Linlin Liu ,Jian Du ,Fenglin Yang

1 Institute of Chemical Process Systems Engineering,School of Chemical Engineering,Dalian University of Technology,Dalian 116024,China

2 Key Laboratory of Industrial Ecology and Environmental Engineering,Ministry of Education,School of Environmental Science and Technology,Dalian University of Technology,Dalian 116024,China

Keywords:Mass exchange network Heat exchange network Superstructure Simultaneous synthesis

A B S T R A C T Integrating multiple systems into one has become an important trend in Process Systems Engineering research field since there is strong demand from the modern industries.In this study,a stage-wise superstructurebased method is proposed to synthesize a combined mass and heat exchange network(CM&HEN)which has two parts as the mass exchange network(MEN)and heat exchange network(HEN)involved.To express the possible heat exchange requirements resulted from mass exchange operations,a so called“indistinct HEN superstructure(IHS)”,which can contain the all potential matches between streams,is constructed at first.Then,a non-linear programming(NLP)mathematical model is established for the simultaneous synthesis and optimization of networks.Therein,the interaction between mass exchange and heat exchange is modeling formulated.The NLP model has later been examined using an example from literature,and the effectiveness of the proposed method has been demonstrated with the results.

1.Introduction

Mass exchange and heat exchange are both essential operations in process industries.Over the past three decades,lots of effort has been made to explore the synthesis methods of mass exchange network(MEN)and heat exchange network(HEN).Some of the approaches have been surveyed by Foo[1],El-Halwagi[2],Noureldin[3]and Foo et al.[4]in their recent publications.However,most of these studies are for an individual MEN or HEN rather than taking the strong interaction between them into account.In a chemical plant,a mass exchange operation usually needs a proper temperature to maintain its specified running.This produces the necessity of synthesizing a combined MEN and HEN(CM&HEN)to improve the overall performance over individual HEN and MEN.

The exploration of CM&HEN synthesis was started by Srinivas and El-Halwagi[5]in 1994.They introduced the synthesis problem of combined heat and reactive mass exchange networks firstly,and then developed a two-step method having the optimization of mass-exchange temperatures considered.In 2007,Isafiade and Fraser[6]addressed the CM&HEN problem by conducting the HEN and MEN synthesis based on pinch technique.A two-step procedure,wherein the minimum consumption of mass separation agent(MSA)/lean stream was obtain at first,then the related streams were collected for HEN synthesis.By the way of enumerating multiple operation cases,this method was able to obtain a near-optimal solution.Later,the same authors[7]extended the above design strategy to a so called internal-based superstructure.The synthesis was executed with the mixed-integer nonlinear programming(MINLP)models established for sub-networks.In 2010,Du et al.[8]proposed a superstructure-based approach to simultaneously integrate the mass transfer temperatures and the CM&HEN.In their work,the thermal property(hot or cold)of streams must be pre-determined so as to construct the heat exchange superstructure before synthesis.This strategy was feasible,however,it would eliminate the good solutions and therefore may yield suboptimal solutions.Then,to avoid the pre-determining action,a new CM&HEN synthesis method was proposed in a recent work of Liu et al.[9]Potential streams which would take heat exchange was identified at the beginning of their study,and then the CM&HEN synthesis and the optimization of mass exchange temperatures were simultaneously carried out by offering each potential stream a place during the sub-HEN synthesis.Nevertheless as taking pinch technology as the fundamental theoretical basis,this method was not possible to produce the solutions featuring nonequivalent mixing of either temperature or concentration.Thus to achieve the total automatic and global synthesis and optimization of a CM&HEN,new approaches are under expectation.

As a special case of general MEN,water allocation network(WAN)has been widely studied on the issue of having heat integration accompanied.The recent works include:Savulescu et al.[10,11]developed a systematic methodology for the simultaneous reduction of energy and water consumption in 2005.Feng and coworkers[12]investigated the feasibility of stream merging for utility saving,and also[13]proposed two methods to reduce the number of temperature local fluctuations regarding their effect on energy performance of WAN.Kim et al.[14]established a MINLP formulation to approach the minimum cost of WAN and HEN by involving water reusing operations.A step-based method was implemented for the problem by Marianne et al.[15]in 2012.The non-isothermal mixing problem was considered by Liao et al.[16]and Luo et al.[17].Kheireddine et al.[18]developed an optimization approach to minimize the operating cost of water networks with merging the mass,heat and property integration together.In a recent report,Wang et al.[19]presented a two-step methodology referring to the retrofit design of cooling water.Through varying the arrangement of exchangers from parallel to series,their work was able to reduce freshwater consumption without involving any additional heat transfer area.All of these researches could offer instructive reference to that of CM&HEN at some degree.

In this paper,stage-wise superstructure model is employed for the synthesis of CM&HEN.To achieve the simultaneous design of MEN and HEN,a novel superstructure for HEN synthesis is proposed,with which it is able to avoid the pre-determination of thermal property for streams and extend the solution space by taking non-equivalent mixing involved comparing with previous work[8,9].The overall synthesis and optimization problem is formulated as a NLP featured mathematical model,wherein the tradeoffs between MEN and HEN as well as between capital cost and operation cost can be investigated at the same time.

2.Problem Statement

In the CM&HEN synthesis problem addressed in this paper,it involves a set of rich process streams,a set of lean streams including the internal process MSAs and external MSAs,and a set of hot and cold utilities.It is desirable to fulfill the mass transfer mission of moving the transferable components from riches into leans with providing proper mass transfer temperatures to assist the operation.To realize the synthesis,the given stream data should include the flow rates of rich streams(Gi),the maximum flow rates for lean streams(,the inlet and outlet concentrations for rich streams(and),the inlet and upper concentrations for lean streams(and),the inlet and outlet temperatures for rich and lean streams(and)as well as their allowable operation ranges.The target of the study is to obtain a CM&HEN by considering the interaction between mass transfer and heat exchange.However,the simultaneous synthesis is not simple for stage-wise superstructure,especially when the thermal property of stream cannot be pre-confirmed.This study will show how to process the simultaneous synthesis and optimization.The tradeoffs between MEN and HEN will be investigated via the objective of minimum total annual cost(TAC).

The equilibrium relationship is able to indicate how transferable components move between the riches and the leans.For one component system,the equilibrium relationship can be expressed as=mi,jxj+bi,j,whereand xjare the equilibrium compositions for transferable components in rich and lean streams,respectively,and mi,jand bi,jare the associated equilibrium coefficients which depend on the mass transfer temperatures related to HEN.Interactions between MEN and HEN complicate significantly the synthesis of CM&HEN.To properly solve this problem,the following assumptions that apply for dilute systems[5]are considered in this paper.They are:(1)Mass flow rate of each rich and lean stream remains constant through the network;(2)each mass exchanger unit operates isothermally;(3)mass exchange temperatures are only related to that of lean streams,and(4)the equilibrium distribution coefficient(mi,j)is a monotonic function of temperature(i.e.,mi,j=whereis the mass transfer temperature).

3.Synthesis and Optimization Method

3.1.Method statement

The synthesis and optimization of CM&HENs are based on that of sub-MEN and sub-HEN.Wherein,the coupling mode of subnetworks is a complicated interactional process rather than a simple aggregation.The major challenge appears as how to implement the integration when the thermal property of stream is un-predeterminable.

In this study,superstructure technique is utilized for the synthesis due to its competitive capacity at optimization comparing with pinch-based method.During process,the sub-MEN synthesis and the sub-network coupling will follow authors'previous work[20,9],wherein a superstructure-based method and a coupling mode were introduced for the MEN and the CM&HEN design,respectively.Then,the key issue of the paper becomes how to synthesis the sub-HENs in CM&HENs using a superstructure-based method.This is a difficult problem because the superstructure must be constructed before the synthesis.

3.2.Sub-HEN synthesis

The main function of sub-HENs in CM&HENs is to provide the appropriate mass transfer temperatures for lean streams.Thus,the operation requirement of sub-MENs will strongly affect the design of sub-HENs.

In a typical stage-wise superstructure[21,22]for HEN synthesis,it will present the potential match between any pair of hot and cold streams,and the match sequence is diversified by subjoining multiple stages in series.However,as the mass transfer temperatures are variables in the overall CM&HEN synthesis problem,this traditional stage-wise superstructure cannot be directly used because of the difficulty of predicting the all related streams with their thermal(hot or cold)and existence property beforehand.For this reason,constructing a superstructure that is accommodative to the uncertain mass transfer temperatures could be a promising approach.Thus,in this study,the so called“indistinct HEN superstructure(IHS)”is proposed.

IHS is a heat exchange superstructure which has potential heat exchange streams involved.Potential heat exchange streams are the streams whose properties are un-confirmable in advance.During synthesis and optimization,potential heat exchange streams could be hot,cold,or even nonexistent according to the mass exchange temperatures and flow rates of the related streams in sub-MENs.Then,there is match possibility between the any two potential streams.

Fig.1.Indistinct HEN superstructure.

Fig.1 has presented an IHS stage for 4 potential streams.As indicated,each potential stream splits into three branches to match with the left streams in a stage.The inter-stage temperature and the stream temperatures around an exchange unit are generally expressed asandwhere q indicates the stage numbers,m and n indicate the unique streams,and l and r present the left side and the right side,respectively.Here,the hot streams are set to flow from the left to the right and cold streams to flow oppositely.Then,when stream m is hot,andrepresent the inlet and outlet temperatures respectively,and when stream m is cold,the mentioned definitions ofandare exchanged.Worth to note during the construction of HISs that if there are streams of known or predictable thermal property,the matches between streams of the same property should been avoided.

The above has introduced how to build an IHS based on the potential heat exchange streams.During the synthesis and optimization of CM&HENs,the property of potential streams will be dynamically identified and the IHS will evolve according to the process data from sub-MEN.The overall application of IHS can be described with the following procedure.

3.2.1.Determine the potential streams and build the IHS

According to the coupling mode of CM&HEN,each lean stream with a start temperature should take heat exchange to meet its mass exchange temperature before going into sub-MEN.After the mass transfer operation,it should go through the sub-HEN again to reach the target temperature if there is requirement.Make comparison between the start temperature and the range of mass transfer temperature,as well as between the range of the mass transfer temperature and the target temperature,and then it can be determined which and how many potential heat exchange streams can produce from lean streams.Arranging all the potential streams in order,then the IHS can be built.In addition,if there are given or external hot/cold streams involved in the system,they can be considered into the IHS with averting the hot–hot and cold–cold matches.

Fig.2.Application procedure of indistinct HEN superstructure.

3.2.2.Identify the matches in IHS

During the synthesis and optimization,once the mass transfer temperatures and the flow rates of lean streams are known,the thermal and the existence properties of streams as well as the logical matches can be identified accordingly.By this way,an IHS can be transformed into a typical superstructure.

3.2.2.1.Identify the existence property.A potential heat exchange stream is taken into account if it has a non-zero flow rate accompanying with a variation on temperature.Otherwise,it is shielded as the stream and the related matches are all not going to be considered during the synthesis.Taking the superstructure in Fig.2(a)for example and assuming stream 3 does not exist,the superstructure will change into the one in Fig.2(b).

3.2.2.2.Identify the thermal property.An existent potential stream is identified as“hot”if it has a higher target/outlet temperature than the start/outlet,and conversely,the stream is identified as“cold”.Heat exchange is not allowed between the streams of a same thermal property.Therefore,the hot–hot and the cold–cold matches should be canceled.Assume that streams 1,2 and 4 in Fig.2(c)are identified as cold stream C1,hot stream H1and cold stream C2,respectively.Then,a typical superstructure stage as Fig.2(c)shows can be formed through shielding matches between C1and C2.

3.2.2.3.Form a superstructure including heaters and coolers.In most occasions,carrying merely the heat exchange between process streams is not enough for the all stream meeting their target temperatures,and thus heaters and coolers involving the hot and cold utilities are usually required.Fig.2(d)has shown a complete stage-wise superstructure including heaters and coolers.The corresponding sub-HEN synthesis is carried out based on it.

3.3.Mathematical formulation

To achieve the simultaneous synthesis and optimization of sub-MEN and sub-HEN for a CM&HEN,a NLP mathematical model is formulated for purpose.The optimization variables and the pretreatment measure,the model constrains as well as the objective function are given as below.

3.3.1.Optimization variables and the pretreatment

In this NLP mathematical model,the optimization variables are set as:

(1)Splitting ratio of rich branchi ∈NR,j ∈NL,and k ∈NK

(2)Concentration conversion ratioi ∈NR,j ∈NL,k ∈NK,and c ∈NC

(3)Splitting ratio of lean branchi ∈NR,j ∈NL,and k ∈NK

(4)Mass transfer temperature of lean stream∈NL

(5)Theoretical tray number of mass exchange unit Ni,j,k,i ∈NR,j ∈NL,and k ∈NK

(6)Splitting ratio of the branch stream in sub-HENm ∈NA,n ∈NA&m ≠n,and q ∈NQ

(7)Temperature conversion ratio,m ∈NA,n ∈NA with m ≠n and q ∈NQ

Ensuring variables have reasonable values are the basic premises for feasible solutions.For this sake,the ratio variables should be transformed into the general process expression by taking following pretreatment measures in the model:

(1)Flow rate of rich branch gi,j,k=,i ∈NR,j ∈NL,k ∈NK,wherei ∈NR,and k ∈NK.

(2)Outletconcentrationofrichstreamina massexchangeunit=i ∈NR,j ∈NL,and k ∈NK,where yi,k,cis the kth interstage concentration of stream i.

(3)Flow rate of lean branch li,j,k=,i ∈NR,j ∈NL,k ∈NK,whereand k ∈NK.

(4)Heat capacity flow rate of the branch stream in sub-HEN Fcpm,n,q=n ∈NA&q ∈NQ,whereand q ∈NQ,where FCPmis the total heat capacity flow rate of heat exchange stream m.

(5)The calculation of each heat exchange unit is carried out based on the identification of hot stream therein.Thus,if stream m is hot,its outlet temperature of unit(m,n,q)is expressed as=m ∈NA,n ∈NA&m ≠n,and q ∈NQ,where TIm,qis the qth inter-stage temperature of stream m.

3.3.2.Model constraints

3.3.2.1.Stream identification.Section 3.2 has introduced how to identify the thermal and existence properties of a potential heat exchange stream.In this model,identification code ID[m]is used to indicate the status of streams.ID[m]=0 means the corresponding potential stream is nonexistent during the on-going synthesis and ID[m]=1 means the potential stream is hot,while ID[m]=?1 is for the cold potential stream.The mathematical expressions of the identification are listed in Table 1.Moreover,the assignments of related process parameters are also given.

Table 1 Identification of hot/cold streams and determination of stream data

3.3.2.2.Constrains for sub-MEN synthesis.The mathematical model for sub-MEN synthesis follows that in literature[17].It contains a list of mass and flow rate balances around the system,superstructure stage,exchange unit,mixer and splitter.Equipment sizing equations are used for the calculation of mass exchangers,and the process specification constrains as well as the feasible constrains are considered to ensure the effectiveness of the solutions.

3.3.2.3.Constrains for sub-HEN synthesis.

(1)Heat balance for each stream When stream m is hot,then:

When stream m is cold,then:

(2)Mass balance for each stream in a stage

(3)Inlet temperature of stream in an exchange unit When stream m is hot,then:

When stream m is cold,then:

(4)Heat balance of stream in a network stage

(5)Heat balance in a heat exchange unit

For the two process streams involved exchanger:

When stream m is hot,then the heat balance for cooler is

When stream m is cold,then the heat balance for heater is

(6)Heat balance for mixer and splitter between adjacent stages

(7)The calculation of heat exchange area

For the two process stream involved exchangers:

m ∈NA, n ∈NA, ID[m ]≠I(mǎi)D[ n]≠0, q ∈NQ;

For heaters:

m ∈NA, ID[m ]=?1;

For coolers:

m ∈NA, ID[m ]=1;

(8)The monotonous trend of temperatures for streams

(9)Non-negative constraints

The variables and process parameters in model are all non-negative.

3.3.3.Objective function

Purpose of this study is to obtain a CM&HEN with the minimum total annual cost.Eq.(16)has shown the elements in TAC,wherein theandindicate the operating cost of external MSAs and the capital cost of mass exchanges,andandindicate the operating cost of hot/cold utilities and the capital cost of heat exchanges.The detail formulations ofandare respectively shown with Eqs.(17)–(20).

3.3.4.Model solution

The NLP mathematical model built in this paper has severe non-linear property since there involves a plenty of non-linear equations.Solving this model would be a very hard work for the traditional gradient-based optimization algorithms even just asking for a feasible solution.For this reason,a commendable stochastic algorithm of hybrid genetic algorithm–simulated annealing algorithm(GA–SA)[23],which has excellent global researching ability for large-scale problem,is applied.To catch the optimization intention,all the mathematical expressions and the algorithm are programmed with language C++.Optimization variables set in Section 3.3.1 are treated as the genes in solution“DNA”and the best results will be achieved until reaching the stopping criteria.

4.Case Study

An example taken from literature[6]is illustrated to show the application of the method.The mass transfer and heat transfer between two hydrogen sulfide-rich gas streams(R1,R2),one process lean stream S1and one external MSA S2are simultaneously considered in the example.The related cost and stream data are given in Tables 2–4.Following the study by Isafiade and Fraser[6],they do not set any target for the temperature of S2as it is an external MSA.Hydrogen sulfide is the component supposed to be removed from the riches to the leans.Eqs.(21)and(22)have shown the equilibrium relationships of hydrogen sulfide in lean stream S1and S2,respectively.To expand the application,four external hot and cold streams are considered by this example and the data are listed in Table 5.

Table 2 Cost data

Table 3 Stream data

Table 4 Thermal data for the streams

Table 6 Potential hot/cold streams

At every beginning of the synthesis,all the certain and potential heat exchange streams should be fixed.Notice from Table 4 that the supply temperature of S1is equal to its target temperature and S2has no special demand of target temperature.Thus,by making comparisons with the upper and lower bounds of mass exchange temperatures,this example is likely to produce one hot potential and one cold potential streams from S1as well as one potential without knowing hot or cold from S2.Therefore,7 heat exchange streams in total including 4 external hot/cold streams can be determined when bypass streams are not taken into account.The 7 heat exchange streams are ranked in order as shown in Table 6.

Then,construct IHS based on the heat exchange streams was identified above.Stream 3 in Table 6 is the only potential whose thermal property is un-predictable.Thus,during the building of IHS,stream 3 has match connections with each of the rest streams,and the hot–hot and cold–cold matches are not allowed for the streams whose thermal properties are certain.

Synthesize and optimize for the most cost-effective CM&HEN based on the established IHS and the corresponding NLP mathematical model,then the desired network is obtained at the TAC of 340.2×103USD·a?1,accompanying with 160.6×103USD·a?1for MEN and 179.6×103USD·a?1for HEN.Fig.3 shows the network configuration,wherein the upper part is sub-MEN and the lower part is sub-HEN.To accomplish the mass transfer task,39.71 kg·s?1of S1,1.51 kg·s?1of S2and four mass exchangers are required by the sub-MEN.The mass transfer temperatures of S1and S2are 368.0 K and 280.2 K,respectively.As results,the potential streams 1 and 2 in Table 6 are nonexistent in the obtained network,leaving the stream 3(310 K–280.2 K)sourcing from S2as a hot stream H3.In the sub-HEN formed for H3and the four external streams,there are four process stream involved exchangers,one heater and three coolers.

In previous work[9],the best solutions were achieved at TAC of 342.5×103USD·a?1with four mass exchangers and seven heat exchangers involve.By making comparison,it can be found that the proposed method is able to obtain a better solution,because the superstructure-based method allows the non-isothermal and nonequal concentration mixing rather than the isothermal and equal concentration mixing.These results have shown the successful application of superstructure technique on CM&HEN synthesis problem.

5.Conclusions

In this paper,the superstructure technique is studied for the simultaneous integration of mass exchange and heat exchange.In order to make it workable to the all possible stream conditions,a superstructure called as IHS is proposed for the synthesis of sub-HEN.Wherein,the all matching possibilities in sub-HEN can be included without predicting streams'existence and thermal property beforehand.To carry out the global optimization,an NLP mathematical model aiming at the minimum TAC is formulated and solved with a hybrid GA–SA approach.Therefore,the tradeoff between sub-MEN and sub-HEN can be fully investigated during the optimization.At last,an example from literature has been examined.The satisfactory results have illustrated the application of the proposed method for the simultaneous synthesis.And in further work,the IHS will be extended to other problems which have indeterminate hot and cold streams.

Nomenclature

A heat transfer area,m2

B exponent in cost equation of heat exchanger

b intercept of equilibrium equation

C unit cost for MSA/lean stream/utility/column tray,USD·a?1

CE pre-exponential factor in cost equation of heat exchanger

CF fixed cost for heat exchanger,USD·a?1

cpheat capacity,kJ·kg?1·K?1

FCP heat capacity flow rate of main stream,kW·K?1

Fcp heat capacity flow rate of tributary stream,kW·K?1

fCannualized capital cost,USD·a?1

fOannualized operating cost,USD·a?1

fTACtotal annual cost,USD·a?1

G mass flow rate of the rich main stream,kg·s?1

g mass flow rate of the rich tributary stream,kg·s?1

h heat transfer film coefficient,kW·m?2·K?1

L mass flow rate of the MSA/lean main stream,kg·s?1

LMTD logarithmic mean heat transfer temperature difference,K/°C

l mass flow rate of the MSA/lean tributary stream,kg·s?1

M equilibrium contribution coefficient in equilibrium equation

N tray number of mass exchanger

Q heat load,kW

Qcu heat load of cold utility,kW

Qhu heat load of hot utility,kW

T actual temperature of process stream,K/°C

TI inter-stage temperature in IHS,K/°C

t temperature at the both end of exchanger in IHN,K/°C

U total heat transfer coefficient,kW·m?2·K?1

x concentration of MSA/lean stream,kg·kg?1

y concentration of rich stream,kg·kg?1

φ/φ1 ratio

Superscripts

H hot stream/heat exchange network

l left side in IHS

lo lower bound

M mass exchange network

MSA mass separation agent/lean stream

R rich stream

r right side in IHS

T temperature

tray tray in mass exchanger

up upper bound

Fig.3.Optimal network using the proposed method.

y concentration of rich stream

* equilibrium concentration/mass transfer temperature

Subscripts

c the cth component,c ∈NC

cu cold utility

hu hot utility

i the ith rich stream,i ∈NR

j the jth MSA/lean stream,j ∈NL

k the kth stage in MEN,k ∈NK

m/n the mth/nth heat exchange stream,m ∈NA

q the qth stage in HEN,q ∈NQ