Automated Targeting Technique for Single-Impurity Resource

Ind. Eng. Chem. Res. 2009, 48, 7647–7661

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Automated Targeting Technique for Single-Impurity Resource Conservation Networks. Part 2: Single-Pass and Partitioning Waste-Interception Systems Denny Kok Sum Ng and Dominic Chwan Yee Foo* Department of Chemical and EnVironmental Engineering, UniVersity of Nottingham Malaysia, Broga Road, 43500 Semenyih, Selangor, Malaysia

Raymond R. Tan Chemical Engineering Department, De La Salle UniVersity, 2401 Taft AVenue, 1004 Manila, Philippines

Part 1 of this pair of articles presents an automated targeting technique to identify minimum fresh resource flow rate/cost targets in a resource conservation network (RCN) with material reuse/recycle. After the potential for conservation through direct reuse/recycle is exhausted, fresh resource consumption can be further reduced by incorporating waste-interception (regeneration) processes. Hence, the proposed automated targeting technique in part 1 of this pair of articles is extended to determine the targets for RCNs with interception placement. The waste-interception systems are modeled as treatment processes with either fixed outlet concentrations or fixed impurity load removal ratios. The approach also distinguishes between single-pass and partitioning regenerators, which have different implications for RCNs. Literature examples and industrial cases are solved to illustrate the proposed approach. Introduction To further reduce fresh material consumption of an RCN after the potential for material recovery through direct reuse/recycle is exhausted, partial treatment of process sources, which also known as interception or regeneration, can be considered. The incorporation of interception/regeneration units in RCNs has been reported extensively for water1-11 and hydrogen3,12-15 networks. Some of these works also report zero-discharge cases with the use of interception units,4,9 which is very attractive for industrial practitioners. To date, most works have modeled the interception units as providing either a fixed outlet concentration (Cout) or a fixed removal ratio (RR).1-15 Moreover, in most of these previous works (except that of a recent work),11 interception units have been modeled as processes that consist of a single inlet stream and a single outlet stream, as shown in Figure 1a. For ease of discussion, these processes are designated as single-pass regeneration systems. Many other interception units actually have more than a single outlet stream. These include membrane separation systems (e.g., microfiltration, ultrafiltration, reverse osmosis), flotation systems (e.g., dissolved air flotation, induced air flotation), gravity and settling systems (e.g., coagulation, flocculation, clarification), and filtration systems (e.g., granular bed, vacuum drum, press, belt filter).16 For this category of interception units, one of the outlet streams always has a lower concentration (higher quality) than the other. For instance, a membrane system will always separate a feed stream into two product streams, namely, a higher-quality permeate stream (with a lower impurity concentration) and a lower-quality retentate stream (with a higher impurity concentration). This type of interception unit will be discussed in this article and will be referred to collectively as partitioning regeneration systems (Figure 1b). It is interesting to note that only limited works have been reported on such interception units in water11 and hydrogen12–15 networks. For the latter, a rigorous targeting procedure to set the minimum * To whom correspondence should be addressed. Tel.: +60-3-89248130. Fax: +60-3-8924-8017. E-mail: [email protected].

fresh material consumption (external hydrogen source) has yet to be established. Previous researchers have utilized targeting techniques only in assessing the performance of several interception units. Hence, it is the subject of this article to develop a generic targeting technique for such systems. Note also that partitioning regeneration systems can also be categorized as fixed-Cout and fixed-RR types.12-15 Hence, part of the subject of this article is the development of appropriate methodologies for such systems. In this work, it is assumed that multiple interception/ regeneration systems can be employed to achieve minimum flow rates and costs. For general cases, the interception unit is modeled as a segregated treatment system where no mixing of inlet streams is allowed. In other words, each process source is sent to an individual interception unit. This assumption arises from the need to assign predefined concentration levels within the cascade, which is inherent in this method. However, as will be shown in the paper, this assumption can be relaxed for some special cases. In the following section, the automated targeting technique presented in part 1 of this pair of articles17 is first developed for an RCN that employs a single-pass regeneration system. The developed technique is then extended for an RCN with a partitioning regeneration system. Automated Targeting for Interception Placement The generic automated targeting technique for an RCN with reuse/recycle is presented in detail in part 1 of this pair of articles,17 which is adapted from the automated targeting technique for the synthesis of mass-exchange networks18 and property-based RCNs.19 As shown in part 1 of this pair of articles,17 the first step in automated targeting is to construct a resource conservation cascade diagram (RCCD), where process sinks and sources can be located at their respective concentration levels before the targeting step is carried out. To incorporate interception/regeneration into the automated targeting technique, a modified RCCD is required. In principle, regenerated water is withdrawn from a process source when it

10.1021/ie900127r CCC: $40.75  2009 American Chemical Society Published on Web 07/21/2009

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Ind. Eng. Chem. Res., Vol. 48, No. 16, 2009

Figure 1. Two models of interception/regeneration systems: (a) single-pass regeneration system, (b) partitioning regeneration system.

Figure 2. Generic RCCD for water network with single-pass regeneration system of fixed Cout.

is sent for regeneration. Hence, it is added as a new sink at each concentration level where a source exists in the RCCD. This allows a portion of the flow rate of the process source(s) to be regenerated to a higher-quality (lower-concentration) level when its recovery is necessary, as determined by subsequent solution of the optimization model. To reuse/recycle this higherquality source flow rate in the RCN, a new source is added at the concentration level where it is regenerated. In this work, two types of regeneration systems are considered, namely, single-pass and partitioning regeneration systems. The detailed automated targeting technique for each type of regeneration system is presented in the following sections. As presented in part 1 of this pair of articles,17 no significant computational difficulties are encountered in solving the linear programming (LP) models of this approach. In this work, LP models were solved using the software Lingo 10.0, with negligible computing times. In practice, automated targeting techniques can be implemented using any LP solver, even those found in common spreadsheet environments. On the other hand, a nonlinear programming (NLP) model might result when additional constraints are included in the model. This is shown in one of the examples. Single-Pass Regeneration System As described earlier, regeneration system are generally categorized as fixed-Cout and fixed-RR types. The former rates a regeneration system based on a constant Cout (e.g., 10 ppm, 5 mol %). In contrast, an RR-type regeneration unit removes a fixed fraction of the impurity load from the inlet stream.

Depending on the inlet concentration, a fixed-RR-type regeneration unit purifies sources to different values of Cout. For instance, a water source of 100 ppm that is fed to the regeneration system of a fixed-Cout model (with Cout ) 20 ppm) will always exit at 20 ppm, whereas the same water source fed to the regeneration unit with RR ) 0.9 will exit at 10 ppm. Targeting technique for these regeneration systems are different and will be presented separately. Regeneration System of the Fixed-Cout Model. To incorporate a single-pass regeneration system of fixed Cout in the automated targeting model, Cout of the regeneration unit is added as a new level (k ) R) in the RCCD, as shown in Figure 2. However, note that this step can be omitted when Cout coincides with any of the sink or source concentrations already present in the RCCD. As shown in Figure 2, the regeneration unit draws water from sources at concentration levels C3 and C4 (with flow rates of FReg1 of FReg2, respectively) and sends the higherquality water to the Cout level. Note that the inlet of the regeneration unit is treated as a water sink, whereas the outlet is taken as a source. The assumption of no flow rate loss or gain is made for the regeneration system, and hence, the regeneration system has constant inlet and outlet flow rates (i.e., FReg1 + FReg2, as shown in Figure 2). As the regeneration process removes impurity load from the water source(s) to improve its quality, better water recovery is expected. This corresponds to reduced fresh water and wastewater flow rates. In practice, any source within the water network can be regenerated for further reuse/recycle, so the regeneration unit should draw water from all concentration levels with water


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Figure 3. Mass-transfer operation for a countercurrent mass exchanger (not to scale).

source(s). To illustrate the proposed approach, an example that involves simultaneous synthesis of water and massexchange networks is presented. Before the example is examined in detail, a model is first presented to demonstrate the use of a mass exchanger as a regeneration unit in an RCN. Modeling of a Mass Exchanger as a Regeneration Unit. El-Halwagi20 defined a mass exchanger as a direct-contact masstransfer unit that employs a mass-separating agent (MSA) as a lean stream to selectively remove certain components (e.g., impurities) from a rich stream (e.g., waste). For the pth rich stream with an impurity concentration of yp, the linearized equilibrium relation governing its impurity transfer to the qth MSA is given by the equation20-23 yp ) mqx*q + bq

(1)

where x*q is the maximum achievable impurity concentration in the MSA and mq and bq are the slope and intercept, respectively, of the linearized equilibrium relation. To ensure a feasible mass transfer, a minimum allowable concentration difference (ξ*) q is set for each MSA. Hence, a practical feasibility line can be established and mathematically represented as ytp ) mq(xt,max + ξq) + b q q

(2)

where xqt,max is the maximum practical achievable concentration in the MSA. Note that different MSAs can take different values of ξq, which leads to different outlet concentrations of the pth rich stream, ypt . When a mass exchanger is used as a regeneration unit in an RCN (e.g., water network), the process source(s) to be regenerated (for further reuse/recycle) hence become(s) the rich stream(s) for the mass exchanger. A simple example is shown in Figure 3, where an MSA is used in a countercurrent massexchange unit to purify a water source in a water network. For this case, the mass-transfer equilibrium relation of the MSA follows eq 2, with mq ) 0.2 and bq ) 0, and the MSA enters at a supply concentration (xsq) of 20 ppm. The minimum allowable concentration difference (ξq) is taken as 50 ppm. At the rich end of the mass exchanger, the inlet concentration of the water source is fixed (ysp ) Ci ) 130 ppm). Hence, ) the maximum practical achievable outlet concentration (xt,max q of the MSA is calculated as 600 ppm using eq 2. In practice, the mass exchanger might not necessarily operate at this concentration, as any lower concentration level might be acceptable for mass-transfer operation to take place. However,

as will be shown in a later section, to maintain a low operating cost (with negligible capital costs for regeneration systems), it is always desirable to operate the mass exchanger value. at a lower flow rate of the MSA that achieves the xt,max q On the other hand, at the lean end of the mass exchanger, the supply concentration of the MSA (xqs ) 20 ppm) sets the lowest outlet concentration (ypt ) to which the water source can be purified. Based on eq 2, this corresponds to 14 ppm (see Figure 3). For an RCN, a lower concentration of the regenerated source is always desired, as this will reduce the flow rate of the fresh resource (e.g., fresh water) and, hence, reduce the total operating costs for the network. It is noted that the tradeoff between operating and capital costs of the regeneration system has been excluded in this model. This latter topic is the subject for future work. From the perspective of the RCN, a mass exchanger can be categorized as a single-pass regeneration system of a fixedCout model. On the other hand, the total impurity load transferred from the pth rich stream to the qth MSA is given by the horizontal axis of Figure 3, as summarized in the equation Gp(ysp - ytp) ) Lq(xt,max - xsq) q

∀i, ∀p

(3)

where Gp and Lq are the flow rates of the pth rich stream (source) and the qth MSA, respectively. Example 1. The tire-to-fuel case20,21,23 presented in part 1 of this pair of articles17 (as example 2 in part 1) is revisited to illustrate how the automated targeting technique is used for cases where mass exchanger is used as regeneration system in an RCN. In this example, two primary wastewater sources are considered for recovery, namely, 0.20 kg/s from the decanter, out out , and 0.15 kg/s from the seal pot, Fseal Fdecanter pot (for a fresh water flow rate of 0.15 kg/s), with impurity (heavy organic) concentrations of 500 and 200 ppm, respectively. Two process sinks that can accept these water sources are also identified (seal pot and water-jet compression station). In addition, the given process constraints on the flow rate and impurity content (heavy organic) are as follows Seal Pot in 0.10 e flow rate of feed water, Fseal pot (kg/s) e 0.20 (4)

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0 e impurity concentration of feed water, In CSeal Pot (ppm) e 500

(5)

respectively.20,21,23 Equation 8 shows the AOC for the water network with regeneration AOC ) [COSTFW FFW +

Makeup to Water-Jet Compression Station in 0.18 e flow rate of feed water, Fwater jet (kg/s) e 0.20

∑ (COST L ) + q q

q

COSTWWFWW]AT

(6) 0 e impurity concentration of makeup water, in Cwater jet (ppm) e 50

(7)

As shown in part 1 of this pair of articles, the fresh water and wastewater flow rate targets were found to be 0.135 and 0.155 kg/s, respectively, when the direct reuse/recycle scheme was considered.17 To further reduce the fresh water consumption, various MSAs can be used in a mass-exchange network to reduce the heavy hydrocarbon content in the water sources.20,21,23 The selection of the appropriate MSA is dependent on its technical feasibility as well as its treatment cost. It is interesting to note that, in part 1 of this pair of articles,17 the optimization model determines that the flare gas from the finishing section is used as a process MSA (S1) to strip away the impurity content from the water sources. However, note that the model presented in part 117 is based on the reuse/recycle scheme. MSA S1 was selected because it is involved in the reuse/ recycle scheme and, furthermore, is available free of charge. In this section, the problem is re-examined by evaluating the use of various MSAs in purifying water sources for further water reuse/recycle. Hence, one can expect better water recovery as compared to the results in part 1.17 Apart from the flare gas (S1), three external MSAs can also be considered for heavy organic removal, namely, solvent extractant (S2), adsorbent (S3), and stripping agent (S4). Equilibrium and operating data for the MSAs, along with their respective unit costs, are given in Table 1. As presented in the modeling section, the minimum outlet concentration (ypt ) to which the water sources can be purified is determined by the inlet concentration of the MSA (xqs ) in use (regardless of the sources being regenerated). Therefore, utilizing eq 2, the minimum outlet concentration of the regenerated water source can be determined as 200, 400, 48, and 14 ppm, for the associated MSAs of S1, S2, S3, and S4, respectively. As shown in eq 3, the impurity load is removed from the water source(s) by the MSA to upgrade the water quality for further recovery. Therefore, the cost of water regeneration is set by the minimum flow rate of the external qth MSA (Lq) that is used to remove the impurity load from the water source. In this example, the optimization objective is set to minimize the annual operating cost (AOC), which includes the fresh water cost, the costs of water regeneration (proportional to the external MSA flow rate), and the wastewater treatment cost. These three parameters are the main contributors to the AOC. The capital cost of piping and mass-exchange network (i.e., stripper) of the water system is excluded. Otherwise, a mixed integer nonlinear programming (MINLP) model might result, which entails additional computational difficulties. The operating costs of pure fresh water (with 0 ppm), COSTFW and wastewater treatment for discharge, COSTWW are assumed as $1/kg and $0.10/kg,

(8)

where COSTq refers to the unit cost of the qth MSA (Table 1);20,21,23 and AT refers to the annual operating time. Solving eq 8 subjected to the constraints in eqs 4 and 6, as well as eqs 1-3 in part 1 of this pair of articles,17 an RCCD for example 1 is generated in Figure 4. As shown, no fresh water is required, and no wastewater is discharged (FFW ) FWW ) 0) by the process. It is also observed that a 0.20 kg/s (FReg2) flow of water from the decanter (500 ppm) is purified in the seal pot (performs as a stripping column) by process MSA of flare gas (S1). This results in a reduced heavy hydrocarbon concentration of 200 ppm. Next, a 0.1613 kg/s (FReg1) flow of this water source is regenerated by the stripper where its heavy hydrocarbon content is stripped away by the external MSA (S4). A water network that achieves the objective function is shown in Figure 5a. The optimization objective of the automated targeting corresponds to the minimum operating cost of the external MSA, namely, $65,250 (365 annual working days). This result is consistent with the original source where the syntheses of the water and mass-exchange networks were carried out separately.20,21,23 It is worth noting that the network design in Figure 5a is different from that of the original work (Figure 5b). For the latter, the entire seal pot outlet stream was stripped by MSA S4 before being reused in the jet compression system (Figure 5b). In contrast, the results of the automated targeting model indicate that only a portion of this stream (0.1613 kg/s) is being treated for recovery (see Figure 5a). It is also interesting to note that, although the two designs in Figure 5 have different network structures, both achieve the target of the minimum operating cost. However, a lower flow rate in the stripping column means a reduced capital cost. In another scenario, when the cost of treatment is reduced from $0.10/kg to $0.01/kg, different optimum results are obtained. As shown in Figure 6, a 0.02 kg/s (FWW) flow of wastewater is discharged from the decanter with no fresh water supplied to the water network. This solution takes into account that the makeup to water-jet compression station is able to operate over a range of water flow rates (between 0.18 and 0.2 kg/s). Because of the decrease in the cost of wastewater treatment relative to that of regeneration, the model preferentially selects the lower-bound flow rate to this sink to improve the overall solution and achieves this result by purging a 0.02 kg/s flow of wastewater to the treatment plant. In addition, less water from the seal pot (0.1613 - 0.1452 kg/s ) 0.0161 kg/s) is regenerated by the external MSA (S4), which eventually leads to a lower annualized cost of $65,029. Note that, in this case, if one were to solve the problem using the conventional pinch approach,23 which is sequential in nature, one would easily miss the global optimum solution. This drawback is mainly due to the limiting data that are normally extracted as fixed values for

Table 1. Data for Various MSAs in Example 120,21,23 MSA, Sq

upper bound on flow rate, Lq (kg/s)

supply concentration, xsq (ppm)

target concentration, xt,max (ppm) q

mq

ξq (ppm)

unit cost of MSA, COSTq ($/kg of MSA)

S1 S2 S3 S4

0.15 ∞ ∞ ∞

200 300 10 20

900 1000 200 600

0.5 1.0 0.8 0.2

200 100 50 50

0.001 0.020 0.040


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Figure 4. RCCD for example 1.

pinch analysis studies.24 Hence, the automated targeting approach presented in this work overcomes this limitation of conventional pinch analysis techniques. Regeneration System of the Fixed-RR Model. Other than the fixed-Cout model, treatment systems of the RR type are also commonly used to purify process sources for further water recovery. Wang and Smith1,25 defined RR of a treatment unit as the ratio of the impurity load removed to the total impurity load in the inlet water source, given by the equation RR )

FinCin,RR - FoutCout,RR FinCin,RR

(9)

where Fin and Fout are the inlet and outlet flow rates, respectively, for a regeneration/interception unit; while Cin,RR and Cout,RR are its inlet and outlet concentrations. Because the treatment system is modeled as a single-pass regeneration system without water losses, the inlet and outlet flow rates are equal (i.e., Fin ) Fout). Equation 9 can thus be simplified as1,25 RR )

Cin,RR - Cout,RR Cin,RR

(10)

Based on eq 10, it is noted that, for a given RR, the outlet concentration of the treatment system can be determined once the inlet concentration is known. Hence, the targeting procedure for this kind of regeneration/interception system resembles that of the fixed-outlet-concentration model. Figure 7 shows the generic RCCD when a fixed-RR regeneration system is used. As shown, two water sources (FReg1 and FReg2) are regenerated from C3 and C4, respectively, to two new concentration levels (Cout,1 and Cout,2) for a given regeneration system of the RR type. Thus, these additional concentration levels are included in the RCCD. Note that the generic RCCD for a network with singlepass regeneration of the fixed-Cout type (Figure 2) is different from that for a fixed-RR model (Figure 7). For the former, only a single concentration level is needed in the RCCD, even though multiple water sources exist in the network, because the outlet concentration is independent of the inlet concentration of the

regenerated sources. This also means that a single treatment system is sufficient to improve the water quality for recovery. In contrast, multiple outlet concentration levels are required for a network with a fixed-RR regeneration system, as water sources can be generated to different concentration levels. In such cases, multiple interception/regeneration systems might be required to improve the water quality to its targeted outlet concentration (subject to the results of the optimization model). As previously mentioned, this is a limitation inherent in the automated targeting approach that needs to be addressed in future research. Example 2 is used to illustrate the proposed approach for an RCN with a fixed-RR regeneration system. Example 2. This example is adapted from a water minimization case study presented by Gabriel and El-Halwagi26 and ElHalwagi,21 with the limiting data given in Table 2. As shown, three water sources can be considered for recovery to two water sinks. The minimum fresh water and wastewater flow rates for the reuse/recycle case are easily located as 5.3 and 35.3 ton/h, utilizing any of the established flow rate targeting tools.27-30 Stream stripping technology can next be used to intercept water sources by removing the impurity content. Cost data for the interception technology at various RRs of impurity for different water sources i (COSTRR i ) are summarized in Table 3. In addition, for comparison purposes, the operating costs of fresh water and wastewater treatment are taken as $0.13/ton (COSTFW) and $0.22/ton (COSTWW), respectively, and the number of annual operating hours (AT) is taken as 8000 h per year.21,26 The objective of this example is to synthesize a costeffective water network (with interception) while satisfying all of the process water demands. Therefore, the optimization objective is to minimize the AOC, given by AOC ) (COSTFWFFW +

∑ COST

RR RR i Fi

+

i

COSTWWFWW)AT

(11)

refers to the treatment flow rate of source i for where FRR i interception technology at various RRs of impurity.

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Figure 5. (a) Water recovery scheme for example 1 with mass-exchange network as a regeneration unit. (b) Original solution for example 1.20,21,23

Figure 6. Water recovery scheme for example 1 with reduced wastewater treatment cost.

Solving eq 11 subject to eqs 1-3 in part 1 of this pair of articles17 results in the RCCD shown in Figure 8. It is worth

noting that, because all water sources are allowed to be intercepted by three RR treatment systems (see Table 3), all 15


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Figure 7. Generic RCCD for single-pass regeneration system of the fixed-RR model. Table 2. Limiting Water Data for Example 221,26 sink j

flow (ton/h)

maximum inlet concentration (ppm)

load (kg/h)

1 2

200 80

20 75

4.0 6.0

source i

flow (ton/h)

concentration (ppm)

load (kg/h)

1 2 3

150 60 100

10 50 85

1.5 3.0 8.5

Table 3. Cost for Stripping Operating at Different Impurity-Removal Efficiencies21,26 source i

removal ratio (RR)

COSTiRR ($/kg removed)

1

0.1 0.5 0.9 0.1 0.5 0.9 0.1 0.5 0.9

0.68 1.46 2.96 0.54 1.16 2.36 0.45 0.97 1.97

2 3

possible concentration levels are included in the RCCD. For example, source 1 of 10 ppm can potentially be reduced to 9, 5, and 1 ppm by using treatment systems with RRs of 0.1, 0.5, and 0.9, respectively. As shown in Figure 8, no fresh water (FFW ) 0) is required by the network, whereas 30 ton/h of wastewater is sent for environmental discharge. In addition, 52.94 ton/h of source 3 (FReg3) is intercepted in the stripping column with RR ) 0.1. Because only a single source is intercepted, a single stripping column is used. However, it should be noted that this approach, depending on the process data, might result in multiple streams required for interception. In such cases, the target determined implies that multiple regenerators with the same RR are to be assigned to each concentration interval. The AOC for this example is determined as $54,420. It is worth noting that the targeted AOC is identical to the result reported by Gabriel and El-Halwagi26 and El-Halwagi,21 in which a reformulated superstructural approach was used to solve the problem. The

network for this case is shown in Figure 9, which is identical to that in previous works.21,26 Partitioning Regeneration System As mentioned earlier, a partitioning regeneration system consists of a feed stream and two outlet streams of different quality, namely, a higher-quality product stream and a lowerquality reject stream (Figure 1b). The flow rates and impurity concentrations of these streams are labeled FF, FP, FR, CF,S, CP,S, and CR,S, respectively. To date, limited works have been reported on partitioning regeneration system in hydrogen12-15 and water11 networks. For the latter, the work is based on the superstructure approach, where all possible connections are incorporated into the mathematical model.11 The approach is different from this work, where the model is based on insight-based targeting concept. For hydrogen networks, previous targeting work15 does not locate the minimum interception flow rate to achieve minimum fresh hydrogen consumption. Hence, as will be shown in the following section, the previous targeting technique for partitioning regeneration units in hydrogen networks15 does not lead to optimal results. Note that the partitioning regeneration system can also be categorized as fixed-Cout and fixed-RR types. Each type of system will be analyzed in the following sections. Modeling for Partitioning Regeneration System. Assuming no material losses and generation, the overall flow rate balance of the regeneration system is given by FF ) FP + FR

(12)

For a water-using system with a single impurity, the impurity load balance can be written as FFCF,S ) FPCP,S + FRCR,S

(13)

To accurately model a partitioning regeneration system, a new parameter, namely, the fluid recoVery factor, RL, is introduced. The water recovery factor is defined as the fraction of the feed stream to that passes through the regeneration system into the higher-quality stream and is assumed to be constant for a given regeneration process. For fluid impurity given in parts per

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Figure 8. RCCD for example 2.

Note that single-pass regeneration systems can be treated as a special case of partitioning regeneration systems, in which RL approaches unity. To construct the RCCD, all concentration levels need to be predetermined. Hence, the impurity concentration term in the reject stream (the CR,S term in eq 13) has to be calculated before the automated targeting model is solved. For impurity concentrations given in parts per million, the impurity concentration (CR,S) can be related to the fluid recovery factor (RL) and the impurity concentrations in the feed (CF,S) and product (CP,S) streams by combining eqs 12-14 as follows

CR,S )

1-

million, this parameter is given by RL )

FP(106 - CP,S) FF(106 - CF,S)

(14)

which can be simplified for dilute solutions to RL )

FP FF

( [ (

CF,S -

Figure 9. Optimal water recovery scheme for example 2.20,26

(15)

106 - CF,S

106 - CP,S

) )]

106 - CF,S 106 - CP,S

RLCP,S (16)

RL

Note that, for both eqs 14 and 16, the concentration term (106) can be changed depending on the concentration units used (i.e., 100 for mass percentage or 1 for mass fraction). From eq 16, it can be seen that CR,S is affected by both CF,S and CP,S. However, because the latter value is a fixed characteristic of the regeneration system, the reject stream concentration, CR,S, is determined by the concentration of the process stream to be regenerated (CF,S). As with earlier cases, no mixing of sources


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Figure 10. Generic RCCD for partitioning regeneration system.

is allowed for the regeneration system; thus, a multiple regeneration system is required if more than one source is required to be treated for recovery. With the above assumption, the outlet concentration of the regeneration system (fixed-RR) can be predetermined based on the source concentration, and an LP model can be formulated. Regeneration System of the Fixed-Cout Model. For a regeneration system of the fixed-Cout model, it is assumed that the regeneration unit always produces a product stream of constant concentration (Cout). In other words, the concentration of the feed stream affects the concentration of only the reject stream, not the product stream. Examples of this kind of regeneration system include dead-end filtration and membrane separation.16 For instance, the product stream or permeate of a membrane-based regenerator will have a fixed concentration if it is operated such that the solute and solvent fluxes have a fixed ratio. Because of the two outlet streams of different concentrations, two concentration levels (i.e., CP,S and CR,S) are added to the RCCD for the placement of a partitioning regeneration unit in the RCN. Note that CP,S is normally given as the specification of the regeneration unit, whereas CR,S can be calculated by eq 16. Figure 10 shows the generic RCCD for a RCN with a partitioning regeneration system, where the regenerator inlet stream serves as a process sink and its two outlet streams serve as process sources of lower and higher concentration levels. Both of these sources have the potential to be reused/recycled to process sinks in the network. It should be noted that such a partitioning regenerator effectively functions as the reverse of a mixing process and thus creates multiple streams whose concentrations can be more closely matched to process sinks within the network. A hydrogen integration case is used here to demonstrate the automated targeting approach. Example 3. The hydrogen recovery case study (example 3) in part 1 of this pair of articles17 is revisited to illustrate the application of the automated targeting technique in placing a partitioning regeneration unit with fixed Cout in the network. The limiting data for this example are provided in Table 4. As shown in part 1,17 the minimum fresh hydrogen and purge gas flow rates fresh hydrogen (FFG) and purge gas (FGD) flow rates for this example were determined to be 268.82 and 102.52 mol/ s, respectively (the latter is used as process fuel), with a pinch

Table 4. Limiting Data for Example 331 j

hydrogen sink

flow rate, FSKj (mol/s)

impurity concentration, Cjmax (mol %)

1 2 3 4

HCU NHT CNHT DHT

2495.0 180.2 720.7 554.4

19.39 21.15 24.86 22.43

i

hydrogen source

flow rate, FSri (mol/s)

impurity concentration, Ci (mol %)

HCU NHT CNHT DHT SRU CRU fresh supply

1801.9 138.6 457.4 346.5 623.8 415.8 ∞

25.0 25.0 30.0 27.0 7.0 20.0 5.0

1 2 3 4 5 6

concentration of 30 mol %. This is identical to the results reported in other earlier works.15,27,31 To further reduce the fresh hydrogen consumption, process hydrogen source(s) can be fully or partially treated for further recovery. In this example, a membrane system with a fluid recovery factor (RL) of 0.95 that will produce a product stream of 2 mol % impurity (CP,S) is used as the interception unit.15 As mentioned previously, the membrane system is categorized as partitioning regeneration system of fixed Cout (i.e., CP,S ) 2 mol %). Next, the impurity concentration of the retentate (reject) stream, CR,S, is determined using eq 16. Because all available process hydrogen sources can be considered for interception, both of the permeate and retentate concentrations are included in the RCCD, as shown in Figure 11. Generally, the cost of interception increases proportionally with the hydrogen flow rate entering the membrane system. Hence, to synthesize a cost-effective hydrogen network, it is necessary to minimize the AOC of the fresh and intercepted hydrogen sources. Thus, the optimization objective in this example resembles eq 17, given as follows minimize AOC ) (AFFG + BFIntH2)AT

(17)

where FIntH2 is the flow rate of the intercepted hydrogen sources; while and A and B are the coresponding unit costs of these sources, as determined from historical data or estimation. In

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Figure 11. RCCD for example 3 (with regeneration system).

this work, the values of A and B are given as $1/mol and $0.01/ mol, respectively. It is assumed that the cost depends mainly on the hydrogen flow rate. However, the relative values of the parameters A and B reflect the lower cost of intercepted hydrogen source, which contains some impurities. Following the proposed automated targeting procedure, the minimum fresh hydrogen flow rate (FFG) is targeted as 196.77 mol/s (Figure 11). The hydrogen network that achieves the minimum hydrogen flow rate targets is shown in Figure 12. As shown in Figure 12, a 94.8 mol/s flow of hydrogen from the CNHT is intercepted by the membrane system to produce a permeate stream of 64.33 mol/s (FIntH2,P), with 2 mol % impurity. On the other hand, a reject stream (FIntH2,R) with a flow rate of 30.47 mol/s (CS,R ) 52.78 mol %) is produced from the membrane system and later discharged from the hydrogen network as fuel (FGD). Note that only a single source (hydrogen from the CNHT) is intercepted for recovery; therefore, one membrane system is sufficient to accommodate the requirement. In an earlier work by Foo and Manan,15 a 102.6 mol/s flow of hydrogen from the CNHT was sent for interception to achieve the same minimum fresh hydrogen consumption (FFG ) 196.77 mol/s). The authors also reported that the pinch concentration migrated to a new concentration (89.11 mol %) with this interception flow rate. As shown by other works,2,7,8 pinch migration during the placement of a regeneration unit means that an interception flow rate higher than the minimum value has been used, which, in turn, leads to a suboptimum solution for the problem. On the other hand, the automated targeting

technique enables the determination of minimum fresh hydrogen and intercepted flow rates to be carried out simultaneously, which leads to optimum results. As shown, a much lower intercepted hydrogen flow rate (FIntH2 ) 94.8 mol/s) is needed to achieve the minimum fresh hydrogen consumption for the network. Furthermore, note that the original pinch concentration for the reuse/recycle case (30 mol %) has been observed, and two other news pinches appear with the use of the interception units, namely, 2 and 52.78 ppm (ε2 ) ε12 ) ε13 ) 0) where the outlet stream of the regeneration unit is located. This result is consistent with the findings of previous works.2,7,8 A sensitivity analysis for the cost of interception (B) was conducted, similar to that in part 1 of this pair of articles.17 Based on the result, a network design similar to that in Figure 12 is achieved when the value of B is lower than $0.75/mol. Once B exceeds $0.75/mol, only fresh hydrogen is needed to fulfill the process requirement. Regeneration System of the Fixed-RR Model. For a partitioning regeneration system with two outlet streams, eq 9 or 10 is insufficient to represent the model. Hence, the removal ratio (RP) in eq 9 is modified so that the outlet stream term in eq 9 (FoutCout,RR) is referred to the main product stream of the partitioning unit, given by RP )

FFCF,S - FPCP,S FFCF,S

(18)


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Figure 12. Optimum refinery hydrogen network for example 3. The numbers represent the total gas flow rate (mol/s) and impurity concentration (mol %).

Figure 13. Water network for example 4.4,32,33

By combining eq 18 with the fluid recovery factor (RL) in eq 14, the impurity concentration of the product stream can be determined from eq 19 CP,S )

CF,S(1 - RP)10

6

RL(10 - CF,S) + CF,S(1 - RP) 6

(19)

As in the earlier case, the concentration term (106) applies only when levels are expressed in parts per million. For a partitioning regeneration system of the fixed-RR model, two additional product and reject concentration levels are added to the RCCD for each water source to be regenerated (similarly to the case of the fixed-Cout model). However, it can be seen that, for any given process stream, the fixed parameters RL and RR fully determine the distribution of solute and liquid between the product and reject streams. Hence, the concentrations of these streams can be determined using eqs 19 and 16, respectively. Given the above information, an automated targeting technique similar to that for the fixed-Cout model is applicable for the regeneration system of the fixed-RR model. The generic RCCD for a partitioning regeneration system is shown in Figure 10, which resembles the case for fixed-Cout model. A papermill case study is utilized to demonstrate the proposed approach. Example 4. The water network of a paper-milling process is shown in Figure 13, with the limiting data given in Table 5.4,32,33

Table 5. Limiting Water Data for Example 44,32,33 j

water sink, SRi

flow rate, FSKj (ton/h)

concentration, Cjmax (ppm)

1 2 3 4 5 6

pressing section forming section DIP-others DIP CP AF

155.40 831.12 201.84 1149.84 34.68 68.70

20 80 100 200 20 200

i

water source, SRi

flow rate, FSRi (ton/h)

concentration, Ci (ppm)

1 2 3 4

pressing section forming section DIP-others DIP

155.40 1305.78 201.84 469.80

100 230 170 250

As shown in Figure 13, the fresh water and wastewater flow rates are 1989.06 and 1680.30 ton/h, respectively. In this case study, the most significant water quality factor was determined to be total suspended solids (TSS). As reported in an earlier work,4 the minimum fresh water and wastewater flow rates for reuse/recycle case were determined as 848 and 539 ton/h, respectively. To enhance water recovery, process water can be intercepted with a water regeneration unit. In this case, a dissolved air flotation (DAF) tank that can reduce the TSS concentration is considered. According to Woods,34 a DAF unit can be modeled as having a single inlet stream and two outlet streams with a constant impurity removal ratio (i.e., the partitioning regenera-

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Figure 14. RCCD for example 4 (multiple regeneration system).

Figure 15. Optimum water network design for example 4 with two DAF tanks as interception units (flow rates given in tons per hour).

tion system of the RR model in this work). For this example, a DAF tank with RP ) 0.9 and RL ) 0.98 is used. From Figure 13 and Table 5, it is observed that four water sources are potential candidates for interception. The impurity concentrations of the product and reject streams for all water sources are determined using eqs 19 and 16, respectively, and all concentration levels are added to the RCCD (Figure 14). For instance, process water from the forming section (SR2, FReg2) of 230 ppm TSS is intercepted to produce a product

stream of 23.47 ppm and a reject stream of 10426 ppm. Both of these additional concentration levels are added to the RCCD (Figure 14). The same procedure applies for other sources as well. Following the proposed procedure, the automated targeting approach is conducted with the optimization objective of minimizing the AOC for fresh and intercepted water. Hence, eq 17 can be modified as


minimize AOC ) (AFFW + B

∑F

Reg,i)AT

(20)

i

where FReg,i represents the regenerated flow rates of sources i and A and B reflect the relative costs of fresh water and regenerated water, respectively. In this example, the relative costs of fresh water (A) and regenerated water (B) are taken as 1 and 0.001, respectively. Solving eq 20 subject to the constraints in eqs 1-3 in part 1 of this pair of articles17 results in the RCCD in Figure 14, with the minimum AOC of $2,572,560 (8000 h per year). However, because of space limitations, the RCCD in Figure 14 does not include all possible concentration levels that were actually coded in the model. As shown in Figure 14, the minimum fresh water flow rate (FFW) is targeted as 320.97 ton/h, and the wastewater discharge flow rate (FWW) is reported as 12.21 ton/h. This is a significant

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reduction as compared to the base-case fresh water flow rates of 1989.06 ton/h (without reuse/recycle) and 848 ton/h (reuse/ recycle case). In this case, two process sources from the forming section (FReg2 ) 134.04 ton/h) and DIP (FReg4 ) 469.80 ton/h) are sent for regeneration to the two different DAF tanks, as shown in Figure 15. As shown, 131.33 ton/h of the former (FReg2,P) and 460.30 ton/h of the latter (FReg4,P) are regenerated as the product streams, whereas the reject streams from these sources (FReg2,R and FReg4,R) are discharged as wastewater. In a different scenario, the use of a single unit of DAF tank can be considered, so as to simplify the network structure in Figure 15. Hence, modification of the automated targeting model is required. Figure 14 indicates that SR2 and SR4 are regenerated (in the DAF tank) for further recovery. In this new scenario, the two streams are allowed to mix before being regenerated.

Figure 16. RCCD for example 4 (single regeneration system).

Figure 17. Optimum water network design for example 4 with one DAF tank (flow rates are in tons per hour).

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Because of the infinite number of possible mixing ratios between SR2 and SR4, both the regeneration flow rates and the inlet and outlet concentrations of the two sources are treated as variables in the revised model. To avoid an infeasible RCCD, the lower and upper bounds of the concentrations of the product (CP,S) and reject (CR,S) streams are included in the model (eqs 21 and 22). Because SR2 and SR4 are available for regeneration, the boundaries of CP,S and CR,S can be determined using eqs 19 and 16, respectively, for the total regeneration cases. In this case, CP,S and CR,S of SR2 are taken as the lower bounds, whereas CP,S and CR,S of SR4 are taken as upper bounds. 23.47 ppm e CP,S e 25.52 ppm

(21)

10246.31 ppm e CR,S e 11127.60 ppm

(22)

Next, the flow rates and load balances of the regeneration system are included in the model (eqs 23 and 24). Note that the product of the unknown regeneration flow rate and concentration in eq 24 leads to a bilinear term and, hence, an NLP problem

∑F

Reg,i

) FP + FR

(23)

regeneration processes, namely, single-pass and partitioning regeneration systems are presented. Because the mathematical model is a linear program (non-linear for the last case), where global optimality is ensured once a solution is found. Literature examples and industrial case studies are used to illustrate the capabilities of the proposed approach. With the current method, it is necessary to assume a unique regeneration/interception unit for each source in the fixed-removal-ratio case; the methodology will be extended to allow this restrictive assumption to be relaxed. Further work also needs to be done on extensions of this approach for total networks that include waste treatment for discharge. Acknowledgment Financial support from the University of Nottingham Research Committee through the New Researcher Fund (NRF 3822/ A2RBR9) and a Research Studentship is gratefully acknowledged. Sponsorship from the World Federation of Scientists (WFS), the Malaysian Ministry of Science, Technology and Innovation (MOSTI), and the De La Salle University Science Foundation is also deeply appreciated.

i

Notation

∑ (F

Reg,iCi)

) FPCP,S + FRCR,S

(24)

i

In addition, it is assumed that the reject stream from the regeneration system is not available for recovery to avoid impurity accumulation. Such constraints are often imposed by plant management to ensure the integrity of a process or product. Hence, the reject stream flow rate (FR) is excluded from the material cascade for further reuse/recycle. Solving eq 20 subject to the constraints in eqs 1-3 in part 1 of this pair of articles,17 as well as eqs 14, 18, 21-24 herein, gives the RCCD shown in Figure 16 (using Lingo 10.0 with a global solver). As shown, SR2 and SR4 are now mixed before being regenerated in the DAF tank (to 25 ppm). As mentioned earlier, only the purified product streams are sent for reuse/ recycle in the network, whereas the reject streams are sent for discharge. This is shown by the FR term that is discharged directly as wastewater (see Figure 16). It is interesting to note that the various network targets (e.g., AOC, fresh water, wastewater and regeneration flow rates) remain the same as in the previous scenario. This indicates that this new scenario is a better option as compared to the earlier case due to the less complex network. However, note that both scenarios have excluded the contribution of the capital cost of the regeneration unit, which might lead to different results if included. The latter remains the subject of future work. Figure 17 shows the network design with one DAF tank. Finally, a sensitivity analysis for the relative cost of regenerated water compared to fresh water was conducted for both scenarios. It is worth mentioning that the same network design is obtained when the relative cost of regenerated water compared to fresh water is lower than 0.87. When the relative cost of regenerated water increases above 0.87, only fresh water is needed for the network; that is, no regeneration unit is needed. Conclusions Part 2 of this pair of articles extended the automated targeting techniques to an RCN with interception placement. The minimum flow rate/cost of fresh resource can be located prior to detailed design using this approach. Two types of interception/

AT ) annual operating time bq ) intercept of the linearized equilibrium relation for the qth MSA CF,S ) impurity concentration in the feed stream Ci ) impurity concentration of source i Cin ) inlet concentration of the regeneration unit Cin,RR ) inlet concentration to the interception unit of the RR model Cjmax ) maximum allowable impurity concentration of sink j Ck ) concentration level k COSTFW ) cost of fresh water COSTiRR ) cost of interception (with different RRs) in purifying water source i COSTq ) cost of qth external MSA COSTWW ) cost of wastewater treatment Cout ) outlet concentration of the regeneration unit Cout,RR ) outlet impurity concentration of an RR-type interception unit CP,S ) impurity concentration in the product stream CR,S ) impurity concentration in the reject stream in Cseal pot ) impurity concentration of the seal pot inlet stream in Cwater jet ) impurity concentration of the water-jet compression station inlet stream FD ) flow rate of discharge waste FF ) flow rate of feed stream to partitioning regeneration unit FFR ) flow rate of fresh resource FFW ) flow rate of fresh water FFG ) flow rate of the fresh hydrogen source FGD ) flow rate of purge hydrogen Fin ) inlet flow rate to a single pass interception unit FIntH2 ) flow rate of the intercepted hydrogen source FIntH2,P ) flow rate of the intercepted hydrogen source (permeate) FIntH2,R ) flow rate of the intercepted hydrogen source (retentate) FiRR ) treatment flow rate of source i for interception unit of RR value out Fdecanter ) outlet flow rate of the decanter Fout ) outlet flow rate from an interception unit FP ) flow rate of the product stream FR ) flow rate of the reject stream FRegi ) flow rate of regenerated source i in Fseal pot ) inlet flow rate of the seal pot out Fseal pot ) outlet flow rate of the seal pot

Ind. Eng. Chem. Res., Vol. 48, No. 16, 2009 FSKj ) flow rate of sink j FSRi ) flow rate of source i in Fwater jet ) inlet flow rate of the water-jet compression station FRegi,P ) flow rate of the product stream for regenerated source i FRegi,R ) flow rate of the reject stream for regenerated source i FWW ) flow rate of wastewater Gp ) flow rate of the pth rich stream i ) index for sources j ) index for sinks k ) index for concentration levels Lq ) flow rate of the qth MSA mq ) slope of the linearized equilibrium line for the qth MSA MSA ) mass-separating agent n ) number of concentration levels q ) index for MSAs RCCD ) resource conservation cascade diagram RCN ) resource conservation network RP ) removal ratio of partitioning regenerator RR ) fixed removal ratio Sq ) qth MSA TSS ) total suspended solids WW ) wastewater xqs ) inlet concentration of the qth MSA xqt,max ) maximum practical achievable concentration of the qth MSA xq* ) maximum achievable concentration of the qth MSA xsp ) inlet concentration of the pth rich stream yp ) concentration of the pth rich stream ypt ) outlet concentration of the pth rich stream RL ) fluid recovery factor δk ) net material flow rate from level k εk ) residue of impurity load from concentration level k ξq ) minimum allowable concentration difference for the qth MSA

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ReceiVed for reView January 23, 2009 ReVised manuscript receiVed May 29, 2009 Accepted June 24, 2009 IE900127R

Automated Targeting Technique for Single-Impurity Resource

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