# 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]

UA (W/℃) | Exchanger Design |

>79,000 | Uneconomical hairpin design |

53,000 – 79,000 | One or more 300-400mm tubes |

26,000 – 53,000 | One or more 100-300mm tubes |

<26,000 | Both double-pipe and multi-tubes should be evaluated. |

**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.**

**Sources:**

[1] | GPSA Midstream Suppliers, Engineering Data Book, 14 ed., vol. SI Volumes 1 & 2, Tulsa, Oklahoma: GPSA, 2016. |

[2] | D. W. G. Robert H. Perry, Perry's Chemical Engineers' Handbook, Kansas: McGraw-Hill Handbooks, 1999. |

[3] | M. I. Stewart, Surface Production Operations - Design of Gas-Handling Systems and Facilities, Third Edition ed., vol. 2, Kidlington, Oxford: Gulf Professional Publishing, 2014. |