Automated Targeting Technique for Single-Impurity Resource

Ind. Eng. Chem. Res. 2009, 48, 7637–7646

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Automated Targeting Technique for Single-Impurity Resource Conservation Networks. Part 1: Direct Reuse/Recycle 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

This pair of articles presents an optimization-based, automated procedure to determine the minimum resource consumption/target(s) for a single-impurity resource conservation network (RCN). This optimization-based targeting technique provides the same benefits as conventional insight-based pinch analysis, in yielding various targets for an RCN prior to detailed design. In addition, flexibility in setting the objective function is the major advantage of the automated targeting approach over a conventional pinch analysis technique. The model formulation is linear, which ensures that a global optimum can be found if one exists. In part 1 of this pair of articles, the model for direct material reuse/recycle is presented. Its application is then demonstrated for single, multiple, and impure external resources using several literature examples. Part 2 of this pair of articles extends the automated targeting technique for RCNs with waste-interception (regeneration) placement. Introduction Because of the growth of world population and concurrent economic development, the demands for natural resources such as natural gas, crude oil, and water are increasing rapidly. For instance, global water withdrawal for most uses (i.e., domestic, industrial, and livestock) is projected to increase by more than 50% by 2025.1 By the same year, residents of Africa and South Asia are expected to be living with a scarcity of water.2 In addition, the total world consumption of marketed energy is projected to increase from 4.71 × 1020 J in 2004 to 5.90 × 1020 J in 2015, and then to 7.41 × 1020 J in 2030.3 This means a 57% increase over the projection period. Fossil fuels (petroleum and other liquid fuels, natural gas, and coal) are expected to continue supplying much of the energy used worldwide. Moreover, the demand for fossil fuels increases strongly in the projections, despite predicted world oil prices that remain above $49 per barrel throughout the period.3 Furthermore, increasing public awareness toward environmental sustainability is reflected in more stringent emission legislation that has motivated the process industries to look into cost-effective and more sustainable manufacturing processes. One of the active areas for cost reduction and sustainable process development is resource conservation, where process integration techniques have been well recognized as a promising tool. El-Halwagi4,5 has defined process integration as a holistic approach to process design, retrofitting, and operation that emphasizes the unity of the process. Both fresh resource consumption and waste generation can be reduced simultaneously through process integration, as evidenced by numerous works reported in the literature.4-10 In the past decade, water and hydrogen network synthesis have emerged as special cases of mass integration in responding to efforts toward resource conservation. The seminal work on insight-based approaches for water network synthesis is presented by Wang and Smith,11 who utilized the pinch targeting * To whom correspondence should be addressed. Tel.: +60-3-89248130. Fax: +60-3-8924-8017. E-mail: [email protected].

tool of the limiting composite curve to locate the minimum fresh water and wastewater flow rates. However, the technique is limited to handling the fixed loads problems (with mass-transferbased water-using processes). Because of this limitation, various targeting techniques to handle the fixed flow rate problems were later developed.12-26 These techniques include both graphical (e.g., water source and demand composite curves,12,13 water surplus diagrams,15 material recovery pinch diagrams,16,18,24 source composite curves20) and algebraic (e.g., evolutionary tables,14 cascade analysis17,19,21,22,25) approaches. Graphical targeting tools provide the conceptual insight for network synthesis, whereas algebraic tools are preferred for rapid and accurate answers or when repeated calculations are needed. Note also that the algorithms proposed to solve fixed-flow-rate problems can be used to solve fixed-load problems and vice versa. Although most of these works reported targeting for a single pure, fresh resource, some of the targeting techniques have been extended to cater to problems with multiple fresh resources,24-26 by assuming that an impure fresh resource is always much less expensive than a pure one. The various targeting tools for fixed-load and fixed-flow-rate problems have been reviewed by Bagajewicz27 and Foo,28 respectively. Even though many network targets can be obtained from the above-mentioned pinch-based targeting techniques, many graphical methods are cumbersome and algebraic approaches require multiple repetitive steps. It is also notable that the main limitation of such approaches is that they can handle only a single objective function, namely, minimum water flow rates. For cases with multiple fresh resources, the assumption of minimum fresh water flow rates does not necessarily lead to optimum solution, because the cost of the individual fresh water resources will determine the total water cost of the network. Once the flow rate targets have been found, the water network that achieves the flow rate targets can be designed using any of the established design techniques. Some of the well-established design tools include water grid diagrams,11 the water main method,8 and water source diagrams29 for fixed-load problems, as well as source-sink mapping diagrams5,6 and nearest-

10.1021/ie900120y 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

neighbor algorithms18 for fixed-flow-rate problems. Subsequently, a preliminary synthesized network can be evolved to yield a simplified network.30,31 Apart from insight-based targeting methods, mathematical optimization approaches using network superstructures for water network synthesis have also received much attention.32-50 Early works in mathematical optimization approaches for water network synthesis were reported by Takama and co-workers.32-34 Later works on this type of technique can be broadly categorized as deterministic35-45 and stochastic46-50 optimization approaches. The insight-based and mathematics-based optimization techniques complement each other well. Whereas the former locates various network targets prior to detailed design, the latter addresses more complex systems, for example, multiple impurities, cost considerations, and various topological and process constraints. In addition, some works that utilized both techniques have also been reported, such as an early effort by El-Halwagi and co-workers for the synthesis of a massexchange network.51-54 Similar works were also reported for water network synthesis.55-57 Other than water network synthesis, another variant of mass integration, namely, utility gas network synthesis (e.g., hydrogen, nitrogen, etc.), has also received considerable attention recently. As in the case of water networks, various targeting techniques for insight-based approaches have been developed. They include value composite curves,58 hydrogen surplus diagrams,59,60 material recovery pinch diagrams,16,61 limiting composite curves,62 cascade analysis,63 and source composite curves.20 On the other hand, mathematical optimization techniques developed for utility gas networks (mainly hydrogen networks) are dominated by deterministic approaches. Such efforts have also considered the use of purification techniques in enhancing hydrogen recovery.64-66 In this pair of articles, the automated targeting technique that was first proposed for the synthesis of mass-exchange networks52 and property-based resource conservation networks (RCNs)67 is adopted for locating the minimum flow rate/cost targets for a single impurity and concentration-based RCN. Resource conservation via direct reuse/recycle is the main focus of this article. Although such networks can be designed automatically using superstructure models, El-Halwagi argued that targeting through optimization provides the same benefits as pinch analysis, in yielding valuable insights for problem decomposition or simplification prior to detailed design.4 The targets represent limiting conditions that can be achieved if there are no further design constraints pertaining to network configuration (e.g., compulsory or forbidden matches between processes); furthermore, the targets can potentially be used as a guide to subsequent, detailed design of the network. This same argument provides motivation for the development of the automated targeting procedure in this pair of articles. In addition, flexibility in changing the objective function is the main advantage of the automated targeting approach over other conventional insightbased techniques (graphical or algebraic methods) in which minimum cost can be determined at the targeting stage. Meanwhile, automated targeting still provides similar insights for process design that can be drawn from insight-based techniques. Several examples are solved to illustrate the proposed approach. Problem Statement In this work, the problem definition of a concentration-based RCN with a single impurity can be stated as follows:

A set of process sources, SOURCES ) {i | i ) 1,2,..., Nsources}, consisting of process streams that can be reused/recycled or discharged. Each source i has a flow rate, Fi, and is characterized by a constant concentration of a single impurity, Ci. A set of process sinks (units), SINKS ) {j | j ) 1,2,..., Nsinks}, that acept sources via reuse/recycle. Each sink j requires a flow rate, Fj, and can accept an average inlet contaminant concentration from the source that is lower than its maximum allowable impurity concentration,Cmax j . The objective of this work is to identify the minimum network targets, prior to the detailed design of an RCN. Depending on the problem, the objective function of some cases can be set to determine the minimum resource flow rate(s) of the network, with others set to minimize total operating costs. Problems to be examined include various RCNs with material direct reuse/ recycle (this article), as well as with interception or regeneration process placement (part 2).68 Automated Targeting Technique The automated targeting technique is adopted from massexchange network52 and property-based RCN67 synthesis. It is conceptually similar to the algebraic targeting technique of cascade analysis,17,21 with the removal of the repetitive computations. Note that, in all cascade analysis techniques, infeasible cascades with material flow balances are first generated to determine the largest material deficit. Next, the fresh resource is added based on the largest material deficit to remove all deficits and yield a feasible material cascade.17,19,21,22,25 The two-step targeting approach is readily replaced by the automated targeting technique presented in this work. Apart from a setting minimum fresh resource target, the automated targeting approach can also be used to trade off interception and fresh resource costs in a RCN. This feature will be shown in part 2 of this pair of articles.68 The first step of the automated targeting technique calls for the construction of a resource conserVation cascade diagram (RCCD), where the impurity concentrations (Ck) of the material sinks and sources are arranged in ascending order, from the lowest concentration level, k ) 1, to the highest level, k ) n (see Figure 1). Additional concentration levels for fresh resource(s) and zero concentration level (e.g., 0 ppm, 0%) are added if they do not already exist among the process sinks and sources. Note that, for networks with impure fresh resources, zero concentration level is unnecessary if the resource has the lowest concentration among all process sinks and sources. In addition, a final fictitious concentration level (e.g., 106 ppm or 100%) is added to allow for the calculation of the residue impurity load. Next, material flow rate cascading is performed across all concentration levels. At each concentration level k, the difference between the total available material sinks (∑jFSKj) and sources (∑iFSRi) is determined. Next, the net material flow rate cascaded from the earlier concentration level k - 1 (δk-1) with the flow rate balance at concentration level k forms the net material flow rate of each kth concentration level (δk), given as δk ) δk-1 +

(∑ i

FSRi -

∑F

)

SKj

j

k k∀K

(1)

Note that the net material flow rate (δk) can take both positive and negative values, with positive values indicating material that flows from the lower concentration level to that higher concentration level or vice versa. Note also that, in Figure 1, the net material flow rate found before the first concentration


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Figure 1. A Generic RCCD for Direct Reuse/Recycle.

level (δ0) corresponds to the fresh resource flow rate (FFR). In contrast, the net material flow rate at the second-to-last concentration (δn-1) level corresponds to the waste discharge flow rate (FD) of the network. This is in agreement with the cascade analysis technique.17,21 As reported by Foo et al.,21 apart from material flow rate cascading, impurity load cascading is also essential to ensure a feasible RCN. Hence, impurity load cascading is performed next. Within each concentration interval, the impurity load is given by the product of the net material flow rate from level k and the difference between two adjacent concentration levels. As in the material flow rate cascade, the residue of the impurity load of each concentration level k (εk) is cascaded down to the next concentration level. Hence, the load balance at the kth concentration level is given by εk ) εk-1 + δk-1(Ck - Ck-1) k∀K

(2)

where εk-1 is the residue impurity load that is cascaded from concentration level k - 1. It is worth mentioning that, because there is no residual impurity load (ε0) and no net material flow rate (δ0) generated before the first concentration level (C1), the residual impurity load at C1 is always taken as zero (ε1 ) 0). On the other hand, the residual impurity load, ε, must take a positive value, which implies that a feasible load cascade is achieved.17,21 As such, the maximum allowable impurity load of sink in each concentration level is fulfilled. Therefore, eq 3 is included as a constraint in the formulation model εk g 0 k∀K

Table 1. Limiting Data for Example 111 sink, SKj

flow rate, Fj (ton/h)

concentration, Cj (ppm)

1 2 3 4 ΣjFj

20 100 40 10 170

0 50 50 400

source, SRi

flow rate, Fi (ton/h)

concentration, Ci (ppm)

1 2 3 4 ΣiFi

20 100 40 10 170

100 100 800 800

global optimal solution. In this work, LP models were solved using Lingo v10.0. However, in practice, automated targeting can be implemented using any LP solver, even those found in common spreadsheet environments. Direct Reuse/Recycle To determine the minimum fresh resource flow rate (FFR), the RCCD (Figure 1) is used with the optimization objective formulated as minimize FFR

Alternatively, the minimum cost solution can be obtained for cases with multiple external fresh resources, in which case the optimization objective is set as

(3)

Note also that, when the residual impurity load is determined to be zero in the model solution at concentration level k (εk ) 0), a pinch concentration is observed. This condition is equivalent to source and sink composite curves that touch each other to form a pinch concentration in the graphical targeting approaches.15,16,18 In physical terms, the zero impurity load means that, at the optimal solution, all sinks above the pinch concentration are saturated with impurity load sent by the sources. It is worth noting that the above formulation is a linear programming (LP) problem that can be solved easily to achieve

(4)

minimize

∑ (COST

FR,zFFR,z)

(5)

z)1

where COSTFR,z and FFR,z are the unit cost and flow rate, respectively, of the external source z. Four literature examples are used to illustrate the direct reuse/recycle case. Example 1 Table 1 lists the limiting data for example 1, which consists of four water sinks and four water sources.11 Two scenarios are analyzed, namely, single and multiple fresh water source(s). For the case with a single fresh water source, the minimum

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Figure 2. RCCD for example 1 (direct reuse/recycle with single fresh water source).

fresh water and wastewater flow rates for direct reuse/recycle case were both reported as 90 ton/h, with the pinch concentration located at 100 ppm.11,17,18 Solving eq 4 subject to the constraints in eqs 1-3 yields the solution in the RCCD shown in Figure 2. As shown, the minimum fresh water (FFW) and wastewater (FWW) flow rate targets are both 90 ton/h, which is identical to the previously reported results. The pinch concentration is identified as 100 ppm (C3), where zero residue impurity load (ε3 ) 0) is observed. A second scenario with multiple fresh water sources is illustrated next. The seminal work in targeting of multiple water sources was that of Wang and Smith,69 who used limiting composite curves for the fixed-load problem. More recently, several targeting tools have also been reported for the fixedflow-rate problem.24-26 The main assumption for all of these works is that a lower-quality external water source is available that is much lower in cost than the higher-quality source. Therefore, the lower-quality source is fully utilized before use of the higher-quality source begins. However, this assumption might be too optimistic in practice, as some pretreatment with associated treatment costs might still be needed for the lowerquality source to be useable. Furthermore, a larger volume of water might be needed if the lower-quality source is used, as compared to when the high-quality supply is utilized, because of its impurity content. Optimization must thus take into account this incremental increase in flow rate, in relation to the relative unit costs of the two external water sources. There might be a “break-even” point, beyond which it is preferable to use the higher-quality source instead. This point will be discussed more clearly using example 1. Moreover, a sensitivity analysis for the cost ratio between lower- and higher-quality water sources will also be presented. In this case, it is assumed that there exist two different qualities of external water sources, namely, 0 and 10 ppm, with corresponding prices of $1.0/ton and $0.8/ton, respectively. Solving the model with the objective function in eq 5 (subject to eqs 1-3) yields the results shown in Figure 3. Note that the concentration level of the impure fresh source (i.e., 10 ppm) is added. As shown in Figure 3, the optimum flow rates are targeted as 20 and 77.78 ton/h for the pure (FFW1) and impure (FFW2) fresh water sources, respectively, resulting in a wastewater flow rate of 97.78 ton/h. Note also that two pinch concentrations (C2 ) 10 ppm and C4 ) 100 ppm) are observed with zero residual impurity loads. The total cost of external water sources is determined to be $82.22/h.

Figure 3. RCCD for example 1 (direct reuse/recycle for multiple fresh water sources).

Note that the optimum ratio of using the two external fresh water supplies depends on both their quality and their relative costs. There is an implied tradeoff as the flow rate of fresh water demand can probably be reduced if a cleaner source is utilized; however, minimizing this demand might not necessarily give the lowest cost because the lower-grade fresh water is less expensive. The sensitivity analysis for the costs of both pure (0 ppm) and impure (10 ppm) fresh water sources is presented next. Figure 4 shows the total fresh water cost for the water network as well as the flow rate consumption of both fresh water sources versus their cost ratio (impure fresh water/pure fresh water). Based on Figure 4, as the cost of impure fresh water increases, the total fresh water cost for the water network increases proportionally and eventually levels off when the cost ratio reaches 0.9 (total fresh water cost reaches $90/h), which is the break-even point for this case study. From Figure 4, it is observed that the requirement for impure fresh water (77.78 ton/h) is higher than that for pure fresh water (20 ton/h) when the cost ratio is lower than 0.9. However, once the cost ratio is higher than 0.9, the use of pure fresh water is favored by the model. This transition occurs as a step change, as shown in Figure 4. In other words, impure fresh water is no longer required once its cost increases to $0.9/ton (based on a pure fresh water cost of $1.0/ton), and any further increase in its price will no longer affect the total fresh water cost. Another sensitivity analysis was conducted to analyze the effects of the cost ratio between the impure and pure fresh water (0.2-1.2) and the concentration of the impure fresh water (10-80 ppm) on the total fresh water cost of the network. As shown in Figure 5, regardless of the concentration of impure fresh water, the total fresh water cost increases as the cost ratio increases from 0.2 to 1.2 and levels off when the total fresh water cost reaches $90/h. On the other hand, as the impure fresh water concentration increases from 10 to 80 ppm (for all cost ratios), the total fresh water cost increases to $90/h. For the case where the cost ratio is fixed at 0.2, the use of the impure fresh water is no longer worthwhile when its concentration is higher than 80 ppm. In this example, the highest cost was determined to be $90/h. The basic tradeoff is that the impure fresh water is potentially less expensive per unit volume than the pure fresh water but more of it is needed because of its concentration. Thus, impure fresh water will be used in place of pure fresh water only if the cost ratio offsets the increased


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Figure 4. Sensitivity analysis of fresh water cost ratio to fresh water flow rates and total water cost.

Figure 5. Sensitivity analysis for example 1: Effects of cost ratio and impure fresh water concentration on total water cost.

flow rate needed to substitute for pure water. Finally, the cost ratio is an important constant in this model that has only been reported once in the literature for multiple fresh water sources.26 However, with the model presented in this work, the results can be obtained with less computational effort. Example 2 Figure 6 shows a pyrolysis process that converts scrap tires into fuel.4,5,70 High-pressure water jets are used to shred the tires before they are fed to the pyrolysis reactor and other downstream processing units. The spent water is filtered and

mixed with a 0.2 kg/s flow of fresh water to compensate for water losses in the shredded tires (0.12 kg of water/s), as well as wet cake from the filtration unit (0.08 kg of water/s). The mixture of filtrate and fresh water is fed to a high-pressure compression station to be recycled to the water-jet shredding unit. The water loss in the wet cake depends on the flow rate of the makeup water to the water-jet compression station. The wet cake from the filtration unit is then forwarded to the solid waste handling section. Because of the pyrolysis reaction, a 0.08 kg/s flow of water is generated. In the high-temperature pyrolysis reactor, the

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Figure 6. Schematic flow sheet of tire-to-fuel process.4,5,70

hydrocarbons from the shredded tires are converted into oils and gaseous fuels. The oils are further processed and purified to produce liquid transportation fuels. Off-gases from the reactor are cooled to condense light oils. The condensate is sent to a decanter that produces a liquid consisting of two phases, namely, organic and aqueous. The organic layer is sent to the separation unit with the liquid product from the reactor, whereas the aqueous layer forms the wastewater effluent. In the finishing section, waste gas is emitted and is sent to the flare. A seal pot is used to prevent the backpropagation of fire from the flare. From Figure 6, two primary wastewater sources are observed, namely, 0.20 kg/s from the decanter (Fout decanter) and 0.15 kg/s from out the seal pot (Fseal pot; for a fresh water flow rate of 0.15 kg/s), with impurity (heavy organic) concentrations of 500 and 200 ppm, respectively. These sources can be reused/recycled within the process to reduce fresh water consumption (0.20 kg/s at present). Two process sinks that can accept these water sources are also identified, namely, seal pot and water-jet compression station. The following constraints on flow rate and impurity content (heavy organic) should be satisfied when water reuse/ recycle scheme is considered to avoid disturbance to the processes: Seal Pot in 0.10 e flow rate of feed water, Fseal pot (kg/s) e 0.20 (6) 0 e impurity concentration of feed water, in Cseal pot (ppm) e 500

(7)

Makeup to Water-Jet Compression Station in 0.18 e flow rate of feed water, Fwater jet (kg/s) e 0.20 (8) 0 e impurity concentration of makeup water, in Cwater jet (ppm) e 50

(9)

In this example, it is interesting to note that the flow rate of the outlet stream from the seal pot will equal the flow rate of the inlet stream. Therefore, the flow rate of this source will always vary with the inlet flow rate, which is specified by the constraint for the sinks mentioned above. Assuming that there

Figure 7. RCCD for example 2 (direct reuse/recycle).

is no water generation and loss in the seal pot, the flow rate balance for this unit is in out Fseal pot ) Fseal pot

(10)

To allow the optimization model to find an optimum solution, the operating ranges of the flow rates for both water sinks (eqs 6 and 8) are added to the model. Note that this is not the case in most pinch-based targeting approaches where the limiting flow rates are always taken as the minimum flow rate for the sink and a constant flow rate for the source.71 Furthermore, it is always assumed that there are no interactions among the various water sinks and sources in fixedflow-rate problem. Therefore, if one were to use the previous targeting approaches15-26 in locating the flow rate targets, one might run into a suboptimum solution. This aspect will be shown in part 2 of this pair of articles,68 when regeneration/interception is considered. This limitation is readily overcome in the newly proposed automated targeting techniques, in which the range of limiting flow rates can be incorporated to determine the optimum solution. Optimizing eq 4 subject to eqs 1-3 (material and impurity load cascades) and eqs 6, 8, and 10 (process constraints), the fresh water and wastewater flow rates are targeted as 0.135 and 0.155 kg/s, respectively, with the pinch concentration located at 200 ppm (C3). The RCCD for this example is shown in Figure 7. As shown, a 0.2 kg/s flow of water is fed to the seal pot (at


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Figure 8. Water network for example 2 with direct reuse/recycle scheme. Table 2. Limiting Data for Example 359 j

hydrogen sink

flow rate (mol/s)

impurity concentration (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 1 2 3 4 5 6

hydrogen source flow rate (mol/s) Impurity concentration (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

Example 3

Figure 9. Refinery hydrogen network. The numbers represent the total gas flow rate (mol/s) and impurity concentration (mol %).59

C4 ) 500 ppm); thus, the same amount (0.2 kg/s) of water source is generated from the seal pot at 200 ppm (C3). It is interesting to note that, when a sensitivity analysis is conducted to vary the flow rate into the seal pot from 0.1 to 0.2 kg/s, the minimum flow rate targets remain the same. Therefore, in this example, a range of flow rates can be fed to the seal pot without affecting the overall water targets; however, this is true only for this particular example and is not generally the case. It is worth mentioning that the flexibility of automated targeting that allows for the inclusion of a range of process constraints (i.e., flow rate and impurity concentration) in the targeting stage also allows for the exploration of alternative network designs. In this example, there is a significant reduction of both fresh water and wastewater as compared to the base case without water reuse/recycle, in which the fresh water and wastewater flow rates are both reported as 0.35 kg/s. This is consistent with the results reported by Noureldin and El-Halwagi.70 Figure 8 shows the network design that achieves the minimum water targets.

Figure 9 shows a refinery hydrogen network taken from Alves and Towler,59 where a certain extent of hydrogen integration is included. The existing fresh (imported) hydrogen consumption is reported at 277.2 mol/s. The limiting data for this example are listed in Table 2. As shown, there are four hydrogenconsuming processes in the network that serve as hydrogen sinks and sources, namely, hydrocracker unit (HCU), naphtha hydrotreater (NHT), cracked naphtha hydrotreater (CNHT), and diesel hydrotreater (DHT). In addition, two internal hydrogen producing facilities are available in this plant, namely, a catalytic reforming unit (CRU) and a steam reforming unit (SRU). To maximize savings, hydrogen from the process hydrogen sources and the internal production facilities should be fully utilized before any purchase of external fresh hydrogen is considered. In this case, the fresh hydrogen supply has an impurity content of 5 mol %. Optimizing eq 4 subject to the constraints in eqs 1-3 results in the RCCD shown in Figure 10. Note that, because the impure fresh hydrogen has the lowest impurity concentration among all process sinks and sources, a zero concentration level is not necessary here (see Figure 10). Hence, the fresh hydrogen resource is located at its concentration level of 5 mol % (C1). The minimum fresh hydrogen and waste discharge flow rates (FFG and FGD) for this example are targeted as 268.82 and 102.52 mol/s, respectively, with the pinch concentration located at 30 mol % (C10). Note that this result is identical to what was reported in earlier works.16,59,63

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of 170 ton/h and generates 110 ton/h of wastewater prior to water reuse/recycle. It is interesting to note that this example is a threshold problem, with an optimal water network of zero discharge,23 which is not commonly found. An additional constraint (eq 11) is included in the automated targeting model to handle this kind of threshold problem. Equation 11 ensures that the model has a zero or positive wastewater flow rate for the network δn-1 g 0

(11)

Optimizing eq 4 subject to the constraints in eqs 1-3 and 11 results in the RCCD in Figure 11. As shown, a network without wastewater discharge is obtained (with a fresh water requirement of 60 ton/h). Note that 1 × 106 ppm is taken as the threshold concentration for this case, as reported by Foo.23 Note also that no modification is needed for the automated targeting model for the other type of the threshold problem, i.e., networks without a fresh water feed,23 as the current model works just as well for such cases. Conclusions Figure 10. RCCD for example 3 (direct reuse/recycle). Table 3. Limiting Water Data for Example 423 water sink, SKj

flow rate, Fj (ton/h)

concentration, Cj (ppm)

water source, SRi

flow rate, Fi (ton/h)

concentration, Ci (ppm)

1 2 3

50 20 100

20 50 400

1 2 3

20 50 40

20 100 250

To further reduce the fresh hydrogen consumption, process hydrogen source(s) can be fully or partially treated for further recovery. This topic is presented in part 2 of this pair of articles.68 Example 4 To illustrate a special scenario of threshold problem, a literature example taken from Foo23 is utilized. Table 3 lists the limiting data23 for example 4, with three water sinks and sources. As shown, the network requires a fresh water flow rate

An automated targeting technique for single impurity RCNs is presented. This new targeting technique has the advantages of both pinch analysis and mathematical optimization approaches. The automated targeting technique provides flexibility in changing the objective function, which is restricted in conventional pinch analysis to just minimizing the demand for fresh external resource. This is the main advantage over other conventional insight-based techniques. Apart from the ability to determine fresh resource(s) and waste discharge flow rates, which can be found with the conventional targeting approaches, this method can also be used to target the minimum total cost of an RCN prior to detailed network design. In addition, targeting for minimum single or multiple fresh resources in an RCN is presented. Because the model formulation is linear, there are no major computational difficulties, and global optimality is ensured once a solution is found. 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. Notation

Figure 11. RCCD for example 4 (threshold problem).

Ci ) impurity concentration of source i Cjmax ) maximum allowable impurity concentration of sink j Ck ) concentration level k COSTFR,z ) cost of external source z in Cseal pot ) impurity concentration in the seal-pot inlet stream in Cwater jet ) impurity concentration in the water-jet compression station inlet stream out Fdecanter ) outlet flow rate of decanter FFG ) flow rate of fresh hydrogen FFR ) flow rate of fresh resource FFR,z ) flow rate of the fresh resource z FFW ) flow rate of the fresh water FGD ) flow rate of waste gas in Fseal pot ) inlet flow rate of seal pot

Ind. Eng. Chem. Res., Vol. 48, No. 16, 2009 ) outlet flow rate of seal pot FSKj ) flow rate of sink j FSRi ) flow rate of source i FW ) fresh water in Fwater jet ) inlet flow rate of water-jet compression station FWW ) flow rate of wastewater i ) index for sources j ) index for sinks k ) index for concentration levels n ) number of concentration levels Nsinks ) number of sinks Nsources ) number of sources RCCD ) resource conservation cascade diagram WW ) wastewater z ) index for fresh water δk ) net material flow rate from level k εk ) residue of the impurity load from concentration level k out Fseal pot

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ReceiVed for reView January 23, 2009 ReVised manuscript receiVed May 29, 2009 Accepted June 24, 2009 IE900120Y

Automated Targeting Technique for Single-Impurity Resource

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