The step-by-step guide: Double-Pipe Heat Exchanger design

Heat Exchangers are an essential unit operation in the design of chemical processes, usually linked directly with energy efficiency aspects of a facility. Wildly used in a plethora of industrial applications such as oil and gas, pharmaceutical, food and drink, and HVAC. In a heat exchanger unit design, key fundamental principles like the zeroth, first, and second laws of thermodynamics are applied.

Heat exchanger design revolves around understanding a basic equation:

Equation 1

Where,

Q is the heat exchanger duty

A is the area for heat transfer

U is the overall heat transfer coefficient

LMTD is the log mean temperature difference

This equation relates the duty of the exchanger (Q) with the surface area available to exchange the heat between fluids at different temperatures (A), the driving force of the exchange (LMTD), and the specific fluid and material properties (U). Each of these can be manipulated in various ways depending on the heat exchanger design. 

A classic example of a heat exchanger is the double-pipe type shown in Figure 1.

Figure 1 Double-pipe exchanger simple schematics [2]

A double-pipe heat exchanger known also as a hairpin-type exchanger (due to its U-shape bend resembling a hairpin) is made up of two concentric pipes [1]. The outer pipe (shell-side) is usually a bare pipe, and the inner pipe (tube-side) is either a bare pipe or more commonly a pipe with longitudinal fins, providing additional surface area for heat exchange (A). Double-pipe exchangers may also be operated with multiple inner pipes to increase the surface area (A), at which point it would be considered a multitube hairpin heat exchanger.

Double-pipe exchangers may be operated either co-currently or counter-currently, changing the heat exchange driving force (LMTD). More commonly they operate counter-currently to maximize the heat exchange.

The compact design with longitudinal finned tubes creates ample surface area for heat transfer, benefiting fluids with low heat transfer coefficients (U) (like most gases) [1]. 

The design of double-pipe heat exchangers offers further benefits due to its construction since the U-shape bend in the hairpin design creates an allowance for thermal expansion of the fluid. The modular construction of the exchanger offers the ability to increase capacity of heat exchange by the introduction of more sections [2].

Hairpin exchangers are versatile but their application to process design depends on the UA requirements of the system. GPSA provides a quick guide in section 9 about when hairpin designs should be considered. See Table 1.[1]. 

Table 1: GPSA Information on When to Consider Different Hairpin Designs Based on the Required UA of the System [1]

Calculations for Double-pipe Exchanger

In Process Ecology’s engineering design practice, we have sized several double-pipe heat exchangers, and below we share a step-by-step guide for the design of these units.

Commonly in these types of calculations, you have a known fluid that is being cooled or heated. Using the equation below you can calculate the duty required for the heat exchanger to achieve the desired temperature change (assuming the known fluid is the hot side of the exchanger).

Equation 2

Where,

Q is the duty of the heat exchanger

m_hot is the mass flowrate of the hot fluid

Cp_hot is the specific heat capacity of the hot fluid

T_{hot in} is the temperature of the hot fluid coming in

T_{hot out} is the temperature of the hot fluid going out 

With the known required duty, Equation 1 can be used to determine the remaining parameters.

Due to the longitudinal fins providing additional surface area, double-pipe exchangers have a more complex equation to determine the total area available for heat transfer. The following equations may be used:

Equation 3

Where,

A_h is the area for heat transfer

d_o is the tube's outer diameter

H_f is the fin height

N_f is the number of fins

Perry’s Chemical Engineering Handbook provides an alternative method for the calculation of surface area for heat transfer based on typical standards for double-pipe exchangers as shown in Figure 2 [2].

Figure 2: Perry’s Chemical Engineering Handbook Table 11-15 Double-Pipe Hairpin Section Data [2]

The overall heat transfer coefficient U may be calculated as per the equation below:

Equation 4

Where,

U_o is the overall heat transfer coefficient

h_o is the outer (shell) heat transfer coefficient

h_i is the inner (tube) heat transfer coefficient

r_w is the wall resistance

r_f is the fouling resistance 

The wall and fouling resistances depend on your pipe material and fluids properties. The inner heat transfer coefficient h_i can be calculated using standard equations such as Nusselt’s number. Calculations can then be made using either the Sieder-Tate correlation for laminar flow or the Petukhov and Kirillov equation for turbulent flow.

The outer heat transfer coefficient h_o, however, must be carefully analyzed as the longitudinal fins create different hydraulic diameters, which in turn change both Reynold’s number and Nusselt’s number. The hydraulic diameter can be calculated as follows.

Equation 5

Where,

D_h is the hydraulic diameter

A_c is the net cross-sectional area in the annulus

P_w is the total wetted perimeter of the annulus

D_i is the shell-side pipe's inner diameter

d_o is the tube-side pipe's outer diameter

δ is the width of the fin

H_f is the height of fin

N_f is the number of fins

With the hydraulic diameter the Reynolds number can be calculated as:

As noted earlier, Nusselt’s number may be calculated with either the Sieder-Tate correlation for laminar flow or the Petukhov and Kirillov equation for turbulent flow similar to h­_i.

With the overall heat transfer calculated and the LMTD of the exchanger defined, the required area can be calculated using Equation 1. This can then be compared with Equation 2 or Perry’s Chemical Handbook calculations to determine the length requirements. An iterative approach to these steps leads to the size of a double-pipe heat exchanger.

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