B2 group 1..Acetone Production.pdf

1.0 INTRODUCTION Acetone (dimethyl ketone, 2-propane, CH3COCH3), formulation weight 58,079 is the simplest and the most important and the simplest of the ketone groups. It is a colourless, mobile, flammable liquid and highly aromatic odour. (1) It is also a key intermediate in the manufacture of some polymers.

Figure 1. Structure of acetone Acetone is important in the manufacture of artificial fibers, explosives, and polycarbonate resins. Because of its importance as a solvent and as a starting material for so many chemical processes, acetone is produced in great quantities. Today, acetone is available at low cost and high purity to laboratories, so it is rarely synthesized outside of industry. (2) There is about 7% increment in the requirement of the acetone worldwide. With this increasing demand the requirement of the acetone in some upcoming years is; Table 1. Project demand of years (3) YEAR 2010 2011 2012 2013 2014 2015 2016 2017

PROJECT DEMAND (MILLION TONNES) 6.7 7.2 7.9 8.4 9.0 9.63 10.3 11.02

Moreover, acetone is used in several areas. About a third of the world's acetone is used as a solvent, and a quarter is consumed as acetone cyanohydrin, a precursor to methyl methacrylate. (4)  Solvent Acetone is a good solvent for many plastics and some synthetic fibers. Acetone is used as a solvent by the pharmaceutical industry and as a denaturant in denatured alcohol. Although

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itself flammable, acetone is used extensively as a solvent for the safe transportation and storage of acetylene, which cannot be safely pressurized as a pure compound.  Chemical intermediate Acetone is used to synthesize methyl methacrylate.  Laboratory Acetone is used as a polar, aprotic solvent in a variety of organic reactions, such as SN2 reactions.  Medical and cosmetic uses Acetone is commonly used in chemical peeling. Furthermore, acetone is produced a lot of ways. These are: 1. The Cumene Hydro peroxide Process for Phenol and Acetone 2. Isopropyl Alcohol (IPA) Dehydrogenation 3. Direct Oxidation of Hydrocarbons to a Number of Oxygenated Products Including Acetone 4. Catalytic Oxidation of Isopropyl Alcohol 5. Acetone as a By-Product of the Propylene Oxide Process Used by Oxirane 6. The p-Cymene Hydro peroxide Process for p Cresol and Acetone 7. The Diisopropylbenzene Process for Hydroquinone (or Resorcinol) and Acetone Acetone production from cumene and IPA are the most common manufacturing ways. In this design project, Isopropyl Alcohol Dehydrogenation method is selected.

Isopropyl Alcohol

Acetone

Hydrogen

In this process, an aqueous solution of pure isopropyl alcohol is fed to the reactor, where the stream is vaporized and reacted over a solid catalyst. The reactions occurring within the reactor are as follows: (1) → Isopropyl alcohol

(main reaction) Acetone

Hydrogen

(side reaction) Isopropyl alcohol

Di-isopropyl ether

Water

(side reaction) Isopropyl alcohol

Propylene

Water

2

Isothermal operation will be carried out at 235°C and the reaction occurs in the gase phase with a pressure of 2.2 bar in a Packed Bed Reactor (PBR). Reaction is endothermic, and the reactor is heated by molten salt. The catalyst used is ZnO/ZrO and the reaction is first order with respect to the concentration of isopropanol in this project. Advantages of Isopropyl Alcohol Dehydrogenation      

Acetone is the primary product Purity is high Aqueous solution of the isopropyl alcohol can be used Conversion to acetone is high Not a dangerous compound present along with acetone Less separation process required and production cost is low (3)

Disadvantages of Isopropyl Alcohol Dehydrogenation    

The flammability of IPA presents safety issues. A poor cleaner for removing non-polar oil and grease. IPA is hygroscopic means that substances have the ability to absorb moisture (water) from the air. IPA has its tendency to absorb atmospheric moisture which dilutes the cleaning power of the solvent and can lead to corrosion. (3)

Table 2. Properties of raw materials and product (3) Properties Water Acetone

Isopropyl alcohol

Hydrogen

Molecular Weight (kg/kmol) Freezing Point (°C)

18

58

60

2

0

-95

-88.5

- 259.2

Boling Point (°C)

100

56.2

82.2

-252.8

Critical Temperature (°C) Critical Pressure (bar) Critical Volume (m3/min) Liquid Density (kg/m3) Heat of Vaporization (J/mol) Standard Enthalpy of Formation at 298K (kJ/kmol)

647.3

508.1

508.3

33.2

220.5 0.056

47 0.209

47.6 0.220

13 0.065

998 40683

790 29140

786 39858

71 904

-242.0

20.43

-272.60

0

Properties of raw materials and product are shown in Table 2.

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Packed Bed Reactor is used for production of acetone. PBRs are tubular reactors filled with catalyst particles. PBR design equation is following:

∫ Where; Entering molar flow of species A Weight of catalyst Conversion of key reactant, A Rate of disappearance of species A per mass of catalyst

Table 3. Advantages and Disadvantages of PBR Advantages High conversion per unit mass of catalyst Continuous operation Low operating cost

Disadvantages Poor temperature control Undesired thermal gradients may exist Unit may be difficult to service and clean Channeling may occur

Sustainability Sustainability in acetone is about delivering energy in a responsible way to meet the world’s growing needs. Three basic cases are significant for acetone:

 Running a safe, efficient, responsible and profitable process  Supplying wider benefits  Helping to shape a more sustainable energy future Safety  Flammability The most hazardous property of acetone is its unusual flammability. 

Acetone peroxide

When oxidized, acetone forms acetone peroxide as a byproduct, which is a highly unstable, primary high explosive compound. (5) 

Health information

Acetone is generally recognized to have low acute and chronic toxicity if ingested and/or inhaled. 

Toxicology

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Health Effect of Acetone Acetone has been studied extensively and is generally accepted to have low acute and chronic toxicity if ingested and/or inhaled. Acetone is not currently regarded as a carcinogen, a mutagenic chemical or a concern for chronic neurotoxicity effects. 

Absorption/Metabolism

Acetone is quickly absorbed by ingestion, inhalation, and dermal exposure. In two experiments with humans, inhalation absorption was in the 70 to 80 percent range. 

Short-Term (acute)

Mild nervous system effects such as eye and respiratory irritation, mood swings, and nausea that abated soon after exposure ended were seen in humans breathing high concentrations of acetone. Accidental poisonings report similar nervous system effects of sluggishness and drowsiness that were not long lasting. (6) 

Carcinogenic (cancer producing)

The one study conducted to investigate potential carcinogenic effects from workers exposed by inhalation to acetone did not find any excess cancer incidence.

Waste Disposal In this project, water is thrown away.The temperature of water is very high, cooler can be used to cooling water. In recent years, many legal restrictions have been placed on the methods for disposing of waste materials from the process industries. The site selected for a plant should have adequate capacity and facilities for correct waste disposal. Even though a given area has minimal restrictions on pollution, it should not be assumed that this condition will continue to exist. In choosing a plant site, the permissible tolerance levels for various methods of waste disposal should be considered carefully, and attention should be given to potential requirements for additional waste-treatment facilities. (3)

Ethics The process has low toxicity to environment and human health. Occurred waste can be recovered and removed.

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Figure 2. Flowchart of acetone process with PBR

In Figure 2., the reaction occurring in the reactor is in vapour phase. Therefore, the IPA should be first vaporized and then passed from the reactor. The process is continuous. Since the dehydrogenation of the IPA is the endothermic reaction, so heat has to be supplied to the reactor. For heating purpose the molten salt can be used. (7) The process starts with feed drum. Feed drum is a kind of tank used for the mixing of the recycle stream and feed stream. In the vaporizer molten salt is used for heating. However, the temperature leaving the vaporizer is not enough for the reaction to carry out. Therefore, heater is used in this step to reach maintained temperature for reactor. In reactor works isothermally so it needs heat. Then, leaving stream is gone out to cooler. In there, temperature is decreasing 100°C approximately. Acetone distillation column is reached by following other equipments in the flowchart. The acetone column is used to separate the acetone from the mixture. Top product of the unit includes acetone (99wt% of acetone which is desired). The capacity of acetone production is 15000 tons/year. In conclusion, Packed Bed Reactor is given in this project. The reactor works isothermally in an endothermic reaction. Operating conditions of reactor is that 235°C as temperature and 2.2 bar as pressure. In addition, although, cooler works isobarically, pressure is 1.5 bar in here. In acetone distillation column, entrance of temperature is 45°C. In approximate 100°C, acetone, that its purity is 99%, is obtained as top product. (8)

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2.0 RESULT Table 4.Optimum Conversions and Reactor Length for Each Tasks Task Number 2 3 4

Optimum Conversion 0.7998362 0.7998276 0.7993745

Reactor Length(m) 3.18 3.05 2.06

1 0.9 0.8 Conversion

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0

1

2

3

4

5

6

7

8

9

10

Length,m

Figure 3.Relation between conversion and length in task two

1 0.9 0.8 Conversion

0.7 0.6 0.5 0.4 0.3

0.2 0.1 0 0

1

2

3

4

5

6

7

8

9

10

Length,m

Figure 4.Relation between conversion and length in task three

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1 0.9 0.8 Conversion

0.7 0.6 0.5 0.4

0.3 0.2 0.1 0

0

1

2

3

4

5

6

7

8

9

10

Lenght,m

Figure 5.Relation between conversion and length in task four

Table 5.Optimum Conversions and Reactor Volume for Each Tasks Task Number 2 3 4

Reactor Volume(m3) 1.208 1.159 0.7828

Optimum Conversion 0.7998362 0.7998276 0.7993745

1 0.9 0.8 Conversion

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0

0.5

1

1.5

2

2.5

3

3.5

4

Volume of Reactor,(m3)

Figure 6.Relation between conversion and reactor volume in task two

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Conversion

1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0

0.5

1

1.5

2

2.5

3

3.5

4

Reactor volume (m3)

Conversion

Figure 7.Relation between conversion and reactor volume in task three

1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0

0.5

1

1.5

2

2.5

3

3.5

4

Reactor Volume (m3)

Figure 8.Relation between conversion and reactor volume in task four

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Conversion

1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 2.20E+05

2.20E+05

2.20E+05

2.20E+05

2.20E+05

2.20E+05

2.20E+05

Pressure(Pa)

Figure 9.Relation between conversion and pressure in task two

1 0.9

0.8 Conversion

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 2.20E+05

2.20E+05

2.20E+05

2.20E+05

2.20E+05

Pressure (Pa)

Figure 10.Relation between conversion and pressure in task three

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3.0 DISCUSSION In this project a reactor designed for production of acetone using catalytic dehydrogenation of isopropyl alcohol. Isothermal operation will be carried out at 235°C and the reaction occurs in the gase phase with a initial pressure of 2.2 bar in a Packed Bed Reactor (PBR). Pure IPA is fed to the reactor. Reaction is endothermic, and the reactor is heated by molten salt. Acetone is produced by the gas phase reaction dehydrogenation of isopropyl alcohol in the presence of ZnO/ZrO (6% - 12% ZrO) as catalyst. The reaction represents as:

isopropyl alcohol

acetone

hydrogen

Five tasks are completed for a given feed conditions. In Task 1, equilibrium conversion is determined. In Task 2, the reactor volume of the single PBR is optimized. In Task 3, the optimum volume of the reactor is determined by using the Ergun equation. In Task 4, carbon foot print is calculated and evaluated. Finally, in Task 5, all results and comparisons are discussed. Firstly, the change in the Gibbs Free Energy is calculated at 25 °C and then equilibrium constant is found according to Gibbs Free Energy formula at 25 °C. Later, equilibrium constant (Kc) is evaluated by Van’t Hoff Equations at 427 °C. The reaction took place at 427 °C because at standard temperature, the reaction can not be observed. Initial concentration of isopropyl alcohol is found from ideal gas equation. Depending on this, concentrations of acetone and hydrogen are written. Equilibrium conversion is taken according to concentration and equilibrium constant calculations. The most important point in Task 1 is, although the reaction is irreversible, this is considered as reversible. This system is accepted reversible to find the equilibrium conversion. Secondly, eighty percent of the equilibrium conversion (Xeq) is considered optimum conversion (Xopt), because the optimum conversion does not exceed eighty percent of the equilibrium conversion at operating conditions. Model equations developed to describe changes in total pressure and conversion through the reactor length. Polymath program is used to solve the developed equations. Design equation and reaction rate equation are written for Task 2. For the reaction rate equation, the equilibrium constant is calculated according to the Arrhenius equation. The ratio of the final pressure to the initial pressure is accepted as 0.95. Differential equations are solved and then the length is read from the graph. At the end of the Task 2, the optimum volume of the reactor is decided. The pressure drop in packed column is calculated using the Ergun equation in Task 3. Given porosity (0.52) and catalyst density (2500 kg/m3) values are used in Ergun equation. Initial and final length of the reactor and initial conversion values are constituted in the program. Conversion versus length graph is generated. The point corresponding to the optimum conversion is considered as the reactor length. At normal condition; the pressure drop should be less than 5% , therefore, some parameters are changed to provide this situation. This parameters are temperature, diameters of reactor and particular. Diameter of particular range is given between 1 and 10 mm and maximum value of pressure drop is preferred for the project. Temperature is decided 350 °C as a result of the literature searches and diameter of reactor given 70 cm.(8) The reactor volume is calculated according to the new length value. If the pressure drop is 11

written with the Ergun equation, the length is reduced. However, the volume also decreases. Accordingly, length in Task 3 is smaller than length in Task 2. In Task 4, in series configuration, total volume of single reactor is equal to summation of volume of sub-reactors. In parallel configuration, inital feed is divided into number of tubes and total volume does not change. There is no difference in total reactor volume between series or parallel operations. Moreover, it is often economically beneficial to operate several PBRs in series or in parallel. If the production capacity is high, it is better to use parallel PBRs. Hence, parallel PBRs are used in the system. Number of tubes is changed to reach the appropriate reactor length. Trial-error done to find a low reactor length because as the reactor size increases, the cost will increase. As a result of this, number of tubes and reactor length are determined respectively 35 and 2.06 m. While diameter of tubes (dt) using, volume of tubes is calculated. For multi-tube packed bed reactor, a shorter length is required. Therefore; the temperature is reduced from 427 °C to 347 °C and given reactor diameter increased from 50 cm to 70 cm. The most important use of acetone is in cosmetics sector, medicine, food, environment etc. As a result of these techniques, acetone is very consumed chemical in the world and it is seen that it increased by 4.8% in 2014. (7) A packed bed reactor is designed for acetone production. As a results, when pressure drop and conversion are considered, length of reactor is available realistically. In conclusion, this process is found to be feasible.

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4.0 NOMENCLATURE Fa : flow rate

[kmol/s]

dt: diameter of tube

[m]

dp : diameter of particle

[m]

dR: diameter of reactor

[m]

Kc : rate constant K1: rate constant K2: rate constant : molecular Weight

[kmol/kg]

Po : initial Pressure

[Pa]

Pi: Partial Pressure

[Pa]

To : initial Temperature

[ oC]

L: lenght of reactor

[m]

Xeq : equilibrium conversion ρ : density

[kg/m3]

ρc : catalyst density

[kg/m3]

µ : viscosity

[kg/ m.s]

Ø : porosity Xopt : Optimum conversion

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5.0 REFERENCES 1. https://tr.scribd.com/doc/30429522/Acetone-Production-Process-From-Iso-propyl-AlcoholIPA. https://tr.scribd.com. [Online] 2. http://science.jrank.org/pages/24/Acetone.html. http://science.jrank.org. [Online] 3. http://www.academia.edu/24843591/Acetone_Reactor_Design_Complete_Project. http://www.academia.edu. [Online] 4. https://en.wikipedia.org/wiki/Acetone#Uses. https://en.wikipedia.org. [Online] 5. https://en.wikipedia.org/wiki/Acetone#Safety. https://en.wikipedia.org. [Online] 6. Acetone: Health Information Summary . 2013. 7. Büşra GüdülL, Merve Karabacak, Barış Avcı. ASETON ÜRETİM PROSESİ. Sivas : s.n., 2015. 8. https://tr.scribd.com/document/87981824/Acetone-Production-Report. https://tr.scribd.com. [Online] 9. http://wiredchemist.com/chemistry/data/entropies-organic. [Online] 10. http://chem.libretexts.org. [Online] 11.Aspen plus interface 2006.5

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6.0 APPENDIX Data Given: Isothermal Packed Bed Reactor

Data Aceton Capacity T P Φ Dr ρc dp Table 6.Given Data in Project



Value 15000 tons/year 235 °C 2.2 bar 0.52 50 cm 2500 kg/m3 10 mm

Capacity of Acetone =9.96*10-3 kmol/s

FB=15000

Task 1: Determination of Equilibrium Conversion (Kc) (CH3)2CHOH(g) ⇆ (CH3)2CO(g)+H2(g) A

⇆

B

C

∆G=-R*T*lnk ∆G=∆Gproduct-=∆Greactant (∆G)A=-173.6 kJ/mol (∆G)B=-153.1 kJ/mol

∆G=(-153.1)-(-173.6)=20.5 kJ/mol ∆G=20500J/mol

(∆G)C=0 kJ/mol (at 25°C) (9)

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∆G=20500

=-(8.314

lnk=-8.274

)*(25+273 K)*(lnk)

k=2.55*10-4 at 25°C equilibrium constant (The Van't Hoff Equation)(10)

T2=700 K

T1=298 K

R=8.314 J/molK (∆H)A=-272.6 kJ/mol (∆H)B=-217.6 kJ/mol (9) (∆H)=55000 J/mol =

k2=Kc=87.74 equilibrium constant at 700 K

Task 2:Optimization of Reactor Volume of Single Packed Bed Reactor CA0= P0=2.2 bar T0=700 K R=0.082 dm3*atm/mol*K =0.039 mol/dm3=0.039 kmol/m3

Kc=

87.74= Xeq=0.9997952 Xop=0.8*Xeq=0.8*0.99839=0.7998362

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Packed Bed Reactor Design Equation: W=FA0*∫ FA0*

=-rA’

-rA=k1*CA0* [

]

=1.39

=0.52 Ac=pi*Dr2/4=pi*0.72/4=0.38 m2 k1=1.39 FA0=FB/x CA0=0.039 kmol/m3

From graph L=3.18 is obtained. Vreactor=Ac,reactor*L=1.208 m3

Check

=

(

Pressure Drop=

) =-0.0011767 0.05 √

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TASK 3: Repeat Task 2 in the absance of Pressure drop (CH3)2CHOH(g)  (CH3)2CO(g)+H2(g) A

=

(



B

C

)

G=FA0*x*Mw/Ac =0.732/0.38=1.88 kgm2/s Ac=pi*Dr2/4=pi*0.72/4=0.38 m2 at 700 K (11) at 700 K (11) dp=0.01 m =0.52 L is read as 3.05 from graph. Vreactor=Ac,reactor*L=1.159 m3 Pressure Drop=

=-0.0011767 0.05 √

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TASK 4: Multitube Packed Bed Reactor FAi

FA0

35 TUBES . . .

T =620 K FAi=FA0/35 flow rate in each tubes FB= 0.00996 kmol/s aceton capacity FA0=FB/Xopt FAi=(0.00996/0.79)/35=3.602*10-4 kmol/s dt=2 inch=0.0508 m Total cross sectional area of tubes=Ac,t=n*pi*dt2/4=0.071 m2 L is read as 2.06 meter from graph. Vtubes=Ac,tubes*L=0.146 m3 Vreactor=Ac,reactor*L=0.7828 m3

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TASK 1 and TASK 2 # ACETONE PRODUCTION FROM ISOPROPANOL DEHYDRATION # TASK 1, TASK2 K1 = 0.000255 # at 25 C T = 700 # K KC = K1 * exp(55000 / 8.314 * (1 / 298 - 1 / T)) # equilibrium cnst at T #from van hoff equation k1 = 351000 * exp(-72380 / (8.314 * T)) Ca0 = (2.2/1.013) / (0.082 / 1000 * T) / 1000 # kmol/m^3gas conv = (KC/(KC + 0.95 * Ca0)) ^ (1 / 2) # equilibrium conversion conV = 0.8 * conv # optimum conversion FB = 0.00996 # aceton capacity (kmol/s) FA0 = (FB/conV) # IPA flow Fb = 0.5787 # aceton flow (kg/s) Fac = Fb / conV Ac = ((3.14) * (Dr) ^ 2) / 4 # m^2 Dr = 0.7 # m d(X)/d(L) = (1 - fi) * Ac * (k1 / FA0) * (Ca0 * (1 - X) / (1 + X)) * (0.95) fi = 0.52 # CHECK PRESSURE DROP WITH HELP OF ERGUN EQUATION G = Fac / Ac # kg/m^2*s d(P)/d(L) = -(G / (rho * dp) * (1 - fi / fi ^ 3) * ((150 * (1 - fi) * nu) / dp) + 1.75 * G) # Ergun equation rho = 2.271655 # kg/m^3 nu = 0.00001815 # Pa*s dp = 0.01 # particle diameter (m) P(0) = 220000 # Pa P0 = 220000 # Pa L(0) = 0 L(f) = 10 X(0) = 0 Pdrop = (P0 - P) / P0 # must be less than 0.05 Vr = 3.14 * (Dr ^ 2) / 4 * L # m^3 optimum volume

TASK 3 # MONDAY B2 GROUP 1 # ACETONE PRODUCTION FROM ISOPROPANOL DEHYDRATION # TASK 3 K1 = 0.000255 # at 25 C T = 700 # K KC = K1 * exp(55000 / 8.314 * (1 / 298 - 1 / T)) # equilibrium cnst at T k1 = 351000 * exp(-72380 / (8.314 * T)) Ca0 = (2.2/1.013) / (0.082 / 1000 * T) / 1000 # kmol/m^3gas conv = (KC/(KC + (P / P0) * Ca0)) ^ (1 / 2) # equilibrium conversion conV = 0.8 * conv # optimum conversion FB = 0.00996 # aceton capacity (kmol/s) FA0 = (FB/conV) # IPA flow Fb = 0.5787 # aceton flow (kg/s) Fac = Fb / conV Ac = ((3.14) * (Dr) ^ 2) / 4 # m^2 Dr = 0.7 # m G = Fac / Ac # kg/m^2*s d(P)/d(L) = -(G / (rho * dp) * (1 - fi / fi ^ 3) * ((150 * (1 - fi) * nu) / dp) + 1.75 * G)

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d(X)/d(L) = (1 - fi) * Ac * (k1 / FA0) * (Ca0 * (1 - X) / (1 + X)) * (P / P0) rho = 2.271655 # kg/m^3 nu = 0.00001815 # Pa*s dp = 0.01 # particle diameter (m) fi = 0.52 P(0) = 220000 # Pa P0 = 220000 # Pa L(0) = 0 L(f) = 10 X(0) = 0 Pdrop = (P0 - P) / P0 # must be less than 0.05 Vr = 3.14 * (Dr ^ 2) / 4 * L # m^3 optimum volume

TASK 4 # MONDAY B2 GROUP 1 # ACETONE PRODUCTION FROM ISOPROPANOL DEHYDRATION # TASK4:MULTITUBE PACKED BED REACTOR

K1 = 0.000255 # at 25 C T = 620 # K KC = K1 * exp(55000 / 8.314 * (1 / 298 - 1 / T)) # equilibrium cnst at T,Van Hoff Equation k1 = 351000 * exp(-72380 / (8.314 * T)) Ca0 = (2.2/1.013) / (0.082 / 1000 * T) / 1000 # kmol/m^3gas conv = (KC/(KC + 0.95 * Ca0)) ^ (1 / 2) # equilibrium conversion conV = 0.8 * conv # optimum conversion FB = 0.00996 # aceton capacity (kmol/s) FAi = (FB/conV) / n # IPA flow for each tube n = 35 # tube number Fb = 0.5787 # aceton flow (kg/s) Ac = n * (3.14 * (dt ^ 2) / 4) # tube cross sectional area m^2 Acr = (3.14 * (Dr ^ 2) / 4) # reactor cross sectional area m^2 dt = 0.0508 # m Dr = 0.7 # m G = Fac / Ac # kg/m^2*s Fac = Fb / conV d(P)/d(L) = -(G / (rho * dp) * (1 - fi / fi ^ 3) * ((150 * (1 - fi) * nu) / dp) + 1.75 * G) # Ergun equation d(X)/d(L) = (1 - fi) * Ac * (k1 / FAi) * (Ca0 * (1 - X) / (1 + X)) * (P / P0) rho = 2.564772 # kg/m^3 nu = 0.000016204 # Pa*s dp = 0.01 # particle diameter (m) fi = 0.52 P(0) = 220000 # Pa P0 = 220000 # Pa L(0) = 0 L(f) = 10 X(0) = 0 Pdrop = (P0 - P) / P0 # must be less than 0.05 Vt = n * (3.14 * (dt ^ 2) / 4 * L) # tube volume Vr = 3.14 * (Dr ^ 2) / 4 * L # reactor volume

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