Optimisation for the retrofit of large scale heat exchanger networks with different intensified heat transfer techniques

Applied Thermal Engineering 53 (2013) 373e386

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Optimisation for the retrofit of large scale heat exchanger networks with different intensified heat transfer techniques Ming Pan a, *, Igor Bulatov a, Robin Smith a, Jin-Kuk Kim b, ** a

Centre for Process Integration, School of Chemical Engineering and Analytical Science, The University of Manchester, Manchester, Oxford Road, M13 9PL, United Kingdom b Department of Chemical Engineering, Hanyang University, Wangsimni-ro 222, Seongdong-gu, Seoul 133-791, Republic of Korea

a r t i c l e i n f o

a b s t r a c t

Article history: Received 12 December 2011 Accepted 16 April 2012 Available online 22 April 2012

Intensified heat transfer (IHT) techniques have recently been used for retrofit in the process industry, leading to significant energy saving in heat exchanger network (HEN) by facilitating heat transfer intensification without network topology modification. In this paper, an optimisation method has been developed for dealing with the retrofit of large scale HENs in which the location of intensified heat transfer within the network and its degree of intensification are systematically identified, given the objective function and design constraints, including topological limitation in the existing heat recovery systems. The optimisation framework developed is based on iterative optimisation of a relatively simple mixed integer linear programming (MILP), which can effectively deal with computational difficulties associated with nonlinearity. In the retrofitted HENs, several conventional intensified heat transfer techniques are available, including tube-side intensification (twisted-tape inserts, coiled-wire inserts and internal fins), and shell-side intensification (external fins and helical baffles). Suitable exchangers can be selected for enhancement by implementing one or more intensification techniques to increase the whole network energy recovery within very low retrofit cost. A large-size industrial case study is considered to demonstrate the validity and efficiency of the proposed optimisation approach.
2012 Elsevier Ltd. All rights reserved.

Keywords: Heat exchanger network (HEN) Retrofit Intensified heat transfer (IHT) Optimisation Tube-side intensification Shell-side intensification

1. Introduction The retrofit of heat exchanger networks (HEN) has recently received greater attention both from the academic and industrial communities. Feng et al. [1] proposed a set of design principles to define the boundary of heat integration in petrochemical complexes, and developed retrofit strategies based on Pinch Analysis for the relevant HENs to achieve significant energy saving with less network modifications. Coletti et al. [2] used a dynamic and distributed mathematical model to simulate an existing crude preheat train network with the consideration of fouling effects for shell and tube heat exchangers, and stated that the optimal retrofitted network based on steady state conditions was not the best when fouling is considered. Piacentino [3] presented an innovative and harmonic use of several existing techniques to analysis the energy consumption of HENs’ for the retrofit, and identify the relaxation strategies for the optimisation.

* Corresponding author. Tel.: þ44 161 3064390. ** Corresponding author. Tel.: þ82 2 2220 2331. E-mail addresses: [email protected] hanyang.ac.kr (J.-K. Kim).

(M.

Pan),

jinkukkim@

1359-4311/$ e see front matter
2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.applthermaleng.2012.04.038

Commonly, improved heat recovery for the existing chemical processes can be achieved through various retrofit techniques, including the facilitation of intensified heat transfer, adding additional heat transfer area, the installation of a new exchanger, and reconfiguration of heat recovery structure (e.g. repiping). Most recently, the implementation of intensified heat transfer (IHT) has notable advantage over other retrofit techniques, as no network structure modification is required for achieving significant energy savings. Intensifying heat transfer is the study of intensified or improved heat transfer performance, which generally means an increase of the heat transfer coefficient. The goal of IHT is to reduce the size and cost of heat exchanger equipment, or to increase the heat duty for a given size heat exchanger. Tube-side IHT devices provide an important tool in heat transfer augmentation, especially for shell and tube heat exchangers with plain tubes. The tube-side enhancement techniques are classified according to two different criteria, including the additional devices which are incorporated into a plain round tube (e.g. twisted-tape inserts and coiled-wire inserts), and the manufacturing of special tube geometries (e.g. internally finned tubes). While for shell-side IHT, externally finned tubes are intended to extend and rough the tube surface in shell-

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M. Pan et al. / Applied Thermal Engineering 53 (2013) 373e386

side, and helical baffles can improve shell-side heat transfer coefficient with low pressure drop and low possibility of flow-induced vibration, which reduces fouling with a trivial increase in pumping. The widely adopted approaches for HEN retrofit can be divided into two groups, namely, Pinch Analysis and mathematical programming. Early studies are mainly based on the use of graphical interpretation of energy recovery characteristics and its manipulation for targeting and designing of energy systems which are widely known as Pinch Analysis. This pinch design concept had been applied to grassroot design as well as retrofitted networks, while mathematical programming techniques are used for the systematic consideration of economic trade-off and/or the provision of automated design procedure for the retrofitting [4e8]. Briones and Kokossis [4] made use of Pinch Analysis to develop different energy recovery levels in the existing HENs, and determined the best economic trade-offs between energy saving and investment. Asante and Zhu [5,6] proposed a design approach for HEN retrofit which consisted of a diagnostic stage using pinch analysis, an evaluation stage and a cost optimisation stage. Suitable modification options were selected from the first two stages and then optimized together in the existing HEN. Based on this work, Zhu et al. [7] developed the network pinch method to retrofit HEN with IHT. They identified suitable exchangers for enhancement and the level of enhancement at the targeting stage, and selected the most suitable technique to fulfil the required enhancement with minimal retrofit cost. Ravagnani et al. [8] addressed pressure drop and fouling effects in HEN design, in which Pinch Analysis was used to identify maximum energy saving potential for the HEN, and then details of heat exchangers for the given HEN were obtained with Bell Delaware method. Considerable works on mathematical programming techniques for the retrofitting of heat recovery systems had been made, due to ability for the effective identification of optimal solution for complex problems. With the nonlinear characteristics in heat transfer and logarithmic mean temperature difference (LMTD), HEN retrofit is usually formulated as a mixed integer nonlinear programming (MINLP) problem. Ciric and Floudas [9,10] applied the Generalized Benders Decomposition technique to solve the MINLP problem, in which the original formulation was decomposed into two sub-problems (MILP and NLP). Yee and Grossmann [11] used arithmetic mean temperature difference (AMTD) to simplify nonlinear expression in heat transfer equations, which might overestimate the driving force if the temperature difference approach of one exchanger side is significantly different than the other side. Relying on the approximate calculation of LMTD, Salama [12] developed two aspects of the minimum rule (MR) technique, namely minimum stream heat capacity flowrates in each exchanger, and minimum temperature differences between its input and output, to reduce the number of constraints and exchanger area calculations in HEN synthesis, while Bogataj and Kravanja [13] presented a new methodology for HEN synthesis based on a stage-wise superstructure, and used a modified outer approximation/equality relaxation algorithm to tighten the lower bound by solving a single multilevel convex lower-bounding MINLP. To avoid the computational difficulties of MINLP problems, some of recent works focused on using MILP formulation [14e17]. Barbaro et al. [14,15] divided processing streams at first to fix the temperature intervals, thus LMTD in each interval is known and constant. This can change an MINLP problem to an MILP problem. However, because of combinatorial complexity, the number of binary variables increased with the number of intervals, and the problems became larger and difficult to solve. Pan et al. [16e18] proposed a novel iterative MILP-based method for HEN retrofit with IHT. Their automated design method had been proposed to

systematically consider heat transfer enhancement in the HEN retrofit with full appreciation of optimisation methods which can overcome the nonlinear drawbacks of existing methods. Although various mathematical programming methodologies have been proposed for HEN retrofit, most of works are based on large-size complex MINLP or MILP models, which are often not readily applicable for retrofit, because there are numerical difficulties related to nonlinearity, problem size and computational time for the optimisation of industrial-scale design problem. More importantly, most of automated design methods suggest retrofitting of heat recovery systems with configurational changes or structural modification for heat exchanging arrangement. The modification of network topology in practise is very difficult, due to not only constraints related to the topology itself, but also safety and maintenance associated with structural changes made in the HEN. Also, structural changes of heat exchangers and their matching arrangement need considerable capital investment, because of piping and civil works required for the retrofit and potential production losses during process modification. In this paper, new optimisation method has been developed to solve large scale HEN retrofit problems with systematic consideration of implementing tube-side and shell-side intensification techniques simultaneously. The objective of the new design methodology is to maximise energy saving without any topology modifications. Most of existing works on HEN retrofit considered topology modifications. Wang et al. [19] recently attempted to address the implementation of intensified heat transfer to the existing heat recovery systems without topology modification. But this study was limited to deal with a small-scale design problem as the methodology is based on heuristics and its application is at user’s discretion. Furthermore, Wang et al. [18] and Pan et al. [16e18] only addressed the heat transfer intensification for increasing the overall heat transfer coefficients, but no details were given for how much enhancement for the tube-side and shell-side is to be made and what kind of intensification techniques are applied. The new approach is, therefore, proposed in this paper to facilitate the automated design of HEN retrofit as well as solve industrial-scale large-size problems more efficiently with rigorous consideration of economic trade-off and full appreciation of comprising different intensified heat transfer techniques. The rest of this paper is structured as follows. Several conventional intensification techniques are firstly introduced in details. This is followed by the description of an MILP-based model for HEN retrofit with IHT, and a solution strategy and optimisation procedure based on two iteration loops. An industrial study is presented to demonstrate the validity and efficiency of the proposed approach.

2. Heat transfer intensification techniques for shell and tube heat exchanger As mentioned above, the novelty of this paper is to comprise different IHT techniques to maximize energy saving in HEN retrofit problems. Thus, in this section, the literatures of conventional intensification techniques for shell and tube heat exchanger are reviewed. Based on this, the intensified level of the presented techniques can be estimated, and consequently to be utilized in mathematical model in section 3. Since shell and tube heat exchanger is most widely used in petrochemical industries, it is assumed that heat recovery in the paper is based on heat transfer through shell and tube exchanger type. Thus, according to the geometry characteristics of this exchanger type, the relevant intensification techniques can be grouped into two parts, tube-side and shell-side, which are presented in details as follows.

M. Pan et al. / Applied Thermal Engineering 53 (2013) 373e386

2.1. Tube-side intensification Plenty of research works have been carried on tube-side intensification in recent years. According to the classification of tube-side intensification (additional devices and special tube geometries), Wang and Sunden [20], and Garcia et al. [21] stated that the most frequently used insert devices in engineering applications are twisted-tape and coiled-wire. Both types of inserts become candidates to update an existing tube exchanger due to their low associated costs. On the other hand, the most popular form of surface enhancement used in industry is internal fins [22]. Generally, utilizing insert devices and surface fins simultaneously to produce an enhancement might be larger than either of implementing them separately, which is termed compound augmentation. Fig. 1 shows the geometry characteristics of twisted-tape inserts, coiled-wire inserts and internal fins. 2.1.1. Twisted-tape inserts Twisted tapes are swirl flow devices that create rotating or secondary flow along the tube length. They consist of a thin strip of twisted metal with usually the same width as the tube inner diameter. The characteristic geometry of twisted-tape inserts are illustrated in Fig. 1(a). This type of inserts is often used in retrofit of existing shell and tube heat exchangers to upgrade their heat duties. Many authors have reported high levels of enhancement for twisted tapes used in laminar flow. Marner and Bergles stated that the performance of twisted tapes for cooling highly viscous fluids in laminar flow exceeded that of internally finned tubes [23]. Rahimi et al. expressed that the role of twisted tapes in increasing turbulence intensity is more significant at lower velocities, in comparison with conditions where the fluid regime is turbulent [24]. However, the reported high levels of pressure drop were expected for this type of insert at low fluid velocities. Al-Fahed et al. described that in laminar flow twisted tapes show substantial increase of friction over that of plain and micro-fin tubes [25]. Moreover, Manglik and Bergles indicated that the friction factor depends primarily on the Reynolds number (Re) and the swirl number. The increase in the swirl flow gives a resultant increase in the friction factor [26]. In turbulent flow, the magnitude of twisted-tape enhancement is generally constant. Manglik and Bergles observed that twisted tapes have a much larger effect on heat transfer if Re is low [26]. The authors explained for Re10,000 that the smooth tube flows were characterized by a well-mixed fluid motion that promoted high heat transfer rates. Consequently, the superimposed tapegenerated swirl flow will have relatively little influence in further agitating the flow. Furthermore, in turbulent flow, twisted tapes

a

present a large pressure drop penalty. This effect is caused by the flow blockage produced by the insert. Additionally, tape thickness is a key parameter to enhance the heat transfer coefficient, but as thickness increases, more pressure drop is caused by the insert. Thus, it can be concluded that a high pressure drop penalty is a consequence of twisted tapes disturbing the entire flow field. The approximately constant trend of the DPei/DPi (DPei: tube-side pressure drop after intensification, (DPi: tube-side pressure drop before intensification) curves is an expected behaviour, which is also reported by Wang and Sunden [20]. They concluded that the friction factor penalty was almost independent of Re. 2.1.2. Coiled-wire inserts Wire coils are tube inserts that act as roughness elements. They induce a swirl effect and hasten the transition from laminar to turbulent flow. Fig. 1(b) presents an image of coiled-wire inserts in a smooth tube, and illustrates its geometry. Coiled-wire inserts are usually used in oil cooling devices, pre-heaters or fire boilers. Their advantages over other enhancement techniques include: low cost, easy installation and removal, preservation of original tube mechanical strength, and possibility of installation in an existing heat exchanger. In laminar region, Kurman [27] have obtained the maximum intensification for the tube-side heat transfer coefficient between 105% and 687%, representing an intensified ratio (hei/hi) of 2.05e7.87, and the minimum intensified ratio (hei/hi) between 1.38 and 3.06. Addressing pressure drop penalty, Garcia et al. [21] found that moderate friction factor augmentations were observed for pure laminar flow conditions, and suggested that coiled-wire fitted inside tubes behave mainly as a smooth tube in the laminar regime. In laminar flow, twisted tapes showed much better heat transfer enhancement than wire coils. Nevertheless, wire coil inserts introduced much lower pressure drop. This was probably because twisted tapes disturb the entire flow field while wire coils mainly disturb the flow near the wall. In turbulent flow, the maximum intensification for the tube-side heat transfer coefficient is in the range of 143e175%. The corresponding maximum pressure drop increases between 691 and 737% over that of the smooth tube [27]. These values correspond to an enhancement ratio (hei/hi) of 2.4e2.8 and a pressure drop ratio (DPei/DPi) of 7.9e8.4. Garcia et al. [21] obtained similar results, and stated that in turbulent flow coiled-wire inserts showed considerable heat transfer augmentations and caused a high pressure drop increase, which mainly depended on pitch to wire diameter ratio. More recent developments have also reported values within the same range, e.g. Eiamsa-ard et al. [28]. The intensification provided by coiled-wire inserts could be attributed

b

c

Tube Twisted-tape inserts

375

Tube

Tube

Internal nal fi ffins ns

Coiled-wire inserts

Twisted-tape inserts

Coiled-wire inserts

Internal fins

Fig. 1. The illustrations of tube-side intensification (twisted-tape inserts, coiled-wire inserts and internal fins).

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M. Pan et al. / Applied Thermal Engineering 53 (2013) 373e386

to better and faster mixing of the turbulent flow due to thinning or interruption of the thermal boundary layer and rising turbulence intensity imparted to the flow between the wire coils. 2.1.3. Internal fins Internally finned tubes are one of the most widely used methods for passive heat transfer intensification. Many geometric configurations for fins are proposed in the literature. In this paper, microfins are investigated (Fig. 1(c)), which are chosen because they have the advantage of combining with other forms of tube-side intensification, such as twisted-tape or coiled-wire. In general, microfins increase the heat transfer area in tube-side but do not effect the development of the flow pattern. In laminar region, Al-Fahed et al. [25] only found a relatively small increase in heat transfer over the plain tube. The increase was in the order of 4%, which was within the uncertainty limit of the data. On the other hand, they also encountered almost no increase in friction factor data for micro-fin tubes over that of the plain tube. Moreover, Jensen and Vlakancic [29] stated that friction factors are insensitive if Re  20,000. They concluded that this specific geometry is not recommended in laminar flow. In turbulent flow, up to 55% enhancement of the tube-side heat transfer coefficient was found by Kurman [27]. Al-Fahed et al. [30] and Brognaux et al. [31] observed that when Re increased, intensified pressure drop increased slightly at first, then reached a plateau, and finally decreased. Moreover, Jensen and Vlakancic [29] found that, until about Re ¼ 20,000, the enhanced friction factor was insensible to Re, after this value it began to decrease with increasing Re. Zdaniuk et al. [22] also carried out experiments for different finned tube geometries. Their results indicated a decrease of the friction factor with increasing Re. 2.1.4. Tube-side intensification without pressure drop penalty The increase of tube-side pressure drop is a major concern when using heat transfer intensified techniques. Intensification methods, such as twisted-tape inserts, coiled-wire inserts and internal fins, have a positive effect on heat transfer intensification, but increase the pressure drop penalty inside the tubes. Zhu et al. [32] stated that pressure drop reduction could be one of the advantages of tube-side IHT techniques, if higher heat transfer coefficients can be achieved for smaller fluid velocities. Thus, if pumping or compression power is a key constraint, heat exchanger geometry modifications should be performed to reduce flow velocity and compensate for the increased pressure drop introduced by the enhancement devices.

One of the proposed modifications is reducing the number of tube passes (Np), which leads to lower tube-side flow velocity. Kurman [27] have used the reduced Np method to evaluate the intensified performances of twisted-tape inserts, coiled-wire inserts and internal fins in several practical exchangers. It was found that, based on the Np reduction and the constraint of DPei/ DPi ¼ 1, twisted-tape inserts could obtain the maximum enhancement of 5%, the enhancement of coiled-wire inserts can be up to 54%, internal fins, acting as integral part of the tube-side heat transfer area, achieved 55% heat transfer enhancement and increased heat transfer area significantly. 2.2. Shell-side intensification The most commonly used intensified heat transfer technologies for shell and tube heat exchangers are extended surfaces, rough surfaces and mechanical. The ones related to the shell-side are extended surfaces (e.g. external fins) and various baffle configurations (e.g. helical baffles). The most commonly used baffle technology is the segmental baffle. The conventional segmental baffle improves the heat transfer in the exchanger shell-side, however, suffers from some significant problems such as high shell-side pressure drop, low shell-side mass flow velocity, fouling and vibration. More recently, different types of helical baffles have been developed to overcome the drawbacks of the conventional baffles. Improved shell-side heat transfer coefficient, low pressure drop, low possibility of flowinduced vibration, and reduced fouling with a trivial increase in pumping are the outstanding advantages of helical baffles. Furthermore, the introduction of external fins on plain tubes is an efficient way to increase the external interface area between tube wall and shell-side fluid, which helps to offset the lower shell-side heat transfer coefficient. Thus, the combination of implementing helical baffles and external fins is usually considered to improve exchanger performance in shell-side. Fig. 2 shows the geometry characteristics of helical baffles (continuous and non-continuous) and external fins. 2.2.1. Helical baffles (continuous and non-continuous) Helical baffles are usually made by joining four elliptical sectorshaped plates in succession and then arranging them in a pseudohelical manner. Each baffle occupies one-quarter of the cross section of the heat exchanger, and is angled to the axis of the heat exchanger. Any two adjacent baffles can then be joined end to end to form a continuous helical baffle as demonstrated in Fig. 2(a).

Fig. 2. The illustrations of shell-side intensification (continuous helical baffles, non-continuous helical baffles and external fins).

M. Pan et al. / Applied Thermal Engineering 53 (2013) 373e386

Another way of connecting the adjacent sector-shaped plates is through a non-continuous configuration as shown in Fig. 2(b), where plates are overlapped. In principal, introducing continuous helical baffles as shell-side intensification tend to promote a smoother flow pattern for the shell-side fluid when compared to the existing structure used of segmental baffles. It is noted that, a segmental baffle can be regarded as an extreme case of a helical baffle where the helix angle is set to zero. Theoretically, a smoother flow pattern of shell-side fluid will inevitably lead to a lower shell-side pressure drop and heat transfer coefficient. Hence, shell-side pressure drop is directly proportional to its heat transfer coefficient [33]. However, regarding high viscous fluid, Elsiedig found that the higher the viscosity of the fluid, the better it responses to heat transfer intensification with helical baffles [34]. This is essentially because of the superior surface film thickness that the fluid exhibits at higher viscosities. This outcome is in a great agreement with the literature [35] describing the significant increase in the heat transfer efficiency of helical baffles for higher viscous fluids. Likewise, non-continuous baffles can smooth the shell-side fluid flow, and therefore, reduce the heat transfer coefficient as the pressure drop of the shell-side is decreased subsequently. Similar to the continuous baffles structure, the higher shell-fluid viscosity, the better it responses to heat transfer enhancement and pressure loss. Elsiedig [34] also found that non-continuous helical baffles showed superior performance to that of continuous baffles. This superiority in performance is mainly owed to two reasons. First of all, the structural design of the non-continuous baffles is more effective in forcing the fluid to flow in a helical rotational passage (Fig. 2(a) and Fig. 2(b)). For the same shell inner diameter and helical angle, the non-continuous design exhibits a lower helical pitch, and therefore the shell-side fluid has to flow through more rotational passes per unit length of the heat exchanger, leading to higher local heat transfer coefficient when compared to the continuous design. Secondly, although the tighter design of non-continuous baffles pushes the pressure drop to higher levels compared to the continuous design by further imposing the perpendicular fluid flow on the tube walls, this increase in pressure level has been proven to be quite insignificant. Average enhancement ratios of 1.15 and 1.3 (he0/h0) for continuous and non-continuous baffles can be concluded based on Elsiedig’s case study [34]. Although the average values of these enhancement ratios do not provide an absolute indication on the maximum enhancement level achievable in each exchanger, it provides a quick, simple and reasonably reliable basis for comparison between the various intensified techniques that is not only strictly valid for one particular HEN, but rather generic to go well with any HEN experiencing retrofit. 2.2.2. External fins The externally finned tube used in shell and tube heat exchangers is often referred to as radial low-fin tube. It is made by an extrusion process in which the wall of a plain tube is depressed by stacks of disks. The undisturbed portion of the tube wall between the disks forms the fins. The fins are actually helical rather that radial, but they can be approximated as radial (annular) fins of rectangular profile for computational purpose [36]. Fig. 2(c) presents the geometric characteristics of an externally finned tube. External fins are used to increase the heat transfer capacity by increasing the tube surface area while keeping constant exchanger size. LMTD can be reduced for a given exchanger surface area, hence, the thermodynamic efficiency of the process is improved. Elsiedig [34] have concluded some guidelines from the performance evaluation of external fins in case studies. First, the

377

sensitivity of an external finned tube heat exchanger is usually affected by the viscosity of the shell-side fluid. Secondly, the tube density (number of tubes to pitch ratio) should be maintained at a reasonable ratio to prevent an excessive reduction in the shellside cross-flow area. Based on his research, almost all exchangers can achieve enhancement of 60% or more of their initial value without having a significant effect on pressure drop increase. Thus, a maximum enhancement of 1.6 would be considered as the upper limit for intensifying a heat exchanger by using external fins. 3. MILP-based optimisation model The new MILP model is mainly based on the model reported by Pan et al. [18], however, a new optimisation framework has been significantly upgraded to address tube-side and shell-side intensifications simultaneously. The modelling of HEN with IHT includes various equations related to heat transfer between streams, for example, intensification of heat transfer, energy balance, heat exchange between hot streams and cold streams, stream temperatures and LMTD. Equations for calculating the LMTD are nonlinear but treated as fixed parameters by fixing stream temperature for the heat exchange, and the LMTD is sequentially updated with an iterative procedure [18]. 3.1. Initial LMTD [18] 0

The initial LMTD (LMTD ) can be calculated with the stream 0 , HTO0 , CTI 0 and CTO0 ) which are fixed in the temperatures (HTIex ex ex ex beginning, as shown in Eq. (1), where EX is the set of all exchangers, 0 and HTO0 HTIex ex are inlet and outlet initial temperatures of hot 0 and CTO0 are inlet and outlet stream in exchanger ex, while CTIex ex initial temperatures of cold stream in exchanger ex.

LMTD0ex ¼



 0 HTI0  CTO0ex  HTO0ex  CTIex 
ex 
; cex˛EX 0  CTO0 0 ln HTIex HTO0ex  CTIex ex

(1)

3.2. Intensified heat transfer In this paper, clean exchangers are assumed, and the calculations of their overall heat transfer coefficients are simplified as follows:

DUex ¼ DTUex þ DSUex ;

cex˛EX

(2)

where DTUex, DSUex and DUex are the reciprocal values of tube-side, shell-side and the overall heat transfer coefficient for exchanger ex, respectively. Based on Eq. (2), the overall heat transfer coefficient of each exchanger (Uex) is obtained:

Uex ¼ 1=DUex ;

cex˛EX

(3)

Note that Eq. (3) is nonlinear, to linearize the nonlinear term, first order Taylor series expansions are utilized, as presented in Eqs. 0 0 and DUex are the initial values of Uex and DUex, (4)e(6). Uex respectively. Positive variables, AUex and BUex are remainder terms, and should be very small, which is to be formulated in the objective function.


0 2
 0 0 Uex ¼ Uex þ ð1Þ  DUex  DUex  DUex ;

cex˛EX

(4)

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M. Pan et al. / Applied Thermal Engineering 53 (2013) 373e386

0 AUex  Uex  Uex ;

cex˛EX

(5)

0 BUex  Uex  Uex ;

cex˛EX

(6)

To select suitable exchangers for intensification, two sets of binary variables are proposed: ETEXex.ti ¼ 1, if the tith type of tube-side intensification is implemented in exchanger ex; otherwise, it is 0. ESEXex.si ¼ 1, if the sith type of shell-side intensification is implemented in exchanger ex; otherwise, it is 0. In this paper, the addressed types of tube-side intensification include non-intensification, twisted-tape inserts, coiled-wire inserts, internal fins, the combination of twisted-tape and internal fins, and the combination of coiled-wire and internal fins. While for shell-side intensification, non-intensification, helical baffles, external fins, and the combination of helical baffles and external fins are considered. Eqs. (7) and (8) and Eqs. (9) and (10) restrict the tube-side and shell-side heat transfer coefficients with or without intensification.

DTUex  MINDTUex;ti  ETEXex;ti ;

cex˛EX;

ti˛TI

DTUex  MAXDTUex;ti  ETEXex;ti ;

cex˛EX;

ti˛TI

DSUex  MINDSUex;si  ESEXex;si ;

cex˛EX;

DSUex  MAXDSUex;si  ESEXex;si ;

cex˛EX;

(7)

X

i cex˛EXcs ;

cs˛CS

ðCMFex  CTOex Þ ¼ CSTOcs ;

(13)

cs˛CS

(14)

ex˛EXocs

HTIex ¼ HSTIhs ; X

i cex˛EXhs ;

hs˛HS

ðHMFex  HTOex Þ ¼ HSTOhs ;

hs˛HS

(15)

(16)

ex˛EXohs

Eqs. (17) and (18) restrict the minimum temperature difference approach (DTmin) in each exchanger,where HTOex is outlet temperature of hot stream in exchanger ex, CTOex is outlet temperature of cold stream in exchanger ex.

cex˛EX

(17)

(8)

HTOex  CTIex þ DTmin ;

cex˛EX

(18)

si˛SI

(9)

3.4. Heat transfer differences [18]

si˛SI

(10)

ETEXex;ti ¼ 1;

cex˛EX

(11)

ESEXex;si ¼ 1;

cex˛EX

(12)

ti˛TI

X

CTIex ¼ CSTIcs ;

HTIex  CTOex þ DTmin ;

where TI and SI are the sets of all types of tube-side and shell-side intensification, MAXDTUex,ti and MINDTUex,ti are the upper and lower bounds of the reciprocal value of tube-side heat transfer coefficients if the tith type of tube-side intensification is implemented in exchanger ex, while MAXDSUex,si and MINDSUex,si are the upper and lower bounds of the reciprocal value of shell-side heat transfer coefficients if the sith type of shell-side intensification is implemented in exchanger ex. In addition, only one type of intensification can be implemented in tube-side and shell-side in an exchanger, as shown in Eqs. (11) and (12).

X

target temperature (CSTOcs or HSTOhs); CSTIcs and CSTOcs are inlet and outlet temperatures of cold stream cs in the whole network, while HSTIhs and HSTOhs are inlet and outlet temperatures of hot stream hs in the whole network, CTIex is inlet temperature of cold stream in exchanger ex, HTIex is inlet temperature of hot stream in exchanger ex.

In Eqs. (19) and (20), the heat transfer in each exchanger is estimated based on LMTD0ex , thus there might be some differences for energy exchange between streams and exchangers. HBAex and HBBex are positive variables, and present these differences. For energy balance between streams and exchangers, HBAex and HBBex should be small and the objective function has been formulated to minimize the sum of this infeasibility in energy balances. In addition, HFCPex and CFCPex are heat-flow capacities (the multiplication between heat capacity and flow-rate) of hot stream and cold stream in exchanger ex, and EXAex is heat transfer area of exchanger ex.

HBAex  HFCPex  ðHTIex  HTOex Þ  EXAex  Uex  LMTD0ex ; cex˛EX

ð19Þ

HBBex  EXAex  Uex  LMTD0ex  HFCPex  ðHTIex  HTOex Þ; cex˛EX ð20Þ

si˛SI

3.5. Energy balance differences [18] 3.3. Stream temperature constraints [18] Eqs. (13)e(16) represent the constraints regulating the stream temperatures in the inlet and outlet of the whole network, where CS and HS are the set of all cold streams and hot streams, i , EXo i respectively; EXcs cs, EXhs and EXohs describe the set of all exchangers located in the network inlet or outlet; CMFex and HMFex are flow fraction of cold and hot streams in exchanger ex, which presents the flow fractions of parallel exchangers (if single exchanger is used, its flow fraction is equal to 1), and restricts that the stream outlet temperature must be equal to the network

Due to the energy balance in heat exchangers, the heat duties of cold stream and hot stream should be the same. However, as stated in Section 3.4, different arrangement of heat transfer through intensification may lead to heat duty differences between cold stream and hot stream in exchangers. Eqs. (21) and (22) are proposed to describe differences in energy balances, and the variables, AEBex and BEBex, are positive and should be small.

AEBex  HFCPex  ðHTIex  HTOex Þ  CFCPex  ðCTIex  CTOex Þ; cex˛EX

ð21Þ

M. Pan et al. / Applied Thermal Engineering 53 (2013) 373e386

BEBex  CFCPex  ðCTIex  CTOex Þ  HFCPex  ðHTIex  HTOex Þ; cex˛EX ð22Þ

379

variables (addressed in Section 3.6) with the restriction of an 0 estimated energy saving value (QS ), as shown in Eqs. (36) and (37).

QS  QS0 3.6. Variable differences

Obj ¼ Since heat transfer coefficients in some exchangers change, differences between initial stream temperatures and updated stream temperatures are existed, which is represented in Eqs. (23) and (24) using positive variables DAHTIex and DBHTIex [18]. 0 HTIex ;

cex˛EX

(23)

 HTIex ;

cex˛EX

(24)

DAHTIex  HTIex  DBHTIex 

0 HTIex

Meanwhile, differences between initial and updated temperatures for hot stream outlet (DAHTOex and DBHTOex), cold stream inlet and outlet (DACTIex, DBCTIex, DACTOex and DBCTOex) are formulated in the same way [18].

DAHTOex  HTOex  HTO0ex ;

cex˛EX

(25)

DBHTOex  HTO0ex  HTOex ;

cex˛EX

(26)

0 ; DACTIex  CTIex  CTIex

cex˛EX

(27)

0 DBCTIex  CTIex  CTIex ;

cex˛EX

(28)

DACTOex  CTOex  CTO0ex ; DBCTOex 

CTO0ex

 CTOex ;

BUex 

0 Uex

cex˛EX

(30)

cex˛EX

(31)

 Uex ;

cex˛EX

(32)

0 ; ADUex  DUex  DUex

cex˛EX

(33)

0  DUex ; BDUex  DUex

cex˛EX

(34)

3.7. Energy saving [18] Eq. (35) presents energy saving (QS) achieved in the HEN, where EXhu and EXcu are the set of all exchangers consuming hot and cold utilities; OCTIex and OHTIex are the inlet temperatures of cold stream and hot stream in exchanger ex in original HEN.

QS ¼

 X  CFCPex  ðCTIex  OCTIex Þ þ HFCPex

ex˛EXhu



þ AUex þ BUex Þ þ

X

ðDAHTIex þ DBHTIex þ DAHTOex

e˛EX

X

þ DBHTOex þ ADUex þ BDUex Þ þ

ðHBAex þ HBBex

e˛EX

þ AEBex þ BEBex Þ

ð37Þ

The new MILP optimisation framework model consists of an objective function given in Eq. (37) and model constraints given from Eqs (1), (2), and (4)e(36). Contrary to the conventional retrofit models, the model proposed is able to find a feasible retrofit solution for achieving certain energy saving in Eq. (36), which requires an iteration loop to update the initial values of model variables, and solve the updated model repeatedly until the objective value in Eq. (37) is close to 0. Once a feasible retrofit solution is found, the estimated value in Eq. (36) will increase gradually in another iteration loop to find the maximum energy saving for all potential retrofit solutions. These two iteration loops are introduced in details in the next section.

(29)

0 Uex ;

X 

ðDACTIex þ DBCTIex þ DACTOex þ DBCTOex

e˛EX

4. Iteration algorithm for optimisation

cex˛EX

In Eq. (3) of calculating overall heat transfer coefficient, initial 0 and DU 0 have been used for linearization, thus, the values, Uex ex differences between initial and updated values of heat transfer coefficient have to been considered as well. AUex and BUex are positive variables and present the differences for Uex, while positive variables, ADUex and BDUex present the differences for DUex.

AUex  Uex 

X

(36)

ex˛EXcu

 ðOHTIex  HTIex Þ (35) 3.8. Objective function The objective of the new MILP-based method is to minimize the summation of differences in energy balances, heat transfers and the

The iterative procedure initially proposed by Pan et al. [18] has been extended to consider tube-side and shell-side intensification simultaneously, which allows finding the optimal retrofit solutions. The first iteration loop is to find the feasible solution for HEN retrofit under certain energy saving (an initial estimated value QS0 in Eq. (36)), while the second iteration loop is to find the maximum energy saving for HEN retrofit. 4.1. The first iteration loop e finding feasible solution (Loop 1) As mentioned in section 3, the objective of new MILP model is to minimize energy balance differences, heat transfer differences, and the differences between initial and updated variables, which cannot be small as the initial situation (i.e. no energy saving, QS ¼ 0) usually distinguishes from the expected retrofit solution (i.e. certain energy saving, QS  QS0 ). Thus, an iteration loop (Loop 1) is needed to update the initial variables with the calculated variables from the MILP model, and repeatedly run the model until the addressed differences in Eq. (37) are small enough, namely achieving feasible solution. It can be noted that, heat transfer coefficients are considered and updated in the procedure, as shown in Steps 6 and 7, which is different to the procedure proposed by Pan et al. [18]. Step 1: Calculate LMTD0ex based on the stream initial tempera0 , HTO0 , CTI 0 and CTO0 ). tures (HTIex ex ex ex Step 2: Solve an MILP model to minimize an objective value (Eqs. (1), (2), and (4)e(37)). Step 3: Obtain the new streams temperatures (HTIex, HTOex, CTIex and CTOex) from the MILP model. Step 4: Calculate LMTDex with the new stream temperatures. If LMTDex is infeasible with new stream temperatures, LMTDex takes LMTD0ex . Step 5: Calculate difference between LMTD and LMTD0ex . Step 6: Obtain differences in energy balances, heat transfers, stream temperatures and heat transfer coefficients.

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M. Pan et al. / Applied Thermal Engineering 53 (2013) 373e386

Step 7: If the summation of differences given in Step 5 and Step 6 are small enough, terminate the procedure; otherwise, update the new LMTD00ex as LMTD00ex ¼ ðLMTD0ex þ 00 as U 00 ¼ ðU 0 þ 1=DU Þ=2, and execute LMTDex Þ=2; new Uex ex ex ex from Step 2 to Step 7 iteratively.

Assume an initial small value of energy saving (QS’) Execute Loop 1

Fig. 3 presents the iterative procedure of Loop 1.

If feasible solution is found in Loop 1

4.2. The second iteration loop e finding maximum energy saving (Loop 2)

No

Stop

Yes Obtain the new energy saving (QS)

The second iteration loop is the same as that proposed by Pan et al. [18]. When Loop 1 finds the solution for HEN retrofit under initial estimated energy saving, Loop 2 will gradually increase the value of energy saving (QS0 in Eq. (36)) and execute Loop 1 until the maximum energy saving is found. Fig. 4 presents that, if Loop 1 can find a feasible solution under the initial assumed energy saving 0 0 (QS ), QS can increase, and Loop 1 will run to find whether there is a feasible solution for the lager QS0 ; once one feasible solution can 0 0 be found in Loop 1 under the updated QS , QS will increase, and 0 Loop 1 runs again until QS reaches its maximum value. 5. Case studies Fig. 5 presents an existing pre-heat train for a crude oil distillation column in a refinery plant. The retrofit objective is to reduce the hot utility (HU) consumption, namely, reduce the heat duty of

Gradually increase QS’ (QS’ > QS) Fig. 4. The procedure of Loop 2.

heat exchanger 30 (target exchanger). The stream data and initial exchanger data can be found in Table 1 and Table 2. The minimum temperature difference approaches (DTmin) before and after heat transfer intensification are 19  C and 5  C. To evaluate the new method, two parts of work are carried out in this section. In the first part, only overall heat transfer is considered for exchanger intensification, and thus the new method can be compared with the added-area method and heuristic method [19] fairly. In the second part, different intensified

Input initial stream temperatures Calculate LMTD’ex based on the initial temperature Solve the MILP problem to minimize Obj Obtain new stream temperatures (HTIex, HTOex, CTIex, CTOex) Calculate LMTDex based on the new temperatures (If LMTDex is infeasible, LMTDex = LMTD’ex) Calculate the difference between LMTD and LMTD’ex Obtain the differences of energy balance, heat transfers, stream temperatures and heat transfer coefficients (AEBex, BEBex, HBAex, HBBex, DAHTIex, DBHTIex, DAHTOex, DBHTOex, DACTIex, DBCTIex, DACTOex, DBCTOex, ADUex, BDUex, AUex, BUex)

If above differences are small enough

Yes Stop

No LMTD’’ex →LMTD’ex (LMTD’’ex = (LMTD’ex+ LMTDex)/2) U’’ex →U’ex (U’’ex = (U’ex+ 1/DUex)/2) Fig. 3. The procedure of Loop 1.

M. Pan et al. / Applied Thermal Engineering 53 (2013) 373e386

12 6

13

20

18

C1

1

5 3

CMF17 = 0.5 21

381

CMF3 = 0.5 C2

17 16

30 29

28 27 26 24

23

4

H1

C3

22

17

H2

15

24 20

H3

31 16

26

2

H4

5

H5

22 12

H6 H7

3 29

8

9

2 25 31 19 15 14 7 11 10 8

9

14

13

27

H8

28

25 4 18

H9

19

H10 H11

7

1

23

10

21

6

11

HU 30

Hot stream: H

Hot utility: HU

C

Cold stream:

Cold utility:

CU

CU

Fig. 5. An existing pre-heat train for a crude oil distillation column in a refinery plant.

techniques are taken into account in details, and the economic benefits of the proposed approach are illustrated.

adding heat transfer areas, because of no fundamental changes in the structure of exchangers and heat recovery networks [37]. The cost of implementing intensified heat transfer in the exchanger is estimated as 1000 þ 200  (Area) ($), while the cost of adding more heat transfer area to the exchanger is expressed as 3460 þ 171.4  (Area) ($) [10]. Table 4 only shows difference in expenditure for the capital cost of heat transfer intensification and heat exchanger area added to the existing exchanger. However, it should be noted that considerable investment is additionally required for piping and reconfiguring the layout of HEN when new area of heat exchangers is introduced. Wang et al. [19] stated that their heuristic approach can find the most appropriate candidate for requiring heat transfer enhancement, namely, exchangers 20, 24, 26 and 28. But, with the new mathematical approach, enhancing exchangers 16, 20, 24 and 28 can save more energy when only four exchangers are only allowed for the intensification in the optimisation As shown in Table 5, heat transfer coefficients increase in the targeted exchangers (exchangers 20, 24, 26 and 28 in heuristic solution, and exchangers 16, 20, 24 and 28 in optimal solution), all exchangers remain unchanged area, and the optimal solution based on the new approach requires less hot utility (52,650 kW vs. 52,729 kW). It is noted that the new proposed method can find the most appropriate heat exchangers for enhancement.

5.1. Intensification with direct increase in overall heat transfer In this section, intensified technique is implemented to directly increase the overall heat transfer coefficients of enhanced exchangers. It is assumed that the maximum intensified coefficient of each exchanger is 1.5 times of its original value. Based on the proposed method, the optimal solution for HEN retrofit with IHT is obtained. The details of optimal retrofitted HENs are shown in Table 3. The comparison of initial and retrofitted HENs (Tables 2and 3) shows that the optimal solution can save up to 6.14% of hot utility consumption. As shown in Table 3, the optimal solution includes 14 exchangers for heat transfer enhancement, without any additional area and topology modification. For example, the heat transfer coefficient of exchanger 4 increases with intensified heat transfer from 0.282 to 0.423 kW/m2  C, and its heat transfer area remains unchanged (175 m2). With fourteen exchangers are intensified, the duty of the hot utility exchanger (exchanger 30) is reduced from 54.703 MW to 51.3 MW (i.e. 6.14% of reduction). The optimisation result is compared with the case where heat transfer area is added (Table 4). Implementing intensified heat transfer techniques requires much lower investment cost than

Table 1 Stream details in case studies. Stream

C1

C2

C3

H1

H2

H3

H4

H5

H6

H7

H8

H9

H10

H11

HU

CU

FCP (kW/ C) Tin ( C) Tout ( C)

323 33.5 95.6

358.5 91.34 157.3

474 151 352

14.2 335 69.4

181.5 253.2 116.1

113 294 130

100 212 156

22.2 213 61.7

39.5 174 43.3

28 364 65.6

176 290 211

24.5 284 65.6

25 240 57.8

69.6 179 69.3

93 1500

9652.5 12.45

FCP: heat-flow capacities (the multiplication between heat capacity and flow-rate). Tinlet, Toutlet: stream temperatures in HEN inlet and outlet.

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M. Pan et al. / Applied Thermal Engineering 53 (2013) 373e386

Table 2 Exchanger details of original HEN in case studies. EXs

HTIex ( C)

HTOex ( C)

CTIex ( C)

CTOex ( C)

LMTDex ( C)

EXAex (m2)

Duty (kW)

hi (kW/m2  C)

h0 (kW/m2  C)

Uex (kW/m2  C)

Max available Uex (kW/ m2  C) Section 5.1

Section 5.2

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

117.2 131.2 174.4 284.2 212.4 174.4 66.3 76.7 62.2 171.1 85.7 169.1 221.1 147.2 109.3 198.4 335.4 174.7 139.7 206.2 178.7 212.7 240.1 253.2 222.7 293.7 249.0 290.4 364.3 1500.0 141.9

66.3 130.0 76.7 174.7 156.1 85.7 61.7 62.2 43.3 57.8 69.3 117.2 147.2 65.6 69.4 131.2 109.3 139.7 65.6 141.9 174.4 169.1 171.1 206.2 210.9 198.4 221.1 222.7 249.0 912.5 116.1

33.5 14.2 33.5 156.7 49.0 66.5 13.0 12.5 12.5 12.6 12.9 85.6 89.2 13.0 13.2 91.3 91.3 121.5 13.3 123.9 156.4 151.1 153.1 162.4 14.0 180.4 203.1 204.7 229.9 236.7 13.5

40.5 14.2 57.5 162.4 66.5 85.6 13.0 12.6 12.5 12.9 13.0 89.2 95.6 13.2 13.3 133.7 109.2 123.9 13.5 156.4 157.3 153.1 156.7 180.4 14.2 203.1 204.7 229.9 236.7 351.9 14.0

51.7 116.4 74.0 54.3 125.5 45.5 50.9 56.6 39.5 90.2 64.2 52.1 87.5 87.0 74.3 51.3 82.2 31.8 83.9 31.2 19.7 34.7 42.6 57.1 202.7 44.9 29.2 35.1 57.1 891.2 114.8

175.0 11.7 116.7 175.0 100.0 650.0 20.0 30.0 55.6 277.8 55.6 22.2 38.1 85.7 42.9 128.6 207.7 207.7 138.5 1384.6 27.7 83.1 41.5 1038.5 66.7 300.0 233.3 1020.0 240.0 180.0 60.0

1130.8 139.8 3860.3 2682.0 5633.4 6176.5 102.4 571.6 745.4 2832.8 1141.5 1150.6 2069.2 2285.9 566.6 7586.7 3210.1 858.6 1816.1 11684.2 296.2 968.6 1724.4 8525.4 2085.1 10771.6 780.5 11903.4 3228.0 54633.2 4683.1

0.250 0.202 0.894 0.565 0.898 0.418 0.205 0.672 0.678 0.226 0.639 1.989 1.243 0.613 0.354 2.300 0.376 0.260 0.313 0.540 1.088 0.671 1.947 0.288 0.309 1.599 0.229 0.666 0.471 0.681 1.362

0.250 0.202 0.894 0.565 0.898 0.418 0.205 0.672 0.678 0.226 0.639 1.989 1.243 0.613 0.354 2.300 0.376 0.260 0.313 0.540 1.088 0.671 1.947 0.288 0.309 1.599 0.229 0.666 0.471 0.681 1.362

0.125 0.101 0.447 0.282 0.449 0.209 0.102 0.336 0.339 0.113 0.320 0.994 0.622 0.307 0.177 1.150 0.188 0.130 0.156 0.270 0.544 0.336 0.974 0.144 0.154 0.799 0.115 0.333 0.235 0.341 0.681

0.188 0.152 0.671 0.423 0.673 0.313 0.154 0.504 0.508 0.170 0.479 1.492 0.932 0.460 0.265 1.725 0.282 0.195 0.235 0.405 0.816 0.503 1.461 0.216 0.231 1.199 0.172 0.499 0.353 0.511 1.021

0.213 0.172 0.760 0.480 0.763 0.355 0.174 0.571 0.576 0.192 0.543 1.690 1.057 0.521 0.300 1.955 0.319 0.221 0.266 0.459 0.925 0.570 1.655 0.244 0.262 1.359 0.195 0.566 0.400 0.579 1.157

EXs: exchangers; HTIex and HTOex: inlet and outlet temperatures of hot streams in exchanger ex; CTIex and CTOex: inlet and outlet temperatures of cold streams in exchanger ex; LMTDex: logarithmic mean temperature difference in exchanger ex; EXAex: heat transfer area of exchanger ex; hi and h0: tube-side and shell-side heat transfer coefficient; Uex: overall heat transfer coefficient of exchanger ex. Table 3 Exchanger details of optimal retrofitted HEN (new method) in Section 5.1. EXs

HTIex ( C)

HTOex ( C)

CTIex ( C)

CTOex ( C)

LMTDex ( C)

EXAex (m2)

Uex (kW/m2  C)

Duty (kW)

1 2 3 4 (intensified) 5 6 (intensified) 7 8 9 10 11 12 13 14 15 16 (intensified) 17 (intensified) 18 (intensified) 19 20 (intensified) 21 (intensified) 22 (intensified) 23 (intensified) 24 (intensified) 25 26 (intensified) 27 (intensified) 28 (intensified) 29 (intensified) 30 31

117.2 131.2 174.4 284.2 212.4 172.6 66.3 76.7 62.2 161.8 79.6 160.9 217.1 147.2 96.4 199.9 335.4 164.5 131.0 195.1 178.7 212.7 240.1 253.2 218.7 293.7 243.7 290.4 364.3 1500.0 133.2

66.3 130.0 76.7 164.5 156.1 79.6 61.7 62.2 43.3 57.8 69.3 117.2 147.2 65.6 69.4 131.2 96.4 131.0 65.6 133.2 172.6 160.9 161.8 195.1 210.9 199.9 217.1 218.7 243.7 948.4 116.1

33.5 13.8 33.5 157.6 49.0 66.5 12.9 12.5 12.5 12.6 12.9 86.5 89.5 12.9 13.2 91.3 91.3 122.5 13.2 124.8 156.1 151.1 153.5 163.8 13.7 186.0 208.4 210.0 236.6 243.7 13.4

40.5 13.9 57.5 163.8 66.5 86.5 12.9 12.6 12.5 12.9 12.9 89.5 95.6 13.2 13.2 134.7 110.3 124.8 13.4 156.1 157.3 153.5 157.6 186.0 13.8 208.4 210.0 236.6 243.7 351.9 13.7

51.6 116.7 74.0 39.7 125.5 38.8 51.0 56.6 39.5 87.0 61.4 48.2 85.7 87.1 68.9 51.5 58.1 20.3 80.6 20.0 18.9 27.5 32.4 47.0 201.0 39.4 18.5 24.8 40.1 908.4 110.9

175.0 11.7 116.7 175.0 100.0 650.0 20.0 30.0 55.6 277.8 55.6 22.2 38.1 85.7 42.9 128.6 207.7 207.7 138.5 1384.6 27.7 83.1 41.5 1038.5 66.7 300.0 233.3 1020.0 240.0 180.0 60.0

0.125 0.100 0.447 0.423 0.449 0.256 0.102 0.336 0.339 0.108 0.210 0.904 0.600 0.306 0.129 1.172 0.281 0.195 0.144 0.405 0.816 0.504 1.455 0.216 0.102 0.897 0.172 0.499 0.351 0.314 0.469

1131.2 136.2 3860.3 2933.1 5633.4 6469.5 102.0 571.6 745.4 2601.2 718.7 968.8 1957.6 2286.0 383.4 7766.4 3393.2 820.2 1603.5 11229.9 426.1 1150.4 1956.1 10541.2 1368.6 10595.6 743.9 12619.9 3376.0 51301.0 3121.6

EXs: exchangers; HTIex and HTOex: inlet and outlet temperatures of hot streams in exchanger ex; CTIex and CTOex: inlet and outlet temperatures of cold streams in exchanger ex; LMTDex: logarithmic mean temperature difference in exchanger ex; EXAex: heat transfer area of exchanger ex; Uex: heat transfer coefficient of exchanger ex.

M. Pan et al. / Applied Thermal Engineering 53 (2013) 373e386

383

Table 4 Comparison between implementing intensified heat transfer (IHT) and adding more heat transfer area (AHTA) in Section 5.1.

IHT AHTA

Area of targeted exchangers (m2)

Cost (Million $)

EX4 (175), EX6 (650), EX16 (128.6), EX17 (207.7), EX18 (207.7), EX20 (1384.6), EX21 (27.7), EX22 (83.1), EX23 (41.5), EX24 (1038.5), EX26 (300), EX27 (233.3), EX28 (1020), EX29 (240) EX4 (262.5), EX6 (796.2), EX16 (131.1), EX17 (310.4), EX18 (311.6), EX20 (2076.9), EX21 (41.6), EX22 (124.7), EX23 (62), EX24 (1557.8), EX26 (336.8), EX27 (348.9), EX28 (1528.5), EX29 (358.5)

1.16 1.46

Table 5 Comparison of retrofitted HENs between heuristic rules [19] and the new approach in Section 5.1. Retrofitted HEN (heuristic) [19] EXs

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

Retrofitted HEN (new approach)

Uex

EXAex

LMTDex

Duty

Uex

EXAex

LMTDex

Duty

(kW/m2 C)

(m2)

( C)

(kW)

(kW/m2  C)

(m2)

( C)

(kW)

0.125 0.103 0.443 0.219 0.449 0.208 0.101 0.337 0.339 0.113 0.320 0.962 0.618 0.307 0.149 1.012 0.161 0.130 0.156 0.348 0.544 0.336 0.911 0.155 0.100 1.200 0.115 0.448 0.235 0.325 0.483

175.0 11.7 116.7 175.0 100.0 650.0 20.0 30.0 55.6 277.8 55.6 22.2 38.1 85.7 42.9 128.6 207.7 207.7 138.5 1384.6 27.7 83.1 41.5 1038.5 66.7 300.0 233.3 1020.0 240.0 180.0 60.0

52.0 116.6 74.4 63.7 125.5 45.7 51.0 56.9 39.6 90.8 64.3 52.7 89.6 87.5 107.8 49.7 92.8 39.4 84.1 26.4 19.6 34.6 44.3 55.8 200.8 33.0 29.5 27.7 55.0 901.4 111.0

1138 140 3843 2443 5636 6174 103 575 746 2852 1143 1127 2107 2303 689 6473 3103 1064 1817 12700 296 966 1677 8982 1338 11895 791 12660 3101 52729 3217

0.125 0.100 0.443 0.282 0.449 0.207 0.101 0.337 0.339 0.113 0.320 0.972 0.618 0.307 0.149 1.231 0.168 0.130 0.156 0.403 0.544 0.336 0.974 0.209 0.104 0.740 0.115 0.444 0.235 0.325 0.487

175.0 11.7 116.7 175.0 100.0 650.0 20.0 30.0 55.6 277.8 55.6 22.2 38.1 85.7 42.9 128.6 207.7 207.7 138.5 1384.6 27.7 83.1 41.5 1038.5 66.7 300.0 233.3 1020.0 240.0 180.0 60.0

51.9 116.6 74.4 54.0 125.5 45.7 51.0 56.9 39.6 90.1 64.3 52.5 89.7 87.5 107.8 52.2 89.9 30.5 84.1 19.9 19.6 34.5 42.4 48.5 200.9 45.5 29.4 27.8 55.0 900.0 111.1

1135 136 3844 2662 5637 6149 103 575 746 2829 1143 1133 2109 2304 689 8265 3137 824 1817 11121 296 964 1715 10517 1393 10104 789 12603 3101 52650 3246

EXs: exchangers; LMTDex: logarithmic mean temperature difference in exchanger ex; EXAex: heat transfer area of exchanger ex; Uex: heat transfer coefficient of exchanger ex. Bold values represent intensified exchangers.

5.2. Intensification with consideration of detailed techniques In this part, various intensification techniques are considered simultaneously to improve energy saving in the whole network

while minimize retrofit cost. The detailed types of intensification include: tube-side (twisted-tape inserts, coiled-wire inserts, internal fins, the combination of twisted-tape and internal fins, and the combination of coiled-wire and internal fins), and shell-side

Table 6 Enhancement level and capital cost of each type of intensification, and the cost of adding more heat transfer area in Section 5.2. P Intensification techniques Intensification: Cost ¼ A þ (B  Area) ($) adding area: Cost ¼ A þ B  DArea ($) A Tube-side Twisted-tape inserts Coiled-wire inserts Internal fins Twisted-tape inserts & Internal fins Coiled-wire inserts & Internal fins Shell-side Helical baffles External fins Helical baffles & External fins Adding more heat transfer area

1000

3460

Max times of intensification

B 25 30 35 50 55

1.20 1.40 1.73 1.88 2.00

30 35 55 200

1.15 1.65 1.75

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M. Pan et al. / Applied Thermal Engineering 53 (2013) 373e386

Table 7 Exchanger details of optimal retrofitted HEN (new method) in Section 5.2. EXs

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

HTIex ( C)

HTOex ( C)

CTIex ( C)

CTOex ( C)

LMTDex ( C)

EXAex (m2)

Duty (kW)

hi (kW/m2  C)

h0 (kW/m2  C)

Uex (kW/m2  C)

114.3 130.2 174.4 284.2 212.4 174.6 65.2 76.6 62.1 169.2 85.7 169.7 218.4 146.3 109.3 184.1 335.4 174.9 138.9 212.0 178.7 212.7 240.1 253.2 213.3 293.7 239.3 290.4 364.3 1500.0 139.4

65.2 130.0 76.6 174.9 156.1 85.7 61.7 62.1 43.3 57.8 69.3 114.3 146.3 65.6 69.4 130.2 109.3 138.9 65.6 139.4 174.6 169.7 169.2 212.0 210.9 184.1 218.4 213.3 239.3 937.7 116.1

33.5 14.0 33.5 156.8 48.9 66.3 13.0 12.5 12.5 12.6 12.9 85.5 89.3 13.0 13.2 91.3 91.3 117.3 13.3 119.7 156.5 151.1 153.1 162.5 13.9 178.2 204.4 205.6 234.2 241.6 13.5

40.3 14.0 57.5 162.5 66.3 85.5 13.0 12.6 12.5 12.9 13.0 89.3 95.6 13.2 13.3 125.3 109.2 119.7 13.5 156.5 157.3 153.1 156.8 178.2 14.0 204.4 205.6 234.2 241.6 351.9 13.9

49.9 116.2 74.0 54.3 125.6 45.6 50.4 56.5 39.5 89.6 64.2 50.2 85.7 86.7 74.4 48.2 82.3 35.8 83.6 34.6 19.7 35.2 40.9 61.4 198.2 30.6 22.4 24.4 37.0 903.3 113.7

175.0 11.7 116.7 175.0 100.0 650.0 20.0 30.0 55.6 277.8 55.6 22.2 38.1 85.7 42.9 128.6 207.7 207.7 138.5 1384.6 27.7 83.1 41.5 1038.5 66.7 300.0 233.3 1020.0 240.0 180.0 60.0

1090 27 3864 2679 5633 6187 78 571 743 2786 1139 1229 2018 2261 567 6086 3210 882 1796 13170 288 955 1772 7481 424 12385 587 13565 3498 52296 4242

0.250 0.202 0.794 0.563 0.896 0.418 0.202 0.672 0.677 0.226 0.639 1.658 1.232 0.604 0.356 2.299 0.376 0.260 0.312 0.561 1.087 0.635 3.367 0.198 0.308 2.604 0.229 1.252 0.940 0.609 1.359

0.250 0.023 1.028 0.563 0.897 0.417 0.125 0.673 0.678 0.222 0.638 3.280 1.242 0.613 0.357 1.716 0.376 0.219 0.309 0.540 1.027 0.671 1.510 0.288 0.036 2.792 0.220 0.966 0.678 0.681 1.146

0.125 0.021 0.448 0.282 0.448 0.209 0.077 0.336 0.339 0.112 0.319 1.101 0.618 0.304 0.178 0.983 0.188 0.119 0.155 0.275 0.528 0.326 1.042 0.117 0.032 1.347 0.112 0.545 0.394 0.322 0.622

Intensified techniques

Retrofit cost ($)

Tube-side

IHT

Shell-side

AHTA

HB

3500

3500

EF

778

3939

HB

2357

3533

TT

34615

8659

IF

1454

4046

TT

IF

HB & EF

26997

44600

TT & IF CW & IF

EF EF

86700 21600

133636 35753

EXs: exchangers; HTIex and HTOex: inlet and outlet temperatures of hot streams in exchanger ex; CTIex and CTOex: inlet and outlet temperatures of cold streams in exchanger ex; LMTDex: logarithmic mean temperature difference in exchanger ex; EXAex: heat transfer area of exchanger ex; hi and h0: tube-side and shell-side heat transfer coefficient; Uex: overall heat transfer coefficient of exchanger ex; CW: coiled-wire inserts; TT: twisted-tape inserts; IF: internal fins; HB: helical baffles; EF: external fins; IHT: intensified heat transfer; AHTA: adding heat transfer area.

(helical baffles, external fins, and the combination of helical baffles and external fins). Based on the literature review in Section 2, the enhancement level and capital cost of each type of intensification are assumed, and presented in Table 6, where the retrofit cost of one exchanger is equal to the fixed charge (A) plus the sum of P retrofit costs related to exchanger area ( (B  Area)). Table 7 shows the retrofit details obtained from the new method. It can be found that, according to the operational constraints of exchangers (Max available Uex in Table 2) and intensified techniques (Max times of intensification in Table 6), the optimal solution includes single technique implementation (e.g. twisted-tape inserts in exchanger 20, internal fins in exchanger 23, helical baffles in exchanger 3, and external fins in exchanger 12), and the combination of both tube-side and shell-side intensification (e.g. in exchanger 29, coiled-wire inserts and internal fins are used simultaneously in tube-side, while in shell-side, external fins are implemented). The retrofitted HEN can achieve 4.28% energy saving, and requires lower retrofit costs compared with the adding area method (186,000 dollars vs. 237,666 dollars). 6. Conclusions Implementation of intensified heat transfer is an efficient way to increase energy recovery in HEN. In order to solve large scale HEN retrofit problems efficiently, a new iterative MILP-based method has been proposed. The proposed design approach is able to give realistic and practical solutions for the debottlenecking of HEN as detailed intensified techniques are systematically applied. This leads substantial capital saving as no structural modification in heat

recovery system configuration is considered. The case study shows that, based on the new approach, more energy saving can be achieved (6.14% and 4.28% of reductions respectively in Sections 5.1 and 5.2) under lower capital costs (around 21% and 22% of reduction respectively in Sections 5.1 and 5.2, compared with the case where adding exchanger areas is considered). More retrofit design aspects, including other types of exchanger (e.g. plate and compact exchangers, double pipe exchangers, etc.), geometric details of heat exchanger design and more rigorous costing and economic tradeoff, will be addressed in the future work. Acknowledgements Financial support from EC Project FP7-SME-2010-1-262205INTHEAT is gratefully acknowledged. This research was also supported by a grant from the LNG Plant R&D Center funded by the Ministry of Land, Transportation and Maritime Affairs (MLTM) of Korean government. Nomenclature

Indices ex ti si cs hs

exchanger type of tube-side intensification type of shell-side intensification cold stream hot stream

M. Pan et al. / Applied Thermal Engineering 53 (2013) 373e386

Sets EX TI SI CS EXcu EXhu i EXcs i EXhs

EXocs EXohs HS

DTUex set of all exchangers sets of all types of tube-side intensification sets of all types of shell-side intensification set of all cold streams set of all exchangers consuming cold utilities set of all exchangers consuming hot utilities set of all exchangers located in the network inlet cold streams set of all exchangers located in the network inlet hot streams set of all exchangers located in the network outlet cold streams set of all exchangers located in the network outlet hot streams set of all hot streams

Uex AUex BUex AEBex BEBex CTIex CTOex DACTIex DACTOex

Parameters 0 initial inlet temperatures of hot streams in exchanger ex HTIex ( C) initial outlet temperatures of hot streams in exchanger ex HTO0ex ( C) 0 initial inlet temperatures of cold streams in exchanger ex CTIex ( C) 0 initial outlet temperatures of cold streams in exchanger CTOex ex ( C) initial logarithmic mean temperature difference in LMTD0 exchanger ex ( C) 0 initial value of Uex (kW/m2$ C) Uex 0 initial value of DUex (kW/m2  C)1 DUex MAXDTUex,ti upper bound of the reciprocal value of tube-side heat transfer coefficients with the tith type of tube-side intensification (kW/m2$  C)1 MINDTUex,ti lower bound of the reciprocal value of tube-side heat transfer coefficients with the tith type of tube-side intensification (kW/m2  C)1 MAXDSUex,si upper bound of the reciprocal value of shell-side heat transfer coefficients with the sith type of shell-side intensification (kW/m2  C)1 MINDSUex,si lower bound of the reciprocal value of shell-side heat transfer coefficients with the sith type of shell-side intensification (kW/m2  C)1 DTmin minimum temperature difference approach ( C) CFCPex heat-flow capacities (the multiplication between heat capacity and flow-rate) of cold stream in exchanger ex (kW/ C) flow fraction of cold stream in exchanger ex CMFex network inlet temperatures of cold stream cs ( C) CSTIcs CSTOcs network outlet temperatures of cold stream cs ( C) heat transfer area of exchanger ex (m2) EXAex HFCPex heat-flow capacities (the multiplication between heat capacity and flow-rate) of hot stream in exchanger ex (kW/ C) flow fraction of hot stream in exchanger ex HMFex network inlet temperatures of hot stream hs ( C) HSTIhs HSTOhs network outlet temperatures of hot stream hs ( C) M a sufficiently large positive number estimated value of energy saving (kW) QS0 Variables Continuous DUex reciprocal value of the overall heat transfer coefficient for exchanger ex (kW/m2  C)1 DSUex reciprocal value of shell-side heat transfer coefficient for exchanger ex (kW/m2  C)1

DAHTIex DAHTOex DBCTIex DBCTOex DBHTIex DBHTOex HBAex HBBex HTIex HTOex Obj QS ADUex BDUex

385

reciprocal value of tube-side heat transfer coefficient for exchanger ex (kW/m2  C)1 the overall heat transfer coefficient for exchanger ex (kW/ m2  C) remainder term for calculating the difference between 0 (kW/m2  C) Uex and Uex remainder term for calculating the difference between 0 (kW/m2  C) Uex and Uex positive variable, energy balance differences between hot stream and cold stream in exchanger ex (kW) positive variable, energy balance differences between hot stream and cold stream in exchanger ex (kW) inlet temperatures of cold stream in exchanger ex ( C) outlet temperatures of cold stream in exchanger ex ( C) positive variable, differences between initial and updated temperatures for cold stream inlet ( C) positive variable, differences between initial and updated temperatures for cold stream outlet ( C) positive variable, differences between initial and updated temperatures for hot stream inlet ( C) positive variable, differences between initial and updated temperatures for hot stream outlet ( C) positive variable, differences between initial and updated temperatures for cold t stream inlet ( C) positive variable, differences between initial and updated temperatures for cold stream outlet ( C) positive variable, differences between initial and updated temperatures for hot stream inlet ( C) positive variable, differences between initial and updated temperatures for hot stream outlet ( C) positive variable, heat transfer differences between streams and exchanger in exchanger ex (kW) positive variable, heat transfer differences between streams and exchanger in exchanger ex (kW) inlet temperatures of hot stream in exchanger ex ( C) outlet temperatures of hot stream in exchanger ex ( C) objective value energy saving in HEN (kW) positive variable, differences between initial and updated values of DUex (kW/m2$  C)1 positive variable, differences between initial and updated values of DUex (kW/m2$  C)1

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