ARTICLE pubs.acs.org/IECR
Integration of Renewable Energy with Industrial Absorption Refrigeration Systems: Systematic Design and Operation with Technical, Economic, and Environmental Objectives Jose María Ponce-Ortega,*,† Eman A. Tora,‡,||,^ J. Betzabe Gonzalez-Campos,§ and Mahmoud M. El-Halwagi‡ Chemical Engineering Department and §Biological and Chemical Research Institute, Universidad Michoacana de San Nicolas de Hidalgo, Morelia, Michoacan, Mexico, 58060 ‡ Chemical Engineering Department, Texas A&M University, College Station, Texas 77843, United States Chemical Engineering & Pilot Plant Department, Engineering Division, National Research Centre, El-Buhoos St., Dokki, Cairo, Egypt, 12311
)
†
ABSTRACT: This paper presents a new methodology for the energy integration of systems that require refrigeration. It considers the integration between process streams as well as that between the heat from process stream excess, solar energy, fossil fuels, and biofuels to run the stripper required by the absorption refrigeration (AR) needed. The proposed methodology consists of two stages: the first one identifies the energy targets, while the second one uses a new mathematical programming model to solve a multiobjective optimization mixed-integer linear programming (MILP) problem, allowing one to determine the minimum cost as well as the minimum greenhouse gas emissions (GHGE) to satisfy the utility requirements identified in the first stage. The proposed model considers the optimal selection of different types of solar collectors, and since the solar radiation depends on the season of the year, the model also accounts for the best combination of fossil and biofuels to complement the energy required for the AR. The proposed methodology is very useful to identify the scenario required to implement the use of clean energies in the refrigeration process. Three problems are presented to show the applicability of the proposed methodology, which does not exhibit numerical complications; these results show that process integration helps to get a given reduction in the GHGE economically attractive involving the use of clean energies, besides identifying the required tax credit to get economic and environmentally efficient cooling systems. In addition, because of the availability of the solar radiation, the solar collectors must be integrated with different types of energy, depending on the season of the year.
1. INTRODUCTION Nowadays, the proper use of energy is of paramount interest to industry, because of the high utility costs as well as the associated environmental pollution. In this context, the synthesis of heat-exchanger networks (HENs) has provided significant economic and environmental benefits, because of the reduction in the external consumption of heating and cooling utilities through the integration of the process streams. A number of methodologies have been reported to synthesize HEN (see, for example, the paper reviews by Gundersen and Naess,1 Jezowski,2,3 and Furmann and Sahinidis4). Several approaches have focused on the synthesis of HEN above room temperature, using cooling water as the cooling medium.5,6 Other methodologies have addressed the problem of cooling systems based on the use of cooling water (e.g., Kim and nez et al.,9 Feng et al.,10 and Ponce-Ortega Smith,7,8 Picon-Nu~ 1113 ). In addition, there are many cases where the use of et al. refrigeration is required because the temperature of the required cooling utility is below room temperature. In this context, absorption refrigeration (AR) units or absorptive chillers are useful means to provide the cooling requirements below room temperature, depending on the absorbent used. Heat is required to run the AR system by heating the absorbent above 80 C and it can be provided by several media (e.g., Ziegler and Riesch14 and Herold et al.15) including fossil fuels, as well as sustainable energies such as biofuels and solar energy. Since the availability and cost of solar energy and r 2011 American Chemical Society
biofuels vary throughout the year, it is very useful to consider the integration of several forms of energy to run the AR for the different periods of the year. Regarding the cooling cycles, they usually have been optimized as separate components (e.g., Florides et al.,16,17 Assilzadeh et al.,18 Lecuona et al.,19 Fathi et al.,20 and Wu et al.21). In addition, mathematical programming approaches have been proposed for the design of energy systems (see Savola and Fogelholm22 and Tveit et al.23 ) and for ammoniawater absorption cycles (Chavez-Islas et al.2426). Recently, some methodologies have been proposed to address the refrigeration process considering the economic and environmental aspects simultaneously.2729 Figure 1 shows a schematic representation of the interaction between process integration and AR. The HPS streams provide the heat to the CPS streams, and there is also a required set of hot and cold utilities to provide the heat when it is not possible to integrate the process. Cold utilities at temperatures above room temperature are available to cool the process streams down at temperatures above room temperature. For temperatures below room temperature, an AR system is used to cool the Received: January 20, 2011 Accepted: June 27, 2011 Revised: June 23, 2011 Published: June 27, 2011 9667
dx.doi.org/10.1021/ie200141j | Ind. Eng. Chem. Res. 2011, 50, 9667–9684
Industrial & Engineering Chemistry Research
ARTICLE
Figure 1. Interaction between process integration and absorption refrigeration (AR).
HPS streams. To operate the absorption refrigeration, heat at high temperatures is required. Heating utilities can be provided by solar collectors, fossil fuels, and/or biofuels. Then, the problem consists of maximizing the heat integration between the process streams and determining the required utilities to minimize the total annual costs (TAC), while reducing the overall greenhouse gas emissions (GHGE). It is worth noting that the objectives pertaining to energy cost and GHGE may contradict each other and the problem becomes a multiobjective optimization problem that requires tradeoffs. The GHGE are gaining much attention, because of the adverse environmental impact that they produce.30 In this context, the use of fossil fuels is the major supplier to GHGE. Solar energy and biofuels provide a more sustainable source of energy with reduced levels of GHGE. The overall GHGE can be determined by the life cycle analysis methodology, which accounts for the overall GHGE from production, extraction, and the use of the fuel.31,32 There are an increasing number of governments providing incentives for reducing the GHGE through tax credits and subsidies. Consequently, the use of cleaner forms of energy becomes economically attractive, even when the current cost is higher than that of other fossil fuels. In addition, several governments have imposed specific targets for the overall GHGE. Therefore, considering simultaneously the economic and environmental aspects is of paramount importance for the design of cooling systems that require a huge amount of energy, such as in the case of AR systems. This paper proposes a new strategy to integrate different types of energies for cooling systems below room temperature through an AR system combining different types of energies to run the AR accounting simultaneously for the economic and environmental aspects. A process-integration framework is used to integrate the heating and cooling tasks of the process with the AR system. In addition to heat integration and optimal selection of external utilities, heat is also extracted from the process to drive the stripping section of the AR cycle. The rest of the required energy is provided by a combination of fossil fuels, biofuels, and/or solar energy. A disjunctive programming optimization model is developed. The model considers the optimization for the selected types of solar collectors as well as the availability of the solar radiation through the year for a given location. The model is formulated as a multiobjective optimization approach to account
for the simultaneous minimization of the total annual cost and the GHGE.
2. PROBLEM STATEMENT The heat balance for the refrigeration system is based on the representation given in Figure 2. Two fluids are identified in the refrigeration system: an absorbent, which can be water or LiBr, and a working fluid, which can be ammonia or water, depending on the required temperature. A low-pressure vapor from the evaporator is absorbed by the absorbent and as a consequence heat is released. The working fluid absorbent solution is pressurized by a pump and then the working fluid is desorbed in a stripper or generator through the addition of heat. The absorbent is returned to the absorber, the high-pressure vapor produced in the stripper is fed to the condenser to be condensed at room temperature. Then, the working fluid at high pressure is expanded and evaporated to extract the required refrigeration by the hot process streams. The pumping energy is not considered, because it is too small, compared to the heating requirements. The coefficient of performance (COP) for the AR system then is defined as follows:14 COP ¼
Q Ref Q Str
Therefore, the heat required in the stripper depends on the heat duty for refrigeration of the hot process streams and the coefficient of performance. The heating requirements for the stripper can be provided by a hot water loop. This way, the recirculating water is used to capture heat from different sources. This paper proposes, in one hand, the use of the heat excess of hot process streams, which are at higher temperature than the minimum allowable in the stripper (i.e., 80 C in this case), and, on the other hand, a combination of different types of energy that can be used for the heating requirements (including the use of solar energy, biofuels, and fossil fuels) can be used to heat the recirculating water used in the cycle to heat the stripper. The hot water is stored in an isolated tank, considering the dynamic performance of the solar collectors. To satisfy the energy requirement for the stripper, the use of excess heat from the hot process streams must be maximized (because, this way, the use of cooling water as well as the associated cost could be 9668
dx.doi.org/10.1021/ie200141j |Ind. Eng. Chem. Res. 2011, 50, 9667–9684
Industrial & Engineering Chemistry Research
ARTICLE
Figure 2. Proposed scheme for the refrigeration system.
reduced); then, there is a compromise between the use of solar, fossil fuels, and biofuels, because, although some of them could be less expensive, the associated GHGE could yield an inoperable processes or the reduction of GHGE could yield an attractive tax credit reduction to yield economical and environmental attractive processes. In addition, it is important to consider the optimal combination for these types of energy, because they are not available year-round at the same price. The problem addressed in the paper can be stated as follows. Given are: • A set of HPS streams that must be cooled (some of them are below room temperature and require refrigeration). Also given are the inlet temperature Tin and target temperature Tout, as well as the heat exchanged or the product of the flow rate times the heat capacity. • A set of CPS streams that must be heated from their supply temperature Tin to their target temperature Tout. Also given are the heat exchanged or the product of the flow rate times the heat capacity. • A set of solar collectors (SC) that are available to be used to run the AR system, including their capital and operational cost functions, as well as their availability to catch solar radiation in the specific place where the solar collector must be installed at each period of the year (t). • A set of available fossil fuels (F) to provide the heat required by the AR system, including the unitary cost for each fossil fuel, as well as the maximum availability and the overall specific GHGE for the combustion of the fossil fuels per unit of provided energy. To determine the overall GHGE for each fossil fuel, the entire life cycle analysis is carried out for each fossil fuel, considering the emissions related to the extraction, transportation, and combustion; this task can be done prior to the optimization process.
• A set of available biofuels (B) to run the AR system with their unitary costs, overall GHGE, and maximum availability for each period t. The overall GHGE for the biofuels are determined prior to the optimization process, considering the life cycle analysis. • Also, a minimum temperature difference for the heat transfer between process streams is given. The problem then consists of the integration of the process and minimizing the total annual cost and the overall GHGE simultaneously, to determine: • The heat integrated between the process streams. • The utility requirements necessary to heat the CPS streams and to cool the HPS streams, respectively. • The overall utilities requirements to cool the HPS streams as well as the distribution for the type of cold utility required. These can be distributed as: (i) Heat used to heat the absorber to run the AR at temperatures above 80 C. (ii) Heat extracted by cooling water at temperatures between 80 C and above room temperature. (iii) Heat extracted using the AR system for temperatures below room temperature. • To run the absorption refrigeration, the model must determine the quantity of energy provided at each period by excess process heat, solar collectors, fossil fuels, and biofuels. The model must consider the availability of energy for each period of the year, because the solar energy and biofuels are strongly dependent on the season of the year.
3. SOLUTION STRATEGY To solve the problem efficiently, the strategy proposed in this paper is presented in Figure 3. It consists of three main steps. In 9669
dx.doi.org/10.1021/ie200141j |Ind. Eng. Chem. Res. 2011, 50, 9667–9684
Industrial & Engineering Chemistry Research
ARTICLE
proposed algorithm presents an optimization formulation to address this problem, and it is presented in the next section.
4. OPTIMIZATION MODEL The mathematical programming model for the energy supply for the refrigeration system is presented in this section. All the symbols used are described in the Nomenclature section, and the model is presented as follows. Objective Function. The objective function is a multiobjective problem that considers the minimization of the TAC, as well as the minimization of the net GHGE, and it is stated as follows: ð1Þ
OF ¼ Min TAC þ Min NGHGEOverall Overall
Figure 3. Proposed solution strategy.
the first step, the stream data, as well as the emissions and unitary costs for the fossil and biofuels, considered are obtained. To determine the overall GHGE for these fossil and biofuels, the life cycle analysis methodology is used to account for the overall emissions from the production to the consumption of the considered fuels (the greenhouse gases, regulated emissions, and energy use in transportation model (GREET) or the Biofuel Energy System Simulator (BESS) software can be used for this task). The data for the available solar collectors must be determined in this stage, as well as the capacity to capture the solar energy radiation at each period of the year for the specific location where the collector must be installed, the procedure described by Tora and El-Halwagi33 is used to determine the available solar radiation in a specific location. Once the process data are obtained, in the second step, the algorithm proposes to yield the grand composite curve (GCC), which is based on the pinch point technology (see Shenoy34). The GCC gives very useful information for the energy targets. First, the minimum hot utility and minimum cold utility are identified at the top and bottom of this curve, respectively. The cold utility can be satisfied by the refrigeration and by the cooling water; however, part of this excess of heat can be used to run the AR. In this context, this paper proposes to maximize the use of the excess of heat to run the AR, and the temperature to provide heat to the stripper Tin Str (usually, this temperature is 80 C) is identified to determine the point Tin Str + (ΔTmin/2); at the same Process must time, all the heat above this temperature QTExcess in Str +(ΔTmin/2) Excess Process be used to run the AR. The heat (QTStrin+(ΔTmin/2)) above the temperature for the water provided by the cooling tower (Tcw) plus the (ΔTmin)/2 and below the Tin Str + (ΔTmin/2) must be fulfilled using cooling water. Finally, the cooling requirement below Tin Str + (ΔTmin/2) must be satisfied using refrigeration QRef. This way, the use of refrigeration is minimized, the use of HPS for heating is maximized, reducing the use of external cooling utilities, and the rest of the cooling utilities are obtained using cooling water. However, there are several ways to provide the heat to run the AR and to produce the refrigeration requirements identified in the GCC; the third step of the
These two objectives (TAC and NGHGE ) oppose each other. This means that the solution for the minimum TAC usually yields the solution with the highest NGHGEOverall. This is because fossil fuels are less expensive (i.e., coal) and usually provide the highest GHGE. On the other hand, the solution for the minimum NGHGEOverall is the most expensive, because usually the cleanest types of energy (i.e., solar energy) are the most expensive. Therefore, an adequate strategy must be implemented to compensate these two objectives. However, prior to presenting the solution approach, the description of the equations is presented as follows. Economic Objective Function. The economic objective function consists in the minimization of the TAC for the design of the refrigeration system as follows: ( min TAC ¼ HY þ
∑ ½CFossil ∑ ðQfFossil f , t Dt Þ t∈T
f ∈F
Solar Dt Þ þ CSolar ½ ∑ ðQtSolar Dt Þ ∑ ½CBiofuel ∑ ðQb,Biofuel op R b t t∈T t∈T
b∈B
∑ ∑
t∈Tb∈B
Biofuel Biofuel ½Rb Qb, t Dt
tank þ kf fCSolar g cap þ C
∑ ∑
t∈Tf ∈F
)
½RfFossil QfFossil , t Dt ð2Þ
This objective function considers the costs associated with the consumption of any fossil fuel f in any period t (QFossil f,t ), the cost associated with the consumption of any biofuel b in any period t Biofuel ), the capital costs associated with the solar collectors (Qb,t (CSolar cap ) (if it is selected), and the capital costs associated with the tank Ctank used for the solar collector (when it is required), as well as the operational cost associated to the function of the solar collector (CSolar op ); the objective function also considers the revenues obtained for the tax credits due to the reduction in the GHGE obtained for the use of solar systems RSolar and . In the previous equation, HY represents the biofuels RBiofuel b operating hours per year for the plant and kf is the factor to annualize the capital costs. The credit for the use of solar collectors due to the reduction in the net GHGE (RSolar) is calculated considering the reduction with regard to a given fossil fuel (i.e., coal), and it is given in units of $/kWh of solar energy. Similarly, the credits for the use of ) and fossil fuels (RFossil ) are obtained considerbiofuels (RBiofuel b f ing the reduction of the GHGE, with regard to the use of a given fossil fuel and they are given in units of $/kWh provided by the given fuel (biofuel or fossil fuel). 9670
dx.doi.org/10.1021/ie200141j |Ind. Eng. Chem. Res. 2011, 50, 9667–9684
Industrial & Engineering Chemistry Research
ARTICLE
Environmental Objective Function. The environmental impact associated to the addressed problem considers the GHGE and this is stated as follows: min NGHGEOverall ¼
Notice here that the heat required for the refrigeration system QRef is fixed by the process, COP is a known parameter that is used to determine the heat QStr required in the stripper. This QStr can be supplied by the excess of heat for the hot process streams (QExcess Process), for the heat provided by the Biofuel combustion of any fossil fuel (QFossil ), and/ f,t ) or any biofuel (Qb,t Solar or by the heat provided by the solar collector (Qt ). The heating capacity of any solar collector (including size besides other characteristics) depends on the available solar radiation related to the location (given for any problem) and the season of the year; therefore, the model must consider the different periods of the year t. Models for the Solar Collectors. There are several types of solar collectors available, and each one has a specific heating capacity with a given solar radiation and area; in addition, each one has associated specific operational and capital costs for a given area. Usually, the most expensive solar collectors require less area and lower operating cost. On the other hand, the leastexpensive solar collectors require more area and higher operating cost. Therefore, the optimization process must select the optimal type of solar collector used, in addition to the optimal required area and their associated operational and capital costs. The following disjunction is used for the optimal selection of the type of solar collector:
QfFossil ∑ ∑ ½GHGEFossil f , t Dt
t∈Tf ∈B
þ
Biofuel Qb, t Dt ∑ ∑ ½GHGEBiofuel b
ð3Þ
t∈Tb∈B
In the previous equation, NGHGEOverall is the total GHGE needed to provide the required heat to run the stripper in the absorption and GHGEFossil are the overall refrigeration system. GHGEBiofuel b f GHGE for the fossil f and biofuel b determined through the life cycle analysis (the GREET software was used in this case), given in units of tons of CO2(eq) reduction/kWh provided. Notice that the emissions of solar collectors are zero, the biofuels can provide huge reductions of GHGE, whereas the fossil fuels provide no reduction for the GHGE. Energy Balance. The energy balance for the required heating in the stripping for the absorption system for each considered period is stated as follows: Q Str ¼
Q Ref ¼ Q Excess Process COP Biofuel þ QfFossil þ Qb, t þ Q Solar ,t t
∑
∑
f ∈F
"t∈T
b∈B
2 6 6 6 6 6 2 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 ∨ 6 6 s ∈ S6 62 6 6 6 6 6 6 66 6 66 6 66 6 6 6 44 4
ð4Þ
3
Y Solar Ctank ¼ FCtank þ VCtank ðQ Solarmax ftg Þ ZSolar s UsefulSolar
QtSolar e Qs, t
ASolar c
CSolar ¼ CuSolar op s 2
3
Ws,Solar 1 As, 1 e ASolar e As, 2 c Solar Solar Solar CSolar Þ cap ¼ FCs, 1 þ VCs, 1 ðAc
7 7 7 7 5
∨
6 6 6 6 4
∑ ðQtSolar Dt Þ
t∈T
As, 2 e ASolar e As, 3 c Solar Solar Solar CSolar Þ cap ¼ FCs, 2 þ VCs, 2 ðAc
¼
FCSolar s
Rs Solar þ VCSolar A s c
is used to account for the economies of scale. To avoid nonconvex relationships, the capital costs for the solar collectors can be linearized in area-wise R segments. To represent the previous disjunction as an algebraic optimization problem, the convex hull relaxation technique can be used.35,36 First, the Boolean variables (upper case) are
2
3
Ws,Solar 2
The previous disjunction states the following. When the Boolean variable YSolar is true, a solar collector is required (and, consequently, its corresponding tank for the heat storage); on the other hand, when the Boolean variable YSolar is false, then no solar collector is required and the heat, area and costs are set as zero. Then, when the Boolean variable YSolar is true, one type of solar collector must be selected and this decision is associated with . Because each type of solar collector the Boolean variable ZSolar s has different efficiency to capture the solar radiation for a given ), then the appropriated equation for each area (QUseful_Solar s,t collector is applied with its corresponding operational cost. To determine the capital cost for any solar collector, an equation with the form CSolar cap
1 , "t∈T Dt
6 7 6 7 7 ∨ ∨ 6 6 7 333 4 5
Ws,Solar R As, R e ASolar e As, Rþ1 c Solar Solar Solar CSolar Þ cap ¼ FCs, R þ VCs, R ðAc
3 7 7 7 7 5
7 7 2 3 7 ¬Y Solar 7 7 6 7 37 7 Solar 7 6 Q ¼ 0 6 7 t 6 7 77 7 6 7 7 7 6 ASolar ¼ 0 7 77 6 c 7 77 6 7 7 7 6 Solarmax ftg 7 7∨6 Q ¼ 07 7 77 6 7 7 7 6 Solar 7 7 7 6 Cop ¼ 0 7 77 6 7 77 6 7 7 7 6 Solar 7 ¼ 0 C 7 7 6 cap 7 77 4 5 77 tank 77 ¼0 C 77 55
transformed to binary variables (lower case), and when the Boolean variables are true, the associated binary variables are one; on the other hand, when the Boolean variables are false, the associated binary variables are zero. The logical relationships state that when the solar collector exists, one type of solar collector must be selected. This is modeled through the following algebraic equation: zSolar ð5Þ ySolar ¼ s
∑
s∈S
When one type of solar collector is selected, then one segment of area must be selected for the proper determination of the capital cost. This is modeled as follows: zSolar ¼ s
∑
r∈R
wSolar s, r
"s∈S
ð6Þ
The continuous variables inside the disjunction then are disaggregated as follows: QtSolar ¼ ¼ ASolar c 9671
qSolar ∑ t, s s∈S
∑ aSolar c
s∈S
s
"t∈T
ð7Þ ð8Þ
dx.doi.org/10.1021/ie200141j |Ind. Eng. Chem. Res. 2011, 50, 9667–9684
Industrial & Engineering Chemistry Research
ARTICLE
aSolar ¼ cs
adis ∑ c r∈R
CSolar ¼ op
cSolar ∑ op s∈S
ð10Þ
CSolar cap ¼
∑ cSolar cap s∈S
ð11Þ
cSolar caps ¼
∑ cdiscap r∈R
"s∈S
s, r
ð9Þ
s
s
s, r
"s∈S
ð12Þ
The relationships in the disjunction are stated in terms of the disaggregated variables: Ctank ¼ FCtank ySolar þ VCtank ðQ SolarMax ftg Þ qSolar t, s
1 UsefulSolar Solar e Qs, t a cs Dt
Solar cSolar ops ¼ Cus
dis Solar As, r wSolar s, r e acs, r e As, r ws, r
month/type of solar collector
[kJ/(m2 month)]
[kJ/(m2 month)]
January
339 264
248 220
February
373 968
273 672
March
571 392
332 964
April May
739 800 767 808
371 304 439 740
June
824 040
477 144
July
796 824
461 232
August
734 328
467 496
September
646 920
418 536
October
512 244
358 668
November
368 280
297 252
December
306 900
266 076
a
PTSC = parabolic trough solar collectors; ETSC = evacuated tube solar collectors.
ð16Þ
" r ∈ R; " s ∈ S
Upper bounds for the disaggregated variables are used to activate them only when the associated Boolean variable is true. Solar Solar Q SolarMax ftg e QMax y Solar Solar qSolar e QMax zs t, s
ð18Þ " t ∈ T; " s ∈ T
Max Solar e ASolar zs aSolar cs cs
Table 1. Useful Collected Energy Per Month for Different Solar Collectorsa for the Location N 34520 and W 116460 ETSC
" r ∈ R; " s ∈ S
ð15Þ
ð17Þ
ð14Þ
PTSC
"s∈S
Solar Solar dis cdis þ VCSolar caps, r ¼ FCs, r ws, r s, r ðacs, r Þ
ð13Þ
" t ∈ T; " s ∈ S
ðqSolar ∑ t, s Dt Þ t∈T
"s∈S
ð19Þ ð20Þ
Max Solar cSolar ops e Cops zs
"s∈S
ð21Þ
Max Solar cSolar caps e Ccaps zs
"s∈S
ð22Þ
" s ∈ S; " r ∈ R
ð23Þ
Max Solar cdis caps, r e Ccaps ws, r
To determine the cost of the tank, the maximum heat load for any period t is considered as follows: Q SolarMax ftg g QtSolar
"t∈T
ð24Þ
Maximum Availability for the Fuels. The availability of the biofuels is season-dependent; therefore, the following constraint must be imposed on the model: Biofuel
Qb, t
e
HeatingbPower AvailMax b, t Dt
" b ∈ B, " t ∈ T
ð25Þ
where HeatingPower is the heating power for the biofuel b and b AvailMax b,t is the maximum amount of the biofuel b available in the period t.
Figure 4. Linearized capital costs functions for the PTSC. 9672
dx.doi.org/10.1021/ie200141j |Ind. Eng. Chem. Res. 2011, 50, 9667–9684
Industrial & Engineering Chemistry Research
ARTICLE
Similarly, for the fossil fuels, the maximum availability is constrained by the following relationship: QfFossil e ,t
HeatingfPower AvailMax f,t
" f ∈ F; " t ∈ T
Dt
from solutions A and B, respectively. Finally, the Pareto curve can be obtained; this Pareto curve shows a set of optimal solutions that compensate the two objectives (TAC and NGHGEOverall) between the two extreme solutions A and B, solutions above the Pareto curve are suboptimal solutions, whereas solutions below the Pareto curve represent infeasible solutions using the proposed optimization approach (because the proposed convex MILP model is able to find the global optimal solution for each point of this curve). The information provided by the Pareto curve could be very important to determine the optimal cost for a given reduction of GHGE, or the optimal reduction of the GHGE for a given TAC. Remarks • To provide the energy requirements, the overall proposed methodology suggests integrating the process streams and satisfying the cooling requirements; this can be done using cooling water and an AR system. To run the absorption refrigeration, the required energy could be supplied by a combination of the excess of process streams, solar energy, fossil fuels, and/or biofuels that must be optimized. • The proposed methodology allows getting a mixed-integer linear programming (MILP) problem that is easy to solve to get the global optimal solution for each point of the Pareto curve. • The proposed methodology accounts for the simultaneous minimization of the TAC and the NGHGE. • The MILP model accounts for the optimal selection of the type of solar collector used considering the solar radiation available during the year in the specific place where it would be installed. • The MILP model considers the optimal selection of different types of fossil fuels and/or biofuels during the year, accounting for their availability for each season.
ð26Þ
The previous constraints are very important to properly consider the use of biofuels, because their availability is strongly dependent on the season. Solution of the Multi-objective Problem. It is worth noting that these two objectives contradict each other, because the reduction in the GHGE represents an increase in the TAC; therefore, a proper methodology must be implemented to solve this problem. In this case, the constraint method is implemented.37 First, the problem is solved for the minimization of the TAC without considering the NGHGE Overall to determine solution A (minimum TAC and maximum NGHGE Overall), then the problem is solved for the minimization of the NGHGE Overall without considering the TAC to determine solution B (maximum TAC and minimum NGHGE Overall). Afterward, the problem is transformed to a single objective problem as follows: ð27Þ
min TAC subject to NGHGEOverall e εi Equations 326
The problem is solved next for several values of εi between maximum NGHGEOverall and minimum NGHGEOverall given Table 2. Data for the Fossil and Biofuels Considered in the Presented Examples fuel
heating power
overall GHGE
cost
[kJ/kg]
[tons CO2 equiv/kJ]
[$/mm kJ]
5. RESULTS AND DISCUSSION Three cases of study are used to show the applicability of the proposed methodology. For all the studied cases, given the data required for the addressed problem (inlet and outlet temperature for the process streams with their associated heat capacity flow rates, as well as the economic and technical information for the solar collectors, fossil fuels, and biofuels); first, the energy targets (overall hot and cold utilities) are determined by the Grand Composite Curve (GCC)34 for a given ΔTmin, then using the information for the energy targets, the mathematical programming formulation programmed in the General Algebraic Modeling System (GAMS) software38 is applied to determine the optimal
Fossil Fuels coal
35 000
2.21357 107
1.5559
oil
45 200
8.05408 108
18.2447
natural gas
54 000
7.90892 108
5.8349
Biofuels 4 480
2.44307 108
2.0303
biogas
52 000
2.68216 108
8.5388
softwood
20 400
3.3482 108
2.5332
hardwood
18 400
3.3482 108
2.8975
biodiesel bioethanol
40 200 29 600
5.13283 108 5.8436 108
31.3092 14.4212
biomass
Table 3. Availability for the Biofuels Availability [kg/month] fuel
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
biomass
1 000
1 000
4 000
5 000
7 000
15 000
biogas softwood
500 3 000
500 3 000
600 2 500
650 2 500
650 2 300
1 000 2 300
10 000
5 000
4 000
4 000
3 000
2 000
1 000 1 500
1 000 1 500
800 2 000
700 2 500
600 2 500
500 3 000
hardwood
3 000
3 000
2 500
2 500
2 300
2 300
1 500
1 500
2 000
2 500
2 500
3 000
biodiesel
5 000
5 500
6 000
7 000
10 000
10 000
10 000
10 000
9 000
8 000
7 000
6 000
10 000
11 000
12 000
12 000
15 000
15 000
15 000
15 000
14 000
13 000
11 000
10 000
bioethanol
9673
dx.doi.org/10.1021/ie200141j |Ind. Eng. Chem. Res. 2011, 50, 9667–9684
Industrial & Engineering Chemistry Research
ARTICLE
Figure 5. Flowsheet for Example 1.39,40
Table 4. Stream Data for Example 140
Table 5. Solutions for the Minimum TAC and Minimum GHGE for Example 1—Tax Credit of $5/ton CO2 equiv
stream
inlet temperature [K]
outlet temperature [K]
Q [kW]
H1
398
338
2325
concept/case
H2
358
298
1125
cost of fossil fuels
$32 870/yr
$0/yr
H3
318
298
875
cost of biofuels
$554/yr
$0/yr
C1
308
513
4100
cost of solar collector
$0/yr
$317 055/yr
C2
308
328
725
credit GHGE reduction
$269/yr
$293 371/yr
overall GHGE
4683 ton CO2 equiv/yr
0 ton CO2 equiv/yr
TAC
$33 155/yr
$293 371/yr
minimum TAC [A]
minimum GHGE [B]
Table 6. Energy Consumption for Each Month for Example 1, for the Case with the Minimum TAC in Scenario with a Tax Credit of $5/ton CO2 equiv month
Figure 6. Grand composite curve (GCC) for Example 1 for ΔTmin = 10 K.40
solution. For all the studied cases, hot water is used as the heattransfer medium in the LiBrwater system, whose coefficient of performance (COP) is 0.7. In all cases, the optimal selection between two solar collectors is considered (i.e., parabolic trough solar collectors (PTSC) and evacuated tube solar collectors (ETSC)). The
coal [kJ/s]
biomass [kJ/s]
January February
676.899 676.720
1.673 1.852
March
671.881
6.691
April
669.929
8.642
May
666.863
11.708
June
652.646
25.926
July
661.845
16.726
August
670.208
8.363
September October
671.658 671.881
6.914 6.691
November
673.386
5.185
December
675.226
3.345
useful collected energy per month per unit area of solar collector for these two units is presented in Table 1 for a location in Dagget in San Bernardino County, CA, whose coordinates are N 34520 and W 116460 .40 The capital cost for the parabolic solar collector is determined using the 9674
dx.doi.org/10.1021/ie200141j |Ind. Eng. Chem. Res. 2011, 50, 9667–9684
Industrial & Engineering Chemistry Research
ARTICLE
Figure 7. Pareto curve (TAC vs GHGE) for Example 1 for scenario A.
Figure 8. Heat consumed for each month for solution of Example 1 with overall the GHGE equal to 1000 tons CO2 equiv.
following relationship: 0:6 CSolar capPTSC ¼ 20AC þ 1:085AC
whereas the operational cost for the PTSC is determined by 0:012 Solar Annual CopPTSC ¼ QSolar 3600 and the PTSC works for temperatures of
