Use of Pinch Concept To Optimize the Total Water Regeneration

Article pubs.acs.org/IECR

Use of Pinch Concept To Optimize the Total Water Regeneration Network Reza Parand, Hong Mei Yao,* Vishnu Pareek, and Moses O. Tadé Centre for Process Systems Computations, Department of Chemical Engineering, Curtin University, GPO Box U1987, Perth, Western Australia 6845, Australia ABSTRACT: In this study, an Extended Composite Table Algorithm is developed to target the minimum freshwater, regenerated water, and wastewater flow rates together with the minimum regeneration concentration and wastewater concentration for total water regeneration network. The approach is first demonstrated by assuming a fixed post-regeneration concentration. Considering that the post-regeneration concentration has the dominant influence on the total cost in the water regeneration problem, this assumption is relaxed by allowing it to shift in a feasible region. A new method, Composite Matrix Algorithm, is proposed to find such a region and a maximum feasible post-regeneration concentration. By incrementally changing the post-regeneration concentration, the relationship between the key parameters in the total water regeneration network can be analyzed quantitatively. Some graphical presentations are introduced to target total water regeneration problem when the removal ratio type regenerator is involved. Moreover, the effect of post-regeneration concentration to the total cost of the network is evaluated and discussed. To facilitate the implementation, MATLAB is used as a programing tool.

1. INTRODUCTION Process integration has been considered in resource conservation1 and sustainable process design2,3 studies. Pinch analysis as one of the powerful tools for process integration has been utilized in the network design of heat exchanger,4 mass exchanger,5 hydrogen,6 water,7,8 and cooling water.9,10 It also has been applied to carbon capture and storage11and carbonconstraint energy planning.12 Water network synthesis can be considered as a special case of mass integration. A large amount of work has been reported using either pinch analysis (PA) based or mathematical-based methodologies.13,14 While PA provides a conceptual view to the problem, mathematical optimization can handle more complicated problems, for instance, multiple contaminant and problem uncertainty. On the basis of PA, water can be minimized via water reuse/ recycle, regeneration−reuse, and regeneration−reuse/recycle.7 Reuse means that outlet water from one operation directs to another operation while recycling allows the effluent to re-enter to the operation where it was produced. In the regeneration scheme, effluent is partially purified by treatment devices (such as strippers, filters, and adsorption) before reusing or recycling to other processes. It is worth mentioning that the regeneration scheme is not applicable for some special cases of water network synthesis known as “threshold problems” due to insufficient water sources.15−17 Parand et al.17 demonstrated that the best option for saving pure utility in the threshold problems is to harvest external impure water sources. Threshold problems are very rare in the water network design. In the context of process integration, the regeneration− reuse/recycle scheme provides more opportunity for utility saving than the network with reuse/recycle only. There are two classes of water regeneration units: the fixed post-regeneration (outlet) concentration type or the removal ratio (RR) type. The seminal work of water regeneration−reuse/recycle using PA was contributed by Wang and Smith,7 where the graphical © 2014 American Chemical Society

limiting composite curve (LCC) originally developed for reuse/ recycle network was extended to target minimum freshwater, regeneration, and wastewater flow rates in the regeneration− reuse/recycle scheme. The optimum regeneration concentration was assumed to be the reuse/recycle pinch point, and the rest of the parameters were minimized based on this assumption. However, as demonstrated by the later works,8,18−21 this assumption is not generic enough and fails to locate minimum targets for the multiple pinch case where more fresh water is required for the network when the LCC has a turning point near the water supply composite curve. Feng et al.21 and Bai et al.20 introduced some valuable conceptual insight to the problem and proposed a sequential optimization approach based on the LCC. It has been demonstrated that the regeneration concentration may locate either below or above the reuse/recycle pinch point. The turning point of LCC dictates the optimum inlet regeneration concentration which eventually leads to minimum freshwater and regenerated water flow rates. An algebraic tool, the mass problem table (MPT),18 also was extended to target the regeneration flow rate and concentration and complemented the graphical LCC method. The major shortage of the methods utilized in the abovementioned references is that they are restricted to fixed load (FL) problems, where flow rate loss/gain is neglected. However, fixed flow rate (FF) water-using processes such as boilers and cooling towers are also quite common, and flow rate loss/gain has to be considered. The first guideline for regeneration placement in FF problems was proposed by Hallale.22 It is suggested that regeneration should be located across the reuse/recycle pinch Received: Revised: Accepted: Published: 3222

August 19, 2013 January 20, 2014 January 29, 2014 January 29, 2014 dx.doi.org/10.1021/ie402712b | Ind. Eng. Chem. Res. 2014, 53, 3222−3235

Industrial & Engineering Chemistry Research

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≤ Cjmax, where Cjmin and Cjmax is the lowest and highest concentration limit. • Water producing processes reused/recycled to process sinks are designated as process sources SRi (i = 1, 2, ..., NSR). Every source has a given flow rate of Fi and an impurity concentration of Ci. • Process sources are purified partially by given regeneration units with known performance index before recovering in the process sinks. As mentioned before, the performance of the regenerator can be assessed either by fixed post-regeneration (outlet regeneration) concentration (C0) or by the removal ratio (RR) calculated by eq 1.7

point to reduce the overall freshwater demand. In this way, water is moved from the surplus region (higher concentration region) to the region with a deficit of water (lower concentration region); therefore, the total water requirement will consequently be reduced. Several later studies followed this concept for various targeting approaches.23−25 Nevertheless, none of these theories can locate minimum freshwater, wastewater, and regeneration flow rates simultaneously. The ultimate flow rate targeting technique26,27 is the only method in the FF problem which can locate all of these parameters at the same time. However, this technique, which is an extended algebraic water cascade analysis method,25 requires an iterative procedure for flow rate reallocation between the freshwater region and regenerated water region. Moreover, this approach cannot address the regeneration problem with the RR type regenerator involved, and it lacks physical insight due to its algebraic characteristic. Composite Table Algorithm (CTA)28 is a hybrid graphical and numerical targeting technique which can handle global water operation (FL, FF, and combined FL and FF operation). Our previous investigation29 has demonstrated the applicability of this approach for various problems in water network synthesis considering the reuse/recycle scheme. Since the graphical presentation of CTA is analogous to the seminal work of pinch analysis (i.e., LCC), this technique has been used for the water regeneration−reuse/recycle network.28,30,31 LCC was formed from the data provided by CTA, and then based on this graphical presentation the targets for the regeneration−reuse/ recycle water network were established. Therefore, in dealing with the highly integrated water network, the proposed methodology is not completely reliable to set the targets. The interpretation of the graphical presentation can be very tedious when the turning points of LCC are not clearly distinguishable. Furthermore, the CTA method has not been reported for the targeting of the network with the RR type regenerator. It is also worth noting that the post-regeneration concentration has the dominant influence on total cost in the water regeneration−reuse/recycle problem because decreasing the post-regeneration concentration leads to the increase of the capital and operating costs of the regenerator exponentially.32 In view of the application limitation of previous studies, this research first develops a pure algebraic targeting technique, the Extended Composite Table Algorithm (ECTA), for the total water regeneration network with the assumption of a fixed postregeneration concentration. Then, this assumption is relaxed by an incremental change of the latter parameter. A new method named Composite Matrix Algorithm (CMA) is introduced to determine the feasible region for all key variables in the total regeneration problem. Using the results achieved, targets are established for the removal ratio type regeneration unit, and the economic optimum scenario is also proposed.

Creg − C0 Creg (1) Creg is the inlet regeneration concentration. RR is defined as the ratio of the total mass load removal during the regeneration process to the amount of total impurity load entered to the regenerator by effluent stream. It is assumed that the flow rate loss for the regeneration unit is negligible. • When the process sources cannot fulfill the process sinks in terms of quality (contaminant mass load) and quantity (flow rate), an external freshwater source (regarded as a process source) with flow rate of Ffw and contaminant concentration of Cfw is introduced to satisfy the requirement of the process sinks. Unused water from process sources will be directed to the waste stream with the concentration of Cww and flow rate of Fww. Figure 1 shows the superstructure presentation of the problem. Given the above-described process, the flow rates of RR =

Figure 1. Source/sink presentation of regeneration water network.

2. PROBLEM DESCRIPTION In the FF model, the outlet and inlet streams from and into a particular process are considered as process sources and sinks, respectively. With this concept, the flow rate passing through the process is not necessarily constant and water loss/gain may occur. The description for the total water regeneration network can be stated as follows: • Processes requiring water are appointed as process sinks SKj (j = 1, 2, ..., NSK). Every sink has a given flow rate Fj and inlet concentration Cj, which must satisfy Cjmin ≤ Cj

freshwater (Ffw), wastewater (Fww), and regenerated water (Freg) along with the concentrations of regeneration (Creg), post-regeneration (C0), and wastewater (Cww) are the important parameters for a total water regeneration system. In this study, the pure freshwater source (Cfw =0 ppm) is supposed to serve the network. Since we are looking at the total water regeneration system, the flow rates of freshwater and regenerated water are assumed to be identical. 3223

dx.doi.org/10.1021/ie402712b | Ind. Eng. Chem. Res. 2014, 53, 3222−3235


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located. By assuming the zero impurity load as the first entry in the fifth column, the interval impurity load (Δmk) is cascaded down which yields the cumulative load (Cum.Δmk). Then, the interval freshwater flow rate for the reuse/recycle scheme (Ffwk) is identified for each concentration level by using eq 2. Note that due to the assumption of pure freshwater supply, contaminant concentration of freshwater (Cfw) is set to be zero. This assumption is applied to all equations in this study. The largest value of the sixth column is the required minimum pure freshwater flow rate target (Ffw = 70 ton/h), and its corresponding concentration level is the pinch concentration (Cpr =150 ppm) for the reuse/recycle network.

The objective is to find the minimum feasible Ffw, Freg, Fww, and Creg and the corresponding Cww with known C0 and specified RR. Then, based on the economic analysis of the total system, the optimum scenario which can meet the minimum total annual cost will be proposed. A literature example is adopted to demonstrate the applicability of the proposed methodology explicitly. In the next section, CTA is extended to find the targets algebraically. In addition, the corresponding limiting composite curve and water supply composite curve will also be presented to provide a conceptual insight for the reader.

3. EXTENDED COMPOSITE TABLE ALGORITHM (ECTA) Taking on the concept proposed by Bai et al.,20 CTA is further developed to set the total regeneration targets for global water operations. The literature example with the limiting data given in Table 1 (FF problem) is adopted.33

⎧ Cum.Δmk ⎪ Ffwk = Ck − Cfw ⎨ ⎪ ⎩ ∀k

The main difference between CTA developed by Agrawal and Shenoy28 and ECTA proposed here is the last two columns of Table 2 for targeting regenerated water flow rate (Freg) and regeneration contaminate concentration (Creg). Interval regenerated water flow rates are calculated via eq 320 and listed in column 7. For now, water regenerator with C0 = 20 ppm is assumed, and later this concentration will be relaxed. Cpr is the reuse/recycle pinch concentration identified in the previous steps as 150 ppm.

Table 1. Limiting Water Data33 sink

Fj (ton/h)

Cj (ppm)

source

Fi (ton/h)

Ci (ppm)

SK1 SK2 SK3 SK4 total

50 100 80 70 300

20 50 100 200

SR1 SR2 SR3 SR4 total

50 100 70 60 280

50 100 150 250

(2)

⎧ Cum.Δmk ⎪ Fregk = 2Ck − C 0 ⎨ ⎪ ⎩ ∀ k → C0 ≤ Ck ≤ Cpr

The Extended Composite Table Algorithm (ECTA) is illustrated in Table 2. The first six steps of this method are for targeting minimum freshwater flow rate and pinch concentration of the reuse/recycle network. The detailed procedure can be found in the literature28 and is briefly described here. In column 2, the concentrations (Ck; k = 1, 2, ..., NC) of the process sinks and sources are grouped together and arranged in an increasing order. One arbitrary value (larger than the others) is added at the bottom of this column (300 ppm for this example). The interval net flow rate (Net.Fk) is tabulated in the third column. The sum of the flow rates of the process sources is subtracted from the sum of the flow rates of the process sinks for each concentration interval (Ck+1, Ck). It is worth mentioning that the last value of this column determines the total system flow rate loss/gain. If the value is positive, the total system encounters water loss and vice versa. For this example, the total flow rate loss is calculated to be 20 ton/h. The interval impurity loads (Δmk) are determined in column 4. These values are calculated by multiplying the interval net flow rate (column 3, Net.Fk) with the difference of contaminant concentration levels (column 2, Ck+1 − Ck), where Net.Fk is

(3)

The largest number in the seventh column targets the minimum regenerated water flow rate (Freg = 37.5 ton/h). The corresponding concentration in column 2 is named the freshwater pinch concentration (Cpfw = 150 ppm). On the basis of the assumption of total regeneration network, the freshwater (Ffw) and regenerated (Freg) water flow rates are identical; hence, Ffw is also set to be 37.5 ton/h. In the next step, the interval inlet regeneration concentrations (Creg) are calculated by eq 420 and entered in column 8. ⎧ Cum.Δmk − Freg(Ck − C0) ⎪Cregk = Freg ⎨ ⎪ ∀ k → Cpr ≤ Ck ⎩

(4)

The minimum Creg is targeted by the maximum value in this column which equals 170 ppm. The associated concentration level in the second column is known as the regeneration pinch concentration (Cpreg = 250 ppm).

Table 2. Implementation of Extended Composite Table Algorithm 1

2

3

4

5

6

7

8

k

Ck (ppm)

Net.Fk (ton/h)

Δmk (kg/h)

Cum.Δmk (kg/h)

Ffwk (ton/h)

Fregk (ton/h)

Cregk (ppm)

1 2 3 4 5 6 7

20 50 100 150 200 250 (300)

50 100 80 10 80 20

1.5 5 4 0.5 4 (1)

0 1.5 6.5 10.5 11 15 (16)

0 30 65 70 55 60 (53.33)

0 18.75 27.78 37.50

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150 113.33 170 (146.67)



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The wastewater flow rate (Fww) and contaminant concentration (Cww) targets are calculated by applying the flow rate (eq 5) and mass balance (eq 6) over the total system, respectively.28 Ffw − Fww =

algebraic targeting technique. Moreover, this approach may fail for the special multiple pinch case.20,30,31 (b) The extended mass problem table proposed by Bai et al.20 to set the targets algebraically for the total water regeneration network is limited to FL operations. The ECTA proposed in this study can handle global water operation (FL and FF) for more generic problems (without the restriction of limiting composite curve shape) in a hybrid manner (both algebraically and graphically). However, ECTA is developed based on the assumption of total water regeneration network (Ffw = Freg). In some cases regenerated water flow rate should be either lower or higher than freshwater flow rate in order to meet the feasibility of the problem,21 and this will be the scope of future studies. To demonstrate the capability of ECTA to handle FL problems, the example of Wang and Smith7 is adopted. Applying ECTA, targets for total water regeneration network (specifically total water regeneration−reuse network for FL problems) are set, and the water network is constructed using the three rules of Prakash and Shenoy34 subsequently. The detailed work is presented in the Appendix. In the following section, the ECTA is further improved by including a procedure for finding a feasible region corresponding to a relaxed post-regeneration concentration. The so-called Composite Matrix Algorithm (CMA) can find targets for a network with any specified RR type regenerator and be useful for the study of total water regeneration network on economic basis.

∑ Fj − ∑ Fi j

i

(5)

Ffw × Cfw − Fww × Cww − Freg(Creg − C0) =

∑ FjCj − ∑ FC i i j

i

(6)

Note that the right side of eq 5 is the total flow rate loss/gain calculated earlier during the ECTA (20 ton/h of water loss for this example). Therefore, the total wastewater flow rate (Fww) is 17.5 ton/h. The only unknown variable in eq 6 is the contaminate concentration of wastewater (Cww) determined as 250 ppm. It is worth mentioning that the final targeting results are the same as in Agrawal and Shenoy.30 The above-described procedure is programmed using MATLAB, and the limiting composite curve along with water supply lines for total water regeneration scheme is depicted in Figure 2.

4. COMPOSITE MATRIX ALGORITHM (CMA) CMA is developed to define the feasible range of key variables for total water regeneration network. In this method, postregeneration concentration (C0) increases from the minimum (C0min) to maximum (C0max) with an incremental step of Δ. In each step, for a given C0, regenerated water flow rate is calculated at every concentration level. The maximum value is extracted to generate a feasible vector of minimum regenerated and freshwater flow rates across the entire C0 range [C0min, C0max ]. The same operation will generate a matrix of regeneration concentration, and the vector of feasible regeneration concentration is extracted by choosing the maximum value in every column of this matrix. In addition, the vectors of freshwater and regeneration pinch concentration, wastewater flow rate, and wastewater concentration can also be derived. Following this method, it is possible to construct the feasible region along with the LCC and target the system for specified RR regeneration type. The trade-off between the parameters can be studied, quantitatively and it will give a chance to analyze the network economically. One important concept is essential to be discussed before describing the procedure of CMA. By increasing the C0, the minimum freshwater flow rate (Ffw) in total regeneration system increases. In the LCC, Ffw is calculated by the inverse slope of the first segment of water supply composite curve below the C0. Therefore, increasing the C0 causes the freshwater flow rate segment approaching the LCC and finally intersects it in C0max (Figure 3). For any C0 higher than C0max, the water supply composite curve will cross the LCC, and this imposes infeasibility on the problem. Therefore, identifying C0max is crucial for the determination of the feasible region of parameters under study in the total regeneration system.

Figure 2. Limiting composite curve and water composite curve for total water regeneration network, where C0 = 20 ppm.

As shown, the water composite curve (in red) is located entirely below the limiting composite curve (in blue) and touches the latter at two pinch points. This graphical presentation provides the conceptual insight for the problem and validates that the prespecified targets obtained algebraically are feasible. One can refer to the previous works28,30,31 to find the detailed procedure of constructing this graph. Additionally, one possible network design which can satisfy the targets was reported by Agrawal and Shenoy30 using Nearest Neighbors Algorithm (NNA) method.34 It was demonstrated that the identified targets can be achieved in practice through the network synthesis. The contributions of this study are highlighted as below. (a) Agrawal and Shenoy28 developed CTA to construct the limiting composite curve. Then, on the basis of this graphical presentation, the targets for total water regeneration network were determined. Therefore, although this technique can handle global water operations (FL and FF), it is not considered as a pure 3225



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⎧ Cum.Δmk MFregkn = ; ⎪ 2C ⎨ k − C0n ⎪ ⎩ ∀ n , k → C0n ≤ Ck ≤ Cpr & ∀ n ∈ N ′

(b). Determine Regeneration Flow Rate, Freshwater Flow Rate, and Freshwater Pinch Concentration Vectors. The maximum value in every column of MFreg is extracted and stored in the regeneration flow rate vector (Freg). Based on the assumption of total regeneration scheme, every value in Freg is equal to freshwater flow rate, i.e., Ffw = Freg. The corresponding concentration level (Ck) to every value in Ffw is set as freshwater pinch concentration. (c). Check the Feasibility Condition of Post-Regeneration Concentration. As discussed earlier, with the increase of postregeneration concentration (C0), the freshwater segment of the water supply composite curve gets closer to LCC and finally touches it. In this substep, the feasibility condition of increasing C0 is necessarily checked. Constructing the Freshwater Line Formula. The freshwater line is the first segment of the water supply composite curve located below the C0 (refer to Figure 4). Define line AB as the

Figure 3. LCC along with water supply composite curves for C0s chosen as 10, 35, and 65.

Without loss of generality, C0max can be located at either the reuse/recycle pinch point (Cpr) or any point on the LCC lower than Cpr depending on the shape of LCC. Figure 3 shows three water supply composite curves for C0s of 10, 35, and 65 located below the LCC for illustrating the concept. Step 1−6. Targeting Minimum Freshwater Flow Rate and Pinch Point Concentration. The first six steps of CMA are the same as ECTA. From those steps, the pinch point concentration (Cpr) and minimum freshwater flow rate (Ffw) for reuse/recycle network can be determined. Step 7. Generate the Post-Regeneration Concentration Vector. This step of the CMA method produces the vector of post-regeneration concentrations via eq 7. Incremental step (Δ) and C0min have been set to be 0.1 and 1, respectively. As discussed, C0max cannot be higher than the reuse/recycle pinch concentration (Cpr). Therefore, C0max is considered as 150 ppm, and this will be updated later through the CMA method if necessary. Applying these constraints, eq 7 generates the vector of C0 = [1, 1.1, 1.2,..., 150]T where n ∈ N′ = 1, 2, 3, ..., 1491. ⎧ C0n = C0 min + Δ ⎪ ⎪ C0 min ≤ C0n ≤ C0 max ⎨ ⎪ max min ⎪ ∀ n ∈ N ′ = 1, 2, ..., C0 − C0 +1 ⎩ Δ

(8)

Figure 4. Freshwater lines and LCC segments for C0s of 30 and 60.

fresh water supply line. For every iteration, the points of A and B can be determined using eq 9. Note that according to the assumption of pure fresh water availability, Cfw is set to zero. Furthermore, cumulative mass load (Cum.Δmk) corresponding to the first concentration level is also zero (Table 2). Hence, x− y coordinates of point A are zeroes for all iterations.

(7)

Step 8. Targeting Maximum Post-Regeneration Concentration. Step 8 is a close loop iteration process and consists of several substeps as follows: (a). Identify Regenerated Water Flow Rate Matrix. In this substep, regenerated water flow rate (MFregkn) is calculated via eq 8 for each C0n. The concentration level (Ck) between postregeneration concentration (C0n) and reuse/recycle pinch concentration (Cpr) should be taken into account for each iteration. Hence, this equation, which is the extension of eq 3, allows the post-regeneration concentration to increase between the minimum and maximum values. In other words, every column of the regenerated water flow rate matrix consists of the values located in the seventh column of Table 2 for a specified post-regeneration concentration.

A=

Cum.Δmk ∀ k = 1 Cfw

∀ n ∈ N′

Bn =

(C0n − Cfw) × Freg n C0n (9)

Determining Limiting Composite Curve Segment Formula. Points G and H (eq 10) are the two following LCC points. The y-coordinate of point H must be equal to or higher than the y-coordinate of point B of the freshwater line. Therefore, the GH line (Figure 4) equation identified in every iteration represents the LCC segment approached by the freshwater line. 3226


Industrial & Engineering Chemistry Research ⎧ Cum.Δmk − 1 Cum.Δmk ⎪ Hn = ⎪ Gn = Ck − 1 Ck ⎨ ⎪ ⎪ ∀ n , k → C0 ≤ C & ∀ n ∈ N ′ & ∀ k ≥ 2 ⎩ n k

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Step 10. Calculation of Feasible Regeneration Concentration Matrix. In this step, the feasible regeneration concentration MCregkn is calculated via eq 12 which is an extension of eq 4. With all the parameters known, the feasible regeneration concentration matrix is formed by considering all concentration levels, which are equal to or greater than the reuse/recycle pinch concentration and all feasible postregeneration concentrations. Specifically, every column of MCreg comprises the values located in the eighth column of Table 2 for a specified C0.

(10)

Freshwater lines and LCC segments for C0s of 30 and 60 are shown in Figure 4 for the purpose of clarification. The intersection of AB and GH lines is thus found, and the corresponding y-coordinate is stored in y_intersect vector. The feasibility condition is checked via eq 11. ⎧ 0 < y _int ersec t n − C0n ≤ ε ⎨ ⎩ ∀ n ∈ N′

⎧ Cum.Δmk − Freg n(Ck − C0n) ⎪ ⎪ MCregkn = Fregn ⎨ ⎪ ⎪ ∀ k , n → Cpr ≤ Ck & ∀ n ∈ N ⎩

(11)

ε for this example is set to be 0.05. This condition ensures that the maximum feasible freshwater line (which its inverse slope targets the maximum feasible fresh water flow rate) associated with the maximum post-regeneration concentration (C0max) is located below and very close to LCC. Hence, for every iteration, the condition should be checked. If it does not meet the accuracy requirement, the procedure goes back to step (a). Otherwise, C0n is set to be the C0max and the procedure is moved to the next step. Although decreasing Δ and ε simultaneously leads to achieving more accurate C0max, this causes longer computational time. In fact, our study on varying these two parameters showed the current values are reasonable and further decrease does not affect the final results (i.e., targeting for RR type regeneration unit and cost evaluation). As a result of the above procedure, the feasible freshwater flow rate (Ffw), regeneration flow rate (Freg), and freshwater pinch concentration (Cpfw) vectors are formed and the maximum feasible post-regeneration concentration (C0max) is set up. For the purpose of clarity, the quantified regenerated water flow rate matrix and vector and freshwater pinch concentration vector for three random iterations with C0s of 10 ppm, 40 ppm and 65 ppm are shown below:

(12)

Step 11. Extraction of Feasible Regeneration Concentration Vector and Regeneration Pinch Concentration Vector. The maximum value in every column of MCreg determines the minimum regeneration concentration associated to every feasible post-regeneration concentration. Therefore, extracting these values forms the regeneration concentration vector (Creg). In addition, the corresponding concentration levels to all of these values are stored in the regeneration concentration pinch vector (Cpreg). The schematic MCreg, Creg, and Cpreg for C0s of 10 ppm, 40 ppm, and 65 ppm are as follows:

The considered concentration levels and post-regeneration concentrations are indicated left and top outside of the regeneration concentration matrix, respectively, for better illustration. As seen from Cpreg, the regeneration pinch concentration switches from 250 ppm to 150 ppm at transient post-regeneration concentration which will be targeted later in this study. Step 12. Calculate Wastewater Flow Rate Vector. The wastewater flow rate (Fwwn) can be readily calculated via eq 13. The total flow rate loss/gain (20 ton/h flow rate loss) is independent of C0. Therefore, all the wastewater flow rates associated to different C0s are 20 ton/h less than the freshwater flow rates.

The values located on the left and top outside of the matrix are just the indication of concentration levels (lower than reuse/recycle pinch concentration) and post-regeneration concentrations, respectively. Cpfw contains freshwater pinch concentrations for every post-regeneration concentration (C0). This quantified vector depicts that with the increase of C0, the freshwater pinch point switches from one turning point of LCC to another point located lower than the original one. This fact is controlled by the shape of LCC, and it is totally dependent on the limiting data of process sources and sinks. The C0 which causes this phenomenon is given the name of “transient postregeneration concentration (C0tr)” in this research and will be investigated further later. Additionally, the maximum post-regeneration concentration (C0max) for this example is targeted to be 69.9 ppm. Step 9. Set Feasible Post-Regeneration Concentration Vector. The post-regeneration concentration vector (C0) is updated using the targeted C0max (for this example 69.9 ppm) in eq 7. The new range of C0n is produced where ∀n ∈ N = 1, 2, ..., 690.

⎧ Ffw − Fww = ∑ Fj − n ⎪ n ⎨ j ⎪ ⎩ ∀n∈N

∑ Fi i

(13)

Step 13. Determine the Wastewater Concentration Vector. Equation 14 is a modified version of eq 6 to calculate the wastewater concentration vector (Cww). For C0s of 10 ppm, 40 ppm, and 65 ppm, the wastewater concentrations are identified as 250 ppm, 250 ppm, and 238.82 ppm. ⎧−Fww × Cww − Freg × (Creg − C0 ) n n n n n ⎪ ⎪ = ∑ F C − ∑ FC j j i i ⎨ j i ⎪ ⎪ ⎩ ∀n∈N

(14)

The procedure of CMA is summarized in Figure 5 to provide a clear depiction of the proposed algorithm. 3227



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Figure 6. Limiting composite curve along with feasible region for total water regeneration network.

Smith7 addressed water network synthesis inclusion of the RR type regenerator. Nevertheless, they dealt with the very simple single pinch problem, and it is restricted to fixed load water operations. Although, Source Composite Curve35 can handle RR type regenerator, it only locates the target for the regeneration−recycle network and very special case of zero liquid discharge. In this section, the capability of the CMA method to set the target for the total water regeneration network including the specified RR regeneration model is demonstrated. The definition of RR (eq 1) is first modified to accommodate the vector calculation (eq 15). Since CMA sets the feasible range of regeneration and post-regeneration concentrations at the first instant, eq 15 produces the feasible range of RR as well. ⎧ Cregn − C0n ⎪ RR n = ; Cregn ⎨ ⎪ ⎩ ∀n∈N

Figure 5. Flowchart for composite matrix algorithm.

5. USING THE CMA RESULTS 5.1. Feasible Region for the Total Water Regeneration Network. Since, for every post-regeneration concentration, the Composite Matrix Algorithm gives the regenerated water flow rate and the regeneration concentration, it is possible to construct water supply composite curves for each set of these values. In Figure 6, water supply composite curves are drawn based on the feasible post-regeneration concentration vector (C0), regenerated water flow rate vector (Freg = Ffw), and regeneration concentration vector (Creg). These curves form a feasible region for the problem under consideration. It can be seen that the feasible region for the total water regeneration network is located entirely below the LCC. This meets the constraints for water network synthesis. Further studies for targeting the network with specified RR regenerator and finding the optimum total cost scenario are all conducted within these constraints so that the results are guaranteed to be feasible. 5.2. Targeting from Removal Ratio Graph. As described, the performance of the water regeneration unit is judged by two criteria: (1) specified post-regeneration concentration and (2) specified removal ratio (RR). Most of the pinch analysis methods have considered the first criterion for targeting the regeneration−reuse/recycle network.8,18−20,22−26,28 A little attention has been paid to the second one.7,35 Wang and

(15)

Plotting C0n, Cregn, Cwwn, Cpfwn, Cpregn, Fregn, Ffwn, and Fwwn versus RRn for every n ∈ N gives an overall picture of the targeted water network with the regenerator specified by RR (Figure 7). For any specified removal ratio, the contaminant concentration targets can be found in Figure 7a and relevant flow rate targets can be identified from Figure 7b. To use this graph, for instance, the regeneration unit with 88% RR performance index is assumed. Drawing the vertical line from the given RR index intersects any of the graphs presented. Now, the projection of these intersections on the yaxis identifies the targets for total water regeneration network. C0, Creg, Freg, and Fww are targeted as 20 ppm, 170 ppm, 37.5 ton/h, and 17.5, respectively. For this specified performance index, the freshwater pinch concentration (Cpfw) and regeneration pinch concentration (Cpreg) are found to be 150 ppm and 250 ppm, respectively. The same targets have been reported for a specified C0 of 20 ppm in the literature30,31 and one possible network design for the total water regeneration system considering these targets have been demonstrated by Agrawal and Shenoy.30 Therefore, using the results from CMA, it is possible to establish the removal ratio graph for a water network problem. With any specified RR type regenerator included, the targets can be easily obtained. 3228



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occurrence. An uncovered lower part of the removal ratio (Figure 7) gives this conceptual insight. One can analyze the interaction between the parameters through the CMA method for the total water regeneration network. This will further give a chance to optimize the network on an economic basis by setting a cost function. These are discussed in the following section.

6. ECONOMIC EVALUATION OF THE TOTAL SYSTEM The higher quality regenerated water (lower C0 or higher RR) leads to less demand for freshwater supply and consequently less waste disposal. This is because the higher quality in-plant purified water (regenerated water) would permit more water reuse/recycle after the regeneration unit. On the other hand, the total cost of the treatment unit increases dramatically with higher regenerator performance. It can be concluded that one of the most important factors in the optimization of water regeneration−reuse/recycle network is the performance of the regeneration unit (C0 or RR). However, not much attention has been paid to the influence of this parameter on the total network cost.32 C0 is assumed to be fixed for most of the pinch analysis targeting methods. This limitation can be overcome by using our proposed CMA method, and this provides an opportunity to study the network from an economic point of view. 6.1. Cost Functions. The cost of freshwater supply (CF), disposal treatment (CD), and regeneration process (CR) are taken into account in this work. As stated, the lower postregeneration concentration results in the lower freshwater requirement. This also can be clearly observed in Figure 7b. Therefore, the freshwater supply cost (CF) also decreases with the decrease of C0. Using the same case as an example, it is supposed that the water system is working 8600 h/yr and the freshwater supply cost is considered to be $1/ton. The governing parameters for the regeneration unit are regeneration flow rate (Freg), post-regeneration concentration (C0), and contaminant regeneration load (Mreg) which is expressed by eq 16.

Figure 7. Removal ratio graph shows the relationship between removal ratio and (a) concentrations and (b) flow rates.

Mreg = Freg × (Creg − C0)

5.3. Pinch Point Migration and Minimum Feasible RR. As illustrated in Figure 7a, the freshwater pinch concentration switches from 150 ppm to 100 ppm at the post-regeneration concentration of 37.6 ppm. The same phenomenon also happens for regeneration pinch concentration at the C0 of 55.6 ppm, where the pinch point migrates from 250 ppm to 150 ppm. It is noticed that the concave turning points of LCC are controlling this kind of pinch movement. As an example, there is another concentration level (200 ppm) between 150 and 250 ppm (Table 2), but it is impossible for 200 ppm to be considered as a potential pinch point. Moreover, depending on the distinct shape of the limiting composite, the pinch migration may not happen or, on the other hand, may occur several times. For this particular example, two transient postregeneration concentrations (C0tr) which cause pinch movement are found as 37.6 ppm and 55.6 ppm. Further to these observations, pinch points are always migrated (if applicable) from higher to lower concentration level with the increase of C0. The other specific feature of the RR graphs is the minimum feasible performance of the regeneration unit. In this example, the regeneration unit with the performance lower than 46% cannot serve this water network due to mass load infeasibility

(16)

Substituting the regenerated flow rate, regeneration concentration, and post-regeneration concentration vectors obtained from CMA in eq 16, the feasible range of the contaminant regeneration load is determined. Figure 8 illustrates the interaction between C0, Freg, and Mreg.

Figure 8. Trade-off between C0, Mreg, and Freg. 3229



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With the increase of C0, although the regenerated water flow rate increases, the mass load picked by the regenerator reduces. This means that the function of the regeneration unit in the total system gradually diminishes and the water network moves toward the pure reuse/recycle configuration. Therefore, if the saving of the resources is the main objective, higher performance of the regeneration unit (lower C0) is a better choice. However, regeneration total cost (including operating and capital costs) rises exponentially in order to produce higher quality water.32 Hence, selecting a high performance regenerator (assumed in most of the water pinch analysis studies) may not guarantee the optimum total cost of the network. The total cost of the regeneration process including annualized capital cost and operating cost is adopted from Feng and Chu32 and modified here as eq 17. It is a function of regenerated water flow rate and post-regeneration concentration. ⎧ ⎪CR n = α × Freg β × n ⎨ ⎪ ⎩ ∀n∈N

quality of regenerated water gives less chance for reuse/recycle after the regeneration unit. This fact may cause the reduction of Cww. Mogden Formula36 is rearranged and modified as eq 18 to consider the operating cost of wastewater treatment. ⎧ ⎛ ⎛ Cwwn ⎞⎞ ⎟⎟ × Fww ⎪CDn = ⎜A + ⎜B × n ⎝ ⎨ ⎝ Ss ⎠⎠ ⎪ ⎩ ∀n∈N

(18) 36

Making the same assumption as in Kim, A = 34 cents/ton, B = 23 cents/ton, and Ss = 336 ppm. Cwwn (ppm) and Fwwn (ton/h) are the wastewater contaminant concentration and the wastewater flow rate, respectively. The wastewater charge (CD) is calculated in k$/yr. The total annualized cost (CT) consisting of freshwater supply cost (CF), regeneration cost (CR), and waste disposal charge (CD) is formed in eq 19.

⎛ C0 max ⎞γ ⎜ ⎟ ⎝ C0n ⎠

⎧CTn = CFn + CR n + CDn ⎨ ⎩ ∀n∈N

(17)

(19)

Now the optimum post-regeneration concentration is taken as the one which leads to the minimum total cost. Optimization results for the example studied in this paper are discussed in the next section. 6.2. Total Cost Evaluation. All cost functions plotted against the feasible range of post-regeneration are depicted in Figure 10. The interaction among cost functions can be vividly

Note that C0max is a constant value which can be found through the CMA method in the preceding sections. β and γ are taken from the literature32 to be 0.14 and 1.75, respectively. With 8600 h/yr of operating cost, α is set for 15 and CR gives the cost in k$/yr. From eq 17, it can be clearly noticed that the C0 and Freg are competing with each other in terms of cost. Therefore, this cost function is in agreement with our discussion about the trade-off between key parameters in the regeneration unit. For the calculation of wastewater disposal charge, it is essential to consider both quantity (Fww) and quality (Cww) of wastewater. The feasible range for these parameters has been identified before, and the correlation between C0, Fww, and Cww is depicted in Figure 9.

Figure 10. Cost function against post-regeneration concentration.

observed. The minimum total cost of 506.4 k$/yr can be determined at 38.3 ppm of post-regeneration concentration (C0opt). Lower than C0opt, the total cost increases with the decrease of C0 because of the rapidly increasing regeneration cost. Higher than C0opt, wastewater and freshwater costs have the dominant influence in the total cost. Three water network scenarios have been under investigation: maximum reuse (scenario 1), total water regeneration with the specified C0 (specified RR) (scenario 2), and optimum total water regeneration (scenario 3). Targeting results and cost evaluations are compared in Table 3. Both scenarios 2 and 3 are obviously favorable compared to the maximum reuse/recycle network because of the smaller demand of freshwater and lower total cost. The optimum case

Figure 9. Interaction between C0, Fww, and Cww.

The trend of wastewater produced with the increase of C0 is identical to that of freshwater intake with 20 ton/h lag due to water loss in the network. However, the change of effluent contaminant concentration (Cww) to the increase of C0 does not follow one specific pattern for the whole range of C0 in this example as shown in Figure 9. It is a plateau (250 ppm) for some extent, and then it is declining gradually. Although there is not one particular trend here, concentration of wastewater cannot be increasing with the rise of C0 for any case. The lower 3230



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forbidden matches are shown with the shaded cells in the matching matrix.

Table 3. Results Comparison for Three Different Scenarios of the Water Network

freshwater flow rate (ton/h) wastewater flow rate (ton/h) regenerated water flow rate (ton/h) wastewater concentration (ppm) post-regeneration concentration (ppm) removal ratio freshwater cost (k$/yr) wastewater cost (k$/yr) regeneration cost (k$/yr) total cost (k$/yr) cost savings compare to scenario 1 cost savings compare to scenario 2

maximum reuse/ recycle28

total regeneration (C0 = 20)30,31

total regeneration (optimum)

scenario 1

scenario 2

scenario 3

70 50 -

37.5 17.5 37.5

40.2 20.2 40.2

200

250

250

-

20

38.3

602 204.7 806.7 -

88% 322.5 76.8 222.6 621.9 22.9%

76% 345.7 88.6 72.1 506.4 37.2%

-

-

18.5%

7. FURTHER DISCUSSION The cost evaluation definitely depends on the unit cost used for the optimization study. The total water regeneration network has an economic justification over the maximum reuse/recycle system when the regeneration cost is relatively lower than the freshwater supply cost and waste disposal charge.32 For instance, if regeneration unit cost α is set to be 30 (instead of 15), the total cost of scenario 2 will be 844 k$/yr. There will be no more cost advantages by using the total water regeneration network (with the fixed C0 = 20). Moreover, the C0opt increases to 47.3 ppm and the cost savings compared to the reuse/recycle scenario reduces to 30% (instead of 37.2%). This means that, with the increased contribution of regeneration cost to the total cost, the optimum network moves toward the maximum reuse/recycle configuration. Therefore, the cost sensitivity analysis is required to find out if the total water regeneration network has the economic incentive compared to the reuse/recycle scenario.36 This may be addressed in the future to complete this work. However, it is believed that this study can provide an effective economic benefit guideline for the total water regeneration network to be implemented. To the best of our knowledge, one work was reported on the post-regeneration optimization.32 In that study, a maximum post-regeneration concentration (C0max) was assumed without a systematic analysis to set this parameter. For the case studied in that paper the C0max was assumed to be 120 ppm; however, applying the CMA approach, the C0max should be 91.4 ppm. Because the regeneration cost is directly related to this parameter, an accurate identification is essential. Second, that study was confined to a fixed regeneration concentration.21 Our work has revealed that regeneration concentration may decrease with the increase of post-regeneration concentration. Third, the wastewater cost was defined as a function of wastewater flow rate only. We have demonstrated that although the flow rate of wastewater decreases with the decrease of postregeneration concentration, the contaminant concentration of wastewater may increase (refer to Figure 9). Hence, seeing both of these parameters in the disposal charge function to determine the optimum post-regeneration concentration is important.

(scenario 3) requires more freshwater and, in turn, generates higher wastewater in contrast with scenario 2. However, the total cost of scenario 3 is lower than the other two. Thus, if economic initiative is the goal, scenario 3 would be the preferred option. The graphical presentation of the optimum targeting results (scenario 3) is shown in Figure 11. The targets obtained for

Figure 11. LCC and water supply composite curve for the optimum total water regeneration network (scenario 3).

8. CONCLUSIONS In this study, the algebraic method, Extended Composite Table Algorithm, is first proposed to target the total water regeneration network for global problems based on the specified post-regeneration concentration. Incorporating the insight from ECTA, the assumption of fixed post-regeneration concentration is relaxed through newly developed Composite Matrix Algorithm. The proposed approach gives an opportunity to address the total water regeneration network with specified removal ratio type regenerator and to study the total water network by taking economic considerations into account. Some new insights are reported, such as pinch point migration and the minimum feasible performance ofthe regeneration unit which can serve the network. It is demonstrated that although, higher quality regenerated water leads to more water conservation, it does not essentially guarantee the economic optimality.

scenario 2 can be referred to Figure 2. Since water supply composite curves for both scenarios are located entirely below the LCC, the feasibility of the results is guaranteed. Moreover, the pinch points show the networks’ bottleneck. Employing NNA,34 one possible network design for optimum scenario (scenario 3) is constructed and depicted via the matching matrix presentation in Figure 12. As shown, all the targets are satisfied through network synthesis. Notice that the outlet (Regout) and inlet (Regin) regeneration streams are considered as one of the process sources and sinks, respectively. To design the network, the sinks are satisfied from the lowest to highest contaminant concentration in increasing order. Consider that the matches between sources and sinks across pinch concentration (except pinch point) are forbidden. These 3231



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Figure 12. Water network design for scenario 3 as a matching matrix.

The methodology and results from this study have potential application to the network with regeneration−recycle and partial regeneration systems,21,37 multiple contaminant problems,38,39 partitioning regeneration units,40 and cost-sensitivity analysis36 for future studies.

Table A3. Network Design for the FL Model Pp

■

P1 P2b P2a P3 P4 total flow rate

APPENDIX: THE APPLICABILITY OF ECTA TO FL WATER NETWORK PROBLEMS The purpose of this appendix is to demonstrate the power of ECTA for targeting the total water regeneration network Table A1. Limiting Data for the FL Problem7 and the Conversion to the FF model Δmp (kg/h)

P1 P2 P3 P4

2 5 30 4

Cin (ppm)

Cout (ppm)

Fp (ton/h)

0 100 50 100 50 800 400 800 Conversion to FF Model

20 100 40 10

(SKj)

Fj (ton/h)

Cj (ppm)

(SRi)

Fi (ton/h)

Ci (ppm)

P1in P2in P3in P4in total

20 100 40 10 170

0 50 50 400

P1out P2out P3out P4out total

20 100 40 10 170

100 100 800 800

regenerated water (ton/h)

20 26.2 25.1 21.1 46.2

46.2

water reuse (Fij) (ton/h) 0 0 0 F2a3 = 18.9 F2a4 = 5.7 24.6

inlet conc. (ppm)

outlet conc. (ppm)

0 0 5 50 100

100 100 100 800 800

procedure of ECTA is shown in Table A2. The regenerated (Freg) and fresh (Ffw) water flow rates’ targets are 46.2 ton/h for the total regeneration−reuse water network, and the corresponding freshwater pinch concentration (Cpfw) is 100 ppm. The regeneration concentration (Creg) and the regeneration pinch concentration (Cpreg) are the same and equal to 100 ppm. Applying the flow rate and mass load balances over the total system wastewater flow rate (Fww) and concentration (Cww) are 46.2 ton/h and 793 ppm, respectively. All the targets are in compliance with the literature7 and show that this water system is a single pinch problem. The second stage in most pinch analysis studies is the network design. Prakash and Shenoy34 proposed three design rules to construct the network for FL problem by using the insight from the targeting stage: (1) All units should have their maximum allowable outlet concentrations. (2) If the operations cross the pinch, the inlet concentration must be forced to the maximum allowable value. This rule can be easily carried out by NNA.

Limiting Data Pp

fresh water (ton/h)

considering FL operations (specifically the total regeneration− reuse water network for FL problems). For this reason, the typical FL example7 is adopted. The limiting data and conversion to water sources and sinks are shown in Table A1. The same as in the literature, the postregeneration concentration (C0) is assumed to be 5 ppm. The Table A2. Implementation of ECTA for FL Problem 1

2

3

4

5

6

7

8

k

Ck (ppm)

Net.Fk (ton/h)

Δmk (kg/h)

Cum.Δmk (kg/h)

Ffwk (ton/h)

Fregk (ton/h)

Cregk (ppm)

1 2 3 4 5 6

0 50 100 400 800 (850)

20 160 40 50 0

1 8 12 20 (0)

0 1 9 21 41 (41)

0 20 90 52.5 51.3 (48.2)

0 10.5 46.2

3232

100 60 93.3 (43.3)



Article

Figure A1. Process flow sheet for FL example (Numbers in [] are contaminant concentrations in ppm and outside [] are flow rates in ton/h).

ppm) are considered as the sources to be fed to the regeneration unit (46.2 ton/h, 100 ppm). P4 is an above-pinch operation. Rule 3 is considered, and also the outlet concentration of the unit (800 ppm) should be maintained. At this stage, the available sources are 40 ton/h of P3 outlet stream at 800 ppm and outlet stream of P2a (6.2 ton/ h, 100 ppm). Hence, 5.7 ton/h (4000/(800−100)) of the cleanest available source above the pinch (P2a outlet stream) is reused to P4. By this end, all the processes are satisfied. The summary of the network design is presented in tabular form (Table A3), and the process flow sheet is depicted in Figure A1. All the targets obtained via ECTA are satisfied through network design. It is also worthy to mention that, as long as the targets can be determined accurately in water pinch analysis studies, one can employ any other network design tool such as water grid diagram7,8 or mass content table8 to design the network in the FL model. This is also applicable for FF operations; however, the only design tool reported for the water regeneration network is NNA.28,37 Recently, Shenoy43 developed the unified water network design method for both FF and FL problems. However, the applicability of this method was just demonstrated for reuse/ recycle water network and zero water discharge with inclusion of the regeneration unit. The extension of this method to the total water regeneration network can be considered as a future research direction. This example shows that the ECTA is also applicable for targeting the total regeneration−reuse water network with FL operations.

(3) If the water-using processes are completely below or above the pinch, the cleanest available source is used to the maximum amount to satisfy these processes. This approach was utilized for reuse/recycle water network design34 and to achieve zero waste discharge for the regeneration−recycle water network.41 The ability of these criteria to construct the total regeneration−reuse water network is demonstrated here. P1 is a below-pinch unit. According to criterion 3, the cleanest available source is freshwater (46.2 ton/h, 0 ppm). Considering the rule 1 at the same time, the outlet concentration of this should be maintained to the maximum value. The required freshwater is calculated as 2000/(100 − 0) = 20 ton/h, which is less than the targeted amount (46.2 ton/ h). The outlet stream of P1 is 20 ton/h at 100 ppm. P2 is also a below-pinch unit. The available sources are fresh water (26.2 ton/h, 0 ppm), regenerated water (46.2 ton/h, 5 ppm), and outlet stream of P1 (20 ton/h, 100 ppm). To satisfy this unit with the cleanest available source (freshwater), 50 ton/ h of this source is needed, which is less than the available amount (26.2 ton/h). Therefore, all of it is exhausted, and the next cleanest source (regenerated water) is utilized to pick up the remaining contaminant load. The corresponding flow rate is deduced as 2380/(100 − 5) = 25.1 ton/h to keep the outlet concentration of P2 to the maximum amount. The outlet stream of P2 is 51.3 ton/h at 100 ppm. P3 is an across-pinch operation with the maximum inlet concentration (50 ppm) below the pinch (100 ppm) and the maximum outlet concentration (800 ppm) above the pinch. Therefore, rule 2 is applied for this unit to be satisfied. As mentioned, this criterion can be implemented through NNA. At this stage, the available sources are the remaining regenerated water (21.1 ton/h, 5 ppm), the outlet stream of P1 (20 ton/h, 100 ppm), and the outlet stream of P2 (51.3 ton/h, 100 ppm). The cleanest available source is regenerated water, and the dirtiest one is the outlet of P1 and P2. However, careful inspection of available water sources reveals that P2 needs both fresh water (26.2 ton/h) and regenerated water (25.1 ton/h) to be fulfilled. Consequently, it is essential to decompose this process to below (P2b) and above (P2a) the regeneration process to have a total water regeneration−reuse network. The same practice also was done in the literature.7,8,42 Considering this issue, the outlet stream of P2a (25.1 ton/h, 100 ppm) and the remaining regenerated water flow rate are chosen as the nearest neighbor to meet the P3 mass load requirement. Using the two equations for NNA34 gives the 21.1 ton/h of regenerated water along with 18.9 ton/h of P2a outlet stream to satisfy the P3. Knowing the fact that the regeneration unit is located across the P2b and P2a unit and the regenerated water flow rate (Freg) and inlet regeneration concentration (Creg) are 46.2 ton/h and 100 ppm, respectively, the outlet of P1 (20 ton/h, 100 ppm) and the outlet of P2b (26.2 ton/h, 100

■

AUTHOR INFORMATION

Corresponding Author

*(H.M.Y.) E-mail: [email protected]. Telephone: +61 8 9266 3677. Fax: +61 8 9266 2681. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS The first author acknowledges the Department of Innovation, Industry, Science, and Research in Australia for International Postgraduate Research Scholarship (IPRS), the Office of Research & Development at Curtin University, Perth, Western Australia for providing Australian Postgraduate Award (APA) and the State Government of Western Australia for providing top up scholarship through the Western Australian Energy Research Alliance (WA:ERA). The authors also acknowledge anonymous reviewers and the editor for their useful comments to improve the original version of paper.

■

NOMENCLATURE

Abbreviations

CMA Composite Matrix Algorithm 3233


Industrial & Engineering Chemistry Research CTA ECTA FF FL LCC MPT NNA PA RR

Article

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Composite Table Algorithm Extended Composite Table Algorithm fixed flow rate fixed load limiting composite curve mass problem table nearest neighbors algorithm pinch analysis removal ratio

Notation

C C0 C0opt C0tr CD CF Cfw Cpfw Cpr Cpreg CR Creg CT Cum.Δm Cww F Ffw Freg Fww MCreg MFreg Mreg SK SR

sink and source contaminant concentration post-regeneration concentration optimum post-regeneration concentration transient post-regeneration concentration disposal charge freshwater supply cost freshwater contaminant concentration freshwater pinch concentration reuse/recycle pinch concentration regeneration pinch concentration regeneration cost regeneration concentration total cost cumulative mass load wastewater contaminant concentration sink and source flow rate freshwater flow rate regenerated water flow rate wastewater flow rate regeneration concentration matrix regenerated water flow rate matrix regeneration mass load sink source

Subscripts

i j k n

■

number number number number

of of of of

process sources process sinks concentration levels post-regeneration concentrations

REFERENCES

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Use of Pinch Concept To Optimize the Total Water Regeneration

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