Flow Rate Targeting for Concentration- and Property-Based Total

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Flowrate Targeting for Concentration- and Property-based Total Water Network with Multiple Partitioning Interception Units Chun Deng, Chunfeng Shi, Xiao Feng, and Dominic Chwan Yee Foo Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.5b03203 • Publication Date (Web): 25 Jan 2016 Downloaded from http://pubs.acs.org on February 4, 2016

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Industrial & Engineering Chemistry Research

Flowrate Targeting for Concentration- and Property-based Total Water Network with Multiple Partitioning Interception Units Chun Deng1, Chunfeng Shi2, Xiao Feng3*, Dominic Chwan Yee Foo4 1

State Key Laboratory of Heavy Oil Processing, College of Chemical Engineering, China University of Petroleum, Beijing, 102249, China 2

3

Central Research Institute, Wanhua Chemical Group Co., Ltd. Yantai, 264006, China

School of Chemical Engineering & Technology, Xi’an Jiaotong University, Xi’an 710049, China 4

Department of Chemical and Environmental Engineering, University of Nottingham Malaysia, Broga Road, 43500 Semenyih, Selangor, Malaysia

Abstract: Multiple partitioning interception units, such as floatation, flocculating settling, ultrafiltration, reverse osmosis, etc. are placed in series in practical wastewater treatment plant for the purpose of regeneration reuse/recycle, and/or for waste treatment for final discharge. Currently, no pinch-based approach addresses the flowrate targeting problem for the water network with multiple partitioning interception units. In this paper, the generalized Improve Problem Table (IPT) is firstly presented to target concentration- and property-based total water network with multiple partitioning interception units. The procedure for the generalized IPT approach is illustrated in detail by solving a revised literature example. The generalized IPT includes the deduced flowrate and mass balance equations for the water network with multiple partitioning interception units and they are utilized to check the feasibility of the results. The Excel Goal Seek feature is applied to determine the optimal solutions and they are validated via automated targeting model (Ng et al., 2009, Ind. Eng. Chem. Res.). The limiting composite curve and water supply line can be plotted on the basis of the data and the optimal solutions to show the net water demand and the optimal water supply of water network. Two revised literature examples are solved to show the feasibility of the proposed IPT in targeting the fixed flowrate (FF) or fix contaminant mass load (FC) water network *

Corresponding author. Tel.: +86-10-8973 9113; E-mails: [email protected] (X. Feng)

1

ACS Paragon Plus Environment


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problems. The applicability of proposed IPT is illustrated by solving the property-based wastewater interception and recovery system of an industrial case study. Keywords: Pinch analysis; Problem table; Water minimization; Reuse/recycle; Interception; Process integration

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Introduction The stringent environmental regulations and also the escalating cost of freshwater as well as wastewater treatment have motivated the process and manufacturing industries to emphasis on waste minimization in their daily operations. In particular, water network synthesis has gained much attention in both industrial and research communities. Over the past decades, much work have been conducted for the synthesis of water network, ranging from both conceptual and mathematical optimization approaches. The basic principles and variety of applications of water network synthesis can be found in the review papers1-3 and textbooks4-7. Pinch analysis is widely accepted as one of the promising tools in addressing water network synthesis problems for the process industries, as reviewed in the literature2. In general, water network synthesis may be classified into two main categories, i.e. fixed contaminant load (FC) and fixed flow rate (FF) problems8, 9. In the former, water-using processes (e.g., washing, scrubbing, and extraction) are characterized by mass transfer operations where a fixed amount of contaminant is transferred from contaminant-rich stream to water, which acts as a mass separating agent. In contrast, water-using processes (e.g., boilers, cooling towers, reactors) are characterized as water sinks/sources that consume/generate a fix amount of water in the FF problems. Hence the primary concern of this latter problem is the water flow rate. As pointed out by Foo2, the limiting water data for FC and FF problems with single contaminant are interchangeable. In the seminal work of FC problem, Wang and Smith10 specialized the mass exchange network (MEN) proposed by El-Halwagi and Manousiouthakis11 into water network synthesis. They proposed the limiting composite curve (LCC) to locate the minimum fresh water and wastewater targets for water system involving mass-transfer processes. However, the approach proposed by 3



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Wang and Smith10 is not applicable for non-mass transfer-based FF operations which are commonly found in the process industry. To overcome the limitation of FC problem, many graphical or tabular approaches are proposed to address the FF problem in the literature8, 9, 12-27, such as water-source and water-sink composites12, water surplus diagram (WSD)8, material recovery pinch diagram (MRPD)14,

15

, water cascade analysis (WCA)9, improved LCC and composite table algorithm

(CTA)16 and its extensions28, 29 , source composite curve (SCC)17, 30. After maximizing the water recovery potential via direct reuse/recycle, freshwater consumption of a water network may be further reduced via regeneration or interception. Wang and Smith10 extended the use of the LCC to determine the water flow rate targets for regeneration reuse/recycling schemes in the FC problem. Later, Castro et al.31 proposed the problem table to target FC water network with regeneration-recycling or regeneration-reuse schemes. The pinch concentration is always set to be optimal regeneration concentration. As pointed out by Feng et al.32, the optimal regeneration concentration can be equal to, higher than or lower than the pinch concentration, depending on shape of the LCC. They in turn proposed an improved LCC and improved mass problem table to determine the targets of a FC water network with regeneration recycling32 or regeneration reuse schemes33. On the other hand, several approaches have also been developed to handle water regeneration placement in the FF problems, such as WSD8, WCA18, 23, 34, improved LCC and CTA16 and its extensions28, 29, SCC17, 26. Besides, considerable amount of works were conducted on the synthesis of distributed effluent treatment network35-37. Wang and Smith35 first proposed the wastewater treatment composite curves to target the minimum treatment flow rate for a distributed effluent treatment network. However, the proposed method fails to predict the lowest possible treatment flow rate when multiple treatment units are used. This limitation was then overcome by Kuo and Smith36, who proposed an improved targeting procedure. More recently, approaches were proposed to identify individual wastewater 4


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streams that generated from the water network17, 21. Besides, a new waste treatment composite curve has also been proposed to locate the minimum treatment flow rate for single treatment unit22 and multiple treatment units38. Besides, Bandyopadhyay39 also proposed an algebraic approach and wastewater composite curve to target the minimum waste treatment flow rate to satisfy environmental discharge limit. Recently, Liu et al.40,

41

introduced design procedure to design

wastewater treatment networks with single contaminant41 and multiple contaminants40. As reported by Kuo and Smith37, there are close interactions among the individual element of a water network, i.e. reuse/recycle, regeneration and effluent treatment systems. Although Kuo and Smith37 provided the seminal contribution for total water network synthesis, the presented work is limited to the FC problem, and yet it is iterative in nature (due to the procedure for regeneration). In the much later works, Ng et al.21, 22 extended the use of MRPD14, 15 and WCA 9, 18 to synthesize a total water network and analyze the interactions of the individual elements of the water network via the selection of regeneration streams. It is worthy to mention that the previous proposed approaches are limited to address problems that are ‘chemo-centric’ or concentration-based. However, many design problems are controlled by properties instead of chemical constituency42. For instance, the selection of solvents typically relies on properties such as equilibrium distribution coefficients, viscosity, and volatility. In addition, effluent legislation is often defined in term of properties (e.g. pH, chemical oxygen demand (COD), turbidity, toxicity, color) apart from pollutant concentration (e.g. suspended solids, etc.)42. Those factors lead to the development of property integration. The framework of property integration for material recovery was established by El-Halwagi and co-workers43-47. Property integration is defined as a functionality-based, holistic approach to the allocation and manipulation of streams and processing units, which is based on the tracking, adjustment, assignment, and matching of functionalities throughout the process42. Several graphical28, 43, 44, 46, 48, 49, algebraic45, 50 and mathematical optimization-based51-57 approaches have been developed for reuse/recycle and interception network. Among these, it is worth mentioning that Deng and Feng28 was originally extended the CTA 16 as the improved problem table (IPT) for concentration- and property-based water networks. A few scenarios were also analyzed, such as multiple resources and regeneration reuse/recycle28. In analyzing a total water network, it is important to understand the characteristics of the 5



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interception unit that is often used as regeneration or waste treatment. For both cases, the interception unit removes a portion of impurity from the water sources, before they may be sent for reuse/recycle (regeneration), or for final environmental discharge (treatment). An interception unit may be generally categorized as fixed outlet concentration (Cout) and fixed removal ratio (RR) types. The former system is characterized by constant Cout (e.g., 20 ppm). In contrast, an RR-type system removes a fixed ratio of contaminant mass load from the inlet wastewater stream. It is also worth mentioning that most works on water network synthesis typically consider single treatment unit with single outlet stream (see Figure 1a). This is termed as the single pass unit 58. However, there exist many treatment units with two outlet streams of significant different flowrates and qualities (e.g. flotation, filtration, ultrafiltration and reverse osmosis). The first work that considers this kind of partitioning treatment units for water regeneration reuse/recycle was reported by Ng et al.58. The authors introduced a new model for partitioning interception system (see Figure 1b) and determined the water regeneration network targets with an optimization framework that is based on pinch analysis technique, known as automated targeting model (ATM)58. Note that the single-pass interception unit (see Figure 1a) can actually be treated as special case of partitioning interception unit (see Figure 1b) if the flowrate of its residual stream is taken as zero. In their later works, the authors approached the problem using a superstructure-based optimization model59, and also extended the ATM for the total water network53 and property-based resource conservation network50. However, these earlier works only consider the use of one partitioning interception unit for the purpose of regeneration reuse/recycle53,

58, 59

. In practical wastewater treatment plant, several

partitioning interception units, such as preliminary treatment unit (i.e. regulation for pH, floatation, biological aerated filter (BAF), flocculating settling, etc.), advanced treatment unit (i.e. ultrafiltration, reverse osmosis, etc.) are placed in series. Those partitioning interception units can be used for regeneration reuse/recycle, and/or for waste treatment for final discharge. The current pinch-based (i.e. graphical or tabular) approaches are not able to determine the flowrate targets of water network with multiple partitioning interception units.

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Figure 1. Two models of interception systems: (a) single-pass interception system, (b) partitioning interception system58 This paper aims to extend the previous proposed IPT28 to determine various flowrate targets for concentration- and property-based total water network with multiple partitioning interception units. The flowrate and mass balance equations for the total water network are deduced and incorporated into the extended IPT. Two revised literature examples and an industrial case study are used to illustrate the applicability of the proposed method.

Problem Statement The superstructural representation for a total water network with multiple partitioning interception units is illustrated in Figure 2. The formal problem for the total water network can be stated as follows: Given a set of process units, their outlets can be defined as set of process sources (NSR) and inlets as set of process sinks (NSK). Each process source has a specified outlet concentration ( CSRi ) or property value ( PSRi ), and limiting outlet flow rate ( FSRi ). The process sources may be considered for reuse/recycle or for final discharge to the environment. Each process sink can accept sources to meet its limiting inlet flow rate ( FSKj ), with an allowable inlet concentration ( CSKj ) or property value ( PSKj ); the latter values should comply with the predetermined constraints, as defined by equations (1) and (2): min max CSKj ≤ CSKj ≤ CSKj

(1)

min max PSKj ≤ PSKj ≤ PSKj

(2)

min max min max where CSKj , CSKj , PSKj and PSKj refer to the lower and upper bounds of acceptable

concentrations, as well as those bounds for properties for the jth process sink, respectively. 7



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To avoid the nonlinearities related to mixing rules for certain properties, such as pH, density (ρ), viscosity (µ), Reid vapor pressure (RVP), electric resistivity (R), paper reflectivity (R∞)52, 54, 56, 57, the property mixing rule may be linearized by equation (3) that follows46, 47. ψ ( P ) = ∑ xSRiψ ( PSRi )

(3)

i

where ψ ( PSRi ) and ψ ( P ) are property operators for the source ( PSRi ) and the resulting mixture ( P ), respectively. For instance, the property operators for pH, density (ρ), viscosity (µ), Reid vapor pressure (RVP), electric resistivity (R), paper reflectivity (R∞) are 10pH, 1/ρ, log(µ), RVP1.44, 1/R, 52, 54, 56, 57

R∞5.92 reported in the literature

. However, for properties, such as contaminant composition

or concentration (i.e. suspended solids), toxicity, chemical oxygen demand (COD), their operators are properties themselves as reported in the literature52, 54, 56, 57. xSRi corresponds to the fractional contribution of SRi in the total mixture flowrate. Thus, the property constraint defined in equation (2) can be converted to the constraint specified by property operator, as shown in equation (4). ψ min ( PSKj ) ≤ ψ ( PSKj ) ≤ ψ max ( PSKj )

(4)

where ψ min ( PSKj ) and ψ max ( PSKj ) are the minimum and maximum operators for the sink property ( PSKj ). Besides, a set of external fresh water sources (NFW) may be utilized to fulfill the requirement of the sinks. Each fresh water source has its specified concentration ( CFWm ) or property value ( PFWm ); its flow rate is to be determined as part of the targeting stage. In order to reduce the flowrates of freshwater sources and wastewater discharge, a set of partitioning interception units (NTU) are to be installed to upgrade the quality of process water sources. Part of the treated water sources would be reused/recycled to the process sinks, and the residual flowrate would be discharged to the environment as wastewater if the environmental limitation is fulfilled. 8


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The objective is to locate the minimum flowrate targets for the total water network prior to detailed design. These include the minimum flowrates for fresh water, wastewater, and partitioning interception units.

Figure 2. Superstructural representation for a total water network with multiple partitioning interception units

Model for Total Water Network with Multiple Partitioning Interception Units For the partitioning interception unit in Figure 1(b), we may define its recovery ratio ( aTUt ) as prod in ) to its inlet flowrate ( FTUt ), give as in equation (5). the purified stream flowrate ( FTUt

aTUt =

prod FTUt in FTUt

∀t ∈ NTU

(5)

In practice, many treatment units for wastewater treatment plant are installed in series. These include sedimentation, flotation, filtration, ultrafiltration and reverse osmosis, which may be modeled as partitioning interception units. Wastewater streams that pass through these interception units will have higher quality, and hence can be reuse/recycled to the process water sinks and/or discharged into environment. Note also that different interception units will have different recovery ratios. For instance, the recovery ratio for ultrafiltration is around 90%～95%, and that for reverse osmosis is approximately 70%. Hence, for water source that passes through tth interception unit, its overall recovery ratio can be determined by the product of all individual recovery ratios of the interception units involved, given as in equation (6). t

a = ∏ aTUt

(6)

t =1

Referring to the superstructural representation in Figure 2, for a total water network that considers reuse/recycle, regeneration and waste treatment using multiple partitioning interception 9



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units, its overall flowrate balance is given by equation (7), loss FFW = Fsys + FTU , E

(7)

where FFW denotes the total flowrate of freshwater allocated to the water network, Fsysloss represents the net water loss for a water network (which is normally a fixed value), FTU , E denotes final wastewater discharge to the environment (from interception units). From equation (7), it can be easily observe that in order to minimize fresh water flow rate, the final wastewater discharge ( FTU , E ) has to be minimized. The net water loss term in equation (7) can be calculated by the difference between the total flowrates of process sinks and sources as shown in Figure 2, given as in equation (8) that follows. N SK

N SR

j

i

loss Fsys = ∑ FSKj − ∑ FSRi

(8)

The excess flowrate from the process sources are typically sent to the waste interception system, which consists of several partitioning units in series, as shown in Figure 2. Thus the inlet in flowrate for the first interception unit ( FTUt , ∀t = 1 ) is taken as the surplus flowrate of water-using

system, which can be determined via overall flowrate balance around water-using system, such as equation (9), NTU

in prod loss FTUt = FFW + ∑ FTUt , sys − Fsys

∀t = 1

(9)

t

NTU

prod It indicates that the flowrate that allocated into the water-using system ( FFW + ∑ FTUt , sys ) minus t

the flowrate of water loss in the system ( Fsysloss ) determines the flowrate of discharged wastewater from the water-using system and all the discharged wastewater streams are sent to the first in interception system ( FTUt , ∀t = 1 ).

Next, the flowrate and mass balance for each interception unit can be performed, such as equations (10) and (11), in prod resd FTUt = FTUt + FTUt

∀t ∈ NTU

in in prod prod resd resd FTUt ⋅ CTUt = FTUt ⋅ CTUt + FTUt ⋅ CTUt

∀t ∈ NTU

resd where FTUt denotes the flowrate of the residual stream of the tth interception unit.

10


(10) (11)

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Typically, as shown in Figure 2, the product of the tth interception unit ( ∀t ∈ NTU , t ≤ NTU − 1 ) can be sent to the subsequent interception unit (t+1)th interception unit ( ∀t ∈ NTU , t ≤ NTU − 1 )) for further treatment, or sent for reuse/recycle in the water-using processes, or being discharged to the environment, with its flowrate balance given in equation (12). The inlet flowrate and concentration for the tth interception unit ( ∀t ∈ NTU , t ≤ NTU − 1 ) are set to follow those of the product stream from the previous interception unit, as described by equations (13) and (14). prod prod prod prod FTUt = FTUt ,TU ( t +1) + FTUt , sys + FTUt , e

in prod FTU ( t +1) = FTUt ,TU ( t +1)

in prod CTU ( t +1) = CTUt

∀t ∈ NTU , t ≤ NTU − 1

∀t ∈ NTU , t ≤ NTU − 1 ∀t ∈ NTU , t ≤ NTU − 1

(12) (13) (14)

prod where FTUt ,TU ( t +1) denotes the product stream flowrate of tth interception unit ( ∀t ∈ N TU , t ≤ NTU − 1 )

prod that is allocated to next interception unit, FTUt , sys denotes the flowrate of product stream of tth

prod interception unit ( ∀t ∈ NTU , t ≤ NTU − 1 ) that is allocated to the water-using system, FTUt , e denotes

the flowrate allocated from tth interception unit ( ∀t ∈ NTU , t ≤ NTU − 1 ) to the environment; which is typically utilized to dilute other waste streams in order to fulfill the environmental regulations. For the final interception unit ( t = NTU ) as shown in Figure 2, its product stream can only be allocated to the water-using system, or discharged into the environment, with its flow rate balance given in equation (15), prod prod prod FTUt = FTUt , sys + FTUt , e

∀t = NTU

(15)

Besides, the residual stream of the tth interception unit has low quality and is typically discharged to the environment. Hence, its flow rate balance is given as equation (16), resd resd FTUt = FTUt ,e

∀t ∈ NTU

(16)

resd where FTUt , e denotes the residual stream flowrate of tth interception unit that is discharged to the

environment. Since the product or residual streams of the interception units may be discharged to the environment, the flow rate balance can be determined by equation (17),

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NTU

NTU

t

t

resd prod FTU , e = ∑ FTUt , e + ∑ FTUt , e

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(17)

Besides, the quality of the discharged wastewater should fulfill the environmental regulations. Typically, the contaminant concentration of the discharged wastewater cannot exceed the maximum limit that is regulated by the environmental agency ( Cemax ), such as equations (18) and (19), NTU

Cemix =

NTU

resd prod prod ∑ FTUtresd,e ⋅ CTUt , e + ∑ FTUt , e ⋅ CTUt , e t

t

FTU ,e Cemix ≤ Cemax

(18) (19)

where Cemix denotes the mean concentration of the discharged wastewater. The difference between the mean concentration of discharged wastewater and the maximum limit that is regulated by the environmental agency ( Cemax ) is defined as ∆Ce , such as that given in equation (20), ∆Ce = Cemix − Cemax

(20)

In the following sections, two literature examples and an industrial case are used to illustrate the IPT procedure for targeting total water network with multiple partitioning interception units. Literature Example 1—FF problem Example 1 is a classical concentration-based FF problem adapted from Polley and Polley13. The limiting water data as well as fresh water concentration and maximum discharge limit are shown in Table 1. Table 2 on the other hand, shows the specifications for three interception units in used, i.e. TU1, TU2 and TU3. As shown, all units have different outlet concentrations and recovery ratio. The flow rate targeting steps are illustrated next.

Table 1. Limiting water data for example 1

Table 2. Specifications for interception units for example 1

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Step 1: All process sources and sinks are located in the first column of the IPT (Table 3), with their concentrations as well as those of the freshwater resources and outlet concentration of interception units arranged in increasing order in the second column. Duplicate values (if any) are removed. An arbitrary concentration ( Carbitrary , in parentheses) is added at the last entry of the column such that it is the largest value among all concentration, e.g. 300 ppm in Table 3. The arbitrary value is used to provide an endpoint for calculation and to assist the construction of the last segment of the LCC. To clearly represent the process sources or sinks in each concentration interval, the streams are represented by vertical arrows (see column 1 of Table 3) starting from their respective concentrations and end at the arbitrary concentration, with their limiting flow rates labeled below. Without the loss of generality, the concentration for the kth row is denoted as Ck , which fulfills the relationship shown as equation (21), C1 < C2 < … < Ck < … < Carbitrary

(21)

Step 2: Calculate the net flow rates ( Fknet ) of each concentration intervals in the third column, which are given by the difference between the total flow rates of the process sources and that of the sinks in each concentration intervals, given as in equation (22). Fknet = ∑ FSKj − ∑ FSRi j

∀CSKj , CSRi ≤ Ck

(22)

i

For instance, within the concentration interval of 100 – 150 ppm, there exist three process sinks (SK1, 50 t/h, SK2, 100 t/h, and SK3, 80 t/h) and two process sources (SR1, 50 t/h and SR2, 100 t/h) in the concentration interval. Hence, the net flow rate within this concentration interval is calculated as 80 t/h by solving equation (22). Note that the net flow rate corresponds to the inverse slope of the segment of LCC. Note also that the last entry of the third column in Table 3 is obtained by taking the difference between the total flow rate of all process sources and that of of all sinks. For Example 1, this corresponds to the 13



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total flow rate loss of 20 t/h ( Fsysloss ), i.e. the total flow rate of water sinks is 20 t/h higher than that of water sources. Step 3: Calculate the net loads ( ∆mknet ) in the fourth column, which is given by the product of the net flow rate with the concentration difference of the corresponding interval. This is given as in equation 23. ∆mknet = Fknet ⋅ (Ck − Ck −1 ) ∀k > 1

(23)

Step 4: Calculate the cumulative load ( ∆mkcum ) in the fifth column by equation (24). The cumulative load for the first row is set to be zero because of no load cumulated. The loads for all earlier rows are summed to obtain the cumulative load for kth row. The LCC in Figure 3 can then be constructed by plotting column 2 (concentration) vs. column 5 (cumulative load) in Table 3. ∆mkcum = 0 ∀k = 1  t =k  cum ∆mk = ∑ ∆mt ∀k > 1 t =1 

(24)

where t specifies index for tth row (t ≤ k). Step 5: Calculate the possible supply flow rates for freshwater resource (FFW) at each concentration level Ck ( CFW < Ck ≤ Carbitrary ) in the sixth column with equation (25). FFW =

∆mkcum Ck − CFW

∀CFW < Ck ≤ Carbitrary

(25)

where CFW denotes the concentration of freshwater resource (FW). For example 1, CFW is assumed to be zero. The maximum value in the sixth column (70 t/h) in Table 3 reveals the flow rate target for fresh water without considering the reuse/recycle of regenerated water, with its pinch concentration ( Cpinch ) located at 150 ppm. In order to reduce fresh water consumption, water regeneration may be considered. However, as discussed in Hallale 8 and Manan et al. 9, in order to reduce fresh resource consumption, regeneration needs to be carried out across the reuse/recycle pinch concentration, i.e. 14


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150 ppm in this case. Since the concentration of the product stream of the first treatment unit TU1 prod ( CTU 1 ) is 150 ppm, the recovery of the product of TU1 would not be able to reduce the fresh water

flowrate. Hence, the product of TU1 is allocated to subsequent interception unit (e.g. TU2) for further purification. This means that the product of TU1 allocated to water-using system ( FTUprod1,sys ) is set to zero. Additionally, since TU1 has a water recovery ratio of unity, the flowrate of its product resd stream is equals its inlet flowrate and FTUresd1,e and CTU 1 are set to zero. Since the concentrations of

prod prod products streams of TU2 ( CTU 2 =100 ppm) and TU3 ( CTU 3 =50 ppm) are both lower than that of the

pinch, the flowrate of FW would be reduced with the recovery of product streams from TU2 and TU3. It turns to the targeting problem with three resources (i.e., freshwater resource, 0 ppm; product stream of TU3, 50 ppm; product stream of TU2, 100 ppm) and the optimal flowrates for those three resources should be determined according to the increase order of concentrations. With the introduction of FTUprod 3 (50 ppm), the flowrate demand in the concentration interval of 50 – 300 ppm can be satisfied by this higher quality streams, which may lead to lower fresh water demand. Note however that the flowrate demand for sinks with concentrations lower than 50 ppm can only be fulfilled by freshwater resource and it limits the flowrate of freshwater. Therefore the maximum value in the concentration interval of 0 – 50 ppm in the sixth column (30 t/h) in Table 3 determines the target of FFW . However, it is not the final optimal flowrate for freshwater. The feasibility condition governed by equation (19) should be checked and the concentration of the discharged wastewater cannot exceed the maximum limit. Step 6: Calculate the minimum flow rates for product streams of interception units that would be recycled to the water-using system using equation (26). In the seventh column, we started with TU3 which will produce highest quality product stream among all interception units. The maximum 15



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value among all entries in this column (i.e. 70 t/h) locates the flow rate target for FTUprod 3, sys without considering other resources of lower quality (e.g. product stream of TU2). Note that the 3 corresponding concentration (100 ppm) is regarded as the interception pinch concentration ( C TU pinch )

for TU3. FTUprod 3, sys =

prod ∆mkcum − FFW (CTU 3 − CFW ) − FFW prod Ck − CTU 3

prod prod ∀CTU 3 < Ck ≤ CTU 2

(26)

prod Since the concentration of the product stream of TU2 ( CTU 2 ) is 100 ppm, which is equal to the

3 prod interception pinch concentration for TU3 ( C TU pinch ). Thus the product stream flowrate of TU3 ( FTU 3, sys )

will not be reduced if TU2 is introduced. The only way to reduce the TU3 product stream flowrate is to make use of fresh water. Note however that the interception pinch of TU3 would be shifted to a new location with the flowrate increase of freshwater flow rate. For instance, as FFW increases is shifted from 100 ppm to 100 from 30 t/h to 50 t/h, the interception pinch concentrations for FTUprod 3 ppm and 150 ppm (double pinched). Once FFW increases further (greater than 50 t/h), the interception pinch concentration for FTUprod is shifted to 150 ppm. Note that, the final optimal target 3 of FFW is 57.5 t/h (see Table 4) and the corresponding interception pinch concentration for FTUprod 3 is 150 ppm. If the interception pinch concentration of the product stream of TU3 is shifted to 150 ppm due to the flowrate increase of FFW , product stream of TU2 can now be considered for usage prod prod prod ( CTU 2 =100 ppm < 150 ppm ). FTU 3, sys can be reduced further with the introduction of FTU 2, sys

prod ( CTU 2 =100 ppm < 150 ppm ). Then the flowrate demand in the concentration interval of 100 – 300

ppm can be fulfilled by FTUprod 2, sys and it indicates that the flowrate demand in the concentration interval of 0 – 100 ppm is fulfilled by freshwater and FTUprod 3, sys . Especially, the demand within the concentration interval of 50 – 100 ppm limits the flowrate of FTUprod 3, sys and thus the maximum value in the concentration interval of 50 – 100 ppm in the seventh column (70 t/h) in Table 3 determines 16


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the target of FTUprod 3, sys . Note that, it is not the final optimal value and the feasibility condition should be checked. Next, calculate the product stream flow rates for TU2 in the eighth column via equation (27). The maximum value in the eighth column in Table 3 gives the minimum flow rate of FTUprod 2, sys , i.e. -20 t/h, and the corresponding concentration (150 ppm) locates the regeneration pinch for TU2. Obviously, the negative value for the flow rate is infeasible and the infeasibility will be removed in next step. FTUprod 2, sys =

prod prod prod prod ∆mkcum − FFW (CTU 2 − CFW ) − FTU 3, sys (CTU 2 − CTU 3 ) prod Ck − CTU 2

∀C

prod TU 2

− FFW − FTUprod 3, sys

(27)

< Ck ≤ Carbitrary

Equations (26) and (27) can be generalized to be equations (28) and (29), respectively. In addition, if the product stream of TU1 is also recycled to process sinks, its flowrate can be calculated by equation (30). Note however that for this case, TU1 is not used. Therefore Equation (29) is prod specialized into equation (27) and it is performed at all the concentration levels higher than CTU 2

and lower than/equal to Carbitrary . It is can be easily identified from the concentration conditions for equations (27) and (29). prod FTUt , sys =

prod ∆mkcum − FFW (CTUt − CFW ) − FFW prod Ck − CTUt

prod ∆mkcum − FFW (CTU ( t ) − C FW ) − prod TU ( t ), sys

F

NTU −1

∑

prod prod ∀CTU (t ) < Ck ≤ CTU ( t −1) , t = N TU

prod prod FTUprod ( t +1), sys (CTU ( t ) − CTU ( t +1) )

t =2 prod TU ( t )

=

− FFW −

Ck − C

NTU −1

∑

FTUprod ( t +1), sys

t=2

prod prod ∀CTU ( t ) < Ck ≤ CTU ( t −1) , t = 1, 2,3,..., N TU − 1

prod ∆mkcum − FFW (CTU (1) − C FW ) − prod TU (1), sys

F

NTU −1

∑

prod prod FTUprod ( t +1), sys (CTU (1) − CTU ( t +1) )

t =1 prod TU (1)

=

− FFW −

Ck − C

NTU −1

∑

FTUprod ( t +1), sys

t =1

prod ∀CTU (1) < Ck ≤ Carbitrary

(30)

Table 3. Improved problem table for Example 1 (preliminary solution)

17


(28)

(29)


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Step 7: Perform the mass balance and check the feasibility. The procedure can be divided into three sub-steps. loss resd Sub-step 1: Write down the values for FFW , FTUprod3,sys , FTUprod2, sys , FTUprod1,sys , FTUresd1,e , CTU 1 , Fsys ,

prod prod in FTU 1 , FTU 2, e , FTU 3, e .

In Step 6, the minimum flowrate of freshwater is determined as FFW =30 t/h. The minimum flowrate of the product stream of TU3 that is allocated to the water-using system is determined as prod resd FTUprod3,sys = 70 t/h). Similarly, FTUprod2, sys is determined as ﹣20 t/h. Additionally, FTU 1, sys , FTU 1, e and

loss resd CTU 1 are determined as zero. The total net flowrate for the system ( Fsys ) is calculated in Step 2 as

20 t/h. Next, FTUin 1 can be calculated as 60 t/h via solving equation (9). The products of TU2 and TU3 are of high quality and hence should be allocated to the water-using processes. Note that they are allowed to be discharged into environment if not being utilized in the water-using processes. Thus the values for FTUprod2, e and FTUprod3,e are assumed to be zero. The values for FFW , FTUprod3,sys , prod resd resd loss in prod prod FTUprod2, sys , FTU 1, sys , FTU 1, e , CTU 1 , Fsys , FTU 1 , FTU 2, e , FTU 3, e are written down and they are marked in

bold as shown in Table 3. prod resd resd in resd Sub-step 2: Calculate the values for FTUin 3 , FTUresd3,e , CTU 3 , FTU 2,TU 3 , FTU 2 , FTU 2, e , CTU 2 ,

FTUprod1,TU 2 , FTUprod1,e ,

FTU , e , Cemix , ∆Ce .

With the determined values FTUprod3,sys = 70 t/h, FTUprod3,e = 0 t/h and given value aTU 3 = 0.75, FTUin 3 can be calculated as 93.33 t/h by solving equations (5) and (12). Next FTUresd3,e is determined as 23.33 resd t/h via solving equation (10). Next CTU 3 is calculated as 250 ppm via solving equation (11). By

solving equation (13), FTUprod2,TU 3 is determined as 93.33 t/h. Next FTUin 2 is calculated as 91.67 t/h via solving equations (5) and (12) with the determined values FTUprod2, sys = ﹣20 t/h, FTUprod2,TU 3 =93.33 t/h, resd prod FTUprod2, e = 0 t/h and given value aTU 2 = 0.8. Next FTU 2, e is determined as 18.33 t/h via solving equation

prod resd (10). CTU 2 is determined as 350 ppm via solving equation (11) accordingly. FTU 1,TU 2 is determined

18


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as 91.67 t/h via solving equation (13). Next FTUprod1,e is calculated as﹣31.67 t/h via solving equations (5) and (10) with the determined values FTUin 1 = 60 t/h and FTUprod1,TU 2 = 91.67 t/h. Next FTU , e can be calculated as 10 t/h via solving equation (7) or (17). Cemix is determined as 750 via solving equation (18). ∆Ce is determined as 550 ppm via solving equation (20) with the given value Cemax =200 ppm. resd prod in resd resd prod prod The values for FTUin 3 , FTUresd3,e , CTU 3 , FTU 2,TU 3 , FTU 2 , FTU 2, e , CTU 2 , FTU 1,TU 2 , FTU 1, e ,

FTU , e , Cemix ,

∆Ce are calculated and they are marked in italic as shown in Table 3.

Sub-step 3: Check the feasibility and determine the optimal targets. Note that FTUprod1,e is﹣31.67 t/h and it indicates the infeasibility for the results. In addition, ∆Ce is 550 ppm and the optimal target for ∆Ce should be zero. The other variables in Sub-steps 1 and 2 can be related with the variable FFW via the equations mentioned in Sub-steps 1 and 2. The Excel Goal Seek feature is utilized to figure out the optimal target ∆Ce by changing the value of FFW . In the Excel Goal Seek control box, ∆Ce is set to be the target value of zero and the value of FFW is set to be altered variable. Once we click the “OK” button on the Excel Goal Seek control box, ∆Ce achieves zero and the values of all other variables are changed to be new results as shown in Table 4. Note that, the optimal flowrates of FFW , FTUprod3 and FTUprod2 are determined as 57.5 t/h, 15 t/h and 7.5 t/h as marked in bold in the sixth, seventh and eighth column of Table 4. In order to validate the optimal solutions, the example is solved using the automated targeting model58 which is presented in supplementary file. The solutions are identical with those determined via IPT and it indicates that the IPT results are feasible.

Table 4. Improved problem table for Example 1(optimal solution)

Step 8: Construct the optimal water supply line and design the optimal water network As shown in Figure 3, the first segment of water supply line can be constructed within the concentration interval of 0 – 50 ppm (Region 1), with its inverse slope corresponding to 57.5 t/h 19



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( FFW ). In other words, only freshwater is allocated to Region 1 to fulfill its water requirement. The second segment of water supply line can be constructed with the concentration interval of 50 – 100 ppm (Region 2) with its inverse slope corresponding to 72.5 t/h, where FFW (57.5 t/h) and FTUprod3,sys (15 t/h) are fed to remove the load of this region. Finally, the third segment of water supply line is constructed for concentration interval of 100 – 300 ppm (Region 3) with its inverse slope corresponding to 80 t/h, where FFW (57.5 t/h), FTUprod3,sys (15 t/h) and FTUprod2, sys (7.5 t/h) are used to remove the load in this region.

Figure 3. Limiting composite curve and optimal water supply line (Example 1)

An optimal water network as shown in Figure 4 that fulfills the optimal solutions can be synthesized using the Nearest Neighbors Algorithm (NNA)15.

Figure 4. Optimal water network for example 1 with multiple partitioning interception units (unit for the flow rate is t/h and unit for contaminant concentration is ppm in parenthesis)

Literature Example 2—FC problem Example 2 is a revised case in the literature of Wang and Smith10. Tables 5 and 6 show the limiting data for water-using processes and specified data for freshwater source and interception units. Note that there is no water loss existed for any water-using processes and it is a typical FC problem.

Table 5. Limiting water data for example 2

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Table 6. Specifications for interception units for example 2

Repeat Steps 1-7, the preliminary solution for example 2 is determined as shown in Table S1. Note that, FTUprod1,e equals - 15 t/h and ∆Ce is 650 ppm. It indicates that the solution is infeasible and non-optimal. The Excel Goal Seek feature is applied to determine the optimal and feasible solutions, which are shown in Table 7. The optimal flowrates of FFW and FTUprod2 are targeted as 72 t/h and 36 t/h, respectively. Repeat Step 8, the optimal water supply line is plotted shown in Figure 5 and Figure 6 illustrates the optimal water network which can be constructed via NNA15 on the basis of optimal solutions in Table 7.

Table 7. Improved problem table for example 2 (optimal solution)

Figure 5. Limiting composite curve and optimal water supply line (example 2)

Figure 6. An optimal water network for example 2 with multiple partitioning interception units (unit for the flow rate is t/h and unit for contaminant concentration is ppm in parenthesis)

Industrial Example 3—Property-based water network The wastewater interception and recovery system is an essential part of refinery plant. The oil-content wastewater streams generated from crude distillation unit, fluid catalytic cracking unit, delayed coking unit, diesel hydrotreating unit, gasoline hydrotreating unit, cooling water system, demineralized water station etc. are sent to wastewater interception unit for treatment. Figure 7 shows the current wastewater interception and recovery system of certain refinery plant in northwestern of China. As shown in Figure 7, the average total flowrate of oil-content wastewater is 21



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939 t/h and its mean COD is 260 ppm. The outlet COD for preliminary treatment unit is 20.22 ppm. The preliminary treatment includes regulation pool, floatation tank, BAF, flocculating settling pool and they are placed in series. 746 t/h of the preliminary treated wastewater is allocated to advanced treatment unit for further treatment. The advanced treatment unit includes five-ultrafiltration equipment and reverse osmosis. The recovery ratio for ultrafiltration and reverse osmosis are 0.9 and 0.78, respectively. The outlet stream with the COD of 2 ppm for advanced treatment unit is allocated to demineralized water station as the feed water. The other 193 t/h of the preliminary treated wastewater is utilized to dilute the residual wastewater generated from ultrafiltration and reverse osmosis and the COD of the mixed wastewater is 45.64 ppm, which is less than the maximum discharge COD (60 ppm) regulated by local environmental agency. The mixed wastewater is discharged to municipal wastewater pipeline for further treatment. There are four cooling water system using freshwater as supplement. The proposed generalized IPT is used to investigate the water conservation potential for the wastewater interception and recovery system. In addition, one more ultrafiltration equipment will be installed to enhance the capacity of advance treatment unit.

Figure 7. Current wastewater interception and recovery system of certain refinery plant

The current feed flowrates for cooling water systems and demineralized water station are extracted as their limiting inlet flowrates (i.e. 140 t/h for 1st cooling water system). The current flowrates of discharged wastewater from them are extracted as their limiting outlet flowrates (i.e. 35 t/h for 1st cooling water system). COD is identified as the key property for the wastewater interception and recovery system. The current CODs of discharged wastewater from cooling water 22


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systems and demineralized water station are extracted as their limiting outlet properties (i.e. 31 ppm for 1st cooling water system). The maximum allowable CODs for the inlet of cooling water systems and demineralized water station are extracted as limiting inlet properties (i.e. 8 ppm for 1st cooling water system). Note that the current water supply for various cooling water systems is freshwater with its COD of 2. It means various cooling water systems are fulfilled by water source with higher quality, which leads to the optimization possibility. The current flowrate and COD of wastewater generated from other units (802 t/h and 300 ppm) are extracted as limiting flowrate and property. In addition, the current CODs for freshwater, outlet of ultrafiltration and reverse osmosis are specified as the limiting properties. Those extracted data are shown in Tables 8 and 9.

Table 8. Limiting data for example 3

Table 9. Specifications for treatment units for example 3

As reported in the literature52, 54, 56, 57, the property operator of COD is itself as shown in equation (31) and the mixing rule shown in equation (3) can be used to determine the mixing COD of sources. ψ (COD) = COD

(31)

Repeat Steps 1-7 with the property operator ψ replacing concentration C, the preliminary solutions for example 3 are determined as shown in Table S2. Note that, in the Sub-step 1 of Step 7, the maximum value (522 t/h) in the property region ( 2 ppm < Ck ≤ 8 ppm ) indicates the minimum flowrate of water with COD of 2 ppm is 522 t/h. The current flowrate of freshwater with COD of 2 ppm is 344 t/h and it is listed in the seventh column. The flowrate of the product of reverse osmosis with COD of 2 ppm is calculated as 178 t/h (= 522 t/h – 344 t/h) and it is marked in bold in the eighth

23



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column of Table S2. Next, the maximum value (344 t/h) in the property region ( 8 ppm < Ck ≤ 31 ppm ) indicates the minimum flowrate of the product of ultrafiltration with COD of 8 ppm is 344 t/h. The total flowrate of wastewater is kept unchanged as 939 t/h. Note that, ∆ψ e equals – 21.92 ppm. It indicates that the property of discharged wastewater (ψ emix ) is less than the maximum limit that regulated by the environmental agency ( ψ emax ). Thus the solution is non-optimal. The Excel Goal Seek feature is applied to determine the optimal and feasible solutions, which are shown in Table 10. Repeat Step 8, the optimal water supply line is plotted shown in Figure 8 and Figure 9 shows the optimal water network which can be constructed via NNA 15 on the basis of optimal solutions in Table 10. The flowrate of freshwater is reduced to be 186.39 t/h and the reduction ratio reaches 45.8%.

Table 10. Improved problem table for Example 3 (optimal solution)


Figure 9. Optimal wastewater interception and recovery system for certain refinery plant (unit for the flow rate is t/h and unit for contaminant concentration is ppm in parenthesis)

Conclusion This paper presents a generalized Improved Problem Table (IPT) approach to target the concentration and property-based total water network with multiple partitioning interception units. The procedure for the IPT approach is illustrated via solving a revised literature example. The flowrate and mass balance equations for the total water network with multiple partitioning interception units are deduced thoroughly and they are embedded in the IPT to check the feasibility of the results. The IPT can be easily handled via Excel or other spreadsheet software and the Excel 24


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Goal Seek feature is applied to locate the optimal solutions and they are validated via automated targeting model58. On the basis of the data and the optimal solutions in IPT, the limiting composite curve and water supply line can be constructed. Two revised literature examples and property-based wastewater interception and recovery system of an industrial case are solved to show the feasibility and applicability of the proposed IPT to targeting FF or FC or practical water network.

Notation aTUt = recovery ratio for tth interception unit Carbitrary /ψ arbitrary = arbitrary concentration/property operator in the final concentration row Cemax /ψ emax = maximum concentration/property operator limit that regulated by the environmental

agency Cemix /ψ emix = mean concentration/property operator of discharged wastewater CFW /ψ FW = concentration/property operator of freshwater resource Ck /ψ k = concentration/property operator for the kth row

Cpinch /ψ pinch = concentration/property operator for the pinch point CSKj = inlet concentration of jth process sink max CSKj = maximum inlet concentration of jth process sink

min CSKj = minimum inlet concentration of jth process sink

CSRi = outlet concentration of ith process source prod CTUt = concentration of product stream of tth treatment unit

COD = Chemical Oxygen Demand FFW = total flowrate of freshwater that allocated to the water network Fknet = the net flow rates of each concentration intervals

FPTin = inlet flowrate of preliminary treatment unit FPTprod,sys = flowrate of product stream of preliminary treatment unit that is allocated to water-using

25



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system FPTresd,e = flowrate of rejected stream of preliminary treatment unit FPTprod,e = flowrate allocated from preliminary treatment unit to the environment FPTprod,UF = flowrate of product stream of preliminary treatment unit that is allocated to ultrafiltration

treatment unit in = inlet flowrate of reverse osmosis treatment unit FRO

resd FRO , e = flowrate of rejected stream of reverse osmosis treatment unit

prod FRO , e = flowrate allocated from reverse osmosis treatment unit to the environment

prod FRO , sys = flowrate of product stream of reverse osmosis treatment unit that is allocated to water-using

system FSKj = required flowrate for the jth process water sink FSRi = available flowrate for the ith process water source loss Fsys = net water loss existed in the water-using network

in = inlet flowrate of tth treatment unit FTUt

prod = purified product flowrate of tth treatment unit FTUt

resd = flowrates of the residual streams of the tth treatment unit FTUt

FTU , E = flowrate distributed from treatment units to the environment prod FTUt , e = flowrate allocated from tth treatment unit to the environment

resd FTUt , e = flowrate of rejected stream of tth treatment unit that discharged into the environment

prod FTUt , sys = flowrate of product stream of tth treatment unit that is allocated to water-using system

prod FTUt ,TU ( t +1) = flowrate of product stream of tth treatment unit that is allocated to next treatment unit

in FUF = inlet flowrate of ultrafiltration treatment unit

prod FUF , e = flowrate allocated from ultrafiltration treatment unit to the environment

resd FUF , e = flowrate of rejected stream of ultrafiltration treatment unit

prod FUF , RO = flowrate of product stream of ultrafiltration treatment unit that is allocated to reverse

26


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osmosis treatment unit prod FUF , sys = flowrate of product stream of ultrafiltration treatment unit that is allocated to water-using

system NFW = set of external sources or resources NSK = set of process sinks NSR = set of process sources NTU = set of partitioning interception units NNA = Nearest Neighbors Algorithm PFWm = property of mth resource PSKj = inlet property of jth process sink min PSKj = minimum property of jth process sink

PSRi = property of ith process source max = maximum property of jth process sink PSKj

xi = fractional contribution of ith source towards the total flow rate of mixture

ψ ( P ) = property operator on the mixture property ( P )

ψ ( PSKj ) = property operator on the sink property ( PSKj ) ψ ( PSRi ) = property operator on the source property ( PSRi ) ψ max ( PSKj ) = maximum property operator on the sink property ( PSKj ) ψ min ( PSKj ) = minimum property operator on the sink property ( PSKj ) resd ψ PT = concentration of rejected stream of preliminary treatment unit resd ψ RO =concentration of rejected stream of reverse osmosis treatment unit resd ψ UF = property operator of rejected stream of ultrafiltration treatment unit

∆Ce / ∆ψ e = the difference between Cemix /ψ emix and Cemax /ψ emax

∆mkcum = cumulative load ∆mknet = net loads

27



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Acknowledgements Financial support provided by the National Basic Research Program of China (No. 2012CB720500) and National Natural Science Foundation of China (No. 21276204 and 21576287) are gratefully acknowledged. The research is also supported China Postdoctoral Science Foundation (No. 2015M570215) and Science Foundation of China University of Petroleum, Beijing (No. 2462015BJB02 and 2462015YQ0305).

Supporting Information

The resource conservation cascade diagram for example 1 and the mathematical formulation for automated targeting model and Tables S1 and S2 are presented in the supplementary file. This information is available free of charge via the Internet at http://pubs.acs.org/.

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cascade analysis technique. AIChE Journal 2004, 50, (12), 3169-3183. 10. Wang, Y. P.; Smith, R., Wastewater minimisation. Chemical Engineering Science 1994, 49, (7), 981-1006. 11. El-Halwagi, M. M.; Manousiouthakis, V., Synthesis of mass exchange networks. AIChE Journal 1989, 35, (8), 1233-1244. 12. Dhole, V. R.; Ramchandani, N.; Tainsh, R. A.; Wasilewski, M., Make your process water pay for itself. Chemical Engineering 1996, 103, (1), 100-103. 13. Polley, G. T.; Polley, H. L., Design better water networks. Chemical Engineering Progress 2000, 96, (2), 47-52. 14. El-Halwagi, M. M.; Gabriel, F.; Harell, D., Rigorous graphical targeting for resource conservation via material recycle/reuse networks. Industrial & Engineering Chemistry Research 2003, 42, (19), 4319-4328. 15. Prakash, R.; Shenoy, U. V., Targeting and design of water networks for fixed flowrate and fixed contaminant load operations. Chemical Engineering Science 2005, 60, (1), 255-268. 16. Agrawal, V.; Shenoy, U. V., Unified conceptual approach to targeting and design of water and 29



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hydrogen networks. AIChE Journal 2006, 52, (3), 1071-1082. 17. Bandyopadhyay, S.; Ghanekar, M. D.; Pillai, H. K., Process water management. Industrial & Engineering Chemistry Research 2006, 45, (15), 5287-5297. 18. Foo, D. C. Y.; Manan, Z. A.; Tan, Y. L., Use cascade analysis to optimize water networks. Chemical Engineering Progress 2006, 102, (7), 45-52. 19. Alwi, S. R. W.; Manan, Z. A., Targeting multiple water utilities using composite curves. Industrial & Engineering Chemistry Research 2007, 46, (18), 5968-5976. 20. Foo, D. C. Y., Water cascade analysis for single and multiple impure fresh water feed. Chemical Engineering Research & Design 2007, 85, (A8), 1169-1177. 21. Ng, D. K. S.; Foo, D. C. Y.; Tan, R. R., Targeting for total water network. 1. Waste stream identification. Industrial & Engineering Chemistry Research 2007, 46, (26), 9107-9113. 22. Ng, D. K. S.; Foo, D. C. Y.; Tan, R. R., Targeting for total water network. 2. Waste treatment targeting and interactions with water system elements. Industrial & Engineering Chemistry Research 2007, 46, (26), 9114-9125. 23. Ng, D. K. S.; Foo, D. C. Y.; Tan, R. R.; Tan, Y. L., Ultimate flowrate targeting with regeneration placement. Chemical Engineering Research & Design 2007, 85, (A9), 1253-1267. 24. Shenoy, U. V.; Bandyopadhyay, S., Targeting for multiple resources. Industrial & Engineering Chemistry Research 2007, 46, (11), 3698-3708. 25. Alwi, S. R. W.; Manan, Z. A., Generic graphical technique for simultaneous targeting and design of water networks. Industrial & Engineering Chemistry Research 2008, 47, (8), 2762-2777. 26. Bandyopadhyay, S.; Cormos, C. C., Water management in process industries incorporating regeneration and recycle through a single treatment unit. Industrial & Engineering Chemistry 30


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Research 2008, 47, (4), 1111-1119. 27. Foo, D. C. Y., Flowrate targeting for threshold problems and plant-wide integration for water network synthesis. Journal of Environmental Management 2008, 88, (2), 253-274. 28. Deng, C.; Feng, X., Targeting for Conventional and Property-Based Water Network with Multiple Resources. Industrial & Engineering Chemistry Research 2011, 50, (7), 3722-3737. 29. Parand, R.; Yao, H. M.; Pareek, V.; Tadé, M. O., Use of Pinch Concept To Optimize the Total Water Regeneration Network. Industrial & Engineering Chemistry Research 2014, 53, (8), 3222-3235. 30. Bandyopadhyay, S., Source composite curve for waste reduction. Chemical Engineering Journal 2006, 125, (2), 99-110. 31. Castro, P.; Matos, H.; Fernandes, M. C.; Nunes, C. P., Improvements for mass-exchange networks design. Chemical Engineering Science 1999, 54, (11), 1649-1665. 32. Feng, X.; Bai, J.; Zheng, X. S., On the use of graphical method to determine the targets of single-contaminant regeneration recycling water systems. Chemical Engineering Science 2007, 62, (8), 2127-2138. 33. Bai, J.; Feng, X.; Deng, C., Graphically based optimization of single-contaminant regeneration reuse water systems. Chemical Engineering Research & Design 2007, 85, (A8), 1178-1187. 34. Ng, D. K. S.; Foo, D. C. Y.; Tan, R. R.; Tan, Y. L., Extension of targeting procedure for “Ultimate Flowrate Targeting with Regeneration Placement” by Ng et al., Chem. Eng. Res. Des., 85 (A9): 1253–1267. Chemical Engineering Research and Design 2008, 86, (10), 1182-1186. 35. Wang, Y.; Smith, R., Design of distributed effluent treatment systems. Chemical Engineering Science 1994, 49, (18), 3127-3145. 31



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36. Kuo, W. C. J.; Smith, R., Effluent treatment system design. Chemical Engineering Science 1997, 52, (23), 4273-4290. 37. Kuo, W. C. J.; Smith, R., Designing for the interactions between water-use and effluent treatment. Trans IChemE, Part A, Chemical Engineering Research & Design 1998, 76, (A3), 287-301. 38. Soo, S. S. T.; Toh, E. L.; Yap, K. K. K.; Ng, D. K. S.; Foo, D. C. Y., Synthesis of distributed wastewater treatment networks for one- and two-contaminant systems. Chemical Engineering Research and Design 2013, 91, (1), 106-119. 39. Bandyopadhyay, S., Targeting minimum waste treatment flow rate. Chemical Engineering Journal 2009, 152, (2-3), 367-375. 40. Liu, Z.-H.; Shi, J.; Liu, Z.-Y., Design of distributed wastewater treatment systems with multiple contaminants. Chemical Engineering Journal 2013, 228, 381-391. 41. Liu, Z.-H.; Shi, J.; Liu, Z.-Y., Design of wastewater treatment networks with single contaminant. Chemical Engineering Journal 2012, 192, (0), 315-325. 42. El-Halwagi, M., Process Integration. Elsevier: San Diego, 2006. 43. Foo, D. C. Y.; Kazantzi, V.; El-Halwagi, M. M.; Manan, Z. A., Surplus diagram and cascade analysis technique for targeting property-based material reuse network. Chemical Engineering Science 2006, 61, (8), 2626-2642. 44. Kazantzi, V.; El-Halwagi, M. M., Targeting material reuse via property integration. Chemical Engineering Progress 2005, 101, (8), 28-37. 45. Qin, X.; Gabriel, F.; Harell, D.; El-Halwagi, M. M., Algebraic techniques for property integration via componentless design. Industrial & Engineering Chemistry Research 2004, 43, (14), 32


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3792-3798. 46. El-Halwagi, M. M.; Glasgow, I. M.; Qin, X. Y.; Eden, M. R., Property integration: Componentless design techniques and visualization tools. AIChE Journal 2004, 50, (8), 1854-1869. 47. Shelley, M. D.; El-Halwagi, M. M., Component-less design of recovery and allocation systems: a functionality-based clustering approach. Computers & Chemical Engineering 2000, 24, (9-10), 2081-2091. 48. Deng, C.; Wen, Z.; Foo, D. C. Y.; Ng, D. K. S.; Feng, X., Improved Ternary Diagram Approach for the Synthesis of a Resource Conservation Network with Multiple Properties. 2. Regeneration Reuse/Recycle. Industrial & Engineering Chemistry Research 2014, 53, (45), 17671-17679. 49. Deng, C.; Wen, Z.; Foo, D. C. Y.; Feng, X., Improved Ternary Diagram Approach for the Synthesis of a Resource Conservation Network with Multiple Properties. 1. Direct Reuse/Recycle. Industrial & Engineering Chemistry Research 2014, 53, (45), 17654-17670. 50. Ng, D. K. S.; Foo, D. C. Y.; Tan, R. R.; Pau, C. H.; Tan, Y. L., Automated targeting for conventional and bilateral property-based resource conservation network. Chemical Engineering Journal 2009, 149, (1-3), 87-101. 51. Ponce-Ortega, J. M.; Hortua, A. C.; El-Halwagi, M.; Jimenez-Gutierrez, A., A Property-Based Optimization of Direct Recycle Networks and Wastewater Treatment Processes. Aiche Journal 2009, 55, (9), 2329-2344. 52. Napoles-Rivera, F.; Ponce-Ortega, J. M.; El-Halwagi, M. M.; Jimenez-Gutierrez, A., Global optimization of mass and property integration networks with in-plant property interceptors. Chemical Engineering Science 2010, 65, (15), 4363-4377. 53. Ng, D. K. S.; Foo, D. C. Y.; Tan, R. R.; El-Halwagi, M., Automated targeting technique for 33



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concentration- and property-based total resource conservation network. Computers & Chemical Engineering 2010, 34, (5), 825-845. 54. Ponce-Ortega, J. M.; El-Halwagi, M. M.; Jimenez-Gutierrez, A., Global optimization for the synthesis of property-based recycle and reuse networks including environmental constraints. Computers & Chemical Engineering 2010, 34, (3), 318-330. 55. Grooms, D.; Kazantzi, V.; El-Halwagi, M., Optimal synthesis and scheduling of hybrid dynamic/steady-state property integration networks. Computers & Chemical Engineering 2005, 29, (11-12), 2318-2325. 56. Ponce-Ortega, J. M.; Mosqueda-Jiménez, F. W.; Serna-González, M.; Jiménez-Gutiérrez, A.; El-Halwagi, M. M., A property-based approach to the synthesis of material conservation networks with economic and environmental objectives. AIChE Journal 2011, 57, (9), 2369-2387. 57. Rubio-Castro, E.; Ponce-Ortega, J. M.; Serna-González, M.; El-Halwagi, M. M.; Pham, V., Global optimization in property-based interplant water integration. AIChE Journal 2013, 59, (3), 813–833. 58. Ng, D. K. S.; Foo, D. C. Y.; Tan, R. R., Automated Targeting Technique for Single-Impurity Resource Conservation Networks. Part 2: Single-Pass and Partitioning Waste-Interception Systems. Industrial & Engineering Chemistry Research 2009, 48, (16), 7647-7661. 59. Tan, R. R.; Ng, D. K. S.; Foo, D. C. Y.; Aviso, K. B., A superstructure model for the synthesis of single-contaminant water networks with partitioning regenerators. Process Safety and Environmental Protection 2009, 87, (3), 197-205.

34


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Tables Table 1. Limiting water data for example 1 Table 2. Specifications for interception units for example 1 Table 3. Improved problem table for Example 1 (preliminary solution) Table 4. Improved problem table for Example 1(optimal solution) Table 5. Limiting water data for example 2 Table 6. Specifications for interception units for example 2 Table 7. Improved problem table for example 2 (optimal solution) Table 8. Limiting water data for example 3 Table 9. Specifications for interception units for example 3 Table 10. Improved problem table for example 3 (optimal solution)

35



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Table 1. Limiting water data for example 1 Limiting inlet flow Process

rate, FSKj

Limiting outlet flow rate, FSRi

(t/h)

(t/h) P1 P2 P3 P4

50 100 80 70

50 100 70 60

Maximum inlet concentration,

Outlet concentration,

max CSKj

CSRi

(ppm)

(ppm)

20 50 100 200

50 100 150 250

Cemax = 200 ppm FFW

To be determined

CFW = 0 ppm

36


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Table 2. Specifications for interception units for example 1 Product stream concentration, Treatment unit TU1 TU2 TU3

Recovery ratio,

prod (ppm) CTUt

aTUt

150 100 50

1 0.8 0.75

37



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Table 3. Improved problem table for Example 1 (preliminary solution) Process Sources and Sinks

Ck (ppm)

Fknet (t/h)

∆mknet (g/h)

0

0

0

∆mkcum (g/h)

FFW (t/h)

FTUprod3 (50 ppm) FTUprod2 (100ppm)

0

20 50

0

0

1500

30

6500

65

70

10500

70

60

-20

11000

55

33.33

-55

15000

60

37.5

-43.33

(16000)

(53.33)

(28)

(-52.5)

1500

50 100

5000

80

4000

100 150 10

500

200 80

4000

250

(20)

(1000)

(300) SK1 SK2 SK3 SK4 SR1 SR2 SR3 SR4 50 100 80 70 50 100 70 60

Eq. (9)

in FTU 1

FFW

prod FTU 1, sys

FTUprod2, sys

FTUprod3,sys

loss Fsys

60

30

0

-20

70

20

38


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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48


Eqs. (10) (12) & (13)

Eqs. (10) (12) & (13)

Eqs. (10) (12) & (13)

Eq. (7) or (17)

in FTU 1

FTUprod 1, sys

FTUprod1,TU 2

FTUprod1,e

FTUresd1,e

resd CTU 1

60

0

91.67

-31.67

0

0

in FTU 2

FTUprod2, sys

FTUprod2,TU 3

FTUprod2,e

FTUresd2, e

resd CTU 2

91.67

-20

93.33

0

18.33

350

in FTU 3

FTUprod3,sys

FTUprod3,e

FTUresd3,e

resd CTU 3

93.33

70

0

23.33

250

FTU , e

Equation (20)

10

Cemix

∆Ce

750

550

39



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Page 40 of 59

Table 4. Improved problem table for Example 1(optimal solution) Process Sources and Sinks

Ck (ppm)

Fknet (t/h)

∆mknet (g/h)

0

0

0

∆mkcum (g/h)

FFW (t/h)

FTUprod3 (50 ppm) FTUprod2 (100ppm)

0

20 50

0

0

1500

57.5

6500

65

15.00

10500

70

18.75

7.50

11000

55

-3.33

-27.50

15000

60

3.13

-15.83

(16000)

(53.33)

(-5)

(-25)

1500

50 100

5000

80

4000

100 150 10

500

200 80

4000

250

(20)

(1000)


Eq. (9)

in FTU 1

FFW

prod FTU 1, sys

FTUprod2, sys

FTUprod3,sys

loss Fsys

60

57.5

0

7.5

15

20

40


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Eqs. (10) (12) & (13)

Eqs. (10) (12) & (13)

Eqs. (10) (12) & (13)

Eq. (7) or (17)

in FTU 1

FTUprod 1, sys

FTUprod1,TU 2

FTUprod1,e

FTUresd1,e

resd CTU 1

60

0

34.38

25.62

0

0

in FTU 2

FTUprod2, sys

FTUprod2,TU 3

FTUprod2,e

FTUresd2, e

resd CTU 2

34.38

7.5

20

0

6.875

350

in FTU 3

FTUprod3,sys

FTUprod3,e

FTUresd3,e

resd CTU 3

20

15

0

5

250

FTU , e

Equation (20)

37.5

Cemix

∆Ce

200

0.00

41



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Page 42 of 59

Table 5. Limiting water data for example 2 Limiting flow

Maximum inlet

Outlet concentration,

rate,

max concentration, CSKj

CSRi

(t/h)

(ppm)

(ppm)

Massload Process

(g/h)

P1

2000

20

0

100

P2 P3 P4

5000 30000 4000

100 40 10

50 50 400

100 800 800

Cemax = 200 ppm

FFW

CFW = 0 ppm

To be determined

42


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Table 6. Specifications for interception units for example 2 Product stream concentration, Interception unit TU1 TU2

Recovery ratio,

prod (ppm) CTUt

aTUt

150 50

1 0.8

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Table 7. Improved problem table for Example 2 (optimal solution) Process Sources and Sinks

Ck (ppm)

Fknet (t/h)

∆mknet (g/h)

20

1000

0

∆mkcum (g/h)

FFW (t/h)

FTUprod3 (50 ppm)

0

50 160

72

9000

90

36

21000

52.5

-22.29

41000

51.25

-22.13

(41000)

(41)

-32.63

8000

100 40

12000

50

20000

400 800 (0)

1000

(0)


Eq. (9)

Eqs. (10) (12) & (13)

Eqs. (10) (12) & (13)

in FTU 1

FFW

prod FTU 1, sys

FTUprod2, sys

loss Fsys

108

72

0

36

0

in FTU 1

prod FTU 1, sys

FTUprod1,TU 2

FTUprod1,e

FTUresd1,e

resd CTU 1

108

0

45

63

0

0

in FTU 2

FTUprod2, sys

FTUprod2, e

FTUresd2,e

resd CTU 2

44


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45 Eq. (7) or (17)

FTU , e

36 Equation (20)

72

0 Cemix

∆Ce

200

0

45


9

550


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 46 of 59

Table 8. Limiting data for example 3 Limiting inlet Process

flow rate, FSKj (t/h)

1# Cooling water system 2# Cooling water system 3# Cooling water system 4# Cooling water system 1#Demineralized water station 2#Demineralized water station 3#Demineralized water station

Limiting outlet flow rate, FSRi

Maximum inlet max property, PSKi

(t/h)

140

35

108

29

46

12

50

13

167

15.3

127

11.7

228

21 Cemax = 60 ppm

FFW

To be determined

CFW = 2 ppm

46


(ppm)

Outlet property, PSRi

(ppm)

8

31

2

22

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Table 9. Specifications for interception units for example 3 Product stream property, Interception unit Preliminary treatment (PT) Ultrafiltration (UF) Reverse osmosis (RO)

Recovery ratio,

prod (ppm) PTUt

aTUt

20.22

1

8

0.8

2

0.78

47



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Page 48 of 59

Table 10. Improved problem table for Example 3 (optimal solution) Process Sources and Sinks

ψ k (ppm)

Fknet (t/h)

∆mknet (g/h)

∆mkcum (g/h)

F2 ppm (t/h)

FFW (t/h)

prod prod FRO , sys (2ppm) FUF , sys (100ppm)

(t/h) 2

0 522

3132

866

12124

8 22 818

3132

522

186.39

335.61

15256

762.8

576.41

344

22618

779.93

593.54

325.22

218719

733.96

547.57

216.31

(217989)

(707.76)

(521.37)

(189.45)

7362

31 729

196101

(-73)

(-730)

300 (310)

SKCW SKDW SRCW SRDW SRDW 344 522 89 48 802 Eq. (9)

Eqs. (10) (12) & (13)

(t/h)

FPTin

FFW

FPTprod,sys

prod FUF , sys

prod FRO , sys

loss Fsys

939

186.39

0

344

335.61

-73

in FPT

FPTprod,sys

FPTprod,UF

FPTprod,e

FPTresd,e

resd ψ PT

939

0

860.30

78.70

0

0

48


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Eqs. (10) (12) & (13)

Eqs. (10) (12) & (13)

Eq. (7) or (17)

in FUF

prod FUF , sys

prod FUF , RO

prod FUF ,e

resd FUF ,e

resd ψ UF

860.30

344

430.27

0

86.03

130.2

in FRO

prod FRO , sys

prod FRO ,e

resd FRO ,e

resd ψ RO

430.27

335.61

0

94.66

29.27

FTU , e

Equation (20)

259.39

ψ emix

∆ψ e

60.00

0.00

49



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Figures Figure 1. Two models of interception systems: (a) single-pass interception system; (b) partitioning interception system 58 Figure 2. Superstructural representation for a total water network with multiple partitioning interception units Figure 3. Limiting composite curve and optimal water supply line (example 1) Figure 4. Optimal water network for example 1 with multiple partitioning interception units (unit for the flow rate is t/h and unit for contaminant concentration is ppm in parenthesis) Figure 5. Limiting composite curve and optimal water supply line (example 2) Figure 6. An optimal water network for example 2 with multiple partitioning interception units (unit for the flow rate is t/h and unit for contaminant concentration is ppm in parenthesis) Figure 7. Current wastewater interception and recovery system of certain refinery plant Figure 8. Limiting composite curve and optimal water supply line (example 3) Figure 9. Optimal wastewater interception and recovery system for certain refinery plant (unit for the flow rate is t/h and unit for contaminant concentration is ppm in parenthesis)

50


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Figure 1. Two models of interception systems: (a) single-pass interception system, (b) partitioning interception system58

51



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Figure 2. Superstructural representation for a total water network with multiple partitioning interception units

52


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53



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 4. Optimal water network for example 1 with multiple partitioning interception units (unit for the flow rate is t/h and unit for contaminant concentration is ppm in parenthesis)

54


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Figure 5. Limiting composite curve and optimal water supply line (example 2)

55



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Figure 6. An optimal water network for example 2 with multiple partitioning interception units (unit for the flow rate is t/h and unit for contaminant concentration is ppm in parenthesis)

56


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Figure 7. Current wastewater interception and recovery system of certain refinery plant

57



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58


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Figure 9. Optimal wastewater interception and recovery system for certain refinery plant (unit for the flow rate is t/h and unit for contaminant concentration is ppm in parenthesis)

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Flow Rate Targeting for Concentration- and Property-Based Total

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