Optimization of Heat Exchanger Networks for the Utilization of Low

Article pubs.acs.org/IECR

Optimization of Heat Exchanger Networks for the Utilization of Low-Temperature Process Heat Arjun Narayan Moorthy,† C.C.S. Reddy,‡ and G.P. Rangaiah*,† †

Department of Chemical and Biomolecular Engineering, National University of Singapore, Engineering Drive 4, Singapore 117585 Singapore Refining Company Private Limited, Singapore 628260

‡

ABSTRACT: A heat exchanger network (HEN), using water as a circulating medium, can recover heat from hot process streams and transfer it to cold process streams. Design optimization of such an HEN for utilization of low-temperature process heat (LTHEN) is a complex task. In this paper, three mixed-integer nonlinear programming models, namely, synthesis, retrofit, and alternate retrofit models are formulated to minimize the total annual cost (TAC), for realistic LTHEN design by considering pressure drops and costs of piping, water tanks, pumps, and heat exchangers. The synthesis model provides the best LTHEN design for complete heat recovery from hot process streams and supplying it to cold process streams via the circulating water stream. The retrofit model considers heat recovery from hot process streams to cold process streams only if it is economical by considering trade-off between the capital cost of new heat exchangers and utility cost of existing heaters/coolers. Finally, the alternate retrofit model is similar to the retrofit model except that the former considers heat exchanger costs for heat exchange between hot/cold process streams and cold/hot utilities. One detailed case study from a petroleum refinery is presented to demonstrate the potential benefits of using the proposed models, which provide realistic and industrially acceptable LTHEN design. Use of multiple LTHEN circuits is considered, and the result is compared with the single circuit solution.

1. INTRODUCTION With the rising energy prices, limited fossil fuel reserves, and increasing concerns about global warming, process industries are striving for efficient utilization of energy. Heat exchanger networks (HENs) are beneficial in chemical processes as they recover and reuse the available heat from process streams in the most economic manner.1 They have been studied to obtain the optimal configuration of heat exchangers (HEs) by matching the hot processes streams to the cold process streams in the best possible way.2 Heaters and coolers supply additional heating and cooling to these streams, if required, to achieve their target temperatures. Masso and Rudd3 first used heuristic structuring strategies to synthesize cost-optimal HENs. Linnhoff and Flower4 showed how pinch analysis can be used to ensure maximum energy recovery in a HEN. For given data on process streams, a problem table or composite curves can be constructed to find the pinch point, which helps to determine the most energy efficient configuration for HEN.5,1 Apart from these methods, optimization methods can be employed in a simultaneous or sequential manner.6 In petroleum refineries, energy usage represents approximately 50% of operating cost.7 This makes reducing energy consumption pivotal to improving the profitability of refineries. Currently, 20−50% of energy utilized in a refinery is rejected as waste heat.8 There may be little incentive to recover this low-temperature energy and utilize it within the same process unit. However, with more units and different complex processes within the refinery, it can indeed be profitable to recover energy from some streams at low temperatures in one process unit and utilize it for streams in another process unit. This requires a low-temperature HEN (LTHEN), which employs a circulating medium as the energy carrier to absorb thermal energy from hot process streams (known as heat sources) in the heat source section of the network, © 2014 American Chemical Society

Figure 1. LTHEN structure for heat exchange between heat sources (in the top) and circulating medium as well as between heat sinks (in the bottom) and circulating medium; it also includes an optional heater (H) and cooler (C).

and if required, additional heating is provided by a heater (Figure 1). Subsequently, the circulating medium transfers the absorbed heat to cold process streams (known as heat sinks) in the heat sink section of the network. For continuity of the network, a cooler is used to cool the medium, if required, to allow for optimal heat transfer in the heat source section of LTHEN. As the medium circulates through the two sections, its temperature changes due to the heat exchange with the various heat sources and sinks in different heat exchange intervals (Figure 1). A good design of LTHEN can reduce the total energy cost by 10−15%.9 There are several challenges in the development of a model for a LTHEN. The majority of the HEN problems have their process Received: Revised: Accepted: Published: 17989

April 15, 2014 July 31, 2014 October 20, 2014 October 20, 2014 dx.doi.org/10.1021/ie5015348 | Ind. Eng. Chem. Res. 2014, 53, 17989−18004

Industrial & Engineering Chemistry Research

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stream temperatures, heat capacity flow rates, or heat duties specified. However, these are unknown for the circulating medium at the design phase of the problem. Lai et al.9 proposed a nonsmooth mixed-integer nonlinear programming (MINLP) model to minimize the total cost (which includes capital cost of new HEs and utility costs for the operation of water heater and cooler) for designing a new LTHEN. However, they did not consider capital cost for piping, water tanks, and pumps and also the operating cost of pumps required for LTHEN operation. It is important to consider all these costs for realistic and industrially acceptable LTHEN design. This paper presents, for the first time, models for LTHEN design with complete or partial heat recovery for low-temperature process heat; they also incorporate piping and other LTHEN equipment capital and operating costs. Note that low temperature in this study refers to above ambient and below 200 °C and not to cryogenic temperature. Three MINLP models, namely, synthesis, retrofit, and alternate retrofit models, are presented, and their effectiveness is illustrated with a case study from a petroleum refinery. For design optimization of practical and economical LTHEN, total annual cost (TAC equal to sum of annualized capital cost and operating cost) is a preferred objective function, and hence, it is used in this study. The proposed models would serve as realistic models for LTHEN design and retrofit, and the case study and its results presented will be useful to both researchers and practicing engineers. The rest of this paper is organized as follows. Sections 2 and 3, respectively, present superstructure and models for LTHEN synthesis, retrofit, and alternate retrofit. Section 4 describes the solution methodology. In Section 5, synthesis, retrofit, and alternate retrofit solutions for the case study are presented and discussed. Section 6 evaluates the case study data for multiple LTHEN circuits and compares the solutions with single circuit solutions. Section 7 summarizes the main findings of this study.

In this model, hot and cold process streams are indexed with ih and ic, respectively. The number of hot streams is K, and the number of cold streams is L. There are m intervals in the heat source section and n intervals in the heat sink section. The maximum number of intervals in each of these sections is assumed be the number of process streams in that section. In Figure 2, the circulating medium in LTHEN is assumed to be water under pressure. It is pumped from the heat source section water supply tank and cooled to the required temperature (i.e., at least 10 °C below the lowest target temperature of hot process streams) in the cooler using cooling water (cold utility), which gains heat in the process, and hence, its temperature increases from TCU,in to TCU,out. Then, the cooled circulating water is used for heat recovery from all hot process streams, which exchange heat with the circulating water in an appropriate temperature interval depending on their supply and target temperatures. In the proposed model, each hot process stream is constrained to exchange heat with the circulating water stream only once, for minimizing the capital cost. This constraint is selected mainly to achieve simple and practical LTHEN design. From an industrial operation point of view, fewer HEs are desired for easy operation, maintenance, and optimizing the plot space, which is especially very important for the retrofit cases. As shown in Figure 2, the heated circulating water is now collected as hot water in the cold section water supply tank. It is pumped to the heater for additional heating, if required, using low pressure (LP) steam as the hot utility; in Figure 2, THU refers to the temperature of the LP steam and also steam condensate as it remains constant during the condensation process. Subsequently, the hot water is used to heat all the cold process streams, which will be heated by the circulating water in an appropriate temperature interval depending on their supply and target temperatures. As for the hot process streams, each cold process stream is constrained to exchange heat with the circulating water only once. For continuity, the water returns to the hot section water supply tank after exchanging heat with all the cold process streams (Figure 2). For the retrofit case, it is assumed that hot process streams are currently cooled using the cold utility (namely, cooling water) in

2. LTHEN SUPERSTRUCTURE REPRESENTATIONS The superstructure for the synthesis model, which employs all new HEs and other equipment in LTHEN, is shown in Figure 2.

Figure 2. Superstructure for LTHEN synthesis model. 17990

dx.doi.org/10.1021/ie5015348 | Ind. Eng. Chem. Res. 2014, 53, 17989−18004


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Figure 3. Superstructure for the LTHEN retrofit model.

to minimize water circulation rate and also to maximize heat recovery/supply in heat source/sink sections. The exchangers in an interval would receive water from the header from the previous interval and subsequently transfer it to the header in the next temperature interval. Thus, in doing so for m intervals in the heat source section, (m + 1) headers are required so that the water stream which is heated does not mix with cooler/ hotter water from the previous/next interval. Ph(m + 1)and Pc are the pressure values at the (m + 1)th water header outlet and heat sink section water supply tank inlet, respectively. Negligible pressure drops and piping costs are assumed in the water tanks and pumps inlet piping. In the heat sink section, Pd is the discharge pressure for the circulating water pump, and Pe and Pc1 are the pressure values at the hot utility heater outlet and first water header inlet, respectively. In this superstructure, (n + 1) water headers are considered. Thus, Pc(n + 1) and Pf are the pressure values at the (n + 1)th water header outlet and hot section water supply drum inlet, respectively.

existing coolers and cold process streams are heated using the hot utility (LP steam) in existing heaters. The retrofit model allows heat exchange between hot/cold process streams with the circulating water only if it is economical to install new exchangers for heat recovery/reuse in the LTHEN. Otherwise, the hot utility will continue to be used to heat the cold process streams to the target temperature, and the cold utility will continue to be used to cool the hot streams. This situation is represented by the superstructure in Figure 3. The difference between this and that in Figure 2 is that there is no constraint requiring process streams to exchange heat only with the circulating water in the LTHEN. To get a more realistic model for the LTHEN design, costs of piping, pumping, and hot and cold water supply tanks will be considered. For estimating pumping costs, pressure drop calculations for a given arrangement will have to be made. Figure 4 shows the superstructure with all pressures required for calculating LTHEN pressure drops and, hence, pump capital and operating costs. In the heat source section, Pa refers to the pump discharge pressure, and Pb and Ph1 are the pressures at the outlet of the cooler and the first water header inlet, respectively. The pressure drop of each new process streamwater HE, cooler, and heater is assumed to be 50 kPa. The pressure drop in the piping in each interval that has a HE is calculated on the basis of the product of heat capacity and flow rate (referred to as simply heat capacity flow rate) of the circulating water and on the piping distance between the water header and the HE. Each interval would lead to heating or cooling of the water medium depending on where in the hot/cold section of the LTHEN it is performed. The number of water headers required is dependent on the number of temperature intervals, as mixing of water is not allowed between different temperature intervals. This is mainly

3. LTHEN MODELS 3.1. Synthesis Model for LTHEN Design. As shown in the superstructure in Figure 2, the synthesis model allows for complete recovery of heat from hot process streams and for reusing it to heat cold process streams via the circulating medium. The objective function for this model is the total annual cost (TAC). The objective function to be minimized is: TAC = (OCCU + OCHU + OCPHC) + {(C HP + C HHE + CCUC + C PH + C TH) + (CCP + CCHE + C HUH + C PC + C TC)}/a 17991

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Figure 4. Superstructure for LTHEN pressure drop estimation, which is applicable to both synthesis and retrofit models.

Fih, thin(ih), and thout(ih) are, respectively, the heat capacity flow rate and inlet and outlet temperatures of the hot process stream, ih. The heat capacity flow rate of water, Fwh(ih) through the hot water stream (ih) HE is given by

In this equation, OCCU refers to the operating cost due to the cold utility at the cooler in the heat source section of LTHEN and OCHU refers to the operating cost due to the hot utility at the heater in the heat sink section (Figure 2). OCPHC refers to the operating cost of pumps in the hot and cold sections. CHP, CHHE, CCUC, CPH, and CTH are the capital costs for heat source section piping, new hot process streamwater HEs, cold utility cooler, and heat source section water pump and tank, respectively. Similarly, CCP, CCHE, CHUH, CPC, and CTC are the capital costs for the heat sink section piping, cold process streamwater HEs, hot utility heater, and heat sink section water pump and water tank, respectively. Parameter “a” in eq 1 is the payback period, used to annualize equipment costs; it is assumed to be 2 years. 3.1.1. Equations for Heat Source Section. The heat transferred by K hot process streams to the circulating water stream in the jh interval of the heat source section is

m

Fwh(ih) ×

jh = 1

(4)

The limit on the water heat capacity flow rate for each hot process stream (ih) is Fwh(ih) ≤ Fw

The temperature constraint for the heat source section interval twh(jh + 1) ≥ twh(jh)

(6)

for jh = 1, 2, ..., m. The constraint for the heat exchange of water with the process stream ih only once in all the heat source intervals is

∑ (zh(ih , jh) × Q ex(ih)) ih = 1

(2)

m

In this equation, Fw refers to the heat capacity flow rate of the circulating water, twh(jh) refers to the temperature of water at the start of the jh interval, and twh(jh + 1) refers to the temperature at the end of jh interval, which is also equal to the temperature at the start of (jh + 1) interval. zh(ih,jh) is a binary variable indicating the presence of a HE between the ih hot stream and water in the jh interval. If present, it has a value of 1; otherwise, it is 0. Qex(ih) is the heat available for transfer from the ih hot process stream to the water stream, whose temperature changes within each interval. Heat transferred by the hot process stream ih is Fih × (th in(ih) − thout(ih)) = Q ex(ih)

(5)

is

K

Fw × (twh(jh + 1) − twh(jh)) =

∑ [zh(ih , jh) × (twh(jh + 1) − twh(jh)] = Q ex(ih)

∑ zh(ih , jh) = 1 (7)

jh = 1

for ih = 1, 2, ..., K. The constraint for the total number of HEs equal to the number of streams is K

m

∑ ∑ zh(ih , jh) = K (8)

ih = 1 jh = 1

The temperature constraint for water in the heat source section is 40 < twh(jh) < 150

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for jh = 1, 2, ..., m. The constraint for the minimum approach temperature on the hot end of the hot streamwater HE is th in(ih) − twh(jh + 1) + LV × (1 − zh(ih , jh)) ≥ 10

for jc = 1, 2, ..., n. The constraint for the total number of HEs equal to the number of streams is L

(10)

∑ ∑ zc(ic , jc) = L

where LV is a large value (=1000). Similarly, the constraint for the minimum approach temperature on the cold end of the hot streamwater H is thout(ih) − twh(jh) + LV × (1 − zh(ih , jh)) ≥ 10

The temperature constraint for the heat sink section is 40 < twc(jc) < 150

(11)

twc(jc + 1) − tcout(ic) + LV × (1 − zc(ic , jc)) ≥ 10 (23)

The constraint for the minimum approach temperature on the cold end of the cold process stream water HE is

where TCU,out is the cooling water outlet temperature. Similarly, the constraint for the minimum temperature approach on the cold end of the cold water utility HE (cooler) is

twc(jc) − tc in(ic) + LV × (1 − zc(ic , jc)) ≥ 10

where TCU,in is the cooling water inlet temperature. Heat removed in the cooler is

THU − twc(n + 1) ≥ 10

(14)

L

THU − twh(m + 1) ≥ 10

∑ (zc(ic , jc) × Q ex(ic)) ic = 1

In this equation, twc(jc) and twc(jc + 1) are the water temperature, respectively, at the start and end of the temperature interval, jc. zc(ic,jc) is the binary variable for the absence (=0) or presence (=1) of cold process stream ic-water HE in the temperature interval, jc.Qex(ic) is the heat absorbed by the heat sink streams. Heat transferred to the cold process stream ic is

Fw × ((twc(n + 1) − twh(m + 1)) = Q HUH

(16)

n

⎛ d ⎞ P b − Ph1 = ⎜( −0.0023 × Fw + 9.0925) × b1 ⎟ ⎝ 100 ⎠

∑ [zc(ic , jc) × (twc(jc + 1) − twc(jc))] = Q ex(ic) jc = 1

(17)

(18)

The temperature constraint for the heat sink section intervals is twc(jc + 1) ≥ twc(jc)

⎛⎛ 2 × dih ⎞ ⎟ ΔP(ih) = ⎜⎜( −0.0023 × Fwh(ih) + 9.0925) × ⎝ 100 ⎠ ⎝

(19)

for jc = 1, 2, ..., n. The constraint for heat exchange of water with process stream (ic) only once in all the heat sink intervals is

⎞ + (hih × g )⎟ + 50 ⎠

n

∑ zc(ic , jc) = 1 jc = 1

(28)

Here, db1 is the distance in meters between the cooler outlet and water header 1 in the heat source section. The pressure drop for the ih hot process streamwater HE and its inlet and outlet piping, assuming 50 kPa pressure drop in each of the HE, is

The limit on the water heat capacity flow rate for each cold process stream (ic) is Fwc(ic) ≤ Fw

(27)

3.1.3. Pressure Drop and Cost Equations. The pressure drop and cost correlations along with utility data, required in the following equations for modeling the superstructure, are summarized in Appendix A. Linearization of piping pressure drop and cost correlations in this appendix is to reduce the nonlinearity of the model. Loss of accuracy in this is minimal as shown by R2 of 0.91 or more for linearized equations (i.e., R2 = 0.99 for HE cost, R2 = 0.98−0.99 for water tank and pump cost, R2 = 0.91 for piping pressure drop, and R2 = 0.98 for piping cost). Pressure drop for piping in the heat source section (between cooler and water header 1) in kPa is10

In the above equation, Fic, tcin(ic), and tcout(ic) are, respectively, the cold process stream heat capacity flow rate, inlet temperature, and outlet temperature. Water heat capacity flow rate, Fwc(ic), through the cold water process stream (ic) HE is given by Fwc(ic) ×

(26)

where THU is the hot utility inlet temperature. Heat gained in the hot utility heater is

(15)

Fic × (tcout(ic) − tc in(ic)) = Q ex(ic)

(25)

where THU is the hot utility outlet temperature, assumed to be constant for the case of saturated steam as the hot utility. The constraint for the minimum temperature approach on the cold end of the heater is

3.1.2. Equations for Heat Sink Section. Heat transferred by the heated water to cold process streams in the interval jc of the heat sink section is Fw × (twc(jc + 1) − twc(jc)) =

(24)

Equations 23 and 24 allow for a minimum temperature approach of 10 °C if zc(ic,jc) = 0. The constraint for the minimum temperature approach on the hot end of the hot water utility HE (heater) is

(13)

Q CUC = Fw × (twc(1) − twh(1))

(22)

for jc = 1, 2, ..., n. The constraint for the minimum approach temperature on the hot end of the cold process streamwater HE is

(12)

twh(1) − TCU , in ≥ 10

(21)

ic = 1 jc = 1

Equations 10 and 11 allow for a minimum temperature approach of 10 °C in the case of zh(ih,jh) = 1, and they are also satisfied for no HE in that interval because of the term with LV. The constraint for the minimum temperature approach on the hot end of the cold water utility HE (cooler) is twc(1) − TCU,out ≥ 10

n

(29)

Here, dih is the distance in meters between the hot process streamwater HE and water header. Since water comes from each

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The total pressure drop in each of heat sink section water headers in kPa is

header for HEs within an interval, this applies to the distance from HE to the header for both inlet and outlet piping. hih refers to the elevation in meters between the water header and the HE for the ih hot process stream. Total pressure drop in each of the hot section water headers in kPa is

⎛ d (jc) ⎞ ΔPhdr(jc) = ⎜( −0.0023 × Fw + 9.0925) × hdr ⎟ ⎝ 100 ⎠ (39)

⎛ d (jh) ⎞ ΔPhdr(jh) = ⎜( −0.0023 × Fw + 9.0925) × hdr ⎟ ⎝ 100 ⎠

where dhdr is the length of the water header in the cold section, in meters. Inlet pressure at each water header inlet in the heat sink section is

(30)

Here, dhdr is the length of water header jh in meters. The inlet pressure at each water header inlet in the heat source section is Ph

(jh)

− Ph

(jh + 1)

Pc(jc) − Pc(jc + 1) + LV × (1 − zc(ic , jc)) ≥ ΔP(ic) × zc(ic , jc) + ΔPhdr(jc)

+ LV × (1 − zh(ih , jh))

≥ ΔP(ih) × zh(ih , jh) + ΔPhdr(jh)

Total pressure drop for all HEs, their inlet and outlet piping, and water headers in the cold section is

(31)

ΔPCEP = Pc1 − Pc n + 1 − ΔPhdr(n + 1)

The total pressure drop for all HEs, their inlet and outlet piping, and water headers is ΔPHEP = Ph1 − Ph m + 1 − ΔPhdr(m + 1)

Pressure at the end of the (n + 1) water header is Pce n + 1 = Pc1 − ΔPCEP

(32)

(33)

⎛ dn + 1,f ⎞ Pce n + 1 − P f = ⎜( −0.0023 × Fw + 9.0925) × ⎟ 100 ⎠ ⎝

The hot section pressure drop between the outlet of the (m + 1)th water header and the inlet of the heat sink section water tank, in kPa, is

(43)

In this equation, dn+1,f is the distance in meters between the (n + 1)th water header and the heat source section water tank. The pressure drop for the new hot water utility HE, in kPa, is

⎛ dm + 1,c ⎞ Phe m + 1 − P c = ⎜( −0.0023 × Fw + 9.0925) × ⎟ 100 ⎠ ⎝ (34)

ΔPHUH = P e − P d = 50

In the above equation, dm+1,c is the distance in meters between hte (m + 1)th water header and the inlet of the heat sink section water tank. The pressure drop across the cold water utility HE (cooler), in kPa, is b

ΔPCUC = P − P = 50

PDc = (P d − P f )

(35)

PPH =

Fw × 0.1019 × PD h × g ηp × ηpm × 4.178 × 1000

(46)

where ηp and ηpm are the efficiency of the pump (=0.75) and motor (=0.95), respectively. The cold section pump power in kW is

(36)

Fw × 0.1019 × PDc × g ηp × ηpm × 4.178 × 1000

PPC = (37)

(47)

Hot section piping cost in US$ is

Here, de1 is the distance in meters between the hot utility heater and water header 1 in the heat sink section. The pressure drop for the cold process streamwater HE and its inlet and outlet piping, assuming a 50 kPa pressure drop in each of the HE, is

⎛ C HP = (0.2861 × Fw + 235.1) × ⎜⎜db1 + ⎝

m+1

⎞

jh = 1

⎠

∑ dhdr(jh) + dm + 1,c⎟⎟

K

+

⎛⎛ 2 × dic ⎞ ⎟ ΔP(ic) = ⎜⎜( −0.0023 × Fwc(ic) + 9.0925) × ⎝ 100 ⎠ ⎝ ⎞ + (hic × g )⎟ + 50 ⎠

(45)

The hot section pump power in kW is

The pressure drop for piping in the cold section between the hot utility heater and header 1, in kPa, is ⎛ d ⎞ P e − Pc1 = ⎜( −0.0023 × Fw + 9.0925) × e1 ⎟ ⎝ 100 ⎠

(44)

The heat sink section pumping differential pressure is

The hot section pumping differential pressure is PD h = (P a − P c)

(42)

The cold section pressure drop between the outlet of the (n + 1)th water header and the heat source section water tank, in kPa, is

Pressure at the end of the (m + 1) header is

a

(41)

th

th

Phe m + 1 = Ph1 − ΔPHEP

(40)

∑ 2 × (0.2861 × Fwh(ih) + 235.1) × dih ih = 1

(48)

Cold section piping cost in US$ is ⎛ CCP = (0.2861 × Fw + 235.1) × ⎜⎜de1 + ⎝

(38)

for ic = 1, 2, ..., L. In the above equation, dic and hic are, respectively, distance and elevation in meters between the cold process streamwater HE and the water header.

n+1

⎞

jc = 1

⎠

∑ dhdr(jc) + dn+ 1,f ⎟⎟

L

+

∑ 2 × (0.2861 × Fw(ic) + 235.1) × dic ic = 1

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The area of hot section HEs, in m2, is given by

The cold section water pump cost in US$ is

⎛⎛ th (ih) + th (ih) ⎞ out Ah(ih , jh) × 250 × ⎜⎜ in ⎟ ⎠ 2 ⎝⎝

C PC = (3331.9 × PPC) + 64768

The operating cost of a cooler in the hot section and of a heater in the cold section are, respectively, in US$/year:

⎛ twh(jh) + twh(jh + 1) ⎞⎞ −⎜ ⎟⎟ = Q ex(ih) × 1000 ⎝ ⎠⎠ 2 (50)

for ih = 1, 2, ..., K and jh = 1, 2, ..., m. The arithmetic mean is used in this and other similar equations to reduce the degree of nonlinearity. The overall heat transfer coefficient value for hot section HEs is 250 W/m2·°C.11 The hot section HEs cost in US$ is K

C HHE =

m

(63)

The area of cold section HEs in m is ⎛⎛ twc(jc) + twc(jc + 1) ⎞ Ac(ic , jc) × 250 × ⎜⎜ ⎟ ⎠ 2 ⎝⎝ (52)

for ic = 1, 2, ..., L and jc = 1, 2, ..., n. The cold section HEs cost in US$ is n

∑ ∑ zc(ic , jc) × (278.97 × Ac(ic , jc) + 37848) ic = 1 jc = 1

(53) 2

The area of the cooler in m is given by ⎡⎛ twc(1) + twh(1) ⎞ ⎛ t inCU + toutCU ⎞⎤ ⎟⎥ ⎟−⎜ A CUC × 800 × ⎢⎜ ⎠⎦ ⎠ ⎝ 2 2 ⎣⎝

TAC = (OCCUCE + OCHUHE + OCPHC) + ((C HP + C HHE + CCUC + C PH + C TH)

(54)

+ (CCP + CCHE + C HUH + C PC + C TC))/a

Here, the overall heat transfer coefficient of the water cooler is 800 W/m2·°C.11 The cold utility cooler cost in US$ is CCUC = (278.97 × A CUC) + 37848

(55)

(56)

The hot section water pump cost in US$ is C PH = (3331.9 × PPH) + 64768

(57)

2

The heater area in m is given by

K ih = 1

+

(58)

ih = 1 jh = 1

∑ (yh(ih) × Q ex(ih)) ih = 1

(66)

Here, the total heat available for transfer from the hot process streams is equal to the heat transferred to the LTHEN and the heat rejected to the cold utility in existing coolers in the heat source section. yh(ih) is a binary variable denoting the presence (=1) or absence (=0) of an existing cooler to cool process streams with cold utility if it is economical to do so. In either case, the following constraint for heat exchange of hot

(59)

The hot water tank cost in the cold section in US$ is C TC = (850.32 × Fw ) + 59613

m

K

Here, the overall heat transfer coefficient of the hot utility heater is 1500 W/m2·°C.11 The hot utility heater cost in US$ is C HUH = (278.97 × AHUH ) + 37848

K

∑ Q ex(ih) = ∑ ∑ (Q ex(ih) × zh(ih , jh))

⎛ twh(m + 1) + twc(n + 1) ⎞ AHUH × 1500 × ⎜THU − ⎟ ⎝ ⎠ 2 = Q HHU × 1000

(65)

where OCCUCE is the operating cost of the cooler in LTHEN and existing coolers for cooling hot process streams (see eq 74 given later) and OCHUHE is the operating cost of the heater in LTHEN and existing heaters for heating cold process streams (see eq 75 given later). Other terms have been defined after eq 1. Note that eq 65 includes the operating cost of existing coolers and heaters if they continue to be used after retrofitting with the LTHEN. In addition to eqs 2−6 and 9−14, equations for the heat source section are as follows. Energy balance for the heat source section in the superstructure (Figure 3) is

The cold water tank cost in the hot section in US$ is C TH = (850.32 × Fw ) + 59613

(64)

Here, E is the electricity cost (=0.0605 US$/kWh). 3.2. Retrofit Model for LTHEN Design. For the retrofit case, it is assumed that hot process streams are currently cooled using a cold utility in existing coolers and cold process streams are heated using a hot utility in existing heaters. The retrofit model considers recovering heat from hot process streams and supplying it to cold process streams only if it is economical. If this exchange of heat within the LTHEN is present, capital cost would be incurred for the new HEs, and this cost would be determined by the heat exchange area required for it (e.g., eqs 51 and 53). If exchanging heat within the LTHEN is not economical, then the corresponding hot/cold streams would continue to be cooled/heated by cold/hot utilities in the existing coolers/heaters in the plant. In such cases, the cost incurred would be the utility costs to heat or cool the process streams. The objective function, TAC, for the retrofit model is given by

(51)

= Q CUC × 1000

OCHU = (8400 × C HU × Q HUH )

12

2

L

(62)

OCPHC = 8400 × (PPC + PPH) × E

ih = 1 jh = 1

CCHE =

OCCU = (8400 × CCU × Q CUC)

Here, 8400 is the total number of operating hours per year, CHU is the cost of LP steam (=0.0506 US$/kWh) and CCU is the cost of cooling water (=0.0013 US$/kWh), both from Turton et al.12 The operating cost of pumps in hot and cold sections are, respectively, in US$/year

∑ ∑ zh(ih , jh) × (278.97 × Ah(ih , jh) + 37848)

⎛ tc (ic) + tcout(ic) ⎞⎞ − ⎜ in ⎟⎟ = Q ex(ic) × 1000 ⎝ ⎠⎠ 2

(61)

(60) 17995



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stream ih with the circulating water stream in LTHEN should be satisfied:

The operating cost of the heater and existing heaters in the heat sink section is

m

OCHUHE = (8400 × C HU × Q HUH)

∑ zh(ih , jh) + yh(ih) = 1

L

(67)

jh = 1

+

The constraint for the maximum number of HEs for heat transfer between hot streams and the circulating water stream is K

m

ic = 1

∑ ∑ zh(ih , jh) + ∑ yh(ih) = K (68)

ih = 1

In addition to eqs 15−19 and 22−27, the equations for the heat sink section are as follows. Energy balance for the heat sink section in the superstructure (Figure 3) is L

L

n

L

TAC = (OCCUCE + OCHUHE + OCPHC)

∑ Q ex(ic) = ∑ ∑ (Q ex(ic) × zc(ic , jc)) + ∑ (yc(ic) × Q ex(ic)) ic = 1

ic = 1 jc = 1

+ ((C HP + C HHE + C HUE + CCUC + C PH + C TH)

ic = 1

(69)

+ (CCP + CCHE + CCUE + C HUH + C PC + C TC))/a

Here, the total heat absorbed by the cold process streams is equal to the heat transferred from the LTHEN and heat gained from the hot utility in existing heaters. yc(ic) is a binary variable that denotes the presence (=1) or absence (=0) of an existing heater to heat process streams if it is economical to do so with the hot utility. In either case, the following constraint for the heat exchange of the cold stream ic with the circulating water stream in LTHEN should be satisfied:

⎛⎛ th (ih) + th (ih) ⎞ ⎛ tCU,in + tCU,out ⎞⎞ out ⎟⎟ Ah(ih) × 800 × ⎜⎜ in ⎟−⎜ ⎠⎠ ⎠ ⎝ 2 2 ⎝⎝

∑ zc(ic , jc) + yc(ic) = 1

= Q ex(ih) × 1000

(70)

n

K

C HUE =

L

∑ ∑ zc(ic , jc) + ∑ yc(ic) = L ic = 1 jc = 1

(71)

K

+

m+1

⎞

jh = 1

⎠

⎛ ⎛ tc (ic) + tcout(ic) ⎞⎞ Ac(ic) × 1500 × ⎜THU − ⎜ in ⎟⎟ ⎠⎠ ⎝ 2 ⎝

∑ dhdr(jh) + dm + 1c⎟⎟

= Q ex(ic) × 1000

ih = 1 jh = 1

L

(72)

L

+

n+1

⎞

jc = 1

⎠

CCUE =

∑ dhdr(jc) + dn+ 1f ⎟⎟

∑ ∑ 2 × (0.2861 × Fw(ic) + 235.1) × dic × zc(ic , jc) (73)

The operating cost of cooler and existing coolers in the heat source section is OCCUCE = (8400 × CCU × Q CUC) K ih = 1

(80)

4. SOLUTION METHODOLOGY The solution methodology for all the three models is summarized in Figure 5. Initial water flow rate (Fw0) for the LTHEN model is obtained from temperature−enthalpy composite curves for the hot and cold process streams, using a 10 °C approach temperature.9 This provides a feasible region of operation for the heat capacity flow rate of water. Using this initial water flow rate, the LTHEN model with HE capital costs, but without pressure drop, piping, and other equipment costs, is solved first for minimizing TAC. The optimization is first performed in this manner to reduce additional computational load and nonlinearity due to pressure drop, piping, and other

n

∑ yh(ih) × 8400 × CCU × Q ex(ih)

∑ yc(ic) × (278.97 × Ac(ic) + 37848) ic = 1

ic = 1 jc = 1

+

(79)

The capital cost of heaters (HEs) for cold process streams to exchange heat with the hot utility in US$ is

m

∑ ∑ 2 × (0.2861 × Fwh(ih) + 235.1) × dih × zh(ih , jh)

⎛ CCP = (0.2861 × Fw + 235.1) × ⎜⎜de1 + ⎝

(78)

The area of cold process, hot stream utility HEs, in m2, is given by

Equations 28−47 for the pressure drop and cost equations from eqs 50−61 and 64 are valid for the retrofit model as well. Hot and cold section piping cost in US$ are, respectively, ⎛ C HP = (0.2861 × Fw + 235.1) × ⎜⎜db1 + ⎝

∑ yh(ih) × (278.97 × Ah(ih) + 37848) ih = 1

ic = 1

(77)

The capital cost of coolers (HEs) for hot process streams to exchange heat with the cold utility in US$ is

The constraint for the maximum number of HEs for the heat transfer between cold process streams and the circulating water stream is L

(76)

where CHUE and CCUE are capital costs for hot process, cold stream utility and cold process, hot stream utility HEs, respectively. Other symbols are defined in connection with the synthesis and retrofit models, in Sections 3.2 and 3.3. The area of hot process, cold stream utility HEs, in m2, is given by

n jc = 1

(75)

3.3. Alternate Retrofit Model for LTHEN Design. The alternate retrofit model is the same as the retrofit model, with the exception of consideration of HE costs for hot process, cold stream utility and cold process, hot stream utility HEs. It can also be used for new LTHEN design. In addition to the equations for the retrofit model, this model involves eqs 77−80. The objective function, TAC, for alternate retrofit model is given by

K

ih = 1 jh = 1

∑ yc(ic) × Q ex(ic) × 8400 × C HU

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Figure 5. Solution methodology for synthesis, retrofit, and alternate retrofit models.

equipment costs. Then, using the water flow rate (FW) obtained, the LTHEN model with all costs including piping and other equipment costs (using linear equations in Appendix A) and also pumping operating costs is solved for the same objective function. As the proposed models are MINLP, there are multiple optimal solutions, and so, the optimizer employed may not give the global optimum. We have solved the models using two solvers: BARON in GAMS and Frontline Premier Solver Pro. Both of them gave the same optimal solution for each case tried. The proposed models are highly nonlinear if nonlinear equations are used for capital cost estimation of HEs, piping, pumps, and water tanks. Hence, the use of the proposed linear equations in Appendix A reduces computational time significantly. The linearized capital cost equation for the HE is applicable only for shell and tube HEs. Hence, users need to replace it if other exchanger types are involved in the application. Obviously, linear equations proposed in Appendix A are valid only within the range shown in Figures A1 to A3.

NLP solver of Frontline Premier Solver Pro and also BARON solver of GAMS. The same optimal solutions were obtained by both these solvers. Note that the results presented and discussed in this and the next sections are for the minimum approach temperature of 10 °C. Sensitivity analysis was conducted for various approach temperatures from 2 to 10 °C in the synthesis model. These results, summarized in Appendix C, show that TAC decreases with the approach temperature. However, 10 °C is selected since the case study involves only shell and tube HEs, and it is well accepted in industrial practice as the minimum approach temperature for shell and tube HEs. For this problem, the synthesis model (without the pressure drop considerations) gave the optimum solution with 2 heat source section intervals and 2 heat sink section intervals. Then, the synthesis model was applied with pressure drops and piping and equipment cost (pumps and water supply tanks) for piping elevations and distances in Table B1 of Appendix B. The same LTHEN structure (Figure 7) was achieved although the optimal TAC found with pressure drops, piping, and other LTHEN costs is 54.8% more than that without pressure drops, piping, and other LTHEN costs, mainly due to capital cost (Table 2). Note that H5 and C5 are in separate sections in the synthesis model solution (Figure 7), probably due to their final temperatures, which are extreme compared to other streams involved. The optimal solution for the retrofit model was found to have the same configuration for both with and without the pressure drop, piping, and LTHEN costs. The optimal LTHEN configuration (Figure 8) shows the arrangement of 4 HEs in the heat source section and also in the heat sink section. For this solution, H5 and C5 process streams are cooled and heated, respectively, by cold and hot utility in the existing HEs. This is more economical than exchanging heat with the circulating water, mainly due to higher utility loads at the heater and cooler in the LTHEN. These higher utility loads are avoided by not requiring heat exchange with H5 (which has to be cooled to the lowest temperature among all hot streams in the case study) and also with C5 (which has to be heated to the highest outlet temperature among all cold streams) in the LTHEN. Thus, the capital cost of new HEs for heat exchange with H5 and C5 in the LTHEN is also avoided. It is evident from Table 2 that TAC is much higher if pressure drop, piping, and other LTHEN costs are considered. With these

5. CASE STUDY In this section, one case study from a Southeast Asian petroleum refinery is presented to illustrate the application and effectiveness of the synthesis and retrofit models. The hot and cold process streams in this case study are presented in Table 1. The solution Table 1. Hot and Cold Process Stream Data for the Case Study hot stream data

H1 H2 H3 H4 H5

cold stream data

Q (kW)

tin (°C)

tout (°C)

1464 2580 1855 1096 1425

180 93 113 158 65

65 60 60 75 50

C1 C2 C3 C4 C5

Q (kW)

tin (°C)

tout (°C)

2295 2160 1300 2970 560

30 40 30 35 76

57 76 50 80 90

methodology shown in Figure 5 was applied. The minimum water flow rate for the LTHEN for the streams in Table 1 is 154 kW/°C from the hot/cold composite curves and operating line in Figure 6. This provides the lower bound on the heat capacity flow rate of circulating water for optimization. Solutions to both the synthesis and retrofit models were found using the 17997



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Figure 6. Hot and cold composite curves along with the circulating water operating line on the temperature−enthalpy diagram for the case study, to determine the minimum heat capacity flow rate for LTHEN.

Figure 7. The optimal solution using the synthesis model with pressure drops, piping, and other LTHEN costs. Pressures shown are gauge pressures.

costs, optimal TAC increased by 54.8% and 58.2%, respectively, in the synthesis and retrofit model solutions, mainly due to capital cost of piping, water pumps, and water tanks. In fact, piping cost is significant, accounting for 64.8% and 59.1% of the additional TAC in the synthesis and retrofit model solutions, respectively. The other LTHEN costs are also quite significant. Hence, it is very important to consider piping and other LTHEN costs for the realistic design of LTHEN. The retrofit model solution uses existing HEs (H5 and C5) by exchanging heat with cooling water and LP steam, respectively (Figure 8). It also uses fewer temperature intervals compared to the synthesis model solution. These reduce TAC for the retrofit (US$1.677 million) compared to the synthesis case (US$2.217 million). Understandably, this reduction in TAC is more for the case with piping and other LTHEN costs (Table 2). For the case study, the optimal solution for the alternate retrofit model is the same as that for the retrofit model (i.e., uses existing HEs for H5 and C5 for exchanging heat with cooling water and LP steam, respectively, and same number of

temperature intervals). This is mainly due to the fact that utilities required in Figure 8 are the same as those obtained from pinch analysis (Appendix D). Compared to the synthesis model solution, the results of the alternate retrofit model in Table 2 show that TAC is reduced from US$3.433 million to US$2.703 million (for the case with LTHEN costs). The TAC for the alternate retrofit model is marginally higher than that for retrofit model (for the case with LTHEN costs) by US$0.05 million. This is because this model solution includes the HE cost for hot/cold process streams, cold/hot utility HEs in addition to all the costs in the retrofit model solution. In the case study, water header lengths are quite significant (at 630 m); see Table B1 in Appendix B. This may have made the cost of piping rather high (more than US$0.5 million) due to the number of headers needed for both the heat source and heat sink sections. This would probably be the situation where the plant is big with very long pipe racks to connect different process streams in the plant. Suppose the plant size is smaller such that the water header piping lengths are halved to 315 m. The associated costs 17998



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Table 2. Results of Solutions for Synthesis, Retrofit, and Alternate Retrofit Model, Each without and with LTHEN Equipment Costs in Million US$ model

synthesis

retrofit

alternate retrofit

without or with LTHEN costs

without LTHEN costs

with LTHEN costs

without LTHEN costs

with LTHEN costs

without LTHEN costs

with LTHEN costs

capital cost of hot section HEs, CHHE or (CHHE + CHUE)a capital cost of cold section HE, CCHE or (CCHE + CCUE)a capital cost of heater, CHUH capital cost of cooler, CCUC hot section piping cost, CHP cold section piping cost, CCP capital cost of hot section pump, CPH capital cost of cold section pump, CPC capital cost of hot section tank, CTH capital cost of cold section tank, CTC total capital cost annualized capital cost

0.707 0.686 0.048 0.108 1.549 0.775

0.707 0.686 0.048 0.108 0.789 0.786 0.163 0.178 0.226 0.226 3.917 1.958

0.596 0.738 0.043 0 1.377 0.688

0.596 0.738 0.043 0 0.58 0.574 0.124 0.15 0.240 0.240 3.285 1.643

0.655 0.778 0.043 0 1.476 0.738

0.655 0.778 0.043 0 0.58 0.574 0.124 0.15 0.240 0.240 3.384 1.692

operating cost for heating, OCHUHE operating cost for heating, OCHU operating cost for cooling, OCCUCE operating cost for cooling, OCCU operating cost of pumps, OCPHC total operating cost TAC

not applicable 1.415 1.415 not applicable 0.027 0.027 0.032 1.442 1.474 2.217 3.433

a

0.751 0.751 not applicable 0.238 0.238 not applicable 0.022 0.989 1.01 1.677 2.653

0.751 0.751 not applicable 0.238 0.238 not applicable 0.022 0.989 1.01 1.727 2.703

Note that (CHHE + CHUE) and (CCHE + CCUE) are applicable to the alternate retrofit model only.

Figure 8. Optimal solution for the retrofit model with pressure drops, piping, and other LTHEN costs. Pressures shown are gauge pressures.

Halving the piping length leads to US$0.275 million in savings for the synthesis solution and US$0.186 million for the retrofit solution. These in conjunction with the payback period of 2 years result in 7−8% decrease in the TAC.

Table 3. Effect of Halving the Water Header Piping Length on Costs in Million US$ model

synthesis

retrofit

water header piping length

halved

original

halved

original

hot section piping cost, CHP cold section piping cost, CCP annualized capital cost TAC

0.514 0.511 1.683 3.158

0.789 0.786 1.958 3.433

0.394 0.388 1.457 2.517

0.580 0.574 1.643 2.653

6. LTHEN DESIGN USING MULTIPLE CIRCUITS The synthesis, retrofit, and alternate retrofit models can also be used to design each circuit in a multiple LTHEN circuit. This is mainly to explore different configurations, with the aim of a lower TAC. Having more circuits is likely to lead to higher capital costs due to piping and other LTHEN costs although operating costs may be reduced. However, this is highly dependent on process stream temperatures and distances between process streams

in the optimal solutions found using the synthesis and retrofit models are shown and compared in Table 3. Other costs not shown in this table are similar to or the same as those in Table 2. 17999



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Figure 9. Optimal solution using the synthesis model for 2 circuits with pressure drops, piping, and other LTHEN costs; circuit 1 is above, circuit 2 is below, and pressures shown are gauge pressures.

Table 4. Optimal Results for Synthesis and Retrofit Models, Each with Piping and Other LTHEN Equipment Costs: Comparison of Two and Single Circuits, in Million US$ model

synthesis

retrofit

two or single circuit

circuit 1

circuit 2

total

single

circuit 1

circuit 2

total

single

capital cost of hot section HE, CHHE capital cost of cold section HE, CCHE capital cost of heater, CHUH capital cost of cooler, CCUC hot section piping cost, CHP cold section piping cost, CCP capital cost of hot section pump, CPH capital cost of cold section pump, CPC capital cost of hot section tank, CTH capital cost of cold section tank, CTC total capital cost annualized capital cost

0.603 0.485 0.040 0.070 0.558 0.297 0.130 0.115 0.181 0.181 2.66 1.33

0.147 0.208 0.046 0.000 0.310 0.335 0.074 0.082 0.091 0.091 1.384 0.692

0.749 0.693 0.085 0.070 0.867 0.632 0.204 0.197 0.272 0.272 4.044 2.022

0.707 0.686 0.048 0.108 0.789 0.786 0.163 0.178 0.226 0.226 3.917 1.958

0.467 0.431 0.042 0.000 0.391 0.238 0.098 0.093 0.174 0.174 2.108 1.054

0.160 0.133 0.042 0.000 0.308 0.247 0.071 0.075 0.086 0.086 1.208 0.604

0.627 0.564 0.084 0.000 0.699 0.485 0.169 0.168 0.260 0.260 3.316 1.658

0.596 0.738 0.043 0.000 0.58 0.574 0.124 0.15 0.240 0.240 3.285 1.643

0.577

0.174 0.751 not applicable 0.238 0.238 not applicable 0.003 0.012 0.415 1.001 1.019 2.659

0.751

operating cost for heating, OCHUHE operating cost for heating, OCHU operating cost for cooling, OCCUCE operating cost for cooling, OCCU operating cost of pumps, OCPHC total operating costs TAC

0.295 0.008 0.018 0.321 1.651

not applicable 0.412 0.708 not applicable 0.000 0.008 0.004 0.022 0.416 0.738 1.110 2.76

within the plant. To investigate this for the case study, process streams H2, H3, H5, C1, C2, and C3 are chosen to be part of the first circuit. The second circuit constitutes process streams H1, H4, C4, and C5. These are chosen on the basis of their proximity

1.415 0.000 0.027 0.032 1.474 3.433

0.009 0.586 1.64

0.238 0.022 1.01 2.653

within the plant. The piping distances for circuits 1 and 2 are given in Appendix B. Figure 9 shows the synthesis model solution for the 2 circuits. Compared to Figure 7, it is evident that there are operational 18000



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Figure 10. Optimal solution using the retrofit model for 2 circuits with pressure drops, piping, and other LTHEN costs; circuit 1 is above, circuit 2 is below, and pressures shown are gauge pressures.

7. CONCLUSIONS In this paper, LTHEN design was presented using the synthesis, retrofit, and alternate retrofit models, each of which minimizes TAC for implementing LTHEN by consideration of all the associated capital and operating costs. The benefits of the proposed models are illustrated with one industrial case study. Results show that the LTHEN cost is significantly increased due to pressure drop, piping, and LTHEN equipment capital and operating costs. These costs are necessary for the installation and operation of the LTHEN and, hence, must be duly considered for realistic design of LTHEN. In particular, piping cost is quite significant. Hence, this leads to fewer temperature intervals in both heat source and sink sections for optimal design of LTHEN. For the case study presented, the retrofit or alternate retrofit model solution is more economical than the synthesis model. In general, when heat recovery from process streams with very low heat duties is ignored, high cold stream outlet temperature and/or low hot stream outlet temperature may result in a more profitable LTHEN design. The potential of two circuits instead of one was also investigated for the case study.

savings from the reduced hot and cold utilities by 1558 and 1769 kW, respectively. This is mainly due to the fact that utilities required in Figure 7 are much higher than the utility targets from pinch analysis (Appendix D). However, comparing Figures 8 and 10, no utility reduction is observed for the retrofit model. This is mainly because utilities required in Figure 8 are the same as the utility targets (Appendix D). Table 4 summarizes the optimal results for the single and double circuit synthesis and retrofit models (with LTHEN Costs). For the synthesis model, the total capital cost has increased slightly for the scenario of 2 circuits. However, there is significant operating cost savings, approximately by half, for 2 circuits. This resulted in significantly lower TAC (=0.67 million US$) due to these savings for the double circuit synthesis model compared to the single circuit synthesis model. Table 4 also compares the retrofit solutions for single and two circuits. As observed earlier, heating and cooling duties are the same in this case but there are some small differences in the various capital costs leading to a slight increase in total capital cost and consequently in TAC for double circuit solution compared to the single circuit solution. Further, although two circuits are likely to provide more operational flexibility in the plant, they will require more plot space, operations monitoring, control, and maintenance. From the industrial operation point of view, fewer equipment and controls are preferred, and hence, a single circuit retrofit solution will be preferred.

■

APPENDIX A: PRESSURE DROP, EQUIPMENT, AND UTILITY COSTS

A.1. Piping Pressure Drop

With the use of economic pipe diameter, piping pressure drop is a function of length of the pipe and heat capacity flow rate of water.13 Using this approach, Reddy et al.10 developed a 18001



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linearized correlation (with R2 = 0.91), for estimating piping pressure drop. In this study, it was used without any changes. It is valid for heat capacity flow rate of water from 30 to 900 kW/°C. A.2. Heat Exchanger Cost

To reduce the nonlinearities of the model and hence reduce computational time, attempts were made to linearize the cost of HEs, water tanks, and water pumps. The cost of a HE is derived on the basis of the data in Seider et al.14 for a fixed-tube HE. A bare module factor of 3.17, a factor of 1.18 for contingencies and contractor fees, and CEPCI of 566.4 as of May 2013 are used to find the total module cost. Figure A1 shows that the resulting bare module cost of a fixed-tube HE is linear for area in the range from 20 to 1000 m2.

Figure A3. Pump cost (US$) variation with the pumping power requirement (kW).

■

APPENDIX B Piping length and HE elevation values used for the pressure drop calculations, piping, and pumping costs in heat source and heat sink sections, for the Case Study (single circuit scenario), are presented in Table B1. In this table, dhdr(jh) refers to the piping Figure A1. Variation of installed heat exchanger cost (US$) with heat exchange area (m2).

Table B1. Piping Length and HE Elevation Values of Single Circuit LTHEN

A.3. Water Tanks Cost description

The cost of the hot and cold water supply tanks in the LTHEN is estimated using the equation in Smith1 with a bare module factor of 3.05 and contingencies/contractor fee factor of 1.18.Tank dimensions are determined by fixing the tank height at 3 meters, 50% water level, and residence time of 10 min. The cost equation for these conditions was found to be nearly linear for (water) heat capacity flow rate in the range of 17.4 to 191.5 kW/K (Figure A2).

symbol

Heat Source Section CW pump to water header 1 db1 each water header dhdr(jh) water HDR to H-1 d1/h1 water HDR to H-2 d2/h2 water HDR to H-3 d3/h3 water HDR to H-4 d4/h4 water HDR to H-5 d5/h5 water HDR to hot water drum dm+1c Heat Sink Section HW pump to water header 1 de1 each water header dhdr(jc) water HDR to C-1 d1/h1 water HDR to C-2 d2/h2 water HDR to C-3 d3/h3 water HDR to C-4 d4/h4 water HDR to C-5 d5/h5 water HDR to cold water drum dn+1f

distance (m) 180 630 50 82 25 93 56 100 110 630 43 37 18 126 61 190

static height, hih or hic (m)

2 5 3.5 2 4

2 2 5.5 10.5 4

length used for the headers in the heat source section. There are m + 1 water headers in the model. dih/hih denotes the piping length/elevation of HE from the water headers. For instance, d1/h1 in Table B1 refers to 50 m piping length between the inlet/ outlet of the HE and the header and 2 m elevation. Piping lengths from water headers to HE (1−5) are for those in the heat source section. Similarly, in heat sink section, dhdr(jc) refers to the piping length used for the headers. There are n + 1 water headers in the model. dic/hic denotes the piping length/elevation of HE from the water headers. For instance, d1/h1 in Table 1, refers to 43 m of piping length between the inlet/outlet of the HE and the header and 2 m elevation. Piping lengths from water headers to HE (6−10) are for those in the heat sink section.

Figure A2. Tank cost (US$) variation with heat capacity flow rate of water (kW/K).

A.4. Water Pumps Cost

The cost of the circulating pump is estimated using the equation in Smith.1 It uses a bare module factor of 3.3 and contingencies/ contractor fee factor of 1.18. The linear correlation derived in the range of interest is shown in Figure A3. 18002



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APPENDIX D Total hot and cold utilities for the alternate retrofit model are 1730 and 0 kW, respectively (Figure 8). We have used the water heat capacity flow rate (211.97 kW/K) from this solution and split the problem into to subproblems, one each for the heat source and heat sink section. Composite curves for each of these subproblems are shown in Figures D1 and D2. With reference to these figures and results in Figure 8, it can be seen that the solution obtained using the alternate retrofit model corresponds to the pinch design.

The piping length and HE elevation values for the double circuit LTHEN model are shown in Tables B2 and B3. Table B2. Piping Length and HE Elevation Values for Circuit 1 description

distance (m)

symbol

Heat Source Section CW pump to water header 1 db1 each water header dhdr(jh) water HDR to H-2 d2/h2 water HDR to H-3 d3/h3 water HDR to H-5 d5/h5 water HDR to hot water drum dm+1c Heat Sink Section HW pump to water header 1 de1 each water header dhdr(jc) water HDR to C-1 d1/h1 water HDR to C-2 d2/h2 water HDR to C-3 d3/h3 water HDR to cold water drum dn+1f

static height, hih or hic (m)

175 480 82 25 56 95

5 3.5 4

105 200 43 37 18 185

Article

2 2 5.5

Table B3. Piping Length and HE Elevation Values for Circuit 2 description

symbol

Heat Source Section CW pump to water header 1 db1 each water header dhdr(jh) water HDR to H-1 d1/h1 water HDR to H-4 d4/h4 water HDR to hot water drum dm+1c Heat Sink Section HW pump to water header 1 de1 each water header dhdr(jc) water HDR to C-4 d4/h4 water HDR to C-5 d5/h5 water HDR to cold water drum dn+1f

Figure D1. Composite curves for heat source section and circulating water stream.

static height, hih or hic (m) g

distance (m) 180 350 50 93 100

2 2

110 230 126 61 190

10.5 4

Figure D2. Composite curves for heat sink section and circulating water stream.

■

■

APPENDIX C The results of the sensitivity analysis using different approach temperatures for the synthesis model are summarized in Table C1.

*E-mail: [email protected]. Notes

Table C1. Results of Sensitivity Analysis Using Different Approach Temperatures for the Synthesis Model approach temperature, °C circulating water flow rate, kW/°C TAC, 1000$ heat source section heat exchanger cost, 1000$ heat sink section heat exchanger cost, 1000$ hot utility duty, kW HUH area, m2 HUH cost, 1000$ cold utility duty, kW CUC area, m2 CUC cost, 1000$

2

4

6

8

165.1

171.83

179.15

187.1

The authors declare no competing financial interest.

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NOMENCLATURE A Area of heat exchanger (m2) a Payback period (years) C Capital cost (US$) CEPCI Chemical Engineering Plant Cost Index d Length of piping (with a subscript as shown in the superstructure) F Heat capacity flow rate (kW/°C) h Elevation of heat exchanger, m HE Heat exchanger K Number of hot process streams L Number of cold process streams LTHEN Heat exchanger network for recovering process heat at low temperatures LV Large value

10 195.81

2717.4 921.8

2855.3 846.7

3021 789.35

3213.2 743.8

3432.5 706.6

833.2

787.8

749.13

715.7

686.5

1485.9 18.17 45.9 621 98.42 65.3

1890.2 22.7 44.18 1025 142.65 77.65

2328.9 27.5 45.5 1464 181.43 88.46

2806.8 32.5 46.9 1942 216.9 98.4

3328.8 37.9 48.43 2464 250.6 107.8

AUTHOR INFORMATION

Corresponding Author

18003


Industrial & Engineering Chemistry Research m n OC P Q T TAC tc Th twc twh yc yh zc zh ΔP

Article

(4) Linnhoff, B.; Flower, J. R. Synthesis of heat exchanger networks I. Systematic generation of energy optimal solutions. AIChE J. 1978, 24, 633−642. (5) Kemp, I. C. Pinch Analysis and Process Integration; a user guide on process integration for the efficient use of energy; Butterworth Heinemann: Burlington MA, 2007. (6) Furman, K. C.; Sahinidis, N. V. A critical review and annotated bibliography for heat exchanger network synthesis in the 20th century. Ind. Eng. Chem. Res. 2002, 41, 2335−2370. (7) Matsufugi, M.; Laval, A. Energy recovery with compact heat exchangers. Pet. Technol. Q. 2012, 1, 65−69. (8) BCS Incorporated. Waste Heat Recovery: Technology and Opportunities in the U.S. Industry; U.S. Department of Energy: Washington, DC, 2008. (9) Lai, S. M.; Wu, H.; Hui, C. W.; Hua, B.; Zhang, G. Flexible heat exchanger network design for low-temperature heat utilization in oil refinery. Asia-Pac. J. Chem. Eng. 2011, 6, 713−733. (10) Reddy, C. C. S.; Rangaiah, G. P.; Lim, W. L.; Naidu, S. V. Holistic approach for retrofit design of cooling water networks. Ind. Eng. Chem. Res. 2013, 52, 13059−13078. (11) Sinnott, R. K. Coulson and Richardson’s Chemical Engineering Series, Vol. 6: Chemical Engineering Design, 4th ed.; Elsevier: Oxford, 2005. (12) Turton, R.; Bailie, R. C.; Whiting, W. B.; Shaeiwitz, J. A. Analysis, Synthesis and Design of Chemical Processes, 3rd ed., Prentice Hall: Upper Saddle River, NJ, 2009. (13) Kim, J. K.; Smith, R. Automated retrofit design of cooling-water systems. AIChE J. 2003, 49, 1712−1730. (14) Seider, W. D.; Seader, J. D.; Lewin, D. R. Product and Process Design Principles: Synthesis, Analysis and Evaluation; John Wiley & Sons: New York, 2003.

Number of hot section intervals Number of cold section intervals Operating cost Pressure at certain points along LTHEN (denoted by a superscript as shown in the superstructure, Figure 4) (kPa) Heat transferred/duty (kW) Temperature (°C) Total annualized cost Temperature of cold process stream (°C) Temperature of hot process stream (°C) Temperature of water in cold section (°C) Temperature of water in hot section (°C) Binary variable for use of an existing heat exchanger in cold section Binary variable for use of an existing heat exchangers in hot section Binary variable for presence/absence of a heat exchanger in cold section Binary variable for presence/absence of a heat exchanger in hot section Pressure drop (kPa)

Indices

ic ih jc jh

Cold process stream index Hot process stream index Cold section temperature interval index Hot section temperature interval index

Subscripts

CEP CHE CP TC CU CUC CUCE

Cold section piping pressure drop Cold section heat exchanger Cold section piping Tank in cold section Cold utility Cold utility cooler Cold utility cooler and existing heat exchangers in heat source section CUE Cold process stream and hot utility heat exchanger ex Exchanger HEP Hot section piping pressure drop HHE Hot section heat exchanger HP Hot section piping TH Tank in hot section HU Hot utility HUE Hot process stream and cold utility heat exchanger HUH Hot utility heater HUHE Hot utility heater and existing heat exchangers in heat sink section hdr Header in both sections ic Cold process stream ih Hot process stream PC Pump in cold section PH Pump in hot section PHC Pumping in hot and cold sections

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REFERENCES

(1) Smith, R. Chemical Process Design and Integration, 2nd ed.; Jon Wiley: New York, 2005. (2) Yee, T. F.; Grossmann, I. E. Simultaneous optimization model for heat integration−II. Heat exchanger network synthesis. Comput. Chem. Eng. 1990, 14, 1165−1184. (3) Masso, A. H.; Rudd, D. F. Synthesis of system design. II. Heuristic structuring. AIChE J. 1969, 15 (1), 10−17. 18004


Optimization of Heat Exchanger Networks for the Utilization of Low

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