Automated Pinch-Based Approach for the Optimum Synthesis of a

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An Automated Pinch-based Approach for the Optimum Synthesis of Water Regeneration-Recycle Network – Study on Interaction of Important Parameters Reza Parand, Hong Mei Yao, Dominic Chwan Yee Foo, and Moses O. Tade Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.6b01372 • Publication Date (Web): 22 Sep 2016 Downloaded from http://pubs.acs.org on September 24, 2016

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Industrial & Engineering Chemistry Research

An Automated Pinch-based Approach for the Optimum Synthesis of Water Regeneration-Recycle Network – Study on Interaction of Important Parameters Reza Paranda,b,*, Hong Mei Yaoa, Dominic C.Y. Fooc, Moses O. Tadéa a Department of Chemical Engineering, Curtin University, GPO Box U1987, Perth, WA 6845, Australia. b Australasian Joint Research Centre for Building Information Modelling, School of Built Environment, Curtin University, GPO Box U1987, Perth, WA 6845, Australia. c Centre of Excellence for Green Technologies/Department of Chemical and Environmental Engineering, University of Nottingham Malaysia, Broga Road, 43500 Semenyih, Selangor, Malaysia.

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Abstract

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In this work, a recently developed Automated Composite Table Algorithm (ACTA) (Parand et al. Clean

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Technol. Environ. Policy. 2016, DOI: 10.1007/s10098-016-1138-7) is improved to explore the

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interactions among important key parameters for a water regeneration-recycle network of single

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contaminant problem. The improved ACTA is based on Pinch Analysis, but is automated for the

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various targeting tasks. In most of the literature for water regeneration-recycle network synthesis,

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the post-regeneration concentration (Co) is treated as a fixed parameter. However, the other key

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parameters (i.e. freshwater, wastewater, regenerated water flowrates, along with wastewater and

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pre-regeneration concentrations) vary with the change of Co. With the use of improved ACTA, the

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interactions among these key parameters are analysed for both types of regeneration units, i.e. fixed

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Co and fixed Removal Ratio (RR). The exploration of these interactions also enables the water

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network to be optimised for economic purposes at the targeting stage. The improved ACTA is

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demonstrated using literature examples for both fixed load and fixed flowrate problems.

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Key words: Pinch Analysis, regeneration-recycle, water minimisation, targeting, Process Integration

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1. Introduction

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Environmental sustainability regulations, the rising cost of raw material and waste treatment, and

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increasingly stringent emission regulations are the factors that encourage resource conservation in

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the process industry in the past decades. Concurrently, Process Integration (PI) has gained good

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attention since the 1970s as a promising tool in resource conservation activities and hence to

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promote sustainable development in the process industry. Most recent PI tools and their

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applications are documented in a handbook1 and an encyclopaedia chapter2.

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Corresponding author. Telephone: +61 8 9266564. E-mails: [email protected], [email protected] (R.Parand); [email protected] (H.M.Yao); [email protected] (D.C.Y.Foo); [email protected] (M.O.Tadé) Page 1 of 33 ACS Paragon Plus Environment


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Among various industrial resources, the one that was being researched the most is arguably water.

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Rapid depletion of water resources along with increased water demand causes a water scarcity

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which severely affects many parts of the world. Therefore, water conservation activities have

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attracted the attention of policy makers, researchers, and industrial practitioners. Among these

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practices, water minimisation through PI has made a remarkable progress since mid-1990s, started

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with the seminal work of Wang and Smith3. Water-using operations are mainly categorised into fixed

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load (FL) and fixed flowrate (FF) processes. The mass transfer is the main concern for the FL

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processes and the water flowrate through the water-using processes is deemed to be constant. For

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the FF model, however, the inlet and outlet flowrates for the processes could vary and hence, the

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flowrate loss/gain could be considered readily. It is worth noting that the FL and FF models are

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interchangeable for single contaminant problems, and thus can be addressed by the same targeting

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tools 4.

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Two major approaches for water network synthesis can be categorised as the Pinch Analysis (PA)

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techniques and mathematical optimization methods. The former offers in-depth view for the

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engineers; but requires problem simplification. On the other hand, mathematical optimization

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approach can solve complex problems (e.g. multiple contaminants, topological constraints, and

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representative cost functions), however, achieving global optimum is a challenge. After two decades

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of development, various promising PI tools for water network synthesis have been developed, and

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documented in several review papers4-9 and a textbook10. The first review paper by Bagajewicz 6

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considers both PA and mathematical programming approaches, with the emphasis on the latter.

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Foo4 reviewed specifically the application of PA methods for single-contaminant problems for both

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FL and FF models. Jeżowski8 classified all key contributions in the alphabetic order by providing the

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problem statements and the solution methods. Gouws et al.7 presented an overview on the batch

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processes. In the review of Khor et al.9, the mathematical optimization based methods were

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systematically discussed by giving the key milestone and challenges. Ahmetovic et al.5 provided an

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overview on synthesis of non-isothermal water network synthesis, in which both water and energy

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integration are considered simultaneously.

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The seminal contribution on regeneration targeting using PA technique was made by Wang and

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Smith3. The graphical Limiting Composite Curve (LCC) was proposed for the water regeneration

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problem. The reuse/recycle pinch is taken as a pinch point in regeneration system. This assumption

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is not generic enough and fails to find the minimum freshwater and regenerated water flowrates 11.

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Kuo and Smith 12 later developed a methodology to deal with more generic problems. This approach

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needs an iterative procedure to migrate the process between freshwater and regeneration regions.

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Feng et al. 13 introduced some valuable conceptual insight to the water regeneration problem with Page 2 of 33 ACS Paragon Plus Environment

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the use of LCC. It was demonstrated that the pre-regeneration concentration (Creg) can be located

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either below or above the reuse/recycle pinch point. The Mass Problem Table 14 was also extended

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as an algebraic targeting technique to complement the graphical LCC. These techniques, however,

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are more favour for the FL model, where water loss/gain is not too significant such as those in the FF

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problems.

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Hallale 15 established the seminal guidelines for regeneration targeting for the FF problems. A water

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network can be divided into two regions, i.e. below the pinch (with surplus of water) and above the

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pinch (with deficit of water). Hallale15 suggested that regeneration unit should be placed across the

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pinch concentration , in order to collect water from region with surplus of water below the pinch,

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partially purify it, and discharge it to the region with deficit of water above the pinch. These

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targeting rules lead to the reduction of overall freshwater demand. Based on the Hallale’s guideline,

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Material Recovery Pinch Diagram (MRPD) 16 and Water Cascade Analysis (WCA) 17 were made use to

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identify freshwater and wastewater flowrates in such systems. However, none of these targeting

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methods is capable to determine the optimum freshwater, wastewater and regenerated water

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flowrates at the same time. This limitation was later addressed through a algebraic method

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proposed by Ng et al. 18. The procedure however is tedious due to its iterative characteristics that is

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based on the work of Kuo and Smith12. The Composite Table Algorithm (CTA) 19 has the same

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capability as Ng et al.’s18 method does, but with less effort required. First, the CTA produces data in

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tabular format. Second, the targets for water regeneration system i.e. freshwater and regenerated

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water flowrates were determined through LCC. Based on the CTA, the improved problem table20 was

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developed for multiple water sources problem which includes regeneration unit. This approach was

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recently extended by Deng et al.21 to consider multiple participating regeneration units. The main

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limitation of CTA19 is that, the reuse/recycle pinch point is taken as the first regeneration pinch

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point. However, as will be shown in this work, the targets may not be reliable for some cases. This is

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mainly because the pinch point for a water regeneration-recycle network may change according to

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the turning point of the LCC 22; the latter phenomena is due to the change of the post- regeneration

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concentration (Co). Thus, this assumption is not generic enough.

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Note that in general, regeneration unit is categorised as fixed Co or fixed removal ratio (RR) types 3.

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Most of PA techniques mentioned above are limited to a fixed Co value in the targeting stage. Some

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works try to relax the assumption of fixed Co but none of them can handle RR-type regeneration unit

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due to complexity of the problem. Xu et al.23 made an attempt to vary the Co and analyse the

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relationship between regeneration concentration and regeneration pinch. Fan et al.24 also have

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considered various range of Co by deploying graphical approach. Two situations have been

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considered, i.e. with the Co being lower or higher than the lowest limiting inlet concentration. Page 3 of 33 ACS Paragon Plus Environment


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Shenoy and Shenoy25 proposed continuous targeting technique to consider a range of Co values for

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zero liquid discharge (ZLD) water network. Yan et al.26 developed the inflection point method to

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relax the assumption of fixed Co in the targeting stage. The relationship between minimum

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freshwater and regenerated water flowrate was studied. Despite of their scientific contributions,

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these methods suffer from several common problems. First, these techniques cannot consider the

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entire range of feasible Co values. Second, they are unable to address the RR-type regeneration unit.

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Third, most of these methods23, 24, 26 are reported for the FL problems.

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At this end, it is worthwhile to point out three important research gaps for the targeting of water

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regeneration-recycle network as follows:

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•

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have been developed for the RR-type regeneration unit. •

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Most developed techniques focus on regeneration units of the fixed Co. Very limited works

There is a lack of in-depth analysis to explore the interactions among various process parameters in the literature.

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Economic analysis is hardly discussed in the literature of PA. This is mainly due to the nature of the techniques that were normally carried out manually.

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The key parameters to design a water regeneration-recycle network are freshwater and regenerated

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water flowrates, as well as pre-regeneration and post-regeneration concentrations. These

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parameters are highly interdependent, and also affect the total cost of the network. The post-

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regeneration concentration (Co) has been treated as a fixed parameter in most of the existing

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literature 3, 13, 18, 19 on water network synthesis. Note that the freshwater and wastewater flowrates

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of a water network will decrease with the decrease of Co value, which in turn leads to reduced

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operating cost. In contrary, the regeneration cost increases with the decrease of Co value, since

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regeneration unit of higher performance is required. Thus, analysing the effect of Co on the total cost

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is an economic optimisation problem. In an earlier work by the authors 22, the composite matrix

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analysis was developed to study the interactions of key parameters in a water regeneration-reuse

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network. The RR-type regeneration units were also addressed. However, the freshwater and

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regenerated water flowrates should be identical for the water regeneration-reuse system because

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water recycling is not allowed. For a water regeneration-recycle network (this study), the freshwater

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and regenerated water flowrates are not necessarily the same. A new algorithm, therefore, needs to

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be developed to cater for this problem. This study aims at developing a methodology that relaxes

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the assumption of fixed Co for water regeneration-recycle network that utilises both fixed Co or RR

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types regeneration units. The automated composition table algorithm (ACTA) that considers ZLD

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possibility in targeting a water regeneration-recycle network was recently proposed by Parand et Page 4 of 33 ACS Paragon Plus Environment

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al.27. The developed algorithm is however limited to fixed Co regeneration units. In this study, the

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recently established ACTA targeting procedure27 is improved by taking the incremental increase of Co

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into consideration. The three main contributions of this study are given as follows:

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•

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To identify a set of optimum key parameters for a water regeneration-recycle system, ahead of network design;

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To explore the interactions among these key parameters ;

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And to identify parameters contributions towards economic performance of a water

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regeneration-recycle network.

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Note that the ACTA can handle medium and large problems since it is fully automated. It is,

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however, limited to single contaminant problems, similar to most PA methods.

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The paper is structured as follows. Next section gives the problem statement. The improved ACTA

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technique is explained step by step based on the FL problem. The interaction among key parameters

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of water generation-recycle network is studied as a result of the improved ACTA. Next, the economic

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evaluation model is presented. The RR-type regeneration unit is discussed. The improved ACTA

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model is also applied for a FF problem, before the concluding remarks are made.

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2. Problem statement Consider a water network that consists of the following units: •

Processes that demand water, designated as process sinks or SKj (j=1, 2, …, m). Every sink

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requires a fixed flowrate of water (FSKj) and has maximum inlet concentration (CSKj), which is

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bound by the highest concentration limit (CSKjmax), i.e. CSKj ≤ Cskjmax

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•

Processes that produce water, in which may be sent for reuse or recycle to the process sinks,

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designated as process sources, or SRi (i= 1, 2,…, n). Each source has a fixed flowrate (FSRi),

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and an impurity concentration (CSRi).

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Water regeneration unit of known performance (fixed Co or fixed RR type), that may be used

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to purify water sources before they are recycled to the process sinks. Water sources enter

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regeneration unit at pre-regeneration concentration (Creg). The flowrate loss for the

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regeneration unit is assumed to be negligible. This is termed as the single pass regeneration

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unit 10.

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•

When the process sinks cannot be satisfied by the process sources, either due to quality

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(contaminant mass load) or quantity (flowrate) constraints, an outsourced freshwater

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(regarded as an external source) with flowrate of Ffw and contaminant concentration of Cfw is

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sources (if any) will be disposed as waste stream (with concentration of Cww and flowrate of

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Fww).

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Figure 1. Superstructure Presentation of the model

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Figure 1 depicts the superstructure presentation of the model. The main objective is to determine

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the various flowrate targets of a water regeneration-recycle network, i.e. Ffw, Fww, Freg, along with

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other important process parameters (e.g. Creg, and Cww). In addition, economic evaluation model is

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incorporated to determine a cost optimum water regeneration network.

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3. Methodology and Example 1 13, 19

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Figure 2 shows the LCC that is widely used for targeting water regeneration-recycle system

.

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Note that each water network has a distinctive LCC with different turning points. The existence of

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two regeneration pinch points (e.g. Pinch 1 and Pinch 2 in Figure 2) is common for a water

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regeneration-recycle system. As shown in previous works 13, 19, the regeneration pinch points dictate

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the shape of the water supply line (WSL), as well as the various water network targets (i.e. the

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freshwater, wastewater and regenerated water flowrates) for a given Co value. It is also worth

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mentioning that for some cases, Pinch 1 and Pinch 2 may overlap for a confined range of Co (i.e. only

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single regeneration pinch exists). This fact will be explained in the later sections. For the LCC in

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Figure 2, the freshwater line starts at the origin and terminates at Creg (indicated by dotted line). The

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inverse slope of this freshwater line identifies the optimum freshwater flowrate (Ffw). The

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regenerated water line, on the other hand, is indicated by the dotted line between Co and Creg, with

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its optimum flowrate (Freg) dictated by the inverse slope of the line. The limiting freshwater supply

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line is also introduced as the first segment of WSL (starts from origin and intersect with LCC at Co)13.

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Figure 2. Graphical presentation for targeting the regeneration-recycle system27

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The LCC sets the boundary for a water regeneration-recycle network. This also means that the WSL

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should always stay below and touch the LCC at the regeneration pinch point(s) for a feasible water

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network. In general, Co could take any point on the LCC, so long as it stays lower than the

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reuse/recycle pinch concentration (Cpr). However, in determining the optimum Co value, the WSL (in

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particular the limiting freshwater supply line) may appear above the LCC, which implies a mass load

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infeasibility problem. Hence, a new pathway is created in order to keep the WSL in the feasible

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region. This will be explained in detail in the following sections. Note that in most cases, the change

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of Co will also lead to different value of Creg.

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Example 1 from Xu et al. 23 is adopted to describe the proposed methodology. The limiting data is

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provided in Table 1. As shown, the network consists of four FL operations. For the base case system,

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the fresh water and wastewater flowrates are identified as 240 t/h (sum of the total water sinks and

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source flowrates). In this example, pure freshwater (Cfw=0) is assumed to serve the network. The

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flowrate of fresh water could be reduced to 86.67 t/h if reuse/recycle scheme is implemented, with

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the reuse/recycle pinch concentration (Cpr) identified at 120 ppm. These values can be readily

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calculated by using existing methodologies such as WCA 17, MRPD 28, CTA 19 , etc.

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Table 1. Limiting data for Example 1

SKj 1 2 3 4

FSKj (t/h) 40 70 10 120

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CSKj (ppm) 0 25 25 90

SRi 1 2 3 4

FSRi (t/h) 40 70 10 120

CSRi (ppm) 120 40 150 120 Page 7 of 33

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The ACTA is improved by considering the range of Co i.e. [Comin, Comax ] incrementally and identifying

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other key parameters. Graphically, the limiting freshwater supply line moves alongside the LCC with

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the change of Co. The pathway is updated (if needed) to keep the WSL below the LCC for all range of

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Co. The feasible Ffw, Freg, Creg, Fww, and Cww for every Co are identified. The improved ACTA is

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implemented by using MATLAB and the detailed procedure is described as follows:

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Step 1. Generation of Co vector

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As mentioned, with the change of Co, other key parameters in a water regeneration-recycle network

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will also vary. Thus, in the first step, it is necessary to produce a range of Co from its minimum (Comin)

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to maximum values (Comax). This is represented using Eq. 1.

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 Co ,n = Comin + ∆   min Comax − Comin max +1 Co ≤ Co,n ≤ Co , ∀n ∈ N = 1,2,...., ∆ 

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In order to plot the vector of Co, the incremental step (Δ) and Comin are set to 0.1 and 1 ppm,

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respectively. As mentioned earlier, Co has to stay lower than the reuse/recycle pinch concentration.

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The latter corresponds to 120 ppm in this example, which then sets the maximum bound of Co, i.e.

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Comax. With the above set-up, Eq. 1 generates the vector of Co=[1, 1.1, 1.2, ….., 120]T.

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Step 2. Determination of freshwater flowrate target (Ffw) for every Co value

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The CTA 19 is employed to identify freshwater flowrate (Ffw) for every Co value. The targeting for

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minimum freshwater flowrate with Comin = 1 ppm (first iteration) is shown for demonstration

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purposes. Other Co values are considered in the following iterations in order to identify the

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associated minimum freshwater flowrate targets. Populating all these targeted values will generate

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the freshwater flowrate vector (Ffw).

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The detailed procedure for targeting minimum freshwater flowrate can be found in Parand et al.27

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and is not included here for the purpose of brevity. The results are also presented in the Supporting

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Information (Table S1).

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Step 3. Checking of feasibility condition for all Co values

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The limiting freshwater supply line (the first segment of WSL below Co) always moves alongside the

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LCC with the increase of Co for a regeneration-recycle water system. For illustration purposes, the

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limiting freshwater supply lines (lines AB) for Co values of 10 ppm, 30 ppm, 35 ppm (generated using

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the CTA) are depicted in Figure 3.

(1)


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Figure 3. Limiting freshwater supply lines for Co values of 10, 30 and 35 ppm in regeneration-recycle system

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In order to maintain the mass load feasibility, the WSL should always stay below the LCC. However,

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there are cases where this requirement is not being fulfilled. Figure 4 shows such a case. A convex

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turning point (CTP) is observed in the LCC below the reuse/recycle pinch point, corresponding to the

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concentration (CCTP) of 40 ppm. For this kind of water networks, the limiting freshwater supply line

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may cross the LCC when it goes over the CTP, which implies infeasibility to the problem. As

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demonstrated in Figure 4, the limiting freshwater supply line (line AB) which corresponds to the Co

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greater than CTP (40 ppm) crosses the LCC (the magnified version around the CTP is also shown for

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clearer illustration).

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Figure 4. WSL with the Co above the convex turning point

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For such a case, it is necessary to determine whether the CTP is the upper bound to relax the Co.

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Note that even though the reuse/recycle pinch concentration (Cpr) is the ultimate upper bound for

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the Co value, the CTP can be a potential upper bound as well. Hence it is necessary to perform such a

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cross-check.



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To avoid the limiting freshwater supply line from crossing the LCC, a new pathway is needed. Figure

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5 shows such a case where the updated LCC provides the possibility of relaxing Co further above the

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CTP (the magnified version around the CTP is also shown for clearer illustration). As such, the

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limiting data need to be modified to reflect this update (to be explained in details in step 4). The

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area enclosed between the original and updated LCC is termed as the infeasible pocket, indicating

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mass load infeasibility in this region.

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Graphically, the updated LCC is achieved by removing the upper lines of the infeasible pocket. When

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the limiting freshwater supply line reaches the CCTP (i.e. 40 ppm, through iteration by increasing Co

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value in step 1), a pseudo segment is introduced by extending the limiting freshwater supply line

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(indicated by line A’B’). The pseudo segment should intersect the LCC below the reuse/recycle pinch

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point (i.e. 120 ppm). As shown in Figure 5, pseudo segment starts at the CTP and intercepts with the

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LCC at the interim point, with concentration (Cint) of 100 ppm. With this updated pathway, the

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limiting freshwater supply line now moves along the pseudo segment (instead of the original LCC)

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for all possible Co values between CCTP and Cint. Thus, all WSLs (that corresponds to the Co values

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ranging between 1 – 120 ppm) are now staying below the original LCC. Note that what was

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explained graphically for this step was converted to algebraic procedure and implemented via

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MATLAB. The details of the formulations are provided in the appendix.

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Figure 5. Updated LCC to remove infeasible pocket for relaxing Co above the CTP

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Step 4. Update of limiting data for infeasible pocket(s) removal

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The limiting data need to be updated in order to reflect the removal of the upper lines of infeasible

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pocket. The updated limiting data are given in Table 2. All modified data (as compared to the original

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ones in Table 1) are shown in bold. The limiting data are updated based on the location of CTP and


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interim point. Also, the numerical index (i.e. pseudo flowrate) which represents the slope of line A’B’

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needs to be considered. The detailed steps to identify these updated data are explained as follows.

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Table 2. Updated limiting data to remove the upper lines of infeasible pocket

SKj Pseudo 1 2 3 4

FSKj (t/h) 20 40 70 10 120

CSKj (ppm) 40 0 25 25 100

SRi Pseudo 1 2 3 4

FSRi (t/h) 20 40 70 10 120

CSRi (ppm) 100 120 40 150 120

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Modification of limiting concentration data

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The CCTP and Cint are found at 40 ppm and 100 ppm, respectively. To remove the upper lines of

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infeasible pocket, all turning points of LCC between CCTP and Cint should be removed. In other words,

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all concentrations for sources (CSRi) and sinks (CSKj) that lie between CCTP and Cint are to be replaced by

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Cint. For this example, this involves SK4; hence its concentration is now changed to 100 ppm (instead

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of 90 ppm).

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Inclusion of pseudo sink and pseudo source

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Once the turning points of LCC between CCTP and Cint are removed, the pseudo segment needs to be

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added for the updated LCC (shown in Figure 5). This can be done by inclusion of a pair of pseudo

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source and sink.

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The pseudo flowrates for both sink and source are calculated using Eq. 2. For this example, when

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the Co reaches the CTP (40 ppm), the freshwater flowrate (Ffw) is calculated as 70 t/h and the interval

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net flowrate (Net Fk) at the same level of Co is 50 t/h (both of these values were obtained using the

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CTA explained in step 2, detailed steps are omitted for brevity). Thus, the pseudo flowrate (Fs) is

291

calculated as 20 t/h.

292

Fs = F fw,n − NetFk , ∀n, k → Co,n = CCTP

293

Now a pair of pseudo sink and source is added to the limiting data, both with flowrates of 20 t/h.

294

The pseudo sink will have a concentration equal to the CCTP, i.e. 40 ppm. This represents the

295

beginning point of the pseudo segment in Figure 5. On the other hand, the pseudo source takes a

296

concentration of Cint (100 ppm), which represents the finishing point of the pseudo segment in Figure

297

5. These pseudo sink and pseudo source are the algebraic representation of the pseudo segment for

298

the updated LCC as illustrated in Figure 5.

(2)



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Page 12 of 33

299

Once the upper lines of infeasible pocket are removed (through the updated limiting data), the

300

targeting procedure goes back to step 1, where the vector of Co is generated again from Comin to

301

Comax. Note that the iteration ensures that all other infeasible pockets (if any) are also eliminated

302

throughout the Co relaxation procedure. When all infeasible pockets below the reuse/recycle pinch

303

point are removed, the algorithm moves forward to step 5.

304

Step 5. Identification of regenerated water flowrate (Freg) and pre-regeneration concentration

305

(Creg) for all Co values

306

In this step, the regenerated water flowrate (Freg) and pre-regeneration concentration (Creg) are

307

calculated for every Co value. The improved CTA27 (provided in the Supporting Information, Table S2)

308

is used for this purpose. Note that the updated limiting data should be used for the implementation

309

of improved CTA. The first five steps are the same as the original CTA27 (Table S1). Two more

310

columns are added to calculate the interval regenerated water flowrate (Freg,k, column 7) and the

311

corresponding pre-regeneration concentrations (Creg,k, column 8) using Eq. 3 and Eq. 4, respectively.

312

These equations are borrowed from Feng et al. 13 and Parand et al. 27 Note that Eq. 3 considers the

313

concentration levels (Ck) that stays between Co and Cpr; while Eq. 4 considers the concentration

314

levels (Ck) between the Cpr and the largest arbitrary value.

315

Freg,k =

316

Creg,k =

317

The largest values among all the entries in columns 7 and 8 give the optimum Freg and Creg values for

318

the given Co. As shown in Table S2, these values are identified as 47.06 t/h and 120 ppm, respectively

319

for Co of 1 ppm. In addition, the Cks at the same level as the targeted Freg and Creg are the

320

concentrations for the regeneration pinch points (i.e. correspond to Pinch 1 and Pinch 2 in Figure 2).

321

As mentioned earlier, these two points may lie on each other for some specific range of Co. This

322

happens for the case in Table S2, where the concentration of Pinch 1 and Pinch 2 are identified at

323

120 ppm for Co = 1 ppm. Graphically, the WSL touches the LCC at only one regeneration pinch point

324

(i.e. 120 ppm). However, this is not the case for the entire range of Co values. The regeneration pinch

325

points switch among the turning points of LCC with the change of Co.

326

To consider the entire range of Co= [Comin,Comax] , Eq. 3 is modified to Eq. 5, where Co and Ffw in Eq. 3

327

are now replaced by Co,n and Ffw,n, respectively, where the subscript “n” indicates the numbers of

328

iterations in the improved ACTA procedure.

Cum.∆mk − F fw × Ck Ck − Co

, ∀k → Co < Ck ≤ C pr

Cum.∆mk − F fw × Ck + Freg × Co Freg

(3)

, ∀k → Cpr ≤ Ck

(4)


Page 13 of 33

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Cum.∆mk − F fw,n × C k

, ∀n, k → Co,n < Ck ≤ Cpr &∀n ∈ N

329

MFreg ,kn =

330

Note that Eq. 5 considers the entire range of Co (generated in step 1) and also the entire range of Ffw

331

(generated via CTA in step 2). By taking these modifications into account, Eq. 5 generates the

332

regenerated water flowrate matrix MFreg. Specifically, every column of MFreg consists of the Freg,k

333

values (generated in column 7 of the improved CTA in Table S2) for a chosen Co . For better

334

illustration, the quantified MFreg with Co of 10 ppm, 35 ppm, and 60 ppm (labelled at the top of the

335

matrix) are provided in Figure 6. Next, the maximum value in every column of MFreg is extracted and

336

stored as the regenerated water flowrate vector (Freg). For Co values of 10 ppm, 35 ppm and 60 ppm,

337

Freg values are identified as 50.90 t/h, 57.47 t/h and 33.33 t/h, respectively (see Figure 6).

338

In addition, extracting the associated concentration level (Ck) of every value in Freg creates the Pinch

339

1 concentration vector (CPinch 1). For instance, CPinch 1 for Co = 10 ppm is identified as 120 ppm

340

(corresponds to Freg=50.90 t/h). For Co = 35 ppm, CPinch 1 moves to 40 ppm (corresponds to Freg=57.47

341

t/h). However, CPinch 1 moves back to 120 ppm for Co = 60 ppm (corresponds to Freg = 33.33 t/h). This

342

means that Pinch 1 switches among the turning points of LCC, with the change of Co (this will be

343

discussed further in later section). The Pinch 1 concentration vector (CPinch 1) for three random

344

iterations is also shown in Figure 6.

C k − C o ,n

(5)

345 346 347

Figure 6. Regenerated water flowrate matrix, regenerated water flowrate vector, and Pinch 1 concentration vector for Co = 10 ppm, 35 ppm, and 60 ppm

348

On the other hand, Eq. 6 is a modified version of Eq. 4, where regeneration concentration matrix

349

MCreg is produced. As compared to Eq. 4, Co, Ffw, and Freg are replaced by Co,n (generated in step 1),

350

Ffw,n (generated in step 2), and Freg,n (generated via Eq. 5), respectively where “n” is the dimension of

351

the vectors.

352

MCreg,kn =

Cum.∆mk − F fw,n × Ck + Freg,n × Co,n Freg,n

, ∀n, k → Cpr ≤ Ck & ∀n ∈ N

(6)



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Page 14 of 33

353

Specifically, every column of MCreg consists of the entries from column 8 of the improved CTA (Table

354

S2) for a chosen Co. The quantified MCreg for three random iterations with Co of 10 ppm, 35 ppm, and

355

60 ppm are provided in Figure 7.

356 357 358

Figure 7. Regeneration concentration matrix, regeneration concentration vector, and Pinch 2 concentration vector for Co = 10 ppm, 35 ppm, and 60 ppm.

359

Next, the maximum value in every column of MCreg is extracted and stored in the regeneration

360

concentration vector (Creg). For instance, Creg of 120 ppm, 85 ppm, and 120 ppm are determined for

361

Co of 10 ppm, 35 ppm, and 60 ppm, respectively (see Figure 7). The corresponding concentration for

362

every Co (designated as Pinch 2, i.e. CPinch 2) is also extracted and stored in the Pinch 2 concentration

363

vector (CPinch 2). As shown in Figure 7, CPinch 2 stays at 120 ppm for Co = 10, 35 and 60 ppm. In the later

364

section, the relationship between the entire range of Co and CPinch 2 will be discussed.

365

Step 6. Determination of wastewater flowrate (Fww) and concentration (Cww) for every Co

366

Flowrate (Fww) and concentration (Cww) of the wastewater streams can be readily calculated using

367

the flowrate and impurity balances in Eqs. 7 & 8, for every Co values. In Eq. 7, the only unknown

368

variable is Fww. At every iteration, Fww,n (where ‘n’ is the dimension of the vector) is calculated and

369

stored in the wastewater flowrate vector (Fww). Since Example 1 is a FL problem with no water

370

loss/gain for its water-using processes, the right hand side terms of Eq. 7 is calculated as zero. This

371

means that all the entries in Fww are identical to those in Ffw.

372

Since pure fresh water is used in this example, i.e. Cfw = 0, the only unknown variable in Eq. 7 is Cww,

373

which is calculated in every iteration. Populating the Cww values for all iteration will form the

374

wastewater concentration vector (Cww).

375

F fw,n − Fww,n = ∑ FSKj − ∑ FSRi , ∀ n ∈ N j

(7)

i


Page 15 of 33

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376


F fw,n × C fw − Fww,n × Cww,n − Freg,n × (Creg,n − Co,n ) =

∑F

SKjCSKj

j

377

−

∑F

SRiC SRi

, ∀n ∈ N

(8)

i

The general structure of the improved ACTA is summarised in Figure 8.

378 379

Figure 8. The general structure of the improved ACTA

380

By this end, the optimum feasible values of all key parameters in a regeneration-recycle network

381

(Ffw, Freg, Creg, Fww, and Cww) have been identified for every feasible Co. Following that, all feasible

382

range of freshwater (Ffw), regenerated water flowrates (Freg), and regeneration concentration (Creg)

383

are produced. WSL for every set of these values may then be constructed. Populating all WSLs hence

384

forms the feasible region, as shown in Figure 9. Note that the feasible region stays entirely below the

385

LCC. This graphical presentation verifies the accuracy of the improved ACTA for targeting a water

386

regeneration-recycle network.

387



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Page 16 of 33

388 389 390

Figure 9. Demonstration of feasible region for Example 1

4. Interactions among important process parameters

391

With the improved ACTA procedure, the interactions among all key parameters of a water

392

regeneration network can now be examined. The correlation of the various Co values and their

393

corresponding optimum flowrates (i.e. Ffw, Freg and, Fww) and concentrations (i.e. Creg, Cww, CPinch 1,

394

CPinch 2) for Example 1 are shown in Figure 10.

395

(a)

396 397 398


Page 17 of 33

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(b)

399 400

Figure 10. Interaction of (a) flowrates; (b) concentrations with varying Co values for Example 1

401

Apparently, the behaviour of the network with the change of Co is hardly predictable because of the

402

nonlinear relationship of the parameters. As a general trend, with the increase of Co (lower

403

regenerator performance), higher freshwater flowrate is required to satisfy the flowrate

404

requirement of the water network, which in turn leads to higher flowrate of wastewater (see Figure

405

10a). Since this example is a FL problem without water loss/gain, the wastewater flowrate is

406

identical to that of freshwater (hence the Ffw and Fww curves are overlapping in Figure 10a). On the

407

other hand, it is also observed that higher Co attributes to lower Cww (Figure 10b). This is because the

408

lower quality regenerated water provides less chance for the regenerated water to be

409

reused/recycled within the network (hence, higher flowrate leads to dilute wastewater). In

410

summary, the regeneration unit of higher performance results in lower freshwater demand. In

411

contrast, the regeneration cost will increase dramatically with the increase of its performance. The

412

trade-off analysis will be presented in the later parts of this paper.

413

Note that in the previous work, Xu et al. 23 attempted to relax the assumption for fixed Co in the

414

targeting stage of water regeneration-recycle system. However, the entire feasible region of Co was

415

not examined. More specifically, the Co values were only analysed up to 18 ppm. As having been

416

shown in this study, the Co values can be increased up to 120 ppm (with feasible values for other key

417

parameters). Note also that the results of this study are validated with those reported in Xu et al. 23.

418

The fresh water (Ffw) and wastewater (Freg) flowrates for Co values between 10 – 18 ppm are

419

completely in agreement with those reported by Xu et al. 23.

420

5. Pinch migration

421

The other valuable insight which is captured from Figure 10b is the pinch migration with the change

422

of Co value. The concentration of the first regeneration pinch point (Pinch 1) switches from 120 ppm Page 17 of 33 ACS Paragon Plus Environment


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Page 18 of 33

423

to 40 ppm at Co= 18.1 ppm. The same observation was also reported by Xu et al. 23. Pinch 1 then

424

switches back to its original concentration of 120 ppm at Co= 40 ppm and remains unchanged from

425

thereafter.

426

Note that the Pinch 2 may also switch between the tuning points of LCC with the increase of Co. This

427

is however not applicable for Example 1. The Co values at which the pinch migration takes place are

428

termed as transient post-regeneration concentration (Cotr), originally introduced by Parand et al. 22.

429

For Example 1, Figure 10b shows that Cotr takes place at 18.1 ppm and 40 ppm.

430

6. Economic evaluation of water regeneration system

431

It is a well-known fact that a regeneration unit that can produce higher quality regenerated water

432

(with lower Co) will lead to higher water saving, and in turn lower fresh water requirement and

433

waste disposal. Note however that the cost of regeneration unit increases dramatically with lower Co

434

value 29. Thus, the performance of regeneration unit has a dominant influence on the total cost of a

435

water regeneration-recycle system. However, there is not much attention being paid to this aspect.

436

The Co value has always been assumed to be the lowest concentration among all limiting

437

concentrations (except 0) for most of PA studies 3, 13, 19. With this assumption, the water

438

regeneration-recycle network may possibly be economically unfavourable due to high regeneration

439

cost. With the establishment of the interactions among various process parameters, the economic

440

performance of a water regeneration-recycle network may be incorporated during the targeting

441

stage. The economic trade-off between various operating (including freshwater supply and waste

442

disposal costs) and regeneration costs can then be explored. In the following section, the various

443

cost functions of a water regeneration-recycle network are established, which are then applied for

444

Example 1.

445

6.1. Cost functions for a water regeneration-recycle network

446

A total water system comprises the water utilisation processes, water regeneration system, and end-

447

of-pipe wastewater treatment facilities 10. The total operating cost (CT) given in Eq. 9 is broken down

448

to the freshwater cost, regeneration cost, and waste disposal cost, respectively.

449

CT = CF + CR + CD

450

where:

451

CF = u fw × Ffw

(9)

(10)


Page 19 of 33

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γ

452

 C max CR = α ×  o  Co 

453

CD = ( A + ( B ×

454

Eq. 10 considers the operating cost of freshwater (CF), which is a linear function of its unit cost (ufw).

455

Eq. 11 shows the expression for regeneration operating cost (CR) taken from Feng et al.

456

shown, CR is function of Comax , which has been assumed arbitrarily by Feng et al.29 without

457

systematic analysis. Thus, the final result obtained in the work of Feng et al.29 could be sub-optimal.

458

The improved ACTA is capable of identifying this parameter very accurately and this crucial for

459

economic analysis. In Eq. 12, the operating cost of wastewater treatment (CD) is mainly based on

460

primary treatment (Mogden Formula).30

461

  × Freg β  

(11)

Cww )) × Fww Ss

(12)

29

As

6.2. Example 1 revisited - total cost evaluation

462

With the identification of feasible range for Ffw, Freg, Fww, and Cww through improved ACTA for

463

Example 1, the objective here is to determine the minimum CT of the water network (given as Eq. 9).

464

Doing so also means the determination of the optimum Co value for the water regeneration-recycle

465

network. It is assumed that the unit cost of fresh water is taken as 1$/t, while the annual operating

466

hours is taken as 8600 h/y. Note that all cost functions and coefficients are given in US dollar. The

467

coefficients of β and γ in Eq. 11 are taken from Feng et al. 29 to be 0.14 and 1.75. The α sets at 10 and

468

CR gives the cost in k$/ y. The Comax value in Eq. 11 was taken as 120 ppm, identified in preceding

469

sections.

470

For Eq. 12, the coefficients A, B and Ss are taken from Kim 30 with the values of 34 ¢/t, 23 ¢/t and 336

471

ppm respectively. Note that CD is also calculated in k$/y.

472

Plotting the various cost elements with the varying Co resulted with the graphs shown in Figure 11.



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Page 20 of 33

473 474

Figure 11. Interaction among costs for Example 1

475

The economic optimum scenario with minimum CT of 778.3 k$/y is identified at Co=25 ppm. For Co

476

values lower than 25 ppm, CT increases due to higher contribution of regeneration cost. For Co value

477

beyond 25 ppm, fresh water and waste discharge costs have dominant influence over the total cost.

478

Detailed results for the example is summarised in Table 3 (along with direct reuse/recycle scenario).

479

In order to compare with the original solution by Xu et al. 23, a scenario with Co=18 ppm is also

480

solved, with results summarised in Table 3.

481

Table 3. Results comparison for three different scenarios of water network for Example 1

Scenarios

Reuse/recycle

Ffw (t/h) Fww (t/h) Freg (t/h) Cww (ppm) Co (ppm) CF (k$/y) CD (k$/y) CR (k$/y) CT (k$/y)

86.67 86.67 123.46 745.3 316 1061.3

Regeneration-recycle with Co=18 ppm from ref. 23 40 40 54.9 127.5 18 344 146.8 484.6 975.4

Regeneration-recycle with Co= 25 ppm (this work) 40 40 80 127.5 25 344 146.8 287.5 778.3

482 483

As shown in Table 3, both scenarios with water regeneration-recycle scheme achieve lower CT and

484

also the lower freshwater demand, as compared to direct reuse/recycle scenario. Note that the

485

requirement for freshwater for both regeneration scenarios are identical. However, lower CT is

486

achieved for the case with optimum Co (25 ppm) identified in this work, since this scenario has a

487

regeneration unit with lower performance, and hence lower regeneration cost. The network for

488

this case may be designed using the enhanced nearest neighbour algorithm (NNA)31, as shown using

489

the matching matrix in Figure 12. Notice that the outlet (Regout) and inlet (Regin) regeneration


Page 21 of 33

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490

streams are considered as source and sink, respectively. To design the network, the sinks are

491

satisfied from the lowest to highest contaminant concentration. The first regeneration pinch point

492

(i.e. Pinch 1) concentration has been identified at 40 ppm. The forbidden matches across the pinch

493

point are shown as shaded cells. Local Recycle (LR) matches are identified and eliminated to simplify

494

the network structure, following the enhanced NNA procedure.31

FSRi(t/h)

495 496 497

CSRi(ppm)

FSKj (t/h)

40

70

10

120 45

80

40

CSKj (ppm)

0

25

25

90 40

95

127.5

SK1

SK2

SK3

SK4

Regin

WW

70

10 45

25 40

75 LR

15

SKj SRi

40

0

FW

80 70 40

25 40 120

Regout SR2 SR1

120 45

120

SR4

10

150

SR3

40

30 10

Figure 12. Network design presented as matching matrix for Example 1 with the regeneration unit of Co = 25 ppm (updated limiting data are shown as strikethrough font)

7. Regeneration unit of removal ratio (RR) type

498

Apart from the regeneration unit of fixed Co type, another important category of regeneration unit is

499

the removal ratio (RR) type. The RR is first reported in the seminal work of Wang and Smith 3 with

500

Eq. 13.

501

RR =

502

Wang and Smith 3 applied the conventional PA technique to identify the flowrate targets for a water

503

regeneration-recycle network, when regeneration unit of known RR is given. However, the case

504

study presented was a simple single pinch problem. This means that the regeneration concentration

505

(Creg) stays constant regardless of the Co value. Note however that the existence of two regeneration

506

pinch points is common for most water regeneration-recycle systems. For those cases, the change of

507

Co will affect the optimum Creg, as has been shown in previous sections. With the establishment of

508

relationship between Co and Creg, one may now determine the optimum RR for a water regeneration-

509

recycle network. Note that the identification of this relationship is case dependant, as Co and Creg

510

have non-linear relationship for most water regeneration-recycle systems. In this study, since the

511

correlation between Co and Creg is explicitly determined through the improved ACTA, the feasible

512

range of RR for a particular network can also be obtained.

Creg − Co

(13)

Creg



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

513

Page 22 of 33

7.1. Example 1 revisited - regeneration unit of RR type

514

Example 1 is revisited here. The feasible range of Co has been produced via Eq. 1, while the optimum

515

value for Creg has been obtained in step 5 of improved ACTA for every Co value. Now, the optimum RR

516

for every Co can be determined via Eq. 13. The relationship between Co and RR for Example 1 is

517

examined and showed in Figure 13.

518 519

Figure 13. Interaction between RR and Co for Example 1

520

Interestingly, as revealed, this graph has discontinuity with partial overlap. This means that two

521

different Co values result with the same RR index within the overlapping region, i.e. [0.50, 0.67].

522

Thus, for instance, the Co values of 31 ppm and 42 ppm are both determined for a RR value of 0.65.

523

In other words, two structurally different water regeneration-recycle networks could be constructed

524

when the regeneration unit with RR of 0.65 is used. The selection of the final network design may

525

be done by taking other considerations into account, e.g. network complexity, controllability,

526

economic feasibility (e.g. cost evaluation scheme in previous section), etc. It is worth mentioning

527

that the existence of different Co values for the same RR may not applied for some networks, as it is

528

fully dependent on the limiting water data.

529

From Figure 13, it can also be observed a linear relationship exists between Co and RR for Co ≥ 40.1

530

ppm. On the other hand, Figure 10 shows that the Creg value stays identical for Co ≥ 40.1 ppm. This

531

means that Eq. 13 represents a linear function of Co and RR.

532

At this end, the designer can make use of Figures 10 and 13 to determine the various water network

533

targets. For a given RR index, the corresponding Co(s) is firstly identified from Figure 13. With this Co

534

value, Figure 10 provides the corresponding values of other key parameters. For example, assuming

535

that a regeneration unit with RR = 0.65 is available. Figure 13 determines that the Co values


Page 23 of 33

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536

correspond to 31 ppm and 42 ppm. Figure 10 is next referred. Magnified version of Figure 10

537

around Co values of 31 ppm and 42 ppm is given in Figure 14 for clear depiction of targeted values. (a)

538

(b)

539 540 541

Figure 14. Interactions among process parameters with Co values for Example 1 (magnified version): (a) flowrates (b) concentrations

542

For Co of 31 ppm, the Ffw and Fww targets are found as 55.48 t/h, while the Freg is determined as

543

64.52 t/h (Figure 14a). Figure 14b next determines the Creg and Cww as 89 ppm and 125.4 ppm.

544

Figure 14b also determines that the Pinch 1 concentration falls at 40 ppm, while the Pinch 2

545

concentration is located at 120 ppm. On the other hand, for Co of 42 ppm, the Ffw and Fww targets are

546

both found as 70 t/h, while Freg is determined as 25.64 t/h (Figure 14a). Creg and Cww are identified as

547

120 pm and 124.3 ppm from Figure 14b. The latter also shows that both Cpinch 1 and Cpinch 2 locate at

548

the same concentration of 120 ppm.

549

The network designs for both of these systems are illustrated in Figure 15. The regeneration unit for

550

both of these networks has an RR value of 0.65, but with different Co values of 31 ppm (Figure 15a)



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Page 24 of 33

551

and 42 ppm (Figure 15b), respectively. Note that the original limiting data (not the updated ones

552

used in Step 4 of the improved ACTA targeting procedure) should be used for the network design.

553

(a) Co=31 ppm

554

FSKj (t/h)

40

70

10

64.52

120 45

55.48

CSKj (ppm)

0

25

25

89

90 40

125.4

SK1

SK2

SK3

Regin

SK4

WW

40

13.55

1.93

56.45

8.07 25 39.52

45

SKj

FSRi(t/h)

CSRi(ppm)

55.48

0

FW

64.52 70 40 120 45

31 40 120 120

Regout SR2 SR1 SR4

150

SR3

10 (b) Co=42 ppm

SRi

75 LR

0.48 45 10

FSKj (t/h)

40

70 26.25

10

120 85.64

25.64

70

CSKj (ppm)

0

25 0

25

90 77.96

120

124.3

SK1

SK2

SK3

SK4

Regin

WW

40

26.25

3.75

43.75 LR

6.25

25.64

60

SKj

FSRi(t/h)

CSRi(ppm)

70

0

FW

70 26.25 25.64 40

40 42 120

SR2 Regout SR1

120 85.64

120

SR4

10

150

SR3

SRi

20 25.64 40 34.36 LR

10

555 556

Figure 15. Network design presented as matching matrix for Example 1 with regeneration unit of RR = 0.65: (a) Co=31 ppm (b) Co=42 ppm

557

For the network in Figure 15a, the outlet streams of process 1 and 2 (SR2 and SR1) are purified in the

558

regeneration unit (Regin) before partially recycled back to the process 2 (SK2). This network has the

559

total of 11 matches. For the network in Figure 15b, the process 4 outlet stream (SR4) is purified by

560

regeneration unit and totally recycled back to this process. This network shows a lower number of

561

matches compared to the network in Figure 15a.

562

8.

Example 2 – Fixed flowrate problem

563

A FF problem is solved here to demonstrate the applicability of the improved ACTA targeting

564

procedure. The water recycling problem in a Kraft pulping process from El-Halwagi 32 (Example 2) is

565

illustrated here, with limiting water data shown in Table 4. This FF case currently requires 640.2 t/h

566

of freshwater, and generates 742.16 t/h of wastewater. By implementing the reuse/recycle scheme, Page 24 of 33 ACS Paragon Plus Environment

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567

the freshwater and wastewater flowrates are identified as 89.90 t/h and 191.86 t/h, respectively,

568

where the pinch point is determined at 30 ppm 18. The possibility of performing regeneration-

569

recycling scheme is analysed next.

570

Table 4. Limiting data for Example 232

SKj 1 2 3 ∑FSKj SRi 1 2 3 4 5 6 7 8 9 ∑FSRi

FSKj (t/h) 467 465 8.2 640.2 FSRi (t/h) 12.98 9.7 10.78 116.5 48 52 52.2 300 140 742.16

CSKj (ppm) 20 20 10 CSRi (ppm) 419 16248 9900 20 233 311 20 30 15

571 572

Following the improved ACTA procedure, the relationship between RR and Co is depicted in Figure

573

16. Assuming that a regeneration unit of RR = 0.76 is used, the corresponding Co value is hence

574

identified as 15 ppm.

575 576

Figure 16. Relationship between Co and RR for Example 2



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Page 26 of 33

(a)

577 (b)

578

(c)

579 580 581

Figure 17. Interaction among process parameters with Co values for Example 2 (a) flowrates (b) contaminant concentrations (c) wastewater contaminant concentration


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582

The corresponding flowrates and contaminant concentrations for the Co ranging between 0 and 30

583

ppm (reuse/recycle pinch point) are shown in Figure 17. For Co of 15 ppm, Figure 17a identifies Ffw,

584

Freg, and Fww as 2.73 t/h, 174.3 t/h and 104.7 t/h, respectively. The corresponding Creg, CPinch 1, and

585

CPinch 2 values are determined as 63.5 ppm, 30 ppm, and 233 ppm, respectively from Figure 17b,

586

while Figure 17c identifies Cww at 2774 ppm. The same targeting results are also reported in Ng et al.

587

18

588

regeneration unit with Co ≤ 10 ppm is used. The same observation is also reported in Ng et al. 18.

589

It is worth mentioning that improved ACTA is also applicable for FF problem with total water loss.

590

For this kind of problem, the possibility for achieving Zero Liquid Discharge (ZLD) network should be

591

analysed before the improved ACTA targeting procedure is carried out. The detailed procedure for

592

analysing a ZLD network is reported in Parand et al.27 .

593

Conclusions

594

An improved Automated Composite Table Algorithm (ACTA) has been developed in this work. The

595

improved ACTA is used for the targeting of water regeneration-recycle network, by relaxing the

596

assumption of fixed post-regeneration concentration (Co) that has been the main assumption in most

597

previous works. Hence, the correlations among various key parameters of a regeneration-recycle

598

water network (i.e. freshwater, regenerated water, and wastewater flowrates, and, pre-

599

regeneration, regeneration pinch concentrations) with the change of Co have been investigated. The

600

contribution of key parameters toward the economic performance has been studied. The latter

601

provides an opportunity to determine the economic optimum scenario at the targeting stage which

602

was lagged behind for most reported PA works. The improved ACTA is capable of identifying key

603

parameters for both types of regeneration units (i.e. fixed Co and fixed RR), and also for both fixed

604

load and fixed flowrate problems. The ACTA is implemented using MATLAB and can deal with

605

medium to large scale problems. It is, however, limited to single contaminant problems, similar to

606

most of PA methods. Further extension may explore the use of partitioning regeneration unit for

607

water purification. Besides, future work may consider the heat integrated water network.

608

Supporting Information

609

This information is available free of charge via the Internet at http://pubs.acs.org/ which include:

610

Table S1 – CTA for targeting minimum freshwater flowrate with Co=1 ppm, and Table S2

611

Determination of Freg and Creg with improved CTA for Co=1 ppm.

. As depicted in Figure 17a, this network encounters zero freshwater feed (0 ppm) when

612 613 Page 27 of 33 ACS Paragon Plus Environment


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Page 28 of 33

614

Acknowledgment

615

The University of Nottingham Malaysia Campus and Curtin University Matched Funding Initiatives

616

on the support of this research work is gratefully acknowledged.

617

Nomenclatures

618

Abbreviations

619 620

ACTA

Automated Composite Table Algorithm

CTA

Composite Table Algorithm

CMA

Composite Matrix Analysis

CTP

Convex Turning Point

FF

Fixed Flow rate

FL

Fixed Load

LCC

Limiting Composite Curve

LR

Local Recycle

MRPD

Material Recovery Pinch Diagram

NNA

Nearest Neighbour Algorithm

RR

Removal Ratio

SK

Sink

SR

Source

WCA

Water Cascade Analysis

WSL

Water Supply Line

ZLD

Zero Liquid Discharge

Symbols Co

post-regeneration concentration

Cotr

transient post-regeneration concentration

CCTP

convex turning point concentration

CD

disposal charge

CF

freshwater supply cost

Cfw

freshwater contaminant concentration

Cint

interim concentration

Ck

concentration level

Cpr

reuse/recycle pinch concentration


Page 29 of 33

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


CR

regeneration cost

Creg

pre-regeneration concentration

CSKj

concentration of process sink

CSRi

concentration of process source

CT

total cost

Cum.Δm

cumulative mass load

Cww

wastewater contaminant concentration

Ffw

freshwater flowrate

Freg

regenerated water flowrate

FSKj

flowrate of process sink

FSRi

flowrate of process source

Fww

wastewater flowrate

MCreg

regeneration concentration matrix

MFreg

regenerated water flowrate matrix

SK

sink

SR

source

Δmk

interval impurity load

621 622

Appendix – numerical procedure for step 3 of the improved ACTA

623

Since the improved ACTA procedure was implemented using MATLAB, numerical procedure is

624

needed for step 3, in order to perform the mass load feasibility check. First, the location of CTP

625

should be identified automatically. Next, it should be determined if the infeasible pocket exists

626

numerically. These numerical procedures are outlined as follows. Example 1 is used for the

627

description.

628

Derivation of limiting freshwater supply line formula for every Co

629

The formula of the limiting freshwater supply line is readily derived. For instance, for line AB in

630

Figure 3, the coordinates of points A and B are determined at each iteration using Eq. A1 (Cfw = 0

631

ppm, assuming that pure fresh water is used). Furthermore, cumulative mass load (Cum. Δmk)

632

correspondent to the first concentration level is also zero (Table S1). Hence, the coordinates of point

633

A are zeroes for all iterations. On the other hand, coordinates of point B are related to Co (ranging

634

from 1 to 120 ppm) and Ffw; the latter is determined in step 2 of the improved ACTA for every Co

635

value.



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

636

A=

Cum.∆mk ∀k = 1 C fw

Bn =

(Co,n − C fw ) × F fw,n Co,n

Page 30 of 33

∀n ∈ N

(A1)

637 638 639

Construction of LCC segment formula

640

As illustrated in Figure 4, when Co passes the CTP, the limiting freshwater supply line (AB) crosses the

641

segment of the LCC located below the CTP. Thus, it is possible to relate the LCC segment formula to

642

the Co.

643

Having introduced line GH as an LCC segment, the coordinates of points G and H are identified using

644

Eq. A2. When the Co shifts from one LCC segment to another, the line formula derived via Eq. A2 is

645

exactly the segment below the one which the Co is currently moving on. For better illustration,

646

consider Figure 4 as an example. The Co is located between 40 and 90 ppm. Hence, points G and H

647

are derived with coordinates of (1,25) and of (2.8, 40), respectively, following Eq. A2.

648

 Cum .∆ m k − 2 Cum . ∆ m k − 1 Hn = G n = Ck −2 C k −1   n , k C C & n N & k ∀ → = ∀ ∈ ∀ >2 o,n k 

(A2)

649 650

Next, the intersection between limiting freshwater supply line (AB) and LCC segment (GH) will be

651

found at each Co value. If the intersection point is between point G and H, this means that the

652

limiting freshwater supply line is located above the LCC, which implies a mass load infeasibility. For

653

the case in Figure 4, all limiting freshwater supply lines until the Co of 40 ppm are feasible. For one

654

incremental step forward (i.e. Co=40.1 ppm), the limiting freshwater supply line intersects with LCC

655

segment at coordinates of (2.79, 39.96) which is between points G (1,25) and H (2.8,40). Since this

656

condition takes place at Co= 40.1 ppm, the algorithm identifies the concentration of CTP at previous

657

iteration (i.e. CCTP= 40 ppm).

658

Determination of the limiting freshwater supply line formula touches the CTP

659

In Figure 5, line A'B' represents the extended limiting freshwater supply line that touches the CTP.

660

Coordinates of points A’ and B’ can be determined using Eq. A3. This line should intersect with the

661

LCC below the reuse/recycle pinch, to allow the LCC to be modified. Thus, the end point (B’) is

662

related to reuse/recycle pinch concentration (Cpr) and the flowrate of limiting freshwater supply line

663

at CTP (determined in step 2). For the case in Figure 5, A’ is defined as (0,0) and B’ is determined as

664

(8.4, 120) using Eq. A3. Page 30 of 33 ACS Paragon Plus Environment

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665


A′ =

Cum.∆mk ∀k = 1 C fw

Bn ′ =

(C pr − C fw ) × F fw,n C pr

∀n → Co,n = CCTP

(A3)

666 667 668

Construction of the LCC segment formula above the CTP

669

In Figure 5, line G'H' is the representation of every LCC segment located above the CTP but below

670

the reuse/recycle pinch point. The coordinates of points G’ and H’ can be determined using Eq. A4.

671

For Example 1 two LCC segments are identified. Segment 1 has the starting point of G’ at (2.8, 40)

672

and ending point of H’ at (5.3, 90). On the other hand, segment 2 has the starting point of G’ at (5.3,

673

90) and the ending point of H’ at (10.4, 120).

674

 Cum . ∆ m k Cum . ∆ m k + 1 H n′ =  G n′ = Ck C k +1   ∀ n , k → C o , n = C CTP & C o , n ≤ C k ≤ C pr 

675

Next, the intersection between line A’B’ and all G’H’ lines is identified. The intersection point should

676

be between point G’ and point H’ to construct the updated LCC. If this condition does not hold, the

677

concentration of CTP shall take the maximum Co value and the algorithm moves to steps 5 and 6

678

(explained in the body of this paper) to identify the other key parameters for the last iteration.

679

For the case in Figure 5, the intersection point between lines A’B’ and G’H’ is found at coordinates of

680

(7,100). This point locates on one of the LCC segments below the pinch point. This point is termed as

681

the interim point, as outlined in step 3.

682

References

683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700

(1) Klemeš, J. J., Handbook of process integration (PI): minimisation of energy and water use, waste and emissions. Elsevier: 2013. (2) El-Halwagi, M. M.; Foo, D. C., Process synthesis and integration. In Kirk-Othmer Encyclopedia of Chemical Technology, John Wiley & Sons, Inc.: 2014. (3) Wang, Y. P.; Smith, R. Wastewater minimisation. Chem. Eng. Sci. 1994, 49, (7), 981-1006. (4) Foo, D. C. Y. State-of-the-art review of pinch analysis techniques for water network synthesis. Ind. Eng. Chem. Res. 2009, 48, (11), 5125-5159. (5) Ahmetović, E.; Ibrić, N.; Kravanja, Z.; Grossmann, I. E. Water and energy integration: A comprehensive literature review of non-isothermal water network synthesis. Comput. Chem. Eng. 2015, 82, 144-171. (6) Bagajewicz, M. A review of recent design procedures for water networks in refineries and process plants. Comput. Chem. Eng. 2000, 24, (9-10), 2093-2113. (7) Gouws, J. F.; Majozi, T.; Foo, D. C. Y.; Chen, C.-L.; Lee, J.-Y. Water minimization techniques for batch processes. Ind. Eng. Chem. Res. 2010, 49, (19), 8877-8893. (8) Jeżowski, J. Review of water network design methods with literature annotations. Ind. Eng. Chem. Res. 2010, 49, (10), 4475-4516. (9) Khor, C. S.; Chachuat, B.; Shah, N. Optimization of water network synthesis for single-site and continuous processes: milestones, challenges, and future directions. Ind. Eng. Chem. Res. 2014, 53, (25), 10257-10275. (10) Foo, D. C. Y., Process integration for resource conservation. CRC Press: Boca Raton, 2012.

(A4)



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(11) Liao, Z.; Wang, J.; Yang, Y. Letter to the editor. AIChE J. 2007, 53, (7), 1898-1899. (12) Kuo, W. C. J.; Smith, R. Design of water-using systems involving regeneration. Process Safety Environ. Prot. 1998, 76, (2), 94-114. (13) Feng, X.; Bai, J.; Zheng, X. On the use of graphical method to determine the targets of single-contaminant regeneration recycling water systems. Chem. Eng. Sci. 2007, 62, (8), 2127-2138. (14) Castro, P.; Matos, H.; Fernandes, M.; Pedro Nunes, C. Improvements for mass-exchange networks design. Chem. Eng. Sci. 1999, 54, (11), 1649-1665. (15) Hallale, N. A new graphical targeting method for water minimisation. Adv. Environ. Res. 2002, 6, (3), 377-390. (16) El-Halwagi, M. M., Process integration. Academic Press: Amsterdam, 2006. (17) Manan, Z. A.; Tan, Y. L.; Foo, D. C. Y. Targeting the minimum water flow rate using water cascade analysis technique. AIChE J. 2004, 50, (12), 3169-3183. (18) Ng, D. K. S.; Foo, D. C. Y.; Tan, R. R.; Tan, Y. L. Ultimate flowrate targeting with regeneration placement. Chem. Eng. Res. Des. 2007, 85, (9), 1253-1267. (19) Agrawal, V.; Shenoy, U. V. Unified conceptual approach to targeting and design of water and hydrogen networks. AIChE J. 2006, 52, (3), 1071-1082. (20) Deng, C.; Feng, X. Targeting for conventional and property-based water network with multiple resources. Ind. Eng. Chem. Res. 2011, 50, (7), 3722-3737. (21) Deng, C.; Shi, C.; Feng, X.; Foo, D. C. Y. Flow rate targeting for concentration-and property-based total water network with multiple partitioning interception units. Ind. Eng. Chem. Res. 2016, 55, (7), 1965-1979. (22) Parand, R.; Yao, H. M.; Pareek, V.; Tadé, M. O. Use of pinch concept to optimize the total water regeneration network. Ind. Eng. Chem. Res. 2014, 53, (8), 3222-3235. (23) Xu, D.-L.; Yang, Y.; Liu, Z.-Y. Predicting target values of the water-using networks involving regeneration recycling. Chem. Eng. Sci. 2013, 104, 525-539. (24) Fan, X.-Y.; Xu, D.-L.; Zhu, J.-F.; Liu, Z.-Y. Targeting of water-using networks involving regeneration with a graphical approach. CleanTechnol. Environ. Policy. 2016, 1-8. (25) Shenoy, A. U.; Shenoy, U. V. Continuous targeting and network design for zero wastewater discharge in water system integration. J. Clean. Prod. 2014, 87, 627-641. (26) Yan, F.; Yan, Z.; Li, W.; Zhang, J. Inflection point method (IPM): A new method for single-contaminant industrial water networks design. Chem. Eng. Sci. 2014, 126, 529-542. (27) Parand, R.; Yao, H. M.; Foo, D. C. Y.; Tadé, M. O. An Automated Composite Table Algorithm Considering Zero Liquid Discharge Possibility in Water Regeneration-recycle Network. CleanTechnol. Environ. Policy. 2016. (28) Almutlaq, A. M.; El-Halwagi, M. M. An algebraic targeting approach to resource conservation via material recycle/reuse. Int. J. Environ. Pollut. 2007, 29, (1), 4-18. (29) Feng, X.; Chu, K. H. Cost optimization of industrial wastewater reuse systems. Process Saf. Environ. Prot. 2004, 82, (3), 249-255. (30) Kim, J. K. System analysis of total water systems for water minimization. Chem. Eng. J. 2012, 193, 304-317. (31) Shenoy, U. V. Enhanced nearest neighbors algorithm for design of water networks. Chem. Eng. Sci. 2012, 84, 197-206. (32) El-Halwagi, M. M., Pollution prevention through process integration: systematic design tools. Academic Press: San Diego, 1997.

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741


TOC graphic

742 743

744 745


Automated Pinch-Based Approach for the Optimum Synthesis of a

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