1. Introduction
Increasing energy consumption and CO2 emissions make it urgent to improve heat transfer efficiency in industries [
1,
2,
3]. This can be achieved by using high-performance heat transfer equipment [
4]. Conventional shell-and-tube heat exchange is one of the most commonly used types of heat transfer equipment nowadays among different type of heat exchangers [
5,
6]. Although the methodologies of design in conventional heat exchangers are relatively mature, it remains challenging to decrease their relatively large approach temperature and big thermal size [
6]. Additionally, shell-and-tube heat exchangers can be easily affected by fouling deposition, especially in high-temperature applications, such as crude oil pre-heating [
7,
8]. Both plate heat exchangers and shell-and-tube heat exchangers offer specific advantages depending on the type of application and industry. However, in terms of energy saving, plate heat exchangers (PHEs) can significantly increase heat recovery through exploitation of small temperature differences, improve thermal-hydraulic behavior, and reduce energy consumption and greenhouse emissions [
6,
9].
There are many forms of corrugated plate and channel arrangements for PHEs [
10]. Fluids stay longer in PHEs when compared with shell-and-tube heat exchangers, since hot and cold streams flow over the entire plates [
11]. For a given duty, the total volume and weight of PHEs are three times smaller than those of shell-and-tube heat exchangers [
2]. High heat transfer coefficient allows for a minimum approach temperature in PHEs to be as low as 2 °C [
6]. Higher heat recovery efficiency, smaller footprint, easier-to-deal-with fouling mitigation and lower capital cost are the main advantages of PHEs over shell-and-tube heat exchangers [
6,
12]. Gasket plate heat exchangers (GPHEs) and welded plate heat exchangers (WPHEs) are the two main types of PHEs [
6], and they have different structures as shown in
Figure 1. For GPHEs, the number of plates can be adjusted by adding or removing plates, which gives a flexible thermal design to meet the process requirement [
6]. The temperature and pressure allowance of GPHEs are 200 °C and 25 bar respectively [
4]. Compared with GPHEs, the integrity of WPHEs is significantly enhanced since plates are welded together. Consequently, WPHEs can tolerate higher temperatures (up to 350 °C) and higher pressures (up to 40 bar), exceeding the gasket limitations [
4]. Owing to the unique structure of WPHEs, they are less likely to suffer from leakage issues and are more suitable for rapid-change conditions [
13]. Based on these distinct features, PHEs are commonly applied in food, petrochemical plants, and other energy-intensive process industries [
14]. With their increasing application in industries, studies of PHEs on their heat transfer behavior are increasing as well. It is important to enhance the thermal-hydraulic behavior of PHEs to reduce the capital cost further and increase energy conversion.
The heat transfer behavior of PHEs is significantly affected by plate geometry, plate type and flow arrangement, which needs to be systematically optimized. In the past few decades, it has been proved that chevron-plates are the most energy-efficient plate type over 60 different types of plates, and commonly used by manufacturers of PHEs [
15,
16]. Researchers have conducted numerous experimental and numerical studies [
17,
18,
19,
20,
21,
22,
23] on how the chevron angle affects heat transfer behavior. Different chevron angles have different Reynolds numbers and friction factors. However, in the process industries, only a small number of fixed chevron angles have been applied as shown in
Figure 2. In this work, the three most commonly used channels are used. The H type channel, where the chevron angle is 60°, has the best heat transfer behavior and the largest resistance to flow because of high turbulence intensities and large velocities [
21]. The L type channel has a chevron angle of 30°. The small chevron angle leads to lower heat transfer coefficient and pressure drop. M type channels, where the hydraulic resistance and heat transfer performance are between the other two, combines the L and H type channels. Thus, the optimization process should account for the trade-off between heat transfer coefficient and hydraulic resistance.
The flow arrangement with the best heat transfer behavior needs to be selected depending on the required design criteria. Although piping and maintenance expenses are relatively low for a single-pass flow arrangement, higher heat transfer coefficients are achieved in multi-pass flow arrangements since fluids stay for a longer time in PHEs [
24].
One of the most dramatic advantages of PHEs is their flexibility to satisfy the required process conditions by choosing different plate types, plate geometries, and flow arrangements [
25]. However, these numerous choices increase the design complexity and the difficulty of searching for the optimal design arrangement. Determination of flow arrangement (pass arrangement for cold and hot streams), plate type and geometry selection, and design constraint considerations (for example pressure drop) are the three key points for the optimum design of PHEs. Most design optimization methods of PHEs are industrially owned, and few are in the open literature.
To develop the thermal design of PHEs, the logarithmic mean temperature difference (LMTD) and ϵ-NTU methodologies are the most commonly used approaches [
6]. Cooper [
26] and Shah [
27] used a trial-and-error method to test different geometries and find the best design solution by employing ϵ-NTU and LMTD approaches. However, these methodologies take a large amount of time, and they fail to include flow arrangement selection. Wang and Sunder [
28] presented an optimization design method for PHEs, which adjusted all the possible plate patterns on the plate surface to maximize the utilization of pressure drop. Again, the optimization process failed to consider different flow arrangements, which might obtain a better result for the design with certain constraints. A screening method was proposed by Gut and Pinto [
29]. The objective of this method is to get rid of inferior results to overcome the limitation of mixed nonlinear programming (MINLP) problem. The objective of this approach was to minimize the total area with consideration of number of passes, feed location, and number of plates as variables. However, plate pattern selection was not considered. Najafi and Najafi [
30] developed an optimization design method of PHEs with multiple objectives by minimizing hydraulic resistance and maximizing total area of PHE simultaneously. This presented challenges to obtain a globally optimal design solution and needs a considerable computation time. Picon-Nunez [
31] applied an optimal plate heat exchanger model to heat recovery. The ϵ-NTU method was employed to select flow arrangements and evaluate the temperature correction factor. However, this method failed to consider the plate pattern selection.
Among all factors that affect heat transfer behavior, flow arrangement is the most complex factor to be integrated into the optimization process since the unsymmetrical passes of hot and cold streams may diminish effective temperature differences. Initially, most of the studies [
32,
33,
34] used the LMTD correction factor to solve this problem. A closed-form formula for two-fluid heat recovery was proposed by Pignotti and Shah [
35] for the analysis of complex flow arrangements. This method was further improved by Pignotti and Tamborenea [
36] by introducing the computer-aided method for calculating the thermal effectiveness of arbitrary flow arrangements by employing a matrix algorithm. The formulas for up to four passes for different flow arrangements relating to the thermal design of PHEs were proposed by Kandlikar and Shah [
37]. The details of traditional thermal design methods, including these formulas, are available in plate heat exchanger design handbooks [
5].
With the development of computation technologies, Tovazshnyansky et al. [
38] proposed a computational method to address different heat transfer arrangements based on blocks of algebraic equations. Arsenyeva et al. [
39] further improved this approach. However, for practical application, the geometry of plates cannot be an arbitrary value and plates should be selected from available commercial plates, as assumed. A method of design for multi-pass PHE was proposed by Arsenyeva et al. [
3], which includes the selection of plate type by using the ϵ-NTU method in the thermal design. The plate geometry data collected from manufacturers can be used to build a mathematical model to evaluate heat transfer behavior. However, this method requires a large amount of computation time and is better to be applied as a rating problem. Traditionally, since the entering flow rates and stream temperature data are given in a sizing problem, the LMTD method is possibly a better option compared to the ϵ-NTU method to simplify the design process [
40]. The ϵ-NTU method might be a favorable option to solve the rating problem, where details of geometries and the size of heat exchangers are fully specified [
2,
5,
6].
Therefore, a comprehensive optimization framework of PHEs should consider plate geometry, plate type, and flow arrangement in the overall design with less computation time. To decrease computation effort, the LMTD approach is firstly applied in this work in the thermal-hydraulic design process by setting up a series of relations between temperatures among each single-pass block with known inlet and outlet temperatures of process streams, which integrated multi-pass flow arrangement, flow geometry, plate type, and chevron angle into automated optimization work. Besides, most of the design methods for PHEs are focused on GPHEs, and only a very few design approaches of WPHE are available. This is because the thermal design of WPHEs is more complex than that of GPHEs [
41]. However, in some severe situations, only WPHE can be applied. To overcome the shortcomings of previous work, this paper also presents a generalized automated methodology for the design and optimization of single multi-pass plate heat exchangers, including both GPHEs and WPHEs. The differences of the design of two different types of PHEs are firstly highlighted in this work, so that users can choose the type of PHE according to their needs. The objective is to automatically derive the optimal solution (assumed to be minimum heat transfer area) from various flow arrangements and available sets of commercial plates within the required duty and pressure drop allowance. Two case studies are presented to apply the new design approach for GPHEs and WPHEs.