Floating Automated Targeting for Resource Conservation Networks

Article pubs.acs.org/IECR

Floating Automated Targeting for Resource Conservation Networks Wui Seng Goh,*,†,‡ Yin Ling Tan,*,‡ and Denny K. S. Ng*,† †

Department of Chemical & Environmental Engineering/Centre of Excellence for Green Technologies, The University of Nottingham, Malaysia Campus, Broga Road, 43500 Semenyih, Selangor, Malaysia ‡ Chemical Engineering Department, Curtin University, Sarawak Campus, CDT 250, 98009 Miri, Sarawak, Malaysia ABSTRACT: Over the past decades, many systematic process integration techniques have been developed for synthesizing resource conservation networks (RCNs). Automated Targeting Model (ATM) is one of the approaches that incorporates insightbased concept into mathematical optimization model to locate various targets for RCNs. However, in order to perform automated targeting, the quality values of process sinks and sources must be first identified and arranged in ascending or descending order. Therefore, for cases where the quality of process sinks and sources are given in a range and not fixed, the conventional ATM will not able to locate the targets accordingly. To overcome such limitation, a novel Floating Automated Targeting Model (FATM) is presented in this work. Two literature case studies are solved to illustrate the proposed approach.

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the synthesis of mass exchanger networks,42−44 water networks, 28,45−47 property-based and concentration-based RCNs.23,48−50

INTRODUCTION Process industries use a tremendous amount of resources (i.e., in the form of mass and energy) to convert various raw materials to desired products. Due to increasing awareness toward sustainability and stringent environmental legislation, this has motivated the industries to look into the possibilities of sustainable utilization of these resources. In particular, resources conservation activities are one of the promising solutions, wherein the resources are reused/recycled and conserved within the processes. However, the main challenge of these activities is to consider the process of interest as a whole and develop a plantwide strategy. Process integration has been identified as a promising tool in evaluating various resource conservation alternatives. It is defined as a systematic and holistic approach to process design, retrofitting, and operation that emphasizes the unity of process.1,2 Over the past decades, significant works have been reported for synthesis of water and gas networks as special cases of mass integration. These developed approaches can be generally categorized into insight-based (which is also known as pinch analysis) and mathematical optimization approaches. Seminal work of the insight-based approach for water network synthesis was initiated by Wang and Smith.3 On the other hand, early works in mathematical optimization technique for water network synthesis were reported by Takama and co-workers.4,5 Note that, these reported networks can be grouped based on the strategies of direct recycle/reuse, 3,6−27 regeneration, 3,24,28−36 waste treatment, 3,24,37−39 and process changes.14,40,41 As presented in the previous works, the main objective is to minimize the fresh resource consumption and waste generation in resource conservation networks (RCNs). It is noted that pinch analysis approaches are useful in identifying various targets of RCN prior to detailed design, while mathematical optimization approaches are often used to handle more-complex problems (e.g., multicontaminant case, case with interaction of process sinks and sources, etc.) due to its high flexibility. In order to take advantage of both approaches, hybrid approaches have been developed. The seminal works on hybrid approaches have been proposed for © 2015 American Chemical Society

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AUTOMATED TARGETING MODEL (ATM) Automated Targeting Model (ATM) is one of the established hybrid approaches. ATM has been extended to synthesize RCNs with continuous process,23,48−50 batch process,51 and interplant network.52 In addition, ATM has also been applied in other areas, such as carbon-constrained energy planning,53 synthesis of integrated biorefinery,54,55 and synthesis of cogeneration systems in integrated palm oil processing complexes.56 ATM was initially proposed by El-Halwagi and Manousiouthakis for the synthesis of mass exchange networks.43 Later, Ng et al. extended the concept of ATM by incorporating cascade analysis11 into mathematical optimization model to locate the minimum flow rate/cost targets for a single impurity and concentration-based direct reuse/recycle RCN.23 The proposed ATM is then further developed to determine the minimum flow rate or cost targets for RCN with interception placements.48 Meanwhile, Ng et al.49 further extended the use of ATM to locate the targets for a property-based RCN.49 Besides, ATM is also used in RCNs with process modification and pretreatment system.49 On the other hand, a new variant of ATM, which is known as bilateral integration problem,49 is introduced to address cases when multiple fresh resources exist at different levels in the property operator scale. As pointed out by Kuo and Smith,38 there are close interactions between reuse/recycle, regeneration, and waste treatment systems. Therefore, a total RCN that integrates all three elements as a whole is presented. Based on this concept, Ng et al.50 further extended ATM to locate targets for total RCNs.50 Note that, the flexibility in setting the optimization Received: Revised: Accepted: Published: 6135

December 27, 2014 April 22, 2015 April 28, 2015 April 29, 2015 DOI: 10.1021/ie5050346 Ind. Eng. Chem. Res. 2015, 54, 6135−6145

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Industrial & Engineering Chemistry Research

≤ FSKj ≤ Fmax SKj ) and is restricted to comply with predetermined max allowable quality of qSKj (qmin SKj ≤ qSKj ≤ qSKj ). Note that, similar to process source, flow rate and qualities of the process sink can be represented by mathematical function. Besides, external fresh resources f, FRf (f∈F) with a quality of qFRf, are readily available to supplement the flow rate to process sink j when necessary, and their total flow rate (FFRf) is to be determined. To further enhance the recovery of process source, SRi may be regenerated/intercepted with a regeneration unit REGu (u∈U). After the recovery is exhausted, SRi can be treated in a treatment system TRv (v∈V) for discharge and comply with the quality discharge limit (qdischarge). The discharge limits are normally given as a range as follows: qLBE ≤ qdischarge ≤ qUBE, where qLBE and qUBE are the lower and upper bounds of quality discharge limit. Note that quality q can be any quality of interest corresponds to the type of RCN (for example, concentration, property, etc.57). In this work, concentration-based RCN and propertybased RCN will be used for illustration. Based on the previous works on property integration (for example, the work of Shelley and El-Halwagi58 and Foo et al.16), a generalized property mixing rule is needed to define all possible mixing patterns among the individual property in synthesizing RCN. Since most of the properties does not have a linear mixing rule, a property operator is introduced and the mixing rule takes the following expression:

objective is one of the main advantages of ATM, as compared to other insight-based approaches. In addition, although ATM is solved via mathematical optimization model, it can still provide insights for process design similar to cascade analysis.11 Based on the conventional ATM,23,48−50 the quality of process sinks and sources are first identified and arranged in ascending or descending order. In other words, in case where the quality of sinks and sources is not predetermined, the conventional ATM cannot be used to solve the design problem. In addition, limiting data are usually provided as fixed values in order to perform ATM. However, in cases such as RCN with process changes, one is not able to obtain the exact value of limiting data.14,40,41 In order to address this issue, Ng et al.49 proposed to include all possible quality levels as variables on the ATM cascade diagram after much analysis. However, this approach is cumbersome, especially when dealing with morecomplex problems that involve many limiting data with unfixed values. For example, in cases where the qualities and flow rates sink and source are given as a range and are dependent on each other, therefore, the limiting data cannot be extracted based on the previous proposed approach.57 Note that since limiting data are not fixed, the conventional ATM, which requires arrangement of qualities, cannot be used. Therefore, there is a need to develop a more generic and less complex approach to overcome the previous limitations. Furthermore, in most of the previous works, it is always assumed that there is no interaction among the process sinks and sources in order to simplify the model. Such assumption may not be applicable for cases where both process sink and source that are originated from a same process unit. In such case, the outlet flow rates and/or qualities of the process (sources) are highly dependent on the operating condition (e.g., flow rate and/or concentration) of the inlet streams (sinks). In order to address the sink−source interaction problem, superstructural-based mathematical optimization model is presented by Chen et al.24 However, the approach does not provide useful insights for process design, such as pinch location of the RCN. Viewing the limitations of previous works, automated targeting is now further extended to locate targets for RCNs with sink−source interaction and process changes. In this work, a novel Floating Automated Targeting Model (FATM) is presented. The proposed model is based on the similar concept of ATM and cascade analysis, which various targets of RCN are located prior to detail design. However, FATM eliminates the need to identify and arrange the quality of process sinks and sources in ascending or descending order before targeting can be performed. On the other hand, by using FATM, limiting data are allowed to be varied (i.e., not fixed value). In addition, since FATM is an extension of ATM, it can also perform targeting for RCNs which are those previously solvable by using ATM. Two literature case studies are solved to illustrate the proposed approach.

ψ (p ̅ ) = ΣixSRiψ (pSRi )

(1)

where ψ(p)̅ and ψ(pSRi) are property operator for the mixture and source i, respectively; while xSRi is the fractional flow rate of SRi in the total mixture. As FATM is developed based on cascade analysis, it inherits the same limitation of handling only a single quality RCN problem. Depending on the problems, the optimization objective function can be set to locate the minimum fresh resource flow rate or cost targets. Flexibility in setting performance target index is one of the well-known advantages of automated targeting, as compared with other insight-based targeting techniques.

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FLOATING AUTOMATED TARGETING MODEL (FATM) As mentioned previously, FATM is an extension of conventional ATM.23,48−50 Therefore, the basic framework of FATM is similar to the original works. However, FATM does not require to construct cascade diagram based on the fixed quality of sinks and sources prior to targeting. The quality levels are allowed to be varied, and hence, they are analogously floating on the cascade diagram. The basic idea of FATM is to postulate all possible flow rates and qualities of process sinks and sources on the cascade diagram by using binary integers. Subsequently, a generic mathematical optimization model is formulated to identify feasible and yet optimum quality and flow rates of the process sinks and sources for the cascade diagram and also for the RCN. Figure 1 shows the generic cascade diagram for FATM. As shown in Figure 1, cascade diagram is first constructed based on the total number of process sinks and sources available. Following the concept of ATM,23 a final fictitious level (qn) is added at the final level (k = n) on the cascade diagram for calculation purposes. For example, if a RCN has four process sinks and four process sources, there are eight

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PROBLEM STATEMENT The problem definition of a single quality q RCN can be stated as follows. Given a set of process source i, SRi (i∈I) that may be reused/recycled to a set of process sink j, SKj (j∈J). Each source has a flow rate of FSRi and is characterized by a quality, qSRi. Both flow rate and quality of process source i can be varied max min max within a range of Fmin SRi ≤ FSRi ≤ FSRi and qSRi ≤ qSRi ≤ qSRi , or the flow rate and qualities can be represented by mathematical function. Meanwhile, each sink requires a flow rate of FSKj (Fmin SKj 6136

DOI: 10.1021/ie5050346 Ind. Eng. Chem. Res. 2015, 54, 6135−6145

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integers, “SR1”, “SK1”, and “F” represent source, sink, and fresh, respectively, while the numbers after the commas represent the quality levels. For example, bSR1,1 means binary integer of source SR1 at level k =1. As presented in Foo,57 there may exist two distinct cases of RCN synthesis, with respect to the quality (e.g., property operator value, concentration, etc.) of the fresh resource. In the first case, the fresh resource has a quality value that is superior (lowest value) among all process sources and sinks. This is similar to the concentration-based RCN, where fresh resource is assumed to be always available at lowest concentration (i.e., highest quality) among all sources and sinks. This type of RCN is termed as a superior case, and the quality levels are arranged in descending order (i.e., from highest quality to the lowest quality). For the second case, in contrast, when the fresh resource’s quality value is available at an inferior level (largest value) among all the process sources and sinks (which this type of RCN will then be termed as an inferior case), the quality levels are arranged in ascending order (i.e., from lowest quality to the highest quality). In order to accommodate both cases, FATM is developed for these two cases and is presented in the following.

Figure 1. Cascade diagram for floating automated targeting model (direct recycle/reuse).

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levels of quality and also the fictitious level. Thus, a total of nine levels are included in the cascade diagram (i.e., n = 9). Note that, since FATM allows quality levels of sinks and sources to be varied, the location of fresh resource’s quality level on the cascade diagram is also subjected to change, with respect to the other sinks and sources quality. Therefore, fresh resource is added as one of the sources in FATM. For cases with multiple fresh resources, additional levels of quality for fresh resources are added. For example, for RCN with two fresh resources, four process sinks, and four process sources, a total of 11 levels of quality (including the fictitious level) are included in the cascade diagram. Each quality level (qk) available on the cascade diagram is assigned as all possible sinks and sources’ quality (qSRi and qSKj), as shown in eq 2, except for the final fictitious level. qk = ∑i (qSRibi , k ) + ∑j (qSKjbj , k )

∀K

SUPERIOR CASE Following the concept of ATM,23 for superior case, the quality levels are arranged in descending order in order to perform targeting. Thus, eq 6 is included in the model. The fictitious level (qn) is set to be the lowest quality level (highest value) as possible. For example, 100% and 1 000 000 ppm are added for quality which measures in term of % and ppm. qk ≤ qk + 1

∀K

(6)

Next, flow rate cascade is performed across all quality levels, as shown in eq 7. The net flow rate (δk) of each kth level is the summation of the net flow rate cascaded from earlier quality level (k − 1), δk−1, with the flow rate balance at quality level k (∑iFSRibi,k − ∑jFSKjbf,k). Note that, in order to locate the total source flow rates and sink flow rates at the respective quality level, the sources’ and sinks’ flow rates are attached with binary integers as shown in eq 7. Note also that the net flow rate can either take positive or negative value, with positive values indicating that resources flow from a higher-quality level to a lower-quality level or vice versa.23

(2)

where bi,k and bj,k are the binary integers to parametrize the existences and locations of the sinks and sources at level k. These binary integers will take the form of “1” when the sinks/ sources are existed in level k and “0” when they are not existed in level k. In order to make sure that only one quality out of all the possible sinks/sources quality appears on each level k, eqs 3−5 are included as sets of constraints in the FATM. For example, consider a case with one source, one sink and one fresh resource, a total of four levels of quality (including fictitious level) are included in the cascade diagram. According to the concept of FATM, only one of the source, sink and fresh resource’s qualities can appear in quality level one (k = 1). ∑i bi , k + Σjbj , k = 1

∀K

δk = δk − 1 + ∑i FSRibi , k − ∑j FSKjbj , k

∀K

(7)

Note also that the net flow rate that enters the level n − 1 (δn−1) corresponds to flow rate of waste discharge in direct reuse/recycle RCN. Therefore, it should not take negative value, and eq 8 is included in the model. δn − 1 ≥ 0

(8) 23

It is noted that, in previous work, fresh resource is available at the highest quality level (i.e., k = 1), thus δ0 is directly set to be fresh resource flow rate. However, in FATM, as the fresh resource will be treated as one of the sources; thus, δ0 is set to be zero. Besides flow rate cascade, a quality load cascade is constructed in order to ensure a feasible RCN.23,48−50 Similarly with the previous work, the quality load of each quality interval k is determined by the product of the net flow rate from level k (δk) and the difference between two adjacent quality levels (Δq). This quality levels difference is calculated via eq 9.

(3)

∑k bi , k = 1

∀I

(4)

∑k bj , k = 1

∀J

(5)

Based on eqs 3−5, if quality of source should appear in quality level one (k = 1), eqs 3 and 4 (i.e., bSR1,1 + bSK1,1 + bF,1 = 1, bSR1,2 + bSK1,2 + bF,2 = 1, bSR1,3 + bSK1,3 + bF,3 = 1) then will cause bSR1,1 = 1, in such that quality of source only appear in level k = 1. Note that, for the subscripts in the abovementioned binary 6137


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Figure 2. Block flow diagram for the tricresyl phosphate manufacturing process.24

Δq = qk − qk + 1

∀K

Table 1. Constraints Associated with Sinks and Sources in Case Study 1

(9)

Residual quality load (εk) balance at the kth quality level can be determined via eq 10. Similar to the flowrate cascade, εk is the summation of the residual quality load cascaded from an earlier quality level k−1 (εk−1) with the product of net flow rate (δk) and adjacent quality levels difference (Δq) at quality level k. εk = εk − 1 + δk(Δq)

∀K

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∀K

(10)

sink (SK1)

0.7 ≤ FSK1 ≤ 0.84

0 ≤ CSK1 ≤ 30

source (SR1)

0.7 ≤ FSR1 ≤ 0.84

CSR1 = h(FSK1, CSK1)

sink (SK2)

0.5 ≤ FSK2 ≤ 0.6

0 ≤ CSK2 ≤ 30

source (SR2)

0.5 ≤ FSR2 ≤ 0.6


sink (SK3)

0.2 ≤ FSK3 ≤ 0.25

0 ≤ CSK3 ≤ 100

source (SR3)

0.2 ≤ FSR3 ≤ 0.25


Washing #1 sink (SK4) source (SR4)

FSK4 = 2.45 FSR4 = 2.45

0 ≤ CSK4 ≤ 5 CSR4 = h(FSK4,CSK4)

Washing #2 sink (SK5) source (SR5)

FSK5 = 2.45 FSR5 = 2.45

CSK5 = 0 CSR5 = h(FSK5,CSK5)

Scrubber #2

Flare Seal Pot

(12)

INFERIOR CASE As mentioned previously, for inferior case, the quality level is arranged in ascending order as the fresh resource’s quality has the largest value among all the process sources and sinks.57 Therefore, eq 6 must be revised as eq 13 in order to model the arrangement of quality levels on the cascade diagram. ∀K

In order to perform FATM, different optimization objectives can be used. For example, the objective is set to minimize fresh resource flow rate, as shown in eq 15.

(13)

Minimize ∑f FFRf

Similarly, a fictitious level, qn (typically a zero, which is the possible lowest value among all quality level), is added at the final quality level (k = n) on the cascade diagram for the inferior case. On the other hand, as for the quality load cascade calculation, eq 9 is revised as eq 14. Δq = qk + 1 − qk

cresol concentration constraint (ppm)

(11)

ε1 = 0

qk + 1 ≤ qk

flow rate constraint (kg/s)

Scrubber #1

In order to ensure a feasible quality load cascade is performed, eq 11 is included as a set of constraints in the optimization model.23 As there is no residual quality load (ε0 = 0) and no net flow rate (δ0 = 0) before the first quality level (k = 0), the residual quality load at q1 is always taken as zero (ε1 = 0), as shown in eq 12. εk ≥ 0

type

unit operation

∀K

∀F

(15)

Alternatively, one can use the minimum cost solution in which the case that the optimization objective is set as eq 16, Minimize ∑f COSTFRf FFRf

∀F

(16)

where COSTFRf is the cost of fresh resources f. Based on the same philosophy of pinch analysis,11 when the residual quality load is determined as zero at level k, the respective quality is identified as the pinch quality. The

(14)

Other than such changes, the other equations remain the same as the superior case (i.e., eqs 2−5, 7−12). 6138


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Industrial & Engineering Chemistry Research Table 2. Modelling Correlations for Sinks and Sources in Case Study 1 unit operation Scrubber #1

Scrubber #2

Flare Seal Pot

Washing #1

Washing #2

modeling correlations

FSK1 = FSR1

(17)

⎡⎛ ⎛F ⎞ HFY1 ⎞⎛ C Y1 − HCSK1 ⎞ HFY1 ⎤ ⎥ 0.45 ln⎜ SK1 ⎟ = ln⎢⎜1 − ⎟+ ⎟⎜ ⎢⎣⎝ FSK1 ⎠⎝ C Y2 − HCSK1 ⎠ FSK1 ⎥⎦ ⎝ HFY1 ⎠

(18)

0.6(C Y1 − C Y2) − FSK1(CSR1 − CSK1) = 0

(19)

FSK2 = FSR2

(20)

⎡⎛ ⎛F ⎞ HFY2 ⎞⎛ C Y2 − HCSK2 ⎞ HFY2 ⎤ ⎥ ⎟+ 0.35 ln⎜ SK2 ⎟ = ln⎢⎜1 − ⎟⎜ ⎢⎣⎝ FSK2 ⎠⎝ C Y3 − HCSK2 ⎠ FSK2 ⎥⎦ ⎝ HFY2 ⎠

(21)

0.6(C Y2 − C Y3) − FSK2(CSR2 − CSK2) = 0

(22)

FSK3 = FSR3

(23)

⎡⎛ ⎛F ⎞ HFY3 ⎞⎛ C Y3 − HCSK3 ⎞ HFY3 ⎤ ⎥ 5.4 ln⎜ SK3 ⎟ = ln⎢⎜1 − ⎟⎜ ⎟+ ⎢⎣⎝ FSK3 ⎠⎝ C Y4 − HCSK3 ⎠ FSK3 ⎥⎦ ⎝ HFY3 ⎠

(24)

0.6(C Y3 − C Y4) − FSK3(CSR3 − CSK3) = 0

(25)

FSK4 = FSR4

(26)

C X2 = 0.001C X1 + 0.8CSR4

(27)

0.35(C X1 − C X2) − FSK4(CSR4 − CSK4) = 0

(28)

FSK5 = FSR5

(29)

C X3 = 0.001C X2 + 0.8CSR5

(30)

0.35(C X2 − C X3) − FSK5(CSR5 − CSK5) = 0

(31)

source. If such source is being used in LQR, additional amount of fresh resource is needed to fulfill the process sinks’ requirement in the RCN. However, the pinch-causing source is an exception as it belongs to both HQR and LQR. On the other hand, fresh resource(s) shall only be used in HQR as this region experiences flow rate deficit. Using fresh resources in the LQR will result higher fresh resources consumption and waste discharge. In this work, Lingo v.13 is used to solve the optimization models. Two literature case studies will be solved for illustration by using the proposed approach. In Case Study 1, a sink−source interaction problem is addressed via FATM and a RCN synthesis with process changes is presented in Case Study 2. Case Study 1. In this case study, resource conservation activity is carried out for a tricresyl phosphate manufacturing process.1 Figure 2 shows the block flow diagram for the process. As shown, the reactants (cresol and phosphorus oxychloride) are mixed and heated before they are fed to the reactor, where inert gas is added as diluent for the reaction. The effluent of reactor is then sent to a flash column for gas and liquid separation. The liquid phase is cooled and washed with fresh water twice to remove cresol content and improve the product purity. This two-stage washing is designed to reduce the cresol concentration from 500 ppm to below 0.007 ppm. As shown in Figure 2, the concentrations of cresol in the product stream are denoted by CX1, CX2, and CX3, while the flow rate is given as FX1, FX2, and FX3. In the current operation, the twostage washing reduces the cresol concentration from 500 to 0.0005 ppm.

Figure 3. Cascade diagram for case study 1.

identification of the pinch point provides valuable insights to decision makers to identify the bottleneck of the network. For example, in superior case, the pinch divides the overall network into two separate regions with respect to the pinch quality, i.e., higher quality region (HQR) and lower quality region (LQR). Process sources in the HQR (including fresh resources) should be fed to process sinks in HQR, except the pinch causing 6139


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Figure 4. Optimal network design for case study 1.

Figure 5. Block flow diagram for metal degreasing process.12

flared. A flare seal pot is used between scrubbing operation and flare system to prevent backward propagation of fire. The flow rates and concentrations of reactor off-gas after scrubbing are indicated by FY1, FY2, FY3, FY4 and CY1, CY2, CY3, CY4, respectively, as shown in Figure 2. In current operation, 6.59 kg/s of fresh water with 0 ppm is used and a total of 6.59 kg/s of wastewater is generated. Note that a significant amount of water is used in this process, i.e., in the washing and scrubbing operations, as well as in the flare seal pot. Therefore, in order to recover the water from this process, water conservation network is synthesized. According to Foo,57 process units which consume water are identified as water sinks. On the other hand, process units that generates water are taken as water sources. Therefore, in this

Table 3. Limiting Data for Scenario 1 in Case Study 2 flow rate (kg/s)

1.44

limiting operator (atm

Sinks (SKj) Degreaser (SK1) Absorber (SK2)

FSK1 = 5.0 FSK2 = 2.0

ψSK1 = 4.87 ψSK2 = 7.36

Sources (SRi) Condensate I (SR1) Condensate II (SR2) Fresh Solvent (FR)

FSR1 = 4.0 FSR2 = 3.0 to be determined

ψSR1 = 13.2 ψSR2 = 3.74 ψFR = 2.71

)

On the other hand, the vapor phase from flash column is sent to a two-stage scrubbing system for purification before it is 6140


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Table 4. Limiting Data for Scenario 2 in Case Study 2 flow rate (kg/s) Sinks (SKj) Degreaser (SK1) Absorber (SK2) Sources (SRi) Condensate I (SR1) Condensate II (SR2) Fresh Solvent (FR)

limiting operator (atm1.44)

FSK1 = 5.0 FSK2 = 2.0

ψSK1 = 4.87 ψSK2 = 7.36

FSR1 = 4.0

ψSR1 = [0.56e(T−100)/175]1.44 430 K ≤ T ≤ 520 K ψSR2 = 3.74

FSR2 = 3.0 to be determined

ψFR = 2.71

Figure 6. Cascade diagram for Scenario 1 in case study 2.

case study, there are five water sinks and five water sources. It is noted that all the water sinks and sources are the same unit operation and quality of the water sources are dependent on the inlet quality of water sinks. Thus, this case study is identified as sink−source interaction problem. Table 1 shows the limiting data associated with the unit operation. Meanwhile, Table 2 shows the modeling correlations that describe the units’ performance. As shown in Table 1, sources’ concentrations are the function [ i.e., CSRi = h(FSKj, CSKj)] of respective sinks flow rates and concentrations, in which the functions can be collectively acquired from Table 2. For example, CSR1 is a function of CSK1 and FSK1, and they can be correlated by using eqs 17−19. According to Chen et al.,24 the Henry’s coefficient (H) is taken to be 0.064 in this case study. As the fresh water is available at the highest quality level (0 ppm), this case study is identified as a superior case. Following the proposed FATM, the MINLP optimization model (eqs

Figure 8. Cascade diagram for Scenario 2 in case study 2.

2−12, 15, 17−31) entails 111 constraints, 56 continuous variables, and 121 integer variables. It is solved via LINGO 13.0 (Branch and Bound global solver), and the resulted final

Figure 7. Optimal network design for Scenario 1 in case study 2. 6141


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Figure 9. Optimal network design for Scenario 2 in case study 2.

cascade diagram is shown in Figure 3. Note that the fresh water consumption is now reduced from 6.59 kg/s to 3.034 kg/s; the flow rate of wastewater discharged is also reduced to 3.034 kg/ s. The target is the same as the results presented in the reported literature.24 Furthermore, a pinch is observed at corresponding source concentration for washing unit #1 (SR4), in which the pinch concentration is 75.786 ppm. According to the philosophy of pinch analysis, this pinch concentration divides the RCN into HQR and LQR. As shown in Figure 3, HQR contains SR5, SK1, SK2, SK4 and SK5; while LQR contains SR1, SR2, SR3 and SK3. Following nearest neighbour algorithm,13 the network design of the case study is showed in Figure 4. As shown, process source from LQR (SR2) is only fed to process sink in the same region (SK3). Meanwhile, process sources from HQR are fed into process sinks in HQR. Note also that the pinch causing source (SR4) is used in both regions (HQR and LQR). Case Study 2. Figure 5 shows a block flow diagram of a metal degreasing process.12 As shown, fresh organic solvent is used in the metal degreasing unit to decompose grease and organic additives. Besides, the solvent is also used in the absorption unit to capture light gases that escape from the solvent regeneration unit before its gaseous overhead is sent to flare. Degreased metal is sent to the metal finishing section to obtain the final metal product. The used liquid solvent is regenerated in a thermal processing unit. Such unit produces an off-gas that passes through a condenser before it can be flared. On the other hand, another off-gas that is produced from the metal degreasing unit is also passed through a condenser before flaring. The regenerated solvent in thermal processing is recycled to the degreasing unit. Since both condensate streams from the condensers contain solvents, such streams can be recovered to the degreasing unit and absorption to reduce the fresh solvent consumption of fresh solvent. As mentioned in the Introduction, FATM can also be used to perform targeting for conventional RCN problem which is solvable by ATM. Therefore, in this case study, two scenarios are analyzed. Scenario 1 is a conventional RCN problem, while scenario 2 is a RCN problem with process changes. Scenario 1. In the current operation, 5.0 kg/s and 2.0 kg/s of fresh solvents are fed to the metal degreasing unit and the absorption unit, respectively. As a result, 4.0 kg/s and 3.0 kg/s of condensates are produced by Condenser I and Condenser II,

as shown in Figure 5. In order to analyze the potential of solvent recovery, property integration technique is adapted. As shown in the previous work,12 the property of the solvent that is taken into consideration is the Reid Vapor Pressure (RVP). Based on Kazantzi and El-Halwagi,12 general mixing rule of RVP is given as follows: RVPM = Σaxa RVPa1.44

(32)

where RVPM, RVPa, and xa are the RVP of the mixture, the RVP for stream a, and the mass fraction of stream a, respectively. Note that the unit of RVP is given as atm. Hence, the property operator for RVP can be expressed as ψ (RVPa ) = RVPa1.44

(33)

Table 3 shows the limiting data for Scenario 1. It is a property-based inferior RCN as the property operator value of fresh solvent is at the lowest (i.e., ψFR = 2.71). In order to determine the minimum flow rate target of fresh solvent, following the proposed FATM, the MINLP optimization model (eqs 2−5, 7−15, 32−33) entails 38 constraints, 17 continuous variables and 25 integer variables. Solving the optimization model in LINGO 13.0 (Branch and Bound global solver), the optimized cascade is obtained (see Figure 6). These results are same with the results presented in reported studies.12,16,49 Figure 7 shows an optimal network design for this scenario. Note that the result obtained is the same as that in the previous work,49 which solved via conventional ATM. To further illustrate the proposed approach, another scenario with process changes will be presented. Scenario 2. According to Kazantzi and El-Halwagi,12 the RVP for condensate from solvent regeneration unit (SR1) is a function of thermal regeneration temperature (T). Therefore, this operating condition (T) can be modified to enable more solvent from SR1 to be reused/recycled. The acceptable operating temperature range of the unit is given as between 430 K and 520 K.12 By changing the operating temperature of the thermal processing unit, the RVP of Condensate I will be varied according to the correlation as shown below: ⎛ T − 100 ⎞ ⎟ RVPCondensate 1 = 0.56 exp⎜ ⎝ 175 ⎠ 6142

(34)


Article

Industrial & Engineering Chemistry Research where RVPCondensate I is the RVP for Condensate I and T (in K) is the operating temperature of the thermal processing unit. Table 4 summarizes the limiting data for this scenario. As shown in the previous work on ATM,49 this problem is solved via ATM by adding two new property operator levels as variables in the possible locations on the cascade diagram after much analysis. This allows flow rate and property load cascades to be performed across the operator level where the absorber exists, since the arrangement of property operator levels are required before optimization is carried out in ATM. In addition, since the solvent regeneration unit only operates at different temperature level, two flow rates constraints with bilinear term are added in the optimization model to restrict the flow rate of Condensate I to appear in one of the two added property levels. Hence, constraints FSR1,ψ5 × FSR1,ψ7 = 0 and FSR5,ψ1 + FSR1,ψ7 = 4 are added, where FSR1,ψ1 and FSR1,ψ7 are Condensate I flow rates that are located in property operator level 5 and property operator level 7, respectively. Note that the first constraint sets either of these flow rate to be zero, and second constraint indicates that the summation of these flow rates leads to the total available flow rate of Condensate I, i.e., 4kg/s (see Ng et al.49 for further clarification). Note that the approach requires comprehensive analysis beforehand in order to determine the location of the new property operator levels that need to be added. Thus, it may result in a complex cascade diagram and model when more than one process change is involved in the RCN. By using FATM, it enables the floating feature for the quality levels to be incorporated into the cascade analysis; hence, each of the quality levels can actually be postulated with any possible values. Therefore, one can directly correlate eqs 33 and 34 with the temperature range (i.e., 430 K ≤ T ≤ 520 K) to become the limiting data for the property operator of source (SR1) prior to targeting. In other words, FATM can be used to optimize the cascade and the process simultaneously. This case study is a property-based inferior RCN as the property operator value of fresh solvent is at the lowest (i.e., ψFR = 2.71). Following the proposed FATM, the MINLP optimization model (eqs 2−5, 7−15, 32−34) entails 41 constraints, 19 continuous variables, and 25 integer variables. Solving the optimization model in LINGO 13.0 (Branch and Bound global solver), the optimized result is obtained (see Figure 8). It is interesting to note that no fresh solvent is needed and also no waste solvent is discharged from this RCN, when the thermal regeneration is operated at 430 K (at which the property operator of Condensate I is determined to be 6.56 atm1.44). These results are the same as the results presented in the reported studies.12,16,49 Figure 9 shows an optimal network design for this case study.

via direct reuse/recycle is the main focus of this work, as for RCN with other types of resource-using strategies (i.e., regeneration networks, total networks), the proposed FATM is also generic enough to be applied as well. The overall idea remains as the postulation approach by using binary integers as discussed in this paper. In other words, the proposed approach is not only applicable for reuse/recycle, it also can be applied for RCN with regeneration and total RCN.

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AUTHOR INFORMATION

Corresponding Authors

*Tel.: +6(03) 8924 8606. Fax: +6(03) 8924 8017. E-mail (Danny K. S. Ng): [email protected]. *E-mail (Wui Seng Goh): [email protected]. *E-mail (Yin Ling Tan): [email protected]/ tan.yin.ling@ curtin.edu.my. Notes

The authors declare no competing financial interest.

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LIST OF NOMENCLATURE

Variables

bi,k = binary integer of source i at quality level k bj,k = binary integer of sink j at quality level k FFRf = flow rate of fresh resource f FSRj = flow rate of process sink j FSRi = flow rate of process sink i FW = flow rate of waste discharge qk = quality at level k qSKj = quality of process source j qSRi = quality of process source i Δq = adjacent quality levels difference at quality level k δk = net flow rate at quality level k δn = net flow rate at quality level n εk = residual quality load at quality level k εn = residual quality load at quality level n Parameters

Fmin SRi = lower bound of flow rate for process source i Fmax SRi = upper bound of flow rate for process source i qmin SRi = lower bound of quality for process source i qmax SRi = upper bound of quality for process source i Fmin SKj = lower bound of flow rate for process sink j Fmax SKj = upper bound of flow rate for process sink j qmin SKj = lower bound of quality for process sink j qmax SKj = upper bound of quality for process sink j COSTFRf = unit cost of fresh resource f n = final quality level qdischarge = quality discharge limit qFRf = quality of fresh resource f qLBE = lower bound of quality discharge limit qUBE = upper bound of quality discharge limit x = fractional flow rate

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CONCLUSION This work presented a novel targeting model for RCN synthesis, known as Floating Automated Targeting Model (FATM). This proposed approach is a more generic and improved version of the original Automated Targeting Model (ATM). It overcomes the previous inherent limitation of ATM, which the limiting data of RCN can allow to be varied. Note that, the proposed FATM basically shares the similar framework with the previous ATM. However, binary integers are used to postulate all possible flow rates and qualities of process sinks and sources in the cascade diagram. In this work, the proposed approach are applied to solve RCN problems with the consideration of process changes and sink−source interactions. Also note that, even though resource conservation

Sets

f = index for fresh resources i = index for process sources j = index for process sinks k = index for quality level u = index for regeneration unit v = index of treatment system Abbreviations

ATM = automated targeting model C = concentration CX1 = concentration of cresol in product stream after cooler 6143


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CX2 = concentration of cresol in product stream after washing unit #1 CX3 = concentration of cresol in product stream after washing unit #2 CY1 = concentration of cresol in reactor off gas after flash column CY2 = concentration of cresol in reactor off gas after scrubber #1 CY3 = concentration of cresol in reactor off gas after scrubber #2 CY4 = concentration of cresol in reactor off gas after flare seal pot F = flow rate FATM = floating automated targeting model FX1 = flow rate of product stream after cooler FX2 = flow rate of product stream after washing unit #1 FX3 = flow rate of product stream after washing unit #2 FY1 = flow rate of reactor off gas after flash column FY2 = flow rate of reactor off gas after scrubber #1 FY3 = flow rate of reactor off gas after scrubber #2 FY4 = flow rate of reactor off gas after flare seal pot H = Henry’s coefficient HQR = high quality region LBE = lower bound LQR = low quality region MINLP = mixed integer non-linear programming q = quality RCN = resource conservation network REG = regeneration unit RVP = Reid Vapor Pressure SKj = process sink j SRi = irocess source i T = temperature of the regeneration unit TR = treatment system UBE = upper bound ψ = property operator δ = net flow rate ε = quality load

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