Contents1.0 Background22.0 Material Balance33.0 Energy Balance54.0 Reactor Sizing Considering the Energy Balance and Main Reaction85.0 Estimation of Diffusion- and Reaction-Limited Regimes19

STAGE 11.0 BackgroundWe are assigned to design a reactor and a separator for the production of isobutylene by performing reaction system analysis and sizing. In this project, we are required to produce as much as 100000 metric tonnes of isobutylene yearly through the process of butane dehydrogenation. Isobutylene (or 2-methylpropene) is a hydrocarbon of industrial significance that is used as an intermediate in the production of a variety of products such as MTBE and ETBE, isooctane from the alkylation process, and also antioxidants. There are several steps or stages that have to be analysed and evaluated thoroughly. This includes performing overall material mass and energy balance for the dehydrogenation process, followed by reactor sizing by taking into consideration the effect of diffusion and also side reactions, and finally, obtaining the weight of catalyst used and other parameters concerned.An overview of the dehydrogenation of isobutene to produce isobutylene; initially, we have decided to select Catofin technology (Domenico Sanfilippo I. M.) which is a technology that use fixed-bed adiabatic reactors. Characteristics of Catofin technology are: Low consumption of isobutane, due to the high selectivity ensured by the Pt catalyst. Heat of reaction supplied by the formation of coke Catalyst endowed to potential poisons such as water vapour and heavy metals, high level of thermal stability, resistance to friction and tolerance.CharacteristicsCatofinOleflexSTARFBD

Type of ReactorFixed-bed adiabaticMobile adiabatic-bedTubular, fixed-bedFluidized-bed

CatalystPlatinumPlatinumPlatinumChromium oxides

PressureLowHighHighLow

TemperatureHighHighHighHigh

Table 1: Comparison of Production TechnologiesThe catalyst chosen is platinum together along with tin as its promoter. The initial temperature of the feed is assumed to be 550oC and the pressure of the inlet is at 1 atm. The same condition is applied to the reactors and the conversion of isobutane is 50% (X=0.5). By performing the necessary mass and energy balance in the first stage, we are able to identify the inlet parameters such as the amount of feed rate flow. Proceeding to the next stage, we have then identified adsorption reaction as the rate limiting step via journal and patent reviews. Before performing the reaction rate law, we have to include the pressure drop that exists in the system and performing the required stoichiometry. Finally, in the third stage, we have to prove that the system is only limited by surface reaction.Hence, whilst carrying out this project, we developed a better insight on the mechanism that occurs in a process such as the internal and external diffusion. We have also learned to apply the fundamentals of CRE knowledge in solving various engineering related problems.

2.0 Material BalanceAssuming an operating hours of 8000 hours for a year as about 760 hours of the rest time is for the plant turnaround works.

Feed:The inert/alkane ratio is increased from 0 to 3 at 550C and 1 atm, the equilibrium conversion increases from 44 % to 64 %. Thus, assume a reaction conversion of 50% and 1 for the steam/isobutane ratio. Also, under typical dehydrogenation conditions (550C, 1 atm) the equilibrium conversion decreases from about 44 % to 25 % when the H2/alkane ratio increases from 0 to 3. Assume the H2/alkane ratio equals to 0.5.

From stoichiometry,

Output:According to the chemical reaction of dehydrogenation of isobutane to isobutylene, 1 mol of isobutane will react to produce 1 mol of isobutylene and 1 mol of hydrogen gas.

iC4H10445.5852 kmol/hr8020.5336 kg/hr12500 kg/hr891.1704 kg/hrSteam222.7926 kmol/hr222.7926 kmol/hr445.5852 kmol/hr12948.7059 kg/hrX=0.5445.5852 kmol/hr25897.4118 kg/hr445.5852 kmol/hr222.7926 kmol/hrSteam8020.5336 kg/hr445.5852 kg/hr

iC4H10

iC4H8

H2

H22

FT = 1336.7556 kmol/hr = 34360.4099 kg/hrFT0 = 1113.9630 kmol/hr = 34363.5306 kg/hr

Figure 1: Material Balance for the Production of 100000 Metric Tonnes Isobutylene

3.0 Energy Balance

The energy required to remove two atoms of hydrogen from alkane molecule is in the range of 113 134 kJ/mol. The highly endothermic nature of the reaction leads to a strong temperature decrease. In the case of the dehydrogenation of propane, there is an adiabatic temperature decrease of 200C. Hence, since dehydrogenation of isobutane requires an energy which is also in the range of 113 134 kJ/mol, the temperature is assumed to be decreased to 350C as outlet temperature of the reactor.IsobutaneH2Steam

IsobutaneH2Steam

IsobutyleneIsobutaneH2Steam

IsobutyleneIsobutaneH2Steam

Figure 2: Calculation Path for Dehydrogenation of Isobutane to Isobutylene

SpeciesA(103)B (105)C (108)D (1012)

Isobutane89.4630.1318.9149.87

Isobutylene82.8825.6417.2750.50

Hydrogen28.840.007650.32880.8698

Steam33.460.68800.76043.593

Table 2: Heat Capacity Constants of Gases in Ideal-Gas State

Reactants:

Isobutane :

Hydrogen :

Steam :

The enthalpy of formation of iC4H10, iC4H8, and H2 areHf iC4H10 = 134.5 kJ/molHfiC4H8 = 16.9 kJ/molHfH2 = 0 kJ/mol

Products:

Isobutane :

Isobutylene :

Hydrogen :

Steam :

STAGE 24.0 Reactor Sizing Considering the Energy Balance and Main ReactionMechanism

Assume Absorption as rate determining step:

Substitute (3) and (4) into (2):

Site balance:

Substitute (5) into (1):

Substitute (6) into (7)

Rate law

(Sanna M. K. Airaksinen, 2002)StoichiometrySpeciesInletChangeOutletConcentration

AIsobutane

EIsobutylene

H2Hydrogen

SSteam-

RearrangingPressure

Table 3: Stoichiometry Table

Design Equation

Combine

(Bruce E. Poling, 2008)

Specifications of the commercial catalyst:

(A. Rosjorde, 2007)

POLYMATH ReportNo Title

Ordinary Differential Equations05-Dec-2013

Calculated values of DEQ variables VariableInitial valueMinimal valueMaximal valueFinal value

1 a 0 0 11.32705 11.32705

2 abc 0.4 0.4 0.4 0.4

3 Ac 0.0019638 0.0019638 0.0019638 0.0019638

4 alpha 0.0143117 0.0143117 0.0143117 0.0143117

5 beta 7708.983 7708.983 7708.983 7708.983

6 Cp_A 0.2062694 0.1791016 0.2062694 0.1791066

7 Cp_E 0.1800602 0.1579131 0.1800602 0.1579172

8 Cp_H2 0.029732 0.0292927 0.029732 0.0292927

9 Cp_S 0.0389464 0.0369578 0.0389464 0.0369581

10 dCp 3.522798 3.522798 8.104152 8.103309

11 delta_E 0 0 0 0

12 delta_H2 0.5 0.5 0.5 0.5

13 delta_S 1. 1. 1. 1.

14 density_b 541.42 541.42 541.42 541.42

15 density_c 984.4 984.4 984.4 984.4

16 density_o 0.6794 0.6794 0.6794 0.6794

17 dH_Rx 1.059E+05 1.059E+05 1.059E+05 1.059E+05

18 Diameter 0.05 0.05 0.05 0.05

19 Dp 0.004572 0.004572 0.004572 0.004572

20 FA0 0.036 0.036 0.036 0.036

21 FE 0 0 0.0109814 0.0109814

22 FT0 0.09 0.09 0.09 0.09

23 G 1.413785 1.413785 1.413785 1.413785

24 gc 1. 1. 1. 1.

25 K 2.1E+12 1.918E+10 2.1E+12 1.92E+10

26 k 5.07E-07 2.228E-09 5.07E-07 2.231E-09

27 KE 7.33E-05 7.33E-05 7.33E-05 7.33E-05

28 KEH2 9.72E-10 9.72E-10 9.72E-10 9.72E-10

29 KH2 3.87E-05 3.87E-05 3.87E-05 3.87E-05

30 L 0 0 72.10088 72.10088

31 MW_A 0.05812 0.05812 0.05812 0.05812

32 MW_H2 0.002 0.002 0.002 0.002

33 MW_S 0.018 0.018 0.018 0.018

34 MWmix 0.030848 0.030848 0.030848 0.030848

35 P0 1.013E+06 1.013E+06 1.013E+06 1.013E+06

36 PA 4.053E+05 0.4205989 4.053E+05 0.4205989

37 PA0 4.053E+05 4.053E+05 4.053E+05 4.053E+05

38 PE 0 0 8.403E+04 0.1846128

39 PH2 2.027E+05 0.4872186 2.553E+05 0.4872186

40 rate 0.0232384 9.382E-10 0.0232384 9.382E-10

41 Sum_delta_Cp 260.0818 230.7057 260.0818 230.7111

42 T 823. 651.4233 823. 651.4514

43 T0 823. 823. 823. 823.

44 Ta 653. 653. 653. 653.

45 U 56.784 56.784 56.784 56.784

46 viscosity_A 1.22E-05 1.22E-05 1.22E-05 1.22E-05

47 viscosity_H2 1.221E-05 1.221E-05 1.221E-05 1.221E-05

48 viscosity_mix 1.84E-05 1.84E-05 1.84E-05 1.84E-05

49 viscosity_S 3.059E-05 3.059E-05 3.059E-05 3.059E-05

50 void 0.45 0.45 0.45 0.45

51 W 0 0 80. 80.

52 X 0 0 0.3050384 0.3050384

53 y 1. 1.675E-06 1. 1.675E-06

54 yA0 0.4 0.4 0.4 0.4

55 yH20 0.2 0.2 0.2 0.2

56 yS0 0.4 0.4 0.4 0.4

Differential equations 1 d(X)/d(W) = rate/FA0

2 d(y)/d(W) = -(alpha/(2*y))*(1+abc*X)*(T/T0)

3 d(T)/d(W) = ((U*a/density_b)*(Ta-T)-rate*dH_Rx)/((FA0)*(Sum_delta_Cp+dCp*X))

Explicit equations 1 T0 = 823

2 K = (2.1e12)*exp((122e3/8.3144)*(1/T0-1/T))

Pa

3 k = (5.07e-7)*exp((141e3/8.3144)*(1/T0-1/T))

mol/(kg.s.Pa)

4 KEH2 = 9.72e-10

Pa^-2

5 KE = 7.33e-5

Pa^-1

6 KH2 = 3.87e-5

Pa^-1

7 delta_S = 1

8 delta_E = 0

9 FA0 = 0.036

Assuming flow rate for one pipe in the reactor

10 P0 = 101325*10

Pa

11 delta_H2 = 0.5

12 FT0 = FA0+FA0*delta_H2+FA0*delta_S

13 yA0 = FA0/FT0

14 abc = yA0*(1+1-1)

15 PA0 = yA0*P0

Pa

16 PA = PA0*(1-X)*y/(1+abc*X)

17 FE = FA0*X

FE=61.8868 mol/s

18 PE = PA0*(delta_E+X)*y/(1+abc*X)

19 yH20 = FA0*delta_H2/FT0

20 yS0 = FA0*delta_S/FT0

21 MW_A = 0.05812

kg/mol

22 Diameter = 0.05

m # For one pipe in the reactor

23 density_c = 984.4

kg/m^3

24 void = 0.45

25 Dp = 0.004572

m

26 PH2 = PA0*(delta_H2+X)*y/(1+abc*X)

27 density_o = 0.6794

kg/m^3

28 rate = k*(PA-(PE*PH2/K))/(1+KEH2*PE*PH2+KE*PE+KH2*PH2)

29 MW_H2 = 0.002

kg/mol

30 viscosity_A = 1.2195e-5

Pa.s

31 viscosity_H2 = 1.2207e-5

Pa.s

32 viscosity_S = 3.0593e-5

Pa.s

33 gc = 1

34 Ac = 3.142*(Diameter^2)/4

35 MW_S = 0.018

kg/mol

36 MWmix = yA0*MW_A+yH20*MW_H2+yS0*MW_S

37 viscosity_mix = (yA0*(viscosity_A)*(MW_A^0.5)+yH20*(viscosity_H2)*(MW_H2^0.5)+yS0*(viscosity_S)*(MW_S^0.5))/(yA0*(MW_A^0.5)+yH20*(MW_H2^0.5)+yS0*(MW_S^0.5))

38 G = FT0*MWmix/Ac

39 beta = (G*(1-void)/(density_o*gc*Dp*void^3))*((150*(1-void)*viscosity_mix)/Dp+1.75*G)

40 alpha = 2*beta/(density_c*(1-void)*Ac*P0)

41 U = 56.784

J/(s.m^2.K)

42 density_b = density_c*(1-void)

43 Ta = 653

K

44 dH_Rx = 105856.1

J/mol

45 Cp_A = (89.46e-3)+(30.13e-5)*(T-273)+(-18.91e-8)*((T-273)^2)+(49.87e-12)*((T-273)^3)

46 Cp_E = (82.88e-3)+(25.64e-5)*(T-273)+(-17.27e-8)*((T-273)^2)+(50.50e-12)*((T-273)^3)

47 Cp_H2 = (28.84e-3)+(0.00765e-5)*(T-273)+(0.3288e-8)*((T-273)^2)+(-0.8698e-12)*((T-273)^3)

48 Cp_S = (33.46e-3)+(0.6880e-5)*(T-273)+(0.7604e-8)*((T-273)^2)+(-3.593e-12)*((T-273)^3)

49 dCp = (Cp_E+Cp_H2-Cp_A)*1000

J/mol.K

50 Sum_delta_Cp = (Cp_A+delta_H2*Cp_H2+delta_S*Cp_S)*1000

J/mol.K

51 L = W/(density_c*(1-void)*Ac)

52 a = 2*3.142*(Diameter/2)*L

From the Polymath results, flow rate of isobutylene, FE for one pipe in the reactor is 0.0109814 mol/s while the isobutylene production from the reactor is 61.8868 mol/s.

Hence, 5636 pipes are required in the fixed bed reactor with a diameter of 3.7537 m.Also, form the polymath graph, the optimum conversion for the reaction is selected at X=0.28.

STAGE 35.0 Estimation of Diffusion- and Reaction-Limited RegimesWeisz-Prater Criterion for Internal Diffusion:

Mears Criterion for External Diffusion:

Hence, the reaction is only affected by surface reaction.6.0 Reference

1. A. Rosjorde, S. K. (2007). Minimizing the entropy production in a chemical process for dehydrogenation of propane. Energy 32, 335343.2. Bruce E. Poling, G. H. (2008). Perry's Chemical Engineers' Handbook 8th Edition. United States of America: McGraw Hill.3. Domenico Sanfilippo, I. M. (n.d.). Dehydrogenation Process. 687-669.4. Sanna M. K. Airaksinen, M. E. (2002). Kinetic Modeling of Dehydrogenation of Isobutane on Chromia. Ind. Eng. Chem. Res. 2002, 41, 5619-5626.5. Sebastian C. Reyes, J. H. (1997). Frequency Modulation Methods for Diffusion and Adsorption Measurements in Porous Solids. J. Phys. Chem B, 614-622.6. Richard M. Felder, W. (2005). Elementary Principles of Chemical Processes 3rd Edition. United States of America: John Wiley & Sons, Inc.7. H. Scott Fogler (2006). Elements of Chemical Reaction Engineering 4th Edition. United United States of America: Pearson Education, Inc.

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