Heat exchanger network retrofit with a fixed network structure

Applied Energy 127 (2014) 25–33

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Heat exchanger network retrofit with a fixed network structure Ning Jiang a,⇑, Jacob David Shelley b, Steve Doyle b, Robin Smith b a b

Institute of Process Equipment and Control Engineering, Zhejiang University of Technology, Hangzhou 310032, China Centre For Process Integration, School of Chemical Engineering and Analytical Science, The University of Manchester, Manchester M13 9PL, UK

h i g h l i g h t s  Heat exchanger network retrofit method with a fixed network structure is proposed.  Cost-effective retrofit is allowed based on an improved sensitivity analysis.  Energy performance is improved by the selective use of heat transfer enhancement.  The method is applicable for streams with linear or non-linear physical properties.

a r t i c l e

i n f o

Article history: Received 31 January 2014 Received in revised form 22 March 2014 Accepted 9 April 2014 Available online 3 May 2014 Keywords: Heat exchanger network Retrofit Sensitivity analysis Heat transfer enhancement

a b s t r a c t Finding cost effective retrofits for heat exchanger networks remains a challenge. Whilst it is often straightforward to find retrofit changes to an existing network that can improve energy performance, in practice such changes are most often uneconomic. This paper will present an approach to heat exchanger network retrofit around a fixed network structure. Network energy performance is improved through the selective use of heat transfer enhancement. A sensitivity analysis is used to find the most effective heat exchangers to enhance in order to improve the performance of the overall network. The sensitivity analysis used is an extension of a previous sensitivity analysis that was introduced to study network flexibility. The proposed method is applicable for heat exchanger networks involving streams with linear or non-linear physical properties. The enhancement of the most sensitive heat exchangers and avoiding new equipment, together with piping and civil engineering costs, allow much more cost-effective heat exchanger network retrofit. Ó 2014 Elsevier Ltd. All rights reserved.

1. Introduction The retrofit of existing heat exchanger networks (HENs) is an important research field. Whilst many retrofit methods have been proposed, the network modifications suggested most often lead to uneconomic projects. It might be suspected that the major problem is justification for the purchase of new equipment. However, the modification of heat exchanger networks to allow new equipment to augment existing equipment is extremely expensive from the point of view of piping and civil engineering costs. Cost-effective retrofit most often involves the fewest modifications to the existing network. The HEN retrofit problem can be described as: given a set of hot and cold streams/utilities with their corresponding physical properties, flowrates and inlet/outlet flow conditions and a set of heat exchangers with specified geometries and assignments of duty/streams/position in an existing HEN, the existing

⇑ Corresponding author. Tel.: +86 (0) 571 8887 1060. E-mail address: [email protected] (N. Jiang). http://dx.doi.org/10.1016/j.apenergy.2014.04.028 0306-2619/Ó 2014 Elsevier Ltd. All rights reserved.

HEN is retrofitted by means of the change of matching, resequencing, reassignments, adding new areas/exchangers, heat transfer enhancement, etc. to achieve some retrofit objective, whilst fulfilling the energy requirements of all process streams. Retrofit objectives vary, but might be to reduce the energy consumption to a specified level, minimise the utility requirements under a fixed budget and retrofit complexity, maximise the retrofit profit, minimise the retrofit cost under a certain energy recovery level, minimise the total annual cost after retrofit, satisfy the increased throughput or changed operation conditions, etc. In addition, the HEN retrofit is normally subject to some significantly different constraints from those for new HEN design. For example, pressure drops may be highly constrained due to the operation requirements of upstream and downstream units; the spatial and repiping constraints impede the implementation of retrofit; some on-site constraints and retrofit feasibility and ease of implementation are difficult to quantify. In summary, the HEN retrofit problem features more complex constraints and objectives. The previous research in HEN retrofit can be grouped into pinch analysis methods, mathematical programming methods and

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N. Jiang et al. / Applied Energy 127 (2014) 25–33

Nomenclature A B BC Bin Bout C CP CPC CPH CPi cp DS dI dO dNS,inlet dNS,outlet dTN,inlet dTN,outlet FT hS hT k ktube L LBB Leff

heat transfer area (m) central baffle spacing (m) baffle cut (–) inlet baffle spacing (m) outlet baffle spacing (m) known temperature matrix (°C) stream heat capacity flowrate (product of mass flowrate and average specific heat capacity) (W K1) heat capacity flowrate for the cold stream (product of mass flowrate and specific heat capacity) (W K1) heat capacity flowrate for the hot stream (product of mass flowrate and specific heat capacity) (W K1) heat capacity flowrate of Stream i (W K1) fluid specific heat capacity (J kg1 K1) shell inside diameter (m) tube inner diameter (m) tube outer diameter (m) inner diameter of the inlet nozzle for the shell-side fluid (m) inner diameter of the outlet nozzle for the shell-side fluid (m) inner diameter of the inlet nozzle for the tube-side fluid (m) inner diameter of the outlet nozzle for the tube-side fluid (m) temperature difference correction factor (–) shell-side heat transfer coefficient (W m2 K1) tube-side heat transfer coefficient (W m2 K1) fluid thermal conductivity (W m1 K1) tube conductivity (W m1 K1) tube length (m) shell-bundle diametric clearance (m) tube effective length (m)

combined methods. The work of Tjoe and Linnhoff [1] is representative of pinch retrofit methods. These workers first applied the pinch concept in retrofitting HENs. However, their method cannot provide information on exactly where the additional areas are added and how many network modifications such as re-piping are required. When applying mathematical programming to HEN retrofit, the HEN retrofit problem is a mixed integer non-linear programming (MINLP) problem. Though theoretically this approach can handle different kinds of constraints simultaneously, obtaining a good solution by solving one single MINLP model in a single step has still not yet to be fully successful due to the non-linearity of the area equations and the complexity of constraints, particularly in large problems. Thus the MINLP problem is normally simplified or decomposed as mixed integer linear programming (MILP) [2], non-linear programming (NLP) or liner programming (LP) by making some assumptions and step-wise manipulation [3,4]. Most work using mathematical programming, required two steps: screening and optimization. Even though the network structure is simplified, solving the MINLP model is still time consuming and solutions are still very often trapped at a local optimum. To overcome this problem, some research has introduced stochastic algorithms, such as simulated annealing algorithms [5], genetic algorithms [6,7], to replace deterministic methods to solve the HEN retrofit MINLP. Asante and Zhu [8] proposed a step-by-step interactive approach for heat exchanger network retrofit by combining the features of pinch and mathematical programming. They introduced the concept of the network pinch that identifies the bottleneck of the existing network and the most effective change. The retrofit MINLP problem was then decomposed into a MILP problem and a NLP problem. Smith et al. [9] further modified

m NB NP NSHELLS NSTREAM NT NUNIT P P1–2 pT Q QC QH R T TC1 TC2 TH1 TH2 Ti TMIX U Z

mass flowrate (kg s1) number of baffles (–) number of tube passes (–) number of shells connected in series (–) number of streams involved in a heat exchanger network (–) number of tubes (–) number of heat transfer units in a network (–) thermal effectiveness of heat exchanger (–) thermal effectiveness of each 1–2 shell connected in series (–) tube pitch (m) heat duty (W) heat duty on the cold stream (W) heat duty on the hot stream (W) ratio of stream heat capacity flowrates (–) temperature (°C) inlet temperature of the cold stream (°C) outlet temperature of the cold stream (°C) inlet temperature of the hot stream (°C) outlet temperature of the hot stream (°C) temperature of Stream i (°C) temperature of the mixing junction (°C) overall heat transfer coefficient(W m2 K1) parameter matrix (–)

Greek letters DPS shell-side pressure drop (Pa) DPT tube-side pressure drop (Pa) DTLM log mean temperature difference (°C) l fluid viscosity (N s m–2) q fluid density (kg m3)

Asante and Zhu’s method to consider temperature-dependent thermal properties of streams and combined structural modifications and cost optimisation in a single step to avoid missing cost-effective solutions. Most previous investigations are struggling to solve the complex HEN retrofit MINLP problem for large problems. Though the mathematical solution of the HEN retrofit problem would be an ideal method, its effectiveness and industrial applicability are quite problematic. Complex modifications recommended by optimising the MINLP are unacceptable in the view of most industrial practice. Wang et al. [10] used heuristic rules to retrofit HENs without solving mathematical programming, which can be a promising strategy for complex industrial revamps. However, their work was based on a HEN sensitivity analysis with the assumption of pure countercurrent heat exchangers, which is obviously unrealistic. Their method gave the amount of energy saving, position and extent of required heat transfer enhancement, but did not consider the retrofit ease of implementation and feasibility of the required heat transfer enhancement. The procedure involves a considerable amount of unavoidable trial-and-error. Thus this work attempts to develop a simple and practical method for HEN retrofit without any topological changes. This method applies a different solution strategy from the MINLP method, and does not rely on mathematical optimisation.

2. Methodology Though topology changes, such as inserting new matches, repiping, resequencing and additional splitting, can be used for

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N. Jiang et al. / Applied Energy 127 (2014) 25–33

the retrofit purpose, they are often too expensive and impractical for industrial HEN retrofit, because the feasibility of implementing these retrofits is problematic and existing equipment is only used in an ad hoc way. The modification of existing units by adding area or augmenting heat transfer is the most cost-effective and reliable way. Thus, this paper will develop an interactive method for HEN retrofit without making changes to the network structure. The proposed retrofit approach exploits a sensitivity analysis to screen the heat exchanger network for the most critical exchangers to modify. In addition to identifying the optimal location to apply enhancement, the approach is also capable of determining whether the level of enhancement is feasible for the given network and how to perform the proposed retrofit in detail. For both area addition and heat transfer enhancement, the feasibility considers deviations from stream target temperatures within the network and any violation of minimum temperature approach. The modification of exchangers is carried out in a realistic way, which has not been taken into account previously. Also, the retrofit approach enables important user interaction, to choose the candidate exchangers, to implement preferred modifications and to reach the level of retrofit desired. Further to this, the pressure drop introduced through the addition of heat transfer enhancement has also been assessed as this may invalidate the chosen form or level of enhancement. The retrofit approach considers the resistances present within each exchanger and therefore whether the tube-side or shell-side heat transfer is limiting. 2.1. HEN simulation and sensitivity analysis Consider first the simulation of a single heat exchanger. In this case the inlet conditions are specified and the outlet conditions need to be calculated, given heat exchanger geometry and stream flowrates and physical properties. If the heat exchanger is countercurrent, the equations describing simulation of a countercurrent heat exchanger are given by Kotjabasakis and Linnhoff [11]:

Q H ¼ CP H ðT H1  T H2 Þ

ð1Þ

Q C ¼ CP C ðT C2  T C1 Þ

ð2Þ

Q H ¼ Q C ¼ UADT LM ¼ UA

ðT H1  T C2 Þ  ðT H2  T C1 Þ   T C2 ln TT H1 H2 T C1

ð3Þ

where QH is the heat duty on the hot stream; QC the heat duty on the cold stream; CPH the heat capacity flowrate for the hot stream (product of mass flowrate and specific heat capacity); CPC the heat capacity flowrate for the cold stream (product of mass flowrate and specific heat capacity); TH1 the inlet temperature of the hot stream; TH2 the outlet temperature of the hot stream; TC1 the inlet temperature of the cold stream; TC2 the outlet temperature of the cold stream; U the overall heat transfer coefficient and A the heat transfer area. Also, if the heat capacity is constant:

R¼

CP C T H1  T H2 ¼ CPH T C2  T C1

ð4Þ

T H1  T C2 UA ðT H1  T H2 Þ  ðT C2  T C1 Þ ¼ exp  CPC ðT C2  T C1 Þ T H2  T C1

 ð5Þ

Combining Eqs. (4) and (5) gives:

  T H1  T C2 UAðR  1Þ ¼ exp CPC T H2  T C1

X ¼ exp

  UAðR  1Þ CP C

ð8Þ

Eliminating TH2 between Eqs. (4) and (6) gives [11]:

ðX  1ÞT H1 þ XðR  1ÞT C1 þ ð1  RXÞT C2 ¼ 0 R – 1

Eliminating TC2 between Eqs. (4) and (6) gives [11]:

ð9Þ

If the inlet temperatures TH1 and TC1 are known, along with U, A, CPH and CPC, then Eqs. (7) and (9) constitute two equations with two unknowns (the outlet temperatures TH2 and TC2). For the special case R = 1:

Q C ¼ CPC ðT C2  T C1 Þ ¼ UAðT H2  T C1 Þ

ð10Þ

Also, for R = 1:

ðT H1  T H2 Þ ¼ ðT C2  T C1 Þ

ð11Þ

Eliminating TC2 between Eqs. (10) and (11) gives:

T H1 þ YT C1  ðY þ 1ÞT H2 ¼ 0 R ¼ 1

ð12Þ

where

Y¼

UA CP C

ð13Þ

Eliminating TH2 between Eqs. (10) and (11) gives:

YT H1 þ T C1  ðY þ 1ÞT C2 ¼ 0 R ¼ 1

ð14Þ

Thus, for the special case of R = 1, Eqs. (12) and (14) replace Eqs. (7) and (9). The analysis will now be extended to non-countercurrent heat exchangers. The equation describing such a heat exchanger is given by:

Q ¼ UADT LM F T

ð15Þ

The temperature correction factor FT creates a potential problem for the simulation of heat exchangers, as the outlet temperatures of the heat exchanger are unknown and FT depends on the outlet temperatures. At first sight this would seem to require iteration. However, manipulation of the equations for FT can avoid iteration [12]. To manipulate the equations, consider the basic definition of FT:

FT ¼

ðUA=CP C ÞCC ðUA=CPC Þ

ð16Þ

The numerator of Eq. (16) is the countercurrent heat duty and the denominator the actual non-countercurrent duty. Equating Eqs. (2) and (3) and rearranging for a countercurrent heat exchanger gives:



UA CPC

 CC

ln ¼h

h

T H1 T C2 T H2 T C1

T H1 T H2 T C2 T C1

i

i

1

¼

 1P ln 1RP R1

ð17Þ

where

R ¼ CPC =CPH ¼ ðT H1  T H2 Þ=ðT C2  T C1 Þ

ð4Þ

and

ð18Þ

The FT correction factor is usually correlated in terms of two dimensionless ratios, the ratio of the two heat capacity flowrates (R) and the thermal effectiveness of the exchanger (P) [13].

F T ¼ f ðR; PÞ ð6Þ

ð7Þ

where

P ¼ ðT C2  T C1 Þ=ðT H1  T C1 Þ

Combining Eqs. (2) and (3) gives:



ðR  1ÞT H1 þ RðX  1ÞT C1 þ ð1  RXÞT H2 ¼ 0 R – 1

ð19Þ

The FT expressions haven been developed for different flow patterns [14]. When using 1–2 heat exchanger with NSHELLS in series, the expressions for FT are [13,14]:for R – 1:

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N. Jiang et al. / Applied Energy 127 (2014) 25–33

i pffiffiffiffiffiffiffiffiffiffiffiffiffiffi h 1P 12 R2 þ 1 ln 1RP 12  FT ¼ pffiffiffiffiffiffiffiffi  2 þ1Þ ðR  1Þ ln 2P12 ðRþ1pRffiffiffiffiffiffiffiffi 2P 12 ðRþ1þ

ð20Þ

R2 þ1Þ

for R = 1:

hpffiffi FT ¼

2P12 1P 12

i

h pffiffi i 2P 12 ð2 2Þ pffiffi ln 2P ð2þ 2Þ

ð21Þ

12

where P1–2 is the effectiveness factor of each shell pass, P is the effectiveness factor across all NSHELLS:For R – 1 [13]:

P¼

1 R



NSHELLS

1P 12 R 1P 12



1P 12 R 1P 12

ð22Þ

NSHELLS

For R = 1 [13]:

P¼

P12 NSHELLS P12 NSHELLS  P12 þ 1

ð23Þ

Eqs. 16, 17, and 20 can be combined to give:

 1P ln 1RP ¼ ðR  1ÞðUA=CP C Þ

i pffiffiffiffiffiffiffiffiffiffiffiffiffiffi h 1P12 R2 þ 1 ln 1RP 12  pffiffiffiffiffiffiffiffi  2 þ1Þ ðR  1Þ ln 2P12 ðRþ1pRffiffiffiffiffiffiffiffi 2P 12 ðRþ1þ

ð24Þ

R2 þ1Þ

Eq. (22) can be rearranged to give:

 ln

   1P 1  P12 ¼ NSHELLS ln 1  RP 1  RP 12

ð25Þ

Combining Eqs. (24) and (25) and rearranging gives:

P12 ¼

2G  2 pffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 GðR þ 1 þ R þ 1Þ  ðR þ 1  R2 þ 1Þ

ð26Þ

where

" pffiffiffiffiffiffiffiffiffiffiffiffiffiffi# UA R2 þ 1 G ¼ exp CPC NSHELLS

ð27Þ

coefficients of the temperatures within Eqs. 7, 9, 12, and 14. For NSTREAM streams involved in the HEN, the number of intermediate streams is (2NUNIT  NSTREAM), which are unknowns. Given the NSTREAM unknown output temperatures, this relates to 2NUNIT unknowns for the whole HEN to be solved through the 2NUNIT equations. Any mixing in a HEN can be described by the mass and energy balance:

1 X T MIX ¼ P CPi  T i i CP i i

ð30Þ

where TMIX is the temperature of the mixing junction (°C), CPi is the heat capacity flowrate of Stream i entering the mixing junction (W K1), and Ti is the temperature of Stream i entering the mixing junction (°C). For network consisting of x mixing points, this will increase the number of equations, and the number of unknowns, by x and therefore increase the matrix and vector size to (2NUNIT + x)  (2NUNIT + x) and 2NUNIT + x, respectively. Given stream heat capacity flowrates, overall heat transfer coefficients, areas and number of shells, then these equations, Eqs. 7, 9, 12, 14, and 30, are linear in temperature, because Eqs. (20) and (21) show that FT is a function of R and P1–2. In turn, Eq. (26) shows that P1–2 is a function of U, A, R, CPC, and NSHELLS. Thus if U, A, R, CPC, CPH, and NSHELLS are fixed then X and Y above are also fixed and if CPi are fixed in Eq. (30), then Eqs. 7, 9, 12, 14, and 30 are a set of linear equations. This set of simultaneous linear equations can be solved efficiently using, for example, the LU Decomposition Method [15]. Manipulating the same set of equations through all units in a HEN, allows a sensitivity analysis in terms of the influence of individual parameter change on the whole network to be quickly carried out. This provides a simple approach to identify the most influential heat exchangers in a given HEN for retrofit. This fast simulation method and sensitivity analysis are also valid for HENs constituted by heat exchangers other than countercurrent or 1–2 type, by substituting the corresponding FT expressions for other heat exchanger design types.

P can then be determined from Eq. (22). Eq. (26) is valid for R = 1, but P must be determined from Eq. (23). Thus, if CPH, CPC, U, A and NSHELLS are known, then P1–2 can be determined from Eq. (26) and substituted into Eq. (20), (21) to obtain FT without knowing the outlet temperatures. This allows a series of NSHELLS for 1–2 heat exchangers to be simulated without iteration [12]. For non-countercurrent heat exchangers Eq. (8) becomes:

X ¼ exp

  UAðR  1ÞF T R–1 CPC

ð28Þ

and Eq. (13) for non-countercurrent heat exchangers becomes:

Y¼

UAF T CPC

R¼1

ð29Þ

Thus Eqs. 7, 9, 12, and 14 can be solved for the outlet temperatures if CPH, CPC, U, A, TH1, TC1 and NSHELLS are known, for both the countercurrent and non-countercurrent heat exchangers. This approach can readily be extended to the simulation of heat exchanger networks without iteration. For a HEN consisting of NUNIT heat transfer units, there will be 2NUNIT equations in total. Through solving this set of equations the intermediate and outlet temperatures of the heat exchanger network may be determined. This may be achieved through the solution of an equation: T = Z1C, where T is a 2NUNITdimensional column vector that refers to the unknown temperatures of the network, C is a 2NUNIT-dimensional column vector, which refers to the known temperatures of the HEN and Z is a parameter matrix of size 2NUNIT  2NUNIT. This matrix features the

Fig. 1. Nonlinear stream heat capacity linearization for a heat exchanger.

N. Jiang et al. / Applied Energy 127 (2014) 25–33

The approach can be adapted to streams with nonlinear heat capacity flowrates. Fig. 1 illustrates the approach for nonlinear stream heat capacity, showing how the enthalpy-temperature profile is linearized between the inlet and outlet temperatures of a heat exchanger. Then a similar approach can be used as for the linear CP case. But this time, the enthalpy of the stream must be defined as a function of temperature, as shown in Fig. 1. Knowing enthalpy as a function of temperature, each time the temperatures are set at an intermediate point in the solution of Eqs. 7, 9, 12, and 14, the inlet and outlet temperatures for each heat exchanger define points on the temperature-enthalpy profile for the stream, as shown in Fig. 1. This defines the enthalpy change for the stream across the heat exchanger, from which CPH and CPC can be calculated. However, the nonlinear temperature-enthalpy profile makes the equation set nonlinear. Different methods can be used to solve the set of nonlinear equations [15]. One way is to use a nonlinear equation solver to manipulate the temperatures and use the LU Decomposition Method to solve the network for each iteration. 2.2. Utility paths This work aims to develop a practical and cost-effective retrofit method, so no topological changes or repiping will be considered. As the retrofit approach does not allow changes in the structure, exchangers to be modified must therefore be situated on a utility path in order to shift heat loads and achieve target temperatures. Utility paths refer to paths between two different utilities in HENs [16]. This represents a route for which heat may be traded between process exchangers within a network and the utilities. Such an example may be seen in Fig. 2. Exchanger A is situated on a utility path and is allocated an additional duty of +W. For the heat loads of the network to balance and target temperatures to be met, the utilities on the same utility path must have a reduction of W. In the context of a retrofit problem, this shift in heat duty could result in a more cost-effective network as the reduction in utility outweighs the cost of enhancement to Exchanger A. It must also be noted that Exchanger B will be subject to a passive change, as the temperature driving forces around the exchanger tighten, whilst the exchanger specifications remain the same. The feasibility of the network retrofit will be violated when a utility path is broken. This can occur when the additional duty to a process exchanger exceeds that of the original utility exchanger. As the utility exchanger is essentially removed from the network, the additional heat load on the exchanger can no longer be shifted and the heat must remain within the stream. As a result, target temperatures will be changed which, depending on the context of the network, could be deemed unacceptable. The proposed retrofit approach has therefore considered the target temperatures of all streams involved, focusing on the ability to shift heat loads around the network through utility paths. This infeasibility is assessed by observing whether the utility falls

Fig. 2. Utility path in a HEN [16].

29

below zero when shifting duty from the utility exchanger to the modified process heat exchanger. If this occurs, then the deviation from target temperature may be considered in relation to user defined boundaries. The extent of this acceptable deviation will therefore depend on the context of the retrofit, which enhances the user driven nature of the retrofit approach. 2.3. Minimum temperature difference As mentioned previously, altering the duty of a single exchanger will result in a passive response throughout the network as temperature driving forces will either be more constricted or relaxed. The retrofit approach has therefore included a heat transfer driving force feasibility check to assess whether minimum temperature approaches have been violated. Whilst a minimum temperature approach is not strictly a constraint, it is useful in most cases to include a minimum temperature difference in order to avoid excessively small temperature differences that make heat exchangers particularly inefficient, and in the case of multiple passes can lead to heat transfer reversal in extreme cases. 2.4. Retrofit procedure Through the application of HEN rapid simulation and sensitivity analysis, considerations of HEN enhancement and retrofit feasibility check, a practical cost-effective retrofit approach can be proposed. This includes the following steps:  Step 1: The retrofit approach initially begins with an analysis of the HEN structure to identify those exchangers on a utility path.  Step 2: Sensitivity analysis is used to identify the most influential heat exchangers on utility paths through their influence on the utility under assessment.  Step 3: Enhance the most influential process heat exchanger identified in Step 2 by heat transfer enhancement (HTE) or area addition, depending on user choice. Check feasibility for utility paths being broken, any violation of minimum temperature difference and stream target temperatures are within acceptable bounds.  Step 4: Adjust stream target temperatures to bring within acceptable bounds if there are violations by adjusting the loads on utility exchangers and if necessary enhancing additional process heat exchangers.  Step 5: Repeat the above steps until the retrofit demand is reached. Fig. 3 presents the retrofit flowchart. The application of sensitivity analysis to retrofit is predominantly based around their ability to determine the change of specific temperatures throughout the network. Given the fact that the utilities in a HEN are used to reach a certain target temperature, by decreasing the temperature change the duty required on the utility exchanger will be subsequently decreased. This will act to lower utility costs and, potentially, the total cost of the network dependant on the cost of the modification. Therefore sensitivity analysis is used to manipulate the inlet temperature of a utility exchanger through applying either area or heat transfer enhancement to various exchangers in the network. The choice of exchangers has been made on the grounds of the most influential exchangers within the network to the temperature of the utility exchanger inlet. Because the retrofit through the guidance of sensitivity analysis is predominantly based around a single temperature, that of the inlet to a hot utility exchanger, a problem may arise when multiple utilities are a feature within a network. As a result, users may define which utility to focus on if the retrofit is constrained by the context of its

30

N. Jiang et al. / Applied Energy 127 (2014) 25–33

represents a deviation from the original base case, the succeeding sensitivity analysis will be based on a newly formulated base case. 3. Case study A simplified preheat train has been chosen as the retrofit case study. The base case HEN can be seen in Fig. 4. Table 1 and 2 give stream and heat exchanger data. All process heat exchangers are 1 shell pass-2 tube pass. HU1 is the hot utility supplied by a fired heater. CU1, CU2, CU3, CU4 are cooling water coolers. The preliminary retrofit objective is to reduce the fuel consumption of fired heater 91 by at least 5%, but maintaining the network structure unchanged. 4. Results and discussion

Fig. 3. Proposed HEN retrofit flowchart.

application. However if such constraints are not present, the proposed retrofit approach will run a simultaneous analysis of each utility to ensure the most cost-effective options are identified. This may arise through the influence which individual exchangers have on a utility or the cost of the utility, for example the cost difference in the use of high and low pressure steam. An analogous idea has been used for considering either heat transfer enhancement (HTE) or area addition. Once again the context of the retrofit problem may result in constraints, such as a lack of space for additional area or the lack of time/resources to afford extended periods of downtime. For both of these constraints, HTE would therefore be the preferred enhancement option. However without these constraints, either additional area or HTE could be the most cost-effective option, therefore initialising a simultaneous assessment and user choice involving both modifications. As enhancement to a process heat exchanger increases, either through HTE or area addition, the retrofit could become infeasible through either breach of the utility path or the violation of a minimum approach temperature. For cases where the minimum approach temperature is limiting, modifications may be made to another exchanger in the network to facilitate further enhancement. This violation may be resolved through the use of sensitivity analysis, which will focus on the inlet and outlet temperatures of the problematic exchanger. Through surveying the influence of each exchanger in the network to these temperatures, sensitivity analysis may identify a potential candidate to modify to resolve the violation of the minimum temperature approach. Independent from whether the temperature difference violation has been resolved, the retrofit approach will shift network heat loads through utility paths to obtain the original target temperatures of the network. If target temperatures are missed, or fall outside of user-defined ranges, then the greatest extent to which the exchanger can be modified is found. If this utility path has not been breached then further enhancement or area may be added. Having obtained the limits for retrofit and calculated the cost savings achievable, users can put additional control over the retrofit through either making further modifications or checking other related issues, for example, pressure drops. If further retrofit is required, then a new base case will be made and the retrofit approach is reinitialised. Because the original modification

The following results illustrate the application of the retrofit approach to the case study. As discussed previously, the retrofit approach first performs a structural analysis to identify exchangers on a utility path. Exchanger 7 is the only heat exchanger not to reside on such a path. As a result, Exchanger 7 has not been considered for retrofit. Heat exchanger 1, 2, 3, 4, 5, 6 are used in the sensitivity analysis stage. Following this utility path identification step, the specific utility to minimise is chosen. Considering the retrofit objective and the fact that the hot utility is much more expensive in comparison to the cold utility, the hot utility has been chosen. Sensitivity analysis is used to identify the most influential exchangers in the network for the specified hot utility. The inlet temperature in the fired heater 91 has been used as the objective temperature for the sensitivity analysis, as any decrease of the inlet temperature in the fired heater 91 will directly reduce the usage of hot utility and relating cost. Fig. 5 presents the sensitivity analysis for this case, showing the change of the inlet temperature to the fired heater with the variation in UA of the individual heat exchangers. Fig. 5 shows clearly that Exchanger 5 exerts the greatest influence on the inlet temperature of the fired heater for the entire range of UA variation. The next most influential heat exchanger is Exchanger 1. The potential load-shifting capacity before a utility path is broken is determined by the minimum load of all the units on a utility path. For this example, all utility paths are bottlenecked by the coolers. Exchanger 5 is connected to cooler 63. The load-shifting of Exchanger 1 is constrained by cooler 61. The duty of cooler 63 is larger than that of cooler 61, which indicates that the potential load-shifting capacity of Exchanger 5 is higher than other exchangers. Thus Exchanger 5 is clearly the most promising candidate exchanger for the following retrofit step.

Fig. 4. HEN for case study.

31

N. Jiang et al. / Applied Energy 127 (2014) 25–33 Table 1 HEN stream data. Stream No.

Name

Supply temperature (°C)

Outlet temperature (°C)

Heat capacity flowrate (kW °C1)

Duty (kW)

1 2 3 4 5 6 7 8 9 10 11

H1 H2 H3 H4 H5 C1 HU1 CU1 CU2 CU3 CU4

310 299 273 230 206 52 500 20 20 20 20

95 120 250 95 178 360 300 30 30 40 30

86 21.4 184.7 23.5 129.4 143.9 – – – – –

18490 3830.6 4248.1 3172.5 3623.2 44321.2 – – – – –

Table 2 Heat exchanger data. Exchanger

Duty (kW)

UA (kW °C1)

NSHELLS

FT

1 2 3 4 5 6 7 61 62 63 64 91

6141 6135 5557 2689 3431 2292 3623 657 1142 817 881 14453

205 259 100 34.2 59.7 59.9 41.4 – – – – –

2 2 1 1 1 1 1 – – – – –

0.878 0.820 0.882 0.937 0.978 0.831 0.985 – – – – –

15

Target temperature change (°C)

Ex1

10

Ex2 Ex3 Ex4

5

Ex5 Ex6

0

-5

-10 -100%

-50%

0%

50%

100%

150%

200%

UAFT variation (%) Fig. 5. Sensitivity analysis result.

For the retrofit step, the extent of modification required for Exchanger 5 should be determined first. From the retrofit objective, a 5% decrease of hot utility, the corresponding temperature increase in the inlet for the fired heater is 5 °C. The sensitivity analysis can give that the required UA enhancement of exchanger 5 is almost 49%, see Fig. 5, which will incur the hot stream outlet temperature of Exchange 5 to decrease 4.4 °C. Thus, the duty enhancement of Exchanger 5 is 812 kW(=4.4 °C  184.7 kW °C1). Noting that the original load of cooler 63 is 817 kW, the load-shifting along the utility path where Exchanger 5 and cooler 63 are located will make the residual load of cooler 63 small at 5 kW. Thus, it makes sense to explore a duty enhancement of 817 kW. If the duties are changed along the utility path, then a check of the temperatures reveals that there are no small temperature differences and the proposed retrofit appears feasible in the context of the network.

Fig. 6. Network changes after enhancement.

Assuming an enhanced UA of 49% for Exchanger 5 with all other exchangers having the original UA from Table 2, the network is simulated in Fig. 6(a). The basis of the simulation is that the process heat exchangers have a fixed UA, but the utility heat exchangers are assumed to have fixed duty. The required target temperatures are no longer achieved. The network then needs to be balanced to achieve the required target temperatures. For this case, this can be achieved by adjusting the duties on the heater and the coolers. The network is simulated for different settings of the cooler duties, keeping the UA of the process heat exchangers fixed until the target temperatures are achieved. The result after balancing is shown in Fig. 6(b), where cooler 63 is spared. The final heater duty is 13,729 kW. This represents a saving 724 kW of hot utility. The saving in cold utility is 742 kW. This discrepancy

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N. Jiang et al. / Applied Energy 127 (2014) 25–33

between the hot and cold utility saving figures is caused by minor differences between the original target temperatures and those achieved in Fig. 6(b). In practice, there is always some tolerance on the target temperatures, depending on the destination of the stream. The design in Fig. 6(b) achieves a saving in hot utility of 5.1%. It should be noted that the change in hot utility is not 817 kW, due to the downstream effects of the enhancement of Heat Exchanger 5. In the overall picture the heat load on any given process exchanger after balancing depends on the UA and temperature driving force of the heat exchanger. Now knowing how much equipment enhancement is required, detailed modification of Exchanger 5 can be explored to achieve the required enhancement. The enhancement of existing heat exchangers can be made by adding new area or enhancing heat transfer. Heat transfer enhancement becomes even more significant in the retrofit design of shell-and-tube heat exchangers. Two commonly used designs are considered here: twisted tapes and coiled wires. Tube inserts are frequently used in tube-side controlling exchangers because inserts are cheap and readily installed in an existing heat exchanger. The heat exchanger model and enhancement models [17] can be conveniently manipulated for design new shell-and-tube heat exchangers or simulating/retrofitting existing ones. The details of Exchanger 5 are given in Table 3. Exchanger 5 is tube-side controlled and a potential candidate for tube insert enhancement. Thus, tube inserts are considered for this case. The performance models for twisted tapes and coiled wires in Ref. [17] are used to calculate the enhanced heat exchanger performance. Given the required duty enhancement of 817 kW on Exchanger 5, different enhancement designs can be obtained. Table 4 gives the performance for three different enhancement options. New area refers to the option of a new unit serially installed at the hot side of the existing exchanger. All the three options in Table 4 can meet the required duty enhancement: installing a new unit of 81.7 m2, twisted-tape tube inserts with a twist ratio of 1.56 and thickness of 3.9 mm, and coiled-wire tube inserts with a pitch of 18.2 mm and thickness of 1.6 mm. The performance is compared in Table 4. Additional area can be connected to the existing one in series, whether on the hot side or the cold side. Installing at the hot side is better because the new unit takes higher flow velocities. Under the serial pattern and new area at the hot side, the load of the original unit reduces to 2983 kW because of the decrease in heat transfer driving force. The new unit takes over the residual 1265 kW of the required 4248 kW load. Table 5 gives the details of the new unit. With the installation of a new unit in series with the original unit, the tube-side stream has a total pressure drop of 27.1 kPa, and the shell-side stream of 44.9 kPa. Compared with installing new units, fitting inserts into tubes of the existing exchanger do not need additional piping or space, but need dismantling and assembly of the equipment. The inserts-induced tube-side pressure drops are 60.9 kPa for twist tapes and 45.8 kPa for coiled wires, which are higher than the case using the new serial unit. However, the shell-side stream pressure drop with tube inserts is kept the same as that in the original exchanger with 22.9 kPa. If the increase in pressure drop using tube inserts enhancement is unacceptable and the heat exchanger features multiple tube passes, then the use of inserts coupled with a decrease in the number of tube passes can still in principle result in a significantly higher overall heat transfer coefficient without an increase in the pressure drop across the heat exchanger. This kind of retrofit is a special case. For this case study, Exchanger 5 is 1–2 type design with floating head. The removal of the pass partition will create a cost for modifying the heads. In this case, the increase in pressure drop is acceptable and no change made to the number of tube passes is required for Exchanger 5. Apparently,

Table 3 Details of existing heat Exchanger 5. Exchanger 5

Streams Specific heat cP (J kg1 K1) Thermal conductivity k (W m1 K1) Viscosity l (mPa s) Density q (kg m3) Flow rate m (kg s1) Inlet temperature (°C) Final temperature (°C) Fouling resistance (m2 K W1) Film heat transfer coefficient (W m2 K1) Pressure drop (Pa) Geometry of heat exchanger Tube pitch pT (m) Number of tubes NT Number of tube passes NP Tube length L (m) Tube effective length Leff (m) Tube conductivity ktube (W m1 K1) Tube pattern (tube layout angle) Tube inner diameter dI (m) Tube outer diameter dO (m) Shell inner diameter DS (m) Number of baffles NB Baffle spacing B (m) Inlet baffle spacing Bin (m) Outlet baffle spacing Bout (m) Baffle cut BC Inner diameter of tube-side inlet nozzle dTN,inlet (m) Inner diameter of tube-side outlet nozzle dTN,outlet (m) Inner diameter of shell-side inlet nozzle dNS,inlet (m) Inner diameter of shell-side outlet nozzle dNS,outlet (m) Shell-bundle diametric clearance (m) Area (m2) Overall heat transfer coefficient (W m2 K1) Duty (kW)

Shellside

Tubeside

2718.5 0.104 0.0986 776 67.93 273 254.42 0.0007 2155.6 22,911

2325 0.0905 1.14 544.5 61.87 193.04 216.89 0.00053 670.4 11,404 0.025 808 2 4.5 4.4 51.91 90° 0.016 0.020 0.9 8 0.488 0.488 0.488 25% 0.3048 0.3048 0.3048 0.3048 0.041 223.2 267.8 3431

different enhancement options feature different merits. If the capital cost data is provided, then economic assessment can be also be made for these options. For example, assuming the capital cost of an exchanger to be $44186 + 388.8A and that of fitting tube inserts $500 + 10A, these enhancement-related investments would be $75,951 for a new unit and $2732 for tube inserts. In addition, the cost of a new unit is likely to be significantly higher due to piping modifications. The designer can make the final enhancement choice, depending on the details of the application and engineering constraints. For example, if the pressure drop of the tube-side stream is a concern, then installing new area might be considered for this case. If the pressure drop of the shell-side stream and capital cost are major factors, then installing tube inserts would be preferred. Parallel additional area is not appropriate and not considered here. The required stream splitting will reduce the flow velocities in the existing exchanger and thus employ the existing area inefficiently. In the parallel pattern, the new unit takes an even higher load allocation and area than the original one, which is unreasonable. So far, it has been demonstrated how to perform the first step retrofit and its impact evaluated. Any further modifications can be made by repeating the procedure. Each retrofit is based on the newly generated network after the last retrofit step. The application of further retrofit to achieve further energy saving is carried out with the assumption of cost of 400 $ kW1 y1 for hot utility and 5.5 $ kW1 y1 for cold utility. For this case, the first retrofit can provide hot utility saving of 724 kW, cold utility saving of 742 kW and operating cost saving of 293,681 $ kW1 y1 by

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N. Jiang et al. / Applied Energy 127 (2014) 25–33 Table 4 Enhancement options for Exchanger 5. Options

hT (W m2 K1)

hs (W m2 K1)

U (W m2 K1)

DA (m2)

Q (kW)

DPT (Pa)

DPS (Pa)

New area Twisted tapes Coiled wires

912.1 1974.2 1974.6

2532.9 2155.6 2155.6

325.4 399.5 399.5

81.7 0 0

1265 4248 4248

15658 60858 45771

21951 22911 22911

Table 5 Design of new unit. New unit in series Number of tubes NT Tube pitch pT (mm) Number of tube passes NP Tube effective length Leff (m) Tube pattern (tube layout angle) Tube inner diameter dI (mm) Tube outer diameter dO (mm) Shell inner diameter DS (m) Number of baffles Area A (m2) Baffle spacing B (m) Baffle cut BC Tube-side inlet nozzle diameter dTN,inlet (m) Tube-side outlet nozzle diameter dTN,outlet (m) Shell-side inlet nozzle diameter dNS,inlet (m) Shell-side outlet nozzle diameter dNS,outlet (m) Shell-bundle diametric clearance LBB (m)

298 31.25 2 3.49 90° 21 25 0.688 7 81.7 0.44 0.25 0.3048 0.3048 0.3048 0.3048 0.0373

implementing a 817 kW duty enhancement on Exchanger 5. Exchanger 5 is limited for further enhancement by the utility path breach. Further retrofit could be carried out by enhancing the next most influential heat exchanger, Exchanger 1 in this case. If it is assumed that the UA of Exchanger 1 is enhanced by 40%, this allows an additional 557 kW of heat exchange, leading to a reduction of 108 kW of hot utility. To balance the network with Exchanger 1 enhanced requires the level of enhancement on Exchanger 5 to be decreased. The resulting cumulative energy saving is 5.7%. Thus the benefits of the second step in the retrofit are marginal and not pursued further. From the case study, it can be seen that the proposed method employs sensitivity analysis to retrofit the existing HEN quickly. Because no network structure changes are used, the recommended retrofit is comparatively low cost. During the retrofit, designers can fully control the procedure and make choices depending on practical constraints and user preferences. Respect of practical constraints and engineering choices is particularly important for retrofit problems, which determines the feasibility and ease of implementation of the design. If there is little retrofit opportunity after screening with the proposed method, mathematical programming methods [4–7] can follow to seek for opportunities by allowing topology changes. 5. Conclusions A simple and practical method for heat exchanger network retrofit is proposed for networks in which the network structure is to be maintained. By considering the importance of practical constraints for retrofit problems, this method adopts a different solution strategy from mathematical optimisation. Based on an improved sensitivity analysis, the most sensitive heat exchangers

in an existing heat exchanger network can be selected quickly without complex computation. Then the chosen candidate heat exchanger can be retrofitted until the feasibility can no longer be maintained. The procedure can be repeated to achieve the retrofit objective. The method searches the retrofit opportunities existing in the network structure, which are comparatively cost-effective because no topological changes are required. During the retrofit, designers can interact with the procedure and make choices depending on practical constraints and user preferences. More investigation on the additivity problem of the sensitivity analysis would enable the proposed strategy to modify more than one heat exchanger simultaneously. Acknowledgement The authors would like to acknowledge the financial support provided by the European Commission 7th Framework Programme: EFENIS (296003). The first author thanks financial support from the National Natural Science Foundation of China (51206147). References [1] Tjoe TN, Linnhoff B. Using pinch technology for process retrofit. Chem Eng 1986;93(8):47–60. [2] Yee TF, Grossmann IE. Optimization model for structural modifications in the retrofit of heat exchanger networks. In: Reklaitis GV, Spriggs HD, editors. Proceedings of the first international conference on foundations of computer aided process operations. Park City, Utah: Elsevier Science Ltd; 1987. p. 653–63. [3] Ciric AR, Floudas CA. A retrofit approach for heat exchanger networks. Comput Chem Eng 1989;13(6):703–15. [4] Yee TF, Grossmann IE. A screening and optimization approach for the retrofit of heat exchanger networks. Ind Eng Chem Res 1991;30(1):146–62. [5] Athier G, Floquet P, Pibouleau L, Domenech S. A mixed method for retrofitting heat-exchanger networks. Comput Chem Eng 1998;22:S505–11. [6] Bochenek R, Jezowski JM. Genetic algorithms approach for retrofitting heat exchanger network with standard heat exchangers. Comput Aided Chem Eng 2006;21:871–6. [7] Rezaei E, Shafiei S. Heat exchanger networks retrofit by coupling genetic algorithm with NLP and ILP methods. Comput Chem Eng 2009;33(9):1451–9. [8] Asante NDK, Zhu XX. An automated approach for heat exchanger network retrofit featuring minimal topology modifications. Comput Chem Eng 1996;20:S7–S12. [9] Smith R, Jobson M, Chen L. Recent development in the retrofit of heat exchanger networks. Appl Therm Eng 2010;30(16):2281–9. [10] Wang YF, Pan M, Bulatov I, Smith R, Kim JK. Application of intensified heat transfer for the retrofit of heat exchanger network. Appl Energy 2012;89(1):45–59. [11] Kotjabasakis E, Linnhoff B. Sensitivity tables for the design of flexible processes (1) – how much contingency in heat exchanger networks is cost effective? Chem Eng Res Des 1986;64(3):197–211. [12] Herkenhoff RG. A new way to rate an existing heat exchanger. Chem Eng 1981;23:213. [13] Bowman RA, Mueller AC, Nagle WM. Mean temperature difference in design. Trans ASME 1940;62(4):283–94. [14] Kern DQ. Process heat transfer. New York: McGraw-Hill; 1950. [15] Press WH, Teukolsky SA, Vettering WT, Flannery BP. Numerical recipes: the art of scientific computing. Cambridge University Press; 2007. [16] Smith R. Chemical process design and integration. New York: Wiley; 2005. [17] Jiang N, Shelley JD, Smith R. Shell-and-tube heat exchanger and tube insert enhancement models. Appl Therm Eng; 2013 (submitted for publication).