Network Modeling and Design for Low Grade Heat Recovery

Article pubs.acs.org/IECR

Network Modeling and Design for Low Grade Heat Recovery, Refrigeration, and Utilization in Industrial Parks B. J. Zhang,* Z. L. Zhang, K. Liu, and Q. L. Chen School of Chemical Engineering and Technology, Guangdong Engineering Technology Research Center for Petrochemical Energy Conservation, Sun Yat-Sen University, No. 135, Xingang West Road, Guangzhou 510275, China S Supporting Information *

ABSTRACT: Low grade heat still widely exists in energyintensive industrial parks, although good energy integration has been accomplished for individual processes or plants. Low grade heat is notably large but difficult to utilize because of the limitation of heat transfer and the scarcity of low grade heat sinks. Large scale utilization of low grade heat is very challenging for energy-intensive industries or industrial parks. A large scale low grade heat recovery, refrigeration, and utilization network system is introduced in this study to improve energy performance for industrial parks. In order to model the large scale system, the system is decomposed into three levels: pipe networks, refrigeration stations and absorption chillers. A mixed integer nonlinear programming model is presented that considers mass and energy networks, pipes, refrigeration stations, absorption chillers, and economic performance. The mathematical model is applied to the optimization and economic analysis for the low grade heat utilization in a petrochemical industrial park in China. The model can be solved in available time using the global solver. The solution results demonstrate the good economic performance of the new low grade heat recovery, refrigeration, and utilization network system for the industrial park.

1. INTRODUCTION Industrial parks require considerable energy to transform crude feeds into final products. High grade energy is first used by energy-intensive processes, such as chemical reaction and distillation processes. Next, the major part of the energy used is released in the form of heat. The heat is further recovered by heat exchanger networks (HENs). A profitable method for heat utilization is to transfer heat to heat sinks at the current technoeconomic level. Nevertheless, the heat cannot be completely recovered because of the limitation of the heat transfer principles and the scarcity of available heat sinks. As a result, tremendous low grade heat has to be emitted into the environment. Low grade heat is estimated between 20% and 50% of the energy used by the process industry.1 How to use low grade heat is very challenging and attractive. Low grade heat recovery and utilization is attracting more attention, except for HEN design, which directly matches heat sources and sinks.2 Nevertheless, the concept of low grade heat is still not transparent for industrial parks or the process industry. In this study, the low grade heat in industrial parks refers to the heat that cannot be recovered using the best HEN designs. This means that the heat consumes additional cold utilities if it is not recovered. Industrial parks have several plants, and each plant has certain low grade heat that cannot be recovered by the HENs. Many publications have focused on the use of low grade heat, including desalination,3 absorption refrigeration,4 and power generation,.5,6 Chan et al.7 recently © XXXX American Chemical Society

reviewed technologies suitable for cost-effective utilization of low grade heat in the process industry. The technologies for low grade heat recovery and utilization have significantly advanced, and absorption refrigeration demonstrates reasonable energy performance and profitability if there are available cold sinks. For an industrial park, the low grade heat sources are numerous and dispersed and the cold sinks are often far from low grade heat sources. We must determine which low grade heat sources should be collected, the locations where refrigeration stations should be built, the profitable refrigeration load in each station, and the optimal energy flow from low grade heat sources to refrigeration stations and to cold sinks. The optimal design for such a network system is challenging and essential for economic performance. This is the focus of this study. Heat integration is an effective method for better heat recovery and energy performance and was thoroughly reviewed by El-Halwagi,8 Morar and Agachi,9 and Klemeš.10 The popular heat integration focuses on heat recovery by HENs and a combination of processes, HENs and steam power systems. Recently, the recovery and utilization of low grade heat attract attentions. Lai et al.11 presented a systematic approach, Received: May 27, 2016 Revised: July 11, 2016 Accepted: August 23, 2016

A

DOI: 10.1021/acs.iecr.6b02033 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Industrial & Engineering Chemistry Research considering both process flexibility and system economics for low grade heat recovery and delivery in crude oil refining complexes. The graphical method and mathematical programming were combined to simplify the mathematical model and reduce the computation effort. Moorthy et al.12 proposed three mixed integer nonlinear programming (MINLP) models for the synthesis, retrofit, and alternate retrofit of a realistic, low temperature HEN design. The models include pressure drops, costs of piping, water tanks, pumps, and heat exchangers. Zhang et al.13−15 proposed hot direct discharges/feeds between upand down-plants to reduce the low grade heat and simultaneously optimized the HENs in up- and down-plants. Hackl and Harvey16 presented a holistic approach based on total site analysis to implement heat recovery and utilization for industrial clusters. These works focused on transferring low grade heat from sources to sinks and did not pay attention to the upgradation of low grade heat. The upgradation of low grade heat expands the utilization methods for tremendous low grade heat in the process industry and further improves the energy performance. Ammar et al.2 reviewed low grade heat sources and uses from the process industry and discussed different aspects that influence the decision making for low grade heat recovery and utilization in the process industry. Ammar et al.3 investigated low grade heat sources of a paper mill. Two methods for using the low grade heat were presented, including using it to heat the feed of the desalination process and upgrading it through a heat pump coupled with a desalination system. Lu and Chen17 presented an integrated design method that utilizes low grade heat for a membrane distillation system to produce pure water. Kapil et al.18 proposed techno-economic analysis to improve low grade heat recovery in the process industry. They analyzed a wide range of low-grade heat recovery technologies, including heat pumping, organic Rankine cycles (ORCs), energy recovery from exhaust gases, absorption refrigeration, and boiler feedwater heating. Law et al.19 proposed the utilization of low grade heat in the food and drinks processing sector. The best available technologies for the waste heat recovery were provided, ranging from heat transfer between sources and sinks to novel technologies for the generation of electricity and refrigeration. Walsh and Thornley20 used the lifecycle greenhouse gas reduction impacts and discounted payback periods to evaluate two technologies for low grade heat utilization: ORCs and condensing boilers. Kwak et al.21 proposed technoeconomic analysis for the key technologies applied to low grade heat recovery and reuse. The technologies include ORCs, boiler feedwater heating, heat pumping and absorption refrigeration in the context of process integration. Zhou et al.22 proposed using low grade heat from power plants for water treatment. They developed a comprehensive forward-osmosis process model, consisting of membrane separation, low grade heat recovery, and draw-solute regeneration models. Miah et al.23 presented a heat integration framework incorporating technological interventions for both simple and complex factories to evaluate all possible heat integration opportunities for low grade heat. The framework includes heat pumps to upgrade low grade heat, which can significantly enhance energy efficiency. Law et al.24 developed a knowledge-based system for the selection and preliminary design of equipment for low grade heat recovery in the process industry. van de Bor et al.25 evaluated several alternative technologies using thermodynamic models for low grade waste heat recovery. The technologies include compression-resorption, vapor compression, trans-

critical heat pumps, and ORC. These publications focused on the evaluation of the available technologies for low grade heat recovery and utilization. The direct use of low grade heat between sources and sinks may be the best choice. Nevertheless, direct use is limited by the scarcity of heat sinks. Low grade heat absorption refrigeration is then suggested as profitable for the process industry if there are available cold sinks. This study investigates how to design the network of a low grade heat recovery, refrigeration, and utilization network (LGHRRUN) system to optimize low grade heat recovery and utilization for industrial parks. Upgrading low grade heat for utilization is a significant way to improve energy performance. Recently, Sarkar26 reviewed various supercritical CO2 Rankine cycle configurations for low grade heat utilization. Supercritical Rankine cycle and its various working fluids, heat sources, heat sinks and analysis approaches, and performance analyses and optimization of various supercritical CO2 Rankine cycle configurations were discussed. Imran et al.27 provided a comprehensive review of volumetric expanders for low grade heat and waste heat recovery using ORC. Wu and Zhu28 introduced a method for synthesizing integrated refrigeration systems in industry. The method combined mathematical optimization techniques and engineering knowledge to produce a systematic procedure capable of solving industrial problems. Hipólito-Valencia et al.29 presented an optimization approach for the energy integration in the azeotropic bioethanol separation process involving energy integration through HENs incorporated into an ORC for low grade heat recovery. The optimization approach yields the solution with the minimum separation cost. Lee et al.30 presented a combined Rankine cycle using low grade waste heat to extract additional power without consuming additional fossil fuel by integrating the CO2−ORC with the steam cycle and a liquefied natural gas evaporation process. Chen et al.31 presented a mathematical model for the synthesis of a HEN which can be integrated with an ORC for the recovery of lowgrade waste heat from the heat surplus zone of the background process. Gutiérrez-Arriaga et al.32 presented a systematic approach for energy integration involving waste heat recovery through an ORC. The approach can address the trade-offs among the different forms of energy and associated costs. González-Bravo et al.33 presented an optimization approach for designing energy integrated biobutanol separation processes to reduce utility consumption and enhance the utilization of waste heat at low temperature. Kim and Yoon34 proposed bladeless jet propulsion microsteam turbines for low-grade heat utilization. The theoretical study predicted the performance of this turbine under the given condition, and the experimental study was performed to obtain the performance factors. Xu et al.35 presented a performance study on a low grade absorption−compression cascade refrigeration system, which consists of an absorption subsystem and a vapor compression autocascade subsystem to obtain cold energy at −170 °C. Oluleye et al.36 developed a method for the conceptual screening and incorporation of low-temperature heat upgrading technologies in process sites. The screening process involves determination of the best technology to upgrade waste heat in process sites. Heat loss and pressure drop in long distance heat transport are significant factors for large scale, low grade heat recovery and utilization. Lin et al.37 proposed the thermal coefficient of performance for the ammonia−water absorption cycle using low grade heat and transporting over a distance of 50 km. For a B


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Industrial & Engineering Chemistry Research

and emitted to the environment. The plants marked with circles in Figure 1 have low grade heat. In the original gross design of the industrial park, the low grade heat emits into the environment by air or water coolers. We denote the plants as source plants. The industrial park also has plants that require cooling to drive their processes. These plants, marked with stars in Figure 1, are called sink plants. Absorption refrigeration is an attractive technology for converting low grade heat for cooling. The low grade heat in the source plants can be collected and used in absorption chillers to obtain cooling. The cooling is then transported to the sink plants. A LGHRRUN system is suggested for the industrial park to improve energy efficiency and reduce emission. In the LGHRRUN system, two medium streams are used. The hot medium streams transport low grade heat from source plants to refrigeration stations. The cold medium streams transport cooling from refrigeration stations to sink plants. In the stage of design for the LGHRRUN system, economic performance is used as the objective value. The way to design the system is challenging for the industrial park because the following aspects have to be traded off. (1) The industrial park has several parcels that can be used to build refrigeration stations, as shown by the blue parts in Figure 1. Parcels are at different distances from the heat source plants and the cooling sink plants. The investment of pipes along the gallery, the pressure drop and heat loss are all dependent on the distances. Hence, it is significant to determine the parcels that are used to build refrigeration stations. (2) The network of hot medium streams requires optimization. Hot medium streams are used to collect the low grade heat from the source plants, carry the heat to refrigeration stations, and then return to the source plants for recycling. The low grade heat in the source plants has different temperature ranges and heat capacity flow rates. The network must determine which low grade heat and how much is collected and to which refrigeration stations the collected heat is transferred. (3) The network of chilled medium streams requires optimization. The chilled medium streams cycle between refrigeration stations and the cooling sink plants. The chilled medium streams take cooling from refrigeration stations and release it to the cooling sink plants. The cooling sink plants are different in quantity and grade demand of cooling. The network must determine which refrigeration station supplies cooling to which sink plants and the quantity and grade of cooling supplied. How to design the LGHRRUN system with minimum cost and satisfying the cooling demand for the industrial park is the motivation in this study. We decompose the LGHRRUN system into three levels: pipe networks, refrigeration stations and absorption chillers. The mass and energy balances are modeled based on the three levels. The economic formulations are then presented to evaluate the entire LGHRRUN system.

500 MW, 50 km real application, the payback period of the transportation pipes is within 15 months. The payback period of the whole facility is approximately 3.7 years. Ammar et al.38 investigated a long distance heat transportation system for low grade heat available in the process industry. The low grade heat is collected through an absorption process using a mixture of water and ammonia as a working fluid, and transferred to faraway heat sinks. They focused on the long distance transportation of low grade heat and suggested that the low grade heat could be transported more than 50 km for the heat sources at temperatures as low as 80 °C and with a payback period of 10 years. Fang et al.39,40 proposed a holistic approach to using low grade heat for district heating and investigated how to collect industrial low grade heat for a district heating system. The key issues of the collection and integration of multiple-grade waste heat sources, long-distance delivery of waste heat and peak shaving were considered. Xia et al.41 presented a method for integrating low-grade industrial heat into a district heating system and investigated how to improve the outlet temperature of heat-collecting water by optimizing the heat exchange flow for process integration. A newly developed thermal theory called entransy analysis was introduced to describe the energy quality loss during the heat integration. These studies investigated the long distance transportation of low grade heat. A large scale low grade heat recovery, refrigeration, and utilization network system is introduced in this study to improve energy performance for industrial parks. In order to model the large scale system, the system is decomposed into three levels: pipe networks, refrigeration stations, and absorption chillers. A MINLP model is presented that considers mass and energy networks, pipes, refrigeration stations, absorption chillers, and economic performance. The mathematical model is applied to the optimization and economic analysis for the low grade heat utilization in a petrochemical industrial park in China. The model can be solved in available time using the global solver. A good economic performance is obtained. The cooling cost for the entire LGHRRUN system is $7.64 per GJ. This cost is equivalent to 21.2% of the power price of $0.13 per kW·h.

2. PROBLEM DESCRIPTION An industrial park is shown in Figure 1. The industrial park contains several plants. Good heat integration has been accomplished for the individual plants. Nevertheless, there is still much low grade heat that has to be cooled by cold utilities

3. MATHEMATICAL MODELING 3.1. Network Modeling. A pipe network structure, shown in Figure 2, is extracted to represent LGHRRUN systems for industrial parks. We denote the plants with low grade heat as source i (i ∈ I), the plants with cooling demand as sink j (j ∈ J), and the candidate parcels for refrigeration stations as s (s ∈ S). Source i can supply a hot medium stream with mass flow

Figure 1. Heat sources and cold sinks in industrial parks. C


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Figure 2. Network flowsheet of LGHRU in industrial parks.

rate Fi° and temperature Ti°. Sink j demands cooling of Qj° at temperature Tj°. There are candidate absorption chillers k (k ∈ K) that can be installed in refrigeration stations. Parameter Li,s is the length of the pipe gallery between source i and parcel s; parameter Ls,j is the length of the pipe gallery between parcel s and sink j. These sets and parameters are all labeled in Figure 2. To represent the network design shown in Figure 2, 0−1 variables are introduced to represent the LGHRRUN system. Variable Ms denotes whether parcel s is used to build a refrigeration station; variable Xi,s denotes whether source i supplies low grade heat to parcel s; variable Ys,j denotes whether parcel s supplies cooling to sink j; variable Zs,k denotes whether parcel s installs absorption chiller k. When parcel s is not used to build a refrigeration station (Ms = 0), low grade heat supplied to the parcel s, cooling exported from the parcel s, and absorption chillers in the parcel s do not exist. As a result, variables Xi,s, Ys,j, and Zs,k are all forced to be equal to zero. These logic relationships between the 0−1 variables can be represented as in eq 1. ⎧ X i , s ≤ Ms ⎪ ⎪ ⎨ Ys , j ≤ Ms ⎪ ⎪Z ≤ M s ⎩ s,k

of the pipe from sink plant j to refrigeration station s for chilled medium streams, respectively. A source plant can supply its hot medium stream to any refrigeration stations. The total hot medium stream exported by the source plant cannot be above the maximum capacity. At the same time, the supply temperature of a hot medium stream must not be greater than the temperature specified by the source plant. These constraints are represented in eqs 2−4). The hot medium stream from a source plant to a refrigeration station is also governed by whether the connecting pipe between them is built, as denoted in eq 5. Fi =

∑ Fi ,s s

(2)

Fi ≤ Fio

(3)

o Tista , s ≤ Ti

(4)

Fi , s ≤ Fio·Xi , s

(5)

where Fi is the total mass flow rate of the hot medium stream exiting source plant i; Fio and Tio are the maximum mass flow rate and starting temperature of the hot medium stream from source plant i, respectively. The total chilled medium stream received by a sink plant is equal to the sum of chilled medium streams from all refrigeration stations, as expressed in eq 6. In a sink plant, the chilled medium streams from all refrigeration stations are first mixed, then used. The energy balance of mixing is expressed in eq 7. Equation 8 shows that the cooling supplied by the chilled medium streams entering a sink plant should be not less than the cooling demand of the sink plant. To satisfy the process requirement of sinks, the temperature of the chilled medium stream is also constrained in eq 9. The temperature of the chilled medium stream exiting the sink plant equals the temperature at the inlet of the pipe from the sink plant to refrigeration stations, as expressed in eq 10. Equation 11 represents the logic constraint of the mass flow rate of the chilled medium stream.

(1)

Hot and chilled medium streams are used in the LGHRRUN system. Hot medium streams are used to move low grade heat from source plants to refrigeration stations. Chilled medium streams are used to move cooling from refrigeration stations to sink plants. In this study, we assume that the density and heat capacity of medium streams do not vary with temperature and that medium streams keep the liquid phase throughout the entire system. Variables are introduced to model the networks of two medium streams, as shown in Figure 2. Fi,s denotes the mass flow rate of the hot medium stream between source plant i and refrigeration station s. Fs,j denotes the mass flow rate of the chilled medium stream between refrigeration station s and end sink plant j. Tsta i,s and Ti,s are the inlet and outlet temperatures of the pipe from heat source plant i to refrigeration station s for end hot medium streams, respectively; Tsta s,i and Ts,i are the inlet and outlet temperatures of the pipe from refrigeration station s to heat source plant i for hot medium streams, respectively; Tsta s,j and Tend s,j are the inlet and outlet temperatures of the pipe from refrigeration station s to sink plant j for chilled medium streams, end respectively; Tsta j,s and Tj,s are the inlet and outlet temperatures

Fj =

∑ Fs ,j s

in ∑ (Fs ,j·Tsend , j ) = Fj · T j s

D

(6)

(7) DOI: 10.1021/acs.iecr.6b02033 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Industrial & Engineering Chemistry Research Q jo ≤ FjCPd (T jout − T jin)

(8)

uh ,minXi , s ≤ ui , s ≤ uh ,max Xi , s

(16)

T jout ≤ T jo

(9)

ud ,minYs , j ≤ us , j ≤ ud ,max Ys , j

(17)

T jout = T jsta ,s

(10)

Fs , j ≤ Fsmax , j · Ys , j

⎛ Di , s ⎞2 Vi , s = π ⎜ ⎟u ⎝ 2 ⎠ i,s

(18)

(11)

(13)

= Fs , jCP

−

Tsend ,j )

= π (Ds , j + εs , j)μ

d

ΔTsd, j (14)

end d d Q jloss = Fs , jCPd (T jsup , s − T j , s ) = π (Ds , j + εs , j)μ ΔT j , s ,s

(15) h

(20)

3600 Vs , jρd 1000

(21)

h,max

where u and u are the lower and upper bounds of velocity of hot medium streams, respectively, ui,s and Vi,s are the velocity and volume flow rate of hot medium streams between source plant i and refrigeration station s, respectively, Di,s is the inner diameter of the pipe between source i and refrigeration station s, ud,min and ud,min are the lower and upper bounds of velocity of chilled medium streams, respectively, us,j and Vs,j are the velocity and volume flow rate of chilled medium streams between refrigeration station s and sink plant j, respectively, Ds,j is the inner diameter of the pipe between refrigeration station s and sink plant j, and ρh and ρd are the densities of hot and chilled medium streams, respectively. Pressure drop is a significant factor that affects the power consumption during the transportation of hot and chilled medium streams. The Fanning formula43 can be used to calculate the pressure drop for long distance pipes, as represented in eqs 22 and 23 for hot medium streams. Note that the total length of the pipe between source plant i and refrigeration station s is two times the distance between them. Equations 24 and 25 are the same for chilled medium streams. The differences of the potential and kinetic energy at the inlet and outlet of pipes are ignored. Finally, eqs 26 and 27 can be used to obtain the power consumption for the transportation of hot and chilled medium streams.

end h h Q sloss = Fi , sCP h (Tssup , i − Ts , i ) = π (Di , s + εi , s)μ ΔTs , i ,i

(Tssup ,j

⎛ Ds , j ⎞2 Vs , j = π ⎜ ⎟ us , j ⎝ 2 ⎠

h,min

(12)

d

(19)

Fs , j =

end h h Q iloss = Fi , sCP h (Tisup , s − Ti , s ) = π (Di , s + εi , s)μ ΔTi , s ,s

Q sloss ,j

3600 Vi , sρh 1000

Fi , s =

where Fj is the total mass flow rate of the chilled medium stream entering sink plant j; Tjout and Tjin are the temperature of the chilled medium stream exiting and entering sink plant j, respectively; CPd is the specific heat capacity of chilled medium streams; Qjo and Tjo are the cooling demand and temperature requirement of sink plant j, respectively. Heat loss from pipes during long distance transportation is considered in this study. Hot medium streams cycle between heat source plants and refrigeration stations. Hence, the heat loss for hot medium streams includes two parts, as represented in eqs 12 and 13. Equation 12 expresses the heat loss when hot medium streams flow from heat source plants to refrigeration stations, and eq 13 expresses the heat loss when hot medium streams flow from refrigeration stations to heat source plants. Equations 14 and 15 are the same for the calculation of cooling loss from chilled medium streams.

d

where CP and CP are the specific heat capacities of hot and chilled medium streams, respectively, D and ε are the inner diameter and the insulation thickness of the pipe, respectively, μ is the total heat transfer coefficient of heat or cooling loss from pipes, and ΔT is the temperature difference between a pipe and the environment. The temperature difference between a pipe and the environment is various along the pipes. In this study, we use constant temperature differences for pipes according to the temperatures in source and sink plants. Parameters ε and μ are specified through the local climate and the insulation materials. The heat loss is further discussed in the example. The example demonstrates that the heat loss is small in complex LGHRRUN systems. Hlebnikov and Siirde also demonstrated that the heat loss is very small when the pipe length is not over 7 km.42 Pressure drop, velocity, diameter and length of the pipes transporting hot and chilled medium streams in industrial parks must be considered. These factors simultaneously affect the operating cost and the investment cost of a LGHRRUN system. Equations 16 and 17 express the constraints for the velocities of hot and chilled medium streams. Medium streams differ in velocity limitations according to their physical properties. Equations 18 and 19 represent the relationship between the mass flow rate, velocity and diameter of the hot medium stream, and eqs 20 and 21 are the same for chilled medium streams.

Hi , s = 2λi , s

Li , s ui , s 2 Di , s 2g

λi , s = 0.11(K /Di , s)0.25

Hs , j = 2λs , j

Ns , j =

(23)

Ls , j us , j 2 Ds , j 2g

λs , j = 0.11(K /Ds , j)0.25 Ni , s =

(22)

(24) (25)

Hi , sVi , sρh g 1000ηi , s

(26)

Hs , jVs , jρd g 1000ηs , j

(27)

where Hi,s is the friction loss (in head) in the pipe between source plant i and refrigeration station s, Hs,j is the friction loss (in head) in the pipe between refrigeration station s and sink plant j, λ is the Fanning friction factor, K is the wall roughness, E


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Figure 3. Network flowsheet of refrigeration station.

∑ Fsh,k = Fh,s

g is the local acceleration of gravity, N is the power consumption of the pump, and η is the total efficiency of the pump. 3.2. Refrigeration Station Modeling. An industrial park may have several parcels for refrigeration stations. A refrigeration station receives low grade heat from source plants, converts it into cooling through absorption chillers, and then delivers the cooling to sink plants. The refrigeration station in an industrial park is extracted and shown in the red box in Figure 3. The refrigeration station may have several absorption chillers, as shown by the ovals in Figure 3. The hot medium streams from source plants are mixed in the refrigeration station and then split into branches that enter the absorption chillers, as demonstrated by the green dashed lines in Figure 3. The hot medium branches exiting the absorption chillers are mixed and then split again and sent back to the source plants, as shown by the green solid lines in Figure 3. The mass flow rate of a hot medium stream entering a source plant is equal to that exiting the source plant. The chilled medium streams exiting absorption chillers are mixed in the refrigeration station, then split and sent to the sink plants, as shown by the blue solid lines in Figure 3. The chilled medium streams that return to the refrigeration station are first mixed, then split into several branches that enter the absorption chillers, as shown by the blue dashed lines in Figure 3. The constraints for refrigeration stations have two parts. One is for hot medium streams; the other is for chilled medium streams. The mass and energy balances for the mixing of hot medium streams entering the refrigeration stations are expressed in eqs 28 and 29. The mixed hot medium stream is split into several branches that enter the absorption chillers. The constraints on temperature and mass flow rate for the splitting are represented in eqs 30 and 31. The used hot medium streams exiting the absorption chillers are mixed, then split and returned to the source plants, as expressed in eqs 32 and 33.

(31)

k

∑ (Fsh,kTsh,k,out) = FshTsh ,out k

Tsh ,out = Tssup ,i

Th,in s

(33)

Th,out s

where and are the temperatures of hot medium streams entering and exiting, respectively, refrigeration station s, h,in h,out Ts,k and Ts,k are the inlet and outlet temperatures, respectively, of absorption chiller k in refrigeration station s, and Fhs,k is the mass flow rate of the hot medium stream entering absorption chiller k installed in refrigeration station s. The chilled medium streams have similar mass and energy balance constraints. Equations 34 and 35 represent the mass and energy balances for the mixing of chilled medium streams from the absorption chillers. Equation 36 shows that the temperature of chilled medium streams exiting a refrigeration station equals the temperature at the inlet of the pipe from refrigeration stations to sink plants. The chilled medium streams are used in sink plants, then return to the refrigeration stations and are mixed. The mass and energy balances for the mixing of chilled medium streams from sink plants are expressed in eqs 37 and 38. Equation 39 shows that the temperature at the outlet of the mixer equals the temperature of chilled medium streams entering the absorption chillers.

∑ Fsd,k = Fsd

(34)

k

∑ (Fsd,kTsd,k,out) = FsdTsd ,out k

Tsd ,out = Tssup ,j

Fsd =

∑ Fi ,s

∑ Fj ,s (37)

d d ,in ∑ (Fj ,sT jend , s ) = Fs T s

(28)

i

(38)

j

∑

(Fi , sTiend ,s )

i

=

FshTsh , in

Tsd ,in = Tsd, k,in

(29)

Td,in s

Tsh , in

=

Tsh, k, in

(35) (36)

j

Fsh =

(32)

(39)

Td,out s

where and are the temperatures of the chilled medium streams entering and exiting, respectively, refrigeration d,out station s, Td,in are the inlet and outlet temperatures, s,k and Ts,k

(30) F


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Figure 4. Flowchart of absorption refrigeration.

respectively, of absorption chiller k in refrigeration station s, and Fds,k is the mass flow rate of the chilled medium stream entering absorption chiller k. For the design problem of the LGHRRUN system, the load limitations of refrigeration stations are expressed in eqs 40 and 41. The installation of absorption chillers is represented in eqs 42 and 43. Fsh ,minMs

≤

Fsh

≤

Fsh ,maxMs

a Tsw, k,mid ≤ Tsa, ,ino k + δs , k

(49)

Tsw, k,in ≤ Tsw, k,mid

(50)

(42)

Q sa, k,minZs , k ≤ Q sa, k ≤ Q sa, k,maxZs , k

Fsd ,maxZs , k

(43)

Q sg, k = Fsh, kCP h (Tsh, k,in − Tsh, k,out)

(44)

Tsg, k,ino + δsg, k ≤ Tsh, k,out

(45)

Tsh, k,out ≤ Tsh, k,in

(46)

Q sg, k,minZs , k ≤ Q sg, k ≤ Q sg, k,maxZs , k

(51) w

Qas,k

where is the heat exchanged in the absorber, CP is the w,mid specific heat capacity of the cooling water, Tw,in are s,k and Ts,k the temperatures of cooling water entering and exiting the absorber, respectively, and Ta,ino and δas,k are the operating s,k temperature and minimum heat transfer temperature difference in the absorber, respectively. The cooling water from the absorber is further used to remove heat from the condenser. The energy balance and heat transfer in the condenser are similar to those of the absorber, as represented in eqs 52−54. The load of the condenser is limited using eq 55.

3.3. Absorption Refrigeration Modeling. Absorption chillers using low grade heat are expected to be installed in the LGHRRUN system. The simplified flowchart of the absorption chillers is shown in Figure 4. An absorption chiller has four main parts: generators, condensers, evaporators, and absorbers. We model the absorption chiller by considering the energy balance in the four parts. To use the model of an absorption chiller in the design of the LGHRRUN system, three conditions are assumed. First, the operation of the absorption chiller is stable. Second, phases in generators and absorbers are in equilibrium. Last, the power consumption and heat loss between generators, condensers, evaporators, absorbers and exchangers are ignored. Pump investment and power consumption in an absorption chiller are often less than 1.6% of the whole machine.44 We ignore them in the design of the entire LGHRRUN system. The heat absorbed by the generator equals the heat released from the hot medium stream entering it. Equation 44 represents the energy balance. To satisfy the requirement of heat transfer, the temperature of the hot medium stream in the generator is constrained by eqs 45 and 46. The load of the generator is limited by hardware capacity, as expressed in eq 47.

Qgs,k

(48)

(41)

Fsh. k ≤ Fsh ,maxZs , k ≤

Q sa, k = Fsw, kCPw(Tsw, k,mid − Tsw, k,in)

(40)

Fsd ,minMs ≤ Fsd ≤ Fsd ,maxMs

Fsd. k

The cooling water removes heat from the absorber and condenser. The energy balance in the absorber is represented in eq 48. To make the cooling water remove the heat from the absorber, the temperature of the cooling water is constrained by eqs 49 and 50. The load of the absorber is limited by the hardware capacity, as expressed in eq 51.

Q sc, k = Fsw, kCPw ·(Tsw, k,out − Tsw, k,mid)

(52)

c Tsw, k,out ≤ Tsc,,ino k + δs , k

(53)

Tsw, k,mid ≤ Tsw, k,out

(54)

Q sc,,min Zs , k ≤ Q sc, k ≤ Q sc,,max Zs , k k k

Qcs,k

(55)

Tw,out s,k

where is the heat exchanged in the condenser, is the temperatures of cooling water exiting the condenser, and Tc,oin s,k and δcs,k are the operating temperature and minimum heat transfer temperature difference in the absorber, respectively. The cooling is obtained in the evaporator through the working fluid vaporizing. The chilled medium stream is chilled in the evaporator. Equation 56 represents the energy balance in the evaporator. The lowest temperature of the chilled medium stream is limited by the operating temperature of the evaporator and the minimum heat transfer temperature difference, as expressed in eqs 57 and 58. The load of the evaporator is limited by the hardware capacity, as expressed in eq 59.

(47)

Tg,ino s,k

where is the heat exchanged in the generator and and δgs,k are the operating temperature and minimum heat transfer temperature difference in the generator, respectively.

Q se, k = Fsd, kCPd (Tsd, k,in − Tsd, k,out) G

(56) DOI: 10.1021/acs.iecr.6b02033 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

Article

Industrial & Engineering Chemistry Research e d ,out Tse,,ino k + δs , k ≤ Ts , k

(57)

Tsd, k,out ≤ Tsd, k,in

(58)

Q se,,min Zs , k ≤ Q se, k ≤ Q se,,max Zs , k k k

(59)

P2 = W hPLhp + W d PLdp

where ρh and ρd are the densities of pipes for hot and chilled medium streams, respectively, δh and δd are the thicknesses of pipes for hot and chilled medium streams, respectively, Wh and Wd are the weights of pipes for hot and chilled medium streams, respectively, and PLhp and PLdp are the prices of pipes for hot and chilled medium streams, respectively. The price of pipes includes insulation installation. The utilities consumed by LGHRRUN systems include the hot medium stream, power and cooling water. The cost is expressed by Equation 68. The first item on the right side of Equation 68 is the cost of the low grade heat; the second term is the cost of the cold utility; the final term is the cost of power used by the pumps. Note that the low grade heat includes the heat lost from pipes from source plants to refrigeration stations and the heat used in absorption chillers but does not include the heat from pipes from refrigeration stations to source plants. The hot medium streams entering the source plants remove the low grade waste heat from processes. The lower the temperature of the hot medium stream, the more heat the hot medium stream can remove. As a result, the cold utility in source plants can be reduced. Hence, the heat lost from pipes from refrigeration stations to source plants cannot be accounted for in business processes.

where Qes,k is the cooling produced by the condenser and Te,ino s,k and δes,k are the operating temperature and minimum heat transfer temperature difference in the evaporator, respectively. The total energy balance of the absorption chiller is expressed in eq 60. The coefficient of performance (COP) COPs,k of the absorption chiller is represented in eq 61. Q sg, k + Q se, k = Q sc, k + Q sa, k

COPs , k =

(60)

Q se, k Q sg, k

(61)

3.4. Economics. The total annual investment cost is used as the objective for the design of a LGHRRUN system that covers all the cooling demands in industrial parks. The investment costs include the absorption chillers (P1), pipes (P2), and utility consumption (P3). The objective is expressed in Equation 62. PB is the useful life of new equipment, and straight line depreciation is used for the new equipment. P=

(P1 + P2) + P3 PB

P3 = GPLh(∑ Q sg, k +

(62)

s,k

The cost of absorption chillers is expressed in eq 63. Equation 64 represents the cost of an absorption chiller that includes four parts: generators, condensers, evaporators, and absorbers. Each part is represented as an exponential function of heat load.45 Note that the cost of the heat exchanger in the absorption chiller is combined with that of the absorber in this study. 0−1 variables Zs,k are used to constrain the constant items. P1 =

∑ ∑ Ps ,k s

g

a

c

Ps , k = α g (Q sg, k)γ + α a(Q sa, k)γ + α c(Q sc, k)γ + α e(Q se, k)γ + (β g + β a + β c + β e)Zs , k

+ GPL (∑ Ni , s + s,i

∑ Ns ,j) s,j

(68)

4. MATHEMATICAL FRAMEWORK The combinational mathematical framework of the LGHRRUN system involves the networks of hot and chilled medium streams, the model of refrigeration stations, and the model of absorption chillers. The mathematical framework is finally denoted as MP and presented below. (MP) min P (annual investment cost of the LGHRRUN system) s.t. eqs 1−27 (networks of hot and chilled medium streams); eqs 28−43 (refrigeration stations); eqs 44−61 (absorption chillers); eqs 62−68 (economic constraints). The mathematical model is a nonconvex MINLP problem. Three modeling efforts are proposed to simplify the solution procedure of the model. First, to avoid an unbound solution, we reformulate the constraints whose divisors are variables. The constraints are eqs 22−25 and 61. Second, factorization via introducing new variables is applied to the constraints that involve multiples of multivariables. The constraints are eqs 18, 20, and 22−27. The mathematical model only involves bilinear and power items through the above two steps. The last step is to use the convex envelopes to replace the bilinear and power items. Readers are referred to the literature46,47 for a comprehensive treatment. Through these modeling efforts, the mathematical model can be solved using the state-of-the-art solvers.

e

(64)

∑ (BM(1 − Xi ,s)) s,i

(65)

⎞ ⎛ ⎛ δh ⎞ W d ≥ 2ρh ∑ ⎜⎜π ⎜Ds , j + ⎟δ hLs , j⎟⎟ − 2⎠ ⎠ s,j ⎝ ⎝

s,k

where G is the operating hours per year and PLh, PLw, and PLp are the prices of low grade heat, cold utility and power, respectively.

where Ps,k is the cost of an absorption chiller and α, β, and γ are regression parameters for the cost functions of generators, condensers, evaporators, and absorbers. The installation cost of a low pressure pipe is correlated with its weight in engineering practice. The weight of a pipe is a function of its diameter, thickness, length and materials. For the transport of regular medium streams, the thickness and material of the pipe are commonly deterministic. Hence, the weights of pipes are represented in eqs 65 and 66. Equation 67 expresses the cost of all pipes in the LGHRRUN system. ⎞ ⎛ ⎛ δh ⎞ W h ≥ 2ρh ∑ ⎜⎜π ⎜Di , s + ⎟δ hLi , s⎟⎟ − 2⎠ ⎠ i,s ⎝ ⎝

∑ Q iloss ) + GPLw∑ (Q sc, k + Q sa, k) ,s i,s

p

(63)

k

(67)

∑ (BM(1 − Ys ,j)) s,j

(66) H


Article


5. EXAMPLE 5.1. Example Description and Data. A petrochemical industrial park in South China is investigated in this study. The industrial park includes a petrochemical plant, several chemical plants, and power plants. There is low grade heat in the four plants. The heat is emitted into the environment through air and water coolers via the existing processes. These source plants can collect the low grade heat, using water as medium streams, and export it. This can reduce the requirement of cold utility and increase some of the income from heat sale for the plants. The maximum flow rate and temperature of the hot medium water supplied by the four plants are shown in Table S1. There are four sink plants that demand cooling. The cooling quantity and temperature requirement are shown in Table S2. Three parcels are candidates for refrigeration stations according to the layout of the entire industrial park. The gallery distances between the parcels and plants are listed in Table S3. Note that source plant i3 and sink plant j1 are the same plant. This plant can supply low grade heat and simultaneously requires cooling. To fully utilize the low grade heat and meet the requirement of cooling in the industrial park, low grade heat absorption refrigeration is suggested to improve energy performance. Where to build the refrigeration stations and how to design the pipe network between the source plants, refrigeration stations and sink plants are challenges. The MINLP model presented in this study is applied to this example to address the problem. In this example, we use symbol h for an hour, y for a year, s for a second, t for a ton, k for a thousand and M for a million. The useful life of new equipment is set to 8 years and operating hours per year is 8,000 h. The prices of power, cold utility and low grade heat are $0.13 per kW·h, $0.001 per MJ, and $0.001 per MJ, respectively. These data are supplied by the plants in the industrial park. 5.2. Computational Study. The MINLP model presented in this study is applied to the example. The model for the example is coded in the GAMS 24.1.3 Environment48 using a 2.1 GHz Intel(R) Core(TM) i7−4550U PC. Global solver Antigone 1.149 in GAMS 24.1.3 is used to solve the MINLP model. The model involves 42 single binary variables, 524 continuous variables, and 899 constraints. The global optimization result is obtained in 15.6 s. The total investment cost is $6.470 × 106 per year. The cost of pipes is $1.823 × 106 per year, and that of absorption chillers is $5.175 × 105 per year. The utility costs of low grade heat, cold utility, and power are $1.516 × 106 per year, $2.218 × 106 per year, and $3.950 × 105 per year, respectively. The pie chart for the costs of pipes, absorption chillers, and utilities is shown in Figure 5. The cost of pipes is greater than that of absorption chillers. This is because the pipes used to connect the source plants, refrigeration stations and sink plants in the industry park are very long. The utility cost is 64% of the total cost. The cost of power is the lowest and the cost of cold utility is the greatest. The cold utility is used to remove the heat from the absorbers and condensers in the absorption chillers. The low grade heat is redundant for the source plants and further consumes additional utilities if it is not recovered. Hence, the price of low grade heat is relatively low and the cost of low grade heat is lower than the cold utility cost. The optimal structure and parameters for the new LGHRRUN system are shown in Figure 6. Two of the three candidate parcels are selected to build the refrigeration stations.

Figure 5. Pie chart of pipes, equipment, and utility costs.

The low grade heat from source plant i1 enters refrigeration station s2, while the low grade heat from source plant i4 enters refrigeration station s1. Refrigeration station s1 only supplies the chilled medium water to sink plant j3. Refrigeration station s2 supplies the chilled medium water to sink plants j1, j2, and j4. Source plant i2 is nearer to refrigeration station s2 than source plant i1. Nevertheless, refrigeration station s2 still uses the hot medium water from source plant i1. This is not only because the flow rate of the hot medium water in source plant i1 is greater but also because the temperature of the hot medium water in source plant i1 is higher. A higher temperature of hot medium water can reduce the pipe diameter required for transporting the same heat. Hence, the investment of pipes can be reduced. The velocity and pump power consumption in the pipes are listed in Table S4. The codes of pipes are marked in Figure 6. The optimal velocity of hot and chilled medium water is between 1 to 2 m/s. This agrees well with the engineering heuristics.50 The heat loss from pipes is listed in Table S4. The total recovered low grade heat is 181.64 GJ per hour. The heat loss from the pipes between the source plants and refrigeration stations is 13.35 GJ per hour, i.e., 7.35% of the total recovered low grade heat. The total cooling is 112.22 GJ per hour. The cooling loss from the pipes between the refrigeration stations and sink plants is 6.38 GJ/h, 5.69% of the total cooling. One absorption chiller is suggested for installation in refrigeration station s1, and four absorption chillers are installed in refrigeration station s2. Because of the limitation of hardware capacity, several absorption chillers have to be installed to meet the large cooling demand. An absorption chiller consumes hot medium water and produces chilled medium water. The medium streams related to the five absorption chillers are shown in Figure 7. 5.3. Cooling Cost Analysis. We can use Equation 69 to obtain the total cost of the specific cooling supply (CC). The total cost for the entire LGHRRUN system is $6.470 × 106 per year; the total cooling is 105.84 GJ/h. Hence, the cooling cost is $7.64/GJ. This cost is equivalent to 21.2% of the power price of $0.13 per kW·h. This indicates that the new LGHRRUN system is competitive with respect to economic performance. CC =

(P1 + P2) PB

+ P3

G ·∑j Q jo

(69)

The four sink plants share the cooling supplied by the LGHRRUN system in the industrial park. The investors of the new LGHRRUN system are also interested in the cooling costs for the individual sink plants. To analyze the cooling costs for individual plants, we present a marginal value-like method. This I


Article


Figure 6. Optimal network structure for the LGHRRUN system in the industrial park.

of sink plant j1 to zero and do not change the cooling demand of the other sink plants. The MINLP model is then solved. The solution result is listed in the third line of Table 1. Third, we use the cost of the entire system minus the new costs and obtain the cost differences caused by specifying the cooling demand of a sink plant as zero. The cost differences are listed in the fourth, sixth, eighth and tenth lines of Table 1. Last, we use the cost difference to divide the cooling demand of the sink plant and obtain its specific cooling cost. The specific cooling costs for individual sink plants are shown in the last column of Table 1. The specific cooling costs for sink plants are shown by the dashed line in Figure 8. We find that the specific cooling cost of plant j3 is largest among the four sink plants and is also larger than that of the entire system. According to the network structure of the new LGHRRUN system, sink plant j3 results in refrigeration station s1 that is independent of refrigeration station s2 and sink plants j1, j2 and j4. To satisfy the cooling demand of sink plant j3, additional refrigeration station s1 is built. The specific cooling cost of plant j1 is largest among the three sink plants j1, j2, and j4 and is larger than that of the new LGHRRUN system. The cooling demand of plant j1 is greatest among the three plants. It is also the farthest sink plant from the refrigeration station. This causes the greatest pipe cost, as shown in Table 1. The specific cooling cost of plants j2 and j4 are lower than that of the entire system. Note that the product of the cooling cost of the entire system and the cooling quantity is not equal to the sum of that for the individual plants. The cost analysis can offer us insight into the new LGHRRUN system and help investors make decisions. 5.4. Sensitivity Analysis. The total investment of the new LGHRRUN system is over ten million dollars, and the system is operated over a long period. The utility price may vary over such a long period. The influence of the prices of cold utility and power on the economic performance of the new LGHRRUN system is investigated. To evaluate the economic performance of the new system, Equation 69 is used to calculate the specific cooling cost. We vary the price of power (PLp) and cold utility (PLw), and iteratively solve the MINLP model. Note that the variables denoting the network (Ms, Xi,s, and Ys,j), the refrigeration chillers (Zs,k) and pipe diameter (Di,s and Ds,j) are fixed at the

Figure 7. Chilled, cooling, and hot water in absorption chillers.

method is described as follows. First, we obtain the pipe cost, absorption chiller cost and utility cost for the entire LGHRRUN system, as listed in the second row of Table 1. Table 1. Optimal Results of Pipes items entire system excluding plant j1 plant j1 excluding plant j2 plant j2 excluding plant j3 plant j3 excluding plant j4 plant j4

cooling supply GJ/h

chiller cost $105/year

pipe cost $105/year

utility cost $105/year

specific cooling cost $/GJ

69.12

5.18

18.23

41.29

7.64

36.72

3.33

11.62

26.78

7.82

91.44 14.40

1.84 4.48

6.61 16.49

14.51 36.01

6.70

82.08 23.76

0.70 3.46

1.74 13.89

5.28 29.03

9.64

74.88 30.96

1.72 3.68

4.34 14.73

12.27 29.97

6.59

69.12

1.50

3.50

11.33

Second, we specify the cooling demand of a sink plant to be zero, solve the MINLP model, and obtain the new pipe cost, new chiller cost and new utility cost. The industrial park has four sink plants. We set the cooling demand of sink plants to zero iteratively. The solution results are shown in the third, fifth, seventh and ninth lines of Table 1. The four lines show that the cooling demands of sink plants j1, j2, j3, and j4, respectively, are zero. For example, we set the cooling demand J


Article


Figure 8. Cost analysis for cooling supply.

Figure 9. Annual profit variation with the price of cooling water and power.

Figure 10. Annual profit variation with the cooling price.

cooling sale. We vary the price of the cooling sale from $0 to $20 per GJ and use eqs 70 and 71 to obtain the curves in Figure 10. When the price of the cooling sale is $7.6 per GJ, the income from the cooling sale equals the annual investment cost. In other words, the annual profit in eq 70 equals zero. Hence, the lowest price of the cooling sale is not less than $7.6 per GJ. Otherwise, the new LGHRRUN system is unprofitable. When the price is $10 per GJ, the annual profit is 2.00 million dollars per year and the static investment payback period is 4.32 years. In the industrial park, the sink plants can allow the price of cooling to be no greater than $18 per GJ. At that price, the annual profit is 8.77 million dollars per year and the static investment payback period is 1.69 years. The new LGHRRUN system is very profitable for the industrial park.

optimal design level in this evaluation procedure. This means that the LGHRRUN system has been built. As a result, the MINLP model is reduced to a nonlinear programming model. The variation of the specific cooling cost with the price of cold utility and power is shown in Figure 9. When the price of cold utility increases from $0.6 to 1.4 per GJ, the specific cooling cost increases from $6.59 to 8.69 per GJ, an increase of 31.87%. When the price of power increases from $0.07 to 0.19 per kW· h, the cooling cost increases from $7.39 to 7.86 per GJ, an increase of 6.35%. The total cooling demand of the four sink plants is 105.84 GJ/h, which is satisfied by the new LGHRRUN system. Note that the cooling produced by the refrigeration stations is greater than the cooling demand of the four sink plants because some cooling is lost from the pipes between the refrigeration stations and sink plants. The price of the cooling sale is significant for the annual profit of the new LGHRRUN system. We use eq 70 to calculate the annual profit and eq 71 to estimate the static investment payback period of the system. PLd is the price of the

⎛ (P + P2) ⎞ annual profit = GPLd∑ Q jo − ⎜ 1 + P3⎟ ⎝ PB ⎠ j K

(70)


Article

Industrial & Engineering Chemistry Research BP =

P1 + P2 d

GPL ∑j Q jo

− P3

ino max mid min out sta w

(71)

6. CONCLUSIONS The utilization of low grade heat is challenging for energyintensive industrial parks. The LGHRRUN system was proposed and decomposed into three levels: pipe networks, refrigeration stations, and absorption chillers. A MINLP mathematical framework was formulated to model and design the LGHRRUN system for industrial parks. The mathematical model was applied to design a new LGHRRUN system for a petrochemical industrial park and could be solved using deterministic optimization in a reasonable solution time. The solution results demonstrate three conclusions. First, the cost of pipe installation is greater than that of the absorption chillers for the industrial park, and the utility cost is greatest among the pipe, chillers and utility costs. Second, the cooling cost for the entire LGHRRUN system is $7.64 per GJ. This cost is equivalent to 21.2% of the power price of $0.13 per kW·h. Last, when the price of the cooling sale is $10 per GJ, the annual profit of the new LGHRRUN system is 2.00 million dollars per year, and the static investment payback period is 4.32 years.

■

Parameters and Variables

α,β,γ parameters for cost functions of absorption chillers [dimensionless] ε thickness of pipe insulation [m] η pump efficiency [dimensionless] δ heat transfer temperature difference in chillers [°C] CC cost of specific cooling supply [$/GJ] COP coefficient of performance [dimensionless] CP specific heat capacity [GJ/(t·°C)] D pipe diameter [m] F mass flow rate [t/h] G operating hours per year [h] L pipe length [m] P cost [$/year] PB useful life of new equipment [year] PL price [$/GJ, $/(kW·h)] Q heat load [GJ/h] T temperature [°C] V volume flow rate [m3/s] W pipe weight [t] Ms 0−1 variables, denoting whether refrigeration station s is built [dimensionless] Xi, s 0−1 variables, denoting whether source plant i and station s are connected [dimensionless] Ys, j 0−1 variables, denoting whether station s and sink plant j are connected [dimensionless] Zs, k 0−1 variables, denoting whether refrigeration chill k is installed in station s [dimensionless]

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.iecr.6b02033. Tables of experimental data and results. (PDF)

■

AUTHOR INFORMATION

Corresponding Author

*Tel.: +86 20 84113731. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

■

ACKNOWLEDGMENTS This research is supported by the National Natural Science Foundation of China (Nos. 21276288 and 21376277) and the project of Guangdong Provincial Natural Science Foundation of China (No. 2015A030313112).

■

DEFINITIONS OF SETS AND PARAMETERS low grade heat source plants cooling sink plants absorption chillers parcels for refrigeration stations

Superscript

° a c con d dp e end g h hp in

REFERENCES

(1) Luong, D. Modeling, Estimation, and Control of Waste Heat Recovery Systems; Ph.D. Thesis; University of California: Los Angeles, CA, 2013. (2) Ammar, Y.; Joyce, S.; Norman, R.; Wang, Y.; Roskilly, A. P. Low grade thermal energy sources and uses from the process industry in the UK. Appl. Energy 2012, 89, 3−20. (3) Ammar, Y.; Li, H.; Walsh, C.; Thornley, P.; Sharifi, V.; Roskilly, A. P. Desalination using low grade heat in the process industry: Challenges and perspectives. Appl. Therm. Eng. 2012, 48, 446−457. (4) Ponce-Ortega, J. M.; Tora, E. A.; González-Campos, J. B.; ElHalwagi, M. M. Integration of Renewable Energy with Industrial Absorption Refrigeration Systems: Systematic Design and Operation with Technical, Economic, and Environmental Objectives. Ind. Eng. Chem. Res. 2011, 50 (16), 9667−9684. (5) Lin, S.; Yip, N. Y.; Cath, T. Y.; Osuji, C. O.; Elimelech, M. Hybrid Pressure Retarded Osmosis-Membrane Distillation System for Power Generation from Low-Grade Heat: Thermodynamic Analysis and Energy Efficiency. Environ. Sci. Technol. 2014, 48 (9), 5306−5313. (6) Lee, S. W.; Yang, Y.; Lee, H.; Ghasemi, H.; Kraemer, D.; Chen, G.; Cuiet, Y. An electrochemical system for efficiently harvesting lowgrade heat. Nat. Commun. 2014, 5, 3942. (7) Chan, C. W.; Ling-Chin, J.; Roskilly, A. P. A review of chemical heat pumps, thermodynamic cycles and thermal energy storage technologies for low grade heat utilisation. Appl. Therm. Eng. 2013, 50 (1), 1257−1273. (8) El-Halwagi, M. M. Process Integration, Process Systems Engineering Series; Elsevier: San Diego, 2006; Vol. 7.

Subscript

i j k s

operation maximum position between absorber and condenser minimum outlet start cooling water

initial value absorber condenser consumption chilled water chilled water pipe evaporator end generator hot water hot water pipe inlet L


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Coal Power Plant Using LNG Cryogenic Exergy. Ind. Eng. Chem. Res. 2014, 53, 9812−9824. (31) Chen, C.; Chang, F.; Chao, T.; Chen, H.; Lee, J. HeatExchanger Network Synthesis Involving Organic Rankine Cycle for Waste Heat Recovery. Ind. Eng. Chem. Res. 2014, 53, 16924−16936. (32) Gutiérrez-Arriaga, C. G.; Abdelhady, F.; Bamufleh, H. S.; SernaGonzález, M.; El-Halwagi, M. M.; Ponce-Ortega, J. M. Industrial waste heat recovery and cogeneration involving organic Rankine cycles. Clean Technol. Environ. Policy 2015, 17, 767−779. (33) González-Bravo, R.; Sánchez-Ramírez, E.; Quiroz-Ramírez, J. J.; Segovia-Hernández, J. G.; Lira-Barragán, L. F.; Ponce-Ortega, J. M. Total Heat Integration in the Biobutanol Separation Process. Ind. Eng. Chem. Res. 2016, 55 (11), 3000−3012. (34) Kim, C. K.; Yoon, J. Y. Performance analysis of bladeless jet propulsion micro-steam turbine for micro-CHP (combined heat and power) systems utilizing low-grade heat sources. Energy 2016, 101, 411−420. (35) Xu, Y.; Chen, G.; Wang, Q.; Han, X.; Jiang, N.; Deng, S. Performance study on a low-temperature absorption-compression cascade refrigeration system driven by low-grade heat. Energy Convers. Manage. 2016, 119, 379−388. (36) Oluleye, G.; Smith, R.; Jobson, M. Modelling and screening heat pump options for the exploitation of low grade waste heat in process sites. Appl. Energy 2016, 169, 267−286. (37) Lin, P.; Wang, R. Z.; Xia, Z. Z.; Ma, Q. Ammonia−water absorption cycle: a prospective way to transport low-grade heat energy over long distance. Int. J. Low-Carbon Technol. 2011, 0, 1−9. (38) Ammar, Y.; Chen, Y.; Joyce, S.; Wang, Y.; Roskilly, A. P.; Swailes, D. Evaluation of low grade heat transport in the process industry using absorption processes. Appl. Therm. Eng. 2013, 53, 217− 225. (39) Fang, H.; Xia, J.; Zhu, K.; Su, Y.; Jiang, Y. Industrial waste heat utilization for low temperature district heating. Energy Policy 2013, 62, 236−246. (40) Fang, H.; Xia, J.; Jiang, Y. Key issues and solutions in a district heating system using low-grade industrial waste heat. Energy 2015, 86, 589−602. (41) Xia, J.; Zhu, K.; Jiang, Y. Method for integrating low-grade industrial waste heat into district heating network. Building Simulation. 2016, 9 (2), 153−163. (42) Hlebnikov, A.; Siirde, A. The major characteristic parameters of the Estonian district heating networks and their efficiency increasing potential. Energetika 2008, 54, 67−74. (43) Yunus, C. Heat and Mass Transfer; McGraw-Hill Education: New York, 2007. (44) Herold, K. E.; Radermacher, R.; Klein, Sanford, A. Absorption Chillers and Heat Pumps, 2nd ed.; CRC Press: Boca Raton, FL, 2016. (45) Hicks, T. G.; Chopey, N. P. Handbook of Chemical Engineering Calculations, 4th ed.; McGraw-Hill Education: New York, 2012. (46) Floudas, C. A. Nonlinear and Mixed-Integer Optimization: Fundamentals and Applications; Oxford University Press: New York, 1995. (47) Floudas, C. A. Deterministic Global Optimization: Theory, Methods, and Applications; Nonconvex Optimization and It’s Applications; Kluwer Academic Publishers: Dordrecht, Netherlands, 2000. (48) Brooke, A.; Kendrick, D.; Meeraus, A. GAMS−A User’s Guide, release 2.25 The scientific press: San Francisco, CA, 1992. (49) Misener, R.; Floudas, C. A. ANTIGONE: Algorithms for coNTinuous/Integer Global Optimization of Nonlinear Equations. J. Global Optim. 2014, 59, 503−526. (50) Sinnott, R. K. Chemical Engineering Design Principles. Practice and Economics of Plant and Process Design, 2nd ed.; ButterworthHeinemann: Oxford, U.K., 2012.

(9) Morar, M.; Agachi, P. S. Review: Important contributions in development and improvement of the heat integration techniques. Comput. Chem. Eng. 2010, 34 (8−9), 1171−79. (10) Klemeš, J. J.; Kravanja, Z. Forty years of Heat Integration: Pinch Analysis (PA) and Mathematical Programming (MP). Curr. Opin. Chem. Eng. 2013, 2, 461−74. (11) Lai, S. M.; Wu, H.; Hui, C. W.; Hua, B.; Zhang, G. Flexible heat exchanger network (HEN) design for low temperature heat utilization in oil refinery. Asia-Pac. J. Chem. Eng. 2011, 6, 713−733. (12) Moorthy, A. N.; Reddy, C. C. S.; Rangaiah, G. P. Optimization of Heat Exchanger Networks for the Utilization of Low-Temperature Process Heat. Ind. Eng. Chem. Res. 2014, 53 (46), 17989−18004. (13) Zhang, B. J.; Luo, X. L.; Chen, Q. L. Hot discharges/feeds between plants to combine utility streams for heat integration. Ind. Eng. Chem. Res. 2012, 51 (44), 14461−14472. (14) Zhang, B. J.; Luo, X. L.; Chen, Q. L.; Hui, C. W. Heat Integration by Multiple Hot Discharges/Feeds between Plants. Ind. Eng. Chem. Res. 2011, 50 (18), 10744−10754. (15) Zhang, B. J.; Li, J.; Zhang, Z. L.; Wang, K.; Chen, Q. L. Simultaneous design of heat exchanger network for heat integration using hot direct discharges/feeds between process plants. Energy 2016, 109, 400. (16) Hackl, R.; Harvey, S. From heat integration targets toward implementation - A TSA (total site analysis)-based design approach for heat recovery systems in industrial clusters. Energy 2015, 90, 163− 172. (17) Lu, Y.; Chen, J. Integration Design of Heat Exchanger Networks into Membrane Distillation Systems to Save Energy. Ind. Eng. Chem. Res. 2012, 51, 6798−6810. (18) Kapil, A.; Bulatov, I.; Smith, R.; Kim, J. Site-wide low-grade heat recovery with a new cogeneration targeting method. Chem. Eng. Res. Des. 2012, 90 (5), 677−689. (19) Law, R.; Harvey, A.; Reay, D. Opportunities for low-grade heat recovery in the UK food processing industry. Appl. Therm. Eng. 2013, 53 (2), 188−196. (20) Walsh, C.; Thornley, P. A comparison of two low grade heat recovery options. Appl. Therm. Eng. 2013, 53 (2), 210−216. (21) Kwak, D.; Binns, M.; Kim, J. Integrated design and optimization of technologies for utilizing low grade heat in process industries. Appl. Energy 2014, 131, 307−322. (22) Zhou, X.; Gingerich, D. B.; Mauter, M. S. Water Treatment Capacity of Forward-Osmosis Systems Utilizing Power-Plant Waste Heat. Ind. Eng. Chem. Res. 2015, 54, 6378−6389. (23) Miah, J. H.; Griffiths, A.; McNeill, R.; Poonaji, I.; Martin, R.; Leiser, A.; Morse, S.; Yang, A.; Sadhukhan, J. Maximising the recovery of low grade heat: An integrated heat integration framework incorporating heat pump intervention for simple and complex factories. Appl. Energy 2015, 160, 172−184. (24) Law, R.; Harvey, A.; Reay, D. A knowledge-based system for low-grade waste heat recovery in the process industries. Appl. Therm. Eng. 2016, 94, 590−599. (25) van de Bor, D. M.; Ferreira, C. A. I.; Kiss, A. A. Low grade waste heat recovery using heat pumps and power cycles. Energy 2015, 89, 864−873. (26) Sarkar, J. Review and future trends of supercritical CO2 Rankine cycle for low-grade heat conversion. Renewable Sustainable Energy Rev. 2015, 48, 434−451. (27) Imran, M.; Usman, M.; Park, B.; Lee, D. Volumetric expanders for low grade heat and waste heat recovery applications. Renewable Sustainable Energy Rev. 2016, 57, 1090−1109. (28) Wu, G.; Zhu, X. X. Design of Integrated Refrigeration Systems. Ind. Eng. Chem. Res. 2002, 41 (3), 553−571. (29) Hipól ito-Valencia, B. J.; Váz quez-Ojeda, M.; SegoviaHernández, J. G.; Ponce-Ortega, J. M. Waste Heat Recovery through Organic Rankine Cycles in the Bioethanol Separation Process. Ind. Eng. Chem. Res. 2014, 53, 6773−6788. (30) Lee, U.; Park, K.; Jeong, Y. S.; Lee, S.; Han, C. Design and Analysis of a Combined Rankine Cycle for Waste Heat Recovery of a M


Network Modeling and Design for Low Grade Heat Recovery

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