Process Design Calculations for Heat Exchangers Equipment

I. Introduction

Process design calculations for heat exchangers are essential in the field of chemical engineering. Heat exchangers play a crucial role in various industrial processes, including heating, cooling, and condensing. These calculations help engineers determine the size, efficiency, and performance of heat exchangers, ensuring optimal operation and energy utilization.

II. Double Pipe Heat Exchangers

Double pipe heat exchangers are a common type of heat exchanger used in many industries. They consist of two concentric pipes, with the hot fluid flowing through the inner pipe and the cold fluid flowing through the annular space between the two pipes. The design calculations for double pipe heat exchangers involve determining the heat transfer area, calculating the overall heat transfer coefficient, and estimating the pressure drop.

1. Determining Heat Transfer Area

The heat transfer area is a critical parameter in heat exchanger design as it directly affects the heat transfer rate. It can be calculated using the following equation:

$$A = \frac{Q}{U \cdot \Delta T_{lm}}$$

where:

• A is the heat transfer area
• Q is the heat transfer rate
• U is the overall heat transfer coefficient
• (\Delta T_{lm}) is the log mean temperature difference

2. Calculating Overall Heat Transfer Coefficient

The overall heat transfer coefficient represents the combined effect of conduction, convection, and radiation on heat transfer. It can be calculated using the following equation:

$$\frac{1}{U} = \frac{1}{h_i} + \frac{r_i}{k} + \frac{r_o}{k} + \frac{1}{h_o}$$

where:

• U is the overall heat transfer coefficient
• (h_i) and (h_o) are the inside and outside heat transfer coefficients
• (r_i) and (r_o) are the inside and outside fouling resistances
• k is the thermal conductivity of the pipe material

3. Estimating Pressure Drop

Pressure drop is an important consideration in heat exchanger design as it affects the flow rate and energy consumption. It can be estimated using the Darcy-Weisbach equation:

$$\Delta P = \frac{f \cdot L \cdot \rho \cdot V^2}{2 \cdot D}$$

where:

• (\Delta P) is the pressure drop
• f is the friction factor
• L is the length of the pipe
• (\rho) is the fluid density
• V is the fluid velocity
• D is the pipe diameter

C. Step-by-step Walkthrough

Let's walk through a typical problem to understand the design calculations for double pipe heat exchangers better.

Problem: A double pipe heat exchanger is used to cool a process fluid from 80°C to 40°C using cooling water. The process fluid flow rate is 2 kg/s, and the cooling water flow rate is 5 kg/s. The inside heat transfer coefficient is 500 W/(m²·K), and the outside heat transfer coefficient is 1000 W/(m²·K). The inner and outer pipe diameters are 0.05 m and 0.1 m, respectively. Calculate the heat transfer area, overall heat transfer coefficient, and pressure drop.

Solution:

1. Determining Heat Transfer Area: Using the equation

$$A = \frac{Q}{U \cdot \Delta T_{lm}}$$

where Q = (m \cdot C_p \cdot \Delta T), m is the mass flow rate, Cp is the specific heat capacity, and (\Delta T) is the temperature difference, we can calculate the heat transfer area.

1. Calculating Overall Heat Transfer Coefficient: Using the equation

$$\frac{1}{U} = \frac{1}{h_i} + \frac{r_i}{k} + \frac{r_o}{k} + \frac{1}{h_o}$$

we can calculate the overall heat transfer coefficient.

1. Estimating Pressure Drop: Using the Darcy-Weisbach equation

$$\Delta P = \frac{f \cdot L \cdot \rho \cdot V^2}{2 \cdot D}$$

we can estimate the pressure drop.

D. Real-world Applications and Examples

Double pipe heat exchangers are widely used in various industries, including chemical processing, oil and gas, and food and beverage. They are suitable for applications where the heat transfer requirements are relatively low, and space is limited. Some examples of real-world applications include:

• Heating or cooling of process fluids in chemical reactors
• Heat recovery from flue gases in power plants
• Preheating of feedwater in steam generation systems

E. Advantages and Disadvantages

Advantages of double pipe heat exchangers include:

• Simple design and construction
• Easy maintenance and cleaning
• Low cost

Disadvantages of double pipe heat exchangers include:

• Limited heat transfer capacity
• High pressure drop
• Limited scalability

III. Shell and Tube Heat Exchangers

Shell and tube heat exchangers are another common type of heat exchanger used in various industries. They consist of a bundle of tubes enclosed in a shell, with one fluid flowing through the tubes and the other fluid flowing over the tubes inside the shell. The design calculations for shell and tube heat exchangers are similar to those for double pipe heat exchangers.

1. Determining Heat Transfer Area

The heat transfer area in shell and tube heat exchangers can be calculated using the same equation as for double pipe heat exchangers:

$$A = \frac{Q}{U \cdot \Delta T_{lm}}$$

2. Calculating Overall Heat Transfer Coefficient

The overall heat transfer coefficient in shell and tube heat exchangers can be calculated using the same equation as for double pipe heat exchangers:

$$\frac{1}{U} = \frac{1}{h_i} + \frac{r_i}{k} + \frac{r_o}{k} + \frac{1}{h_o}$$

3. Estimating Pressure Drop

The pressure drop in shell and tube heat exchangers can be estimated using the same Darcy-Weisbach equation as for double pipe heat exchangers:

$$\Delta P = \frac{f \cdot L \cdot \rho \cdot V^2}{2 \cdot D}$$

C. Step-by-step Walkthrough

Let's walk through a typical problem to understand the design calculations for shell and tube heat exchangers better.

Problem: A shell and tube heat exchanger is used to heat water from 20°C to 60°C using steam. The water flow rate is 10 kg/s, and the steam flow rate is 2 kg/s. The inside heat transfer coefficient is 1000 W/(m²·K), and the outside heat transfer coefficient is 5000 W/(m²·K). The tube diameter is 0.02 m, and the tube length is 5 m. Calculate the heat transfer area, overall heat transfer coefficient, and pressure drop.

Solution:

1. Determining Heat Transfer Area: Using the equation

$$A = \frac{Q}{U \cdot \Delta T_{lm}}$$

where Q = (m \cdot C_p \cdot \Delta T), m is the mass flow rate, Cp is the specific heat capacity, and (\Delta T) is the temperature difference, we can calculate the heat transfer area.

1. Calculating Overall Heat Transfer Coefficient: Using the equation

$$\frac{1}{U} = \frac{1}{h_i} + \frac{r_i}{k} + \frac{r_o}{k} + \frac{1}{h_o}$$

we can calculate the overall heat transfer coefficient.

1. Estimating Pressure Drop: Using the Darcy-Weisbach equation

$$\Delta P = \frac{f \cdot L \cdot \rho \cdot V^2}{2 \cdot D}$$

we can estimate the pressure drop.

D. Real-world Applications and Examples

Shell and tube heat exchangers are widely used in various industries, including petrochemical, power generation, and HVAC. They are suitable for applications where high heat transfer rates are required, and fouling is a concern. Some examples of real-world applications include:

• Condensing of steam in power plants
• Cooling of turbine oil in gas turbines
• Heating or cooling of process fluids in chemical plants

E. Advantages and Disadvantages

Advantages of shell and tube heat exchangers include:

• High heat transfer capacity
• Versatility in design and configuration
• Suitable for high-pressure and high-temperature applications

Disadvantages of shell and tube heat exchangers include:

• Complex design and construction
• Difficult maintenance and cleaning
• Higher cost compared to other types of heat exchangers

IV. Heat Transfer Coefficients and Pressure Drop

In heat exchanger design, it is essential to accurately calculate the heat transfer coefficients and pressure drop to ensure optimal performance. Kern's method is commonly used to calculate heat transfer coefficients, while Bell's method is used to estimate pressure drop.

A. Kern's Method for Calculating Heat Transfer Coefficients

Kern's method is a widely accepted approach for calculating heat transfer coefficients in heat exchangers. It involves the following steps:

1. Determine the individual film coefficients for the hot and cold fluids.
2. Calculate the overall heat transfer coefficient using the following equation:

$$\frac{1}{U} = \frac{1}{h_i} + \frac{r_i}{k} + \frac{r_o}{k} + \frac{1}{h_o}$$

1. Calculate the correction factor, F, based on the flow arrangement and number of tube passes.
2. Calculate the corrected overall heat transfer coefficient using the equation:

$$U_c = F \cdot U$$

1. Calculate the individual film coefficients using the equation:

$$\frac{1}{h_i} = \frac{1}{U_c} - \frac{r_i}{k}$$

$$\frac{1}{h_o} = \frac{1}{U_c} - \frac{r_o}{k}$$

B. Bell's Method for Calculating Pressure Drop

Bell's method is commonly used to estimate pressure drop in heat exchangers. It involves the following steps:

1. Calculate the Reynolds number, Re, using the equation:

$$Re = \frac{\rho \cdot V \cdot D}{\mu}$$

1. Calculate the friction factor, f, using the appropriate correlation for the flow regime (e.g., laminar, transitional, or turbulent).
2. Calculate the pressure drop using the Darcy-Weisbach equation:

$$\Delta P = \frac{f \cdot L \cdot \rho \cdot V^2}{2 \cdot D}$$

C. Step-by-step Walkthrough

Let's walk through a typical problem to understand Kern's and Bell's methods better.

Problem: A shell and tube heat exchanger is used to heat oil from 40°C to 80°C using hot water. The oil flow rate is 5 kg/s, and the hot water flow rate is 10 kg/s. The inside heat transfer coefficient is 2000 W/(m²·K), and the outside heat transfer coefficient is 5000 W/(m²·K). The tube diameter is 0.03 m, and the tube length is 4 m. Calculate the overall heat transfer coefficient and pressure drop.

Solution:

1. Calculate the overall heat transfer coefficient using Kern's method.
2. Calculate the pressure drop using Bell's method.

D. Real-world Applications and Examples

Kern's method and Bell's method are widely used in the design and analysis of heat exchangers in various industries. Some real-world applications include:

• Design of heat exchangers for chemical processes
• Optimization of heat exchanger networks in refineries
• Performance evaluation of heat exchangers in HVAC systems

V. Rating of Existing Units

Rating existing heat exchangers involves evaluating their performance and determining if they meet the required specifications. Two commonly used methods for rating existing heat exchangers are the LMTD (Log Mean Temperature Difference) method and the Effectiveness-NTU (Number of Transfer Units) method.

A. LMTD Method

The LMTD method is based on the assumption of a constant heat transfer coefficient and a constant specific heat capacity. It involves the following steps:

1. Calculate the LMTD using the equation:

$$\Delta T_{lm} = \frac{\Delta T_1 - \Delta T_2}{\ln\left(\frac{\Delta T_1}{\Delta T_2}\right)}$$

1. Calculate the correction factor, F, based on the flow arrangement and number of tube passes.
2. Calculate the heat transfer area using the equation:

$$A = \frac{Q}{U \cdot \Delta T_{lm}}$$

B. Effectiveness-NTU Method

The Effectiveness-NTU method is based on the concept of heat exchanger effectiveness and the number of transfer units. It involves the following steps:

1. Calculate the heat capacity rate ratio, C_r, using the equation:

$$C_r = \frac{C_{min}}{C_{max}}$$

1. Calculate the heat exchanger effectiveness, (\varepsilon), using the equation:

$$\varepsilon = \frac{1 - \exp(-NTU \cdot (1 - C_r))}{1 - C_r \cdot \exp(-NTU \cdot (1 - C_r))}$$

1. Calculate the number of transfer units, NTU, using the equation:

$$NTU = \frac{UA}{C_{min}}$$

1. Calculate the heat transfer area using the equation:

$$A = \frac{Q}{U \cdot \Delta T_{lm}}$$

C. Step-by-step Walkthrough

Let's walk through a typical problem to understand the LMTD method and the Effectiveness-NTU method better.

Problem: An existing shell and tube heat exchanger is used to cool a process fluid from 80°C to 40°C using cooling water. The process fluid flow rate is 2 kg/s, and the cooling water flow rate is 5 kg/s. The inside heat transfer coefficient is 500 W/(m²·K), and the outside heat transfer coefficient is 1000 W/(m²·K). The log mean temperature difference (LMTD) is 30°C. Calculate the heat transfer area using the LMTD method and the Effectiveness-NTU method.

Solution:

1. Calculate the heat transfer area using the LMTD method.
2. Calculate the heat transfer area using the Effectiveness-NTU method.

D. Real-world Applications and Examples

The LMTD method and the Effectiveness-NTU method are widely used in the rating and evaluation of existing heat exchangers in various industries. Some real-world applications include:

• Performance assessment of heat exchangers in power plants
• Retrofitting of heat exchangers in chemical processes
• Optimization of heat exchanger networks in refineries

VI. Conclusion

Process design calculations for heat exchangers are crucial for ensuring efficient and effective heat transfer in industrial processes. By understanding the fundamentals of heat exchangers and applying the design calculations discussed in this outline, engineers can optimize the performance of heat exchangers and improve overall process efficiency.

Summary

Process design calculations for heat exchangers are essential in the field of chemical engineering. Heat exchangers play a crucial role in various industrial processes, including heating, cooling, and condensing. This content covers the design calculations for double pipe heat exchangers, shell and tube heat exchangers, heat transfer coefficients, pressure drop, and rating of existing units. It also includes real-world applications, advantages, and disadvantages of different types of heat exchangers. The content is structured to maximize student comprehension and help them achieve high marks in their exams.

Analogy

Heat exchangers can be compared to a car radiator. Just as a car radiator transfers heat from the engine coolant to the surrounding air, heat exchangers transfer heat between two fluids. The design calculations for heat exchangers are like determining the size and efficiency of the radiator to ensure optimal cooling of the engine.