Step-wise synthesis of work exchange networks involving heat integration based on the transshipment model☆

Yu Zhuang ,Linlin Liu ,2,Qilei Liu ,Jian Du ,*

1 Institute of Chemical Process Systems Engineering,School of Chemical Engineering,Dalian University of Technology,Dalian 116012,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

1.Introduction

With the aggravation of energy crisis and the wide application to principle ofmomentumtransport,heattransport,masstransportand reaction engineering in chemicalprocess,our primary focus has been from mass and heat to momentum(work)[1,2].The design of work exchange networks,as a key part of energy recovery systems,will have significant influence on energy consumption in process systems[3].However,the research on synthesis of work exchange networks is still in early stages.

Work can be exchanged between work sources and work sinks through direct or indirect work exchangers.The direct work exchanger is mainly composed of a pair of combined operated piston pumps.The pressure work(mechanical energy)can be transferred from work sources to work sinks directly with the work sources and work sinks alternatively flowing into and out of the piston pumps[4].But in the indirect work exchanger,the energy is exchanged in two steps:the pressure energy of work sources is converted to mechanical energy through expanders at first and further converted to the pressure energy of the work sinks through compressors.The utilization of this device is very wide and itstechnology isquite mature,butthe disadvantage ofindirect work exchangers is that the energy efficiency is relatively low[5,6].But forthe abovementioned directwork exchangers,the recovery efficiency of piston pumps is 100%in theory.This is the reason why the direct work exchange network synthesis is studied in this paper.

Given the urgency ofachieving significantgoalforimproving the energy efficiency,work integration and a closer interaction between work and heatshould be regarded as available alternatives.Thus itis essential to integrate both work and heat in the same network in order to realize more energy conservation[7–9].Shinetal.[10]presented a mixed integer linear programming(MILP)formulation to optimize boil-off gas compression operations for minimizing the total average energy consumption in an LNGreceiving and re-gasification terminal.Additionally,DelNogaletal.[11]designed the optimalmixed-refrigeration for multistage refrigeration processes with compressors.In their subsequent work,they introduced an optimal power system for utility networks considering expanders and electric motors as drivers to meet the requirements on the given power demand of several compression stages[12,13].In spite of immense scientific research progress on the mathematical programming techniques for work integration,the direct work exchangers are not taken into account in all these approaches.

Until now,research approaches for synthesis of direct WEN involve graphical methods and transshipment model methods.Huang and Fan[14] first proposed the operational principles of direct work exchangers to exchange work between two streams,which employed pressure(P)versuswork(W)diagram to integrate the WEN according to the one-toone stream matching.However,it should be noted that this method is complex for work exchange networks synthesis with multiple streams,where the identified target cannot be the optimal solutions because of no work integration as a whole.Based on the unique characteristics of direct work exchangers,Liuet al.[15]developed a graphical integration method only applied to isothermal process for work exchange network plotting the composite curves of work sources and work sinks in the lnP versus Wdiagram,where two assistant work sink composite curves were pictured to help identify the feasible match between work sources and work sinks to meet the pressure constraints.Recently,Zhuanget al.[16]presented the condensed transshipment model to synthesize the directwork exchange network ofisothermalprocess by constructing intermediate pressure to obtain the initialWEN and then merging the adjacent pressure intervals to optimize the WEN.Though,in the two papers reported,the shaftwork was calculated and evaluated in the isothermal process as linear constraints,not being able to realistically reflect the relationship between pressures and temperatures of gas streams when they flow into and out of the work-exchange equipment.

Despite the extensive study on the synthesis of direct work exchange networks,research on work integration in adiabatic process is rarely reported.In our present paper,the transshipment model of adiabatic process is established to formulate the NLP model.After that,we focus on the WEN synthesis with heat integration to attain the minimal total annual cost(TAC)with the introduction of heat-exchange equipmentthat is achieved by the following strategies in sequence:introducing heat-exchange equipment directly,adjusting the work quantity of the adjacent utility compressors or expanders,and approximating upper/lower pressure limits consequently to obtain considerable cost savings of equipment investment as well as utility operation.Ultimately,the optimal work exchange network con figuration can be gained with the minimum TAC.

2.Problem Statements

A chemical process hasNHhigh-pressure streams(work sources)surization utility(compression work orpressurized steams)and depressurization utility provided by expanders or pumps are used to balance the global energy because the total work quantity of high-pressure streams is commonly not equalto thatof low-pressure streamsderiving from the pressure driving force in chemical engineering kinetics.

Additionally,for simplification of solving,the following assumptions are made:

(1)All streams behave as ideal gas[17].

(2)All compressors and expanders are reciprocating without clearance volume.

(3)Each stream in the WEN is above its dew point with no phase change.

(4)Adiabatic reversible compression/expansion is considered.

(5)The work efficiency is always 100%in differentpressure intervals,where frictional loss is neglected.

Based on these assumptions,a work exchange network is first designed to attain the minimum utility consumption on condition that allstreams can satisfy the constraints ofpressures and temperatures.Afterwards,heat-exchange equipment is introduced to achieve the stepwise design of both work and heat integration with the objective of the minimum total annual cost.

3.Syntheses of WEN Based on Transshipment Model

3.1.Formulation of transshipment model

To construct the transshipment model,the pressure difference between the high-pressure stream and the corresponding low-pressure stream should be equal to or greater than the minimum approach pressure on the basis of the approach for division of pressure intervals presented by Zhuanget al.[16].In addition,based on the proposed CTM(condensed transshipment model)by Chen[18],two-segment transshipment model[16]is also adopted in this paper.

In conclusion,the objective functions and constrains to formulate an NLP model can be obtained as follows according to the above analysis.

(1)Objective function

where all the variables must be non-negative,and obviously,the residualwork quantity ofinitialand finalpressure intervalshould be equalto zero,which is represented in the following equation:

3.2.Optimization of work exchange network confi guration[16]

As for the feasible match between HP and LPviathe direct work exchangers,the inlet pressure of LP should be higher than the outlet pressure ofHP while the outlet pressure ofLP should be lower than the inlet pressure of HP,the corresponding pressure constraints represented by Eqs.(9)and(10),to guarantee the momentum transfer rate.Furthermore,the constraints can be solved by the presented strategy of construction of intermediate pressures and then using the stream split can generate the initial work exchange network.where ΔPmindenotes a minimum pressure approach whose value may significantly determine the utility consumption as well as the optimal network.However,how to get an optimal value of the minimum pressure approach is not a concern in this paper.We only consider it as a constant variable in our transshipment model.

Combined with Eqs.(9)and(10),the following pressure constraint of HP can be further found:

On the basis of the above established transshipment model,the work cascade diagram can be gained by solving each sub-network with the objective of minimum utility consumption.Afterwards,each feasible match between high-pressure streams and low-pressure streams will be identified by analysis of all the sub-networks.Hence,the initial work exchange network con figuration associated with these feasible matches is to be obtained.

Subsequently,the strategy for merging of the adjacent pressure intervals is employed to further reduce the number of work-exchange equipment and decrease the utility consumption,which produces the optimal work exchange network con figuration because an excess of units have to be utilized in order to recover more work.

3.3.Matching rules for synthesizing WEN

For a feasible match between work sources and work sinks through the direct work exchangers and a reasonable merging among the adjacent pressure intervals,the following matching rules between HP and LP should be abode by based on the above analysis.The specific rules can be concluded as:

(1)If the inlet and outlet pressure difference of high-pressure streams is less than double of the minimum approach pressure,high-pressure streams cannot be matched with any lowpressure streams.

(2)Even though the inlet and outlet pressure difference of highpressure streams is greater than or equal to double of the minimum approach pressure as well as work quantity of HP is equal to that of LP,HP cannot be matched with LP on condition that the following relation is satis fied:

(3)The HP and LP can be matched with each other as long as the following pressure constrains represented by Eqs.(9)and(10)are satis fied.

(4)On the premise that the pressures of HP and LP meet the relations of Eqs.(9)and(10),meanwhile,the work quantity of HP is larger than that of LP;the stream splitting should be utilized for HP,which should also coincide with Rule(2).If the streams are be split into several branches with different flow rates,the sub-streams are reformed to their original states at the end of each interval by mixers,where the mass balances at the mixing point can be expressed as follows in the principle of isobaric mixing:

(5)The priority selection is to match the HPand LP with similarwork quantity when various matching options exist.Moreover,if the work quantity of HP(LP)is larger than that of the matching LP(HP),the formerone should considermatching multiple streams.

(6)The excess work quantity of HP(LP)can be supplemented by utility expanders(or utility compressors),which have to be allocated in parallel with work exchangers in order to satisfy the pressure constrains.

Based on the above proposed rules,Rules(1)–(3)indicate the necessary and sufficient conditions for stream matching in WEN synthesis to obtain the initial work exchange networks.Rule(6)signifies that the utility equipmentshould be allocated in parallelwith the corresponding work exchanger where the branch streams are subsequently mixed in the principle of isobaric mixing according to Rule(4).In addition,Rule(5)is alternative to optimize the initial WEN for obtaining the optimal con figuration so that the number of work exchangers,expanders and compressors is further decreased together with the reduction in the utility consumption.

4.WEN Synthesis Involving Heat Integration by Introducing Heat-exchange Equipment

It is obviously indicated from Eqs.(4)and(5)that shaft work has exceedingly complex non-linear relation with both pressure ratio and inlet temperature,which signifies that shaft work and heat content can be integrated because inlet temperature variation leads to an enormous change of the whole utility consumption as well as the work exchange network con figuration.Additionally,since work is of higher quality and more expenditure,it is of dramatically vital signi ficance in economic aspects to substitute work by heat by means of replacing the utility expanders or compressors with heat-exchange equipment.

Based on this viewpoint,the heat-exchange equipment is introduced to further synthesize the optimal work exchange network with heat integration.To be in pursuit of the objective of WEN design involving heat integration,it is a relatively straightforward and extremely efficient method to remove the utility equipment in parallel or in series with the corresponding work exchanger in Fig.1.Fig.1(a)illustrates that the utility expander is allocated on the branch stream in parallel with direct work exchangers while the utility compressor is con figured on the LP stream in series with the direct work exchanger,shown as Fig.1(b).This figure is regarded as an illustrative example to demonstrate whether the parallel or series utility equipment should be eliminated or not.

Furthermore,theP–Tcomparison diagram of parallel expanders and series compressors before and after the heat integration is drawn to investigate whether the inlet and outlet pressures and temperatures of the sub-network will keep unchangeable when the heat-exchange equipment is introduced,as shown in Fig.2.The results indicate that the supply and target states can keep unchanged with the introduction of heat-exchange equipment adjacent to the utility equipment in parallel with the work exchanger.But for the heat-exchange equipment in series with the utility equipment,the supply and target temperatures and pressures will change.Because the supply and target state of each sub-network are both fixed with constant temperatures and pressures,thus the strategy of synthesis of optimized work exchange network with heat integration is proposed by introducing heat-exchange equipment adjacent to the utility equipment in parallel with the corresponding work exchanger in order to further decrease the utility consumption and reduce the number of utility equipment.

4.1.Rules of introduction of heat-exchange equipment

In the optimal work exchange network,several compressors or expanders consume smaller work and operates at lower energy efficiency resulting in excessive equipment investment,removal of which will achieve considerable savings of equipment investment.In addition,it is of vital significance in the economic aspects that the expanders or compressors are substituted by heat exchangers,which means that the heat replaces a small amount of work,because of higher quality and cost of work compared with that of heat.Therefore,we propose the strategy oftrade-offbetween work and heatby introducing the heat-exchange equipment ahead of the direct work exchangers to change the inlet temperature of the corresponding streams,which proceeds to alter the work quantity provided by HP(or consumed by LP).When the work quantity ofHP is justequalto thatof LP,the parallel expander or compressor can be removed.As a consequence,the introduction of heat-exchange equipment should abide by the following rules.

(1)The heat-exchange equipment should be introduced at the inlet of the work exchanger where a utility expander of compressor exists in parallel.

(2)The heat-exchange equipment should appear in pairs which involve a cooler and a heater.

Fig.1.Utility equipment in parallel or series with work exchangers.

Fig.2.P–T comparison diagrams of parallel expanders and series compressors before and after the heat integration.

Fig.3.Strategy of direct introduction of heat exchangers.

(3)As for a work exchanger,only one stream is considered to be heated or cooled.If work quantity of HP is more than that of LP,the cooler/heater will be placed at the inlet/outlet of HP or the heater/cooler should be placed at the inlet/outlet of LP,andvice versa.

(4)The inlet and outlet pressures and temperatures of each pressure interval keep unchangeable no matter whether coolers or heaters are introduced or not.

(5)To eliminate the utility expanders or compressors in parallelwith the work exchangers and achieve the trade-offbetween heatand work,the following strategies are adopted in sequence,which include introducing heat-exchange equipment directly,adjusting the work quantity of the adjacent utility compressors or expanders,and approximating upper/lower pressure limits.

4.2.Strategy of heat-exchange equipment applied to work exchange networks

After introduction of heat-exchange equipment,the outlet pressure of streams will vary along with the various inlet temperatures so that the inlet and outlet pressures of work exchangers willchange.Obviously,this nonlinear constraint is solved with increased difficulties and even results in an infeasible match between HP and LPviadirect work exchangers.Hence,the reasonable solving strategies should be proposed to solve the more complicated optimization model.

The first step is to adopt the strategy of direct introduction of heatexchange equipment,considering the placement of heat-exchange equipment at high-pressure streams as an example.The corresponding inlet and outlet streams states are illustrated in Fig.3.Regarding the ideal gas,the relationship between pressures and temperatures of streams through the heat-exchange equipment is represented by Eqs.(14)and(15).Combined with Eqs.(7)and(8),an objective function of Eq.(16)is formulated,where the target function value is set to zero by optimizing the temperature of HP at the inlet of the work exchanger as the decision variable.

Then the feasible solution can be obtained by the goal seek on the EXCEL.

Fig.4.Introduction of heat exchangers in the same stream.

Fig.5.Introduction of heat exchangers in the different streams.

However,if the feasible solution is inconsistent with the pressure constraints expressed by Eqs.(9)and(10),the strategy of adjusting the work quantity of the adjacent utility compressors or expanders should be employed.The precondition for successful application of this strategy is that the work exchanger must be strung with utility expanders or compressors in a series.

In respect to this strategy,two cases are carried out with the aim of identifying the optimal con figuration for the WEN with introduction of heat-exchange equipment.

In case 2,the heaters and coolers are in series with the utility expanders or compressors in the different streams,as shown in Fig.5.Take thefirst step to guarantee the relation ofHP pressures and LP pressures,represented by Eq.(19).And then optimization of WENwith heat exchangers can be gained by continuing to employ the strategy of the direct introduction of heat-exchange equipment.

Furthermore,if both the two strategies result in the infeasible match due to dissatisfaction with pressure constraints,the final strategy of approximating the upper or lower pressure limit should be adopted.Moreover,this strategy can only be applied to the following four cases.

(1)When the following two conditions are simultaneously satis fied,larger work quantity of HP compared with that of LP and inlet pressure of HP satis fied with Eq.(20),coolers can be placed at the inlet of HP to adjust the inlet pressure to meet the pressure constraint expressed by Eq.(21).

(2)When the following two conditions are simultaneously satis fied,smaller work quantity of HP compared with that of LP and inlet pressure of LP satis fied with Eq.(22),coolers can be placed at the inlet of LP to adjust the inlet pressure to meet the pressure constraint expressed by Eq.(23).

Table 1The utility cost parameters

(3)While the following two conditions are simultaneously satis fied,larger work quantity of HP compared with that of LP and outlet pressure of LP atis fied with Eq.(24),heaters can be placed at the inlet of LP to adjust the outlet pressure to meet the pressure constraint expressed by Eq.(25).

Table 2Stream data for the case

(4)While the following two conditions are simultaneously satis fied,smaller work quantity of HP compared with that of LP and outlet pressure ofHP satis fied with Eq.(26),coolers can be placed atthe inlet of HP o adjust the outlet pressure to meet the pressure constraint expressed by Eq.(27).

Based on the above analysis,this strategy can facilitate the reduction of utility consumption of compressors or expanders in parallel with the work exchangers to a certain extentwithout complete removal of these utility compressors or expanders.It is found that these three strategies can contribute to trade-off between heat and work at the extreme in order to achieve the considerable savings in work-exchange equipment investment and utility consumption.

從重慶醫(yī)科大學(xué)動物實驗中心領(lǐng)取6～8周，體質(zhì)量20 g左右的雄性C57BL/6 WT小鼠36只，隨機分為3組（每組12只），雄性TLR4-/-小鼠36只，隨機分為3組（每組12只），兩種小鼠的各組均按照1.2中方法分組，分別給予：Ⅰ、無菌生理鹽水，Ⅱ、大劑量LPS（20 mg/kg），Ⅲ、CA-074（10 mg/kg）+大劑量LPS（20 mg/kg）方式處理，12 h后收集外周血及肝組織進行檢測。

4.3.Economic analysis

In this section,TAC,composed of investment cost and operational cost,for three different work exchange networks which involve initial WEN,optimal WEN and WEN with heat-exchange equipment isrespectively computed and analyzed compared with the results ofinitial WEN to further demonstrate the feasibility and effectiveness of the strategy of introduction of heat-exchange equipment.The specific cost formulas are expressed as follows.

Table 3Division of pressure intervals for the case

(1)Expander investment cost and compressor investment cost[19]:

where the pressurized and depressurized utility consumption denoted byWPUandWEUrespectively can be obtained by the equations similar to Eqs.(5)and(6).

The utility cost parameters are shown in Table 1.

Specially,the LP Steam Generation and MP Steam Generation are labeled as coolant in Aspen Energy Analyzer.This means that LP steam and MP steam which have been already used are heated again by hot streams to generate the available utility steams.Therefore,the cost parameters of LP steam and MP steam are both negative.

5.Case Studies

This case taken from Liuet al.[15]consists of three high-pressure streams and two low-pressure streams.The corresponding data are listed in Table 2.

In the calculation,the minimum pressure approach is taken as 70 kP.According to the assumptions,the pressurization of LP streams and depressurization of HP streams are reckoned as ideal adiabatic process with constant adiabatic exponent equal to 1.41.On the basis of data in Table 2,the whole system is divided into seven pressure intervals,as illustrated in Table 3.In accordance with the constructed transshipment model,the work balance calculation and matching between HP streams and LP streams are conducted in each pressure interval,the solution of which can be obtained by utilizing the simplex method of non-linear programming in EXCEL,represented in the work cascade diagram as shown in Fig.6.

Subsequently,as for the optimization procedure,the adjacent pressure intervals should befirstmerged on the basis ofthe proposed merging strategy[16].Then,the WEN con figuration may be adjusted to the optimal constitution targeted with the deep reduction of the minimum utility consumption as wellas the decreasing tendency ofthe numberof work-exchange equipment based on the matching rules presented in Section 3.3.The results are listed in Table 4.

Compared with solutions reported by Liuetal.[15]using a traditional graphical method,it is found that the total work recovery is 482.87 kW,the minimum pressurization utility consumption is 177.21 kW,and the minimum depressurization utility is 215.40 kW.This result is just compatible with the characteristic ofideally reversible shaft work in isothermal and adiabatic process.In other words,compression work in isothermal process is the least while the expansion work of adiabatic process is the least.Accordingly,the integrated optimal work exchange network with the minimum utility consumption and the minimum number of work-exchange equipmentcan be obtained,as shown in Fig.7.As a result of the above analysis,the proposed method is of stronger feasibility and higher efficiency.

To achieve the WEN synthesis with heat integration,the first step is to consider the direct introduction of heat-exchange equipment where we should con firm if the pressure difference of streamsviadirect work exchangers meets the requirement on the formulated pressure constraints.However,this is not satis fied hereby.Subsequently,the work quantity of utility expander or utility compressor adjacent to the relevant work exchanger is adjusted to satisfy the pressure constraints,but HP1 and LP2 are still unsatis fied with them.Finally,the pressure of streams approximates the upper or lower pressure limit to decrease the work quantity of utility expanders or compressors in parallel to the best extent possible.The optimized work exchange network with heat-exchange equipment is depicted in Fig.8.

Fig.6.Work cascade diagram of the case.

Table 4Comparison of this paper with literature for the case

Compared the optimal WEN in Fig.7 with that in Fig.6,it can be found that on one hand for equipment investment,six more coolers or heaters are added to the WEN and the number of utility expanders and utility compressors is one less than that in Fig.6,respectively.On the other hand for utility consumption,the heat and cold utility consumption are respectively 347.41 kW and 338.36 kW,resulting in a reduction of 46.53 kW depressurization utility consumption and 37.44 kW pressurization utility consumption.After that,we further consider the economic analysis on the three different WEN structures by calculating the corresponding TAC to show the superiority ofthe proposed approach,the results of which are listed in Table 5.

Fig.7.The work exchange network for the case.

Fig.8.The optimal work exchange network with heat-exchange equipment.

Table 5 illustrates that the TAC of optimal WEN decreases by 38.19%in contrastto initialWEN,while TAC of the optimalWENwith introduction of heat-exchange equipment has a considerable reduction by 15.68%compared with optimal WEN without heat integration,thus it is clear from the above results that the proposed method is proven to be feasible and effective.

Table 5Cost comparison of three network con figurations

6.Conclusions

A novelmethodology for synthesis ofdirectwork exchange networks in adiabatic processis firstproposed in thispaper,where a nonlinearprogramming(NLP)model is solved to get the optimal WEN by regarding the minimum utility consumption as objective function and optimizing the initialnetwork con figure in accordance with the presented matching rules.Moreover,the trade-off between work and heat to attain the minimal total annual cost(TAC)can be achieved by introduction of heat-exchange equipmentusing the following strategies in sequence:introducing heat-exchange equipmentdirectly,adjusting the work quantity of the adjacent utility compressors or expanders,and approximating upper/lower pressure limits consequently to obtain considerable cost savings ofexpandersorcompressorsaswellaswork utility consumption.From case study we can see that the TAC of optimal WEN decreases by 38.19%in contrastto initialWEN,while TAC ofthe optimal WENwith introduction of heat-exchange equipment has a considerable reduction by 15.68%compared with the optimal WEN without consideration of heat integration,thus it is clear from the above results that the proposed method is proven to be feasible and effective.

Nomenclature

Aheat exchange area,m2

CCcompressor cost,USD·a-1

CEexpander cost,USD·a-1

CHEheat exchanger cost,USD·a-1

CWEwork exchanger cost,USD·a-1

Fvolume flow rate of streams,m3·s-1

FCP heat capacity flow rate,kW·K-1

HP high-pressure streams(work sources)

hheat transfer film coefficient,kW·m-2·K-1

ihigh-pressure streami

jlow-pressure streamj

kpressure intervalk

LP low-pressure streams(work sinks)

nikmolar flow rate of high-pressure stream i into the pressure intervalk,mol·s-1

njkmolar flow rate of low-pressure stream j into the pressure intervalk,mol·s-1

nsmolar flow rate of the branch of a stream,mol·s-1

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