Sustainable Integration of Trigeneration Systems with Heat Exchanger

Article pubs.acs.org/IECR

Sustainable Integration of Trigeneration Systems with Heat Exchanger Networks Luis Fernando Lira-Barragán,† José María Ponce-Ortega,*,† Medardo Serna-González,† and Mahmoud M. El-Halwagi‡,§ †

Chemical Engineering Department, Universidad Michoacana de San Nicolás de Hidalgo, Morelia, Michoacán de Ocampo, 58060, México ‡ Chemical Engineering Department, Texas A&M University, College Station, Texas 77843, United States § Adjunct Faculty at the Chemical and Materials Engineering Department, King Abdulaziz University, Jeddah, 21589, Saudi Arabia ABSTRACT: A novel superstructure-based approach for synthesizing sustainable trigeneration systems (i.e., heating, cooling, and power generation cycles) integrated with heat exchanger networks is presented in this paper. The trigeneration system accounts for steam and organic Rankine cycles and an absorption refrigeration cycle. The steam Rankine cycle can be driven by multiple primary energy sources (i.e., solar, biofuels, and fossil fuels) for sustainable generation of power and process heating. The waste energy from the steam Rankine cycle and/or the excess of process heat can be used to drive both the organic Rankine cycle and the absorption refrigeration cycle to produce power and process cooling below the ambient temperature, respectively. The synthesis problem is formulated as a multiobjective mixed-integer nonlinear programming problem for the simultaneous consideration of the economic, environmental, and social dimensions of sustainability. Two example problems are presented to show the applicability of the proposed methodology.

1. INTRODUCTION Nowadays there are several energy problems around the world such as the depletion of nonrenewable fuels, as well as the global warming and the climate change caused by the greenhouse gas emissions (GHGE) released to the environment from the combustion of fossil fuels (i.e., oil, coal, and natural gas). Currently the cheapest way to obtain energy is from fossil fuels, and several governments have promoted the use of cleaner forms of energy (i.e., solar, wind, biofuels, waste process heat, etc.) through tax credits. Utility systems (i.e., combined cooling, heating, and power) are widely used in industrial processes to meet the heating, cooling, and electricity demands (see Figure 1), where usually fossil fuels are burned. To reduce the consumption of external utilities, heat exchanger networks (HENs) have been implemented to maximize the recovery of process heat by exchanging it between hot process streams (HPS) that have to be cooled and cold process streams (CPS) that have to be heated.1−4 The methodologies for synthesizing HENs have been widely classified as sequential approaches based on pinch analysis,5,6 stochastic methods,7−9 and mathematical programming based techniques.10−13 It should be noted that the above-mentioned methodologies have been concentrated on the synthesis of stand-alone HENs and have not taken into account the interactions between the HEN and the utility system. To address the problem of heat and power integration with the industrial processes, a number of methods have been reported in the literature. Some of them are based on thermodynamic principles and heuristic rules,14,15 and others use optimization techniques.16−18 In addition, total site analysis, which is an extension of pinch analysis, has played an important role in solving the problem of heat and power integration in a set of processes served by a central utility system.19−23 Furthermore, nonlinear targeting © 2014 American Chemical Society

models to get the maximum economic savings integrating heat pumps in total sites were presented by Bagajewicz and Barbaro.24 For processes that operate above ambient temperature, normally recirculating cooling water systems are used to provide the required cooling utility. Recently, some works have considered the cooling tower design together with the synthesis of the associated HEN or cooling water network to properly take into account their interactions.25−28 Also, for processes that require below ambient cooling, Ponce-Ortega et al.29 and Lira-Barragán et al.30 published mathematical programming based approaches to address the problem of multiobjective optimization of absorption refrigeration (AR) cycles that are integrated with HENs. Traditionally, the economic, environmental, and social dimensions of sustainability31,32 have not been simultaneously considered to evaluate the performance of industrial processes. In recent years, different multiobjective optimization approaches that only include economic and environmental aspects have been proposed to solve different engineering problems.33−38 Then, some works have balanced simultaneously the economic, environmental, and social objectives.39−41 It should be noticed that significant socio-economic and environmental benefits can be achieved through the optimal synthesis of trigeneration systems (i.e., cogeneration systems combining heat, cooling, and power production) that are integrated with HENs and use renewable energy resources as primary heat sources to reduce fossil fuel consumption and GHGE. Therefore, the objective of this paper is to present a Received: Revised: Accepted: Published: 2732

July 5, 2013 December 31, 2013 January 16, 2014 January 16, 2014 dx.doi.org/10.1021/ie4021232 | Ind. Eng. Chem. Res. 2014, 53, 2732−2750

Industrial & Engineering Chemistry Research

Article

Figure 1. Conventional industrial plant requiring energy in terms of hot utilities, cold utilities, refrigeration, and electricity.

and fossil fuels). The waste heat from the SRC can be used as hot utility in the HEN, in the AR cycle, and in the ORC. In addition, it requires an efficiency factor to simulate SRC performance and the inlet temperature to the associated condenser. • Also given is an ORC to produce electricity that can be sold. This power cycle requires an efficiency factor to be modeled as well as the inlet and outlet temperatures of the associated condenser. • A single-effect AR cycle is given to supply the cooling requirement (cold utility below the ambient temperature) for the HPS and its coefficient of performance. The AR generator requires heating with a minimum temperature of 80 °C. • A solar collector is given to provide a heat source to drive the SRC. Capital and operational cost functions as well as the capacity to catch solar radiation for each period of the year t are specified for each type of solar collector. The number of jobs that can be generated per kilojoule produced by each solar collector must be also given. • Given is a set of available fossil fuels F to provide external energy to the integrated system. For each fossil fuel available are also given the unitary cost, maximum availability, overall specific GHGE, and number of jobs that can be generated per kilojoule produced. • Also given is a set of available biofuels B to supply heat to the SRC to run it, including their unitary costs, entire unit GHGE, maximum availability for each period t, and number of jobs that can be generated. • Cooling water used as cooling utility with known supply and outlet temperatures as well as film heat transfer coefficient and unitary cost is given . • Also, the minimum approach temperature (ΔTmin) for heat exchange is given. Then, the problem to be addressed involves the design and integration of an HEN, an SRC, an ORC, and an AR cycle into an industrial facility and the selection of multiple primary energy

mathematical programming formulation for the simultaneous synthesis of sustainable trigeneration systems and HEN, where simultaneously is proposed the energy integration between the process streams and the thermodynamic cycles (a single-effect AR to supply below-ambient cooling, a steam Rankine cycle (SRC), and an organic Rankine cycle (ORC) to produce electricity). The proposed mathematical model is based on a superstructure that includes all feasible heat integration options and connections between the system components. The synthesis problem is formulated as a multiobjective mixed-integer nonlinear programming problem accounting for economic, environmental, and social objectives. The environmental objective is evaluated by the overall GHGE, and the social objective is quantified by the number of jobs generated. The multiobjective optimization model is solved with the ε-constraint method. The optimal solutions lead to the Pareto set for the problem that shows the trade-offs between the total annual profit, the GHGE, and the number of generated jobs in the entire life cycle of the integrated energy system. The capabilities of the proposed approach are illustrated through its application to two example problems. The results indicate that the integration of HENs and trigeneration schemes yields significant energy savings and more environmentally benign solutions.

2. PROBLEM STATEMENT The problem addressed in this paper can be stated as follows. • Given is a set of HPS that are required to be cooled from their supply temperature TH,in to their target temperature TH,out (some of them require refrigeration). Given are also the heat capacity flow rates and the film heat transfer coefficients for all the streams. • Also given is a set of CPS requiring heating with known supply temperature TC,in and target temperature TC,out, as well as heat capacity flow rates and film heat transfer coefficients. • Given is an SRC available for power production, which can be driven by different primary energy sources (solar energy, biofuels, 2733

dx.doi.org/10.1021/ie4021232 | Ind. Eng. Chem. Res. 2014, 53, 2732−2750


Article

Figure 2. Schematic representation of the proposed integrated system.

Figure 3. Proposed superstructure for the integrated energy system.

sources to simultaneously maximize the total annual profit (TAP), minimize the overall GHGE, and maximize the number of jobs (NJOBS) created by the project. The general integration problem considered in this paper is shown in Figure 2. Notice that multiple primary energy sources (fossil fuels, biomass, biofuels, and solar energy) can be supplied to the SRC to generate

electricity and low pressure steam (LPS). Part of the steam generated is used to satisfy heating demands of the process in the HEN. Another portion of the steam (i.e., waste heat from the SRC) can be used to drive the AR cycle that provides the refrigeration demands of HPS in the HEN and/or can be rejected to the organic working fluid in the ORC evaporator. In the 2734



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strict) and impact directly the objective functions (TAP, GHGE, and NJOBS). Although some fossil fuels are cheaper, the associated GHGE and NJOBS could yield unfeasible solutions. In addition, when the environmental constraint for the overall GHGE is rigorous, the solutions could yield an attractive tax credit reduction; but the profit is not attractive. For this reason, it is important to present the results through Pareto curves to visualize the trade-offs between the economic, environmental, and social objectives.

integrated energy system under consideration, the AR cycle and the ORC can also use excess of process heat; furthermore, the ORC is allowed to reject heat to CPS. Hence, there are connections between the HEN and the three thermodynamic cycles at different levels of temperature to reduce the overall energy consumption and to produce electricity that can be sold. Figure 3 shows the proposed superstructure for the energy integration, which considers heat exchange between HPS and CPS, in addition to heat transfer between HPS and the AR cycle (remember that the necessary condition for the existence of the exchangers AR1 is that the HPS must have inlet temperatures higher than 80 °C + ΔTmin), the ORC, and cooling water (cooling utility). Finally, for the HPS requiring cooling below ambient temperature, a set of coolers is placed at the cold end (AR2) of the superstructure to reach the target temperature of each HPS. The superstructure also takes into account the heat integration between the CPS and the ORC, in addition to the hot utility (provided by the SRC) to achieve their target temperatures. Notice that any match between HPS and CPS is allowed for all internal stages of the superstructure. In this sense, the number of inner stages is set as the maximum of HPS or CPS. Typically, SRCs consume huge amounts of fossil fuels (releasing CO2 to the environment) and, at the same time, reject considerable quantities of waste heat through the cycle condenser. For this reason, this work proposes the following: • The SRC uses multiple energy sources to generate electricity, including renewable energies. The energy sources considered are solar energy, biofuels, and fossil fuels. Then, the use of clean energies allows obtaining economic benefits through tax credits. • There should be energy integration between the SRC, the ORC, the AR cycle, and the HEN to take advantage of the waste energy available in the SRC. • The operation of an ORC using waste energy has demonstrated to be a novel design to improve the overall efficiency to produce electricity. • All the possible interconnections of heat exchange between the HEN and the three cycles should be considered. It is important to note that the AR cycle is used to satisfy the cooling requirements for the HPS because this type of refrigeration is suitable for systems where low-temperature cooling requirements are not very large and that have heat sources available to be supplied to the AR cycle. In this sense, this work proposes that the excess heat of the HPS with an inlet temperature higher than 80 °C + ΔTmin could be used for this purpose, in addition to the waste heat available in the SRC condenser. On the other hand, to implement the proposed methodology, the following information is required: the useful energy collected by the solar collector per area and the overall GHGE for the fossil fuels and biofuels. To determine the useful energy collected, it is necessary to know the following information: first, the location of the project must be established to obtain the solar radiation data at each period of the year; also, the efficiency of the solar collector to capture the solar radiation is required. The overall GHGE for fossil fuels and biofuels are computed using the life cycle analysis methodology to account for the overall emissions from the production to the consumption for the considered fuels (the GREET or BESS software can be used in this task). Additionally, the model considers the availability for the different types of external energy sources (mainly for the biofuels considered because these depend highly on the season of the year), which can lead to the selection of fossil fuels or solar energy (only for cases where the environmental restrictions are very

3. MODEL FORMULATION Before presenting the mathematical formulation, the sets required in the model are established. The sets representing HPS, CPS, and stages in the superstructure are HPS, CPS, and ST, respectively; while the index i is used for the HPS, j denotes the CPS, and the index k is a stage in the superstructure. The sets used to denote fossil fuels, biofuels, and time periods (months for this case) are F, B, and T, respectively, and their corresponding indexes are f, b, and t. The Nomenclature includes all the symbols used in the model. Additionally, to clearly present the proposed model formulation, this has been subdivided in the following sections: section 3.1 contains the mathematical programming model for the thermodynamic cycles (SRC, ORC, and AR) and their interactions, while section 3.2 shows the required relationships to determine the optimal size for the solar collector and the maximum availabilities for fuels; the objective functions considered in this work as well as the procedure used to generate the Pareto curves are included in section 3.3; finally, the model representing the proposed superstructure for the HEN is presented in the Appendix. 3.1. Thermodynamic Cycles and Their Interactions. This work considers a coefficient of performance for the AR cycle (COPar), an efficiency factor for the SRC (μran), and another efficiency factor for the ORC (μorc). Additionally, the optimal size for the solar collector is determined considering simultaneously the monthly solar radiation available on the selected site and the maximum availabilities to satisfy the energy requirements of the systems. Interactions between the Thermodynamic Cycles and the HEN. The proposed configuration takes into account several interactions between the thermodynamic cycles considered (AR cycle, ORC, and SRC) and the process streams to achieve an integrated scheme. As can be seen in Figure 2, the energy sources are only fed to the SRC; in this context, QExternal represents the total external energy provided by the solar collector (QSolar ), t ) and fossil fuels (QFossil biofuels (QBiofuel b,t f,t ) to the SRC: Q External = Q tSolar +

+ ∑ Q Fossil , ∑ Q bBiofuel ,t f ,t b∈B

t∈T

f ∈F

(1) ran

Furthermore, the power generated by the SRC (Power ) depends on an efficiency factor (μran) to represent the performance of this cycle. Thus, the power produced by the SRC is directly related to the external heat supplied as follows: Power ran = Q External μran

(2)

Once the external energy is used to produce power, low pressure steam at the exit of the turbine of the SRC (Qmps ran ) is available to provide energy to run the AR cycle (Qmps ar )and the 2735



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ORC (Qmps orc ) and to supply, as hot utility, the heat required by CPS (Qlps j ): mps Q ran

Q armps

=

+

mps Q orc

+

∑

qjlps

Solar Cop = CuSolar ∑ (Q tSolarDt )

Solar Ccap = FCSolar y Solar + VCSolar (AcSolar )α

(3)

j ∈ CPS

(4)

where Qcw ran is the heat at low temperature that the SRC rejects to cooling water. On the other hand, the AR cycle supplies the cooling load below the ambient temperature required by HPS (qar2 i ). The excess heat of the HPS (qar1 i,k ) as well as part of the energy provided by the SRC (Qmps ar ) is used to drive the AR cycle. This energy balance is stated as follows: ∑i ∈ HPS qiar2 COP

=

ar

∑ ∑

+ Q armps qiar1 ,k

i ∈ HPS k ∈ ST

Q bBiofuel ≤ ,t

(5)

where COPar denotes the coefficient of performance for the AR cycle. Finally, the next energy balances show the performance of the ORC: Power orc = μorc Power

orc

∑ ∑

mps + Q orc qiorc1 ,k

i ∈ HPS k ∈ ST

=(

∑ ∑

qiorc1 ,k

+

∑ ∑ j ∈ CPS k ∈ ST

(6)

Q Fossil f ,t

(7)

≤

Heating Power Availmax f ,t f Dt

,

f ∈ F, t ∈ T

(13)

(14)

The first two objective functions (max TAP, min NGHGEOverall) usually contradict each other, generating Pareto curves; whereas the social objective function (max NJOBS) is evaluated for each optimal point of the curve. Hence, the constraint method42 is used to carry out this task, which first determines points A (minimum profit and the minimum NGHGE Overall ) and B (maximum profit and maximum NGHGEOverall), and subsequently, the model is transformed into a single objective problem (profit maximization) and restricting the NGHGEOverall for several values of εa between the minimum NGHGEOverall and the maximum NGHGEOverall given by the solutions A and B. This is stated as follows:

(8)

∀t∈T

b ∈ B, t ∈ T

OF = {max TAP; min NGHGEOverall ; max NJOBS}

where Powermax represents the maximum power that can be sold. 3.2. Optimal Size for the Solar Collector and Maximum Availability for Fuels. The proposed model considers that a solar collector can provide energy to the SRC; in this case, the useful solar energy (QUseful_Solar ) is obtained accounting for the t available solar radiation in the specific location where the solar collector can be installed as well as the efficiency of the equipment. Then, the following relationships show the performance of the solar collector and determine its size. In addition, if the solar collector is not required, then the solar energy supplied to the system is zero (i.e., QSolar = 0, ∀ t ∈ T). t Q tSolar

,

3.3. Objective Functions. The proposed formulation is a multiobjective MINLP problem accounting for the economic, environmental, and social aspects of sustainability. The first objective consists in maximizing the total annual profit (economic objective), the next target is minimizing the net GHGE (environmental function), and finally the social objective is to maximize the jobs generated by the project (social function).

In this case, Power is the power produced in the ORC, μorc denotes the efficiency factor for the ORC, the symbol qorc1 i,k is used to represent the heat transferred from the HPS to the ORC, and qorc2 j,k is the heat transferred from ORC to the CPS. The heat entering the ORC cycle and coming from the SRC is Qmps orc , is the heat removed from the ORC with cooling whereas Qcw orc water. Additionally, an upper limit for the maximum power that can be produced by the system (i.e., the electricity produced by the SRC and the ORC) is required. Thus, prior to implement the overall system, a study about the maximum amount of power that can be sold to other industries or local governments must be carried out. This constraint is modeled as follows:

1 ≤ Q tUseful_SolarAcSolar , Dt

Dt

In the constraint eq 12, is the heating power for biofuel b and Availmax b,t represents the maximum amount of biofuel b available in period t. Similarly, if the availability of fossil fuels also presents a seasonal restriction; it is considered as follows:

orc

Power ran + Power orc ≤ Power max

Heating bPowerAvailbmax ,t

(12)

mps Q orc )

cw qjorc2 + Q orc ) ,k

(11)

HeatingPower b

i ∈ HPS k ∈ ST

−(

Solar

It should be noticed that the cost for the solar collector includes Solar an operational cost (CSolar op ) and a capital cost (Ccap ); this last one Solar depends on a fixed cost (FC ) and a variable cost (VCSolar). In represents the optimal area of the solar previous equations, CSolar c collector, Dt is a conversion factor to change the units of time, CuSolar is the unitary operational cost, ySolar represents a binary variable used to model the existence of the solar collector, and finally αSolar is an exponent for the area to consider the economies of scale in the capital cost for the solar collector. On the other hand, usually the availability of biofuels fluctuates during the year; therefore, the next relationship models this variation.

The overall energy balance for the SRC is represented by the following equation. mps cw Power ran = Q Exernal − (Q ran + Q ran )

(10)

t∈T

min TAC subject to NGHGEOverall ≤ εa , evaluating NJOBS

(15)

model relationships

In this procedure, the NJOBS are quantified in all the optimal solutions considered in the Pareto curve. Finally, the important

(9) 2736



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Tax Credits Reduction (TCR). This term includes the revenues obtained from the tax credits for the reduction in the GHGE and all of them are calculated taking into account the reduction of GHGE compared to a fossil fuel of reference (i.e., coal):

role of the third objective function (max NJOBS) for the decision makers should be noted. 3.3.1. Economic Objective Function. In this work, the economic objective function is the profit maximization. In this regard, the profit consists of the next terms: Selling of Power (SP). The most important income is the selling of power, which is generated by the SRC and the ORC. This function is represented as follows:

TCR = HY {RSolar[ ∑ (Q tSolarDt )] t∈T

+

SP = HYDsh (GaPow ranPower ran + GaPow orcPower orc)

t∈T b∈B

(16)

+

where HY represents the hours of operation per year of the plant; Dsh is a conversion factor to standardize the units of time. GaPowran and GaPoworc are the unitary gains obtained by the selling of power for the SRC and ORC, respectively. The last parameters can be computed through the following relationships:

SuPPower represents the unitary price of selling for the power, whereas the power production costs for the SRC and the ORC are PPCostran and PPCostorc, respectively.

+

∑ i ∈ HPS

∑ j ∈ CPS

(

)

⎫β ⎪ ⎪ ⎬ + 1/3 ⎤ ⎪ + δ⎥ ⎪ ⎦ ⎭

⎧ ⎫β 1 ⎪ ⎪ orc1 1 qi , k h + h ⎪ ⎪ i orc1 orc1 ⎬ + ∑ Ci ⎨ 1/3 orc1 orc1 ⎤ ⎪ ⎪ ⎡ orc1 ⎛ dt i , k + dt i , k + 1 ⎞ k ∈ ST orc1 ⎜ ⎟ + δ⎥ ⎪ ⎪ ⎢(dti , k )(dti , k + 1)⎝ 2 ⎠ ⎦ ⎭ ⎩⎣

(

)

∑ i ∈ HPS

⎧ ⎫β 1 ⎪ ⎪ ar1 1 qi , k h + h ⎪ ⎪ i ar1 ⎬ ∑ Ciar1⎨ 1/3 ar1 ar1 ⎞ ⎡ ⎤ ⎪ ⎪ ⎛ k ∈ ST ar1 ar1 ⎜ dti , k + dti , k + 1 ⎟ + δ⎥ ⎪ ⎪ ⎢(dti , k )(dti , k + 1)⎝ 2 ⎠ ⎦ ⎭ ⎩⎣

(

⎧ ⎪ qicw ⎪ cw ∑ Ci ⎨ ⎪ ⎡ cw − 1 i ∈ HPS )(dticw − 2) ⎪ ⎢(dt ⎩⎣ i

(

1 hi

(

⎫β ⎧ ⎪ ⎪ 1 ar2 1 qi h + h ⎪ ⎪ i ar2 ar2 ⎬ + + ∑ Ci ⎨ 1/3 ar2 1 ar2 − ⎤ ⎪ ⎪ ⎡ ar2 − 1 + (TOUTi − TIN ) ⎞ i ∈ HPS ar2 ⎛ dti ⎜ ⎟ + δ⎥ ⎪ )(TOUTi − TIN ) ⎪ ⎢(dti 2 ⎝ ⎠ ⎦ ⎭ ⎩⎣

(

(17)

In eq 17, RSolar, RBiofuel , and RFossil are the tax credits for solar b f energy, biofuels, and fossil fuels, respectively. Capital Cost for Exchangers (CACE). Equation 18 determines the capital cost for all heat exchangers considered in the proposed superstructure shown in Figure 3. To calculate the log mean temperature difference (LMTD) for the heat exchange units, this work uses Chen’s approximation43 to avoid logarithmic terms in the optimization model.

GaPow orc = SuPPower − PPcostorc

⎧ ⎛1 1⎞ ⎪ qi , j , k ⎜ h + h ⎟ ⎪ ⎝ i j⎠ exc ∑ Ci , j ⎨ t ti , j , k + 1 + d d ⎡ ⎪ i ,j ,k k ∈ ST ⎪ ⎢⎣(dti , j , k)(dti , j , k + 1) 2 ⎩

∑ ∑ [R Fossil Q fFossil Dt ]} f ,t t∈T f ∈F

GaPow ran = SuPPower − PPcostran

⎡ ⎢ ⎢ ⎢ CACE = k f ⎢ ∑ ⎢ i ∈ HPS ⎢ ⎢⎣

∑ ∑ [R bBiofuelQ bBiofuel Dt ] ,t

)

∑ j ∈ CPS

+

1 hcw

)

)

dticw − 1 + dticw − 2 2

)

⎫β ⎪ ⎪ ⎬ 1/3 ⎤ ⎪ + δ⎥ ⎪ ⎦ ⎭

⎧ ⎫β 1 1 ⎞ orc2⎛ ⎪ ⎪ qj , k ⎜ h + h ⎟ ⎪ ⎪ ⎝ j orc2 ⎠ ⎬ ∑ C jorc2⎨ 1/3 orc2 orc2 ⎤ ⎪ ⎪ ⎡ orc2 k ∈ ST orc2 ⎛ dt j , k + dt j , k + 1 ⎞ ⎜ ⎟ + (d )(d ) t t δ ⎥ ⎪ ⎪ ⎢ j,k j,k+1 2 ⎝ ⎠ ⎦ ⎭ ⎩⎣

⎧ ⎫β⎤ ⎪ ⎪ ⎥ ⎛1 1 ⎞ ⎥ qjlps⎜ h + h ⎟ ⎪ ⎪ ⎪ ⎪ ⎥ ⎝ ⎠ j lps ⎬ + ∑ Cjlps⎨ ⎥ lps lps − 2 ⎞ ⎤1/3 ⎪ ⎥ ⎪⎡ ⎛ (TIN j ∈ CPS − TOUTj) + dt j lps ⎪ ⎢(TIN ⎟⎟ + δ ⎥ ⎪ ⎥ − TOUTj)(dt jlps − 2)⎜⎜ 2 ⎪ ⎢⎣ ⎪ ⎝ ⎠ ⎦⎥ ⎭ ⎩ ⎦⎥

where kf is the factor used to annualize the inversion, δ is a small value used to avoid infeasibilities in the optimization process, and orc1 cw ar2 orc2 lps are the area cost Ci,jexc, Car1 i , Ci , Ci , Ci , Cj , and Cj coefficients for exchangers between process streams, ar1 exchangers, orc1 coolers, units that exchange heat between HPS with cooling water, ar2 coolers, exchangers transferring heat from the ORC to the CPS, and heaters using LPS as hot utility, respectively; finally, h represents the film heat transfer coefficients. Fixed Cost for Exchangers (FICE). The fixed cost for the heat exchanger units is presented as follows:

(18)

FICE = k f [

∑ ∑ ∑

C Fexc z + i ,j i , j , k

i ∈ HPS j ∈ CPS k ∈ ST

+

∑ ∑

+

∑

C Far2 ziar2 i

i ∈ HPS

+

∑ j ∈ CPS

C Far1 ziar1 ,k i

i ∈ HPS k ∈ ST

C Forc1 ziorc1 ,k i

i ∈ HPS k ∈ ST

∑ ∑

+

∑

C Fcw zicw i

i ∈ HPS

+

∑ ∑

C Forc2 z jorc2 ,k j

j ∈ CPS k ∈ ST

C Flps z jlps] j (19)

ar1 orc1 cw ar2 orc2 lps where Cexc Fi,j , CFi , CFi , CFi , CFi , CF , and CFj represent the fixed

costs for exchangers, ar1 coolers, orc1 coolers, cw coolers, ar2 2737



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can be used for this purpose)44 given in units of metric tons (t) of CO2 equiv reduction per kilojoule (kJ) provided. 3.3.3. Social Objective Function. A sustainable process must include economic, environmental, and social criteria.45−47 In this regard, there are several aspects that can be evaluated within the social scope in the proposed project; however, a relevant point of view is the creation of jobs owing to this factor can improve the economic conditions of local regions and surroundings. Then, this work considers the social impact associated with the generation of jobs once the project is operating. The generated jobs are determined indirectly for the production of the biofuels and fossil fuels as well as for the operation of the solar collector to satisfy the energy requirements in the system. To carry out this task, the JEDI (jobs and economic development impact) model is useful for quantifying the number of jobs that can be generated per kilogjoule produced by each energy source (solar collectors, fossil fuels, and biofuels). Miller and Blair48 have used the JEDI model in the economic and social sciences, which is based on an input−output analysis. The input−output analysis is based on the use of multipliers, where a multiplier is a simple ratio of total systemic change over the initial change resulting from a given economic activity. This provides estimates of the total impact resulting from an initial change on economic output (e.g., employment) through the implementation or termination of a project. The size of the multiplier depends on several economic factors, such as the level of local spending for a given industry, degree of sales outside the local region, industry type, and other regional considerations. Self-sufficient areas in which businesses purchase more local inputs and export greater amounts have higher multipliers. On the other hand, smaller areas of concern with decreasing self-sufficiency have lower multiplier factors. Additionally, some industries might be much more dependent than others on the local area for materials and labor. The multipliers are estimated through economic input−output models. Input−output models, which were originally developed to trace supply linkages in the economy, quantify the effects of change of expenditure within a regional economy on multiple industrial sectors. Since the construction and operational phases of a project involve the input of materials, work force labor, goods, and services from a number of sectors, the accrued jobs that are ultimately generated by expenditures of energy source supply chains depend on the extent to which those expenditures are spent locally and on the structure of the local economy. According to the spending pattern and the specific state economic structure, different expenditures support different levels of employment, income, and output. Input− output analysis can be considered as a method for evaluating and summing the impacts of a series of effects generated by input expenditure. To determine the total effect for yielding biofuels, fossil fuels, and solar collectors, three separate impacts are examined: direct, indirect, and induced. • Direct effect is the immediate (or on-site) effect created by an expenditure. For example, in constructing a plant, direct effects include the on-site contractors and crews hired to construct the plant. Direct effects also include the jobs at the plant that build the process equipment. • Indirect effect is the increase in economic activity that occurs when contractors, vendors, or manufacturers receive payment for goods or services and in turn are able to pay others who support their business. For instance, indirect effects include the banker who finances the contractor, the accountant who keeps the contractor’s books, and the steel mills and electrical manufacturers and other suppliers that provide the required materials.

coolers, orc2 heaters, and lps heaters, respectively; z is the binary variable used to consider the existence of the heat exchange unit. Operational Cost (OPC). Equation 20 includes the operational costs for the cw coolers inside the superstructure for the energy integration, and this takes into account the operational costs for the condensers within the SRC and the ORC. This is modeled as follows:

∑

OPC = Ccw[

cw cw qicw + Q ran + Q orc ]

i ∈ HPS

(20)

Notice that the condensers used by the power cycles remove the heat that cannot be integrated with the other components of the overall energy system. Energy Sources Cost (ESC). The external energy requirements of the integrated energy system considered are supplied by primary energy sources, including fossil fuels, biofuels, and solar energy. Therefore, the ESC consists of the costs for the demand of fossil fuels and biofuels, as well as the operational and capital costs for the solar collector in the optimal solution. ESC = HY { ∑ [C Fossil ∑ (Q fFossil Dt )] f ,t f ∈F

+

∑

[CbBiofuel

b∈B

+

t∈T Solar Dt )]} + HYCop ∑ (Q bBiofuel ,t t∈T

Solar k f Ccap

(21)

where CFossil and CBiofuel are the unitary cost for fossil fuel f and the f b unitary cost for biofuel b. Finally, the economic function is established as the sum of the incomes (SP and TCR) minus the costs generated by the project (CACE, FICE, OPC, and ESC). This can be written as follows: max Profit = SP + TCR − CACE − FICE − OPC − ESC

(22)

It is important to note that the revenues obtained from the selling of power and the tax credits reduction usually represent a higher amount than the costs considered by the project; if this is the case, the economic function is positive. Nevertheless, for some cases the economic objective function can generate negative values; in these cases, there are no gains and the costs produced by the project are greater than project incomes. 3.3.2. Environmental Objective Function. The environmental objective function is an indirect environmental impact assessment through the overall quantification of the GHGE. The GHGE for the solar collector are assumed to be zero; however, when fossil fuels and biofuels are burned, these release GHGE that represent an adverse effect on the environment. Therefore, the environmental objective function is stated as follows: min NGHGEOverall =

∑ ∑ [GHGEFossil Q fFossil Dt ] f ,t t∈T f ∈B

+

∑ ∑ [GHGEbBiofuelQ bBiofuel Dt ] ,t t∈T b∈B

(23)

In the function eq 23, NGHGEOverall represents the overall GHGE discharged to the environment by fossil fuels and biofuels to satisfy the energy requirements, while GHGEbBiofuel and GHGEFossil are the individual GHGE for fossil fuel f and biofuel f b. It is important to mention that the individual GHGE are determined through the life cycle analysis (the GREET software 2738



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• Induced effect is the change in wealth that occurs or is induced by the spending of those persons directly and indirectly employed by the project. The total effect from a single expenditure can be calculated by summing all three effects, using regional-specific multipliers and personal expenditure patterns.40,41,49 Hence, the social function consists in maximizing the number of jobs created by the project for the production of fossil fuels, biofuels, and the solar collector. max NJOBSOverall =

Table 3. Streams Data for Example 1

∑ ∑ [NJOBFossil Q Fossil Dt ] f ,t f ∑∑

[NJOBbBiofuel Q bBiofuel Dt ] ,t

t∈T b∈B

+

∑ [NJOBSolarQ tSolarDt ]

(24)

t∈T

NJOBFossil , f

Solar

NJOBBiofuel , b

where and NJOB represent the number of jobs generated per kilojoule provided by fossil, biofuels, and solar collector, respectively.

4. RESULTS AND DISCUSSION Two examples are solved applying the mathematical formulation to show the main advantages of the proposed methodology. In Table 1. Useful Collected Energy per Month for the Solar Collector (PTSC) month

PTSC [kJ/(m2 month)]

January February March April May June July August September October November December

409 293 443 016 577 530 571 860 555 768 454 410 443 610 439 425 394 470 410 967 407 430 522 288

inlet temp [°C]

outlet temp [°C]

FCp [kW/°C]

H1 H2 H3 C1 C2

125 85 45 35 35

65 25 25 240 55

38.75 18.75 43.75 20 36.25

initialization procedure has been implemented. First the model without considering the nonlinear part of the capital cost for the heat transfer units was solved (this is a mixed-integer linear problem); then this solution is used as an initial guess for the nonlinear mixed-integer problem. The number of major iterations to solve the problem was set as 100. Furthermore, global optimization approaches can be used to identify the global optimal solution; it should be noted that most of the deterministic global optimization approaches require good limits for the continuous variables involved in the nonconvex terms and this way the obtained solution with the solver DICOPT can be used as initial guess. Finally, the solved BARON was implemented for the case studies analyzed but no further improvements were obtained. Additionally, the following parameters are fixed in the examples considered: • The location considered for the installation of the project is Morelia, Mexico, which has the coordinates N 19° 42′ 08″ and W 101° 11′ 08″. Table 1 shows the useful energy that can be collected per month by the solar collector in that place. The useful collected energy is computed considering the solar radiation available in the specific place and the efficiency to catch the solar energy of the solar collector (parabolic trough solar collector, PTSC). • The AR cycle uses hot water as the heat transfer medium in conjunction with the LiBr−water system. • The parameter HY used in both examples was 8760 h/year. • The efficiency factors and coefficient of performance involved in the formulation are μran = 0.35, μorc = 0.3 and COPar = 0.7. • The unitary price of the power SuPPower = $0.14/kWh and the power production costs are PPCostran = $0.10/kWh and PPCostorc = $0.115/kWh. • The fixed and variable capital costs for the solar collector are $75,526.61 and $40.78/m2, respectively, while the unitary operational cost is $0.14/kWh and finally αSolar is 1. • The temperatures for the used utilities are the following: Tar1 IN orc1 orc1 cw = 50 °C, Tar1 OUT = 80 °C; TIN = 45 °C, TOUT = 165 °C; TIN = 30

t∈T f ∈B

+

stream

this sense, the solver DICOPT in conjunction with the solvers CONOPT and CPLEX implemented in the General Algebraic Modeling System (GAMS) were used.50 It should be noted that the nonlinear and nonconvex terms are included in the economic objective function (specifically in the capital cost for the heat transfer units), and for solving this problem the following

Table 2. Data for the Fossil Fuels and Biofuels Considered in the Examples Presented no.

fuel

heating power [kJ/kg]

1 2 3

coal oil natural gas

35 000 45 200 54 000

1 2 3 4 5 6

biomass biogas softwood hardwood biodiesel bioethanol

17 200 52 000 20 400 18 400 40 200 29 600

overall GHGE [t of CO2 equiv/kJ] Fossil Fuels 2.213 57 × 10−7 8.054 08 × 10−8 7.908 92 × 10−8 Biofuels 2.443 07 × 10−8 2.682 16 × 10−8 3.348 2 × 10−8 3.348 2 × 10−8 5.132 83 × 10−8 5.843 6 × 10−8 2739

cost [$/mm kJ]

generation of jobs [Jobs/kJ]

1.5559 18.2447 5.8349

1.062 81 × 10−11 1.816 77 × 10−11 5.254 31 × 10−11

2.0303 8.5388 2.5332 2.8975 31.3092 14.4212

6.696 4 × 10−8 5.254 31 × 10−7 1.466 91 × 10−8 5.436 41 × 10−8 2.465 82 × 10−6 2.874 53 × 10−6



Article

Table 4. Monthly Amount Available for the Fossil Fuels and Biofuels for Example 1 [kg/month] fuel

Jan

Feb

Mar

Apr

May

Jun

Jul

Aug

Sep

Oct

Nov

Dec


10 000 5 000 30 000 30 000 5 000 10 000

10 000 5 000 30 000 30 000 5 500 11 000

40 000 6 000 25 000 25 000 6 000 12 000

50 000 6 500 25 000 25 000 7 000 12 000

70 000 6 500 23 000 23 000 10 000 15 000

150 000 10 000 23 000 23 000 10 000 15 000

100 000 10 000 15 000 15 000 10 000 15 000

50 000 10 000 15 000 15 000 10 000 15 000

40 000 8 000 20 000 20 000 9 000 14 000

40 000 7 000 25 000 25 000 8 000 13 000

30 000 6 000 25 000 25 000 7 000 11 000

20 000 5 000 30 000 30 000 6 000 10 000

in this example. Additionally, the sale of up to 5 MW of electric power is possible. When the proposed methodology is applied for this example considering a tax credit of $5/t of CO2 equiv, the Pareto curves shown in Figure 4 are generated. In Figure 4, the Pareto curves are obtained graphing the behavior of the total annual profit when the overall GHGE fluctuate between the minimum emissions and profit until the maximum profit and emissions. The continuous line represents the optimal solutions when the power generation can be equal to or lower than 5 MW (Powermax ≤ 5 MW), while the dashed line illustrates the best solutions when the power production is strictly restricted to 5 MW (Powermax = 5 MW). Notice that the Pareto solutions for the last case (Powermax = 5 MW) can be considered as suboptimal solutions with respect to the Pareto curve that frees this restriction and only considers an upper limit for the power generation of 5 MW. Another important aspect to note is the behavior for the gain owing to in the first part (when the overall GHGE are zero) there are not gains (this region corresponds to economic losses). However, when the GHGE increase, the gains also augment. Additionally, both lines (continuous and dashed) are separated in the first part of the graph (for GHGE values between 0 and 80 000); then, these two lines are joined in the last part (for GHGE values of 80 000−97 658.34). For discussion of the results obtained, the points A, A′, B, C, and C′ are identified in the Pareto curves (notice that points A and C correspond to the continuous line, while points A′ and C′ are in the dashed line and solution B is the same for both lines). Points A and A′ represent designs for the lowest overall GHGE (in this case the solar collector allows achieving a value of zero owing to the total energy required by the system is provided by the solar collector) and the minimum profit

Figure 4. Pareto solutions for example 1. ar2 ar2 orc2 °C, Tcw OUT = 40 °C; TIN = −5 °C, TOUT = −5 °C; TIN = 31 °C, ar1 ar1 T T and °C; °C, °C. = 30 = 275 = 274 Torc2 OUT IN OUT • The unitary cost for the cold utility Ccw is $10/(year K). • The number of jobs generated by the solar collector is 9.95459 × 10−10 jobs/kJ. • The minimum approach temperature is 10 °C. Additionally, according to Vélez et al.51 the maximum amount of power that can be produced by the ORC is 2000 kW. On the other hand, Table 2 contains the fossil fuels and biofuels considered in both examples, as well as their heating power, overall GHGE, cost, and number of jobs created by each fuel. 4.1. Example 1. This example considers a pharmaceutical plant to be installed in Morelia, Mexico. This plant includes three HPS and two CPS shown in Table 3, while Table 4 contains the maximum amount monthly available for the biofuels considered

Table 5. Details for the Solutions Identified in Example 1 Powermax ≤ 5 MW concept fossil fuels cost [$/year] biofuels cost [$/year] solar collector cost [$/year] power produced [kW] selling of power [$/year] tax credits reduction [$/year] capital cost for exchangers [$/year] fixed cost for exchangers [$/year] operational cost [$/year] energy sources cost [$/year] Profit [$/year] overall GHGE [t of CO2 equiv/year] jobs

point A (min Profit, min GHGE)

Powermax = 5 MW

point C (selected solution)

point B (max Profit, max GHGE)

point A′ (min Profit, min GHGE)

point C′ (selected solution)

0 0 2,088,605 1903.85 667,108 189,860 77,011

276,743 51,329 0 2386.25 813,462 20,755 77,011

684,631 21,302 0 5000 1,752,000 10,331 29,309

0 0 4,449,575 5000 1,627,954 404,479 57,944

1,649,719 51,329 0 5000 1,629,644 205,762 57,315

29,302

29,302

25,116

29,302

25,116

0 2,088,605 −1,337,951 0

4,027 328,073 395,804 40 000.00

0 705,933 1,001,973 97 658.34

22,028 4,449,575 −2,526,417 0

21,727 1,701,048 30,200 40 000.00

171

1076

707

364

1089

2740



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Figure 5. Configuration for solution A of example 1.

Figure 6. Configuration for solution B of example 1.

(where even that there is a negative value for the gain, generating economic losses), and finally the number of jobs that can be created by the project is the lowest with respect to all the identified solutions (remember that the most important difference in solutions A and A′ consists in the amount of power produced; see Table 5). Otherwise, point B is the best economic solution and the worst environmental solution, and the corresponding number of generated jobs is relatively low. Point C shows a balanced solution because it includes a moderate level of gains and emissions and a reasonable number of jobs, while point C′ is the solution corresponding to point C, but the power output must be equal to 5 MW. Table 5 presents the detailed costs and the characteristics for the three objective

functions for solutions A, C, B, A′, and C′ with the purpose of displaying the main differences between them. Figure 5 shows the optimal configuration for solution A. In this representation, the SRC produces 1903.85 kW using only a solar collector of 37 193.58 m2 as primary energy source and the residual energy from the power cycle is used as hot utility. Also, there is a heat exchanger to transfer 1785.71 kW from the HPS 1 to the AR cycle (notice that this amount of energy is enough to run totally the AR cycle and to satisfy the cooling requirements). Figure 6 presents the optimal design for solution B, which uses a combination of fossil fuels and biofuels to supply the required energy to the SRC to produce 5 MW of electric power, and the waste energy from the cycle can be taken to heat the CPS and to 2741



Article

Figure 7. Configuration for solution C of example 1.

Figure 8. Energy sources required for each month in solution C of example 1.

Figure 10. Sensitivity analysis for different values of the tax credit of example 1.

Table 6. Stream Data for Example 2 stream

inlet temp [°C]

outlet temp [°C]

FCp [kW/°C]

H1 H2 H3 H4 H5 H6 C1 C2 C3 C4

65 60 57 110 220 280 95 15 10 60

60 15 15 80 75 125 110 25 40 120

1,060 6.67 33.33 1,350 50.59 100.74 2,900 13.33 193.33 671.43

Figure 9. Energy sources required for each month in solution C′ of example 1.

Thus, the cooling that could be carried out through the heat exchange with CPS or cooling water (this last option generates an operational cost) is effectuated by the AR cycle. Therefore, this is the best option found by the optimization process to take advantage of the available thermal energy in the SRC (typically this energy is wasted without reuse as is proposed by the present methodology).

run the AR cycle. It is important to note that the residual energy available in the SRC for solution B is significantly larger than the energy available in the SRC for solution A; then, a significant amount of energy is used by the AR cycle to refrigerate the HPS in a wider range than the one that is strictly necessary (i.e., the HPS 2 is cooled by the AR cycle since its inlet temperature of 85 °C). 2742



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Table 7. Monthly Amount Available for the Fossil Fuels and Biofuels for Example 2 [kg/month] fuel

Jan

Feb

Mar

Apr

May

Jun

Jul

Aug

Sep

Oct

Nov

Dec


40 000 14 000 80 000 90 000 30 000 50 000

50 000 13 000 80 000 90 000 35 500 55 000

130 000 24 000 75 000 75 000 46 000 62 000

100 000 25 500 55 000 75 000 25 000 62 000

180 000 18 500 53 000 63 000 30 000 75 000

350 000 30 000 43 000 63 000 30 000 75 000

300 000 30 000 35 000 45 000 30 000 75 000

320 000 20 000 35 000 45 000 30 000 75 000

80 000 17 000 40 000 50 000 25 000 64 000

90 000 15 000 35 000 75 000 20 000 60 000

70 000 12 000 35 000 75 000 23 000 55 000

50 000 10 000 30 000 90 000 27 000 50 000

Figures 8 and 9 show the type of primary energy source required per month for solutions C and C′. Notice that the most important primary energy source is coal for solution C, while for solution C′ it is natural gas. Finally, Figure 10 shows a comparison of the results for the case when the tax credit changes from $5/t of CO2 equiv to $30/t of CO2 equiv. As can be seen, the total annual profit is increased when the tax credits augment. Also, the gain value varies considerably throughout the Pareto curve that represents the solutions for a tax credit of $5/t of CO2 equiv, while in the Pareto curve that contains the solutions for a tax credit of $30/t of CO2 equiv, the profit only has important variations when the overall GHGE fluctuate from 0 to 40 000 (i.e., if a comparison of the profit for the GHGE values of 40 000 and 60 000 in both Pareto curves is carried out, it can be seen that the Pareto curve of $5/t of CO2 equiv presents significant differences, while in the other curve the same does not happen). 4.2. Example 2. Table 6 presents the characteristics for the six HPS and four CPS considered in this example, while the maximum amount monthly available for the biofuels for this case is shown in Table 7. Additionally, the maximum power that can be sold is 12 MW and the tax credit has a value of $5/t of CO2 equiv. Once the proposed formulation is applied to this case, the Pareto curves shown in Figure 11 are obtained. These Pareto curves show the behavior of the profit when the overall GHGE range from their minimum value (i.e., zero) to the maximum GHGE (which is obtained maximizing the profit, and for this case it has a value of 226 696.50 t of CO2 equiv/year). Furthermore,

Figure 11. Pareto solutions for example 2.

Figure 7 illustrates the optimal configuration obtained for point C, where the solar collector is not required. In addition, this solution uses 575.35 kW from the SRC to produce 172.60 kW of shaft work in the ORC (this represents another important advantage of the proposed configuration because it allows the use of waste energy to produce power). Also, notice that the condenser of the ORC rejects 402.75 kW to cooling water because this amount of heat cannot be used according to the temperature constraints imposed on such a heat transfer unit. Then, this causes a negative charge in the profit because this heat must be transferred to cooling water. Table 8. Details for Solutions of Example 2 Powermax ≤ 12 MW concept fossil fuels cost [$/year] biofuels cost [$/year] solar collector cost [$/year] power produced [kW] selling of power [$/year] tax credits reduction [$/year] capital cost for exchangers [$/year] fixed cost for exchangers [$/year] operational cost [$/year] energy sources cost [$/year] Profit [$/year] overall GHGE [t of CO2 equiv/year] jobs

point A (min Profit, min GHGE)

point C (environ preference)

Powermax = 12 MW point D (econ preference)

point B (max Profit, max GHGE)

point A′ (min Profit, min GHGE)

point C′ (environ preference)

point D′ (econ preference)

0 0 6,845,577

2,805,629 238,511 431,196

550,634 136,831 0

1,588,233 61,461 0

0 0 11,598,143

2,804,891 238,511 4,066,946

4,797,764 136,831 0

7 525.65 2,468,055

6 555.54 2,297,059

4 701.36 1,630,013

12 000 4,160,785

12 000 4,017,182

12 000 3,982,491

12 000 3,982,491

622,282

453,697

55,678

29,807

1,054,304

827,975

627,975

127,781

108,509

123,443

81,230

113,276

121,696

121,696

46,046

46,046

46,046

46,046

41,860

50,232

50,232

109,998

0

3,080

7,816

60,316

56,477

56,477

6,845,577

3,475,336

687,465

1,649,694

11,598,143

7,110,349

4,934,596

−4,039,066 0

−879,135 40 000.00

825,657 80 000.00

2,405,806 226 696.50

−6,742,109 0

−2,528,288 40 000.00

−552,535 80 000.00

560

9364

3046

2038

948.00

9700

3085

2743



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Figure 12. Configuration for solution A of example 2.

Figure 13. Configuration for solution B of example 2.

the continuous line represents the optimal solutions when Powermax ≤ 12 MW, while the dashed line illustrates the optimal solutions when Powermax = 12 MW. In this regard, the dashed line represents suboptimal solutions with respect to the continuous line. Notice that the Pareto curves start with economic losses and

end at the same point producing positive gains. In Figure 11, the points A, A′, B, C, C′, D, and D′ have been marked for further discussion. Point A is the optimal solution with the lowest overall GHGE (zero) and the worst profit (this solution represents economic losses), and the number of jobs that can be created by 2744



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Figure 14. Configuration for solution C of example 2.

Figure 15. Configuration for solution D of example 2.

the project is the lowest with respect to all the solutions presented. Point B represents the best economic and the worst environmental solution (because this solution implies the highest value for the overall GHGE), and the corresponding number of generated jobs is low.

Additionally, point C represents the best social function containing the highest number for the creation of new jobs (9364 jobs), while the environmental function has a good value (40 000 t of CO2 equiv/year); however, the economic function represents losses for $4,039,065/year. Then, to overcome this last aspect, 2745



Article

the three objective functions (TAC, GHGE, and NJOBS) for all the solutions mentioned above. The optimal configuration for the energy integration for solution A is shown in Figure 12, where a PTSC is required to provide the total heat to the system with an area of 121 910 m2. It is important to note that the HPS 5 transfers 4285.46 kW to drive the ORC, which produces 1285.64 kW of electricity. Also note that all the energy available in the condenser of the SRC (11 588.60 kW) is used to run the AR cycle and as hot utility for CPS. Figure 13 illustrates the optimal design for solution B, which combines fossil fuels and biofuels to provide the heat necessary to produce 11 665.03 kW of electric power in the SRC. The energy available in the condenser is mainly used to run the AR cycle, this last one being the only option for cooling. Again, the cooling that could be carried out exchanging heat with CPS or cooling water is effectuated through the AR cycle. Therefore, this is the best option found by the optimization process to use the available energy in the condenser. The optimal design for solution C is shown in Figure 14. In this solution a solar collector of 7294.45 m2 is required, plus a combination of fossil fuels and biofuels to provide 18 730.10 kW to the SRC to produce 6555.54 kW of electricity. Also note that the HPS 4 and 5 transfer 3447.50 kW to refrigerate the HPS 1, 2, and 3 through the AR cycle. On the other hand, Figure 15 presents the optimal configuration for solution D, where the ORC produces 132 kW using 439.98 kW coming from the waste energy available in the SRC. Note that the ORC rejects 307.98 kW into cooling water because the CPS 2 and 3 exchange heat with the HPS; nevertheless, for other cases the heat transfer between the condenser of the ORC and CPS can be an important option to reduce the consumption of cold utility. Figures 16 and 17 show the type of primary energy source required monthly for solutions C and D, respectively. Notice that, for solution C, natural gas is the main primary energy source and the contribution of the solar collector is small compared with the 18 730.10 kW of total energy required by the system. In solution D coal is the main fuel and almost does not use clean energies. Figure 18 illustrates a comparison with the case when the tax credit increases to $30/t of CO2 equiv. In this case, the same effect over the profit behavior as example 1 can be seen. Finally, Table 9 shows the problem characteristics for the two examples illustrated. In this sense, these examples have been run in a computer with an i7 processor at 2.1 GHz and 8 GB of RAM.

Figure 16. Energy sources required for each month for solution C of example 2.

Figure 17. Energy sources required for each month for solution D of example 2.

5. CONCLUSIONS This paper has presented a new mathematical programming model for the optimal integration of heat engines, absorption refrigeration cycles, and heat exchanger networks considering simultaneously the maximization of the total annual profit, the minimization of the overall greenhouse gas emissions, and the maximization of the number of jobs that can be created by the use of different types of primary energy sources. The approach also determines the optimal use and distribution of sustainable energy sources (solar and biofuels). Pareto solutions are produced to discuss the trade-offs among the economic, environmental, and social objectives of sustainability. The proposed approach is based on a new superstructure that allows an efficient and novel heat recovery and integration between the considered subsystems. Results show the benefits of considering energy integration of the available heat in the SRC through different uses (i.e., the organic Rankine cycle can produce electricity, which can be used as hot utility and to run the absorption refrigeration cycle).

Figure 18. Sensitivity analysis for different values of the tax credit for example 2.

Table 9. Characteristics for the Proposed Methodology in the Examples Presented concept

example 1

example 2

no. of constraints no. of continuous variables no. of binary variables CPU time [s]

263 292 45 0.109

764 787 193 0.094

also point D has been selected, which presents a satisfactory profit ($825,657/year), balanced overall GHGE (80 000 t of CO2 equiv/year), and an important number of jobs created (3046 jobs). Finally, points A′, C′, and D′ are the corresponding solutions when the power production is fixed at 12 MW. Table 8 shows the details for the costs as well as their characteristics for 2746



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Typically, this heat is wasted without being used for relevant applications as proposed by the present methodology. Results show also that several interesting scenarios can be identified in the Pareto solutions to trade-off the objectives considered and to promote sustainable processes. This way, in scenarios where the economic objective function is prioritized, the environmental aspect is deteriorated and the social aspect is not benefited substantially (in this case usually fossil fuels are used as the major energy source). On the other hand, when the environmental aspect is prioritized over the economic objective function and the social aspect, the major energy source is obtained through the solar collector. However, between these two extreme solutions there are several solutions that properly compensate the considered objectives, where a combination of fossil fuels, biofuels, and a solar collector can promote good economic objective functions without affecting significantly the environment and producing a significant social benefit. In addition, in all the identified solutions, the proper integration for the heat available in the system is considered. Finally, the proposed approach is general and it was formulated in a way that does not represent significant numerical problems during its solution.

j ∈ CPS, k ∈ ST

The HPS can transfer their remaining energy to cooling water at the exit of the internal stages of the superstructure. (ti ,NOK + 1 − tiar2)FCpi = qicw ,

(tiar2 − TOUTi)FCpi = qiar2 ,

+

∑

qiorc1 + qicw + qiar2 , ,k

∑

(TOUTj − t j ,1)FCpj = qjlps ,

TI INi = ti ,1 ,

k ∈ ST i ∈ HPS

ti , k ≥ ti , k + 1 ,

+

qjlps ,

(A.9)

i ∈ HPS

(A.10) (A.11)

tiar2 ≥ TOUTi ,

i ∈ HPS

(A.12)

TOUTj ≥ t j ,1 ,

j ∈ CPS

(A.13)

t j , k ≥ t j , k + 1,

j ∈ CPS, k ∈ ST

(A.14)

g. Existence for Heat Exchange Units

The following relationships are required to determine the existence of the heat transfer units; in this regard, a binary variable (z) must be associated with each unit and is only activated if the unit exists. First, for heat transfer units between process streams:

The next relationships are required to determine the internal temperatures of the proposed superstructure. Then, for each HPS the energy balance is stated as follows:

qi , j , k − Q imax zi , j , k ≤ 0, ,j

i ∈ HPS, j ∈ CPS, k ∈ ST (A.15)

qi , j , k + qiar1 + qiorc1 , ,k ,k

For the heat transferred from the HPS to the AR system:

j ∈ CPS

i ∈ HPS, k ∈ ST

i ∈ HPS, k ∈ ST

ti ,NOK + 1 ≥ tiar2 ,

(A.2)

∑

j ∈ CPS

The temperatures in the superstructure decrease from left to right. This behavior is modeled through the next relationships.

b. Energy Balance for Internal Stages of the Superstructure

(ti , k − ti , k + 1)FCpi =

(A.8)

f. Constraints for Temperature Feasibilities in the Superstructure

k ∈ ST

j ∈ CPS

i ∈ HPS

TINj = t j ,NOK + 1 ,

(A.1)

∑

(A.7)

Similarly, the inlet temperature for any CPS is equal to the temperature of the last border of the superstructure.

i ∈ HPS

qi , j , k +

j ∈ CPS

It is important to note that the inlet temperature for any HPS is equal to the temperature of the first border of the superstructure.

Similarly, for any CPS, the total energy exchanged for any CPS j is equal to the energy exchanged with any HPS i in any stage of the superstructure plus the energy received from the AR cycle (qorc2 j,k ) and the SRC (qlps j ).

∑ ∑

(A.6)

e. Assignment of Temperatures for Extreme Borders of the Superstructure

k ∈ ST

k ∈ ST

(TOUTj − TINj)FCpj =

i ∈ HPS

Once the CPS have exchanged heat in the inner stages of the superstructure, the target temperatures can be achieved gaining energy from the low pressure steam from the SRC, which is used as hot utility.

qiar1 ,k

qjorc2 ,k

(A.5)

d. Energy Balance for the Stage of Cold Process Streams and Hot Utility

The total energy that can transfer any HPS i is equal to the sum of the energy exchanged in any stage of the superstructure with any CPS j (qi,j,k), the energy transferred to the AR cycle (qar1 i,k ) and the orc1 ORC (qi,k ), and the energy exchanged with the cooling water ar2 (qcw i ) and the refrigeration requirements (qi ): qi , j , k +

i ∈ HPS

Likewise, the HPS that require refrigeration can be cooled exchanging their residual energy with the absorption AR system.

a. Total Energy Balances for the Process Streams

∑ ∑

(A.4)

c. Energy Balances for the Stages of Hot Process Streams and Cold Utilities

APPENDIX: MODEL FOR THE HEAT EXCHANGER NETWORK The proposed superstructure is shown in Figure 3. Figure 3 considers all the possible heat exchange among the HEN, SRC, ORC, and AR cycle. The following relationships model the heat exchangers necessary to carry out the energy integration.

k ∈ ST j ∈ CPS

qi , j , k + qjorc2 , ,k

i ∈ HPS

■

(TINi − TOUTi)FCpi =

∑

(t j , k − t j , k + 1)FCpj =

qiar1 − Q imax z ar1 ≤ 0, ,k i,k ,k

(A.3)

and for the CPS:

i ∈ HPS, k ∈ ST

(A.16)

For the heat transferred from the HPS to the ORC: 2747


Industrial & Engineering Chemistry Research qiorc1 − Q imax z orc1 ≤ 0, ,k i,k ,k

Article

i ∈ HPS, k ∈ ST

Similarly, for the refrigeration units:

(A.17)

ar2 dtiar2 − 1 ≤ tiar2 − TOUT + ΔTiar2max(1 − ziar2),

For the coolers using cooling water: qicw − Q imaxzicw ≤ 0,

i ∈ HPS

Notice that for the cold end of this exchanger, the temperatures are known parameters (TOUTi − Tar2 IN ). Then, this constraint is not required. On the other hand, for the heat transfer units connecting the CPS with the ORC:

For the coolers used to refrigerate the HPS through the AR system: qiar2 − Q imaxziar2 ≤ 0,

i ∈ HPS

(A.19)

For the heat exchanged between the CPS and the ORC: qjorc2 − Q jmax z orc2 ≤ 0, ,k j,k ,k

j ∈ CPS, k ∈ ST

orc2 orc2max dt jorc2 (1 − z jorc2 , k ≤ TIN − t j , k + ΔT j , k ),

(A.20)

j ∈ CPS, k ∈ ST

Finally, for the CPS and the hot utility from the SRC: qjlps − Q jmaxz jlps ≤ 0,

j ∈ CPS

j ∈ CPS, k ∈ ST

lps dt jlps − 2 ≤ TOUT − t j ,1 + ΔT jlpsmax(1 − z jlps),

Notice that the constraint for the hot side for the previous match is not required because these temperatures are given by the data of the problem (TOUTi − Tar2 IN )). Finally, all the temperature differences for the heat exchangers required must be greater than the minimum approach temperature.

(A.22)

dti , j , k + 1 ≤ ti , k + 1 − t j , k + 1 + ΔTimax , j (1 − zi , j , k), i ∈ HPS, j ∈ CPS, k ∈ ST

(A.23)

Notice that, when the heat transfer unit exists, the binary variable z is 1 and consequently the temperature difference is calculated properly; on the other hand, when the unit does not exist, the binary variable z is 0 and the upper limit ΔTmax is used to relax the constraint. Similarly, for the heat exchangers that transfer heat from HPS to the AR cycle in each stage, the following relationships are used. dtiar1 ,k

≤ ti , k −

ar1 TOUT

+

ΔTiar1max(1

−

dtiar1 ,k+1

≤ ti , k + 1 −

(A.24)

ar1 TIN

+

ΔTiar1max(1

−

■

(A.25)

Likewise, the following relationships are required for the heat exchangers between HPS and the ORC.

≤

tiar2

−

+

ΔTicwmax(1

−

zicw ),

i ∈ HPS, k ∈ ST

(A.36)

ΔTmin ≤ dticw − 1 ,

i ∈ HPS

(A.37)

ΔTmin ≤ dticw − 2 ,

i ∈ HPS

(A.38)

ΔTmin ≤ dtiar2 − 1 ,

i ∈ HPS

(A.39)

ΔTmin ≤ dt jlps − 2 ,

j ∈ CPS, k ∈ ST

j ∈ CPS

(A.40) (A.41)

AUTHOR INFORMATION

(A.27)

■

The authors declare no competing financial interest.

ACKNOWLEDGMENTS The authors acknowledge the financial support from the Mexican Council for Science and Technology (CONACyT) and the Council for Scientific Research of the Universidad Michoacana de San Nicolás de Hidalgo.

■

(A.28) cw TIN

(A.35)

Notes

cw dticw − 1 ≤ ti ,NOK + 1 − TOUT + ΔTicwmax(1 − zicw),

dticw − 2

i ∈ HPS, k ∈ ST

(A.26)

For the coolers that use cooling water:

i ∈ HPS

ΔTmin ≤ dtiar1 ,k ,

*E-mail: [email protected]. Tel.: +52 443 3223500, ext 1277. Fax. +52 443 3273584.

orc1 orc1max dtiorc1 (1 − ziorc1 , k + 1 ≤ ti , k + 1 − TIN + ΔTi , k ),

i ∈ HPS, k ∈ ST

(A.34)

Corresponding Author

orc1 orc1max dtiorc1 (1 − ziorc1 , k ≤ ti , k − TOUT + ΔTi , k ),

i ∈ HPS, k ∈ ST

i ∈ HPS, j ∈ CPS, k ∈ ST

ΔTmin ≤ dt jorc2 ,k ,

ziar1 , k ),

i ∈ HPS, k ∈ ST

ΔTmin ≤ dti , j , k ,

ΔTmin ≤ dtiorc1 ,k ,

ziar1 , k ),

i ∈ HPS, k ∈ ST

j ∈ CPS (A.33)

− zi , j , k),

i ∈ HPS, j ∈ CPS, k ∈ ST

(A.32)

Finally, the constraint required for the heat exchanger units between the CPS and the hot utility:

For designing HENs, an important criterion is the minimum approach temperature because this value affects directly the utility requirements and also the capital costs for the heat transfer units. This is modeled as follows: First, the constraints required for the heat exchange units between process streams are presented. dti , j , k ≤ ti , k − t j , k +

(A.31)

orc2 orc2max dt jorc2 (1 − z jorc2 , k + 1 ≤ TOUT − t j , k + 1 + ΔT j , k ),

(A.21)

h. Feasibilities for Temperature Differences

ΔTimax , j (1

(A.30)

i ∈ HPS

(A.18)

i ∈ HPS

NOMENCLATURE

Parameters

Avail = maximum availability, kg/month

(A.29) 2748



Article

Subscripts and Superscripts

C = cost, $ Cp = specific heat capacity, kJ/kg K COP = coefficient of performance Cu = unitary operational cost, $/kJ Dsh = time conversion factor, s/h Dt = time conversion factor, s/month FC = fixed charge, $/year FCp = heat capacity flow rate, kJ/s K GaPow = unitary gains obtaining by selling power, $/kW GHGE = unitary greenhouse gas emissions, t of CO2 equiv/kJ h = film heat transfer coefficient, kW/m2 K HeatingPower = heating power, kJ/kg HY = hours of operation per year, h/year kf = factor used to annualize capital costs NJOBS = number of generated jobs, jobs NOK = total number of stages Qmax = upper bound for heat exchange, kJ/s QUseful_Solar = usable solar radiation in the specific location, kJ/ m2 month R = tax credit for the reduction of GHGE, $/kJ SuP = unitary price for the power, $/kW TIN = inlet temperature, K TOUT = outlet temperature, K VC = unit variable charge, $/m3 year Greek Symbols

■

α = exponent for area cost of the solar collector β = exponent for area cost of exchangers δ = small number (i.e., 1 × 10−5) μ = efficiency factor ΔTmax = upper bound for temperature difference, K ΔTmin = minimum approach temperature difference, K εa = parameter of the interval between the minimum and maximum GHGE for the constraint method, t of CO2 equiv/kJ

ar = absorption refrigeration ar1 = heat exchange unit where the heat excess from hot process streams is removed ar2 = stage of the superstructure where the hot process streams are cooled b = biofuel cap = capital cw = cold water f = fossil fuel i = hot process stream j = cold process stream k = index for stage (1, ..., NOK) and temperature location (1, ..., NOK + 1) lps = stage of the superstructure where the cold process streams exchange heat with low pressure steam max = maximum op = operational orc = organic Rankine cycle orc1 = heat exchanger where hot process streams transfer energy to ORC orc2 = heat exchanger where the ORC transfer energy to cold process streams ran = steam Rankine cycle t = period

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Variables

Ac = area, m2 CACE = capital cost for exchangers, $/year dt = temperature approach difference, K ESC = energy sources cost, $/year FICE = fixed cost for exchangers, $/year NGHGE = greenhouse gas emissions, t of CO2 equiv/year OPC = operational cost, $/year Power = power output, kW PPCost = power production cost, $/kW q = heat transferred in the heat exchanger units, kJ/s Q = heat exchanged between the energy subsystems, kJ/s QExternal = total energy supplied to the SRC, kJ/s Qmps = available heat in the condenser of the SRC, kJ/s SP = selling of power, $/year t = internal temperature, K TAP = total annual profit, $/year TCR = tax credit reduction, $/year y = binary variable used to model the existence of the solar collector z = binary variables used to model the existence of heat exchange units Sets

B = {b|b is a biofuel} CPS = {j|j is a cold process stream} F = {f |f is a fossil fuel} HPS = {i|i is a hot process stream} ST = {k|k is a stage in the superstructure, k = 1, ..., NOK} T = {t|t is a period of time} 2749



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Sustainable Integration of Trigeneration Systems with Heat Exchanger

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