Design optimization of shell and tube heat exchangers sizing with heat transfer enhancement

Highlights

• A disjunctive optimization model for shell and tube heat exchanger is developed.

• The model includes automatically selection of heat transfer enhancement techniques.

• Detailed geometrical components of exchanger can be obtained after optimization.

• Optimal solutions include the investigation of local and global optimums.

• Performance and benefits of proposed model are demonstrated.

Abstract

Heat transfer enhancement (HTE) is an efficient technology to improve the performance of shell and tube heat exchangers (STHEs). While there exist many commercial software packages, heat exchanger design still highly depends on users’ experiences, resulting in long computing time and inferior solutions. Therefore, a systematic optimization methodology is required in order to achieve an efficient and accurate design solution. This paper presents a generalized disjunctive programming (GDP) model for the optimization of STHE design. It is formulated as a mixed integer non-linear programming (MINLP) problem, involving selection for 12 technology combinations (four tube-side techniques, three shell-side techniques), and all discrete decisions for each selection are modeled by disjunctions. The model is then applied to minimize the total capital cost. Both global optimization solver BARON, and general MINLP solver DICOPT are tested. The results show that the developed method provides a better design solution compared with conventional STHE design procedures.

Introduction

A shell and tube heat exchanger (STHE) is a very generalized heat transfer device widely used in the oil, gas and chemical industries, because of its simple structure and common applicability. To increase the economic benefits, there is a strong incentive to reduce the cost of STHEs. Many conventional heat exchanger design models based on plain tubes and normal segmental baffles have been developed for optimizing the STHE sizing. These models apply various algorithms and optimization approaches. Chaudhuri et al. (1997) proposed an efficient exchanger design strategy by simulated annealing (SA) and developed a command procedure coupled with HTRI®. However, the relationship between the design constraints and exchanger geometries are not clear, since the HTRI® does not provide detailed mathematical models. Mizutani et al. (2003) formulated an MINLP mathematical model for exchanger design optimization. In their work, the Bell-Delaware is used to evaluate the shell-side thermodynamic performance. Because of the high non-convexities of the Bell-Delaware method, optimization may be trapped in a local optimum. To overcome the limitations of mathematical approaches, an approach based on genetic algorithms (GA) was proposed to optimize the STHE using the Bell-Delaware method without simplifications (Ponce-Ortega et al., 2009). Better detection of global optimum than the gradient method was shown, but a high computation resource was needed, since the evaluation of each individual with an initial population is time demanding.

To reduce the computational complexities, Onishi et al. (2013) proposed a sequential optimization method of partial objectives through the division of the model into sets of related equations, which simplified the previous MINLP model. Gonçalves et al. (2017) transferred the MINLP problem into a mixed integer linear programming (MILP) model with a set of binary variables to make this model used as part of a complex heat exchanger network design. The results showed that the proposed procedures can lead a large reduction of computational effort.

Furthermore, a great number of papers were published to conduct a better evaluation through new algorithms. Sanaye and Hajabdollahi (2010) reported an STHE design model, which respectively used ε–NTU method to model the Bell-Delaware procedures and Fast and elitist non-dominated sorting genetic algorithm (NSGA-II) to obtain the two objectives, including the maximum effectiveness and the minimum total cost. Rao and Saroj (2017) developed an economic optimization approach of STHE using Jaya algorithm. This model involved the details of maintenance since fouling is considered. Dhavle et al. (2018) applied an AI-based optimization method referred as cohort intelligence (CI) in solving the design and economic optimization of the STHEs.

In order to break geometry bottlenecks for heat transfer, heat transfer enhancement (HTE) techniques have been developed to improve the performance of STHE through the modifications of surface or structure. The main advantages of the HTE applications in different fields involve: (a) Reducing the required exchanger area for STHE design. (b) Avoiding adding additional area, repiping work and installing new exchangers for heat exchanger network retrofit. (c) Increasing the conversion from pressure drop to heat transfer coefficients to avoid exceeding the limitation of process pump capacity.

Heat transfer intensified techniques can be applied in tube-side and shell-side enhancement. Smith (2016) identified the tube-side enhancement techniques based on two enhanced approaches. The first approach is to introduce the turbulent flow by installing the spiral structure in the tube or twisting the form of the tube, such as twisted-tape and coiled wire inserts. The other method is to modify the geometrical area, such as internal fins that simultaneously extend the transfer surface area and change the flow pattern inside the tube. Manglik and Bergles (1993a, 1993b) proposed the relevant correlations of twisted-tape insert to calculate the tube-side heat transfer coefficient and pressure drop, covered with laminar and turbulent flow. Studies (Date, 2000; Sarma et al., 2005) demonstrated the flow behaviour on the tube-side with twisted-tape inserts under different twist ratios. For coiled-wire, Sethumadhavan and Raja Rao (1983) and Uttarwar and Raja Rao (1985) respectively analyzed the effect of coiled-wire insert in laminar and turbulence flow. The empirical correlations for predicting the heat transfer coefficients and friction factors were developed by Ravigururajan and Bergles (1996) as taking into account for various coil wire configurations and roughness geometries. In order to improve the computational efficiency of proposed methods for twisted-tape and coiled-wire, Jiang et al. (2014) integrated the previous approaches and proposed more reliable and simple correlations to predict the heat transfer performance of tube-side with twisted-tape and coiled-wire insert. In this paper, detailed relationship for inserts geometries and heat transfer coefficient, pressure drop is discussed under a wide range of Reynold number. Then the new correlations are tested by enhancing an existing heat exchanger with fixed twist ratio and helical pitch. The results show twisted-tape insert increases tube-side film coefficient to 2 times and coiled-wire insert raise to 3 times. However, optimal geometries have not been investigated for different operating conditions. Furthermore, Watkinson et al. (1975) and Huq et al. (1998) investigated the performance of helical internal fin tubes at low Reynold number. For high Reynold region, the relevant correlations were conducted by Jensen and Vlakancic (1999) and then modified by Webb et al. (1999) However, there are still 20–30% errors for the methods conducted by Webb. Thus, Zdaniuk et al. (2008) developed new empirical equations to reduce errors based on experimental works.

Numerous papers have been published for shell-side intensified techniques. Stehlik et al. (1994) showed that helical baffles could promote the heat transfer by 1.39 times and reduce the pressure drop by 0.26–0.6 times as that of cross-flow in the segmental baffle. Kral et al. (1996) analyzed the impacts of helical angle for the conversion from pressure drop to heat transfer rate. Wang et al. (2010) divided helical baffles into continuous and non-continuous baffles, and Zhang et al. (2009) proposed the correlations to calculate shell-side heat transfer coefficients and friction factors. On the other hand, the literature (Ganapathy, 1996; Hashizume, 1981; Mukherjee, 1998) highlighted that external fins can increase 2–4 times heat transfer surface area compared with conventional tubes, with a dramatic increase of pressure drop. In order to investigate the performance of external fins in shell and tube exchangers, relevant correlations were proposed by Serth and Lestina (2014) and tested by Pan et al. (2013). Pan et al. (2013) integrated the design models of three tube-side and two shell-side heat transfer enhancement techniques which include tube inserts, tube fins and helical baffles to apply various of techniques flexibly based on existing heat exchanger network. They analyzed the enhancement levels of these techniques and compared with plain tube-single segmental baffle STHE. However, two drawbacks still need to be solved. First, more accurate correlations of twisted-tape and coiled-wire inserts (Jiang et al., 2014) have not been applied and integrated. Second, the results are based on simulation with fixed exchanger and HTE geometries rather than optimization.

In recent years, many commercial software packages such as HTRI® and Aspen EDR® are able to consider the selections of a variety of heat intensified techniques for STHEs. Nevertheless, for Aspen EDR®, it is time consuming to evaluate multiple solutions conducted from the iterations, because the software package is unable to automatically select optimal HTE techniques versus minimum total cost. The latest rigorous point-wise approach of HTRI® also requires a lot of computational time and strongly depends on a proper initialization (HTRI). In the existing STHE design methods, human factors normally lead to different qualities of design, because different users have to carry out various operations to converge the software, such as the selection of baffle type and tube inserts, adjusting tube pitch, tube diameter and twisted pitch. These operations cause various degrees of deviations for different users, and further increase computation time.

In order to overcome the existing drawbacks, this paper aims to extend the existing mathematical models to achieve automated heat exchanger design with heat transfer enhancement, based on the improved simplified Delaware method for single segmental baffle of shell-side (Wang et al., 2012) calculation and Dittus-Boelter correlation for plain tube of tube-side calculation. Accurate correlations of tube inserts, finned tube and helical baffle are integrated and improved. Generalized disjunctive programming (GDP) is introduced in this model to select all discrete decisions, which mainly include the number of tube passes, TEMA tube sizes, helical angle and tube configurations. In this work, simultaneous optimization is carried out for exchanger and HTE technology geometries and the most appropriate HTE technique selection can be achieved. Rigorous design constraints and a wide range of flow regime are involved by proposed mathematical model to conduct a practical solution.