Optimal Synthesis of Heat-Integrated Water Regeneration Network

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Optimal Synthesis of Heat Integrated Water Regeneration Network Shweta Kamat, Santanu Bandyopadhyay, Gopal Sahu, and Dominic Chwan Yee Foo Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.8b04703 • Publication Date (Web): 18 Dec 2018 Downloaded from http://pubs.acs.org on December 22, 2018

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Industrial & Engineering Chemistry Research

Optimal Synthesis of Heat Integrated Water Regeneration Network

Shweta Kamat Santanu Bandyopadhyay Department of Energy Science and Engineering, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India

Gopal Chandra Sahu Aditya Birla Science & Technology Centre, PFIC (unit of Grasim Industries Limited), Plot No. 1 & 1- A/1, MIDC Taloja, Tal. Panvel, Dist. Raigad 410208, India Dominic C. Y. Foo* Department of Chemical and Environmental Engineering/Centre of Excellence for Green Technologies, University of Nottingham Malaysia, Broga Road, 43500 Semenyih, Selangor, Malaysia

_________________________________________________________ *Corresponding. Emails: [email protected], [email protected] (S. Kamat) [email protected] (S. Bandyopadhyay) [email protected] (G. C. Sahu) [email protected] (D. C. Y. Foo)

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Industrial & Engineering Chemistry Research 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

Abstract Optimal synthesis of heat-integrated water network (HIWN) accounts for the simultaneous conservation of energy and water resources. A significant amount of research work, ranging from complex non-linear formulations to simplified linear models, has been carried out for the synthesis of HIWNs. The incorporation of interception units leads to additional water and energy conservation but results in non-linear formulations for heat-integrated water regeneration network (HIWRN) synthesis. This paper proposes a linear mathematical formulation, based on the transshipment model, for the optimization of HIWRNs using distributed interception units. As a result of a reduced number of variables, and the absence of non-linearities, the convergence efficiency is enhanced. The use of distributed interception units allows the regeneration streams to maintain their temperatures, thereby saving a significant amount of energy. A three-stage sequential approach and a simultaneous strategy are proposed for HIWRN synthesis. Although the simultaneous solution strategy provides cost optimal results, the three-stage sequential strategy is preferred in areas dealing with water scarcity and intermittent supply. The solution strategy is applicable to single as well as multiple-contaminant problems for single pass interception units with a fixed outlet and fixed removal ratio (RR). The methodology is demonstrated through literature examples for both types of interception units.

Keywords: Heat integration; water network; regeneration; optimization; process integration; targeting.


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1. Introduction The use of conventional fuels (e.g., coal) to generate energy used for industrial processes (including water pumping) leads to a large amount of greenhouse gas emission, thereby affecting climate change. It has been reported that the atmospheric CO2 concentration has exceeded 400 ppm since 20131. A recent report by the United National World Water Assessment Programme2 claimed that over 80% of wastewater, in which over 95% in least developed countries is released to the environment without prior treatment. These untreated wastewater sources have led to serious water scarcity issues2. The excessive water and energy consumption along with the emission of greenhouse gases negatively impact the sustainability of the ecosystem. It is extremely essential to conserve the existing water and energy resources within the industry. Water conservation can be carried out through re-use/recycle, while energy can be conserved through the recovery of thermal energy. Savulescu and Smith3 demonstrated that water networks with minimum water consumption may have different energy targets. Water and energy consumptions were reduced together through simultaneous heat and water integration. The seminal work in this area was reported in late 1990s, with the introduction of the synthesis of heat-integrated water networks (HIWNs)3. In the latter, water sources (wastewater streams) are recovered to the water demands (units where water is needed) through direct re-use or recycle schemes. Heat-integrated water regeneration networks (HIWRNs), on the other hand conserves additional water through the use of interception units that partially or completely treated water sources before their re-use or recycle to water demands4,5. Interception units may be classified as a single pass (with single inlet and outlet streams) and partitioning units (more than one outlet streams). Both these units can be categorized as fixed removal ratio (RR) and fixed outlet contaminant types6. It should be noted that simultaneous heat and water integration is an active area of research. Figure S1 in Supporting Information shows the growing publication trend in this area. From years 20052018, 56 papers have been published in this field7. These papers adopted methods based on Pinch Analysis and/or Mathematical Programming for the optimal synthesis of HIWNs and HIWRNs. A pinch-based technique for HIWN synthesis was developed by Savulescu and Smith3, where heat was recovered through indirect transfer. Later, Savulescu et al.8 introduced source-demand energy composite curves to explore different mixing options for maximum heat recovery through direct and indirect heat transfer. In the following decade, several other pinch-based targeting techniques



have been proposed to minimize energy consumption and water flow rates for the HIWNs. These include graphical tools such as two-dimensional energy grid diagram with maximum re-use9 and without re-use10, water energy balance diagram11, heat surplus diagram12, super-imposed mass and energy curve13, temperature-concentration diagrams14, and enthalpy difference-flow diagram15. The network complexity in HIWN was reduced through heat exchange between neighboring streams16,17; while energy targeting was improved by allowing only hot (or cold) streams to mix18. It may be noted that the above-mentioned techniques based on pinch analysis provide physical insights into the problem, but are restricted to single-contaminant HIWNs. Also, these methods require water to be minimized prior to energy minimization. These methods are preferred at the locations where water is scarce. However, a HIWN requiring the least amount of freshwater does not necessarily consume the minimum energy. In cases when energy and water costs are comparable, it is essential to optimize their consumption. Industries mainly focus on the minimization of the total operating costs (TOC) and total annualized cost (TAC). TOC minimization is preferred when the industry focuses on long-term benefits; while TAC is minimized to achieve investment cost recovery. The TAC minimization problem is complex and is used only when overall costs need to be minimized. On contrary to this, TOC minimization is simple and is generally used when energy and water targets need to be found prior to the design of HIWNs. Mathematical programming tools are used for the minimization of TAC or TOC. Bagajewicz et al.19 targeted water and energy through two linear programming (LP) formulations and synthesized a HIWN by minimizing the TAC using a mixed integer non-linear programming (MINLP) model. Du et al.20 formulated sequential and simultaneous models based on the stage-wise superstructure21 and compared them to achieve cost-efficient results from the latter. Leewongwanawit et al.22 proposed a MINLP that minimized TAC, including water, utility, and heat exchanger cost. Leewongtanawit and Kim23 incorporated piping costs in the TAC and proposed an iterative strategy to enhance the convergence by relaxing the MINLP into non-linear programming (NLP) and mixed integer linear programming (MILP) models in a step-wise manner. Bogataj and Bagajewicz4 provided a model to optimize energy and water by introducing a slack variable for external heating and cooling into the objective function comprising of water cost. This


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model incorporated non-isothermal mixing by introducing mixers and splitters, but it did not completely consider the energy-water trade-off. Dong et al.5 developed a modified state space representation and optimized energy and water through a MINLP formulation. Ahmetović and Kravanja24 formulated a MINLP model, where the integer variable was required to identify the role of streams. This model was improved by the appropriate placement of heaters and coolers and reformulated as an NLP25. In the preliminary studies on HIWRN synthesis, NLP formulation4 or stochastic perturbation5 were used to provide an initial guess for the MINLP formulation of TAC minimization. It was found that the incorporation of interception units reduced the water as well as energy consumption. Hence, most of the recent studies consist of HIWRN synthesis. Ahmetović et al.26 first optimized the water system, identified hot and cold streams through a convex hull formulation, and finally addressed the optimization of the energy system by minimizing TAC. The lack of simultaneous energy and water optimization in the first step was overcome by minimizing the TOC through an NLP model27. The main limitation of their work was that the process to process heat exchange was neglected. Ibrić and co-workers28,29 overcame this drawback by incorporating pinch location model30 within the TOC minimization formulation. The TOC minimization model was converted into a MINLP model when the selection of interception units was required31. The number of interconnections and network complexity was reduced through pre-screening rules, and thus, making the procedure iterative32. Research is directed towards the simplification of TOC minimization models to reduce the computational time. To further improve heat integration, Ibrić et al.33 included non-water consuming processes (e.g. reactor feed, waste gas or liquid). Recent studies focus on the optimization of interplant HIWRN using centralized interception units34,35. A major drawback of these heat integration models28-34 is the use of a maximum operator in an equation, which makes it non-differentiable. To tackle this problem, Tan et al.36,37 proposed the floating pinch method that eliminated non-differentiability at the cost of integer variables. Liao et al.38 proposed a MILP model for utility targeting and a MINLP model for the design of the HIWN. The non-linearity in this model was eliminated by Hong et al.39 by replacing the product of temperature and flow rate with a residual energy term. However, when this model was extended to incorporate interception units, a MINLP formulation was required40.



Most of these studies were restricted to processes that required the removal of a fixed contaminant loads8-35,38-40. However, most general problems may be represented as a fixed flow rate problem. Due to the increased flexibility, researchers have recently focused on the development of models that can handle fixed flow rate problems. Some of the HIWN synthesis techniques for fixed flow rate problems are discussed. George et al.41 proposed an LP model for the case of isothermal mixing and an NLP model with discontinuous derivatives for non-isothermal mixing using the transshipment model. Sahu and Banyopadhyay42 proposed LP models with isothermal as well as non-isothermal mixing using the concepts of Pinch Analysis, but the procedure was iterative. This problem was overcome through the development of MINLP formulations for TOC36 and TAC37 minimization. Ghazouani et al.43,44 modified the transshipment model41 by introducing numerous user-defined temperature intervals to eliminate the non-linearity arising due to non-isothermal mixing. On the other hand, Kermani et al.45 eliminated the non-linearity by carrying out nonisothermal mixing at known temperatures. However, the efforts carried out to eliminate the nonlinearity in these models would be overshadowed upon the incorporation of interception units due to the non-linearity introduced. The aim of this paper is to develop linear models for HIWRN synthesis. According to the literature review, HIWN synthesis problem could be tackled by an LP formulation for isothermal41,42 and non-isothermal mixing42. The simplest form of HIWRN synthesis was an NLP formulation26. The non-linear formulation may converge slowly or might not converge at all. The objective of this study is to eliminate the non-linearity and simplify the HIWRN synthesis problem. In this paper, three-stage sequential and simultaneous strategies are used for optimizing the HIWRN. For the former, LP formulation is used in three sequential stages to minimize the freshwater, regeneration water, and utility consumption. Energy and water are simultaneously optimized by minimizing the TOC through an LP model. Note that the nonlinearity arising in the model for the interception unit of the RR type has been eliminated by the use of distributed interception units. If uniform interception was used, all streams would have been mixed prior to treatment, thereby producing streams with an average quality and temperature. As distributed interception units, streams with different qualities and temperatures are treated separately. This makes it possible to separately utilize these streams depending on their qualities post-treatment. Also, heating or cooling of streams is not required prior to regeneration, making it possible to save energy.


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The paper is structured as follows. In the following section, the problem definition is presented. Simplification of outlet contaminant concentration for RR type of interception unit, through the proposed model, is discussed next. Models are formulated for the minimization of freshwater and utility, with sequential and simultaneous optimization approaches. These solution strategies are demonstrated through illustrative examples of HIWRNs with interception units of the fixed outlet and RR types.

2. Problem Definition A schematic of the HIWRN is shown in Figure 1. The general problem of HIWRN synthesis may be defined as follows: Qhu S0

HEAT EXCHANGER NETWORK

D0

S1 D1 R1 Sk Dk Rk

SNs

DNd RNs

Qcu



Figure 1: HIWRN with interception unit



There is a set of Ns internal sources. Each internal source (i = 1, 2, …, Ns) provides water at a flow rate of Fsi, a contaminant concentration of Csi,v (of vth contaminant out of total Nc contaminants) and temperature of Tsi.



A set of Nd internal demands is given. Every internal demand (j = 1, 2, …, Nd) requires water at a flow rate of Fdj and temperature of Tdj such that the contaminant concentration does not exceed its maximum permissible value Cdj,v (of vth contaminant).



There is an external source termed as freshwater, available at a contaminant concentration of Cf,v, and temperature of Ts0.



Similarly, there is an external demand (waste) with an upper limit on temperature, Td0, specified by the temperature discharge limit.



Note that no limit is set on its contaminant concentration, Cw,v, as it is assumed that the waste will be treated prior to environmental discharge.



It is assumed that an interception unit is associated with each internal source and has an operating temperature equal to that of the source. Thus, Ns interception units are considered. However, the actual number of interception units can be less than Ns, as some sources may not be sent for regeneration.



Each interception unit, (r=1, 2… to Ns), treats Fur amount of water and makes it available for the internal demands at a temperature of Tur (=Tsi) and a contaminant concentration of Cur,v.



Each source mixes isothermally to satisfy the flow requirements of internal demands. The unutilized sources will be discharged as wastewater, Fd0.



For cases where internal sources and regenerated water sources are not able to meet the flow and/or contaminant concentration requirements of demands, some amount of freshwater, Fs0, is required.



Maximum heat exchange is carried out between streams that require heating (cold streams) and cooling (hot streams).



For cases where the demand temperatures are not met, due to minimum driving force requirement of heat exchangers, hot utility, Qhu, and/or cold utility, Qcu, are required.

The objective of this paper is to formulate a HIWRN synthesis problem which optimizes freshwater and regeneration flow rates, as well as the requirement of hot/cold utilities. Two


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different strategies are adopted for this purpose, i.e., sequential and simultaneous methodologies. The proposed methodology removes the non-linearity associated with sequential41 as well as simultaneous34 optimization of HIWRN.

3. Determination of outlet concentration of fixed RR-type interception unit Interception unit of RR-type is characterized by the ratio of contaminant load removal to the load that it receives. The interception unit neither consumes fresh water nor generates wastewater. Let fir denote the flow transferred from ith source to rth interception unit and frj denotes the flow transferred from rth interception unit to jth demand. The outlet contaminant concentration of the rth interception unit is given by Eq 1, where ɛ is a small number (10-6) in order to avoid any indeterminate form. 𝐶𝑢𝑟,𝑣 =

∑𝑖 𝑓𝑖𝑟𝐶𝑠𝑖,𝑣 (1 ― 𝑅𝑅) ∑𝑗𝑓𝑟𝑗 + 𝜀

∀ 𝑟 ∈ {1,2,…𝑁𝑠},v ∈ {1,2,…𝑁𝑐}

(1)

As there is an individual interception unit to treat the stream from each source, the contaminant concentration at the inlet of each unit is known. In absence of flow loss, inlet and outlet flow rates of the interception unit are equal. Thus, the outlet contaminant concentration can be found out prior to optimization for a given RR value (Eq 2). 𝐶𝑢𝑟,𝑣 = 𝐶𝑠𝑖,𝑣 (1 ― 𝑅𝑅)

∀ 𝑟 ∈ {1,2,…𝑁𝑠},v ∈ {1,2,…𝑁𝑐}

(2)

With Eq 2, the RR-types units are now similar to interception units of the fixed outlet type. This novel approach eliminates the non-linearity associated with a variable outlet contaminant concentration31-35. This approach also separates the streams to be treated. Thus, the treated streams can be separately utilized depending on their qualities and temperatures.

4. Mathematical Formulation A hybrid approach is used for HIWRN synthesis, where water (fresh and regenerated) flowrates and utility are targeted using Mathematical Programming, followed by the design of HEN using Pinch Analysis36,37. Mathematical models for the minimization of freshwater (M1), regenerated



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water (M2), and utility (M3) are given as follows. The solution strategies used for achieving these targets will be discussed in the next section. Minimization of freshwater (M1) or regenerated water (M2) The water network with re-use/recycle and regeneration can be represented by the matching matrix form as shown in Figure 2. Let fij be the flow transferred from ith source to the jth demand, fiw be the flow transferred from ith source to waste and ffj be the flow transferred from freshwater source to jth demand. The flow balance for every source and demand including the interception unit is given by Eq 3 and Eq 4, while the flow balance for the interception unit is expressed by Eq 5. Eq 6 expresses the contaminant load balance for all the demands and Eq 7 gives the non-negativity constraints. ∑𝑗𝑓𝑖𝑗 + 𝑓𝑖𝑤 + ∑𝑟𝑓𝑖𝑟 = 𝐹𝑠𝑖 ∀ 𝑖 ∈ {1,2,…𝑁𝑠}

(3)

∑𝑖𝑓𝑖𝑗 + 𝑓𝑓𝑗 + ∑𝑟𝑓 𝑟𝑗 = 𝐹𝑑𝑗 ∀ 𝑗 ∈ {1,2,…𝑁𝑑}

(4)

∑𝑖𝑓𝑖𝑟 =

if 𝑖 = 𝑟 { ∑0 𝑓 otherwise 𝑗

𝑟𝑗

∀ 𝑟 ∈ {1,2,…𝑁𝑠}

(5)

∑𝑖𝑓𝑖𝑗 𝐶𝑠𝑖,𝑣 + 𝑓𝑓𝑗𝐶𝑓,𝑣 + ∑𝑟𝑓𝑟𝑗𝐶𝑢𝑟,𝑣 ≤ 𝐹𝑑𝑗𝐶𝑑𝑗,𝑣 ∀ 𝑗 ∈ {1,2,…𝑁𝑑}, 𝑣 ∈ {1,2,…𝑁𝑐} ∀ 𝑖 ∈ {1,2,…𝑁𝑠}, ∀ 𝑗 ∈ {1,2,…𝑁𝑑}, ∀ 𝑟 ∈ {1,2,…𝑁𝑠}

𝑓𝑖𝑗, 𝑓𝑓𝑗, 𝑓𝑖𝑤, 𝑓𝑟𝑗, 𝑓𝑖𝑟 ≥ 0

(6) (7)

The objective is to minimize freshwater requirement (Eq 8) or the amount of regeneration (Eq 9) subject to the constraints expressed by Eqs 3-7. The freshwater minimization model is M1; while the model for the minimization of regenerated water is M2. Minimize 𝐹𝑓 = ∑𝑗𝑓𝑓𝑗

(8)

Minimize 𝐹𝑢𝑟 = ∑𝑟∑𝑗𝑓𝑟𝑗

(9) Fdj

Fd1

Fd2

Fdj

Fu1

Cd2,v

Cdj,v

Cr1,v Cr2,v Cri,v

Cd0,v

D1

D2

Dj

R1

D0

Cdj,v Cd1,v Fsi

Csi,v

Fs0

Cs0,v

S0

ff1

ff2

ffj

Fs1

Cs1,v

S1

f11

f12

f1j

Fs2

Cs2,v

S2

f21

f22

f2j

Fsi

Csi,v

Si

fi1

fi2

fij

Fu1

Cu1,v R1

fr11

fr12

fr1j

Fu2 R2

Fu2 Ri

f1r1

Fd0

f1w f2r2


f2w firi

fiw

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Fu2

Cu2,v R2

fr21

fr22

fr2j

Fu2

Cui,v

fri1

fri2

frij

Ri

Figure 2: Matching matrix for water network with re-use/recycle and regeneration These are LP models that may be applied for single and multiple contaminant problems. Note that with the conversion between outlet concentration and RR (see Eq 2), the model is applicable to interception units of the fixed outlet and RR types. Minimum utility targeting (M3) A set of temperature intervals (k=1,2,.., TI) are found in order to target utility using the transshipment model41. Let Hikj, Hikr, Hrkj, Hfkj, and Hikw be the amounts of heat supplied in the kth temperature interval by the flows fij, fir, frj, ffj and fiw if the source temperature is greater than the demand temperature. In case the demand temperature is greater than the source temperature then Cikj, Cikr, Crkj, Cfkj, and Cikw are the amounts of heat to be gained in the kth temperature interval by the flows fij, fir, frj, ffj and fiw. Correlations between the flow rates and heat surplus and deficit are expressed as Eqs S1-S8 and explained with the help of Figure S2 in the Supplementary Information. HSk and HDk are the terms associated with heat surplus and heat deficiency respectively in the kth temperature interval. Rsk, Qh,k and Qc,k denote the residual heat, hot utility and cold utility respectively in the kth temperature interval. The general framework of the transshipment model for utility targeting is represented by Figure 3. The heat surplus and heat deficiency constraints are given by Eq 10 and Eq 11 respectively. Eq 12 expresses the energy balance for each temperature interval. The condition for no stream above the highest and below the lowest temperature level is given by Eq 13 and the non-negativity constraint for heat transfer variables is given by Eq 14. 𝐻𝑆𝑘 = ∑𝑖∑𝑗𝐻𝑖𝑘𝑗 + ∑𝑖∑𝑟𝐻𝑖𝑘𝑟 + ∑𝑟∑𝑗𝐻𝑟𝑘𝑗 + ∑𝑗𝐻𝑓𝑘𝑗 + ∑𝑖𝐻𝑖,𝑘,𝑤∀ 𝑘 ∈ {1, 2,…𝑇𝐼}

(10)

𝐻𝐷𝑘 = ∑𝑖∑𝑗𝐶𝑖𝑘𝑗 + ∑𝑖∑𝑟𝐶𝑖𝑘𝑟 + ∑𝑟∑𝑗𝐶𝑟𝑘𝑗 + ∑𝑗𝐶𝑓𝑘𝑗 + ∑𝑖𝐶𝑖,𝑘,𝑤 ∀ 𝑘 ∈ {1, 2,…𝑇𝐼}

(11)

𝑅𝑠𝑘 ― 𝑅𝑠𝑘 ― 1 ― 𝑄ℎ,𝑘 + 𝑄𝑐,𝑘 = 𝐻𝑆𝑘 ― 𝐻𝐷𝑘

∀ 𝑘 ∈ {1, 2,…𝑇𝐼}

(13)

𝑅𝑠0 = 𝑅𝑠𝑇𝐼 𝑅𝑠𝑘,𝐻𝑆𝑘,𝐻𝐷𝑘,𝑄ℎ,𝑘,𝑄𝑐,𝑘 ≥ 0

(12)

∀ 𝑘 ∈ {1, 2,…𝑇𝐼}


(14)


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The terms Hi,k,r, and Ci,k,r will always be equal to zero for the proposed model because the temperature of each interception unit equals the temperature of the source of the stream to be treated. The minimum utility targeted (Eq 15) subject to Eqs 3-7, Eqs 10-14, and Eqs S1-S8 in the Supporting Information. The minimum utility targeting model is linear. Minimize 𝑄ℎ𝑢 = ∑𝑘𝑄ℎ,𝑘

(15)

𝑄ℎ𝑢 = ∑𝑘𝑄ℎ,𝑘 T1

R0=0

HS1

T1-ΔTmin

Qc,1

HD1

Qh,1 R1

T2

HS2

T2-ΔTmin

Qc,2

HD2

Qh,2

Tm

Tm-ΔTmin

Rm-1

HSm = Himj + Hfmj + Himw + Hrmj

Qc,m Qh,m

HDm = Cimj + Cfmj + Cimw + Crmj

Rm

Tm+1

RK-1

HSK-1

Tm+1-ΔTmin

Qc,K-1

Qh,K-1

HDK-1

RK=0

TK

TK-ΔTmin

𝑄𝑐𝑢 = ∑𝑘𝑄𝑐,𝑘

Figure 3: General representation of the transshipment model for utility targeting

4.3.

Solution strategy

Two solution strategies, namely three-stage sequential minimization, and simultaneous optimization, are proposed for targeting by combining the mathematical models from the previous section.


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Three Stage Sequential Approach This approach is based on the principles that paved the way for heat integration in water networks8 and is preferred at locations with water scarcity. Once the freshwater is targeted, there can be numerous water networks. Due to the absence of restrictions (e.g., penalty), the amount of regeneration and utility requirements may vary from network to network. It is essential to minimize the regeneration and utility requirements as well. This can be done by following the steps given below. Step 1: The freshwater requirement is minimized using the model M1. Step 2: The amount of regenerated water is minimized by using the model M2. Note that, the minimum freshwater requirement Ff obtained in Step 1 is included as a new constraint (Eq 16) apart from those in M1. (16)

∑𝑗𝑓𝑓𝑗 = 𝐹𝑓

Step 3: The minimum utility is targeted by using M3 for the minimum freshwater (Eq 16) and regeneration (Eq 17) evaluated in steps 1 and 2 respectively. ∑𝑟∑𝑗𝑓

𝑟𝑗

(17)

= 𝐹𝑢𝑟

The sequential minimization approach is summarized in a flowchart in Figure 4. The utility minimization problem is an LP. As discussed in the previous section, outlet contaminant concentration is known for both types of interception units, making the freshwater and regenerated minimization steps LP formulations.



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Start

Step 1: Minimize fresh water, Ff, using model M1

Step 2: Minimize regenerated water, Fur, using model M2 subject to minimum fresh water, Ff, from Step 1

Step 3: Minimize hot utility, Qhu, using M3 subject to minimum fresh water, Ff from Step 1 and minimum regenerated water, Fur from Step 2

End

Figure 4: Flowchart of the sequential minimization approach Simultaneous Approach The simultaneous strategy involves the minimization of TOC31-34; the latter is a function of freshwater and regeneration flowrates, as well as hot and cold utility requirements. Cfw, Cww Creg, Chu, and Ccu are the costs of fresh water, wastewater, regeneration, hot utility, and cold utility respectively. Linear relations are assumed between the costs and the entities. The objective function is given by eq 18, subject to the constraints in Eqs 3-7,Eqs 9-13, and Eqs S1-S8 in the Supporting Information. The overall problem is an LP. 𝑀𝑖𝑛𝑖𝑚𝑖𝑧𝑒 𝑇𝑂𝐶 = 𝐶𝑓𝑤∑ 𝑓𝑓𝑗 + 𝐶𝑤𝑤∑ 𝑓𝑖𝑤 + 𝐶𝑟𝑒𝑔∑ ∑ 𝑓𝑟𝑗 + 𝐶ℎ𝑢∑ 𝑄ℎ,𝑘 + 𝐶𝑐𝑢∑ 𝑄𝑐,𝑘 𝑗

𝑖

𝑟 𝑗

𝑘

𝑘

(18)

The three-stage sequential and simultaneous methodologies are demonstrated through illustrative examples from literature. GAMS 24.2.2 software with CPLEX solver (12.6.0.0) is used to solve the optimization models.


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5. Illustrative Examples The limiting process data5 for Example 1 and 2 are shown in Table 1. The cost of fresh water, wastewater, regeneration, hot utility, and cold utility are set as $1 t-1, $1 t-1, $ 0.5 t-1, $ 120 kW1y-1,

and $ 10 kW-1y-1 respectively for all examples. As distributed regeneration is used, the total

cost of regeneration is assumed to be a function of the flow rate itself as in case of distributed treatment networks46. There is no heat loss or gain in the interception unit. The minimum approach temperature is considered to be 30℃. The freshwater supply has a temperature of 20℃ and the wastewater will be discharged at 30℃. Table 1: Limiting process data5 for Examples 1 and 2 Demands (Dj) D1 D2 D3 Sources (Si) S1 S2 S3

Flow rate (kg/s) 100 40 166.67 Flow rate (kg/s) 100 40 166.67

Concentration (ppm) 50 50 800 Concentration (ppm) 100 800 1100

Temperature (℃ ) 100 75 100 Temperature (℃ ) 100 75 100

Example 1: Fixed outlet concentration-type single pass interception units (single contaminant) Interception units with fixed outlet concentration of 80 ppm are considered for use. The three-stage sequential approach is first considered for the minimization of water and utility requirements. In Step 1, fresh water is minimized (Eq 8) subject to Eqs 3-7 using model M1. The minimum freshwater consumption is found to be 52.5 kg/s. In Step 2, regeneration is minimized (Eq 9) subject to Eqs 3-7 and the minimum freshwater (Eq 16) obtained in Step 1. The total amount of water to be regenerated is found to be 87.5 kg/s. The hot utility is minimized (Eq 15) in Step 3 subject to Eqs 10-14, Eqs S1-S8 in the Supporting Information along with the minimum freshwater (Eq 16), and regenerated water (Eq 17) constraints. Water network and utility targeting results are shown in Tables 2 and S1 in the Supporting Information. The hot utility (Qhu) was found to be 6615 kW and the cold utility (Qcu) was 4410 kW. As the temperatures and outlet contaminant concentrations of the interception units, R1 and R3 are the same, flows from sources, S1 (25 kg/s) and S3 (62.5 kg/s) can be combined into a single interception unit at 100 oC. Note that the



minimum fresh water, hot and cold utility for direct re-use/recycle scheme (no regeneration) were targeted as 77.28 kg/s, 10963.62 kW and 7717.78 kW41. The use of interception unit in this work reduces freshwater and well as utility requirements. Table 2: Water network by using three-stage sequential approach for Example 1 Cdj (ppm) Fdj (kg/s) Tdj(oC) Csi (ppm) Fsi (kg/s) Tsi(oC) 0 52.50 20 100 100 100 800 40 75 1100 166.7 100 80 25 100 80 0 80 62.5 100

S0 S1 S2 S3 R1 R2 R3

50 50 800 100 - 1100 433.33 100 40 166.7 25 0 62.5 52.5 100 75 100 100 75 100 30 D1 D2 D3 R1 R2 R3 D0 37.5 15 47.5 25 27.5 15 25 104.2 62.5 25 62.5

On the other hand, the problem is solved for minimum TOC by using simultaneous approach, with the objective in Eq 18 subject to constraints in Eqs 3-7, Eqs 10-14, and Eqs S1-S8 in the Supporting Information. The resulting water network and utility targeting are shown in Tables S2 and S3 in the Supporting Information. Despite the water network in Table S2 is structurally different from that of the sequential approach (Table 1), their utility requirements are identical. Note that this observation is specific to this example and cannot be generalized. The heat exchanger network for the utility target through sequential and simultaneous approaches is given in Figure 5 by using the pinch design method47. It is essential to note that the heat exchangers 1 and 4 can be combined, resulting in five heat exchangers. Three heaters and two coolers are required.


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f cp (kW/℃)

100 ℃

115.5

75 ℃

2887.5 kW 1

50 ℃

2887.5 kW 4

2310 kW

C

30 ℃

C

30 ℃

5

105

6

1050 kW

2100 kW

2

105

3

4725 kW 1

157.5

100 ℃

4

2

H

5

1050 kW

315 kW

H

63

6

3

1575 kW 63

100 ℃

H 1575 kW

1575 kW

75 ℃ 70 ℃

45 ℃

20 ℃

Figure 5: Heat exchanger network for Example 1 (sequential and simultaneous approach) For the solution in Table S2 in the Supporting Information, it is assumed that the unit cost of interception unit is fixed at $ 0.5 t-1. Next, this unit cost of regeneration is varied between $ 0.5 t-1 to $ 2 t-1 to determine its effect on the freshwater and regenerated water flowrates, as well as hot and cold utilities. Figure 6 shows that with the increase in regeneration cost, the freshwater, and wastewater flowrates decrease to 46.5 kg/s and then increase up to 77.28 kg/s, but the amount of regeneration decreases. The hot and cold utility requirements increase with the increase in the regeneration cost. The water costs include the cost of fresh water, amount of regeneration and the wastewater; while the utility cost comprises of the cost of hot and cold utility. Figure 7 next shows the changes in water and utility cost, as well as TOC with an increase in unit cost of regeneration. It is shown that with the increase in unit cost of regeneration, the energy cost increases, while water cost first decreases and then increases. As a result of this, TOC first decreases and then increases. The minimum TOC is located at the regeneration unit cost of $ 0.8 t-1.


200 180 160 140 120 100 80 60 40 20 0

Page 18 of 32

12000

8000 6000 4000 Minimum freshwater and waste water

Utilities (kW)

10000

2000 0

0

0.4

0.8 1.2 1.6 Regeneration unit cost ($/t)

Regenerated water

Fresh water

2

2.4 Waste water

Figure 6: Effect of varying regeneration unit cost on water flow rates and utilities (Example 1) 7 Cost (million $/y)

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

Water flowrates (kg/s)


6

Coptimum

5 4 3 2 1 0 0.0

0.4

0.8 1.2 1.6 Regeneration unit cost ($/t)

Water Cost (m$/y)

Energy Cost (m$/y)

2.0

2.4

Total Cost (m$/y)

Figure 7: Effect of varying regeneration unit cost on water, energy and total operating costs (Example 1)

Example 2: RR-type interception units (single contaminant) Example 1 is revisited here (data are shown in Table 1), where RR-type interception unit(s) is used. The RR value for all units is assumed as 0.9. Since the inlet concentrations of the regeneration units (correspond to the contaminant concentrations of internal sources) are 100 ppm, 800 ppm and 1100 ppm for the regeneration units of R1, R2 and R3, the outlet concentration of these units can be determined (using Eq 2) as 10 ppm, 80 ppm, and 110 ppm respectively.


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The three-step sequential approach is first attempted. The minimum freshwater requirement is found to be 0 kg/s by M1, minimizing Eq 8 subject to Eqs 3-7 (Step 1). A case of zero discharge liquid (no waste) is observed. Solving Eq 9 subject to Eqs 3-7 and Eq 16 for no fresh water use gives the minimum regeneration flowrate as 159.4 kg/s (Step 2). Hot utility target (Eq 15) is obtained from Step 3, and it satisfies Eqs 10-14, Eqs S1-S8 in the Supporting Information, Eq 16 for zero freshwater consumption and Eq 17 for a regeneration flowrate of 159.4 kg/s (see water network in Table S4 in the Supporting Information). The hot and cold utilities have the same magnitude, i.e. 1800 kW (see Table S5 in the Supporting Information). The significant reduction in utility consumption is due to the use of distributed interception units as the streams from sources to regeneration units do not require heating or cooling. Upon using the simultaneous optimization (Eq 18 subject Eqs 3-7, Eqs 10-14, and Eqs S1-S8 in the Supporting Information), the same results are obtained for freshwater and regenerated water flowrates, as well as hot and cold utilities. The resulting water network is also found to be the same as the sequential approach (Table S4 in the Supporting Information). The TOC is obtained as $ 2.75 million. Similar to the earlier example, interception units R1 and R3 can be combined into a single unit, as their temperatures and removal ratios are identical (i.e. only two interception units are needed). From the utility target (Table S5 in the Supporting Information), the pinch intervals are identified to be 105/75 ℃ and 100/70 ℃. There is one hot and one cold stream. The hot stream, at 100 ℃, needs to be cooled to 75 ℃; while the cold stream, at 75 ℃, needs to be heated to 100 ℃. Thus, there is no stream in the pinch interval, one stream each above and below the pinch. There is no need for heat exchangers, but one heater and one cooler are required as shown in Figure S3 in the Supporting Information. In order to make comparisons with literature26,48, the example is reworked by using the freshwater, regeneration, hot, and cold utility costs to be $ 0.375 t-1, $ 1 t-1, $ 377 kW-1y-1, and $ 189 kW-1y-1. Interception units of removal ratio of 95 % are considered with an investment cost of $ 16800 (Fur t/h)0.7y-1. As the proposed methodology minimizes TOC, the investment cost is not a part of the objective function, but it is considered later for comparative purposes. The wastewater discharge limit is set to be 10 ppm. Minimum approach temperature of the heat exchangers is considered to be 10℃. The three-stage sequential and simultaneous approaches are used and the resulting water networks Table 3 and 4. The utility targeting and HEN resulting from the three-stage sequential approach



Page 20 of 32

are shown in Table S6 in the Supporting Information and Figure 8. The results obtained are compared with the literature in Table 5. Upon using the three-stage sequential strategy, the freshwater consumption and amount of regeneration are found to be similar to the literature results. However, the hot and cold utility consumptions are found to be considerably low due to two separate interception units. As a result of this, the TOC reduces by 29 %, but the investment cost of the interception units increases by 21 %, as compared to the work of Ahmetović et al.26 and Jagannath and Almansoori48. Upon observing the order of magnitude, it can be concluded that significant TOC savings are possible from a small amount of investment in form of regeneration units. The number of heat exchangers is also reduced from two26,48 to one. Table 3: Water network using three-stage sequential approach for Example 2 (using costs from literature) Cdj (ppm) Fdj (kg/s) Tdj(oC) Csi (ppm)

Fsi (kg/s)

Tsi (oC)

0 100 800 1100 10 80 110

0 100 40 166.7 36.73 0 78

20 100 75 100 100 75 100

S0 S1 S2 S3 R1 R2 R3

40

50 40 75

800 166.7 100

100 0 100

0 75

1100 0 100

0 30

D1

D2

D3

R1

R2

R3

D0

6.32

18.95

38 40 88.7

36.73

15.68

78

21.05

78 85 ℃

100 ℃

f cp (kW/℃) 40

50 100 100

C

1680 kW

1680 kW

H 2520 kW 90 ℃

75 ℃

Figure 8: Heat exchanger network for Example 2 (using costs from literature) On the other hand, the use of simultaneous strategy leads to zero utility consumption and no heat exchange requirement. This can be explained with the help of Table 4, where every source is allocated to demand at the same temperature. The TOC is decreased by 43 %, however at a cost of


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41 % increase in investment cost of the interception unit, as compared to the work of Ahmetović et al.26 and Jagannath and Almansoori48. Similar to the three-stage sequential strategy, significant savings can occur through a small investment. As there is no need for heat transfer, the cost of utility as well as heat exchangers would be zero, causing significant savings. Table 4: Water network using simultaneous approach for Example 2 (using costs from literature) Cdj (ppm) Fdj (kg/s) Tdj(oC) Csi (ppm)

Fsi (kg/s)

Tsi(oC)

0 100 800 1100 10 80 110

0 100 40 166.7 28.95 39.47 50

20 100 75 100 100 75 100

S0 S1 S2 S3 R1 R2 R3

50 100 100

50 40 75

800 166.7 100

100 28.95 100

800 39.47 75

1100 50 100

0 30

D1

D2

D3

R1

R2

R3

D0

50

28.95

21.05 0.53

39.47 116.7

50

28.95 39.47 50

Table 5: Comparison of results (obtained from costs in literature) with literature26,48

Parameters Freshwater consumption (kg/s) Regeneration (kg/s) Hot utility consumption (kW) Cold utility consumption (kW) Total operating cost (m$/y) Investment cost of interception unit (m$/y)

This paper Three-stage Simultaneous sequential

Ahmetović et al.26

Jagannath and Almansoori48

0

0

0

0

114.737

114.737

114.737

118.42

4818.95

4818.65

1680

0

4818.95

4821.36

1680

0

6.03

6.03

4.26

3.41

0.11

0.11

0.14

0.16



Example 3: Multiple contaminants problem The methodology is demonstrated for a multiple contaminants problem (with contaminants C1, C, C2, and C3). The limiting process data41 for this example are given in Table 6. Interception unit(s) of fixed outlet type is used, with the outlet concentrations of 60 ppm (C1), 80 ppm (C2), and 30 ppm (C3) respectively. Table 6: Limiting process data41 for Example 3 Demands (Dj) D1 D2 D3 Sources (Si) S1 S2 S3

Flow rate (kg/s) 30 40 20 Flow rate (kg/s) 30 40 20

Concentration Concentration Concentration Temperature C1 (ppm) C2 (ppm) C3 (ppm) (℃ ) 0 0 0 100 50 40 15 75 50 50 30 35 Concentration Concentration Concentration Temperature C1 (ppm) C2 (ppm) C3 (ppm) (℃ ) 100 80 60 100 150 115 105 75 125 80 130 35

The three-stage sequential approach is adopted to find the minimum freshwater through M1 (57.5 kg/s), regenerated water using M2 (26.25 kg/s), and hot (6772.5 kW) and cold utility requirements through M3 (4357.5 kW). The resulting water network, utility targeting results, and heat exchanger network are given in Tables S7, S8, and Figure S4 in the Supporting Information. There are three heaters, four coolers, and five heat exchangers. As no flow is allocated to the interception unit R2, only two interception units (R1 and R3) are needed. Note that since the temperatures of interception unis R1 and R3 are different, thus they will remain as two independent units. The simultaneous optimization approach (Eq 18 subject to Eqs 3-7, Eqs 10-14, and Eqs S1-S8 in the Supporting Information) provides the same results as the three-stage sequential technique in terms of fresh water consumption, amount of water to be regenerated, hot and cold utility, however with different HIWRN structure (see HIWRN in Table 7, utility targeting result in Table S9 in the Supporting Information and heat exchanger network in Figure 9). Like that of the sequential approach, four coolers and three heaters are obtained, but the number of the heat exchangers is reduced to three. The TOC was obtained as $ 4.9 million. In case no interception units are used, the freshwater consumption is 70 kg/s and the hot and cold utility requirements are 8190 kW and 5250 kW respectively41. It can be induced that the use of interception units not only reduces the fresh water consumption but also the utility requirement.


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For comparative purpose, the problem is re-worked for freshwater, regeneration, hot, and cold utility costs of $ 0.45 t-1, $ 0.0067 t-1, $ 377 kW-1y-1, and $ 189 kW-1y-1 25. Interception units of removal ratio of 90 %, 70 %, and 98 % for contaminants A, B, and C are considered, with an investment cost of $ 12600 (Fur t/h)0.7y-1. The investment cost of the interception unit is not a part of the objective function as the focus is TOC minimization. The wastewater discharge limit is set to be 30 ppm. Minimum approach temperature of the heat exchangers is considered to be 10℃. Table 7: Water network by using simultaneous approach for Example 3 Cdj,1 (ppm) Cdj,2 (ppm) Cdj,3 (ppm) Fdj (kg/s) Tdj (oC) Csi,1 (ppm) 0 100 150 125 60 60 60

Csi,2 (ppm) 0 80 115 80 80 80 80

Csi,3 (ppm) 0 60 105 130 30 30 30

Fsi (kg/s) 57.5 30 40 20 6.25 20 0

Tsi (oC) 20 100 75 35 100 75 35

S0 S1 S2 S3 R1 R2 R3

0

50

50

100

150

125 126.08

0

40

50

80

115

80

92.17

0

15

30

60

105

130

100

30

40

20

6.25

20

0

57.5

100

75

35

100

75

35

30

D1

D2

D3

R1

R2

R3

D0

30

20

7.5 6.25

6.25 20

6.25 20


17.5 20 20


f cp (kW/℃) 52.5 73.5

50 ℃

3675 kW

Page 24 of 32

787.5 kW

C

1

100 ℃

2625 kW

1470 kW

C

2

100 ℃

2100 kW 84

C

3

75 ℃

84

35 ℃

3780 kW 126

100 ℃

84

H 75 ℃

1

70 ℃

30 ℃ 1680 kW 30 ℃

C

30 ℃

420 kW 2

H 2520 kW

31.5

35 ℃

3

45 ℃ 35 ℃

2100 kW

H 472.5 kW

20 ℃

Figure 9: Heat exchanger network for Example 3 (simultaneous approach) The water network, utility targeting, and HEN are shown in Tables S10, S11, and Figure S5 in the Supporting Information for the three-stage sequential approach, and in Tables S12, S13, and Figure S6 in the Supporting Information for the simultaneous approach. Results obtained by using threestage sequential and simultaneous strategies are the same. Freshwater and wastewater are found to be 30 kg/s. The amount of water regenerated is 73.57 kg/s; while the hot, and cold utility consumption is found to be 1260 kW, and 3780 kW. These results match with literature results26, but three interception units are used in the proposed methodology as compared to a single interception unit in the literature, thereby increasing the investment cost of interception units. Overall summary The computational performance for all examples are summarized in Table 8. It can be observed that the use of the simultaneous strategy is computationally better than the three-stage sequential strategy as the former requires a single step and has CPU time comparable to each step of the latter. Also, the variables and constraints in the third step of the sequential strategy are large as compared to the simultaneous strategy. However, this observation is example specific as the blocks of variables and constraints are less in the third step of sequential strategy as compared to the simultaneous strategy. Despite of being computationally superior, the simultaneous strategy might


Page 25 of 32 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


not always be used in actual practice. In case of intermittent water supply, the main objective would be the minimization of freshwater. Thus, the three-stage sequential approach would be required. As the proposed model is an LP, the CPU time is very short. This advantage allows one to quickly set the water flow rates and utility targets, prior to the design of HENs. Table 8: Computational parameters for Examples 1, 2, and 3 Parameters Number of variables

Strategy Three-stage sequential Simultaneous

Number of constraints

Three-stage sequential Simultaneous

CPU time (seconds)

Three-stage sequential Simultaneous

Step

Example 1

Example 2

Example 3

1 2 3 1 2 3 1 2 3 -

34 34 884 619 19 20 849 582 0.088 0.096 0.094 0.091

34 34 884 619 19 20 849 582 0.091 0.096 0.091 0.089

34 34 961 672 25 26 936 639 0.085 0.074 0.084 0.115

6. Conclusion HIWRN was synthesized through sequential as well as simultaneous optimization techniques using MINLP models. Researchers have focused on the simplification of these optimization models and eliminated the integer variables to improve the solutions. However, the non-linearity arising from the incorporation of interception units needs to be removed. LP models are proposed in this paper for the optimization of water, regeneration, and utility consumption. These models are implemented to optimize the HIWRN sequentially and simultaneously. The proposed methodology is demonstrated with the help of three examples, i.e. fixed outlet-type interception units with single and multiple contaminants, as well as RR-type interception unit with a single contaminant. It is observed that incorporation of interception units reduces the water and utility requirements, thereby reducing the TOC. A case with no heat transfer requirement was also observed. The effect of varying regeneration cost on the various water flow rates, utility requirement and consequently their cost is shown. This study also shows the reduction of utility as a result of different regeneration temperatures. The proposed models are restricted to isothermal



mixing and single pass interception units. Future research is directed towards the incorporation of non-isothermal mixing to further reduce the utility consumption. Water loses that are experienced in interception units, known as partitioning units, due to its water recovery ratio have not been considered in the existing HIWRN models. These models need to be extended towards partitioning units as well. Supporting Information This information is available free of charge via the Internet at http://pubs.acs.org/.


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Nomenclature ΔTmin Ccu Cdj,v Cf,k,j Cf,v Cfw Chu Ci,k,j Ci,k,r Ci,k,w cp Creg Cr,k,j Csi.v Cur,v Cww Fw Fdj ffj fij fir frj fwi Ff Fsi Fur HDk Hf,k,j Hi,k,j Hi,k,r Hi,k,w Hr,k,j HSk Nd Ns

Minimum Approach temperature of a heat exchanger Cost associated with cold utility ($/kW) Maximum concentration of vth contaminant acceptable by jth demand (ppm) Heat deficit in the kth temperature interval by flow ffj (kW) Concentration of vth contaminant in fresh resource (ppm) Cost of fresh water ($/t) Cost associated with hot utility ($/kW) Heat deficit in the kth temperature interval by flow fij (kW) Heat deficit in the kth temperature interval by flow fir (kW) Heat deficit in the kth temperature interval by flow fiw (kW) Specific heat capacity (kJ/kg-℃) Cost of regeneration ($/t) Heat deficit in the kth temperature interval by flow frj (kW) Concentration of vth contaminant of ith source (ppm) Concentration of vth contaminant at outlet of rth interception unit (ppm) Cost of wastewater ($/t) Waste resource flow rate (kg/s) Flow required by jth demand (kg/s) Resource flow rate required by jth demand (kg/s) Flow transferred from ith source to jth demand (kg/s) Flow transferred from ith source to rth interception unit (kg/s) From transferred from rth interception unit to jth demand (kg/s) Waste discharged by ith source (kg/s) Fresh resource flow rate (kg/s) Flow provided by ith source (kg/s) Amount of water regenerated rth interception unit (kg/s) Heat deficit in kth temperature interval (kW) Heat supplied in the kth temperature interval by flow ffj (kW) Heat supplied in the kth temperature interval by flow fij (kW) Heat supplied in the kth temperature interval by flow fir (kW) Heat supplied in the kth temperature interval by flow fiw (kW) Heat supplied in the kth temperature interval by flow frj (kW) Heat surplus in kth temperature interval (kW) Number of internal demands Number of internal sources and maximum number of interception units



Qc,k Qcu Qh,k Qhu Qs RR Rsk Tck Tdj Thk TI Tsi

Cold utility requirement in the kth temperature interval (kW) Cold utility (kW) Hot utility requirement in the kth temperature interval (kW) Hot utility (kW) Heat supplied by hot streams (kW) Contaminant removal ratio of an interception unit Residual heat from kth stage (kW) Cold temperature boundary at kth interval (℃) Temperature required by jth demand (℃) Hot temperature boundary at kth interval (℃) Number of temperature intervals Temperature of ith source (℃)

Abbreviations HIWN HIWRN LP MILP MINLP NLP RR TAC TOC

Heat integrated water network Heat integrated water regeneration network Linear programming Mixed integer linear programming Mixed integer non-linear programming Non-linear programming Fixed removal ratio type interception unit Total annual cost Total operating cost


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Table of Contents Graphic: S0 Sk

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Rk SNs RNs

D0

Cold streams or heat demands (HD) Heat transfer

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

Hot streams or heat sources (HS)

Dk

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Optimal Synthesis of Heat-Integrated Water Regeneration Network

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