Robustness analysis of heat-integrated batch process networks

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Robustness analysis of heat-integrated batch process networks Parikshit Shahane, Channamallikarjun S Mathpati, and Sujit Suresh Jogwar Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.8b03632 • Publication Date (Web): 04 Dec 2018 Downloaded from http://pubs.acs.org on December 8, 2018

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Industrial & Engineering Chemistry Research

Robustness analysis of heat-integrated batch process networks Parikshit S. Shahane,

†

Sujit S. Jogwar,

∗,‡

and Channamallikarjun S. Mathpati

†Department of Chemical Engineering, Institute of Chemical Technology, Mumbai, India ‡Department of Chemical Engineering, Indian Institute of Technology, Mumbai, India E-mail: [email protected]

Abstract Heat integration in batch processes strongly depends on the production schedule due to time-dependent availability of hot and cold process streams. Schedule delays in batch process operation are inevitable and can significantly reduce the practical benefits promised by heat integration. This paper presents a systematic framework to analyze the effect of schedule delays on achievable heat recovery in batch process systems. To this end, a time delay analysis method is proposed to generate heat recovery profile as a function of stream delay. The analysis computes maximum theoretical heat recovery (with a modified heat exchanger network) as well as practically achievable heat recovery (with the same network). The results of time delay analysis are then used to define three robustness measures to assess the sensitivity of a heatintegrated batch process network towards schedule delays. The presented framework allows identification of sensitive process streams as well as provides an operational measure to screen competing design alternatives. Two relevant example systems are considered to illustrate the effectiveness of the proposed framework.

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Introduction Heat integration plays a key role in improving economic as well as environmental efficiency of a process system through reduced consumption of utilities. Even though the initial developments in heat integration mainly focused on continuous processes, 1 in the recent decades, the focus has shifted towards batch processes. 2 The key challenge for the design of a heat-integrated batch process comes from the time-dependent availability of hot and cold process streams. This is typically accounted for by considering either direct, 3–9 indirect 10–14 or mixed (combined direct and indirect) 12,15–19 integration mode. Direct integration approach involves thermal coupling between streams available during the same time interval. Within any interval, direct integration synthesis problem is similar to energy integration in continuous processes and thus any of the continuous targeting methods can be used for the design of these systems. Zhao et al. 5 proposed a three step approach for heat exchanger network (HEN) design wherein the first step involves continuous targeting to get an initial design. In the subsequent steps, this design is optimized for maximization of common exchangers across intervals. Foo et al. 6 extended the minimum units targeting and network evolution techniques developed for batch mass exchange network to HEN synthesis. In a different vein, batch scheduling-based approaches 4,7–9 have also been developed for the synthesis of directly integrated systems wherein co-existence of hot and cold streams is maximized to enable energy integration. Indirect integration approach tackles the issue of non-co-existence of hot and cold streams by using heat storage. Heat available with the hot process stream is transferred to a heat transfer medium (HTM). Such a hot HTM is stored in a heat storage tank (HST) till a cold process stream requiring heating is available. Stoltze et al. 10 showed that incorporating a sufficiently large number of HSTs, one can achieve energy recovery computed by neglecting time-dependence of stream availability (equivalent to a continuous process) and used a combinatorial method to reduce the number of HSTs while maintaining the same extent of heat recovery. Krummenacher & Favrat 12 used a concept of storage pinch 2


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to determine the minimum number of HSTs as a function of the extent of heat recovery. On the other hand, superstructure-based optimization formulations have also been developed 13,14 to rigorously design such indirectly integrated systems. Mixed integration is a combination of direct and indirect modes wherein co-existing streams undergo direct heat exchange and further heat recovery is achieved through heat storage. One of the fundamental approaches for such design is the time dependent heat cascade analysis (TDHCA) 20 wherein heat is first cascaded to lower temperatures via direct integration and later to subsequent intervals via indirect integration. In our previous work, 19 we introduced a concept of pseudo-process streams to reformulate indirect integration as direct integration and presented a pseudo direct energy integration (PDEI) technique to systematically merge direct and indirect integration in order to achieve maximum heat recovery. Depending on the selected mode of integration, one can generate a cadre of optimal designs ranging from the most energy efficient (but with high capital cost) to the least capital intensive (and low energy efficiency) 19 and a trade-off of capital and operating cost is considered to arrive at the final optimal design. Schedule delays are quite common in batch processes and effective handling of such delays while maintaining production goals is one of the major operational challenges in such systems. For heat-integrated batch systems, the effect of delay is more profound as it disturbs the co-existence of hot and cold streams, and severely affects practical heat recovery (as illustrated later via a motivating example in this paper). However, there is no systematic framework to analyze the impact of schedule delay on operation of heatintegrated batch processes. The only previous study in this context proposes the use of sensitivity tables to predict the effect of a stream delay on the key outlet temperatures. 21 This preliminary time sensitivity analysis assumes that the effect of delay is linear and can therefore result in poor predictions (even for simple systems like the motivating example considered in the next section where such assumption does not hold).

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For a general batch process without energy integration, delays are handled in a proactive or reactive manner. In the case of a proactive approach, a robust schedule is generated at the design stage by using stochastic modeling. 22–26 On the other hand, a reactive approach focuses on developing a new schedule (rescheduling) based on the current state of operation and the remaining time horizon. 27–31 It is worth noting that such a reactive scheduling, triggered by a process disturbance, can also affect practical heat recovery in the case of heat-integrated designs. In a different vein, integration of scheduling and dynamic optimization/advanced control has also been proposed to address delays arising out of processing time variations. 32–34 However, incorporation of heat integration into such integrated approaches is challenging and has not been pursued yet. Lastly, simultaneous or sequential integration of scheduling and energy integration is one of the established methods for designing heat-integrated batch systems. 9,35–39 As per our knowledge, none of these approaches consider effect of schedule delays on the overall heat recovery or integrated design. Interestingly, in one of the works, stream delay has been used as an additional degree of freedom to improve hot and cold stream overlap, leading to better energy efficiency. 9 Motivated by this, we present a systematic framework to analyze the effect of schedule delay on the heat recovery of batch systems. Specifically, heat recovery is computed for two scenarios with respect to the structure of heat exchange network (HEN). If variable HEN structure is considered, the proposed time delay analysis provides the maximum possible heat recovery in the case of a delay which can be accomplished by installing redundant heat exchange capacity during the design stage. On the other hand, if the HEN structure is kept the same, the analysis provides the actual recovery for such a delayed case. Subsequently, the information is condensed to compute robustness of the system at the level of a process stream (to identify critical streams) and at the network-level (to compare design alternatives). The rest of the paper is organized as follows. A motivating example is considered to

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illustrate the effect of schedule delay on heat recovery. The proposed time delay analysis framework is then presented in the following section. Robustness quantification section outlines the procedure to assess sensitivity of a batch system to schedule delays. This is followed by an application of the proposed framework to a benchmark example system.

Motivating Example Let us consider an example system which consists of three cold and two hot process streams. The stream data for this example is given in Table 1. The corresponding (basecase) schedule is depicted in Figure 1. Based on the start (tin ) and end (tout ) times of the process streams, this schedule can be divided into 4 time-intervals; 0-0.5h, 0.5-1.0h, 1.0-2.0h and 2.0-2.5h. Table 1: Stream data for motivating example with 3 cold and 2 hot streams Stream C1 C2 C3 H1 H2

Tin [◦ C] 70 70 20 170 150

Tout [◦ C] 200 140 140 60 30

MC p [kW/◦ C] 4.5 8.0 5.0 4.0 3.0

tin [h] 1.0 0.0 1.0 0.5 1.0

tout [h] 2.0 1.0 2.0 2.0 2.5

t=0.1h H1 H2 C1 C2 C3

0

0.5 0.6

1 Time (h)

2

2.1

2.5

Figure 1: Schedule for the motivating example (dash represents a delayed schedule) For this system, the maximum heat recovery of 1090 kWh can be obtained by using PDEI algorithm. 19 This requires implementation of mixed heat integration and the corresponding HEN structure is depicted in Figure 2. The integrated structure uses 3 heat 5



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storage tanks at 140◦ C, 80◦ C and 30◦ C. Also note that stream H1 undergoes only direct heat integration. 55 kwh

25 kwh

360 kwh

H1

90 kwh

170 oC

80 oC

140 oC

60 oC

C 210 kwh

H2

150 kwh

150 oC

30 oC 75 kwh 225 kwh

190 kwh

200 oC

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30 oC

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C2

C1

70 oC 140 kwh

180 kwh

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INTERVAL-1 (0h - 0.5h)

H

40 kwh

170 oC

C

20 oC

INTERVAL-3 (1h - 2h)

60 oC H2 150 oC

165 kwh

15 kwh C

30 oC

100 kwh 140 oC

C2 H

70 oC

140 oC

30 oC


INTERVAL-2 (0.5h - 1h)

Figure 2: Maximum recovery HEN structure for the motivating example (blue denotes a heat transfer medium (HTM) stream) Let us now consider that stream H1, originally scheduled from 0.5h to 2.0h, is delayed by 0.1h. From Figure 1, it can be seen that the updated schedule has five time-intervals. The interval 1 gets extended by 0.1h, interval 2 gets shortened by 0.1h and there is a new interval 2.0-2.1h. Due to cyclic operation of the HTM, it can only transfer 90 kWh during interval 1. This heat is now transferred over a longer interval. Thus the heat transferred to C2 in interval 1 drops from 180 kW to 150 kW. This causes the exit temperature of C2 to drop from 92.50◦ C to 88.75◦ C, increasing the heating utility load from 190 kWh to 246 kWh. Due to shortening of the next interval, cooling and heating utility for interval 2 drops to 32 kWh and 80 kWh, respectively. While the third interval remains the same as earlier, the hot stream H1 in the new interval 4 does not have a cold stream to extract available heat. This results in additional cooling load of 44 kWh. Overall, the heating and cooling duty increases by 36 kWh (3.3% of the design value), reducing the practical heat recovery to 1054 kWh. Alternatively, if we consider this new schedule as a fresh problem and design a max6


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imum heat recovery network around it, the heat recovery value changes to 1086 kWh (0.4% reduction from the design value). The corresponding HEN structure is depicted in Figure 3. It can be noted that this increase in heat recovery requires two additional heat exchangers, one in interval 1 and the other in interval 4, and an additional heat storage tank at 160◦ C. This design also requires that stream H1 undergoes indirect integration. 55 kwh

170 oC

o

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90 kwh o

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75 kwh 225 kwh 200 oC

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30 oC 70 oC

H

C2

C1 70 oC

140 oC

140 kwh C3 140 oC

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H


INTERVAL-3 (1h - 2h) H2

144 kwh 170 oC

C

3 kWh

150 oC

32 kwh

H1

33 kwh

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C 32 kwh

H1 170 oC

12 kWh C

o

o

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160 C


80 kwh C2 140 C

H

60 oC 30 oC

140 C

o

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H2

70 oC

150 oC

140 oC

INTERVAL-2 (0.6h - 1h)

132 kwh

12 kWh C

30 oC

30 oC

INTERVAL-5 (2.1h - 2.5h)

Figure 3: Maximum recovery HEN structure for the motivating example with delay of 0.1h in stream H1 (blue denotes a HTM stream) This simple example demonstrates that a small delay in a process stream can have significant impact on the actual heat recovery. One can reduce this impact by building additional redundant heat exchange facility and achieve robust design at the cost of capital expenditure. This motivates us to systematically assess the impact of a delay on the heat recovery of an integrated design.

Time delay analysis (TDA) In this section, we introduce time delay analysis as an approach for understanding the effect of schedule delay on heat-integrated batch system. Time delay analysis is an ex7



haustive process to compute heat recovery as a response to delays in the batch schedule. We are interested in computing maximum possible heat recovery (HRmax,δ ) as well as practical heat recovery (HRδ ) as a function of a schedule delay (δ). The corresponding algorithm is depicted in Figure 4. Initially, the heat recovery maximization problem is solved for the given schedule. This is considered as the base case against which the effect of a delay will be compared. The corresponding heat exchanger network is denoted as HEN0 and the heat recovery is HRmax,0 . To study the effect of a delay, it is considered that one process stream is progressively delayed by a set amount of ∆t until the total delay in the stream matches with the set maximum value of delay (δmax ). In some cases, multiple streams can be coupled together through timing constraints. For example, if the inlet stream of a process unit is delayed, the outlet stream can also be delayed by the corresponding amount. If both these streams are part of the heat integration system, only one of these streams should be incorporated for the time delay analysis. To this end, a set S of such independent streams is constructed. For each value of the delay δ in the selected process stream Si , a disturbed schedule is computed. Specifically, the start time of stream Si is increased by δ, the start time of any coupled stream is modified as per the corresponding timing constraint and the start times of the other streams are kept the same as the original schedule. The heat recovery maximization problem is then solved for this schedule to obtain a new heat exchanger network (HENi,δ ) and modified heat recovery (HRmax,i,δ ). This represents the maximum possible heat recovery for the considered delay and may require additional heat exchange units. For the same disturbed schedule, using the basecase HEN structure HEN0 , the heat recovery is recomputed by updating the duties of heat exchangers as illustrated in the motivating example. This represents the actual heat recovery (HRi,δ ) if such a delay is encountered by the base case network. Once all the possible delays for the selected process stream are considered, HRmax,i,δ and HRi,δ are plotted as a function of δ to visualize the impact of delay on the maximum and practical heat recovery. The same

8


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Start

Design HEN for the base case with maximum heat recovery Design: HEN0, HR: HRmax,0

i=1

Consider process stream Si for time delay analysis

=

t

For stream Si, tin = tin,base+ For a linked stream, tin = tin,base + f( ) For other streams, tin = tin,base

Compute updated recovery for HEN0 with the disturbed schedule Design: HEN0 HR: HRi,

Design HEN for the disturbed schedule with maximum heat recovery Design: HENi, HR: HRmax,i,

= + t

Yes

Robustness analysis of heat-integrated batch process networks

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