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