Optimal Design of Inherently Safer Domestic Combined Heat and

Research Article pubs.acs.org/journal/ascecg

Optimal Design of Inherently Safer Domestic Combined Heat and Power Systems Luis Fabián Fuentes-Cortés, Juan Martinez-Gomez, and José María Ponce-Ortega* Chemical Engineering Department, Universidad Michoacana de San Nicolás de Hidalgo, Edificio V1, Ciudad Universitaria, Morelia, Michoacán 58060, Mexico ABSTRACT: The residential co-generation system is a promising strategy to satisfy the electricity and hot water demands in residential complexes. This is an attractive option from both economic and environmental points of view; however, the associated risk has not been accounted for. It is very important to consider the risk associated with residential co-generation systems because the involved units use volatile fuels such as natural gas or liquefied petroleum gas. Therefore, this paper presents an optimization approach for designing residential co-generation systems through a multi-objective optimization formulation that simultaneously accounts for minimizing the total annual cost and the environmental impact as well as the associated risk to satisfy the electricity and hot water demands in a residential complex. The proposed model incorporates the optimal selection for the technologies used as well as the operation. A case study for a residential complex in Mexico is presented to show the applicability of the proposed approach, where it was shown to be possible to obtain attractive solutions from economic, environmental, and safety points of view. KEYWORDS: Safety, Domestic combined heat and power systems, Optimal design, Multi-objective optimization

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INTRODUCTION Combined heat and power (CHP) systems are attractive options for energy supply in housing complexes because the simultaneous production of heat and power is more efficient than the single production alone; furthermore, in CHP systems, the costs and greenhouse gas emissions (GHGEs) are reduced compared with conventional generation.1 However, the design of such systems involves multiple problems; many of them have been solved by optimization algorithms.2 The most important issues that have been addressed are related to selecting CHP technology,3 sizing the central co-generation unit,4 sizing the thermal storage system,5 determining the interactions with the grid of the local power company,6 determining the operating scheme for the prime mover,7 smoothing the gaps between the thermal and electrical demands,8 and even locating the system.9 It should be noted that most of the methods used in the studies mentioned above have addressed only economic10 and environmental11 targets in the design problems. Also, several different technologies have been proposed to provide access to alternative sources of fuel for CHP units.12 Furthermore, other works have recently determined the targets for domestic CHP systems13 and addressed the design problem accounting simultaneously for economic and environmental aspects.14 One important point that must be considered in the on-site power generation is related to safety.15 Therefore, there is a need to account for the inherent safety in the design stage to reduce or eliminate the associated hazard. A process is described as inherently safer if it reduces or eliminates one or © XXXX American Chemical Society

more hazards associated with the materials and operations used in the process, when it is compared to some alternative process, and this reduction or elimination is accomplished by characteristics that are permanent and inseparable parts of the process. To appreciate this definition, one must understand the meaning of hazard as an inherent physical or chemical characteristic that has the potential for causing harm to people, property, or the environment. The key to this definition is that the hazard is intrinsic to the material or to its conditions of storage or use. For these reasons, the inherently safer approach to risk management is an essential aspect of any safety program. Furthermore, there will be no risk of failure of the layers of protection, and there will be anticipated mechanisms for the occurrence of hazardous events. Inherently safer design is a fundamentally different way of thinking about processes and plants. It focuses on the elimination or reduction of the hazards, rather than on management and control. This approach will ultimately result in safer and more robust processes, and these inherently safer processes will also be more economical.16 Therefore, the risk factor associated with power generation facilities is one of the dimensions of sustainability.17 Although several recent papers have considered the environmental aspect in power plants,18 the inherently safer design is still a pending task in this area. Received: August 26, 2015 Revised: November 25, 2015

A

DOI: 10.1021/acssuschemeng.5b00941 ACS Sustainable Chem. Eng. XXXX, XXX, XXX−XXX

Research Article

ACS Sustainable Chemistry & Engineering

Figure 1. Schematic representation for the addressed problem.

safer design remains a pending task in this area.31 This design factor is especially important in developing countries (like Mexico), where the fuel distribution to end users is via storage systems for on-site consumption.32 In this case, accidents in the form of explosion can occur, associated with the use and storage of this type of fuel, such as boiling liquid−expanding vapor explosion (BLEVE), vapor cloud explosion (VCE), jet fire, and flash fire.33 This paper presents a new method for the optimal design of a CHP system to be implemented in a residential complex accounting simultaneously for economic, environmental, and safety aspects. We propose a new superstructure and a mixedinteger nonlinear programming (MINLP) model for selecting the prime mover, involving internal combustion engines (ICE), fuel cells (FC), microturbines (MT), and Stirling engines (SE), as well as the optimal sizing and operation. Furthermore, the associated thermal storage system is designed simultaneously. As an economic objective function, we consider the minimization of the total annual cost (TAC) to satisfy the electricity and hot water demands for a residential complex, whereas the environmental objective function accounts for minimization of the associated greenhouse gas emissions (GHGEs), and the safety objective entails minimization of the risk. In this context, a quantitative risk analysis (QRA) applied to CHP technologies and fuel storage units to quantify the associated risk in residential areas. The risk is quantified in terms of social risk using a new approach.

Even though inherently safer optimal design and its principles have been widely used in the design of chemical plants, the topic is relatively new in the design of power plants and distributed generation systems, such as the case of CHP technologies.19 In centralized generation, this approach has been used in the design of nuclear plants.20 Among the issues that could be considered for the design of distributed generation schemes, using principles of inherent safety, is the location of the system, considering that distributed generation is done on-site for consumption; this is, at a housing complex.21 Implementation of CHP systems involves the operation of equipment that produces heat and power and, sometimes, the associated thermal storage equipment, which interacts with distribution to the houses; therefore, inherently safer design becomes a pressing need.22 This problem becomes greater when it is considered that the CHP equipment uses fuels such as natural gas, which carries risks in storage and distribution.23 Besides these aspects, inherent safety criteria may be considered for selecting the technological structure, physical location of the system,24 storage systems, and equipment sizing.25 However, in designing distributed generation systems, usually safety has not been considered. In this context, most of the design constraints involve existing public policies.26 Other studies have emphasized adjustments in urban development models.27 There have also been reported approaches to reduce the environmental impact28 and analyses based on features of technologies using hydrogen for power generation.29 Also, risk analysis combined with an exergy approach for local energy plants has been presented.30 However, the inherently B


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PROBLEM STATEMENT The problem addressed in this paper is schematically described in Figure 1, and it can be stated as follows. Given are the hourly seasonal thermal consumptions associated with hot water for sanitary use, as well as the power demands of a housing complex, the average hourly seasonal temperature, the prices for fuel and hourly electricity rates, and the operational efficiencies, pressure, and temperature of the CHP technologies. The problem then involves determining the optimal configuration of the co-generation system that meets the energy demands considering factors such as the sizing and selection of the prime mover, sizing of the thermal storage system, sizing of the fuel storage tank, and the purchase−sale scheme of power with the grid of the local electric company, while accounting for the simultaneous assessment of the total annual cost, the analysis of the environmental risk using the GHGE associated with the consumption of the fuels, and the analysis of social risk associated with possible accidents like BLEVE, VCE, jet fire, or flash fire. Figure 2 shows the algorithm implemented for quantifying the QRA.34

housing complex, the hot stream is mixed with cold water to reach the temperature needed for domestic use. Therefore, the algorithm must determine the type and size of the CHP system, the size of the thermal storage tank, and the auxiliary heating system needed to meet the hot water demands, as well as the interactions with the local electric company. The optimization formulation accounts for the minimization of the total annual cost of the system, the associated risk, and its greenhouse gas emissions.

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MODEL FORMULATION

The proposed optimization model is based on the superstructure shown in Figure 3, which corresponds to a MINLP problem, and the corresponding constraints are given as follows. Objective Functions. The objective functions determine the optimum system design accounting for three different objective functions, i.e., the inherent safety, the economic viability, and the environmental impact, to yield a multi-objective MINLP model. Each objective function is described as follows. Risk. The safety objective function considers the minimization of the total risk associated with the CHP units of the system in a given quadrant of the geographic area occupied by the housing complex, the operation and existence of which involve risks. This way, the total risk for the domestic CHP system is determined as follows:

Risk =

∑ Risk τ

(1)

τ ∈Τ

where the set τ comprises all the units involved that represent potential risks, such as the ICE, MT, FC, SE, and SF. Economic Objective. The economic objective function accounts for the minimization of the total annual cost (mixed-integer nonlinear programming) for the CHP system to satisfy the electricity and hot water demands of a residential complex. The TAC includes all the involved costs [i.e., capital (CostCapT), operating (CostOpT), and maintenance (CostOMT), as well as the purchasing of power from the grid of the local electrical company (CostPowerGRID)] minus the income for the sale to external users [including the incomes generated from the sale of electricity (PowerSaleT) and thermal energy (HeatSaleH)]. The TAC for the residential CHP system is stated as follows:

TAC = CostCapT + CostOpT + CostOMT + CostPower GRID − PowerSale T − HeatSale H

(2)

Environmental Objective. The proposed environmental objective function for the CHP system involves minimizing the total greenhouse gas emissions (GHGET) associated with fuel consumption of the different CHP technologies (GHGECHP) and the energy bought from the electric company (GHGEGRID), which is stated as follows:

Figure 2. Implemented quantitative risk analysis.

This work proposes a superstructure (see Figure 3) that operates cooperatively with the grid of the local energy company, thereby eliminating the need for storage equipment for power. The proposed superstructure is basically formed by four CHP technologies (i.e., ICE, SE, MT, and FC), an auxiliary water heater and a thermally insulated storage tank (ST), and a fuel storage tank (FS). CHP technologies are used to meet the electricity and hot water demands. First, the produced electricity is sent to the housing complex, and the excess of produced electricity is then sent to the grid of the electric company (i.e., when the CHP system produces surplus energy, it is sold to the local electric company). Furthermore, when the CHP system produces less electricity than needed in the housing complex, the needed electricity is purchased from the local electric company. Because the hot water demand behavior in the housing complex is different than the electricity demand, there is included an insulated tank for storing hot water from the CHP system in the proposed scheme when there is a surplus. Finally, before sending the water to the

GHGET = GHGECHP + GHGEGRID

(3)

Energy Balances. The energy balances of the proposed system are defined by the following relationships. These relationships include the analysis of the energy supply, the operation of the equipment, and the thermal storage tank. Balance of Supply of Electrical Energy. The electricity demand of the housing complex (WDt,s) is satisfied by the sum of the energy ) and energy produced by the CHP purchased from the grid (Wpurchase t,s ), considering each technology separately (WICE‑H , system (WCHP‑H t,s t,s SE‑H , WFC‑H WMT‑H t,s t,s , and Wt,s ). The solution of the proposed MINLP problem defines which of these factors will be included in the final solution. The multiperiod model is defined on an hourly (t = 1, ..., 24 h) and seasonal (s = spring, summer, fall, and winter) basis for a demand of a typical day.35 ‐H ‐H ‐H ‐H WtD, s = Wtpurchase + WtICE + WtMT + WtFC + W tSE ,s ,s ,s ,s ,s ,

∀ t ∈ T, C

∀s∈S

(4) DOI: 10.1021/acssuschemeng.5b00941 ACS Sustainable Chem. Eng. XXXX, XXX, XXX−XXX

Research Article


Figure 3. Proposed superstructure for designing domestic CHP systems. in the balance (Qloss t,s ). It is important to note that the water temperature inside the thermal storage tank is a decision variable (TST t,s ). These balances are then stated as follows for the different time periods:

Energy Balance for Electricity Generation in the CHP System. The electricity produced by each CHP unit (Wt,sCHP‑Technology, CHPTechnology: ICE, MT, FC, SE) can be distributed according to the , i.e., that needs of energy for domestic consumption (WCHP‑Technology‑H t,s sent to the housing complex) and the energy sold to the grid as surplus ), which is stated as follows: production (WCHP‑Technology‑sale t,s

W‐ST ST water W‐ST ST ICE ICE ICE Stwater , s Cpt , s Tt , s = St − 1, s Cpt − 1, s Tt − 1 + Gt , s Cpt , s Tt , s MT MT FC FC FC SE SE SE + GtMT , s Cpt , s Tt , s + Gt , s Cpt , s Tt , s + Gt , s Cpt , s Tt , s

‐Technology ‐Technology‐H ‐Technology‐sale W tCHP = W tCHP + W tCHP , ,s ,s ,s

∀ t ∈ T , ∀ s ∈ S , ∀ CHP‐Technology

ST ST loss − GtST , s Cpt , s Tt , s − Q t , s ,

(5)

This interaction with the grid of the local electric company makes it possible to get income from the sale of power to an external client and also to smooth the gaps between the demands for electricity and heat.36 Thermal Storage. A challenge in the design of CHP systems is the one associated with synchronizing the operation of the system with the energy demands (electrical and thermal); this way, an appropriate thermal storage device is needed, and in this case an insulated tank is used. The hot water stored in the tank at time t and season s (Swater t,s ) is the result of the addition of hot water stored at the previous time period, t−1 (Swater t−1,s ) plus the water sent to the tank from the CHP ) minus the water sent to meet the demands of system (GCHP‑Technology t,s the housing complex (GST t,s ), which is stated as follows:

MT MT FC FC FC SE SE SE + GtMT , s Cpt , s Tt , s + Gt , s Cpt , s Tt , s + Gt , s Cpt , s Tt , s ST ST loss − GtST , s Cpt , s Tt , s − Q t , s ,

∀ t = 1, ∀ s ∈ S

(7a)

The convective loss (Qloss t,s ) is determined by the area of the storage tank (A), which is determined by the volume of the tank. It is noteworthy that the size of the tank is a decision variable. Also, it is important to note that the environmental temperature has variations throughout the day (Tamb t,s ). U is the overall heat transfer coefficient for the storage tank, which is a constant in the optimization formulation determined from the type of construction material, and SMAX‑ST is the highest storage capacity for the tank that is an optimization variable. The relationships required to determine the convective loss are then as follow:

(6)

amb Q tloss = UA(TtST , s − Tt , s ), ,s

ICE MT FC SE ST Stwater = Stwater ,s 0, s + Gt , s + Gt , s + Gt , s + Gt , s − Gt , s ,

∀ t = 1, ∀ s ∈ S

(7)

W‐ST ST water W‐ST ST ICE ICE ICE Stwater , s Cpt , s Tt , s = St 0, s Cpt 0, s Tt 0 + Gt , s Cpt , s Tt , s

ICE MT FC SE ST Stwater = Stwater ,s − 1, s + Gt , s + Gt , s + Gt , s + Gt , s − Gt , s ,

∀ t ∈ T , ∀ s ∈ S, t > 1

∀ t ∈ T , ∀ s ∈ S, t > 1

(6a)

A=

Similarly, the energy balance in the thermal storage tank is stated just considering the heat capacities (Cp) and temperatures (T) for the involved streams. The convective loss through the tank wall is included

1 MAX‐ST 2/3 (S ) 6

∀ t, ∀ s

(8) (8a)

The thermal storage has been set above 70 °C to prevent the biological growth of Legionella:37 D


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Figure 4. Event tree for an instantaneous release. TtST , s ≥ 70 °C,

∀ t, ∀ s

‐Technology ‐Technology ‐Technology ‐Technology Q tCHP = GtCHP CpCHP (TtCHP ,s ,s ,s t ,s

(9)

− Ttamb , s ),

In this case, we considered only the storage of hot water that is provided from the CHP system. The temperature is defined by the operational scheme of the CHP units, where the provided hot water is between 90 and 100 °C. This temperature is addressed below in eq 14, and it is a parameter in the design of the CHP system. Therefore, in the absence of a heating device to provide additional heat to the water in the storage tank, the highest temperature that can be achieved is the supply temperature. Balance for the CHP Units. The main parameters that define the CHP‑Technology

operation of the CHP units are the thermal (ηQ

) and electrical

(ηW ) efficiencies. Both represent the relationship between the ) or heat (QCHP‑Technology ), products, either electricity (WCHP‑Technology t,s t,s ) in energy units. An and fuel required to produce them (FCHP‑Technology t,s additional parameter, which becomes a decision variable, is the partial ). This parameter represents the ratio between load (PLCHP‑Technology t,s electricity production in a given period and the production capacity of the unit under full load (PLMAX‑CHP‑Technology). No unit can operate below a certain value of partial load (PLMIN‑CHP‑Technology) because of their design conditions. This condition is restricted in relationships (12) and (13). Furthermore, the heat transfer from each CHP unit is defined by eq 14 for the different considered technologies. In these equations, yCHP‑Technology is a binary variable used to determine the existence of the CHP technology in the optimal solution, which can be ICE, MT, FC, or SE. When the binary variable is 1, the unit exits; otherwise, if the binary variable is 0, the unit does not exist. This way, in a generic form, for any CHP technology considered, the following relationships are needed: ηW

=

‐Technology W tCHP ,s ‐Technology FtCHP ,s

ηQ

CHP‐Technology

=

‐Technology Q tCHP ,s ‐Technology FtCHP ,s

∀ CHP‐Technology


W MAX‐CHP‐Technology

≤ PL

y

ρ water‐ST

,

∀ t ∈ T, ∀ s ∈ S

(17) (18)

Sizing of the Fuel Storage Tank. The size of the fuel storage tank significantly impacts the CHP system, because fuel storage is needed to satisfy peak demands, which has economic and safety implications. In this case, it is better to model the economic order quantity (EOQ) based on the annual fuel demand.38 The annual fuel demand (FD) is the result of the sum of seasonal demand times the fuel consumed for MT FC SE all CHP units (FICE t,s , Ft,s , Ft,s , Ft,s ). Here, HD is the number of days making up each of the seasonal periods, and HHVNG is the highest heating value of the fuel (in this case natural gas, NG), so that the fuel demand in mass units is obtained as follows:

(11)

(12)

FD =

‐Technology PLMIN‐CHP‐Technologyy CHP‐Technology ≤ PLtCHP ,s MAX‐CHP‐Technology CHP‐Technology

Stwater ,s

S MAX‐ST ≤ SUB‐STy ST

(10)

,


(16)

Sizing of the Thermal Storage Tank. The sizing of the thermal storage tank (SMAX‑ST) is defined by two factors. The first one is the maximum water stored during all the operation periods (Swater t,ssc ), and the second one is the maximum available capacity in the market (SUB‑ST). The existence of this element in the optimal solution is defined by the binary variable yST, and ρwater‑ST is the density of the stored water in the ST:

,

‐Technology W tCHP ,s

(15)

‐Technology W CHP‐Technology ≥ W tCHP , ,s

,

∀ t ∈ T , ∀ s ∈ S , ∀ CHP‐Technology ‐Technology PLCHP = t ,s

W MAX‐CHP‐Technology ≤ W UB‐CHP‐Technology yCHP‐Technology ,

S MAX‐ST ≥


(14)

Determining the Size of the System. The size of the system is determined by the size of the central co-generation unit (which can be ICE, MT, FC, and/or SE) and the size of the thermal storage tank, which are determined as follows. Sizing the CHP Prime Movers. The size of the CHP units (WMAX‑CHP‑Technology) is determined by the highest (upper bound) capacity available in the market (WUB‑CHP‑Technology) and the highest load required for operating the system during any time period in all ). The existence of the units is defined by the scenarios (WCHP‑Technology t,s the binary variable yCHP‑Technology:

CHP‑Technology

CHP‐Technology


, ∀ CHP‐Technology

MT FC SE ∑s HD ∑t (FtICE , s + Ft , s + Ft , s + Ft , s )

HHV NG

(19)

The EOQ model depends on the demand, but also it depends on two additional economic factors. The first one is the cost of ordering

(13) E


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ACS Sustainable Chemistry & Engineering (CO), i.e., to refill the storage tank. The second one corresponds to the cost of maintaining the fuel inventory. Thus, a relationship considering both factors associated with the maintaining cost (CostOMFS) results in the following expression to sizing the fuel storage tank: SFS =

τ M ma = 7 e[(0.642 ln f

(20)

SMIN‐FS ≤ SFS ≤ S MAX‐SF

(21)

Risk τ =

Inherent Safety. Quantitative risk analysis (QRA) is a tool for risk assessment. The first step in the implementation of a QRA corresponds to the identification of incidents i. An incident is the loss of matter or energy, either by leak or spill. HAZOP (“hazard and operability”) is a common method used for identification of incidents.39 The correct implementation of HAZOP provides the potential incidents that may occur in each technology and storage unit.40 The potential incidents identified in the CHP units and the storage tanks are used to determine the accidents that can occur from these incidents. An event tree approach is often used to make this task, which graphically represents the transition of an incident under certain circumstances.41 Figure 4 shows an event tree related to an instantaneous release. According to the characteristics of the incident, the nature of the released material and the environmental conditions may evolve the incident to an accident a, such as BLEVE, VCE, flash fire, or jet fire.42 Probit Functions. The consequences to the people are determined on the basis of the characteristics and conditions of each accident. Each accident produces different physical variables; for instance, BLEVE produces radiation and overpressure, where radiation causes more damage than overpressure. For assessment of overpressure (P), there are models that provide good approximations, as TNT or TNO. On the other hand, it is necessary to quantify the damage that these variables could cause on persons and facilities. To quantify the damage, Probit functions are used to evaluate different types of risk. Equation 22 is a Probit function associated with deaths from the effects of radiation exposure (radiation intensity, I, for time t). Equation 23 represents the deaths caused by overpressure.43

Y = − 39.83 + 3.0186 ln(tI 4/3)

(22)

Y = − 77.1 + 6.91 ln(P)

(23)

τ

NG

)

)+

MIE1/3

,

∀τ

∀τ

M mτ = 0.6 − 0.85 log MIE,

(25)

(26)

∀τ

(28)

∀τ

i

(29)

∀ i, ∀ a, ∀ τ

(30)

The affected population is a function of the area affected by the accident, where the population density (δc) depends on the people leaving in a given area c. This changes according to the area affected by the accident a, such a way that there can be obtained linear correlations for calculating the affected area as a function of the capacity and operating conditions of each unit. Each unit may have different incidents and accidents; thus, it is needed to specify which incidents i can occur in the unit τ, which is modeled through the binary parameter λτ,i. When the parameter λτ,i takes the value of one means that the incident i might exist for this unit in that place. Similarly, there is needed to establish the accidents that may occur from incidents i in the unit τ, which is modeled with the binary parameter αi,a that takes the value of 1 when the accident a might exist from an incident i. For determining the interaction between the system’s components (e.g., fuel tank, combustion chamber engine, etc.), the risk was assumed to be linearly additive. It should be noticed that this risk may be nonlinear; however, in this paper linearity was assumed for this additive risk interaction to avoid further numerical complication in the optimization process, and to manipulate all the risk functions as known relationships determined before the optimization process, leaving only the capacity and existence as optimization variables. In future works, it would be interesting to include this nonlinear interaction for the risk. Furthermore, in the proposed approach, the used technologies are simulated for different capacities to determine the associated Probit functions. This way, these Probit functions are known before the optimization process, and all the nonlinear and nonconvex behavior is associated with parameters determined before the optimization process. This way, the risk calculation does not involve additional nonconvex terms, and the model can be solved easily. In addition, the inherent safety approach is based on eliminating or reducing the hazards associated with a set of conditions, it uses the properties of a material or process to eliminate or reduce the hazard. Minimizing, moderating, substituting, and simplifying are the four basic strategies accounted for in the inherent safety approaches to reduce or eliminate the hazard. This way, in the proposed approach in this paper, minimization is one of the strategies used, this is shown in the sizing of the fuel storage tank, where the goal is focused on obtaining solutions that consider optimal fuel storage values, minimizing the amount of fuel of the storage fuel looking for the optimal size that ensures the lowest consequence (see eq 19). Moderating, also called attenuation, is another strategy of inherent safety used in the proposed approach, because the selection of technologies is based on the operating conditions; thereby, the obtained conditions are more stable, and this way conditions are avoided that might be close or equal to the fuel ignition point (see eq 25). To determine the efficiency of these two strategies, a quantitative risk analysis is applied, involving the inventory and operating

The probability of delayed ignition can be obtained through eq 26. This probability depends on the minimum ignition energy of the emitted flow, if the ignition is indoor or outdoor, and possible ignition sources that are in the environment.46 τ pdel = 0.3 ∏ Miτ , ‐ign

a

Ai , a , τ = k1Capacityτ + k 2 ,

(24)

0.0024(p τ )1/3

∀τ∈T

The probability of accidents is obtained from eq 24. The affected area Ai,a,τ depends on the type of accident, the circumstances in which this occurs, and the amount of inventory. The affected area is calculated as a function of the capacity as well as the operating conditions of each CHP and storage unit. In this way, linear relationships between the affected area Ai,a,τ and different capacities (Capacity = SFS or WMAX‑CHP‑Technology) were obtained for each unit τ and accident a:

Analysis of Frequencies. The frequency of each accident depends on the initial frequency associated with the occurrence of the incident and the associated probabilities that the latter results in an immediate or delayed ignition. The frequency of incidents can be calculated from databases related to each technology44 (usually these are related to the involved substances, in this case fuels), and it depends on the operating temperature and pressure of each technology or storage unit (τ = SF, ICE, MT, FC, or SE). Equation 25 shows the dependence of the probability of immediate ignition from the operating pressure and temperature:45 τ pimm = (1 − e−9.5(T /AIT ‐ign

,

∑ ∑ ∑ αi , aλτ , iAi , a , τ δcpa , τ , c

The Probit value can be transformed into a probability percentage of affectation through eq 24:

⎛ |Y − 5| Y − 5 ⎞⎟ p = 50 × ⎜1 + erf ⎝ |Y − 5| ⎠ 2

) − 4.67]

Risk Function. The allocation of each unit τ in quadrant c represents a risk to the near population in case of an accident in such unit. The social risk associated with the allocation of the unit τ, in the quadrant c is obtained through eq 29, which represents the product of the probability pa,τ of the accident a, the area affected by the accident Ai,a,τ, the population density δc, as well as binary parameters αi,a and λτ,i.

2COF D UCOMSFHHV NG

τ

(27) F


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ACS Sustainable Chemistry & Engineering conditions; thus, the proposed solution searches for minimizing the inherent risk. Economic Variables. The economic variables are associated with the sizing and operation of the system, which are useful to determine the economic objective function (i.e., the TAC), and these are described as follows. Capital Costs. The total capital cost (CostCapT) corresponds to the purchase of the equipment, which comprises the capital cost for the CHP units (CostCapICE, CostCapMT, CostCapFC, CostCapSE), the hot water storage tank (CostCapST), and the fuel storage tank (CostCapSF):

CostOMCHP‐Technology ‐Technology = UCOMCHP‐Technology ∑ HD ∑ W tCHP ,s s

CostOMFS = UCOMFS

(31)

CostPower GRID = t ,s

Sales of Electricity. The sale of electricity (PowerSale ) is carried out in two directions. The first customer is the housing complex ), and the second one is the grid of the electrical (WCHP‑Technology‑H t,s ). Both clients buy energy at the lowest company (WCHP‑Technology‑sale t,s unit price in the market (VCP):

(32)

‐H ‐H ‐H PowerSale T = VCP ∑ HD ∑ (WtICE + WtMT + WtFC ,s ,s ,s s

+

(33) ST

(34)

In the previous relationships, kF is a factor used to annualize the inversion. This annualization factor accounts for the value of the money over time, the life of the project (in this case 15 years), and the interest rate (in this case 10%), and this considers that the total cost will be paid in several periods. This annualization approach is very useful to sum the capital and operating costs associated with the TAC. Operating Cost. The total operating cost (CostOpT) is the annual cost of inputs required to operate the system. In this case, it consists of the costs for the fuel (CostOpFuel) and cold water (CostOpCW) considering the local market prices.

CostOpT = CostOpFuel + CostOpCW

(35)

CostOp

= UCCW ∑ HD ∑ s ‐H + GtCW ) ,s

+

+

GtFC ,s

+

t

MT FC SE GHGECHP = GHGFCHP ∑ HD ∑ (FtICE sc , ssc + Ft , ssc + Ft , ssc + Ft , ssc)

(36)

GtMT ,s

‐sale ‐sale ‐sale + WtMT + WtFC + W tSE ) ,s ,s ,s

(43) Greenhouse Gas Emission (GHGE). CHP systems consume fossil fuels that involve the generation of greenhouse gases (mainly CO2 emissions). In the proposed approach, there are two sources of emissions: first, direct emissions associated with the consumed fuel in the CHP unit (GHGECHP‑Technology), and then emissions associated with the local electrical company (GHGEGRID). Here, a unit factor for the emissions is considered (GHGFCHP, GHGEGRID). In the case of the fuel, the emissions depend on the quality and characteristics of the fuel used. In the case of those generated by the grid, these depend on the generation characteristics associated with the local electrical company. s

t

(44)

The cost for the supplied water (CostOpCW) is determined considering the unit cold water cost (UCCW) multiplied by the ) and the sum of the needed water in the CHP units (GCHP‑Technology t,s water used to regulate the temperature of the hot water supplied to the ): housing complex (GCW‑H t,s

(GtICE ,s

t

s

The cost of fuel (CostOp ) is determined considering the total annual demand of fuel (FD) times the unit price for the fuel consumed in each technology based on the prices of the local energy market (UCFCHP‑Technology):

CW

+

‐sale WtICE ,s

HeatSale H = UCH ∑ HD ∑ (Q tICE + Q tMT + Q tFC + Q tSE ) ,s ,s ,s ,s

Fuel

CostOpFuel‐Technology = UCF × F D

‐H W tSE ,s

(42) Heat Sales. Similarly to the previous term, the sale of heat (HeatSaleH) sent to the housing complex represents an income. It is calculated on the basis of the heat produced in the CHP system ) and the heat unit price in terms of the local market (QCHP‑Technology t,s (UCH):

FS

CostCapST = kF(FCSTy ST + VCST [S MAX‐ST]β )

(41)

t T

Similarly, for the thermal storage tank and the fuel storage tank, the capital cost functions (CostCapFS, CostCapST) are determined by fixed (FCFS, FCST) and variable unit costs (VCFS, VCST) associated with their size (SFS, SMAX‑ST) and considering the factor for the economies of scale (βFS, βST): CostCapFS = kF(FCFS + VCFS[SFS]β )

∑ HD ∑ UCPtscWtpurchase ,s s

),

∀ CHP‐Technology

(40)

Cost of Power Purchase. The cost for the purchased power ) involves the purchase of electricity at peak periods (CostPowerGRID t,s ) (i.e., at the time periods during the day when the (Wpurchase t,s production of electric energy from the CHP unit is insufficient to meet the demands) and the unit cost of energy (UCPt). It should be noted that UCP changes every hour of the day according to the policies of the local power company:

CostCapCHP‐Technology = kF(FCCHP‐Technology yCHP‐Technology CHP‐Technology

(39)

+ CostOMSE + CostOMFS

The capital cost for each CHP unit (CostCapCHP‑Technology) is determined mainly by the size of the equipment, which accounts for a fixed part (FCCHP‑Technology) and a variable part (VCCHP‑Technology) that is multiplied by the size of the equipment (WMAX‑CHP‑Technology) elevated at the exponent βCHP‑Technology, which represents the scaling factor to account for the economies of scale.

+ VCCHP‐Technology [W MAX‐CHP‐Technology ]β

F HHV NG

CostOMT = CostOMICE + CostOMMT + CostOMFC

CostCapT = CostCapICE + CostCapMT + CostCapFC + CostCapSE + CostCapSF + CostCapST

(38)

t D

GHGEGRID = GHGFGRID ∑ HD ∑ Wtpurchase scc , ssc s

t

(45)

Optimization Strategy. The optimization formulation is stated as a multi-objective mixed-integer nonlinear programing problem, whose objective function is given as the simultaneous minimization of the Risk, the TAC, and the GHGET, subject to satisfy the relationships (1)−(45). To solve this problem, first the single objective solution for minimizing the TAC is obtained; this solution provides the upper bound for the Risk and GHGET. Then, to obtain the upper bound for the TAC, the single optimization problem for minimizing the GHGET and Risk are solved, one of these solutions provides the upper bound for the TAC. Based on these previous extreme solutions, then the epsilon constrain method is implemented, where the solution of a set

GtSE ,s

t

(37)

Cost for the Operation and Maintenance. The costs for the operation and maintenance of the different units, including the fuel storage tank, are calculated based on the unit costs (UCOMCHP‑Technology, UCOMSF) associated with the total production , FD): of the equipment (WCHP‑Technology t,s G


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Figure 5. Conditions for the addressed case study. of several single optimization problems for minimizing the TAC under upper constraints for the GHGET and Risk yield a set of Pareto optimal solutions that compensate the considered objectives.47−50 This is stated mathematically as follows:

min TACi

homes in the housing complex used as a case study. The economic objective is the minimization of the total annual cost. The considered technical and operating parameters in the case study are presented in Table 1.53,54 The supply temperature for the sanitary hot water is fixed at 50 °C. The environmental objective is to minimize the overall GHGE, and the unit factors needed are shown in Table 2. For the case study, all the units consume natural gas.56 Table 2 also shows the economic data for the local energy market for heating. Figure 6 shows the behavior of the average price of electric energy during the day. On the one hand, the scheme of selling power of the electrical company is shown in this Figure 6, which represents variations during the day, reaching its highest price during peak hours. On the other hand, the sale of electric energy scheme of the CHP system is fixed at the lowest price. This consideration allows a competitive price for the end user, which can get electricity at the lowest cost.

(46)

subject to relationships (1)−(45) and also subject to

GHGET ≤ εi

(47)

Risk τ ≤ ϕi

(48)

where i = 1, 2, 3, ..., n, a nd n is the number of scenarios considered for the solution in the Pareto diagram.

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CASE STUDY A residential complex from the Michoacán State of Mexico was considered as case study. It is located in the city of Morelia, near to a mountainous zone, and consists of 1440 homes. Figure 5 shows the seasonal hourly profiles for the demanded energy and annual temperature associated with the location. In central Mexico, the weather conditions have no significant variation throughout the year.51 The energy demand profiles have been obtained by applying a survey and direct measurements. The survey was administered directly into the homes, and the direct measurement was conducted in randomly selected households. From these data, the profiles, represented with a smooth curve, were designed like an hourly consumption profile.52 The population density (δ) for this case is 0.045 individual/m2. Figure 5 also shows the distribution of the

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RESULTS In the housing complex used as case study, four possible locations for the CHP units and the storage thank for natural gas were identified (see Figure 7). Instantaneous and continuous releases are identified as potential incidents in the storage units. In the CHP units, there was identified a continuous release as possible incident. This way, BLEVE, VCE, and jet fire are the potential accidents. The initial frequencies for each incident are presented in Table 3.44 The probabilities for immediate and delayed ignition were calculated H


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ACS Sustainable Chemistry & Engineering Table 1. Technical and Economic Parameters for the Considered CHP Technologies and Auxiliary Equipment53 parameter

ICE

MT

FC

SE

ST

FS

electrical efficiency (ηW, %) thermal efficiency (ηQ, %) maximum size (WUB, GUB, and SUB; kWe, m3, kg) minimum partial load (PLMIN, %) unit cost of cold water (UCCW, $/L) fixed cost (FC, $) variable cost (VC, $) scale factor (β, −) annualization factor (kF, −) maintenance cost (UCOM, $/kWh) operating temperature (T, °C) operating pressure (P, kPa) outlet temperature (Tout, °C)

37.25

26

38

30

47.5

47.5

50

60

15,800

12,500

2,000

1,500

200

2,250

35

60

50

42.5

0.001

0.001

0.001

0.001

100 400

100 450

100 2500

100 450

120 125

240 250

1 0.23

1 0.23

1 0.23

1 0.23

1 0.23

0.8 0.23

0.015

0.065

0.015

0.015

Figure 7. Possible locations for installing the CHP and the storage units.

Table 3. Initial Frequencies for the Identified Incidents in the Case Study

360

338

139

649

30

310

552

157

500

1372.3

90

90

90

90

parameter GHGE (gr CO2/kWh of fuel consumption) unit sale value of thermal energy for internal consumption (UCPH, $/kWh) highest heating value for natural gas (HHVNG, kWh/kg)

503 0.18

technology

frequency

FS

5.00 × 10−7

continuous release

ICE MT FC FS SE

1.10 1.20 1.10 1.61 1.08

× × × × ×

10−4 10−3 10−3 10−4 10−4

Table 4. Probability of Immediate and Delayed Ignition for the Case Study

Table 2. Data for Emissions and Heat Sale55 CHP system

incident instantaneous release

0.008

GRID, local electric company

incident

technology

pimm‑ign

pdel‑ign

instantaneous release

FS

0.2

0.4

continuous release

ICE MT FC SE FS

0.8 0.95 0.72 0.83 0.3

0.282 0.394 0.281 0.41 0.1

350

13.05

Table 5. Frequency of Accidents for the Case Study technology

incident

accident

ICE

continuous release

MT

continuous release

FC

continuous release

FS

instantaneous release continuous release

SE

Figure 6. Prices of electric energy through the day.55

continuous release

jet fire VCE jet fire VCE jet fire VCE BLEVE VCE jet fire VCE jet fire VCE

frequency 8.80 3.10 9.60 4.73 7.92 4.33 3.50 6.45 4.83 4.51 8.96 3.67

× × × × × × × × × × × ×

10−5 10−6 10−4 10−5 10−4 10−5 10−7 10−8 10−5 10−5 10−5 10−6

probability of deaths. For each accident, there were obtained the correlations to determine the affected area depending on the capacity and operating conditions for each technology. The software SCRI was used to determine the profiles of each accident.57 The population density for each division is 0.045 individual/m2, and this value is multiplied by each area to obtain the social risk for each accident. The affected area is a

through eqs 24 and 25, respectively (see Table 4). In addition, Table 5 shows the frequencies of each accident. The affected area was determined based on a 50% probability of deaths. The Probit function for deaths by radiation is based on eq 22 for BLEVE and jet fire. Whereas, for VCE the Probit function related to deaths due to overpressure is based on eq 23. In addition, eq 24 is used to transform the Probit values in I


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the selection of different configurations and operations for the involved equipment. The sizing of the system is also shown in nominal terms. Figure 11 shows the Pareto front for the three identified objectives (TAC, GHGE, and Risk). The solution of Scenario 1 is the most desirable from the economic point of view, which has the lowest TAC ($226,060/year). It should be noted that the most advantageous solutions from the economic point of view (Scenarios 1, 4, 5, 7, 8, 10, and 12) are associated with the use of the internal combustion engine The Scenario 2 shows the most convenient solution from the environmental point of view because it produces the least amount of emissions (1,905 tons of CO2/year). However, it also shows the high social risk (1,213 fatalities). For the reduction of emissions, the selected technologies are fuel cell (Scenarios 2, 13, and 14) and the internal combustion engine (Scenarios 1 and 12). From the safety point of view, the Scenario 4 corresponds for the safest solution (881 fatalities). However, it represents the worst result in terms of economic (TAC: $367,580/year) and environmental (GHGE: 2,133,222 tons of CO2/year) perspectives. The best solutions from the safety point of views (Scenarios 3, 6, 9, 11, 13, and 14) are associated with using fuel cells as CHP central units. An immediate consideration could lead to the conclusion that the size of fuel storage tank defines the number of fatalities in case of an accident. However, Figure 12 shows that this relationship between the size of the storage unit and fatalities, especially with regard to Scenario 2, is not the only factor that determines the risk. The type, size, and operation of the central CHP unit determine the amount of fuel and the magnitude of a potential accident. A suitable solution for the case study, considering the above-mentioned factors, could be Scenario 14. This solution uses a fuel cell. In economic terms (TAC: $ 293,650), it is 29.9% higher than the lowest TAC (Scenario 1) and 20.1% lower than the highest (Scenario 3). In environmental terms (GHGE: 1,943,555 tons CO2/year), it is 1.9% higher than the lowest scenario in production of emissions (Scenario 2) and 8.8% lower than the highest emissions (Scenario 3). Considering the safety viewpoint, in case of an accident the fatalities (890 fatalities) are reduced by 26.6% with respect to the scenario with highest risk (Scenario 2) and increase 1% with respect to the scenario with the lowest risk (Scenario 3).

function of the inventory (capacity) and operating conditions (temperature and pressure). The affected area for the accident VCE is influenced by dispersion of gases. Analyzing the tentative quadrants where is possible to install the units (see Figure 7), it is possible to identify that quadrants 1 and 2 are the locations where there is less population. Then, the affected area is determined for the four possible locations. Figure 8

Figure 8. Areas of affectation due to BLEVE for the case study.

shows the radius of affectation due to radiation of BLEVE, here is possible to observe three radius of affectation with black, red, and blue lines, which correspond to probabilities of affectation of 100, 50, and 0%, respectively. The results show that quadrants 2 and 3 represent more hazardous locations due to the affectation radius. For BLEVE and VCE, simulations were performed to determine the affected area. Figure 8 shows the behavior for dispersion, which was assessed by considering the most prevailing weather conditions. The profiles of Figure 9

■

CONCLUSIONS This paper has presented a new superstructure for the optimal design of CHP systems for residential use considering inherent safety factors as well as economic and environmental objectives. The proposed superstructure involves the selection of multiple technologies to satisfy electricity and hot water demands, while it considers the ambient temperature and energy market conditions. Based on this superstructure, a mathematical programming formulation has been developed for the simultaneous minimization of the total annual cost, the associated greenhouse gas emissions, and the risk associated with the type, operating conditions, and size of the involved units, as well as the allocation and population density. A proper solution approach based on the epsilon constraint method has been implemented to show compensated solutions that tradeoff the economic, environmental, and safety objectives. The proposed approach was applied to a case study in the State of Michoacán in the central part of Mexico. The results show balanced solutions among economic costs, generated greenhouse gas emissions, and the risk quantified in terms of

Figure 9. Dispersion due to a continuous release for the case study.

represents the concentration of the released substances and consequently the affected area, whether these ignite or explode. It should be noted that quadrant 1 represents the safest location for the units. The individual risk contour was calculated for a probability of affectation of 50%, and this is because BLEVE is the only accident that contributes to the individual risk in the residential area (see Figure 10). The value obtained was 3.5 × 10−7/year, which involves an acceptable level of risk considering 10 × 10−6/year as acceptability criterion. The extreme solutions generated from the optimization process are shown in Table 6. The Scenarios 1, 2, and 3 show the minimum values for the TAC, GHGE, and Risk, respectively. Associated with each scenario, there is considered J


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Figure 10. Individual risk contours for the case study.

Table 6. Optimal Results for the Extreme Solutions for the Case Study objective functions

description of the system

Scenario

TAC ($/year)

GHGE (tons of CO2/ year)

Risk (no. fatalities)

CHP central unit

sizing of CHP unit (kWe)

sizing of thermal storage (m3)

sizing of fuel storage (kg)

1 2 3 4 5 6 7 8 9 10 11 12 13 14

226,060 300,990 367,580 253,340 253,500 328,890 244,230 244,400 319,790 235,730 310,680 228,340 301,580 293,650

1,964 1,905 2,133 2,095 2,095 2,095 2,057 2,057 2,057 2,019 2,019 1,981 1,981 1,943

1,045 1,213 881 1,048 1,047 890 1,048 1,047 890 1,047 890 1,047 890 890

ICE FC FC ICE ICE FC ICE ICE FC ICE FC ICE FC FC

131.5 108.6 117.0 129.9 122.9 94.0 129.9 122.9 94.0 129.9 94.0 132.0 94.0 94.0

14.9 17.0 18.4 15.0 15.3 16.6 14.9 15.3 16.6 15.0 16.6 14.9 16.6 16.6

1,073.6 1,033.8 1,031.8 1,077.5 1,077.3 1,043.8 1,077.5 1,077.3 1,043.8 1,077.0 1,043.8 1,076.4 1,043.8 1,043.7

Figure 11. Pareto front for the case study.

K


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Figure 12. Relationship between size of storage tank for fuels and the risk.

T t U UCCW UCF UCOM UCPH UCPW

the fatalities associated with an accident. The results also highlight the importance of the risk in the optimal design of residential CHP systems, which is an issue that has not been accounted for in previously reported approaches.

■

AUTHOR INFORMATION

Corresponding Author

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

VCunit VCSW

Notes

The authors declare no competing financial interest.

■ ■

WDt WUB

ACKNOWLEDGMENTS The authors acknowledge financial support from CONACyT and the UMSNH.

Y β δ η ρW‑ST

NOMENCLATURE

Indexes

a c i t s τ

Accident Quadrant Incident Time period, h Seasonal periods (spring, summer, fall, winter) unit

Continuous Variables

A Ai,a,τ CostCap CostOp CostOM CostPower

Parameters

AIT Cp CO FIR FCunit GDt GHGF HD HHVNG I kF MIE Mτi Pτ pa,τ PLMAX PLMIN SUB‑ST

Temperature, °C Time of radiation exposure, s Convective factor, kWh/m2 °C Unit cost for cold water, $/kg Unit cost for fuel, $/kWh Unit cost for operating and maintenance, $/kW Unit cost of heat from the CHP system, $/kWh Unit cost of power from the net of the electrical company, $/kWh Unit variable cost, $/kWh Unit value of sale for electrical energy to the grid, $/kWh Electricity demand for household kWh Upper bound for the capacity of electrical production, kWh Probit value Scale factor for the capital cost Population density, habitants/m2 Efficiency Water density in the storage tank, kg/m3

Auto-ignition temperature, °F Heat capacity, kWh/kg °C Ordering cost, $ Initial frequency leak, year−1 Fixed cost, $ Hot water demanded by the housing complex, kg Factor for emissions, ton CO2/kWh Operating days (annual), day Highest heating value of the fuel (natural gas) Radiation intensity, W/m2 Factor used to annualize the inversion, year−1 Minimum ignition energy, MJ Multipliers Operation pressure, kPa Probability of damage Maximum partial load Minimum partial load Upper bound for thermal storage capacity, kg

F FD G GHGE GHGET HeatSaleH IRx,y PL P pτimm‑ign pτdel‑ign PowerSale L

Convective area for storage tank, m2 Affectation area, m2 Annualized cost of capital, $/year Operating cost, $/year Operating and maintenance cost, $/year Cost of power purchase from the grid of the electrical company, $/year Fuel consumed, kWh Fuel demand Water flow rate, kg/h Direct emissions, annual CO2 ton Total of direct emissions from the proposed superstructure, annual CO2 ton Heat sold by the CHP system to the housing complex, $/year Individual risk in the position (x,y), year−1 Partial load Overpressure, N/m2 Probability of immediate auto-ignition Probability of delayed auto-ignition Annual sale of electrical energy to the grid of the electrical company $/year DOI: 10.1021/acssuschemeng.5b00941 ACS Sustainable Chem. Eng. XXXX, XXX, XXX−XXX

Research Article

ACS Sustainable Chemistry & Engineering PowerSaleCHP‑H Annual electricity sold by the CHP system at the housing complex, $/year Q Thermal load produced, kWh Qloss Heat loss by convection, kWh t Riskτ Risk for the unit fatalities Swater Stored hot water, kg t SMAX‑ST Maximum capacity for thermal storage tank, kg TST Temperature of water in the thermal storage t tank, °C W Electricity produced, kWh Wsale Electricity sold to the grid of the electrical t company, kWh WMAX Maximum electrical load produced, kWh Wpurchase Electricity purchased from the grid of the t electric company, kWh

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Binary Parameters

λτ,i Binary parameter for the existence of an incident i in the unit τ αi,a Binary parameter for the existence of an accident a from the incident i Binary Variables

y Existence for units Acronyms and Abbreviations, Sub- and Superscripts

amb BLEVE CHP CHP-Technology CW D FC FS GHGE GRID H HAZOP ICE MAX MIN MINLP MT purchase QRA sale SE ST T TAC UB VCE

■

Ambient conditions Boiling liquid−expanding vapor explosion Combined heat and power ICE, MT, FC, or SE Cold water Demand Fuel cell Fuel storage Greenhouse gas emission Grid of the electrical company Sent to the housing complex Hazard and operability analysis Internal combustion engine Maximal value Minimal value Mixed-integer nonlinear programming Microturbine Energy purchased from the grid Quantitative risk analysis Energy sold to the grid Stirling engine Thermal storage tank Total (sum of multiple factors as a final result) Total annual cost Upper bound Vapor cloud explosion

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Optimal Design of Inherently Safer Domestic Combined Heat and

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