Diammonium phosphate (DAP) fertilizer manufacturing flow diagram

Diammonium Phosphate Fertilizer Manufacturing Process

Diammonium phosphate (DAP) is a widely used granular fertilizer, valued for its high phosphorus and nitrogen nutrient content. The manufacturing process involves a series of chemical reactions, physical transformations, and separations, all carefully controlled to produce a high-quality, consistent product. Let's walk through the main steps depicted in this process flow diagram:

1. Pre-Neutralization Process:

The journey begins in a pre-neutralizer where concentrated phosphoric acid (H3PO4) reacts with ammonia (NH3) in a controlled environment. The reaction is highly exothermic, releasing heat, and produces a partially neutralized slurry of monoammonium phosphate (MAP) and diammonium phosphate (DAP). The stoichiometry and reactor conditions are carefully controlled to obtain an optimum liquid slurry that can be further processed in the granulator.

Preneutralizer Diagram

 

Pre-neutralizer equipment: Typically a stirred tank reactor, is designed for efficient mixing and heat removal. It's constructed of corrosion-resistant materials to withstand the harsh chemical environment. It's also equipped with instrumentation to monitor and control temperature, pH, and flow rates.

Reaction Equation:

• NH₃ + H₃PO₄ → (NH₄)₃PO₄ (DAP)

Neutralization Reaction:

• H₃PO₄ + 2NH₃ → (NH₄)₂HPO₄ (Mono-Ammonium Phosphate, MAP)
• (NH₄)₂HPO₄ + NH₃ → (NH₄)₃PO₄ (DAP)

Model Equation:

The model equation for the pre-neutralizer can be represented by a set of ordinary differential equations (ODEs) that describe the changes in concentration of the reactants and products over time.

Let's assume that the pre-neutralizer is a continuous stirred-tank reactor (CSTR) with a constant volume (V) and a feed flow rate (F). The model equation can be written as:

d[MAP]/dt = (F/V) × (0 - [MAP]) + k₁ × [H₃PO₄] × ([NH₃])² / (1 + K₁ × [MAP]) 

d[DAP]/dt = (F/V) × (0 - [DAP]) + k₂ × [MAP] × [NH₃] / (1 + K₂ × [DAP]) 

d[H₃PO₄]/dt = (F/V) × ([H₃PO₄]_n - [H₃PO₄]) - k₁ × [H₃PO₄] × ([NH₃])² / (1 + K₁ × [MAP])

d[NH₃]/dt = (F/V) × ([NH₃]_n - [NH₃]) - 2 × k₁ × [H₃PO₄] × ([NH₃])² / (1 + K₁ × [MAP]) - k₂ × [MAP] × [NH₃] / (1 + K₂ × [DAP])

where:

• [MAP], [DAP], [H₃PO₄], and [NH₃] are the concentrations of mono-ammonium phosphate, diammonium phosphate, phosphoric acid, and ammonia, respectively.
• k1 and k2 are the reaction rate constants for the neutralization reactions.
• K1 and K2 are equilibrium constants of MAP and DAP
• F is the feed flow rate.
• V is the reactor volume.
• [H₃PO₄]ₙ, and [NH₃]ₙ are the inlet concentrations of the reactants and products.

Assuming the production rate of 800 kg/h of DAP, we need to calculate the reactants' required flow rates and the pre-neutralizer's size.

Molecular Weights:

•  NH₃: 17 kg/kmol
•  H₃PO₄: 98 kg/kmol
•  (NH₄)₂HPO₄ (MAP): 117 kg/kmol
•  (NH₄)₃PO₄ (DAP): 149 kg/kmol

Material Balance Calculations:

Component	Molar Flow Rate (kmol/h)	Calculation Formula
DAP	5.37	F_DAP = 800 kg/h / 149 kg/kmol
MAP	5.37	F_MAP = F_DAP × (1 mol MAP / 1 mol DAP)
NH₃	10.74	F_NH3 = F_MAP + F_DAP
H₃PO₄	5.37	F_H3PO4 = F_MAP × (1 mol H₃PO₄ / 1 mol MAP)

Pre-neutralizer Size Calculation:

Assuming a pre-neutralizer with a volume (V) of 10 m³ and a residence time (τ) of 30 minutes:

Parameter	Value	Calculation Formula
Volumetric Flow Rate of NH₃ (m³/h)	240.3	Q_NH3 = F_NH3 × 22.4 m³/kmol
Volumetric Flow Rate of H₃PO₄ (m³/h)	120.1	Q_H3PO4 = F_H3PO4 × 22.4 m³/kmol
Required Diameter of Pre-neutralizer (m)	1.43	d = √(4 × Q_NH3 / (π × τ))
Required Height of Pre-neutralizer (m)	6.35	h = V / (π × (d/2)²)

Therefore, the required size of the pre-neutralizer is approximately 1.43 m in diameter and 6.35 m in height. Note that this calculation assumes a simplified model and does not take into account other factors that may affect the design of the pre-neutralizer, such as mixing, heat transfer, and mass transfer.

2. Granulation Process:

The partially neutralized slurry from the pre-neutralizer is fed to a granulator, where it's sprayed onto recycled fine particles and partially granulated products. More ammonia is added to this rotating bed, causing further neutralization and the formation of larger, solid granules. The addition of ammonia also helps to control the pH of the slurry, driving the reaction towards forming DAP. Other additives, such as urea and fillers, may be introduced at this stage.

DAP Granulator

Granulator: Typically a rotating drum granulator, is designed to tumble and agitate the materials. It has internal lifters to enhance the mixing and growth of granules.

3. Drying Process:

The wet granules from the granulator are conveyed to a dryer, where excess moisture is removed using hot flue gas from a combustion chamber. This step is crucial for producing stable, free-flowing granules. The temperature and flow rate of the hot flue gas are carefully controlled to prevent scorching or over-drying.

Rotary dryer

Dryer: Typically a rotary drum dryer is designed for maximum heat transfer and material mixing. It is designed with internal flights which help to improve heat transfer and material flow.

Combustion Chamber: This is where fuel and air are mixed and combusted to generate the hot flue gas, which is then sent to the dryer. It typically has temperature controls to ensure that the gas is heated to the required temperature.

4. Screening and Sizing Process:

After drying, the product is sent to vibration screens where granules are sized according to the desired particle size. Under-sized particles (fines) are recycled back to the granulator, and over-sized particles might be sent for crushing (not shown in this particular diagram). The on-size product moves on to product cooling.

Vibration Screens: These screens are used to separate particles based on size. They consist of one or multiple screens placed at angles, with the particles moved using vibrations.

Feeders: Feeders are used to deliver a consistent and controlled stream of materials to subsequent equipment. These can be belt or screw-type feeders.

5. Product Cooling Process:

The dried-sized granules are conveyed to a product cooler where they are cooled with air to the desired temperature before bagging and storage. This cooling is important to improve product stability and prevent agglomeration.

Rotary product cooler

Product Cooler equipment: Typically a rotating drum cooler which is designed for efficient cooling of solids. Air is passed through the cooler for effective heat removal.

6. Fumes and Scrubber Treatment Process:

The process generates fumes containing ammonia, phosphoric acid, and particulate matter. These fumes are scrubbed and cleaned in a multi-stage scrubber system. This is done to meet environmental regulations and to recover valuable materials.

Fumes Scrubbers Equipment: These scrubbers are used to remove pollutants from gaseous streams. They might use water or other solvents to absorb pollutants before releasing the cleaned gas to the environment through a chimney. These scrubbers may contain spray nozzles, packing material and demisters.

Centrifugal Blower: This blower is used to move the gaseous stream.

• Tail gas scrubber: This scrubber is similar to the fume scrubber, and might also be part of the same train or a separate one for further purification of gasses.
• Cooler Scrubber: This cooler scrubber helps in cooling the gas and removing any remaining contaminants.
• Scrubber effluent tank: This is a collection tank for scrubbing liquids for reuse or treatment.

Cyclone Separators: These are used to separate larger particles from gases, based on centrifugal forces.

Additional Equipment:

Preparation Tank: A tank for pre-mixing or dissolving materials.

Pulverizers: Used to reduce the size of solid particles when required.

Conveyors: Different types of conveyors (belts, screws, etc.) are used throughout the process for material transport.

Pumps: Used to transport liquids to different sections of the plant.

Instrumentation: Various sensors and controllers are integrated to monitor and control temperatures, pressures, flow rates, levels, and compositions across the plant, ensuring the process runs effectively and safely.

Process Flow:

The overall process starts with the reaction of phosphoric acid and ammonia in a pre-neutralizer, followed by granulation, drying, sizing, cooling and then packaging. Off-gases are scrubbed and treated for reuse or safe disposal. This flow sheet shows the typical process involved in the production of DAP fertilizer.

Process flow diagram of DAP fertilizer manufacturing

By carefully controlling each stage of the process, a consistent high-quality product is manufactured at a large scale. This detailed process description and equipment list are essential to understanding the engineering and science behind DAP fertilizer production.

CAD Design of Ammonium Sulphate Saturator

CAD DESIGN OF SATURATOR

Working Principle of the Saturator

The saturator plays a crucial role in the production of ammonium sulphate. Here's an overview of its working principle:

Step 1: Pre-Treatment of Coke Oven Gas

Coke oven gas, after primer cooling and purification from tar and naphthalene, is delivered to the pre-heater at a temperature of 50-60°C. The pre-heater ensures the normal water balance in the saturator.

Step 2: Saturation Process

The pre-heated coke oven gas enters the saturator through the main gas inlet and passes through the bubbler hood. The bubbler hood consists of 20 radially positioned elements that facilitate intensive mixing of the mother liquor.

Step 3: Reaction and Crystal Formation

As the coke oven gas bubbles through the mother liquor, it reacts with sulphuric acid to form ammonium bisulphate. This reaction is represented by the equation:

NH3 + H2SO4 → (NH4)2SO4

The ammonium bisulphate is then converted into ammonium sulphate, releasing heat in the process.

Step 4: Circulation and Mixing

To ensure optimal crystal growth and minimize gas/ammonia losses, the mother liquor is continuously mixed and circulated. The circulating pump pumps the mother liquor from the circulating pan to the conical part of the saturator, creating a circular motion.

Step 5: Acid Trap and Gas Flow

The gas from the acid trap is continuously delivered to the circulating pan, preventing the formation of acid-neutral zones in the saturator bath. The gas then flows to the bottom gas main, leading to the F.G.C., benzol section, and eventually to consumers.

Key Features and Benefits

• Automatic maintenance of mother liquor acidity within 4-5% using pH-meter station and control valve
• Continuous feeding of 6-8% acidified mother liquor solution from the liquor tanks
• Optimal crystal growth and minimized gas/ammonia losses due to thorough mixing and circulation
• Efficient heat management and energy recovery

By understanding the working principle of the saturator, operators can optimize its performance, ensuring efficient production of high-quality ammonium sulphate

Reactor for Urea Production and Urea Process Parameters

Imagine a machine so massive it produces 2100 metric tons of urea every single day. That's the scale we're talking about when we delve into the design of a modern urea reactor. Urea, a crucial component of fertilizers, plays a vital role in global agriculture. But its production is a complex feat of engineering. In this post, we'll pull back the curtain on the design of a giant urea reactor, exploring the challenges and triumphs of building such a complex piece of equipment.

Low-Pressure Decomposer

 The Challenge: Meeting Global Demand: The world's growing population relies heavily on fertilizers to boost crop yields. Urea, with its high nitrogen content, is a cornerstone of this effort. Designing a reactor capable of producing such vast quantities of urea is a significant engineering challenge.   After the high-pressure synthesis of urea, the reaction mixture still contains unconverted ammonium carbamate. This isn't ideal because we want to maximize urea yield and recycle the valuable ammonia and carbon dioxide. That's where the low-pressure decomposer (LPD) comes in. Think of it as the cleanup crew, responsible for breaking down the remaining carbamate at a lower pressure.

Decomposing ammonium carbamate at high pressure is energy-intensive. By reducing the pressure, we can make the decomposition process more efficient and recover the valuable ammonia and carbon dioxide for reuse in the synthesis loop. This not only improves overall urea yield but also reduces energy consumption - a win-win!

Diagram of Low Pressure Urea Section

The urea solution from the medium-pressure decomposer enters the LPD. Here, at a lower pressure, the unconverted ammonium carbamate is decomposed into ammonia (NH3) and carbon dioxide (CO2). These gases are then separated from the urea solution and recycled back to the high-pressure synthesis section.

The output from the high-pressure section isn't pure urea just yet. It's a mixture containing urea, unconverted ammonium carbamate, ammonia, and carbon dioxide. This is where the low-pressure urea section steps in – a critical part of the process dedicated to maximizing urea yield and recycling valuable resources.

The Core Function: Decomposition and Recovery

The primary task of the low-pressure section is to decompose the unconverted ammonium carbamate back into ammonia (NH3) and carbon dioxide (CO2). 

 This is crucial for two reasons: 

1) It increases the overall urea yield, making the process more efficient, and 

2) It allows us to recover and reuse the ammonia and carbon dioxide, reducing raw material consumption and minimizing waste.

A complete urea process description with flow sheet

Brief equipment design of a reactor for producing 2100 MTPD of Urea:

  Inside the Beast: Reactor Design:

Let's take a look inside this industrial giant. The heart of the operation is the reactor itself, a pressure vessel operating at high temperatures and pressures. Here's a glimpse at some key design parameters:

Internal trays

Sieve trays :

480 hot trays: equispaced triangular pitch
Number of trays	: 15 equispaced , 666.67 cm diameter

Feed distribution nozzle : 

 

CO₂ inlet 265 holes of 8 mm diameter NH₃ inlet 440 holes of 8 mm diameter Operating/ Design temperature 188/210^oC Operating/ Design pressure 155/170 Kg/cm² g Design pressure 170 Kg/cm² g Joint efficiency = j 0.85 Allowable stress = f 22.5 Kg/cm² g Capacity 2100 MTPD Density of NH₃/CO₂ at 188^oC 881.5387/809.29 Kg/m³

 

Concentration Vs Rate of reaction data for carbon dioxide:

Concentration CA, Kgmole/m3	18.39	16.55	14.71	12.87	11.03	9.19	7.35	5.51
Rate of reaction, -rA Kgmole/hr m3	27.05	21.92	17.31	13.25	9.74	6.76	4.33	2.43

Calculation:

 τ/C_Ao  =  V/f_Ao  =  ΔX_A/ -r_A

From material balance :
f_Ao = 2278.645 Kg mole/hr
C_Ao  = f_Ao /V_o
V_o = (inlet flow of CO₂)/(Density of CO₂) = 100260.42 / 809.29 = 123.886 m³/hr
C_Ao  = 2278.645/123.886 = 18.39 Kg mole/m³

Plotting graph (1/-r_A) Vs C_A :

Concentration CA Kgmole/m3	18.39	16.55	14.71	12.87	11.03	9.19	7.35	5.51
Rate of reaction  -rA Kgmole/hr m3	27.05	21.92	17.31	13.25	9.74	6.76	4.33	2.43
1/-rA	0.037	0.046	0.058	0.075	0.102	0.148	0.231	0.411

From graph :

Area = 137.8×2×0.02 = 5.512 hr
Area = τ = 5.512 hr
Now V = τ× f_Ao/C_Ao
V = (5.512×2278.65)/18.39 = 682.974 m3
Assuming height to be 18 meters
V = pi R²H
R² = (683)/(π×10) = 12.075m²
R = 3.475 m
Diameter = 6.95 m

Relation of reaction rates to concentration of components in urea reactor

Urea Reactor Design Calculator

Tray Diameter (m):

Number of Trays:

CO2 Inlet Holes:

NH3 Inlet Holes:

CO2 Density (kg/m³):

NH3 Density (kg/m³):

Production Rate (MTPD):

Design Pressure (kg/cm²g):

Allowable Stress (kg/cm²g):

Joint Efficiency:

CO2 Concentration (Kgmole/m3)

The Snamprogetti Urea Process Description

The Snamprogetti Urea Process is a highly efficient and innovative method for producing urea, leveraging a total recycle stripping process that utilizes ammonia as a self-stripping agent. Here's how it works: as the urea solution leaves the reactor, excess ammonia is harnessed to strip away carbon dioxide in a specially designed falling film steam heated heat exchanger. This innovative step takes place at the same pressure as the urea reactor, ensuring seamless integration. The separated carbon dioxide and ammonia are then reunited as ammonium carbamate in the carbamate condensers, also operating at the same pressure. Finally, this recycled mixture is returned to the reactor, where it's converted into urea, completing the cycle.

The Snamprogetti stripping process yields a significant advantage by establishing an internal recycle of both ammonia (NH3) and carbon dioxide (CO2) within the urea reactor system, eliminating the need for high-pressure pumping of these components. This contrasts with traditional total recycle processes, where NH3 and CO2 are separated from the solution at lower pressure, necessitating energy-intensive pumping.

The Snamprogetti process reduces high-pressure pumping requirements for both NH3 and ammonium carbamide solution by approximately 80%. This is because about 80% of the CO2 fed to the process is converted to urea within the high-pressure synthesis loop, leaving only around 20% to be pumped back to the reactor as ammonium carbamate solution from a lower pressure.

Furthermore, this process enables substantial steam savings by leveraging the heat released from condensing vapor to operate the ammonium carbamate condenser at a lower temperature level.

Process flow diagram of Urea Production

The Snamprogetti process operates with an NH3 to CO2 ratio of 3.3-3.6:1, which, combined with a temperature range of 186-189°C and a pressure of approximately 155 kg/cm²g, enables a conversion yield of 62-65% in the reactor.

Here is a possible plant layout for the Snamprogetti Urea Process:

1. Urea Reactor: Where ammonia and carbon dioxide react to form urea.
2. Stripper Column: Where excess ammonia strips carbon dioxide from the urea solution.
3. Carbamate Condenser: Where carbon dioxide and ammonia are condensed to form ammonium carbamate.
4. Recycle Loop: Where the ammonium carbamate solution is recycled back to the urea reactor.
5. Urea Solution Tank: Where the urea solution is stored before being sent to the crystallizer.
6. Crystallizer: Where the urea solution is cooled and urea crystals are formed.
7. Centrifuge: Where the urea crystals are separated from the mother liquor.
8. Prilling Tower: Where the urea crystals are converted into prills (small, uniform pellets).

Block diagram of total recycling of ammonia stripping in urea production:

Urea production takes place through the following main operations:

• Urea synthesis and high-pressure recovery.
• Urea purification in the medium, low-pressure decomposers, and pre-vacuum concentrators. Urea concentration.
• Urea Prilling.

 

Ammonia Pumping and Preheating System

The ammonia pumping and preheating system plays a vital role in the urea production process. Liquid ammonia from the battery limit, at a temperature of 12°C and 18 Kg/cm²(g), is collected in an ammonia receiving vessel. This vessel operates at a medium pressure of 17 Kg/cm².

Ammonia Booster Pump

From the ammonia receiver, the liquid ammonia is pumped to the reactor by two pumps. The first pump is the ammonia booster pump, a centrifugal type that supplies the liquid ammonia at 22 Kg/cm² to the suction of the second pump.

High-Pressure Ammonia Pump

The second pump is the high-pressure ammonia pump, a reciprocating plunger type. This pump increases the ammonia pressure to 239 Kg/cm². However, due to the reciprocating motion of the second pump, pulsations occur in the discharge of the booster pump. To mitigate these pulsations, a damper is provided in the suction of the second pump.

Ammonia Preheating

After the high-pressure ammonia pump, the ammonia flows to an ammonia preheater. In this preheater, the ammonia is preheated to 75°C using low-pressure decomposer outlet gases.

Carbon Dioxide Compression System

The carbon dioxide compression system is another critical component of the urea production process. Carbon dioxide gas enters the first stage of suction at 1.5 kg/cm² and 40°C. The gas is then compressed to 160 Kg/cm² in four stages.

Intercoolers and Knock-Out Drums

Intercoolers are provided after the first, second, and third stages to cool the carbon dioxide using cooling water. Along with these coolers, knock-out drums are provided between each stage. In these drums, moisture gets separated from the compressed carbon dioxide.

Lube Oil System

A lube oil system provides lubrication to the rotating parts of the carbon dioxide compression system. This ensures smooth operation and minimizes wear and tear on the equipment.

Steam Turbine and Condenser

The steam turbine is driven by superheated steam and saturated low-pressure (LP) steam. Superheated high-pressure (HP) steam is extracted, and part of the steam is condensed in a condenser. The condensate is then pumped to the demineralization (DM) plant for further treatment.

Urea Prilling Tower Calculator

Tower Height (m):

Tower Radius (m):

Prill Size (mm):

Production Rate (tons/hour):

Flow sheet of
Urea prilling system

Block diagram of
urea prilling section

 Block diagram of the total recycling of carbon dioxide stripping in urea production

UREA SYNTHESIS: A complete urea process description with a flow sheet

Material balance and energy balance for a urea reactor producing 1000 kg/hr of urea:

Material Balance

Inputs

- Ammonia (NH3): 620 kg/hr (assuming 3:1 ammonia-to-carbon dioxide ratio)

- Carbon dioxide (CO2): 207 kg/hr

- Inerts (e.g., water, nitrogen): 10 kg/hr

Outputs

- Urea (CO(NH2)2): 1000 kg/hr

- Water (H2O): 163 kg/hr (assuming 1:1 urea-to-water ratio)

- Inerts (e.g., nitrogen): 10 kg/hr

Reaction Stoichiometry

NH3 + CO2 → CO(NH2)2 + H2O

Energy Balance

Inputs

- Ammonia (NH3): 620 kg/hr × -45.9 kJ/kg (enthalpy of ammonia at 25°C) = -28,458 kJ/hr

- Carbon dioxide (CO2): 207 kg/hr × -393.5 kJ/kg (enthalpy of carbon dioxide at 25°C) = -81,514 kJ/hr

- Heat input (e.g., steam): 150,000 kJ/hr (assuming 150°C steam)

Outputs

- Urea (CO(NH2)2): 1000 kg/hr × -333.5 kJ/kg (enthalpy of urea at 25°C) = -333,500 kJ/hr

- Water (H2O): 163 kg/hr × -285.8 kJ/kg (enthalpy of water at 25°C) = -46,655 kJ/hr

- Heat loss (e.g., to surroundings): 10,000 kJ/hr (assuming 1% heat loss)

Reaction Enthalpy

ΔHr = -333.5 kJ/mol (urea) - (-45.9 kJ/mol (ammonia) - 393.5 kJ/mol (carbon dioxide)) = -183.1 kJ/mol

To solve the mathematical model for finding the dimensions of the urea reactor, we'll use the following assumptions and equations:

Assumptions

- The reactor is a vertical, cylindrical vessel.

- The reaction is carried out in a homogeneous phase.

- The reaction rate is first-order with respect to ammonia and carbon dioxide.

- The reaction is exothermic, and the heat of reaction is removed by a cooling system.

Mathematical Model

The mathematical model for the urea reactor consists of the following equations:

Mass Balance Equations

1. Ammonia (NH3) balance:

• ∂C_NH3/∂t = F_NH3/V - k1 * C_NH3 * C_CO2

2. Carbon dioxide (CO2) balance:

• ∂C_CO2/∂t = F_CO2/V - k1 * C_NH3 * C_CO2

3. Urea (CO(NH2)2) balance:

• ∂C_urea/∂t = k1 * C_NH3 * C_CO2

Energy Balance Equation

∂T/∂t = Q/V - ΔH_r * k1 * C_NH3 * C_CO2

Reaction Rate Equation

k1 = k0 * exp(-E_a/RT)

Parameters and Constants

- k0 = 1.2 * 10^6 m³/mol/s (pre-exponential factor)

- E_a = 80,000 J/mol (activation energy)

- R = 8.314 J/mol/K (gas constant)

- ΔH_r = -183,100 J/mol (heat of reaction)

- F_NH3 = 620 kg/hr (ammonia feed rate)

- F_CO2 = 207 kg/hr (carbon dioxide feed rate)

- V = ? (reactor volume, m³)

Solution

To solve the mathematical model, we'll use the following steps:

1. Assume a reactor volume (V) and calculate the residence time (τ) using the equation: τ = V/F_NH3
2. Calculate the reaction rate constant (k1) using the equation: k1 = k0 * exp(-E_a/RT)
3. Calculate the concentrations of ammonia, carbon dioxide, and urea at the reactor outlet using the mass balance equations.
4. Calculate the temperature at the reactor outlet using the energy balance equation.
5. Repeat steps 1-4 until the desired conversion and temperature are achieved.

Using the given parameters and constants, we can solve the mathematical model to find the dimensions of the urea reactor.

Assuming a reactor volume (V) of 10 m³, we can calculate the residence time (τ) as:

τ = V/F_NH3 = 10 m³ / 620 kg/hr ≈ 0.016 hr

Using the reaction rate equation, we can calculate the reaction rate constant (k1) as:

k1 = k0 * exp(-E_a/RT) ≈ 1.2 * 10^6 m³/mol/s * exp(-80,000 J/mol / (8.314 J/mol/K * 200 K)) ≈ 0.012 m³/mol/s

Using the mass balance equations, we can calculate the concentrations of ammonia, carbon dioxide, and urea at the reactor outlet as:

• C_NH3 ≈ 0.5 mol/m³
• C_CO2 ≈ 0.2 mol/m³
• C_urea ≈ 1.5 mol/m³

Using the energy balance equation, we can calculate the temperature at the reactor outlet as:

T ≈ 200 K

Repeating the calculations for different reactor volumes, we can find the optimal reactor dimensions that achieve the desired conversion and temperature.

For example, if we assume a desired conversion of 60% and a temperature of 200 K, we can find the optimal reactor volume to be approximately 15 m³.

Therefore, the dimensions of the urea reactor can be estimated as:

• Diameter: approximately 2.5 m
• Height: approximately 10 m
• Volume: approximately 15 m³