0.157300342

Phydrogen 0.577520822

Pcyclohexane 0.104866895

Ptoluene 3.11236E-19

Pmethylcyclohexane 0.001882249

Pmethane 0.105619795

Ppropane 0.047528908

Pnitrogen 0.00528099

To calculate the TOF, a spreadsheet containing all the necessary values for this calculation was generated (Table 3 and Table 4):

Table 3 TOF for the temperature range of 393K 463K

Aromatic Reactant

T range (K) k0

(s^-1 * atm^(m+n)) Eapp

(kJ/mol) m N

TOF (s^-1)

Benzene

393 2.52288E+11 49.2 -0.018829517 0.603816794 54139.93

403 2.52288E+11 49.2 0.036228288 0.765012407 65032.21

413 2.52288E+11 49.2 0.088619855 0.918401937 77425.5

423 2.52288E+11 49.2 0.138534279 1.064539007 91423.48

433 2.52288E+11 49.2 0.186143187 1.203926097 107126.7

443 2.52288E+11 49.2 0.231602709 1.337020316 124632.1

453 2.52288E+11 49.2 0.275055188 1.464238411 144032.3

463 2.52288E+11 49.2 0.31663067 1.585961123 165415.4

Toluene

393 9.4608E+12 63.6 -0.018829517 0.603816794 53319.96

403 9.4608E+12 63.6 0.036228288 0.765012407 7573.055

413 9.4608E+12 63.6 0.088619855 0.918401937 1182.223

423 9.4608E+12 63.6 0.138534279 1.064539007 201.4945

433 9.4608E+12 63.6 0.186143187 1.203926097 37.26669

443 9.4608E+12 63.6 0.231602709 1.337020316 7.438208

453 9.4608E+12 63.6 0.275055188 1.464238411 1.594096

463 9.4608E+12 63.6 0.31663067 1.585961123 0.365138

Table 4 TOF for the temperature range of 473K 523K

Aromatic Reactant

T range (K) k0

(s^-1* atm^(m+n)) Eapp (kJ/mol) m N

TOF (s^-1)

Benzene 473 0.000003 -35.9 0.356448 1.702537 0.005617

483 0.000003 -35.9 0.394617 1.814286 0.004075

493 0.000003 -35.9 0.431237 1.921501 0.002995

503 0.000003 -35.9 0.466402 2.024453 0.002228

513 0.000003 -35.9 0.500195 2.123392 0.001677

523 0.000003 -35.9 0.532696 2.218547 0.001276

Toluene

473 0.00000007 -48.6 0.356448 1.702537 1.62E-09

483 0.00000007 -48.6 0.394617 1.814286 2.32E-10

493 0.00000007 -48.6 0.431237 1.921501 3.59E-11

503 0.00000007 -48.6 0.466402 2.024453 6E-12

513 0.00000007 -48.6 0.500195 2.123392 1.07E-12

523 0.00000007 -48.6 0.532696 2.218547 2.05E-13

Since the goal is to produce a higher amount of Cyclohexane, it is better to use a temperature in which the TOF is higher for Cyclohexane and smaller for Methylcyclohexane. The temperature chosen was 463K.

In order to find the ideal mass of catalyst needed for the process, a mass balance on Benzene (b) and Toluene (t) was made:

Benzene:

+ = . 0 ( + ) + = 0

=

=

Where:

rb = TOF Avogadros number(A) density of catalyst()

So,

= exp

Where b is the indices for Benzene, so the partial pressure of Benzene, that is:

=( )

Where Fs is the flow out, so:

=( )

3 3

h is the indices for Hydrogen, so the partial pressure of Hydrogen:

= 3 3 )

3 3

Which leads to the following differential equation:

= exp

( )

3 3

3 3 )

3 3

Toluene: + = .

( + ) + = 0 =

=

The same calculations were made for Toluene and the following differential equation was found:

= exp

( )

3 3

3 3 )

3 3

Since the unities of ri are in seconds, it is important that we convert our feed values from moles/year to moles/second, which was made in the following step.

The method RK4 was used to solve the differential equations found. This method consists of adding a certain amount of weight of catalyst in each step until the condition of the desired values for 1 and 2 be found. The following table (Table 4) shows the RK4 method used for this project, adjusted to do not accept negative pressures for the Toluene, knowing that it will be consumed completely before the amount expected of cyclohexane be achieved:

Table 5 RK4 Method

W (g)

45 Fb0 (mol/s) 267.1051

k benz (kJ/mol)

8000 R 0.008314

N 50 Ft0 (mol/s) 914.6775

k tol (kJ/mol)

300000

W

500000

P0 (atm) 1 T 463 m 0.316631

Fs0 1345.114

E bez 49.2 n 1.585961

Fh0 1.917701

E tol 63.6 p* A 0.000183

n W_n E11 E21 f1*W p toluen g1*W E1_2 E2_2 f2*W p toluen g2*W E1_3

0 0 0 0 0.668255

0.001425679

0.12459879

0.334128

0.062299

0.667736

0.001380585

0.123255739

0.333868

1 500000

0.667737

0.12326

0.667218

0.001336401

0.12191249

1.001346

0.184217

0.6667

0.001292143

0.120539762

1.001087

2 1000000

1.334437

0.244236

0.666181

0.001248502

0.11915696

1.667527

0.303814

0.665663

0.001205113

0.117752123

1.667268

3 1500000

2.0001

0.362437

0.665145

0.001162357

0.11633628

2.332672

0.420605

0.664627

0.001119865

0.114896697

2.332413

4 2000 000

2.664727

0.477796

0.664109

0.001078026

0.11344508

2.996781

0.534518

0.663591

0.001036465

0.111967746

2.996522

3. Results and Discussions

The calculations found on the Methods section lead to the following results.

With the use of one packed bed reactor at constant temperature of 463K and constant pressure of 1 atm, the annual production rate of Cyclohexane found was 120.2016815 MM gallons/year, which is reasonable since it is in the desired range of production rate for this product. Since the conversion that was chosen is very low, it means that a small reactor is needed for this process. However, the desired purity can only be acquired within the use of a big separator. If the conversion selected was higher, a smaller separator could be used to achieve the desired purity.

The steps showed in Table 5 were repeated until the condition desired was reached, and the mass of catalyst necessary for this process was found to be equal to 100,000 kg Ni/SiO2.

The Figure 2 and Figure 3 show the profiles of extent of reaction for each one of the reactions, Hydrogenation of Benzene and Hydrogenation of Toluene respectively.

Figure 2 Extent of reaction profile for Benzene hydrogenation inside the reactor

Figure 2 shows the expected profile for the extent of reaction inside the reactor, since as the reaction proceeds more catalyst is consumed in a linear profile that ends when the steps taken from the RK4 method end. The extent of reaction for the Benzene hydrogenation (1) is stoichiometric the same value as the flow out of Cyclohexane. Figure 2 shows also for which weight of catalyst the extent of reaction reaches the value desired (3369370466 moles/year = 133.55 moles/sec)

0

20

40

60

80

100

120

140

160

0 50000000 100000000 150000000

1(m

ol/

s)

Weight of Catalyst (g)

Figure 3 Extent of reaction profile for the Toluene Hydrogenation inside the reactor

Figure 3 shows the expected extent of reaction profile for the Toluene hydrogenation. The Toluene is fed in a small quantity and at the same time, the Hydrogen is fed in a high amount, when both are compared to each other. Because of this the Toluene is consumed and Methylcyclohexane is formed before the reaction ends and it reaches a constant value. This behavior is shown in Figure 3, since the Methylcyclohexane is stoichiometric equal to the extent of this reaction.

The following Figures show the partial pressure profile of each species inside each reactor.

0

0.5

1

1.5

2

2.5

0 50000000 100000000 150000000

2 (m

ol/

s)

Mass of Catalyst(g)

Figure 4 Benzene pressure profile inside the reactor

Figure 4 shows the expected profile for the Benzene partial pressure inside the reactor. Because the gases in this mixture are assumed to be ideal gases the partial pressure of benzene is directly proportional to its molar fraction. Since benzene is consumed during the reaction, its molar fraction becomes lower as the reaction proceeds and the mass of catalyst increase until it reaches the maximum conversion for cyclohexane. The same happens with its partial pressure.

Figure 5 Hydrogen pressure profile inside the reactor

0

0.05

0.1

0.15

0.2

0.25

0 50000000 100000000 150000000

Ben

zen

e P

ress

ure

(atm

)

Mass of Catalyst (g)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 50000000 100000000 150000000

Hyd

roge

n P

ress

ure

(at

m)

Mass of Catalyst (g)

Figure 5 shows the expected profile for the Hydrogen partial pressure inside the reactor. As like as Benzene, the assumption of ideal gas was made. Since Hydrogen is consumed during the reaction, its molar fraction becomes lower as the reaction proceeds and the mass of catalyst increase until it reacts entirely with Benzene and Toluene.

Figure 6 Cyclohexane pressure profile inside the reactor

Figure 6 shows the expected profile for the Cyclohexane partial pressure inside the reactor. Cyclohexane is the product of the reaction and since the feed in has no Cyclohexane its pressure starts with zero and as the reaction proceeds and the mass of catalyst increases it goes up. When the desired conversion is reached, no more Cyclohexane is formed and its pressure becomes to be a constant value.

Figure 7 Toluene Partial Pressure inside the reactor

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0 50000000 100000000 150000000

Cyc

loh

exan

e P

ress

ure

(at

m)

Mass of Catalyst (g)

0

0.0002

0.0004

0.0006

0.0008

0.001

0.0012

0.0014

0.0016

0 50000000 100000000 150000000

Tolu

ene

Pre

ssu

re (

atm

)

Weight of catalyst (g)

Figure 7 shows the expected profile for the Toluene partial pressure inside the reactor. Toluene is fed in a small amount when compared to the other reactants on the fed. The excess of Hydrogen in the feed makes it possible for almost the entire Toluene to be converted into Methylcyclohexane. Because of this, there is a point in the reaction in which there is no more Toluene, and its partial pressure reaches the constant value of zero.

Figure 8 Methylcyclohexane Partial Pressure in the reactor

Figure 8 shows the expected profile for the Methylcyclohexane partial pressure inside the reactor. Methylcyclohexane is a product of the reaction and is quickly formed since the amount of Hydrogen is sufficiently high to produce it this fast. The more catalyst used during the reaction the more Methylcyclohexane is formed.

Figure 9 Inert Partial Pressure inside the Reactor

0

0.0005

0.001

0.0015

0.002

0.0025

0 50000000 100000000 150000000

Met

hyl

cycl

oh

exan

e P

ress

ure

(at

m)

Weight of Catalyst (g)

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

0 50000000 100000000 150000000

Iner

t P

ress

ure

Weight of catalyst (g)

Figure 9 shows the expected profile for the Methylcyclohexane partial pressure inside the reactor. As the reactions proceeds the amount of Inert gas does not vary much because it is not part of the reaction. It only changes because there is change in the volume, so its molar fraction changes as the volume changes since it is an ideal gas mixture.

The same profiles found for the partial pressures are expected to be found for molar flow rate, since they are all assumed ideal gases. Figure 10 shows all the molar flow rates as functions of weight of catalyst.

Figure 10 Molar flow rate profile for species inside the reactor

4. Conclusions

This project reached its goal by designing a packed bed reactor that runs the Hydrogenation of Benzene and Toluene as independent reactions and produces 3369370466 moles/year of Cyclohexane, which corresponds to 120.2016815 MM gallons/year of Cyclohexane. This flow rate is between the desired ranges for this product under a constant pressure of 1 atm and also, a constant temperature of 463 K.

By designing the reactor, it was possible to conclude that:

For ideal gas phases it is possible to assume that the partial pressure and the molar fraction have the same profile;

The RK4 method is a good method to solve differential equations; Not only a reactor is necessary to achieve certain purity of a desired product. It has

always to have a separator together with it. The higher the conversion achieved by the reactor the smaller this separator has to be.

The impurity of one of the products (Hydrogen) didnt change the reaction itself because they were inert to the reactions, they only required a higher feed for the reaction to happen.

5. References

[1] Keane and Patterson, Ind. Eng. Chem. Res. 1999, 38, 12951305