Article pubs.acs.org/IECR
Improved Ternary Diagram Approach for the Synthesis of a Resource Conservation Network with Multiple Properties. 1. Direct Reuse/ Recycle Chun Deng,*,† Zengkun Wen,§ Dominic Chwan Yee Foo,# and Xiao Feng⊥ †
State Key Laboratory of Heavy Oil Processing, College of Chemical Engineering, China University of Petroleum, 18 Fuxue Road, Changping 102249, Beijing, China § COOEC-ENPAL Engineering Company, Ltd., 197 Songling Road, Laoshan 266100, Qingdao, Shandong, China # Department of Chemical and Environmental Engineering/Centre of Excellence for Green Technologies, University of Nottingham Malaysia, Broga Road, 43500 Semenyih, Selangor, Malaysia ⊥ New Energy Institute, China University of Petroleum, 18 Fuxue Road, Changping 102249, Beijing, China S Supporting Information *
ABSTRACT: Environmental sustainability, rising cost of raw materials, and increasingly stringent emission legislation have motivated process industries to search for resource conservation alternatives. Process integration has been proven to be an effective technique for the synthesis of resource conservation network (RCN). In this first part of the series, the earlier developed clustering technique and ternary diagram by El-Halwagi et al. (AIChE J. 2004, 50 (8), 1854−1869) are extended for the synthesis of RCN with multiple properties. An analytic hierarchy process (AHP) is newly introduced to determine the quality ranking of the sources and sinks, which provides the basic information for the synthesis of RCN. In addition, the mean normalization approach (MNA) is proposed to normalize the property operators to avoid the possibility of the dimensionless property operators being in large magnitude difference when the property operators are divided by randomly selected reference values. Besides, the available region (AR) of sources and feasible solution region (FSR) for sinks are clearly defined, and the optimal mixing point for sources is normally located at the boundary of the FSR. Moreover, the steps for the synthesis of RCN with multiple properties are illustrated systematically via two literature examples and an industrial case. The results for two literature examples are identical to those reported in the literature and hence verify the effectiveness of the newly proposed approach. In addition, the results show that the optimal flow rates for fresh resources are the same with different matching sequences of sinks. However, a sink of higher quality is recommended to be matched prior to those of lower quality. The flow rate of fresh resource will increase if the arm or the flow rate contribution of the source of higher quality is not minimized. This is shown using the case of a hydrogen network. In addition, 10.2% of desalted water is reduced in the industrial case of a refinery sour water network.
1. INTRODUCTION Process industries are characterized by the use of enormous amounts of material resources. Owing to the growing world population and rapid economic development, the demands for natural resources are increasing rapidly. Furthermore, the increase of public awareness of environmental sustainability, rising cost of raw materials, and increasingly stringent emission legislation have motivated process industries to search for more efficient and sustainable alternatives for the usage of material resources. Resource conservation through direct material reuse/ recycle among processes without adversely affecting the process performance is one cost-effective solutions. Process integration for resource conservation has witnessed significant progress in the past two decades with the development of systematic methodologies and tools. Numerous industrial applications have also been demonstrated for the conservation of water, hydrogen, and other industrial resource such as volatile organic compounds. El-Halwagi1,2 defined process integration as a holistic approach to process design, retrof itting, and operation, which emphasizes the unity of the process. Within the framework of process integration, the techniques for the synthesis of resource © 2014 American Chemical Society
conservation network (RCN) can be mainly categorized into insight-based pinch analysis and mathematical optimization approaches. The basic principles and various applications of RCN tools are found in various review papers3−7 and textbooks.1,8,9 The conventional integration techniques for RCN synthesis, such as water and hydrogen integration, are mainly concentration-driven. On the basis of the extension of a hydrogen surplus diagram,10 Zhao et al.11 proposed an impurity deficit diagram to locate the flow rate targets for a hydrogen network with multiple impurities. They presented different targeting procedures when the matching order for the streams differs according to different impurities. However, the design procedure is not presented clearly. Later, Liu et al.12 introduced an evolutionary method to design RCN with multiple impurities. Besides, Liu et al.13 introduced the concept of concentration potentials of the demand and source for the Received: Revised: Accepted: Published: 17654
April 24, 2014 August 14, 2014 October 16, 2014 October 16, 2014 dx.doi.org/10.1021/ie501627e | Ind. Eng. Chem. Res. 2014, 53, 17654−17670
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water system with multiple contaminants. The performing order of the allocation in the design stage processes is determined by the increasing order of inlet concentration potentials of the processes.13 However, as pointed out by ElHalwagi,2,14 not all RCN problems are “chemo-centric”. In contrast, many material reuse/recycle problems are driven and governed by properties or functionalities of streams rather than by their chemical constituency. For instance, usage of solvents always relies on their characteristics, such as equilibrium distribution coefficients, viscosity, and volatility. Besides, the makeup water for a wet air cooler involves limits on properties such as pH (for the consideration of corrosion) and conductivity (consideration of fouling). Hence, there is a necessity to develop a systematic design methodology to address the RCN problems that are driven by properties and functionalities. The framework of property integration for RCN was established by El-Halwagi and co-workers,1,2,14 which is defined as a f unctionality-based, holistic approach to the allocation and manipulation of streams and processing units, which is based on the tracking, adjustment, assignment, and matching of f unctionalities throughout the process. For RCN with a single property, Kazantzi and El-Halwagi15 presented a graphical pinch diagram to locate minimum resource consumption targets, similar to those developed for concentration-based RCN problems.1,16 Later, Foo et al.17 introduced the property cascade technique to target the property-based RCN. Besides, Deng et al.18 presented an improved version of the composite table algorithm originally proposed by Agrawal and Shenoy19 to determine the targets of a property-based water network with multiple resources. Moreover, Ng et al.20,21 proposed the automated targeting model (ATM) to determine the target of conventional and bilateral property-based RCN21 and incorporated waste interception and treatment systems.20 Note that the ATM was originally developed for concentration-based RCNs.22 Shelley and El-Halwagi14 first presented the concept of clustering to track functionality and properties of the complex hydrocarbon mixtures. A ternary diagram was introduced in which optimal mixing strategies for the recovery and allocation of process sources are identified for the sinks. Later, El-Halwagi et al.2 addressed the general problem of allocation of sources and sinks with reuse/recycle and interception. However, the reference values for properties were selected randomly, which may lead to cases where the dimensionless property operators would be in large magnitude difference. Besides, the case study presented is relatively simple (with only two sinks, one process source, and two fresh sources).2 For RCN with multiple sinks and sources, the quality ranking of sources and sinks is not apparent. However, the quality ranking of sources and sinks is important information when RCN is synthesized. The essence of the developed approach2 is reviewed in section 3. In addition, to overcome the limitation of the ternary diagram, Qin et al.23 proposed an algebraic approach to locate rigorous targets for RCN with more than three properties.23 Besides, mathematical optimization approaches have also been developed for the synthesis of RCN with multiple properties. Many superstructure models are proposed in the literature, such as source−sink representation for mass and property integration24 and with economic and environmental objectives,25 mathematical model for resource conservation network synthesis,26 and optimization of recycle and reuse water networks.27
In this paper, an improved technique for the synthesis of property-based RCN with multiple properties is presented. The approach is extended from the clustering technique and ternary diagram proposed by El-Halwagi and his co-workers.1,2,14 Part 1 of the series of papers aims to present the improved technique for the synthesis of RCN with direct reuse/recycle scheme. The analytic hierarchy process (AHP) is newly introduced to calculate weight factors and to identify the quality ranking of sources and sinks with multiple properties to provide useful information for the synthesis of RCN. To avoid the uncertainty of the random selection of a reference property operator, this paper first introduces the mean normalization approach (MNA) to normalize the dimensionless property operators and the property operators would be of the same magnitude. Two literature examples and an industrial case are solved to illustrate the proposed approach.
2. PROBLEM STATEMENT The problem can be stated as follows. Figure 1 presents a set of process sources (NSR) and a number of process sinks (NSK).
Figure 1. Schematic representation of the property-based RCN with direct reuse/recycle scheme.
Each process source has its own outlet properties (PSRi,p) and a limiting outlet flow rate (Flim SRi). They can be considered for direct reuse/recycle to the process sinks or be discharged if the environmental regulation is fulfilled. Each sink requires a given limiting inlet flow rate (Flim SKj), and its inlet properties (PSKj,p) have to satisfy the constraint in eq 1 min max PSK ≤ PSK j ,p ≤ PSK j,P j,p
(1)
max where Pmin SKj,p and PSKj,p are the specified minimum and maximum bounds on admissible properties for process sink j. To avoid the nonlinear nature for the property mixing rules, property operators were introduced,17,28 thus providing the linear mixing rule shown in eq 2
ψP̅ =
∑ xSR
i
× ψSR
i ,p
i
(2)
where ψSRi,p and ψP̅ denote the property operators for the pth property of the source and the mixing stream. xSRi represents the fractional contribution of source i into the total flow rate of the mixture. Therefore, we can rewrite the sink constraints in eq 1 in terms of the property-mixing operator as in eq 3 min max ψSK ≤ ψSK ≤ ψSK j,p
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j,p
j,p
(3)
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max where ψmin SKj,p and ψSKj,p denote the minimum and maximum property operators for the pth property of sink j. For simplicity, ψSRi,p and ψSKi,p will be shown as ψ in the remainder of the paper. In addition, a number of fresh (external) resources (NFR) with specified properties (PFRi,p) can be purchased to supplement the use of process sources in sinks. Part 1 of this series of papers aims to present a conceptual approach for the synthesis of RCN with a direct reuse/recycle scheme.
where Cp denotes the mean cluster for the pth property resulting from mixing the individual clusters of NSR streams and βi denotes the fractional lever arm of cluster CSRi,p of stream SRi, which is given by βSR = i
3. CLUSTERING TECHNIQUE AND PROPERTY-BASED DESIGN APPROACH1,2,14 In this section, the clustering technique for three properties and the property-based design approach proposed by El-Halwagi and his co-workers1,2,14 are discussed to lay the foundation for the improved technique. Shelley and El-Halwagi14 showed that the clusters which acted as surrogate properties could be introduced to track the properties in a conservation manner instead of components. The basic mathematical expressions for clusters are summarized as follows.14 The operator ψSRi,p for the pth property PSRi,p (given in eq 2) is then normalized into a dimensionless operator (ΩSRi,p) by dividing it by a reference value ψSR i ,p ΩSR i ,p = ref ψp (4)
i ,p
(5)
ΩSR i ,p (6)
There are two key characteristics for property clusters: intraand interstream conservation. Therefore, it is possible to track properties in a conservation manner via the deduced property clusters. (1). Intrastream Conservation. For any stream SRi, the sum of clusters must be conserved to be unity, that is Np
∑ CSR
i ,p
=1
∀ i ∈ NSR (7)
p=1
(2). Interstream Conservation. If two or more streams are mixed, the resulting individual clusters are conserved. It is represented in the form of lever-arm rules. The lever-arm additive rule for clusters can be expressed by eq 8 NSR
Cp =
∑ βSR CSR i
i=1
i ,p
p ∈ Np
i
∀ i ∈ NSR
(10)
represent three clusters, CSRi,1, CSRi,2, and CSRi,3, respectively. Any point in the ternary diagram can be denoted by the coordinate (CSRi,1, CSRi,2, CSRi,3). Two sources (SRi and SR(i+1)) with different cluster values can be marked in the ternary diagram as shown in Figure 2. In addition, the boundaries of the feasible region (BFR) for a sink can be presented in the ternary diagram, and the BFR can be accurately represented by a hexagon. The vertices of the hexagon are characterized by the coordinates min max min max max min max min (Ωmin SKj,1, ΩSKj,2, ΩSKj,3), (ΩSKj,1, ΩSKj,2, ΩSKj,3), (ΩSKj,1, ΩSKj,2, ΩSKj,3), max max min max min min max (ΩSKj,1, ΩSKj,2, ΩSKj,3), (ΩSKj,1, ΩSKj,2, ΩSKj,3), and (ΩSKj,1, Ωmin SKj,2, max ΩSKj,3). Once two sources (SRi and SR(i+1)) are mixed, the straight line connecting sources SRi and SR(i+1) denotes the locus of all mixtures. According to the fractional contributions of the streams, the resulting mixture divides the mixing line in ratios βi and βi+1 as illustrated in Figure 2. The segment AB locates in the feasible region (FR) for the sink, which means that the mixture corresponding to segment AB fulfills the requirements of the sink. If SRi is more expensive than SR(i+1), the portion of the level arm of SRi (βi) has to be minimized to minimize the utilization of SRi. Thus, point A in Figure 2 can be identified as the optimal mixing point. Note that the reference values for properties are selected arbitrarily and there is no guarantee that the dimensionless property operators are of the same magnitude. Besides, in the design approaches (e.g., nearest-neighbor algorithm29 and process-based graphical approach30) of RCN with a single concentration/property, a sink of the highest quality (lowest inlet impurity concentration/property) is to be considered earlier for matching with sources of similar quality. Note that the matching sequence of sinks is determined via the order of
∀ i ∈ NSR
AUPSR i
i
Figure 2. BFR for sink and determination of optimal mixing strategies for sources.
Finally, the cluster for the pth property for stream SRi (CSRi,p) is defined by eq 6: CSR i ,p =
(9)
A ternary diagram is commonly used in physical chemistry, mineralogy, metallurgy, and other physical sciences to show the compositions of systems composed of three species. El-Halwagi and his co-workers1,2,14 adopted the ternary diagram to address the source−sink mapping problem with three properties. As shown in Figure 2, the three vertices of the ternary diagram
Np p=1
∀ i ∈ NSR
∑ xSR AUPSR i=1
where ψref p denotes the arbitrary reference value. There is a necessity to introduce a normalization approach to eliminate such an arbitrariness. Next, an augmented property (AUP) index for each stream (i.e., SRi) is defined as the summation of the dimensionless property operators:
∑ ΩSR
AUP NSR
AUP =
AUPSR i =
xSR i AUPSR i
(8) 17656
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decreasing quality. The flow rate of the source of highest quality (i.e., freshwater, hydrogen utility) is minimized via maximizing the usage of other sources of lower quality (i.e., internal water/ hydrogen source). A similar concept is adopted here for the design of RCN with multiple properties, in which the quality rankings of the sources and sinks are determined. Those aspects were not clearly presented in the literature.1,2 In this paper, AHP is introduced to determine the quality ranking of the sinks and sources.
compared to the property on the right (i.e., property 2). The scaling is not necessarily 1−9. However, for qualitative data such as preference, ranking, and subjective opinions, it is suggested to use a scale from 1 to 9, and the explanation for the scale is shown in Table 1. Table 1. Fundamental Table for the Nine-Order Proportional Scale31 intensity of importance on an absolute scale
4. ANALYTIC HIERARCHY PROCESS FOR THE QUALITY EVALUATION OF SOURCES AND SINKS WITH MULTIPLE PROPERTIES AHP is one of multiple criteria decision making methods that was originally developed by Saaty.31 AHP is widely applied in decision situations that include choice, ranking, prioritization, resource allocation, and quality management. In the following section, the individual steps to carry out the AHP for quality evaluation of sources and sinks with multiple properties are illustrated. (1). Multilevel Hierarchical Analysis Framework. As shown in Figure 3, level 0 is the goal of the analysis, which is to
definition
1
equal importance
3
moderate importance of one over another another essential or strong importance very strong importance
5 7
explanation two activities contribute equally to the objective experience and judgment slightly favor one activity over another experience and judgment strongly favor one activity over another activity is strongly favored and its dominance demonstrated in practice evidence favoring one activity over another is of the highest possible order of affirmation when compromise is needed
9
extreme importance
2, 4, 6, 8
intermediate values between the two adjacent judgments if activity a has one of the above numbers assigned to it when compared with activity b, then b has the reciprocal value when compared with a
reciprocals
Suppose property 1 is of moderate importance over property 2, according to the definition shown in Table 1, we can mark 3 on the left side of the relative scale between property 1 and property 2, as shown in Figure 4a. Similarly, we mark 5 on the left side of the relative scale between property 1 and property 3 as shown in Figure 4b. This indicates property 1 is of strong importance over property 3. Besides, we mark 3 on the left side of the relative scale between property 2 and property 3 to indicate that property 2 is of moderate importance over property 3, as shown in Figure 4c. Next, on the basis of pairwise comparisons, we next make a comparison matrix. There are three comparisons, and thus we would make a 3 × 3 comparison matrix. Note that the diagonal elements of the matrix are always set to unity. To fill the upper triangular matrix, the following rules are used: (1). If the judgment value is on the lef t side of 1, an actual judgment value is used. (2). If the judgment value is on the right side of 1, a reciprocal value is used. According to the pairwise comparison, property 1 is of moderate importance over property 2; thus, we put 3 in the first entry of column 2 in the matrix (see Table 2). By comparison of property 1 and property 3, property 1 is of strong importance over property 3; thus, we put an actual judgment of 5 on the first entry of column 3 in the matrix. By comparison of property 2 and property 3, property 2 is of moderate importance over property 3; thus, we put an actual judgment of 3 on the second entry of column 3 in the matrix. On the other hand, reciprocal values of the upper diagonal are used for pairwise comparison in the lower diagonal of the comparison matrix, as shown in Table 2. Note that all of the elements in the comparison matrix are positive. (3). Determination of Eigenvalue and Eigenvector. The eigenvalue and eigenvector for the comparison matrix can
Figure 3. AHP hierarchy diagram.
evaluate the quality ranking of sources and sinks. Level 1 is multiple criteria that consist of several factors (properties) in the paper. The last level (level 2) is the alternative choices, in which the latter refers to the sources and/or sinks for the case of RCN synthesis. (2). Pairwise Comparison and Comparison Matrix. Suppose we have three properties: properties 1, 2, and 3. For any two of the three properties in the synthesis of RCN, which property is much more important than the other and how great is the importance in comparison with the others? Let us make a relative scale as shown in Figure 4 to measure how great is the importance for the property on the left (i.e., property 1) as
Figure 4. Pairwise comparison on the nine-order proportional scale for three properties. 17657
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Table 2. Pairwise Comparison Matrix Level 1 with Respect to the Goal (Level 0) criterion
property 1
property 2
property 3
property 1 property 2 property 3
1 1/3 1/5
3 1 1/3
5 3 1
principal eigenvector
λmax
normalized principal eigenvector
0.9161 0.3715 0.1506 = 3.0385; CI = 0.01925; CR = 3.3%
0.6370 0.2583 0.1047
Table 3. Random Consistency Index (RI)31 n RI
1
2
3
4
5
6
7
8
9
10
0
0
0.58
0.9
1.12
1.24
1.32
1.41
1.45
1.49
In level 1, we have one comparison matrix that corresponds to pairwise comparisons between three factors (i.e., properties) with respect to the goal. Thus, the comparison matrix of level 1 has a size of 3 × 3. Next, each choice (i.e., two sinks) in level 2 is connected to each factor at level 1, and we have two choices and three factors. Then we will have three comparison matrices at level 2, and each of these matrices has a size of 2 × 2. Repeating step 2 for every choice (i.e., two alternative sinks) with respect to each criterion (i.e., property), the three pairwise comparison matrices are generated as shown in Table 4. Next,
be determined easily with any matrix software (i.e., Matlab, Mathematic). The maximum eigenvalue is called the principal eigenvalue (λmax), which is calculated as 3.0385. The corresponding eigenvector (i.e., the principal eigenvector) is determined as (0.9161, 0.3715, 0.1506)T. The summation of the elements of the principal eigenvector is 1.4382. Each element of the eigenvector is divided by 1.4382, and then the principal eigenvector can be normalized to be (0.6370, 0.2583, 0.1047)T. For instance, 0.9161 is divided by 1.4382 and results in 0.6370. Next, the information of the principal eigenvalue is used to check whether the judgment is consistent. (4). Consistency Index and Consistency Ratio for Consistency Check of the Judgement. If property 1 is of moderate importance over property 2, whereas property 2 is of moderate importance over property 3, then property 1 is logically of importance over property 3. This means the judgment is consistent. On the contrary, if property 3 is of importance over property 1, then the judgment is inconsistent. For a first-order comparison matrix, property 1 is of equal importance over property 1. For a second-order comparison matrix, if property 1 is of moderate importance over property 2, then property 1 is logically of importance over property 2. In other words, the consistency for the comparison matrix with first or second order is undoubted. To give a measure of consistency for the comparison matrix with greater than or equal to the third order, Saaty31 defined that the consistency index (CI) as a deviation or degree of consistency using eq 11 CI =
λmax − n n−1
n≥3
Table 4. Pairwise Comparison Matrix Level 2 with Respect to Each Criterion in Level 1
CI RI
n≥3
sink 1
sink 2
principal eigenvector
1 3 λmax = 2 sink 1
1/3 1
0.25 0.75
sink 2
principal eigenvector
3 1
0.75 0.25
sink 2
principal eigenvector
1/3 1
0.25 0.75
property 2 alternative sink 1 alternative sink 2 property 3 alternative sink 1 alternative sink 2
1 1/3 λmax = 2 sink 1 1 3 λmax = 2
step 3 is repeated to determine the principal eigenvalues and principal eigenvectors for those comparison matrices, given in the last column of Table 4. We then repeat step 4 to confirm that those comparison matrices are second order, which means that the judgment is consistent. (5). Overall Weight of Each Alternative Choice Based on the Weight of Levels 1 and 2. The overall weight is just normalization of a linear combination of multiplication between weight and priority vector. The weight for each factor (i.e., property 1) corresponds to the principal eigenvector of the comparison matrix in level 1, which is listed in the first row of Table 5. The principal eigenvector of the comparison matrices for choices (i.e., alternative sink 1) with respect to the factors (i.e., properties 1, 2, and 3) are also shown in Table 5, that is, rows 3 and 4 for alternative sinks 1 and 2. Then a linear combination of multiplication for sink 1 can be determined by the product of the weighting factor with the respective principal eigenvector of each property, that is, 0.3791 (= 0.6370 × 0.25 + 0.2583 × 0.75 + 0.1047 × 0.25). Similarly, the linear combination of multiplication for alternative sink 2 is calculated as 0.5625. Next, the linear combinations of multiplication for two choices (alternative sink 1 and alternative sink 2) are
(11)
where n denotes the order of the comparison matrix. For the principal eigenvalue (λmax = 3.0385) and third order of the comparison matrix, CI is calculated as 0.01925 by solving eq 11. In addition, Saaty31 proposed that the CI has to be divided by an appropriate CI, which is defined as a random consistency index (RI). The RI is shown in Table 3. Then, Saaty31 introduced the consistency ratio (CR), which is a comparison between the CI and RI and can be determined by eq 12: CR =
property 1 alternative sink 1 alternative sink 2
(12)
For a value of CR that is ≤10%, the inconsistency is acceptable. If the CR is >10%, we need to revise the subjective judgment. For the given example, we have CI = 0.01925 and RI for n = 3 is 0.58, so then the CR is calculated as 3.3% (
