Mechanical design for height of a formaldehyde fixed bed reactor

Height of Fixed Bed Reactor for Formaldehyde Production

The production of formaldehyde through the oxidation of methanol is a crucial process in the chemical industry. A fixed bed reactor filled with a silver catalyst is commonly used for this process. To ensure safe and efficient operation, a mechanical design is required for the construction of the reactor.

Process Design Parameters

The following process design parameters have been developed by process design engineers:

- Catalyst: Silver

- Reactor length: 5 m

- Reactor diameter: 2.4 m

- Catalyst form: Crystalline granular form

- Tube height: 4 m

- Inlet stream temperature and pressure: 149.6 °C and 28.0 psi

- Outlet stream temperature and pressure: 343 °C and 25.0 psi

- Material of construction: Carbon steel

Mechanical Design Considerations

The mechanical design of the reactor must take into account various safety parameters, structural supports, and other considerations, including:

- Corrosion allowance: The shell thickness will be increased to provide a corrosion allowance.

- Pressure shocks: The head section will be designed to withstand pressure fluctuations.

- Structural supports: The reactor will be designed with adequate structural supports to ensure stability and safety.

- Manhole provisions: The reactor will be equipped with manhole provisions for easy access and maintenance.

- Flange fittings: The reactor will be designed with flange fittings to facilitate connections to other equipment.

Mechanical Design Calculations

The mechanical design solver will calculate the following:

- Height of the reactor

- Head thickness

- Shell thickness

- Crown radius and knuckle radius for the ellipsoidal head

The mechanical design of the fixed bed reactor for formaldehyde production is a critical step in ensuring safe and efficient operation. By considering various safety parameters, structural supports, and other considerations, the reactor can be designed to meet the required process conditions and ensure reliable operation.

 

Mechanical design of fixed bed reactor model

 

Inner Diameter of the reactor Di = 2.4 m

Radius of the reactor r = 1.2m

Minimum thickness of reactor t = PDi

                                                     2fj – P

Where P is the design pressure = 3.5* 10⁵ N/m²

           f is the design stress       = 95*10⁶ N/m²

           Thickness of the reactor =    3.5*10⁵*2.4             

                                                        2*0.85*95*10⁶ – (3.5*10⁵)       

                                                = 5mm

  Assume Corrosion allowance as t = 3mm

     T = 5mm+ 3mm

         = 8mm

Outer Diameter of the reactor Do = Di + 2T

                                                      = 2400mm + 2*8

                                                      =2416mm

                                                 Do = 2.416m

Crown Radius Ro = 0.82Do

                              = 1.98m

Knuckle Radius r_o = 0.148Do

                              = 0.357m

Outside height of the ellipsoidal head:

     ho = Ro - [ (Ro-0.5D_o)(Ro+0.5D_o-2r_o)]

            =   1.98-[(1.98-(0.5*2.416))(1.98+(0.5*2.416)-(2*0.357)]

         =0.19m

Total height of the reactor H = h + 2ho

Where h = height of the reactor = 5m

                       H = 5 + 2*0.19

                           = 5.5m

Fixed bed reactor model

Formaldehyde Fixed Bed Reactor

A Closer Look at Formaldehyde Fixed-Bed Reactors

CH2O as we know is a vital chemical used in various industries, from plastics and adhesives to textiles and pharmaceuticals. But have you ever wondered how it's produced? In this post, we'll delve into the world of formaldehyde production, focusing on the fixed-bed reactor design.

This process involves the oxidation of methanol to produce CH2O. Here's a simplified overview of it:

1. Methanol Feed: Methanol is fed into the FBR, where it's mixed with air.
2. Catalytic material: The methanol-air mixture passes over catalytic pellets, typically silver or iron oxide.
3. Oxidation Reaction: The metal oxide facilitates the oxidation reaction, converting methanol into HCHO.
4. Formaldehyde Production: The resulting CH2O gas is then collected and processed for use in various applications.

A design specification for a FBR:

General Information

1. Type: Fixed Bed Reactor (FBR)

2. Process: Catalytic oxidation of methanol to formaldehyde

3. Capacity: 10,000 kg/h formaldehyde

FBR Design Parameters

1. Diameter: 2.5 meters

2. Length: 10 meters

3. Bed Height: 5 meters

4. Bed Volume: 25 cubic meters

5. Void Fraction: 0.4

Operating Conditions

1. Temperature: 250-300°C

2. Pressure: 2-3 bar

3. Inlet Gas Flowrate: 50,000 Nm³/h

4. Methanol Concentration: 30% (vol.)

5. Air/Methanol Ratio: 10:1

Metal Oxide Properties

1. Type: Silver or iron oxide

2. Particle Size: 3-5 mm

3. Density: 0.5-0.7 g/cm³

4. Surface Area: 100-200 m²/g

Materials of Construction

1. Shell: Stainless steel (SS 316L)

2. Metal Oxide Support: Ceramic or stainless steel

3. Insulation: Refractory ceramic blanket

Safety Features

1. Pressure Relief Valve: Set at 3.5 bar

2. Temperature Control: Thermocouples and temperature controllers

3. Emergency Shutdown: Automated shutdown system

4. Fire Suppression: Water spray system

Instrumentation and Control

1. Temperature Indicators: Thermocouples and temperature indicators

2. Pressure Indicators: Pressure gauges and transmitters

3. Flow Indicators: Flow meters and indicators

4. Control System: Distributed control system (DCS) with programmable logic controller (PLC)

Maintenance and Inspection

1. Regular Maintenance: Every 6 months

2. Catalytic Substance Replacement: Every 2-3 years

3. Inspection: Every 5 years

Note: These design specifications are hypothetical and may not reflect actual design parameters for a commercial conversion unit.

A calculator for FBR design:

In the conversion unit, silver (Ag) serves as the agent to facilitate the oxidation of methanol (CH3OH) to formaldehyde (HCHO). The reactants, methanol and air, are fed into the reaction vessel, resulting in the production of formaldehyde, water (H2O), oxygen (O2), and nitrogen (N2). 

The reaction kinetics are described by the rate equation

-r_A = k₁p_A/1+k₂p_A

 

where p represents the partial pressure in atm and A refers to methanol. 

This rate expression is a simplification of the complex reaction mechanism, which involves the catalytic oxidation of methanol to form formaldehyde and water through the reaction 

CH3OH + ½ O2 → HCHO + H2O.

Enter Input Parameters

• Methanol feed rate (kmol/h)
• Air feed rate (kmol/h)
• Operation temperature (°C)
• Operation pressure (atm)
• Catalyst activity (k1, h⁻¹)
• Catalyst inhibition constant (k2, atm⁻¹) 

To get results

• Formaldehyde production rate (kmol/h):
• Methanol conversion (%):
• Reaction vessel volume (m³):

Calculate

Methanol feed rate (kmol/h):

Air feed rate (kmol/h):

Reactor temperature (°C):

Reactor pressure (atm):

Catalyst activity (k1, h⁻¹):

Catalyst inhibition constant (k2, atm⁻¹):

Please note that this is a simplified calculator and does not take into account many factors that can affect the actual performance of a reaction chamber.

A mathematical model for the fixed bed reactor:

Assumptions:

• The process equipment is a plug flow reactor (PFR) with a constant cross-sectional area.
• The reaction is a first-order reaction with respect to methanol concentration.
• The reaction is catalyzed by a silver-based agent.
• The substance is uniformly distributed throughout the model.
• The reaction temperature is constant throughout the model.

Model Equations:

• Mass Balance Equation:

∂C_A/∂t + v * ∂C_A/∂z = -r_A

where C_A is the concentration of methanol (A), v is the superficial velocity, z is the axial coordinate, and r_A is the reaction rate.

Reaction Rate Equation:

r_A = k * C_A

where k is the reaction rate constant.

Metal oxide Activity Equation:

k = k_0 * exp(-E_a/RT)

where k_0 is the pre-exponential factor, E_a is the activation energy, R is the gas constant, and T is the reaction temperature.

Boundary Conditions:

C_A(z=0) = C_A0 (inlet concentration)

C_A(z=L) = 0 (outlet concentration)

where L is the length of the FBR.

Dimensionless Variables:

• Damköhler Number (Da):

Da = k * L / v

• Thiele Modulus (φ):

φ = L * sqrt(k/D_A)

where D_A is the diffusivity of methanol.

Model Solution:

The model equations can be solved using numerical methods such as the finite element method or the method of lines.

Here's a sample solution using MATLAB:

% Parameters

k_0 = 1.23e6; % pre-exponential factor

E_a = 50000; % activation energy

R = 8.314; % gas constant

T = 250; % reaction temperature

L = 10; % reactor length

v = 0.1; % superficial velocity

C_A0 = 1; % inlet concentration

% Catalyst activity equation

k = k_0 * exp(-E_a/(R*T));

% Damköhler number

Da = k * L / v;

% Thiele modulus

phi = L * sqrt(k/0.1);

% Model solution

[t, C_A] = ode45(@(t, C_A) -k * C_A, [0 10], C_A0);

% Plot results

plot(t, C_A);

xlabel('Time (s)');
ylabel('Methanol Concentration');

So, let's break down the MATLAB code that solves the mathematical model of the fixed bed reactor! The code starts by defining the parameters of the reaction, such as the pre-exponential factor (k_0), activation energy (E_a), gas constant (R), and reaction temperature (T). It also defines the length of the reaction unit (L), superficial velocity (v), and inlet concentration of methanol (C_A0). Then, it calculates the reaction rate constant (k) using the catalyst activity equation. The Damköhler number (Da) and Thiele modulus (phi) are also calculated to characterize the reaction. Finally, the code uses the ode45 function to solve the differential equation that describes the reaction and plots the methanol concentration as a function of time. This code helps us visualize how the reaction proceeds over time and how the different parameters affect the outcome. Give it a try!

Note that this is a simplified model and does not take into account many factors that can affect the actual conversion unit performance.

Calculating the analytical way to find if catalytic tubes are used: 

For the reaction enabler bulk density  100lb/ft³.

log₁₀k₁ = 11.43-3810/T

log₁₀k₂ = 10.79-7040/T

Where T is reaction temperature 520 K

But we know that,

C_A = P_A/RT , P_A = C_ART

And C_A = C_AO (1-X_A) / (1+ε_AX_A)

Finally, the rate expression is

1/-r_A = [(1+ε_AX_A)/k₁RTC_AO(1-X_A)] + k₂/k₁

Where ε_A is the fractional change in volume

ε_A = (moles of products - moles of reactants)/ moles of reactants

     = ( 2 + 1.88) – (1 + 0.5 + 1.88 ) / (1 + 0.5 + 1.88 )
     = 0.147

C_AO = P_AO / RT= 1 atm/RT
Substituting the values εA and CAo in the final rate expression and plotting the graph between 1/-r_A Vs X_A.

XA	1/-rA
0	81632.7
0.1	92036.3
0.2	105041
0.3	121761
0.4	144054
0.5	175265
0.6	222082
0.7	300109
0.8	456163
0.9	924327

From the graph the area under the curve for X_A = 0.9 = 205000 Kg-sec / K-mole
The design Equation for a fixed-bed vessel is 

W / F_AO = dX_A / -r_A

W / F_AO = 205000 Kg-sec / K-mole

F_AO = molar feed rate of methanol

= 201.80 K-mol/hr

= 0.0506 K-mol/sec

Weight of the Ag₂O =205000 X 0.0506 =11,491.38 Kg

But from the bulk density of silver oxide = 100lb/ft³

= 100 X 0.453 Kg/0.3048m³= 1599 kg/m³

Volume of the Ag₂O bed = Weight of the Ag₂O/ It's Density  

= 11,491.38 Kg/1599 Kg/m³

Ag₂O volume  = 7.186 m3

Assume the Volume of the reaction vessel to be three times the Ag₂O volume since gas flows into it (V_r = 3V_c)

V_r = Volume of the reaction container

V_c =  Ag₂O bed volume

Therefore, Volume of the reaction container = 21m³

As,
Volume of the cylindrical type reactor unit = 21m³

π d²L/4 = 21

Assume the L/D ratio is 2
The diameter of the cylindrical reaction vessel = 2.4m
Its Length  = 5m

Total Heat evolved in the reaction processing unit Q = 896043 Kcal/hr
U = Overall Heat Transfer Coefficient = 900 W/m^{2 o}K

Tln = (149.6-60)-(343-100)/ln{(149.6-60)/(343-100)}= 153.35 ^oC
Heat Transfer Area AH = Q / U X T_ln = 35.33 m²

Number of Tubes present in the reaction chamber N_t = AH /πdl
Assume the diameter of the tube = 0.1m
Assume the length of the tube = 4m
Therefore Number of Tubes N_t = 25