Minimizing the Energy Requirement in Batch Water Networks

Article pubs.acs.org/IECR

Minimizing the Energy Requirement in Batch Water Networks Nitin Dutt Chaturvedi* Department of Chemical and Biochemical Engineering, Indian Institute of Technology Patna, Bihta, Patna 801103, Bihar, India ABSTRACT: Energy and water are the major resources required in process industries. Simultaneous energy and water minimization gives an extra opportunity for optimization by exploring the interlinks between energy and water and hence gives overall benefits. Minimizing energy and water simultaneously has been extensively explored using mathematical optimization and graphical methods for the continuous process in the last few decades. However, very few works have been proposed for energy and water minimization in the batch process. No insight-based/ graphical method has been reported for energy and water minimization in the batch process. In this paper, a graphical technique to determine the minimum energy requirement for batch water allocation networks is described where the role of concentrations of impurities can be neglected. The proposed methodology calculates the minimum requirement of utilities before entering into the detailed design of the water allocation network and/or heat exchanger network. The graphical method gives more visualization and physical understanding of the problem as compared to the mathematical programming based methods. The proposed method is based on the period grand composite curve and guarantees the optimum solution. Demonstrations of the proposed method are carried out using illustrative examples. A reduction of 54.7% in hot utility and 66.7% in cold utility is observed when compared to the utilities requirement when integration between intervals is not considered in one of the illustrative examples.

1. INTRODUCTION Energy and water are considered as the most important resources for a process industry. Minimizing energy and water has been extensively studied in the last few decades. Researchers have studied energy and water in two ways: first, minimizing energy1 and water2 individually, and second, minimizing energy and water simultaneously. Simultaneous energy and water minimization gives additional benefits by exploring the interlinks between energy and water networks. Over the years, simultaneous energy and water minimization for a continuous process have been the areas of extensive research.3 However, lesser works are reported related to simultaneous energy and water minimization for a batch process. Batch processing is common in pharmaceutical, polymer, food, and specialty chemical industries in view of its suitability and flexibility when it comes to producing small quantities of high value products. Methodologies developed for simultaneous energy and water minimization for continuous processes can be categorized under two heads: first, methodologies based on conceptual tools, and second, methodologies based on mathematical programming. In one of the earlier works based on conceptual tools, Savulescu et al.4 proposed a methodology based on pinch analysis which includes direct/indirect heat exchange while designing a water allocation network (WAN). The methodology is further extended by Sorin and Savulescu5 to include network simplification. For multiple pinches problems, Wan Alwi and Manan6 introduced a graphical tool known as the © 2016 American Chemical Society

network allocation diagram to calculate targets for multiple pinches problems. These works does not include area minimization for heat exchange. To overcome this limitation, a conceptual method is proposed by Leewongtanawit and Kim7 for heat integrated water allocation network (HIWAN) which is capable of modifying energy composite curves in order to minimize exchanger areas for heat recovery. A conceptual technique which is applicable to both types of water-using operations (mass exchange based and no mass exchange based) is proposed by Manan et al.8 for simultaneous reduction of water and energy in a continuous process. In another work, Wan Alwi et al.9 introduced superimposed mass and energy curves for simultaneously targeting and designing a heat and mass recovery network. These methods are restricted to single contaminant processes. To overcome this limitation, Hou et al.10 introduced the concept of temperature and concentration order composite curves for designing optimum HIWAN which is applicable to multicontaminant problems. In a recent work, Liao et al.11 proposed a graphical method to design a heat exchanger network (HEN) of water allocation heat exchanger network (WAHEN) which is capable to deal with nonisothermal stream mixing and splitting. Note that the major Received: Revised: Accepted: Published: 241

July 4, 2016 November 18, 2016 December 16, 2016 December 16, 2016 DOI: 10.1021/acs.iecr.6b02543 Ind. Eng. Chem. Res. 2017, 56, 241−249

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Industrial & Engineering Chemistry Research

water regeneration units along with WAN and HEN. Zhou and Li33 presented a mathematical approach for optimization of a property-based WAN and HEN which is capable of accounting for both linear and nonlinear dependent properties. Zhou et al.34 developed a single-step methodology for the simultaneous optimization of integrated WANs and HENs where both direct and indirect heat exchanges are explored. Ghazouani et al.35 presented an MILP model to minimize total annual operating cost of HIWANs where heat integration is carried out using a modified trans-shipment model. In a recent work, Jagannath and Almansoori36 proposed a sequential methodology for the synthesis of HIWANs consisting of two mathematical models where the first model minimizes water and energy costs and the second model develops stage-wise HEN. However, a few works based on mathematical programming have been proposed for energy and water minimization in the batch process. These include works by Halim and Srinivasan37 who presented a method which minimizes water and energy sequentially along with batch process scheduling; Seid and Majozi38 who addressed minimization of both water and energy, along with optimizing the batch process schedule; and Adekola et al.39 who developed a mathematical model to minimize wastewater and energy simultaneously in a batch process. A review of methodologies for water and energy integration for nonisothermal water networks is presented by Ahmetović et al.3 From the above literature review it can be concluded that extensive graphical and mathematical programming based works exist in literature for continuous processes which considers both wastewater minimization and heat integration simultaneously. However, very few works based on mathematical programming have been proposed for energy and water minimization in the batch process. No insight-based/graphical method for has been found for simultaneous energy and water minimization in the batch process.3 In this paper, a graphical methodology has been proposed for minimizing energy in batch water networks with negligible contaminant effect. The methodology is based on the period grand composite curve and is demonstrated using illustrative examples. In the next section problem definition for the utility targeting in a batch WAN with negligible effect of contaminants is given.

drawback of all of these methods is that optimum energy integration of the overall WAN cannot be guaranteed. Techniques based on mathematical programming overcome this drawback to some extent. These include recent works by Hong et al.12 who developed a mixed integer nonlinear programming (MINLP) model for minimizing the total annual cost of HIWAN enabling free split freshwater and wastewater. Yan et al.13 proposed a nonlinear programming (NLP) model for optimizing HIWANs synthesis where the existence of process match and identification of stream are included in formulation without discrete variables in order to reduce the MINLP model to the NLP model. Liao et al.11 proposed a mathematical procedure for targeting and designing WAHENs that accounts for the splitting and nonisothermal mixing alternatives in the network with an objective to minimize total annualized cost. Gabriel et al.14 proposed a procedure for optimizing the benefits of the water−energy nexus while integrating heat, power, and water for industrial processes. Earlier, Bagajewicz et al.15 proposed a sequential procedure for optimizing WAN in which, initially, a linear programming (LP) model is solved to calculate water and utility targets, and then a mixed integer linear programming (MILP) model is developed to design WAN and HEN. Laio et al.16 presented a method for designing and optimizing HIWAN enabling operation split. Feng et al.17 presented a sequential mathematical model for designing optimum HIWAN. Dong et al.18 developed a mathematical model to minimize the total annualized cost of the HIWANs with multicontaminant WANs. Leewongtanawit and Kim19 proposed a mathematical model to design HEN and multicontaminant WANs simultaneously. The model investigates design interactions between two subsystems to optimize cost and environmental effect. Kim et al.20 developed an MINLP model to minimize the total annual cost of the HEN, where wastewater involves effluent streams containing multiple contaminants. Ahmetović et al.21 have used mathematical programming techniques to minimize energy requirement and to optimize WAN for corn-based bioethanol plants. George et al.22 developed a linear mathematical model for heat integration in HIWANs with fixed flow rate WANs. Zhou et al.23 proposed a mathematical model for the optimization of interplant HENs and integrated interplant HENs and WANs with fixed flow operations. This work is further extended to include integrated interplant water-allocation and heat-exchange networks with fixed load operations.24 Yang and Grossmann25 presented a simultaneous optimization model wtih trade-offs among raw materials, investment cost, and energy consumption in a process flow-sheet. Rojas-Torres et al.26 introduced a methodology for water integration in industrial facilities based on properties including the dependence of the properties on temperature. Tan et al.27 proposed a hybrid approach that combines an insight-based pinch approach with MINLP for synthesis of heat integrated resource conservation networks (HIRCNs). Later, Tan et al.28 presented a MINLP formulation for the synthesis of HIRCNs which is applicable for both concentration and property based fixed flow rate problems. Ibrić et al.29 developed a simultaneous mathematical model for optimizing the pinched and threshold HIWANs. Ahmetović et al.30 presented an optimization model to design HIWANs and wastewater treatment networks simultaneously. JiménezGutiérrez et al.31 presented an MINLP model for integrating mass, energy, and properties simultaneously with an objective to minimize total annual cost. Ibrić et al.32 presented a two-step methodology for synthesis of HIWANs which incorporates

2. PROBLEM DEFINITION The general problem for calculation of minimum energy requirement in a batch WAN, where role of impurity concentrations can be neglected, is defined next: • A set of internal demands (MD) is given. A flow (Fdj) is accepted by each demand at a given temperature (Tdi) for a fixed interval of time. • A set of internal sources (Ms) is given. A known flow (Fsi) is produced by each source, at a given temperature (Tsi) for a fixed interval of time. And these flows are reused/recycled to internal demands, appearing during or after the availability of source flows. Time intervals (say E1, E2, E3, ...) are created within the time horizon of the batch WAN such that all end points of sources and/or demands must coincide with end points of these time intervals. No sources and/or demands should end in between the time intervals. Note that the summations of all source flows in an interval are considered to be equal to the net flow requirements of all demands in that interval as each internal demand is satisfied by different internal sources only and each 242

DOI: 10.1021/acs.iecr.6b02543 Ind. Eng. Chem. Res. 2017, 56, 241−249

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Case1: No Integration between Intervals. For this case, requirement of hot and cold utility for each individual interval can be determined using ERA40 at zero ΔTmin. In addition, as there is no integration between intervals, net requirement of hot or cold utility can be calculated using lemma 1. Lemma 1: For the case where there is no integration between intervals, the sum of total individual interval hot or cold utility requirements is the net hot or cold utility requirement of the batch WAN. Case 2: Direct or Indirect Integration between Intervals. To examine the effect of direct heat integration between intervals, consider two general time intervals El and Ek. For integrating these intervals, constraints related to time and temperature need to be addressed. As per time constraints, first cooling and heating demands of an interval have to be fulfilled in the same time interval. Second, a time interval El can utilize a heat source (negative slope segment in optimized GCC) from time interval Ek if and only if l ≥ k. Next, as per temperature constraints, feasible heat transfer through heat exchanger requires a minimum approach temperature difference (specified ΔTmin) between heat source and heat sink. In the case of direct integration among different intervals, specified ΔTmin is the minimum driving force; on the other hand for indirect integration it is 2ΔTmin.41 Note that this problem is actually a heat integration problem in a batch water network. However, the proposed methodology is generic and can be applied for all types of stream (not only water). In further sections, optimized GCC, reformed optimized GCC, and finally period GCC are constructed, taking into consideration these two constraints. Generation of Optimized GCC. Consider a general batch WAN having n time intervals (E1, E2, E3, ..., En), for the first interval E1, the minimum requirement of hot utility can be determined using ERA considering all the available heat sources and demands in this interval which generates optimized GCC at zero ΔTmin. Note that below the pinch region of optimized GCC there is unutilized heat that can be passed to the next interval E2. Generation of Reformed Optimized GCC. For feasible heat transfer between two time intervals E1 and E2, optimized grand composite curves of E1 and E2 have to be reformed in order to provide required minimum approach temperature between the heat source and the heat sink. To incorporate minimum approach temperature, shifting of streams is required. For direct integration, the source segments (negative slope segments in optimized GCC) are shifted downward, and the sink segments (positive slope segments in optimized GCC) are shifted upward by (1/2)ΔTmin. While, for indirect integration, downward shifting of source segments and upward shifting of sink segments by ΔTmin carried out. Regions which are intersecting after shifting in different segments are to be eliminated to form a reformed optimized GCC as these intersecting regions lack in temperature driving force that is required for intertime interval heat integration.42 Generation of Period GCC. Hot segments of reformed optimized GCC after elimination of pockets below the pinch region are the available extra heat from interval E1 that can be passed to subsequent intervals.41 To utilize the heat from reformed optimized GCC of interval E1 in interval E2, below the pinch, heat source segments (after elimination of pockets) of reformed optimized GCC of interval E1 and heat source and sink segments of reformed optimized GCC of interval E2 are integrated in order to form period GCC of interval E2. Next,

individual time interval is equivalent to a continuous WAN. Heat transfer between streams (streams from sources to demands) is needed to satisfy the temperature constraint of every internal demand which can be performed either through nonisothermal mixing or through a heat exchanger. For sources and demands which are in the same time interval nonisothermal mixing is possible; however, heat integration among sources and demands of different intervals are allowed through heat exchanger only. For additional cooling or heating load after heat transfer between various streams, external hot and cold utilities are used. The goal is to determine the minimum external requirements of hot and cold utilities for the batch WAN. The entire time period of the batch WAN is divided into several time intervals, and each individual time interval is equivalent to a continuous WAN. Hence, the total requirement of cold or hot utility is the summation of the requirements of utilities across all intervals. n

Qu =

∑ Q uk k=1

(1)

Let Qs be the total surplus energy available in sources and Qd be the net energy requirements in demands. The specific heat capacity of water (cp) is taken as 4.2 kJ/(kg K) and T0 is the reference temperature, and then Qs and Qd be may be expressed as follows: Es

Qs =

∑ Fsi(Tsi − T0)cp i=1

(2)

Ed

Qd =

∑ Fdj(Tdj − T0)cp j=1

(3)

Let Qcu and Qhu be the heat extracted by the cold utility and the heat transferred by the hot utility, and the overall energy balances of the batch WAN can be expressed as Q s + Q hu = Q d + Q cu

(4)

Equation 4 can be rewritten as follows: Δ = Q d − Q s = Q hu − Q cu

(5)

The optimized grand composite curve (GCC) for an interval can be obtained via energy recovery algorithm (ERA)40 at zero ΔTmin, as nonisothermal mixing is allowed within each interval. Note that optimality of ERA is proved by Sahu and Bandyopadhyay.40 The segment of GCC denotes a heat source or a heat sink at a particular temperature interval which can be identified based on the slope of the segment. A sink has positive slope while a source has negative slope. In the next section, a batch process is analyzed in the view of energy integration in batch WANs, and theorems are developed to calculate targets.

3. ANALYSIS OF ENERGY INTEGRATION IN BATCH WANs Each time interval created via division of time horizon can be regarded equivalent to a continuous process as all sources and/ or demands that exist within a time interval exist for the complete time interval. Next, there could be two possible cases for integration between intervals. Case1: No integration between intervals Case 2: Direct or Indirect integration between intervals 243


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5.1. Illustrative Example 1: Direct Heat Integration. The process data, which contain flow requirements/availabilities, temperatures, and time duration of six internal sources of water and six internal demands of water, are given in Table 1.

the below pinch heat source segments (after elimination of pockets) of period GCC of interval E2 are integrated with heat source and sink segments of reformed optimized GCC of interval E3 to form period GCC of interval E3. Problem table algorithm (PTA) proposed by Linnhoff and Flower43 or modified problem table algorithm (MPTA) proposed by Bandyopadhyay and Sahu44 may be utilized for this integration. Hence, in general form, period GCC of an interval Ek can be generated by integrating below the pinch heat source segments (after elimination of pockets) of period GCC of interval Ek−1 with heat source and sink segments of reformed optimized GCC of interval Ek. Note that as interval E1 is the first interval, no heat is available from previous interval; hence, the reformed optimized GCC of interval E1 and period GCC of interval E1 are equivalent. Net Requirement of Utilities. The total requirement of the hot utility (Qhu) is the summation of the requirements of hot utilities of period GCCs of all intervals. This proves the following theorem based on the period grand composite curve of intervals for determining utility targets of batch WAN with negligible contaminant effect. Theorem 1: Consecutively transferring below the pinch heat of a period GCC (hot streams of GCC after elimination of pockets) to its next interval for generating its period GCC leads to an overall minimum utility requirement.

Table 1. Process Data of Illustrative Example 1 temperature (°C)

water flow rate (kg/h)

duration (h)

Sources S1 S2 S3 S4 S5 S6

160 240 220 100 225 270

D1 D2 D3 D4 D5 D6

220 130 100 215 110 300

40 20 15 45 5 10

0.0−1.5 0.0−4.5 0.0−4.5 1.5−4.5 4.5−6.0 4.5−6.0

40 20 15 45 5 10

0.0−1.5 0.0−4.5 0.0−4.5 1.5−4.5 4.5−6.0 4.5−6.0

Demands

Note that the process data are hypothetical and are used for illustrative purposes; however, methodology is generic. The goal is to calculate the minimum requirement of hot utility and cold utility maintaining a specified ΔTmin of 10 °C for heat exchange via heat exchangers through direct integration. The time horizon is divided into three time intervals as per step 1 such that no water source or demand ends or starts between these intervals (Table 2). If integration between intervals is not considered then requirement of individual intervals can be calculated using ERA.40 Total requirement of hot utility and cold utility of three intervals in this case are 16695 kJ and 13702.5 kJ. In the first interval E1, there are three sources and three demands. With these three sources and three demands, ERA at zero ΔTmin is applied to generate optimized GCC of interval E1 (Figure 1). It is calculated that there is no hot utility for interval E1. Next, the optimized GCC is reformed by shifting the segments of optimized GCC; for direct integration, source segments are shifted downward by (1/2)ΔTmin and sink segments are shifted upward by (1/2)ΔTmin (Figure 2). Note that, in case of indirect integration, downward shifting by ΔTmin for source segments and upward shifting by ΔTmin for the sink segments has to be carried out. The intersecting regions are to be identified after shifting and to be eliminated. Since no pseudo-hot stream is available from the previous interval for interval E1 as it is the first interval, reformed optimized GCC and period GCC are same for this interval. The pseudo-hot streams that can transfer heat to subsequent intervals are extracted after eliminating pockets, and these segments are listed in Table 3. In the similar way (i.e., using steps 2 and 3), reformed optimized GCC for interval E2 is formed. After that, pseudostreams from interval E1 (Table 3) and individual segments of reformed optimized GCC of interval E2 are combined using MPTA (Table 4) to generate period GCC of the second interval (Figure 3). The hot utility requirement is calculated to be 5670 kJ. Next, period GCC of the last interval E3 is generated, and requirement of hot utility of interval E3 is calculated to be 1890 kJ. According to step 7, the total hot utility is the summation of hot utilities of period GCCs of all

4. TARGETING ALGORITHM The following algorithm is proposed to calculate the minimum requirement of hot and cold utility for a batch WAN with negligible impurity concentrations based on Theorem 1. Step 1: Break down the time horizon of the batch process into time intervals (say E1, E2, E3, ..., En), such that end points of these intervals are chronologically marked water sources and demands end points. Step2: Apply ERA to the first interval and calculate the hot utility requirement (Qhu 1 ) of first interval Step 3: Reform the optimized GCC of the first interval according to direct/indirect integration to generate reformed optimized GCC. For direct integration, shift source segments downward and sink segments upward by (1/2)ΔTmin. For indirect integration, shift source segments downward and the sink segments upward by ΔTmin. Identify the intersecting regions of different segments after shifting and eliminate them. Step 4: Generate the reformed optimized GCC of the second time interval using Step 2 and Step 3. Step 5: Generate period GCC of the second time interval considering all segments of the reformed optimized GCC of interval E2 along with the below pinch source segments of period GCC of interval E1 (after elimination of pockets) through PTA or MPTA taking the minimum approach temperature as zero (i.e., ΔTmin = 0) and calculate the requirement of the hot utility of the second interval (Qhu 2 ). Step 6: Repeat step 5 until the last interval to generate period GCC of all the intervals. Step 7: Sum up the hot utility requirement of period GCCs of all intervals to calculate total hot utility requirement and calculate total requirement of cold utility using eq 5. 5. ILLUSTRATIVE EXAMPLES In this section, the proposed algorithm is applied to different batch WANs and minimum utility requirement is calculated in order to demonstrate applicability of the proposed algorithm. 244


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Industrial & Engineering Chemistry Research Table 2. Time-Interval Data for Illustrative Example 1 E1 (0.0−1.5 h) temp. (°C) Sources 160 240 220 Demands 220 130 100

E2 (1.5−4.5 h)

E3 (4.5−6.0 h)

water flow (kg)

MCpΔt (kJ/°C)

temp. (°C)

water flow (kg)

MCpΔt (kJ/°C)

temp. (°C)

60 30 22.5

252 126 94.5

240 220 100

60 45 135

252 189 567

225 270

31.5 63

60 30 22.5

252 126 94.5

130 100 215

60 45 135

252 189 567

110 300

31.5 63

water flow (kg)

MCpΔt (kJ/°C)

Table 4. Period GCC Generation of Interval E2 (Using MPTA) temp. (°C)

total MCpΔt (kJ/ °C)

net MCpΔt (kJ/ °C)

net enthalpy (kJ)

cascaded heat duty (kJ)

revised cascade (kJ)

235 230 215 212.22 155 135 125 105 95

378 −126 189 −567 220.5 −252 −126 378 −94.5

378 252 441 −126 94.5 −157.5 −283.5 94.5 0

0 1890 3780 1225 −7210 1890 −1575 −5670 945

0 1890 5670 6895 −315 1575 0.00 −5670 −4725

−5670 −3780 0 1225 −5985 −4095 −5670 −11340 −10395

Figure 1. Optimized GCC for interval E1 (illustrative example 1).

Figure 3. Period GCC for interval E2 (illustrative example 1).

utility can be observed in comparison to the utilities requirement when integration between intervals is not considered. Heat exchanger network and water allocation data are shown in Figure 4 and Table 5. There are three heat exchangers in the network. The first heat exchanger is between S1-D3 and S4-D4 having a heat duty of 4331.25 kJ. The second heat exchanger is between S2-D3 and S4-D4 of 1023.75 kJ heat duty. Further, between S3-D1 and S4-D2 there is a third heat exchanger, which is of heat duty 3780 kJ. Hence, the total heat exchange is 9135 kJ. For the case of indirect heat integration, the requirements of hot utility and cold utility are determined to be 8505 kJ and 5512.5 kJ. 5.2. Illustrative Example 2: Indirect Heat Integration. The limiting data for this example are given in Table 6. There are 9 sources and 10 demands in this example, which can be categorized into two time intervals (as per step 1). Heat

Figure 2. Reformed optimized GCC and period GCC for interval E1 (illustrative example 1).

Table 3. Pseudo-Streams from E1 Transferred to E2 (Illustrative Example 1) TS (°C)

TT (°C)

MCpΔt (kJ/°C)

235 155 125

230 125 95

126 220.5 94.5

intervals which is calculated to be 7560 kJ. The requirement of the cold utility can be calculated using eq 5 as 4567.5 kJ. A reduction of 54.7% in the hot utility and 66.7% in the cold 245


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Figure 4. Heat exchanger network for illustrative example 1.

Table 5. Water Allocation Matrix for Illustrative Example 1 E1 S1 (60 kg, 160 °C) S2 (30 kg, 240 °C) S3 (22.5 kg, 220 °C) E2 S2 (60 kg, 240 °C) S3 (45 kg, 220 °C) S4 (135 kg, 100 °C) E3 S5 (7.5 kg, 225 °C) S6 (15 kg, 270 °C)

D1 (60 kg, 220 °C)

D2 (30 kg, 130 °C)

D3 (22.5 kg, 100 °C)

9.375 28.125 22.5

30 0 0

20.625 1.875 0

D2 (60 kg, 130 °C)

D3 (45 kg, 100 °C)

D4 (135 kg, 215 °C)

0 0 60

0 0 45

60 45 30

D5 (7.5 kg, 110 °C)

D6 (15 kg, 300 °C)

7.5 0

0 15

Table 6. Process Data of Illustrative Example 2 temperature (°C)

water flow (kg)

duration (h)

Sources S1 S2 S3 S4 S5 S6 S8 S8 S9

195 125 145 160 180 120 130 155 100

D1 D2 D3 D4 D5 D6 D7 D8 D9 D10

155 185 115 135 170 135 160 170 105 115

100 50 150 50 175 200 225 200 112.5

0.0−1.2 0.0−1.2 0.0−1.2 0.0−1.2 1.2−2.4 1.2−2.4 1.2−2.4 1.2−2.4 1.2−2.4

75 125 75 50 25 250 200 175 125 162.5

0−1.2 0−1.2 0−1.2 0−1.2 0−1.2 1.2−2.4 1.2−2.4 1.2−2.4 1.2−2.4 1.2−2.4

Demands

exchange between different time intervals is considered through indirect heat integration only. A total of 5775 kJ hot and 9187.5 kJ of cold utilities are required when heat integration between intervals is not considered. According to the proposed algorithm (steps 2−4), reformed optimized GCC of the two intervals is created via shifting source and sink segments of optimized GCC. For indirect integration, source segments are shifted downward by ΔTmin, and the sink segments are shifted upward by ΔTmin. The intersecting portions of the shifted segments are removed. For the first interval, period GCC and reformed optimized GCC are

the same (Figure 5). Next, below the pinch source segments of reformed optimized GCC of interval E1 after elimination of pockets are carried to interval E2 as pseudo-streams. Applying PTA or MPTA with pseudo-streams of interval E1 and all 246


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Table 7. Water Allocation Matrix for Illustrative Example 2 E1 S1 (100 kg, 195 °C) S2 (50 kg, 125 °C) S3 (150 kg, 145 °C) S4 (50 kg, 160 °C) E2 S5 (175 kg, 180 °C) S6 (200 kg, 120 °C) S7 (225 kg, 130 °C) S8 (200 kg, 155 °C) S9 (112.5 kg, 100 °C)

Figure 5. Reformed optimized GCC or period GCC for interval E1 (illustrative example 2).

streams of reformed optimized GCC of interval E2, period GCC of interval E2 is generated (steps 5 and 6). The total requirements of the hot and cold utilities are determined to be 5250 and 8662.5 kJ (step 7). Therefore, the requirement of the hot utility reduced from 5775 to 5250 kJ, and the requirement of the cold utility reduced from 9187.5 to 8662.5 kJ; i.e., a reduction of about 9% and 6% in the hot and cold utilities. Heat exchanger network and water allocation data are shown in Figure 6 and Table 7. In this network, there is only one heat exchanger which is of 525 kJ heat load. Apart from this, the network contains two cold utility exchangers having heat duties of 6825 kJ and 1837.5 kJ on S3-D3 and S2-D5, respectively. In addition, there are two hot utility exchangers, which are on S3D1 in both intervals, and both are of heat duty of 2625 kJ.

D1 (75 kg, 155 °C)

D2 (125 kg, 185 °C

D3 (75 kg, 115 °C)

D4 (50 kg, 135 °C)

D5 (25 kg, 170 °C)

2.5

89.275

0

0

8.225

0

0

25

25

0

72.5

0

50

25

2.5

0

0

14.275

0

35.725

D6 (250 kg, 135 °C)

D7 (200 kg, 160 °C)

D8 (175 kg, 170 °C)

15

55

105

25

0

0

210

15

0

0

0

0

130

70

0

0

0

0

0

D9 (125 kg, 105 °C) 0 31.25

93.75

D10 (162.5 kg, 115 °C) 0 143.75

18.75

benefits in overall cost. A graphical method to calculate the minimum hot and cold utility requirements in batch WANs with negligible contaminant concentrations is proposed in this paper. The methodology is based on period GCC and guarantees the minimum utility targets. Period GCC is generated via integration of an interval with extra heat from previous intervals. The total hot utility requirement is the sum total of requirements of hot utility of period GCCs of all intervals. The proposed methodology is illustrated through examples which demonstrate significant reductions in utility requirements. The proposed method is graphical; hence, it gives clear physical insight into the problem compared to methods based on mathematical programming. In addition, the proposed methodology guarantees the optimum solution. Future works are directed toward inclusion of contaminant

6. CONCLUSIONS Simultaneous energy and water minimization explores the interlinks between energy and water and, hence, gives extra

Figure 6. Heat exchanger network for illustrative example 2. 247


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Industrial & Engineering Chemistry Research effect and exploring flexibilities in schedule, which may further reduce water and energy requirements.

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AUTHOR INFORMATION

Corresponding Author

*Tel.:+916123028281. E-mail: [email protected]. ORCID

Nitin Dutt Chaturvedi: 0000-0002-2594-7095 Notes

The author declares no competing financial interest.

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Article

Industrial & Engineering Chemistry Research Multipurpose Batch Plants Using a Flexible Scheduling Framework. Ind. Eng. Chem. Res. 2013, 52 (25), 8488. (40) Sahu, G. C.; Bandyopadhyay, S. Energy Conservation in Water Allocation Networks with Negligible Contaminant Effects. Chem. Eng. Sci. 2010, 65 (14), 4182. (41) Chaturvedi, N. D.; Bandyopadhyay, S. Indirect Thermal Integration for Batch Processes. Appl. Therm. Eng. 2014, 62 (1), 229. (42) Bandyopadhyay, S.; Varghese, J.; Bansal, V. Targeting for Cogeneration Potential through Total Site Integration. Appl. Therm. Eng. 2010, 30 (1), 6. (43) Linnhoff, B.; Flower, J. R. Synthesis of Heat Exchanger Networks: I. Systematic Generation of Energy Optimal Networks. AIChE J. 1978, 24 (4), 633. (44) Bandyopadhyay, S.; Sahu, G. C. Modified Problem Table Algorithm for Energy Targeting. Ind. Eng. Chem. Res. 2010, 49 (22), 11557.

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Minimizing the Energy Requirement in Batch Water Networks

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