Simultaneous synthesis of heat-integrated water networks by a nonlinear program:Considering the wastewater regeneration reuse

Fangyou Yan,Wei Li,Jinli Zhang

1 School of Chemical Engineering and Material Science,Tianjin University of Science and Technology,Tianjin 300457,China

2 Key Laboratory for Green Chemical Technology MOE,School of Chemical Engineering and Technology,Tianjin University,Tianjin 300072,China

3 Key Laboratory of Systems Bioengineering MOE,School of Chemical Engineering and Technology,Tianjin University,Tianjin 300072,China

Keywords:None-linear programming Heat-integrated water network synthesis Wastewater regeneration reuse

ABSTRACT Heat-integrated water network synthesis (HIWNS) has received considerable attention for the advantages of reducing water and energy consumptions.HIWNS is effective in water and energy sustainability.Mixed integer non-linear programming (MINLP) is usually applied in HIWNS.In this work,a novel nonlinear programming (NLP) was proposed for HIWNS by considering wastewater reuse and wastewater regeneration reuse.Integer variables are changed to non-linear equation by the methods for identifying stream roles and denoting the existence of process matches.The model is tested by examples with single and multiple regeneration unit problems.The testing results showed that the NLP is an alternative method for HIWNS with wastewater reuse and regeneration reuse.

1.Introduction

Both water and energy are essential resources for the chemical industry besides the routine human life.The more demands of water and energy occur in the manufacture processes,the more pollutions need to be post-treated.It is essential to pursue suitable routes to reduce both water and energy consumptions in the chemical industry.The heat-integrated water networks synthesis(HIWNS) would provide an efficient way to reduce the water consumption as well as the energy consumption.

The conceptual method was widely used for HIWNS.The first conceptual method for HIWNS was reported by Savulescu and Smith [1],in which water and energy networks were designed sequentially.The water and energy networks were simultaneously synthesized in subsequent work [2,3].A graphical tool was developed by Honget al.[4] to improve the conceptual understanding for the implications of heat exchanger networks structures in heat integrated water allocation networks.The temperature and concentration order composite curves method was developed by Houet al.[5].As one of the main approaches for HIWNS,the mathematical optimization method synthesizing heat-integrated water network sequentially [6,7] or simultaneously [8–11] was also widely used for HIWNS.Liaoet al.[12]solved HIWNS by two steps:first,heat exchange matches were obtained first by solving a mixed integer linear programming (MILP) model;then the detailed network design step was implemented.A two-step method was developed for the HIWNS by Boixet al.[13]:an MILP model was developed to solve the water and energy network by multiobjective optimization firstly;then the best results of multiobjective optimization are improved by integrated the energy into the water network.Ahmetovi? and Kravanja [14,15] developed MINLP models for simultaneous HIWNS considering process-to-process streams.Ghazouaniet al.[16] developed an MILP model for minimizing the total operating cost of HIWNS considering nonisothermal mixing.Zhouet al.[9] developed a simultaneous method for HIWNS based on the stream identification method in the work of Liaoet al.[12].An optimization methodology based on MILP was developed for HIWNS in industrial pulp and paper case study [17].

Most methods for HIWNS are developed only based on the wastewater reuse.The wastewater regeneration reuse is an effective approach to reduce the fresh water consumption,which will lead to the reduction in total annual cost,accordingly.The researches on simultaneous HIWNS with wastewater regeneration reuse are scarce.The possibility of waste water regeneration was considered in the work of Bogataj and Bagajewicz[18]for simultaneous HIWNS.Donget al.[19] simultaneously solved the HIWNS problem considering all possible water reuse and treatment options.Ibri?et al.[20] proposed a simultaneous optimization model for HIWNS problem involving wastewater treatment.Ahmetovi?et al.[21]proposed a general superstructure and a simultaneous optimization model for the designing of a heat-integrated water-using and wastewater treatment network (HIWTN) by mixed integer non-linear programming (MINLP).Ibri?et al.[22]developed a compact superstructure for the simultaneous synthesis of nonisothermal water network synthesis involving wastewater treatment units.Honget al.[23] presented a mathematical programming model for heat integrated water-using networks(HIWUN),in which wastewater treatment units and multiple contaminants are embedded.

In our previous work [24],a nonlinear programming (NLP)model was developed for the simultaneous HIWNS with wastewater reuse.Methods for identifying stream roles and denoting the existence of process matches were developed to remove discrete variables.In this work,we developed a simultaneous HIWNS superstructure considering the wastewater regeneration reuse.Based on the methods for identifying stream roles and denoting the existence of process matches,an NLP model was developed for the simultaneous HIWNS with wastewater regeneration reuse.The NLP model was tested by HIWNS problems with single and multiple regeneration units.

2.Problem Statement

The superstructure of simultaneously HIWNS used in this work was presented Fig.1.The interconnections,flowrates,contaminant concentrations,and the temperatures of each stream are determined in the heat-integrated water network.The objective is minimizing the total annual cost at the condition of specifying certain terms such as the maximum inlet and outlet contaminant concentrations of process units,the contaminant loads to be transferred from process unit,the removal percent of contaminants for regeneration units,the maximum outlet contaminants concentrations of discharged water,the inlet and outlet temperatures of the process unit,the inlet and outlet temperatures of the regeneration unit,discharged wastewater temperature and freshwater temperature.

Fig.1.The superstructure of heat-integrated water network synthesis involving regeneration reuse:freshwater splitter(FS),process unit(PU),regeneration unit(RU),water mixer (M),wastewater splitter (S),regenerated water mixer (RM),regenerated water splitter (RS);the red circle is heater and blue circle is cooler.

The freshwater stream is split into multi-streams by the freshwater splitter.Freshwater is a cold or bypass stream.Freshwater,regenerated water and wastewater from other process unit mix in the water mixer.The outlet stream of a water mixer is a hot,cold or bypass stream.A heater or cooler may be used by the inlet stream process unit.The outlet streams of process units can be hot,cold or bypass streams,and they are split into multi-streams by the wastewater splitter.The streams from wastewater splitter are reused by other process unit,regenerated by regeneration unit and discharged into the environment.Regenerated water from other regeneration units and waste water from process units is regenerated in regeneration units.The waste water for regeneration mixes in the regenerated water mixer.The wastewater streams for regeneration are hot streams or bypass streams.A cooler is presented before wastewater stream inter into the regeneration unit if it is necessary.The regenerated water streams are cold streams or bypass streams,and are divided into multistreams by regenerated water splitters.The wastewater stream for discharging is a hot or bypass stream.A cooler is presented before wastewater stream is discharged if it is necessary.

As shown in Fig.2,a stage-wise superstructure [25] is used for heat exchanger network synthesis.The number of stages (NOK),freshwater splitters (|FS|) and regenerated water splitters of each regeneration unit (|RS|) are adjusted as following:NOK≤max(NHU,NCU),|FS|≤|PU|+1,|RS|≤|PU|+1.

3.Mathematical Model

3.1.Freshwater splitters

The freshwater in the freshwater splitter is split into multiple streams,which are consumed by process units and sent to the next freshwater splitter.The flowrate balance of freshwater splitter is presented in Eqs.(1) and (2).

The total freshwater is sent to the first freshwater splitter.

Fig.2.Heat exchanger network superstructure [25].

The stream between the adjacency freshwater splitters is a cold or bypass stream.

3.2.Water mixers

Freshwater from freshwater splitters,regenerated water from regenerated water splitters and wastewater from wastewater splitters mix in the water mixer.The flowrate balance of water mixer is presented in Eq.(6).

The heat balance is presented in Eq.(8).

3.3.Mass load for process unit

3.4.Limit for inlet and outlet concentrations of contaminants

3.5.Wastewater splitters

The streams from wastewater splitter can be sent to water mixers,regenerated water mixers and discharged water mixers.The flowrate balance for wastewater splitter is given by Eq.(12).

3.6.Regenerated water mixer

The waste water streams for regeneration mix in the regenerated water mixer.The flowrate,heat and mass balances for regenerated water mixer are presented in Eqs.(13)–(15).

3.7.Mass balance for regeneration unit

3.8.Regenerated water splitters

The streams from a regenerated water splitter are sent to the next regenerated water splitter,to another regenerated water mixer (only for the first regenerated water splitter),to discharged water mixer (only for the first regenerated water splitter) and the water mixer.The flowrate balance for each regenerated water splitter is given by Eqs.(17)–(19).

The inlet flowrate of the first regenerated water splitter is the regenerated water flowrate.

The stream between the adjacency regenerated water splitters is a cold or bypass stream,which is presented by Eq.(21).

The inlet temperature of the first regenerated water splitter is equal to the outlet temperature of the regenerated unit.

3.9.Discharged water mixer

The outlet streams of wastewater splitter and regenerated water splitter (only for the first regenerated water splitter) mix in the discharged water mixer.The flowrate balance for discharged water mixer is given by Eq.(23).

The mass balance for each contaminant is presented in Eq.(24).

The heat balance is presented in Eq.(25).

3.10.Limit for discharged water concentrations of contaminant s

3.11.Identification of the inlet and outlet streams of process units

The roles(hot,cold or bypass stream)of inlet and outlet streams of process units are identified by Eqs.(27)–(30).

3.12.Hot and cold utility load

Cold utilities are used in the streams into process unit,into the regeneration unit,and for discharge.Cold utility loads are given by Eqs.(31)–(33).

3.13.Heat balance at each stage

Heat balance for hot stream at each stage is given by Eqs.(35)–(38).

Heat balance for cold stream at each stage is given by Eqs.(39)–(42).

3.14.Constraints for approach temperatures

As shown in Eqs.(43)–(52),ten nonlinear constraints are developed to ensure the feasible driving forces.A small positive bound,ε,is specified to avoid infinite areas.ε is 0.1 K in this work.

The Feasibility of temperatures and assignment of superstructure inlet and outlet temperatures are presented in appendix.

3.15.Objective function

The total annual cost (TAC) is defined as the objective function,which consists of freshwater cost,regeneration cost,utility cost and heat exchanger cost.The infinitesimal numbers,δ and γ are set as 10-5in this work.

3.16.NLP model

The NLP model is minimizing theobjective function53 subject to constraints Eqs.(1)-(52) and Eqs.(A1)-(A24).Eqs.(A1)-(A24) are shown in the Supplementary Material .

3.17.Models implementation

The optimization problems are solved by BARON solver with the default options in GAMS 24.2.All the optimizations were implemented on a personal computer with Intel Core 2.6 GHz and 8 GB RAM.

4.Examples

Four examples are used to demonstrate the NLP model for HIWNS considering wastewater reuse and wastewater regeneration reuse in this section.The cost and operating parameters for Example 1 are derived from the work of Bogataj and Bagajewicz[18].The cost and operating parameters for Examples 2 and 3 are presented by Donget al.[19].The cost and operating parametersfor Example 4 are derived from the work of Ahmetovi?et al.[21]These parameters are presented in Table 1.

Table 1 Cost and operating parameters for examples 1–4

Example 1.The first example involves two process units and one regeneration unit.The process unit parameters and regeneration unit parameters shown in Table 2 are from the work of Bogataj and Bagajewicz [18].The regeneration unit parameters are shown in Table 3.The maximum concentration of contaminants for discharged water was 20×10-6[20].Lower bound on the exchanger minimum approach temperature(EMAT)is 1°C,which is the same with that of Ibri?et al.[20] and Ahmetovi?et al.[21].

The optimal configuration for example 1 is shown in Fig.3,which is the same with that of Ibri?et al.[20] and Ahmetovi?et al.[21].The calculations required a total computation time of 16 s.The NLP method is compared with MINLP method in Table 4.TAC(5038790.46979 USD?a-1)is a little smaller than these in other works,which is result from δ and γ in the objective function.Two heat exchangers,one cooler and one heater are used in the optimal structure.The hot utility consumption rate is 1905.32 kW.The freshwater flowrate and regenerated water flowrate were 27.78 kg?s-1and 41.67 kg?s-1,respectively.The freshwater flowrate is equal to the minimum freshwater consumption rate [26].

Example 2.The second example is a HIWNS problem with three process units and two regeneration units.The process unit parameters and regeneration unit parameters for Example 2 are presented in Tables 5 and 6.These parameters are derived from the work of Donget al.[19].The maximum concentration of contaminant for discharged water was 10×10-6as given in Ref.[19].Lower bound on EMAT is 10℃,which is the same with that in Refs.[19–21].

The optimal configuration for Example 2 is shown in Fig.4 withTAC=6420938.3 USD?a-1.The total computation time is 697 s.There are two heat exchangers,one cooler and one heater in the optimal configuration.The hot and cold utility consumption rates are 3780 kW and 3780 kW,respectively.No freshwater is consumed in the network.The results of optimal configuration are compared with MINLP methods in Table 7.TAC(6420938.3 USD?a-1) of NLP model is smaller than 6,555,774.1 USD?a-1,6506179.1 USD?a-1and 6506179.1 USD?a-1in Refs.[19–21].

Table 2 Process unit parameters for example 1

Table 3 Regeneration unit parameters for example 1

Table 4 Solution comparison for example 1

Fig.3.Optimal network design for Example 1.

Example 3.The process unit parameters and regeneration unit parameters for Example 3 are derived from the work of Ibri?et al.[20].The process unit parameters are shown in Table 8.The regeneration unit parameters are shown in Table 9.The maximum concentration of contaminants for discharged water was 10×10-6as given in Ref.[20].Lower bound on EMAT is 1°C,which is the same with that of Ibri?et al.[20].

The optimal configuration is obtained from the NLP model as shown in Fig.5.The total computation time is 420 s.Three heat exchangers and one heater are used in the optimal structure.The hot-utility consumption rate is 504 kW.TACis 1094050.6 USD?a-1.The freshwater flowrate and regenerated water flowrates for regeneration units 1 and 2 were 17.643 kg?s-1and 21.09 kg?s-1,respectively.TAC of this work (1094050.6 USD?a-1) is slightly greater than that (1,087,259.5 USD?a-1) of Ibri?et al.(2014) as shown in Table 10.The freshwater flowrate (12.035 kg?s-1) is greater than the minimum freshwater consumption rate [26].

Example 4.The process unit parameters and regeneration unit parameters for Example 4 in Table 11 are derived from the work of Ahmetovi?et al.[21].The regeneration unit parameters are shown in Table 12.The maximum concentration of contaminants for discharged water was 30 ppm as given by Ahmetovi?et al.[21].Lower bound on EMAT is 10°C,which is the same with that in Refs.[20,21,23].

The optimal configuration obtained in 14 s from the NLP model are shown in Fig.6.TACis 1820345.3 USD?a-1.Two heat exchan-gers,two cooler and one heater are applied in the optimal structure.The hot-utility consumption rate is 1260 kW.The coldutility consumption rate is 3780 kW.The freshwater flowrate and regenerated water flowrates for regeneration unit were 30 kg?s-1and 73.572 kg?s-1,respectively.The comparison results in Table 13 show thatTAC of this work is slightly larger than these of Ibri?et al.[20,27]and Hong et al.[23].This is mainly resulted from the more sophisticated HIWNS superstructure in these works.The stream from regenerated water mixer can be sent to the discharged water mixer in the work of Ibri?et al.[20,27].Multiple wastewater splitters are used for one process unit in the work of Honget al.[23].TAC of this work is approximate to that of Ahmetovi?et al.[21].The freshwater flowrate is equal to the minimum freshwater consumption rate [26].

Table 5 Process unit parameters for example 2

Table 6 Regeneration unit parameters for example 2

Table 7 Solution comparison for Example 2

Table 8 Process unit parameters for Example 3

Table 9 Regeneration unit parameters for Example 3

Table 10 Solution comparison for Example 3.

Table 11 Process unit parameters for Example 4

Table 12 Regeneration unit parameters for Example 4

Table 13 Solution comparison for Example 4

5.Conclusions

In this work,a superstructure is developed for simultaneous HIWNS considering wastewater regeneration reuse.A nonlinear programming model is developed for the simultaneous HIWNS with wastewater regeneration reuse.Methods for identifying stream roles and denoting the existence of process matches were developed to remove the discrete variables.The nonlinear programming model can be solved by BARON solver with the default initial point of GAMS.Tested on four examples with single and multiple regeneration units,it can be found that the NLP is an alternative method for HIWNS with wastewater reuse and regeneration reuse.

Fig.4.Optimal network design for Example 2.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Fig.5.Optimal network design for Example 3.

Fig.6.Optimal network design for Example 4.

Acknowledgements

This work was financially supported by the Major Science and Technology Project of Xinjiang Bingtuan (2017AA007/02).

Supplementary Material

Supplementary data to this article can be found online at https://doi.org/10.1016/j.cjche.2020.11.044.

Nomenclature

AFrannual investment factor for regeneration unit

Barea cost exponent for heat exchangerCarea cost coefficient for heat exchanger,USD?m-2

CCUcold utility cost,USD?W-1?a-1

CFfixed charge of heat exchanger,USD

CFWcost of freshwater,USD?kg-1

CHUhot utility cost,USD?W-1?a-1

CP {j|jis a cold stream}

cpheat capacity of water,J?kg-1?K-1

cdsoutlet concentration of contaminantsfor discharged water

Ε exchanger minimum approach temperature,°C

ECrinvestment cost exponent for regeneration unit,USD?kg-1

FDdischarged water flowrate,kg?s-1

Fpwater flowrate of process unitp,kg?s-1

Fp′,pwater flowrate from wastewater splitterp′to water mixerp,kg?s-1

Fp,rwater flowrate from wastewater splitterpto regenerated water mixerr,kg?s-1

FS {fs|fsis a freshwater splitter}

|FS| the number of freshwater splitters

fsfreshwater splitter

Hworking times of plant per year,s

HP {i|iis a hot stream}

ICrinvestment cost coefficient for regeneration unitr,USD?kg-1

ihot stream

jcold stream

kindex for stage 1,???,NOKand temperature location 1,???,NOK+1

mp,smass load of contaminantsto be removed in processp,mg?s-1

Ncthe number of cold streams

Nhthe number of hot streams

NOKtotal number of stages

OCroperating cost coefficient for regeneration unit,USD?kg-1

PU {p|pis a process unit}

|PU| the number of process unit

p/ppprocess unit

qcudcold utility used in the streams for discharged,kW

qcurcold utility used in the streams into the regeneration unitr,kW

qi,j,kheat exchanged between hot streamiand cold streamjat stagek,kW

RPr,sremoval percent of contaminants,%

RS {rs|rsis a regenerated water splitter}

|RS| the number of regenerated water splitter for each regeneration

RU {r|ris a regeneration unit}

|RU| the number of regeneration unit

r/rrregeneration unit

rsregenerated water splitter

S {s|sis a contaminate}

ST {k|kis a stage in the superstructure}

scontaminates

TDtemperature of discharged water mixer,°C

TDHtemperature of the stream into cold utility for discharged water if it is a hot stream,°C

TDWtemperature of wastewater for discharge,°C

TFWtemperature of freshwater,°C

TINCUinlet temperature of cold utility,°C

TINHUinlet temperature of hot utility,°C

TOUTCUoutlet temperature of cold utility,°C

TOUTHUoutlet temperature of hot utility,°C

TRINrinlet temperature of regeneration unitr,°C

TROUTroutlet temperature of regeneration unitr,°C

ti,ktemperature of hot streamiat temperature locationk,°C

tj,ktemperature of cold streamjat temperature locationk,°C

uindividual heat transfer coefficient for wateri,kW?m-2?°-C-1

uCUindividual heat transfer coefficient for cold utility,kW?m-2?°C-1

uHUindividual heat transfer coefficient for hot utility,kW?m-2-?°C-1