CHEMICAL ENGINEERING TRANSACTIONS VOL. 52, 2016 A publication of The Italian Association of Chemical Engineering Online at www.aidic.it/cet Guest Editors: Petar Sabev Varbanov, Peng-Yen Liew, Jun-Yow Yong, Jiří Jaromír Klemeš, Hon Loong Lam Copyright © 2016, AIDIC Servizi S.r.l., ISBN 978-88-95608-42-6; ISSN 2283-9216 Simultaneous Optimization of Short-Term Scheduling and Heat Integration Schemes for Multipurpose Batch Plants Lei Sun, Xiong Zou, Hongguang Dong*, Shuming Wang School of Chemical Engineering, Dalian University of Technology, NO. 2 Linggong Road, 116024, Dalian, P.R. China hgdong@dlut.edu.cn A new synthesis methodology is developed to optimize process scheduling and direct heat integration schemes for multipurpose batch plants simultaneously. Firstly, the concept of associated task is introduced to describe the heat transfer requirements of production tasks and an improved State-Tasks-Network representation is adopted to capture all streams-streams, units-streams and units-units heat integration opportunities. Besides, the detailed design of heat transfer schemes and time sharing mechanism of heat exchangers are also involved in the proposed framework by considering heat transfer tasks-units allocation constraints. Then, a mixed integer linear programming (MILP) model is formulated to maximize profit. It should be noted that the trade-off between utility consumption and equipment cost has been taken into account. At last, an illustrative example is presented to demonstrate the validity and advantages of the proposed approach. 1. Introduction The emphasis on process sustainability has incentivized academics and industries to develop different energy recovery methodologies for batch processes in the past two decades, such as Pinch technology and Mathematical programming approaches. Due to the complexity caused by time dimension coupling, most of previous methods explored opportunities for heat integration under predefined production schedule, which always lead to suboptimal configurations (Halim and Srinivasan, 2009). Gradually, simultaneous consideration of production scheduling and heat recovery opportunity becomes more attractive. Barbosa-Póvoa et al. (2001) studied the economic savings in utility requirements while considering possible direct plant heat integration with associated costs of the involved auxiliary equipments. Adonyi et al. (2003) introduced S-graph approach to derive an effective algorithm for solving batch process scheduling problem with one to one energy integration. Then Holczinger et al. (2012) further improved this methodology by allowing heat exchange between one stream to multiple streams. Majozi (2006) proposed a continuous time framework to determine the production schedule that is concomitant with direct process-process heat integration for multipurpose batch plants. Later, a more generalized superstructure including indirect heat integration was developed by Seid and Majozi (2014). Castro et al. (2015) proposed a new continuous-based MILP formulation to handle stream to stream heat exchange matches for single stage multiproduct batch plants. All of aforementioned approaches considered heat integration schemes incompletely and heat exchanger is present for each integration pairs. (D) stream-unit(C) stream-unit(B) unit-unit(A) stream-stream Figure 1: Four types of heat integration schemes for multipurpose batch plant DOI: 10.3303/CET1652060 Please cite this article as: Sun L., Zou X., Dong H., Wang S., 2016, Simultaneous optimization of short-term scheduling and heat integration schemes for multipurpose batch plants, Chemical Engineering Transactions, 52, 355-360 DOI:10.3303/CET1652060 355 130℃ Cooling 70℃ Reaction2 aHeating 70℃ 70℃ 100℃ Reaction1 100℃ Reaction3 aCooling Separation 70℃ 100℃ 100℃ Heating1 70℃ Heating2 43℃ feedA feedB feedC prod1 prod2 coldA IntBC hotBC IntAB HotAB ImpE 40% 50% 50% 60% 40% 60% 20% 10% 90% 80% △H r =120kJ/kg △H r =-100kJ/kg S1 S4 S2 S6 S11 S3 S5 S7 S8 S10 S9 Figure 2: An improved STN involving associated tasks for illustrated example In this work, four types of heat integration schemes, as illustrated in Figure 1, are all taken into consideration. Furthermore, exchanger timing sharing mechanism is also involved in the proposed framework. In previous literatures, the heat requirements of reaction processes were replaced by the enthalpy change of process streams, which is unreasonable in a situation where reactions run without temperature control. A concept of associated task is introduced to describe the heat transfer requirements for production tasks (reaction and/or separation), such as 'aHeating' task for Reaction2 in Figure 2. Based on the improved State Task Network (STN), all heat integration schemes could be represented by the matches between heat exchange tasks pairs and the heat transfer equipments. 2. Problem statement The problem considered in this paper can be stated as follows. Given: (1) Production scheduling data; (2) Data required for heat integration including inlet / outlet temperature of tasks and utilities, enthalpy of reactions, material heat capacity and minimum allowable temperature differences; (3) Processing recipe and the corresponding relationships between tasks and units; (4) Costs of utilities, materials and heat exchange equipments, selling price of final products. Determine: An optimal production schedule and heat integration schemes to achieve maximum profit. The following hypotheses are presented for this problem: (1) A heating/cooling task can match with one or multiple cooling/heating tasks, but only one tasks-pair can occur in a specified heat transfer equipment at each event point p ; (2) Duration of each task is predefined as a parameter. 3. Mathematical model 3.1 Sets I: tasks; Ij: tasks which can occur in unit j ; Iac: associated cooling tasks; Iah: associated heating tasks; Ic: stream cooling tasks; Ih: stream heating tasks; Ipp: processing tasks; Ippa: processing tasks that have associated tasks; Iaippa: associated task of processing task ippa; J: units; Ji: units which are suitable for performing task i ; Jec: coolers; Jeh: heaters; Jpp: processing units; Jer: heat exchangers; Ja: associated units; Jajpp: associated unit of processing unit ppj ; P: event points; S: states; Ihh=Iah∪Ih; Icc=Iac∪Ic; Ia=Iac∪Iah; 3.2 Constraints The proposed new synthesis procedure is formulated as a mixed-integer linear programming, which could be divided into four blocks: sequencing of production tasks, associated task constraints, heat integration constraints and heat exchange equipment constraints. Due to space limitations, the reader is referred to the work of Ierapetritou and Floudas (1998) for the scheduling constraints of production. Associated task constraints: These parts of constraints describe the relationship between processing tasks and its associated tasks. (1) Associated task allocation constraints: When processing task occurs in the processing unit, its associated task can be performed in the associated unit and heat exchangers simultaneously. 356 er er , ,, , , , , , , , , , J J ippa jpp ppa pp a a 1 ( ) M , I J I J P ippa jpp ippa ippa jpp ippa ppa ppa a a pp er a a a pp er er er i j pi j p i j j p i j p i j j p j j ippa jpp ppa pp a a wv + wvv wv wv + wvv i , j ,i , j ,p            (1) where, i,j,pwv is a binary variable signifying the beginning of task i in unit j at event point p , ',i,j,j pwvv is a binary variable signifying the beginning of tasks i in unit 'j at event point p when multipurpose problem exist. M is a large number. (2) Mass balances constraints: ippa jpp , , ppa pp a a, , , , , I J I J Pippa jpp ippa ppa pp a a a pp er er er ippa jpp i j p ppa pp a ai j p i j j p j J B = B + BB ,i , j ,i , j ,p       (2) where, , , ',/i,j,p i j j pB BB is the amount of material processed. (3) Energy calculation: a r , , , i a iH I J Pa ai j p i j p a Q = B ,i , j ,p    (3) where, , ,i j pQ is energy required by task i in unit j at event point p , r iH is reaction enthalpy of task i . (4) Associated task timing constraints:   ippa, , , , ppa a pp er a, , , ,M 2 I I J J UJ Pippa ippappa pp ppa ppa a s s ippa i j p i j p ppa a ppi j p i j p T T - - wv - wv ,i ,i , j , j ,p      (4)   ippa, , , , ppa a pp er a, , , ,+ M 2 I I J J UJ Pippa ippappa pp ppa ppa a s s ippa i j p i j p ppa a ppi j p i j p T T - wv - wv ,i ,i , j , j ,p      (5)   ippa, , , , ppa a pp er a, , , ,M 2 I I J J UJ Pippa ippappa pp ppa ppa a f f ippa i j p i j p ppa a ppi j p i j p T T - - wv - wv ,i ,i , j , j ,p      (6)   ippa, , , , ppa a pp er a, , , ,+ M 2 I I J J UJ Pippa ippappa pp ppa ppa a f f ippa i j p i j p ppa a ppi j p i j p T T - wv - wv ,i ,i , j , j ,p      (7) where: , , s i j pT / f i, j,pT is starting/ finishing time of task i in unit j at event point p . Heat integration constraints: (1) Timing constraints: At an event point p , the finishing time of heating and cooling tasks which need heat integration should be identical. Relaxation has been made on starting time of heating and cooling tasks.  , , , , , , hh cc er aM 2 I I J UJ Phh cc hh cc f f i ,j,p i j p i j p i j p hh ccT T - - wv - wv ,i ,i , j ,p     (8)  , , , , , , hh cc er aM 2 I I J UJ Phh cc hh cc f f i ,j,p i j p i j p i j p hh ccT T + - wv - wv ,i ,i , j ,p     (9) (2) Energy calculation:   h c icp I UI J Pin outi,j,p i,j,p i i iQ = B T - T ,i , j ,p   (10) where, icp is specific heat capacity of task i , and, / in out i iT T is inlet/ outlet temperature of task i . (3) Feasibility constraints : When heat integration occurs in a specific heat exchange unit at event point p , the average heat flow of heating and cooling tasks should be equal.    , , , , erJ Phh er hh cc er cc hh hh cc cc i j p i i j p i i I i I Q = Q , j ,p       (11) ah c , , max , , a, , I I ( ) ( ) Q (1 ) J P ah c a c c aah a ah c i i j p i i j p ai j p i i Q Q - - wv , j ,p        (12) ah c , , max , , a, , I I ( ) ( ) Q (1 ) J P ah c a c c aah a ah c i i j p i i j p ai j p i i Q Q - wv , j ,p         (13) where, i is constant term in the processing time of task i . Eq(12) and Eq(13) are also applicable to associated cooling tasks and stream heating tasks. 357 (4) Energy balances constraints: cc hh cc hh , , , , , , , , er I I I I J P cc er hh er cc er hh er cc hh cc hh cw st i j p i j p i j p i j p er i i i i Q + Q = Q + Q , j ,p          (14) c cah ah ah , , max a I II I I Q (1 ) J Pst c a c aah a ah aah a c cah ah ah cw i j p i ,j ,p ai ,j ,p i ,j ,pi ,j ,p i ii i i Q + Q Q + Q - - wv , j ,p            (15) c cah ah ah , , max a I II I I Q (1 ) J Pst c a c aah a ah aah a c cah ah ah cw i j p i ,j ,p ai ,j ,p i ,j ,pi ,j ,p i ii i i Q + Q Q + Q - wv , j ,p             (16) Eq(15) and Eq(16) are also applicable to associated cooling tasks and stream heating tasks. (5) Minimum thermal driving forces constraints:  min hh cc er aT - M 2 I I J UJ Pcc hh cc hh in out i i i ,j,p i ,j,p hh ccT - T - wv - wv ,i ,i , j ,p      (17)  min hh cc er aT - M 2 I I J UJ Pout in cc hhcc hh i ,j,p i ,j,p hh cci iT - T - wv - wv ,i ,i , j ,p      (18) where, minT is the minimum temperature differences. Heat exchange equipment allocation constraints: At an event point p, one heating task can only be integrated with one cooling task in a heat exchanger. hh cc , , , , er I I J P hh er cc er hh cc i j p i j p er i i wv = wv , j ,p      (19) Eq(20) and Eq(21) describe that heat integration between streams tasks and associated tasks are available in the associated units. h , , , , ac a I I J P ac a h a h i j p i j p ac a i wv wv ,i , j ,p      (20) c , , , , ah a I I J P ah a c a c i j p i j p ah a i wv wv ,i , j ,p      (21) , , eh ec er a P I 1 , J UJ UJ UJ M j i j p p i y wv j     (22) where, jy is a binary variable signifying if heat exchange unit is used. 3.3 Objective function hh eh er a ec er a eh ec er a s j P S P I J UJ UJ P I J UJ UJ J UJ UJ UJ price costst costcw eqst cw hh cc hh cc cc s,p ji ,j,p i ,j,p p s p i j p i j j z = d - Q - Q - y                   (23) Eq(23) is the objective function in terms of profit maximization. The profit equals to the difference between product revenue and costs of utilities as well as costs of heat exchange equipments. Where, sprice is the price of state s, s,pd is the amount of state s being delivered to the market at event point p, costst/ costcw is the cost of steam/ cooling water and jeq is the cost of each heat exchange equipment in one batch. 4. Example In order to demonstrate the effectiveness of the proposed framework, one illustrative example with two cases is presented. The improved STN representation of process flowsheet is shown in Figure 2, and Table 1 lists the processing data. Prices of product 1 and 2 are both 10 $/kg, steam (170 - 160 °C) cost is 1 $/MJ and cooling water (20 - 30 °C) cost is 0.02 $/MJ. Minimum thermal driving force has been specified as 10 °C. 358 Table 1: Data for the illustrative example Task (i) Unit (j) Max batch size(kg) αi(h) Cp(kJ /kg℃) State Storage capacity(kg) Cooling/C CR/EXR/E1/E2 100 0.8 2.2 S1 feed A 1,000 aCooling/Ca EXR/ E1/E2 100 0.9 2.4 S2 feed B 1,000 Heating1/H1 HR/EXR/E1/E2 100 0.8 2.5 S3 feed C 1,000 Heating2/H2 HR/EXR/E1/E2 100 0.8 2.9 S4 cold A 100 aHeating/Ha EXR/ E1/E2 100 1.2 3.0 S5 Int AB 200 Reaction1/R1 RR1/RR2 50/80 1 3.5 S6 hot BC 150 Reaction2/R2 RR1/RR2 50/80 1.2 3.0 S7 hot AB 200 Reaction3/R3 RR1/RR2 50/80 0.9 2.4 S8 Imp E 200 Separation/S SR 200 1.2 2.8 S9 prod 1 1,000 S10 prod 2 1,000 S11 Int BC 150 Table 2: Computational results for the case study Literature Case1 Case2 Product produced(kg) 348.833 348.833 348.833 Steam(MJ) 59.2 59.2 77.95 Cooling water(MJ) 17.522 17.522 36.273 Number of heat exchange equipment 20 5 4 Profit($) 3,368.783 3,378.783 3,329.657 The annual cost of each heat exchange equipment is 10,000 $ in case 1, but 20,000 $ in case 2. The time horizon of each batch cycle is 8 h and total number of batch cycles every year is 1,000. Firstly, the example is solved by the new formulation with combining Seid and Majozi (2014)'s method and our improved STN representation. And the optimized Gantt chart and heat exchange network as shown in Figure 3 indicate that all heat integration opportunities could be captured with 20 heat transfer equipments used. Figure 4 shows the optimization results generated by the proposed model. The readers could easily find the production sequences, heat integration schemes and detailed implementation structures in a single Gantt chart. As shown in Table 2, our configuration of case 1 obtains more profits and only 5 heat exchange equipments were required. This improvement benefits from equipment cost consideration and timing sharing of equipment, such as heat exchanger EXR has been used 4 times and associated unit jacket E1 and E2 has been used 3 and 5 times respectively. 6MJ 3.2h2h R2,RR1 st 3.5h2.3h R2,RR2 st 9.6MJ 2.4h 3.2h H2 C 3.2h2.4h 3.549MJ 6MJ 4.4h3.2h R2,RR1 st 4.7h3.5h R2,RR2 st 9.6MJ H1 3.9h st 4.8MJ 4.7h E1 E2 EXR1 E1 E2 HR 1.8h1h H2 C 1.8h1h 10.179MJ EXR1 1.804MJ cw H2 C 4.4h3.6h 0.836MJ 4.4h3.6h EXR1 CR st 6.9MJ H1 5.1h 5.9h cw 6.512MJ C 5.2h 6h HR CR 4.7h 5.6h 3.111MJ R3,RR2 st 4.5MJ cw=0.389MJ 1.5MJ 5.6h4.4h R2,RR1 H2 4.8h 5.6h E1 EXR1 EXR2E2 5.9h 6.8h 2.683MJ R3,RR2 cw=0.335MJ 3.5MJ 6.8h5.9hR3,RR1 H2 6h 6.8h cw cw 4.982MJ E1 E2 EXR1 8.8MJ 8h6.8h R2,RR1 st 8h6.8h R2,RR2 st 6MJ E1 E2 2 3 4 5 6 7 8 Time(h) R1/50 R1/80 R2/50 R2/50 R2/50 R2/50 R2/80 R2/80 R2/73R3/80 R3/80 R3/35 S/115 2 3.2 4.4 5.6 5.9 6.8 8 2.3 3.5 4.7 5.6 5.9 86.8 6.8 8 S/80 5.6 1 Units RR1 RR2 SR R1/50 R1/80 1 1 1.3 Figure 3: Gantt chart and heat integration schemes by modified Seid and Majozi's method (2014) 359 Heat integration steam Cooling water 1 2 3 4 5 6 7 8 Time(h) Units CR HR EXR RR1 RR2 SR E1 E2 Ca/20 Ca/77.1 Ca/45 Ca/52.9C/59.3 C/59.3 C/5.4 C/49.3 H1/78 H1/78 H2/100 H2/100 H2/60 Ha/50 Ha/50 Ha/50 Ha/80Ha/80 Ha/43.3 Ha/80 R1/50 R1/50 R1/80 R1/80 R2/50 R2/50 R2/50 R2/43.3 R2/80 R2/80 R2/80R3/65 R3/80 R3/50 S/195 3.6 4.4 5.2 6 3.9 4.7 5.1 5.9 1 1.8 2.4 3.2 4.4 5.6 6.86 4.7 5.9 1 2 3.2 4.4 5.6 5.9 6.8 8 1 1.3 2.3 3.5 4.7 5.6 5.9 86.8 6.8 8 A B C 45 50 2.9 1 2 3 4 5 6 7 8 Time(h) Units CR HR RR1 RR2 SR E1 E2 Ca/80 Ca/46.3 C/100 C/73.3 H1/78 H1/78H2/100 H2/82 Ha/50 Ha/50 Ha/80Ha/80 Ha/50 Ha/80 R1/50 R1/50 R1/80 R1/80 R2/50 R2/50 R2/43.3 R2/50 R2/80 R2/80 R2/80R3/80 R3/68.7 R3/46.3 S/115 0.8 1.6 1.5 2.3 3.9 4.7 5.1 5.92.7 3.5 1 1.3 3.5 4.7 5.9 6.8 8 1 1.3 2.3 3.5 4.7 5.6 5.9 86.8 6.8 8 Ca/68.7 H2/78 Ha/43.3 2.3 5.6 S/80 D case1 case2 Figure 4: Gantt chart of our optimal solution for case1 and case 2 In Figure 4, dashed circle (A), (B), (C) represents stream-stream, unit-unit, unit-stream heat integration schemes respectively. In circle (B), associate task of R3 is satisfied by cooling water in an associated unit jacket E2 and the other parts is heat integrated with associated heating task in a heat exchanger EXR. In circle (C), Reaction3 occurs in two reactors simultaneously and both associated cooling task matches with stream heating task H2 in a heat exchanger EXR. All aforementioned configurations have never been involved and carefully studied in previous literatures. Case 2 shows the impact of heat transfer equipment's cost on the scheduling and heat integration. With the increasing equipment's cost, the number of heat transfer equipment decreases while the utility consumption increases. At this time, only one heat integration scheme occurs (D). 5. Conclusion This article presents a general framework to integrate short-term scheduling and direct heat integration in multipurpose batch plants. Four types of heat integration schemes are incorporated into the synthesis framework. 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