Chenglin Chang,Yufei Wang*,Xiao Feng

State Key Laboratory of Heavy Oil Processing,China University of Petroleum,Beijing 102249,China

Keywords:Indirect integration Intermediate- fluid Across plants Pipeline Optimization

ABSTRACT Totalsite heatintegration(TSHI)provides more opportunities for energy saving in industry clusters.Some design methods including directintegration using process streams and indirectintegration using intermediate- fluid circuits,i.e.,steam,dowtherms and hotwater,have been proposed during lastfew decades.Indirectheatintegration is preferred when the heat sources and sinks are separated in independent plants with rather long distance.This improves energy efficiency by adaption of intermediate fluid circle which acts as a utility provider for plants in a symbiotic network.However,there are some significant factors ignored in conventional TSHI,i.e.the investment of pipeline,cost of pumping and heat loss.These factors simultaneously determine the possibility and performance of heat integration.This work presents a new methodology for indirect heat integration in low temperature range using hot water circuit as intermediate- fluid medium.The new methodology enables the targeting of indirectheatintegration across plants considering the factors mentioned earlier.An MINLP modelwith economic objective is established and solved.The optimization results give the mass flow rate of intermediate- fluid,diameter of pipeline,the temperature of the circuits and the matches of heat exchanger networks(HENS)automatically.Finally,the application of this proposed methodology is illustrated with a case study.

1.Introduction

In recent years,increasing consumption of fossil fuels has gained growing concerns about energy efficiency all around the world[1,2].To mitigate the future climate challenges and rising fuel price risks,most industries are seeking strategies to reduce energy efficiency.Actually,energy efficiency can be significantly enhanced by better heat recovery technologies.Those approaches are seen as sustainable solutions for industries and are expected to improve energy efficiency at economical cost.

Many methods and concepts had been explored to optimize energy systems in chemical processes.Pinch technology was first developed by Linnhoff as an applicable design method for HENS in an individual process[3,4].Dhole and Linnhoff extended pinch technology into TSHI for fuel co-generation,emissions,and cooling[5].In their work,only differentlevels ofsteamwere used as the intermediate to accomplish indirect heat integration between processes.TSHI had received growing interests since 1990s.It allows industrial clusters to accommodate heating and cooling demands of different processes in an overall perspective[6–8].Ahmad and Hui studied both indirect heat integration using different levels of steam and direct heat integration using processes streams[9].Hui and Ahmad continued theirwork by integrating energy and capitalcalculations[10].Another continuous work was done by Hui and Ahmad,and only indirectly heatintegration using differentlevels of steam was considered between different processes[11].Their studies were all based on graphical targeting tools of pinch technology.

Bagajewicz and Rodera found thata single plantcan further improve energy efficiency by sharing energy with other plants[12].They developed an energy targeting procedure for heat integration between two plants.Based on mathematical programming,they studied direct heat integration using processes streams and indirect heat integration using intermediate- fluid circuits which needed not to be isothermal.Bagajewicz and Rodera developed another procedure for heat integration across plants using intermediate- fluid circle and calculated targets for several industrial cases[13].They also developed an MILP model to determine the optimal location of the fluid circuits in indirect heat integration.Bagajewicz and Rodera extended their work for systems with more than two plants[14].They pointed out that direct integration may achieve less energy savings than indirect integration,as there would be a large heatloss for process streams participated in heattransfer across plants especially when the distance was long.Thus,indirect heat integration between independent plants using transfer mediate was preferred[15].Hackl and Andersson analyzed the synergy effects of cooperation between different plants[16–18].In their work,they suggested hot water circles to build a more interconnected utility system.This enables heat integration between plants in order to achieve an industrial symbiosis and decrease resource energy consumption.No energy-capital trade-off calculations were carried out in their studies.

Most researches above only consider heat recovery aspects.However,Wang and Feng found that distance was also a key factor which was not fully considered in conventional TSHI[15].Firstly,heat loss results in a large decline in the heatquality during long distance transportation,so that the temperature of intermediate- fluid mightnot be high enough to satisfy the heat sinks.Secondly,the investment of pipeline,cost of pumps and additional heat exchangers was very high,especially when the distance between plants is long.Thirdly,the pump power for transporting fluid during transportation should be considered.Nevertheless,their studies only simulated the TSIH with considering distance factors.The mass flow rate and temperature of intermediate- fluid circuit were not optimized,which have a significant impact on the economic aspect of TSIH.

This work presents a mathematical programming approach for indirect heat integration across plants considering the factors mentioned.As the work focus on low temperature range,hot water is used as the intermediate- fluid medium.An MINLP model based on economic objective is established and solved.The optimization can give the mass flow rate of intermediate- fluid,diameter of pipeline,the temperature of the intermediate- fluid circuits and the matches of HENS automatically.The proposed methodology can be used by industrial clusters to explore energy and cost savings opportunities.The application is illustrated with a case study based on two plants within an industry cluster.

2.Methodology

This section presents a systematic methodology to target maximum waste heat recovery in low temperature range across individual plants within one industrial cluster.Economical intermediate- fluid circuit between independent plants can be established to accomplish indirect heat integration synergies.The methodology consists of several steps below.

2.1.Definition

A plant is defined as an independent production unit which consists of one or more processes served by a utility system[19].There is a large amountofexcess heatejected to cold utility in some plants.Meanwhile,some cold streams are located in other plants.Sharing and use of waste heat between these plants show significant energy savings.As the distance is long,indirectly heat integration between these plants using intermediate- fluid circuit is considered.For the purposes of developing the problem statement,the heat source and sink plant are additionally defined as follows.

(1)Heat source plant is characterized with excess heat by several hot steams,where it is allowable for pipeline's series and parallel between each stream.

(2)Heat sinks plant is characterized with several cold steams,where it is allowable for pipeline's series and parallel between each stream.

It is noted that when it is a two-plant heat integration problem,the two plants are a pure heat sink plant and a pure heat source plant respectively.When the problem consists of more than two plants,some of plants in the problem can be a heat sink plant and a heat source plant at the same time.

2.2.Superstructure of the MINLP model

Floudas etal.have established an MINLP model of heatexchange between one cold stream and many hot streams or one hot stream and many cold streams[20].In their work,a procedure is presented for automatic generation of optimal configurations for HENS.The superstructure in Fig.1[20]includes alternatives for splitting,mixing and bypass of stream,where streams can be mixed non-isothermally to increase the amountof heatrecovery with minimalheattransfer area.Heatintegration between plants using intermediate- fluid circuits can be seen as heat exchange between one cold stream and many hot streams or one hot stream and many cold streams.This superstructure also includes options for series and parallel matching as well as splitting,mixing and bypassing between streams.

2.3.Objective and related constraints

Some key factors should be optimized,i.e.,the mass flow rate,supply and return temperatures of the intermediate- fluid circuit,and the matches between the intermediate- fluid and process streams.

2.3.1.The overall economic objective

The proposed economic objective is defined as follow:

where CCUand CHUare the price of the cold and hot utilities respectively,Qtriand Qtkpare the load ofcold and hotutilities located over the hot and cold streams of i and p respectively.CostHeriand CostHekpare the capital costsofadditionalexchangersin sourcesplantand sinksplant,respectively.Pumping is the operation costofpumps and Costpump is the capitalcost of pumps.Costpipe is the capitalcost ofthe pipeline.In the above relation,Afis the annual factor of cost which is calculated as follows:

where,n isthe lifetime ofthe exchangerin termofyearand I isthe annual interest rate.

2.3.2.Constraints

The hot water circuit between plants is showed in Fig.2.The mathematicalmodelforindirectheatintegration synthesis includes allpossible connections.Notation used in the formulation is indicated as below.

IH {i:i is a hot stream}

PC {p:p is a cold stream}

Mari,Makpthe mass flow rate of water from splitrand splitk

Mbri,Mbkpthe mass flow rate of water from Mixiand Mixp

Mcri,j,Mcrp,qthe mass flow rate of water from splitiand splitpto Mixiand Mixp

Mcri,j,Mckr,qthe mass flow rate of water from splitiand splitrto Mixjand Mixq

Tinri,Tinkpthe temperature of water from Mixiand Mixpto exchanger i and p

Toutri,Toutkpthe temperature of water from exchanger i and p

Ybri,Ybkpbinary variables which define the existence of additional heat exchangers i and p.

Constraints for splitters:

Fig.1.Superstructure of heat integration between sources and sink plant.

Constraints for mixers:

Fig.2.Superstructure in source and sink plant.

Constraints for each heat exchanger between process stream and intermediate- fluid:

Heat transfer constraints:

Log mean temperature difference of each heat exchanger:

Cold utility of each process stream:

The area of each heat exchanger:

The capital cost of each heat exchanger:

2.3.3.The heat loss and electric cost

The heat loss model is simplified by only considering heat transfer resistance in insulation layer,as resistance in insulation layer is much larger than the other resistance,especially when the insulation layer is thick.The simplified models are shown in Eqs.(55)and(56)

where Twis the temperature ofintermediate- fluid.Teis the environmentaltemperature,L is the distance between plants,R is the heattransferresistance,rTis the pipe radius including insulation layer,rpis the bare tube radius and k is the thermal conductivity of insulation.The diameter of pipe can be calculated through Eq.(57),where M is the mass flow,Dinis the pipe diameter,ρ is the density of intermediate- fluid,and u is the flow velocity.It is assumed that the density of intermediate- fluid does not change with temperature.The pump power required to transport water from plant to plant can be calculated through Eqs.(58)and(59),where λ is the friction factor,L is the pipe length,Pe is the cost of the unit electricity and η is the pump efficiency.

3.Case Study

The model can be applied for indirectheat integration across several plants.But for space reason,a case study with only two plants is presented here based on a heat integration project in South China:an aromatic plant and a butadiene plant.Only streams with heat duty lager than 1000 kW are selected for consideration.

3.1.Data acquisition

It is assumed that all the HENS within individual plants are well established so that there is no need to optimize HENS.Table 1 shows that the aromatic plant is the source plant and butadiene plant is thesink plant.In this case,the density of hot water is assumed as 950 kg·m-3,the flow velocity of hot water is set to be 2 m·s-1,the distance between plants is:L=2.5 km.The cost of capital and utility are[19]:

Table 1 Streams data for case study

Fig.3.HENS in source plant.

Steam cost=120(USD?kW-1·a-1)

Cooling water cost=10(USD ?kW-1?a-1)

Heat exchangers capital cost=10000+150Area(USD)

Interest rate=10%and plant life=5 years

Dout(m)=1.052Din+0.005251

Wtpipe(kg?m-1)=644.3Din2+72.5Din2+0.4611

Pcul(USD?m-1)=0.82Wtpipe+185Dout0.48+6.8+265Dout

3.2.Result

The optimization contains inter variables to decide the existence of heatexchanger.The case study contains90 continuous variables,9 integer variables and 59 constraints.The problem is solved less than 1 min of CPU time on a desktop PC(Inter(R)Core(TM)i5 CPU 3.33 GHz,with 4.00 GB of RAM)using the GAMS24.21.The minimized overall annual cost is 1590522USD and the heat recovered is about 11411 kW.The hot water networks in source and sink plants are showed in Figs.3 and 4,respectively.In Fig.5,the two curves are Composite Curve of hot streams in source plant(upper one)and cold streams in sink plant(lower one),and the straight line is the profile of the intermediate fluid.The capital cost and profit is showed in Table 2.

3.3.Discussion

In Table 2,the capital and operation cost of pump is about 1.2× 104USD·a-1and 3.4× 104USD·a-1and the heat loss is 688 kW,while the annualized pipe and additional heat exchanger cost is about 2.1× 105USD·a-1and 2.9×105USD·a-1,respectively.This suggests that the in fluence of pump is much less than the pipeline and heat loss for long distance.The flow rate of the hot water needs to be large enough to recover the heat from heat source plant to heat sink plant,but the increased flow rate will directly increase the diameter of pipe and pump power so that both investment and operation cost will increase.As heat needs to be transferred twice from hot streams to hot water and from hot water to cold streams,the minimum temperature approach is higher than conventional HEN design and the overall ΔT for indirect heat integration is 18°C(Fig.5).

Fig.4.HENS in sink plant.

Fig.5.Composite curve and intermediate fluid T–H profiles of heat integratio.

Table 2 Annualized cost and profit of the project

4.Conclusions

Heatintegration across plants in industrialclusters is an efficientway to improve energy and economic efficiency.Asystematic methodology is presented to design indirect heat integration across independent plants,and the model is based on a superstructure proposed by Floudas et al.[20].The model is an MINLP which can be used to evaluate waste heat qualities and reuse feasibilities,and to identify indirect heat integration options with economic objectives.The optimized results give the mass flow rate of intermediate- fluid,diameter of pipeline,temperature of intermediate- fluid circuits and matches of HENS automatically.The results also confirm that the distance is a very important factor,as the capital cost of pipe and additional heat exchangers play a very important role in heat integration between plants.The methodology has been illustrated with a case study for two plants within one industrial cluster.

Nomenclature

A,B,C constant coefficients

Cp heat capacity of intermediate- fluid,kW·K-1

CPriheat capacity of hot stream i,kW·K-1

CPkpheat capacity of cold stream p,kW·K-1

G gravity acceleration,m·s-2

i hot streams in sources plant

j cold streams in sinks plant

Kricoefficients of hot stream i,kW·m-2·K-1

Kkpcoefficients of cold stream p,kW·m-2·K-1

Ω in finite number of relatively large