Retrofit of a Heat-Exchanger Network by Considering Heat-Transfer

Article pubs.acs.org/IECR

Retrofit of a Heat-Exchanger Network by Considering Heat-Transfer Enhancement and Fouling Yufei Wang and Robin Smith* Centre for Process Integration, School of Chemical Engineering and Analytical Science, University of Manchester, Manchester M13 9PL, U.K. S Supporting Information *

ABSTRACT: Many design methods for the retrofit of heat-exchanger networks have been proposed during the last 3 decades. Conventional retrofit methods use additional area to accommodate the increasing heat duty. However, the implementation of additional area may prove difficult because of topology, safety, and downtime constraints. This problem can be mitigated through the use of heat-transfer enhancement. This Article investigates the influence of heat-transfer enhancement on fouling in heatexchanger networks. A novel design approach is used to solve heat-exchanger network retrofit problems on the basis of heattransfer enhancement by considering fouling. Simulated annealing is used to optimize the retrofit problem under fouling conditions. The results show that heat-transfer enhancement is a very attractive option for retrofitting when fouling is considered. The consideration of fouling in heat-transfer enhancement has the potential to make a significant impact on retrofit design and to make the design more cost-effective than conventional design approaches.

1. INTRODUCTION Heat-exchanger network retrofitting is an important way to increase the energy savings from an existing network. Many heat-exchanger network retrofit-related studies have been carried out in the last 3 decades. Among this research, Pinch technology1 and mathematical programming2 are the most widely used methods for heat-exchanger network retrofitting. The network-pinch approach3 is another widely used methodology that can identify network structural bottlenecks. Most approaches require additional heat-transfer area throughout the network to accommodate the increased heat duty. In practice, the implementation of additional heat-transfer area may be difficult because of the constraints of topology, safety, and maintenance. Besides, for network-topology modifications the capital cost associated with the related pipe and civil work is high, and the negative financial impact of production losses resulting from plant shut down during the lengthy periods of a retrofit is also a concern. Heat-transfer enhancement is a technique that can improve heat-transfer performance. It can make heat exchangers smaller and cheaper. The implementation of heat-transfer enhancement is a relatively simple task that can in principle eliminate civilengineering work and can be completed during a normal shutdown period. According to the features of heat-transfer enhancement applied to a retrofit design, heat-transfer enhancement can take the place of expensive modifications of the physical area. In recent years, practical heat-transferenhancement techniques have been developed, and many papers are devoted to this area.4 The most common techniques for tube-side heat-transfer enhancement are internal fins, twisted-tape inserts, coiled-wire inserts, and wire-mesh inserts (hiTran).5 For the shell side, the most common techniques are helical baffles and external fins. Polley et al.6 first mentioned the possibility of applying heattransfer enhancement to a heat-exchanger network retrofit. In © XXXX American Chemical Society

their work, they analyzed the potential benefit of using heattransfer enhancement in retrofitting by considering the aspects of fouling and pressure drop. However, no practical methodology for applying heat-transfer enhancement was proposed. Zhu et al.7 developed an approach to retrofit heat-exchanger networks by considering heat-transfer enhancement based on the network-pinch approach. In their work, the network-pinch approach was applied first to determine the heat-exchanger candidates for the enhancement as well as the augmentation level of the enhancement. Then, the most suitable heat-transferenhancement technique was selected for each candidate using a pressure-drop criterion. However, this method only considers heat-transfer enhancement after the additional area requirements have been determined, so an optimal cost cannot be guaranteed. Wang et al.8 proposed a heuristic methodology to find the best candidate exchanger in a network to be enhanced. Their methodology considers the impact of network pinch and the passive response of the network, but it cannot determine the augmentation level of the enhancement. Wang et al.9 proposed a simulated-annealing-based optimization methodology to determine which exchangers should be enhanced as well as the augmentation level of each enhancement automatically. In this Article, Wang et al.’s work9 is further developed by taking fouling into consideration. Fouling is an important issue that can affect the operation of a heat-exchanger network in practice. It decreases the heat transfer in a heat exchanger, resulting in a reduction in heat recovery. Moreover, it can increase the pressure drop across the affected equipment. Because heat-transfer enhancement will change the geometric characteristics of the tube, fouling is the Received: January 2, 2013 Revised: May 19, 2013 Accepted: June 7, 2013

A

dx.doi.org/10.1021/ie4000097 | Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

Industrial & Engineering Chemistry Research

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considers heat-transfer enhancement and fouling simultaneously in a heat-exchanger network retrofit. The candidate exchangers for enhancement are analyzed with or without taking fouling into consideration according to the exchanger position in a network and the characteristics of each exchanger. Also, networks with different structures are analyzed by taking fouling into consideration. Two case studies of two heatexchanger network retrofit problems with different characteristics are solved with the proposed methodology.

main reason that is normally attributed for the lack of heattransfer enhancement’s wide use in the design of heatexchanger networks. Therefore, it is important to research the performance of heat-transfer enhancement when taking fouling into consideration. The research on heat-exchanger network optimization when fouling is considered is still in its infancy. Most research10 optimizes the fouling-cleaning schedule of heat-exchanger networks. By cleaning the fouling deposits out of heat exchangers, the exchangers can be restored to their normal thermal and hydraulic performances. However, these methods do not consider the interaction between fouling and the characteristics of a heat-exchanger network. Many heatexchanger-network optimization methodologies11 that consider fouling do so from the viewpoints of reliability and control. These studies can consider the impact of fouling on the operation of a heat-exchanger network, but fouling is still handled by cleaning and cannot be mitigated through the network-design stage. Some heat-exchanger-network design methodologies consider the design of the network and individual heat exchangers simultaneously,12 but the optimization of the network and heat exchangers is normally decoupled and the optimization procedures are so complex that these large-scale problems are difficult to solve. Coletti et al.13 proposed a heat-exchanger-network synthesis methodology that considers fouling, but in their work the way to reduce fouling was not involved. Some other methodologies to mitigate fouling in heat-exchanger networks are to optimize the operation conditions. With the development of the foulingthreshold model,14 it was found that fouling may be completely avoided by changing the operating conditions of the heat exchangers. Wilson et al.15 considered the fouling-threshold model in crude-oil preheat trains by using a graphical tool named the temperature-field plot. This method can identify the exchangers that are prone to fouling, but no methodology for reducing fouling within a network was reported. Yeap et al.16 studied both pressure drop and fouling problems in heatexchanger-network retrofitting. A modified temperature-field plot was presented that included both the thermal and hydraulic affects in their network analysis, and the detailed relation among fouling, pressure drop, and heat-transfer coefficients was analyzed. However, the characteristics of a heat-exchanger network were not involved, and most of their work was focused on the individual heat exchanger. Rodriguez and Smith17 presented a method for mitigating fouling in existing heat-exchanger networks by optimizing the operating conditions of the heat-exchanger networks. This method can identify the impact of network structure when fouling is considered. However, this work did not give an explicit interpretation on the relation between network characteristics and fouling. Moreover, it did not consider the impacts of network structure and exchanger position on fouling. Few studies have been done on the performance of heat-transfer enhancement that take fouling into consideration, and only Yang and Crittenden5 mentioned that hiTran can reduce the fouling rate. In most methodologies developed for heat-exchangernetwork retrofitting, heat-transfer enhancement is used only as a complementary tool for reducing the amount of additional area, hence lowering the retrofit investment. As a result, the strengths of heat-transfer enhancement have not been fully exploited. To utilize fully the strengths of heat-transfer enhancement and to apply heat-transfer enhancement without fear of fouling, this Article proposes a novel approach that

2. MODELS OF FOULING The model used in our methodology to predict fouling in a heat exchanger is Polley’s threshold model.14 This model is improved from the threshold model of Ebert and Panchal.18 In the model, the fouling rate under given conditions is a result of two competing terms; namely, a deposition term and a mitigation term. The model is shown below fouling rate = (deposition term) − (deposition removal term)

⎛ −E ⎞ dR f = αPRe−0.8Pr −0.33 exp⎜ ⎟ − γPRe 0.8 dt ⎝ RTw ⎠

(1)

where αP and γP are parameters determined by regression in Polley’s threshold model, Rf is the fouling resistance, Re is the Reynolds number, Pr is the Prandtl number, R is the gas constant, Tw is the wall temperature, and E is the activation energy. The threshold temperature, above which fouling is expected to occur, can be calculated for a given shear stress by setting eq 1 to zero. The relationship between the threshold temperature and shear stress is shown in Figure 1. For wall temperatures and

Figure 1. Threshold film temperature as a function of flow shear stress.

shear stresses to the right of and below the threshold line, fouling can be neglected. For conditions above the threshold line, fouling is expected to occur and it becomes more severe as the conditions move away from the threshold line. It is noted that the fouling threshold model can be used only for crude-oil fouling on the tube side. Because of the lack of a fouling model, in this work only the crude-oil fouling in the tube side is considered. Although shell-side fouling and other fouling mechanisms are not considered, they do not affect the analysis of the relation between fouling and heat-exchanger networks. The underlying assumption is that the fouling fluid (crude oil) is on the tube side and that this dominates the fouling performance of the heat exchanger. B



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Ree = 1.8526Re0 − 0.3945

3. MODELS OF HEAT-TRANSFER ENHANCEMENT The overall heat-transfer coefficient (U) is defined as follows 1 1 1 = + + R ft + R fs U hft hfs (2)

4. OPPORTUNITIES TO REDUCE FOULING Because the fouling-threshold model can be used only to predict crude-oil fouling, in this Article the opportunities to reduce fouling are restricted to a crude-oil preheat train. However, the analysis in this work can be used in other fouling mechanisms by considering the impacts of temperature and shear stress. From eq 1, the most important factors that affect fouling in a crude-oil preheat train are the exchanger wall temperature and the rate of shear experienced by the fluid as it flows through the exchanger. The opportunities for reducing fouling by changing the wall temperature and shear stress are discussed. 4.1. Reducing Fouling by Applying Heat-Transfer Enhancement. From eq 1, in a crude-oil preheat train the temperature of the heat-transfer surface has a great impact on fouling rate, especially at the hot end of the preheat train. In a preheat train, the high wall temperature tends to accelerate the deposition. Consequently, the wall temperature should be kept low to reduce fouling. The surface temperature of a heat exchanger is a function of the heat-transfer coefficients and the bulk temperature of the hot and cold streams. The relevant equations are shown below TO − TI Tw,O = TO − dOhO dOhO d + 2λ ln dO + 1 dh

where hft and hfs are the film transfer coefficients for the tube and shell side in a heat exchanger, respectively, and Rft and Rfs are the fouling resistance for the hot and cold side in a heat exchanger, respectively. In eq 2, the difference between the internal and external tube diameter and the heat resistance of the metallic wall of the tubes is neglected. When a heat exchanger is clean, eq 2 is rewritten as below: 1 1 1 = + U hft hfs

(3)

From eq 3, if the two values are very different then the value of U tends to be closer to the smaller one. The side with the smaller heat-transfer coefficient is called the controlling side. It is defined that hs/ht is the control ratio rh. If rh > 1, resulting in the tube side having a larger heat-transfer resistance,7 then the enhancement technique should be applied to the tube side to achieve a more effective improvement. However, if rh < 1 then the enhancement technique should be applied to the shell side. Heat-transfer enhancement can be added to the tube side, the shell side, or both the tube and shell sides of one exchanger with an increasing ratio of heat-transfer coefficients. After enhancement, the value of U can be expressed as 1 1 1 e = e + U hft hfs

(tube‐side enhancement)

1 1 1 = + e Ue hft hfs

(shell‐side enhancement)

1 1 1 e = e + U hft hfse

(both sides enhancement)

heft

(8)

(

Tw,I = TI +

(4)

I I

( ) )

w

I

(9)

TO − TI

(

dIhI dOhO

+

dIhI 2λ w

( ) + 1)

ln

dO dI

(10)

where subscripts I and O refer to the inside and outside of tube, respectively, d is the diameter, and λ is the thermal conductivity of the tube wall. We assume that the hot stream flows on the outside of the tubes and that the cold stream flows through inside of the tubes. In eqs 9 and 10, TO − TI is larger than zero. Therefore, for eq 9 as the denominator term becomes smaller, the wall temperature becomes smaller. For eq 10, when the denominator term becomes larger, the wall temperature becomes smaller. It can be deduced that increasing hI (coldside heat-transfer coefficient) or decreasing hO (hot-side heattransfer coefficient) reduces the wall temperature. When the cold stream flows through the outside of the tube and the hot stream flows through the inside of tube, the same conclusion is reached: the cold-side heat-transfer coefficient increases or the hot-side heat-transfer coefficient decreases, reducing the wall temperature. As a result, in a heat exchanger the wall temperature can be reduced by increasing the cold-side heat-transfer coefficient, decreasing the hot-side heat-transfer coefficient, or a combination of both changes. In a crude-oil preheat train, a decrease in the wall temperature means a reduction in the fouling rate. According to the previously mentioned threshold models, fouling may be completely eliminated when the wall temperature is reduced. Heat-transfer enhancement can increase the heat-transfer coefficient in a heat exchanger. It can be used to increase the cold-side heat-transfer coefficient to decrease the wall temperature. For a typical crude-oil preheat train, crude oil is a cold stream and normally flows through the tube side of an

(5)

(6)

hefs

where and are the heat-transfer coefficients of the tube and shell side after enhancement, respectively, and Ue is the overall heat-transfer coefficient after enhancement. Although some research has been conducted to observe the fouling performance of tubes with different enhancement devices, useful fouling models are rare in the literature. Yang and Crittenden5 proposed a modified version of the model of Yeap et al16 to predict the fouling rate in an exchanger enhanced by hiTRAN, as shown in eq 7. This model is used in our work to predict the fouling rate in the enhanced heat exchangers. αYfvTs 2/3ρ2/3 μ−4/3 dR f = − γYτw dt 1 + βY v 3f 2 ρ−1/3 μ−1/3 Tw 2/3 exp(E /RTw ) (7)

where αY, βY, and γY are parameters determined by regression in Yeap’s model, f is the Fanning friction factor, v is the flow velocity, ρ is the fluid density, μ is the fluid viscosity, and τw is the shear stress. Because eq 7 is relatively difficult to calculate, Yang and Crittenden19 provided a simple equation to predict the fouling rate in an enhanced heat exchanger in the form of Polley’s threshold model, in which an equivalent Reynolds number is used. The equivalent Reynolds number is shown in eq 8 C



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temperature at first and then exchanges heat with the hot stream at a relatively high temperature. The highest wall temperature in the design with vertical heat transfer is 325 °C. The right-hand side network depicts the crisscrossed heattransfer design. In this design, the cold stream exchanges heat with the hot stream at a relatively high temperature at first and then exchanges heat with the hot stream at a relatively low temperature. In the crisscrossed design, the highest wall temperature is 290 °C, which is much lower than that in the vertical heat-transfer design. If fouling is considered then it is likely that the exchanger at the hot end of the vertical heattransfer design will suffer severe fouling deposition. However, from the figure it can be seen that the design with crisscrossed heat transfer requires more heat-transfer area. The purpose for changing the heat-transfer pattern from vertical to crisscrossed is to decrease the wall temperature of the hottest place in the network where fouling is most likely to occur. However, this requires more heat-transfer area. It should be noted that it is difficult to identify which heattransfer pattern is better without making a trade-off between the heat-transfer-area cost and fouling-related cost. When heat-transfer enhancement is considered in heatexchanger network retrofit optimization, the need for additional area can be replaced by heat-transfer enhancement, which will incur a lower capital cost. Therefore, in an optimization that considers fouling and heat-transfer enhancement, the crisscrossed heat-transfer pattern may be more promising because of the lower capital cost that results from heat-transfer enhancement.

exchanger. Therefore, the tube-side heat-transfer enhancement can be applied to increase the heat-transfer coefficients and reduce the fouling rates. This option should be implemented when heat-transfer enhancement is applied to a crude-oil preheat train. From the research of Yang and Crittenden,5 hiTRAN tube inserts can promote shear stress in the tube side. Therefore, hiTRAN can reduce fouling as a result of shear stress. However, it also influences the tube-wall temperature. 4.2. Reducing Fouling by Modifying the Network Structure. The wall temperatures of exchangers are not only affected by the heat-transfer coefficients of both the cold and hot sides, but are also affected by the temperatures of the hot and cold streams. By selecting different matches, the distribution of temperature in the network can be different. In heat-exchanger network design based on the stream matches that appear in the composite curves, the heat-flow pattern in a heat-exchanger network can be classified in broad terms as having either vertical heat transfer or crisscrossed heat transfer. Vertical heat transfer can make good use of the overall temperature difference between the hot and cold streams. In composite curves, the stream matches in a vertical heat transfer appear vertically aligned. A vertical heat-transfer network is normally desired in heatexchanger network designs as long as there are no significant differences in the film-transfer coefficients throughout the network. However, if the fouling aspect is considered in the network design, the vertical heat transfer may not be that beneficial. In vertical heat transfer, the cold streams at progressively higher temperatures are matched with increasingly hotter hot streams, which results in a wall temperature profile that continuously increases from the cold to the hot end of the network. In other words, the hottest part of the cold stream exchanges heat with the hottest part of the hot stream. As a result, at the hot end of a heat-exchanger network the wall temperature will reach its maximum value. This hottest part is very likely to have severe fouling deposition. Crisscrossed heat transfer requires more heat-transfer area because it cannot make good use of the overall temperature difference between the hot and cold streams. This means that for a heat-exchanger network with crisscrossed heat-transfer design the capital cost is higher. However, in designs with crisscrossed heat transfer the hottest spot in the hot stream does not exchange heat with the hottest spot in the cold stream. The wall temperature in the hottest place is thus lower. An example is used to illustrate designs with vertical and crisscrossed heat transfer. The example heat-exchanger networks are shown in Figure 2. The left-hand side network features vertical heat transfer. In this case, the cold stream exchanges heat with the hot stream at a relatively low

5. SENSITIVITY TO FOULING The main affect of fouling deposition is a reduction in the overall heat-transfer coefficient, and the main affect of heattransfer enhancement is an increase in the overall heat-transfer coefficient. Therefore, the reduction in the overall heat-transfer coefficient from fouling can be considered as an inverse process of applying heat-transfer enhancement. The sensitivity to heattransfer enhancement has been analyzed by Wang et al.,8 and the sensitivity to fouling can be analyzed in the same manner as that of heat-transfer enhancement. Figure 3 compares the sensitivity to fouling and enhancement of a heat exchanger. In the figure, the gradient of a stream line equals the CP value of the stream. From the figure, it can be seen that the duty improvement from the enhancement (or the reduction in the fouled condition) equals the smaller CP value of the two streams multiplied by the change in the minimum temperature difference. Therefore, the sensitivity to both fouling and heat-transfer enhancement depends on the CP value of the two streams and the temperature difference between the two streams. The sensitivity to heat-transfer enhancement is also dependent on location in a heat-exchanger network due to the passive response in downstream heat exchangers. Figure 4 shows an example of the original heat-exchanger network (Figure 4A), the heat-exchanger network with enhancement (Figure 4B), and the heat-exchanger network with fouling (Figure 4C). When enhancement is applied to heat exchanger 2, the duty of heat exchanger 2 will increase, whereas because of the passive response, the duty of exchanger 1 decreases. When fouling is present in heat exchanger 2, the duty of the heat exchanger will be reduced. Again because of the passive response, the duty of exchanger 1 will increase. This example clearly shows that all

Figure 2. Example of different heat-transfer patterns. D



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Figure 3. Sensitivity to enhancement and fouling in a heat exchanger.

progressive decline in the effectiveness of heat transfer in the affected equipment. To study effectively the performance of a heat-exchanger network affected by fouling, the dynamic nature of this process must be modeled. For this, a nonsteady-state model for heat-exchanger networks is developed. The aim of the dynamic model is to be able to predict the performance of a heat-exchanger network under fouling conditions for a given time horizon. In our nonsteady-state heat-exchanger-network simulation, the time horizon is divided into a number of time intervals of equal length as defined below:

downstream exchangers will counteract part of the influence of both fouling and enhancement. The exchangers with a large CP value and minimum temperature difference are sensitive to both fouling and heattransfer enhancement. Also, the positions of the exchangers affect the sensitivity to fouling and enhancement. The discussion of the sensitivity to fouling and enhancement makes clear that when an exchanger is sensitive to fouling and enhancement, the enhancement not only can improve the energy recovery in the locations sensitive to heat-transfer enhancement, but it can also reduce the fouling rate in the locations sensitive to fouling.

Δt =

6. OPTIMIZATION OF HEAT-EXCHANGER NETWORK BY CONSIDERING HEAT-TRANSFER ENHANCEMENT AND FOULING Simulated annealing is used here to optimize heat-exchanger networks by considering heat-transfer enhancement and fouling. Including the fouling aspects in the optimization is complex because of the dynamic nature of the fouling process. A nonsteady-state simulation of heat-exchanger networks is thus required. 6.1. Non-Steady-State Simulation of Heat-Exchanger Networks. The affects of fouling on the thermal performance of heat-exchanger networks are not instantaneous. The formation of deposits on heat-transfer surfaces causes a

tF NT

(11)

where tF(y) is the time horizon of the study, NT is the number of time intervals, and Δt is the duration of each time interval. In each time interval, all operation conditions of the network are assumed to be constant. The network is then simulated by solving the steady-state model for each time interval. The dynamic nature of fouling is modeled by using the fouling resistance as a link between different time interval simulations. The relationship between the fouling resistance of a heat exchanger from two consecutive time intervals is shown below Rft + 1 = Rft + Rf ′t Δt E

(12)



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where Rf t+1 and Rf t are the fouling resistance in the time intervals t + 1 and t, respectively. Rf ′t is the average fouling rate in the time interval t. Regarding the length of each time interval, there is a trade off between the accuracy of the dynamic simulation and the computation time: the shorter the time interval the higher the accuracy of the simulation. 6.2. Area-Based Calculation. Simulating the performance of a heat exchanger requires calculating the outlet temperature of both streams given their inlet conditions, physical properties, and the characteristics of the equipment. Depending on the information available for the heat exchanger, two different cases are considered: (1) The heat load of the exchanger is known, and the heattransfer area needs to be calculated (duty-based calculation). (2) The exchanger area is known, but its heat load is unknown (area-based calculation). In the duty-based calculation, the size of the exchangers is estimated to accommodate a specified duty. Duty-based calculations are widely used in heat-exchanger network design. When compared with area-based calculations, the model for duty-based calculations is much simpler. However, in heatexchanger-network simulation that takes fouling into consideration, area-based calculations need to be used. This is because models that use duty-based calculations would predict a constant duty regardless of the amount of fouling deposited. In this work, we used the area-based model proposed by Kotjabasakis and Linnhoff,20 which is shown in eqs 13 and 14.

Figure 4. An example of sensitivity to fouling and enhancement.

Figure 5. Existing heat-exchanger network in case 1. F



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(1 − RB)Th,out + (B − 1)RTc,in + (R − 1)Th,in = 0

optimization. The general results of the area-based calculations are in accordance with the results of the duty-based optimization. When fouling is considered in the optimization it should be noted that only fouling at the hot end of the crude-oil preheat train is considered. The dominant fouling mechanism is chemical-reaction fouling. The model used here is the threshold model of Polley et al.14 Because crude oil normally flows through the tube side, only the tube-side heat-transfer enhancement is considered in this case study. The correlated parameters used in the threshold model of Polley et al.14 are shown below.

(13)

R(1 − RB)Tc,out + (B − 1)RTh,in + (R − 1)BRTc,in = 0 (14)

where R = CPc/CPh, B = exp[(UA/CPc)(R−1)], Th,in is the hot stream inlet temperature, Tc,in is the cold stream inlet temperature, Th,out is the hot stream outlet temperature, Tc,out is the cold stream outlet temperature, CPc is the heat capacity flow rate of cold stream (kW/°C), and CPh is the heat capacity flow rate of hot stream (kW/°C). The main difference between area-based calculations and duty-based calculations is that the models of heat exchangers are different. In the duty-based method, the duty of all heat exchangers is specified. In area-based calculations, heatexchanger models are specified in area and utility-heat exchangers are specified in duty. The process for specifying the duty of utility-heat exchangers is to maintain the target temperatures of the streams. 6.3. Optimization Algorithm. In this work, simulated annealing (SA) is used as the optimization tool. SA is a widely used optimization algorithm derived from the Metropolis algorithm.21 SA is a stochastic-optimization methodology that uses random changes to search the solution space and can avoid being trapped in the local optima. When the fouling-threshold model is considered in the optimization, the problem is very difficult to solve with a gradient-optimization algorithm. Therefore, SA is used in this work. The basic idea of the optimization is to change the heattransfer coefficient and the position in the network of heat exchangers. When the enhancement device is applied to an exchanger, the fouling model will change from that of a baretube model to an enhanced-tube model. After each change, the network is simulated, and the optimal heat-exchanger network will be found after a large number of changes. The detailed descriptions of SA and its use in the optimization of heatexchanger network retrofitting can be found in the literature.9,17

E = 46.2 (kJ ·mol−1) α = 58 950 (m 2·kW −1·h−1)

γ = 5.7 × 10−10 (m 2·kW −1·h−1)

By using the threshold model of Polley et al.,14 all of the heat exchangers are going to foul, but exchangers 29, 28, and 27 are identified as exhibiting an increased tendency to foul, as shown in Table 2. Table 2. Initial Fouling Rate of the Exchangers in Case 1 exchanger number 4 22 23 24 26 27 28 29

additional area (m2)

duty based area based

1.1 × 10 1.0 × 106

104.4 0

6

× × × × × × × ×

10−5 10−5 10−5 10−4 10−4 10−4 10−4 10−4

Table 3. Key Exchangers in the Network with and without Fouling enhanced exchanger initial energy cost (MGBP/y) energy cost after enhancement (MGBP/y)

with fouling

without fouling

20, 24, 26, 28, 29 21.8 19.9

4, 20, 24, 26, 28 20.5 19.4

The results in Table 3 show that because of fouling the initial energy costs of the network are different. The fouling decreases heat transfer, increasing the energy consumption. A larger energy cost is observed in the network with fouling. It is also noted that the enhanced exchangers in the network with and without considering fouling are different. This is because the reduction in heat transfer due to fouling in exchanger 29 is much more severe than that in exchanger 4. Without mitigating the impact of fouling, the performance of exchanger 29 will drop significantly. It is said that heat-transfer enhancement devices can reduce fouling, so when fouling is considered, exchanger 29 is much preferred to be enhanced to promote

Table 1. Comparison between Duty-Based and Area-Based Optimization annual energy cost savings ($)

6.7 5.1 7.1 1.3 2.9 2.4 3.1 6.5

In this case, the maximum number of heat-transfer enhancements is set to five. The time interval is 10. Optimization is carried out to assess the enhanced exchangers and the energy -saving performance of the network with and without fouling. The results are shown in Table 3. The computing time for this case study is 2 hours.

7. CASE STUDY 7.1. Case Study 1: Large-Scale Crude Heat-Exchanger Network. A network from the literature8,9 is used in this work, and the network is optimized under fouling considerations. The aim of this case study is to compare the results of the proposed method to the results in the literature. The objective is to minimize the total cost, including the annual operating cost and the annualized retrofit investment. The existing network is shown in Figure 5. First, the network is optimized with an area-based calculation, and only the heat-transfer enhancement is considered. The results are shown in Table 1. From Table 1, it can be seen that the area-based optimization can eliminate the need for unwanted additional area (when only enhancement is considered, additional area is not desired) effectively because the area is specified. In the duty-based optimization, additional area is allowed to be added, resulting in energy savings that are slightly higher than that of the area-based

methodology

initial fouling rate (m2·K·kW−1·h−1)

G



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Figure 6. Heat-exchanger structure in case 2.

On the basis of these model parameters, the initial fouling rate of each exchanger can be calculated through the foulingthreshold model. The results are shown in Table 5. From the

heat transfer and mitigate fouling. The results in Table 3 also suggest that the energy savings from enhancement in the network considering fouling is larger than that in the network without considering fouling. This is because the heat-transfer enhancement in the case with fouling not only increases heat transfer but also reduces fouling. By contrast, the heat-transfer enhancement in the case without fouling is only used to increase heat transfer. 7.2. Case Study 2: Simple Crude-Oil Preheat Train. Because case 1 is a large-scale network and the related calculation is very time-consuming, a simple crude-oil preheat train is used to illustrate the impact of network structure and fluid properties on fouling. It is known that fouling exerts a great impact on the performance of a heat-exchanger network. Heat-transfer enhancement has the ability to mitigate the impact of fouling, as discussed in the preceding case study. In this second case study, a simple crude-oil preheat train is analyzed to assess the performance of the heat-exchanger network and the enhanced heat-exchanger network under fouling considerations. In this case study, the objective is to reduce the total annual cost. The heat-exchanger data and stream data are provided in the Supporting Information, and the network structure is shown in Figure 6. In this case, only fouling in stream C3 is considered. The time period is divided into 10 time intervals. The computing time of this case study is half of an hour. In this case, several sets of model parameters for Polley’s fouling-threshold model are used. These parameters, which are regressed from different crude-oil fouling data, are presented in Yeap and Rodriguez’s work.16,17 The parameters are shown in Table 4.

Table 5. Initial Fouling Rate of the Exchangers on Stream C3 under Different Model Parameters fouling rate (m2·K·kW−1·h−1) parameter set 1 2 3 4 5 6 7 8

1 2 3 4 5 6 7 8

6.4 2.2 4.8 1.2 2.7 3.7 5.2 1.0

× × × × × × × ×

3

10 105 105 105 103 106 105 106

E (kJ·mol−1)

γ (m2·K·kW−1·h−1·Pa−1)

38 48 59 41 55 55 48 46

7.3 × 10−5 4.3 × 10−5 1.2 × 10−4 4.2 × 10−4 1.1 × 10−1 3.2 × 10−7 2 × 10−7 1.1 × 10−6

× × × ×

10−4 10−4 10−5 10−3

× 10−3 × 10−3 × 10−3

exchanger 2 4.21 3.29 0 6.42 0 1.19 8.78 0

× 10−5 × 10−4 × 10−4 × 10−3 × 10−4

exchanger 3 0 1.28 0 1.26 0 4.89 4.03 0

× 10−4 × 10−4 × 10−4 × 10−4

results, it can be seen that different model parameters will induce different fouling-threshold conditions and different sensitivities to temperature and shear stress. Different correlations have been regressed from the practical fouling data of the different crude oils. It is thus not surprising that different correlations will yield different fouling rates and threshold conditions. Because the structure of a network can affect the fouling rate in exchangers, the heat-exchanger network is modified by switching the position of heat exchangers 1 and 2 to change the network from a vertical heat-transfer pattern to a crisscrossed heat-transfer pattern. The modified structure contains the crisscrossed heat-transfer pattern, and the initial structure contains the vertical heat-transfer pattern. The modified heatexchanger-network structure is shown in Figure 7, and the fouling rate of each heat exchanger under the modified structure is shown in Table 6. Because only the positions of exchangers 1 and 2 are changed and exchanger 3 is upstream of exchangers 1 and 2, the fouling rate of heat exchanger 3 will not be affected. The difference in the fouling rate between the initial network and the modified network is also shown in Table 6. From Table 6, it can be seen that the fouling rate of exchanger 1 decreases after structure modification because of wall temperature reduction, and the fouling rate of exchanger 2 increases after structure modification because the wall temperature increases. Also, the total change in the fouling rates in exchangers 1 and 2 are shown in Table 6. It can be seen that the total fouling rate decreases. This is because in the fouling-

Table 4. Parameters for Polley’s Fouling-Threshold Model parameter set α (m2·K·kW−1·h−1)

exchanger 1 1.16 6.54 1.03 1.40 0 2.63 1.75 1.63

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Figure 7. Modified heat-exchanger structure in case 2.

Table 6. Initial Fouling Rate of the Exchangers on Stream C3 in a Modified Network Structure fouling rate (m2·K·kW−1·h−1) parameter set

exchanger 1

1 2 3 4 5 6 7 8

8.95 5.31 0 1.12 0 1.97 1.36 8.34

change in fouling rate (m2·K·kW−1·h−1)

exchanger 2

× 10−5 × 10−4

6.65 4.29 0 8.83 0 1.57 1.12 1.49

× 10−3 × 10−3 × 10−3 × 10−4

exchanger 1

× 10−5 × 10−4

−2.65 −1.23 −1.03 −2.80 0 −6.60 −3.90 −7.96

× 10−4 × 10−3 × 10−3 × 10−4

× × × ×

10−5 10−4 10−5 10−4

× 10−5 × 10−5 × 10−4

exchanger 2 2.44 1.00 0 2.41 0 3.80 2.42 1.49

× 10−5 × 10−4 × 10−4 × 10−4 × 10−4 × 10−4

total −2.10 −2.30 −1.03 −3.90 0 −2.80 −1.48 −6.47

× × × ×

10−6 10−5 10−5 10−5

× 10−4 × 10−4 × 10−4

energy performance in the initial structure. This is because after optimization the initial structure (vertical heat transfer) can recover more heat than the modified structure under clean conditions, and even though the modified structure can have better performance under fouling conditions, it may not compensate for the difference in the clean conditions. To analyze the reason that only parameter sets 6−8 have better performance in the modified structure, the relation between temperature and fouling rate for each parameter set is plotted, which is shown in Figure 8. The objective for changing the vertical heat-transfer pattern to the crisscrossed heat-transfer pattern is to reduce the wall temperature in the hottest place. If the fouling rate is very sensitive to temperature, then the reduction in temperature can result in a large decrease in the fouling rate, which can be very attractive. From Figure 8, it can be seen that the fouling rate under parameter sets 6−8 are more

threshold model the rise of the wall temperature results in an increasing trend in which the fouling rate becomes larger. Therefore, the crisscrossed heat-transfer-pattern network can also decrease the fouling rate in this way. Optimization is carried out to assess the energy saving performance of the network under different fouling-model parameters. In the optimization, the network structure is not optimized, and only the initial structure and the modified structure, shown in Figures 6 and 7, are considered. Only additional area is considered in this optimization to accommodate for the increased heat duty. The results are shown in Table 7. Interestingly, from the results shown in Table 6, the modified structure (crisscrossed heat transfer) can reduce the fouling rate. However, from the results of the optimizations shown in Table 7, only parameter sets 6−8 have better energy performance in the modified structure (crisscrossed heat transfer), whereas the other parameter sets still have better Table 7. Optimization Results of the Network under Different Fouling Parameter annual total cost ($) parameter set

initial structure

1 2 3 4 5 6 7 8

× × × × × × × ×

5.27 6.12 5.15 6.79 5.13 7.55 7.11 6.32

6

10 106 106 106 106 106 106 106

modified structure 5.66 6.26 5.53 6.80 5.52 7.44 7.07 6.10

× × × × × × × ×

106 106 106 106 106 106 106 106

Figure 8. Relation between the fouling rate and temperature under different fouling-model parameters. I



Article

8. CONCLUSIONS This work considers heat-exchanger network retrofitting under fouling conditions. On the basis of models of fouling and heattransfer enhancement, opportunities to reduce fouling are studied, and optimization studies are conducted to determine the most economic network by considering heat-transfer enhancement coupled with the phenomenon of fouling. The dynamic nature of fouling is simulated by using temperature intervals. The most important variables that affect fouling are the wall temperature and shear stress. A lower wall temperature or a larger shear stress can lead to a lower fouling rate. From our study, there are two ways to reduce wall temperature. One way is to add heat-transfer enhancement to the cold side in a heat exchanger to increase the cold-side heat-transfer coefficients, and the other is to change the network structure to reassign the temperature distribution in the network. Two case studies on crude-oil preheat trains are given. It can be found through case study that the enhancement tends to be added to exchangers that are prone to fouling because of the fact that it can reduce fouling. Through case study, the different fluid properties of crude oil are considered. With different fluid properties, the threshold condition varies significantly. When the different heat-exchanger-network structures and different fluid properties are considered simultaneously, the crisscrossed heat-transfer structure may be used when the fouling rate of the crude oil is very sensitive to temperature. When the fouling rate of the crude oil is not very sensitive to temperature or fouling is eliminated by heat-transfer enhancement, the structure with a vertical heat-transfer pattern would be better to use.

sensitive to temperature than the fouling rate under the other parameter sets, so the performance of the modified network under fouling consideration is better. In Figure 8, the fouling rate under parameter set 4 is also quite sensitive to temperature, and from the optimization results the total annual cost for both structures is very close. Therefore, the fouling-model parameter can affect both the performance of the heat-exchanger network and the individual heat exchanger significantly. In other words, different fluid properties have a different impact on heatexchanger-network performance. Optimization is carried out again to consider both heattransfer enhancement and fouling. The optimization results are shown in Table 8, and the fouling rates in the enhanced heat Table 8. Optimization Results of the Network by Considering Fouling and Heat-Transfer Enhancement annual total cost ($) parameter set

initial structure

1 2 3 4 5 6 7 8

× × × × × × × ×

5.04 5.92 5.01 5.99 5.01 7.42 7.01 5.01

modified structure

6

5.52 6.14 5.44 6.26 5.44 7.26 6.98 5.44

10 106 106 106 106 106 106 106

× × × × × × × ×

106 106 106 106 106 106 106 106

■

Table 9. Initial Fouling Rate of the Enhanced Exchangers under Different Model Parameters −1

parameter set 1 2 3 4 5 6 7 8

exchanger 1 4.80 5.89 0 9.75 0 2.34 1.58 0

−5

× 10 × 10−4 −4

× 10

× 10−3 × 10−3

exchanger 2

exchanger 3

0 3.05 0 3.16 0 1.24 9.01 0

0 6.77 × 10−5 0 0 0 4.13 × 10−4 3.48 × 10−4 0

× 10−4 −4

× 10

× 10−3 × 10−4

ASSOCIATED CONTENT

S Supporting Information *

−1

fouling rate (m ·K·kW ·h ) 2

Stream and exchanger data for case 2. This material is available free of charge via the Internet at http://pubs.acs.org.

■

AUTHOR INFORMATION

Corresponding Author

*Tel: +44-1613064382. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS Financial support from FP7-SME-2010-1 (262 205 Intensified Heat Transfer Technologies for Enhanced Heat Recovery) is gratefully acknowledged.

exchangers in the initial structure are presented in Table 9 to show the change in the fouling rate. From Table 8, when fouling is considered the results show that using heat-transfer enhancement is more cost effective. When compared to the design with additional area, the design with enhancement is cheaper, and, more importantly, it can reduce fouling. From the results in Table 8, it can be seen that under parameter sets 6 and 7 the performance of the modified structure is still better than the performance of the initial structure. However, under parameter set 8 the performance of the modified structure is no longer better than the performance of the initial structure because the fouling is completely eliminated by the heat-transfer enhancement. From the results, it can be concluded that heat-transfer enhancement, fluid properties, and network structure can affect network performance and the fouling rate significantly.

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REFERENCES

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Retrofit of a Heat-Exchanger Network by Considering Heat-Transfer

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