Minimization of local impact of energy systems through exergy analysis

Energy Conversion and Management 76 (2013) 874–882

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Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman

Minimization of local impact of energy systems through exergy analysis Gabriele Cassetti ⇑, Emanuela Colombo Department of Energy, Politecnico di Milano, via Lambruschini 4, Milano, Italy

a r t i c l e

i n f o

Article history: Received 8 March 2013 Accepted 24 August 2013

Keywords: Energy systems Exergy analysis Quantitative risk analysis Major accidents

a b s t r a c t For the acceptability of energy systems, environmental impacts are becoming more and more important. One primary way for reducing impacts related to processes is by improving efficiency of plants. A key instrument currently used to verify such improvements is exergy analysis, extended to include also the environmental externalities generated by systems. Through exergy-based analyses, it is possible indeed to evaluate the overall amount of resources consumed along all the phases of the life cycle of a system, from construction to dismantling. However, resource consumption is a dimension of the impact of a system at global level, while it may not be considered a measure of its local impact. In the paper a complementary approach named Combined Risk and Exergy Analysis (CRExA) to assess impacts from major accidents in energy systems is proposed, based on the combination of classical exergy analysis and quantitative risk analysis (QRA). Impacts considered are focused on effects on human health. The approach leads to the identification of solutions to minimize damages of major accidents by acting on the energy system design. Ó 2013 Elsevier Ltd. All rights reserved.

1. Introduction In the energy sector, the evaluation of environmental impact is gaining growing relevance. This can be divided in two categories [1]:  local impact, due to emission of dangerous substances capable of altering the local ecosystem,  global impact, due to overall resource consumption during the entire life cycle of the process or plant. In Table 1, general issues specifically related to the two different categories of impacts are represented. At the global level, a principal way to reduce impacts related to processes is by improving the efficiency of plants, and an analysis currently used to verify such improvements is exergy analysis. Exergy represents the useful energy, or the maximum work, that can be obtained from a process and its analysis allows identifying and evaluating the process irreversibility. Exergy analysis is therefore an instrument that can lead to reducing energy consumption of systems and the associated environmental impacts by reducing irreversibility. In this sense, exergy is used to assess resource consumption (i.e. raw material and energy) of energy systems [2], and since the last ⇑ Corresponding author. E-mail addresses: [email protected] (G. Cassetti), [email protected] (E. Colombo). 0196-8904/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.enconman.2013.08.044

decade a number of methodologies of analysis based on this concept [3] has developed. A brief list of these methodologies includes Cumulative Exergy Consumption [4], Exergetic Life Cycle Analysis [5], Extended Exergy Accounting [6], Exergoenvironmental Analysis [7], Exergoecological Analysis [8] and the Environomic method [9]. Nevertheless exergy-based methodologies are not designed to measure the local impact due to emissions [3]. One of the main reasons is the lack of a relation between the potential damage of the emissions (e.g. because of their toxicity) and their exergy content. 2. Exergy-based analyses for environmental impact assessment Exergy is an appropriate measure to evaluate resource consumption (mainly energy and raw material). Flows of energy and raw material absorbed by the system may be converted in exergy flows and then compared and combined, in order to determine the influence of non-ideality of processes in the output, localize and quantify inefficiencies along the chain and guide improvements [4]. Exergy-based analyses existing in literature measure the environmental impacts of energy systems by using different indicators. One of the first analyses developed is Cumulative Exergy Consumption (CExC). Objective of CExC is ‘‘the assessment of the exergy content of natural resources, renewable and non-renewable, absorbed by all the subsystems of the productive chain for a given product or service’’[4]. The conjecture at the basis of CExC is that

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Nomenclature c cv C_ e E_ F k _ m p P r R R_ t T x Y Z_ h

specific cost (€/J) control volume cost rate (€/s) specific exergy (J/kg) exergy (W) injury probability (%) probit constant (ad) flow rate (kg/s) probability (%) or frequency (y1) of occurrence of accident pressure (Pa) specific risk (adverse effect t1/J) risk (adverse effect t1) risk flow (adverse effect t1/s) time (y) temperature (K) injury factor of hazard probit (ad) component costs (€/s) type of fluid adopted (ad)

the total exergy consumed to produce a product is the sum of the exergy consumed by the delivered materials, semi-finished products and energy carriers. The concept of exergy as measure of resource cost is shared also in the definition of the Exergetic cost of a system [8]. Both the formulations of CExC and exergetic cost introduce the so called Thermo-ecological cost, which includes the compensation of environmental losses caused by rejection of harmful substances in the surrounding environment. The thermo-ecological cost is defined as the additional consumption of exergy required to compensate any alteration of the environment from its reference state [10]. The conversion of energy and raw materials in exergy flows is the basic concept developed also in the Exergetic Life Cycle Assessment (ELCA) [11], based on the extension of the Life Cycle Assessment using exergy as quantifier of resource consumption. Other approaches along the lines of the ones previously presented are given in the formulation of Extended Exergy Accounting [6], Exergoenvironmental Analysis [7] and Environomics [9]. Extended Exergy Accounting (EEA) is one of the most recent developments in literature, and it widens the approach of the previous ones. The concept of exergy is used here to convert, in addition to energy and raw material flows, capital and labor, through specific macroeconomic models, and environmental impact, hence to include and measure also such externalities. In EEA environmental impact is measured in terms of amount of exergy required to compensate environment exergy depletion due to resource consumption of the system. Environomics and Exergoenvironmental Analysis are instead extensions of the Thermoeconomic Analysis [12,13] and are currently used for design optimization of energy systems. Thermo-economics basically combines the second law principle and

Superscripts CI capital investments O&M operation and maintenance Subscripts cond condenser D destruction drill drilling evap evaporator F fuel in inlet L loss ORC Organic Rankine Cycle out outlet P product pump pump turb turbine

classical economic analysis with the purpose of minimizing the cost of the product of the system [13]. In the Environomic method, monetary penalties due to environment depletion and remediation are included in the economic analysis. Environmental impact is expressed through monetary proxy [9]. In Exergoenvironmental Analysis, the Life Cycle Assessment (LCA) is integrated in the theoretical structure of Thermoeconomics. Environmental impact is therefore expressed through the LCA indicator Ecoindicator [7]. Ecoindicator is the current indicator used in LCA analysis to estimate the environmental impact of a system or chain of processes. It aggregates measures of effects on Human Health, Resource Consumption and Ecosystem Quality. Exergoenvironmental analysis therefore differentiates from the previous analyses mentioned, expressing environmental impact through a current indicator used in environmental analyses (the Ecoindicator). In Fig. 1, the conceptual boundaries considered by each analysis are represented, including also Industrial Ecology [14] and Ecological Exergy [15]. They are introduced for completeness as they do not focus on energy system design and/or optimization, and are therefore of minor relevance for the purpose of the paper. They are respectively designed for assessing the rate of exploitation of the output produced by a system (the manufactured product) and the exergy alteration of the ecosystem. 3. Extension of domain analysis Exergy – based methodologies consider different spatial and time boundaries. This means that these methodologies are designed to evaluate impacts from different perspectives, operations and life cycle, at local or global level.

Table 1 Categories of environmental impacts. Scale of analysis

Local impacts

Global impacts

Specification of impacts

Atmosphere contamination Hydrosphere contamination Lithosphere contamination Biosphere contamination Human Health, Ecosystems

Atmosphere contamination Global resource consumption

Targets of impacts

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Fig. 1. Boundaries of exergy based analyses.

They are mainly designed to embrace life cycle time boundaries, although with some distinctions. In CExC, the cumulative processes from the first phases of system life cycle (e.g. extraction of fossil fuels in a process die, construction) up to the operative phase are potentially included; on the contrary, in ELCA, Exergoenvironemtal analysis and EEA the complete life cycle of the system is considered (from cradle to grave). Environomic method can be performed considering both life cycle and operating phase time boundaries, according to the economic analysis associated. With respect to spatial boundaries, CExC, ELCA and Exergoenvironmental analysis are conceived to consider generally the global perspective. EEA instead can be performed considering both local and global perspective. Finally, Environomic method is conceived to analyze impacts on the local perspective. From Fig. 2 it appears that exergy based methodologies are mainly designed to assess impacts from a global perspective, whereas the local perspective remains scarcely addressed. In this paper, an exergy-based methodology to measure local impacts due to major accidents considering the human health dimension is presented. This is obtained by integrating exergy analysis with quantitative risk analysis. The driving idea is, hence, to define a model for assessing and reduce impacts of energy systems starting from the thermodynamics of processes, and adopting risk as proxy of social externalities affecting human health and safety.

4. Integration of risk analysis to evaluate local impact The model integrates the results of the exergy analysis and the quantitative risk analysis (QRA) of the system to minimize the local impact similarly to the dual productive structure of Thermoeconomics. As mentioned, Thermoeconomic analysis combines exergy analysis and economic analysis by using the exergy costing principle [16]. Quantitative risk analysis allows assessing local impacts in terms of: – Effects on human health [17]. – Contamination of atmosphere, hydrosphere and lithosphere [18]. – Ecosystem quality and biodiversity loss. Quantitative risk assessment is specific for any type of system and it is expressed by numerical quantities, which provide information for risk management decisions in coherence with the applicable Health, Safety and Environment (HSE) regulations [19]. The risk R associated to processes of a system may be expressed as fatal accident probability from hazards (adverse effects t1)s, representing the number of possible deaths due to major accident hazards involving dangerous substances. The result of quantitative risk analysis is presented in terms of individual risk as vulnerability of a single individual in the surrounding environment [20] of the system. The numerical value of risk R is estimated by mathematical models that evaluate the entity of the consequences and the probability of system failures which lead to major accidents such as leaks, emissions, dispersions, fires and explosions [21]. 4.1. Determination of individual risk The model considers the general expression of risk as product of the probability of injury from a hazard (or fatality) F and its probability (or frequency) of occurrence p1 [22,23]:

R ¼ p  Fs

ð1Þ

In Eq. (1), the power s enforces the relevance of F with respect to p

Fig. 2. Scale and phase of analysis of exergy based methodologies.

1 This expression of risk is extremely general, since the evaluation of the probability of occurrence p includes also the Frequency and Reliability Analysis of the system [22], but it is effective for the current intentions of the paper.

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5.1. Relation between risks and exergy

Table 2 Hazards and injury factors. Hazard

Injury factor x 2

Fire Explosion Toxic gas

Thermal radiation intensity I (W/m ) Overpressure p0 (N/m2), Impulse J (N s/m2) Concentration C (ppm), Dosage Ct (ppm s)

In all generality, referring to the generic component k within a plant, injury factor xi,k of the i-th hazard in k can be related to process parameters of k [21]. For example, considering the component k in thermodynamic equilibrium at steady state the injury factor xi,k may be expressed as:

xi;k ¼ xi;k ðua;k Þ Table 3 Transformation of percentages to probits. %

0

1

2

3

4

5

6

7

8

9

0 10 20 30 40 50 60 70 80 90

– 3.72 4.16 4.48 4.75 5.00 5.25 5.52 5.84 6.28

2.67 3.77 4.19 4.50 4.77 5.03 5.28 5.55 5.88 6.34

2.95 3.82 4.23 4.53 4.80 5.05 5.31 5.58 5.92 6.41

3.12 3.87 4.26 4.56 4.82 5.08 5.33 5.61 5.95 6.48

3.25 3.92 4.29 4.59 4.85 5.10 5.36 5.64 5.99 6.55

3.36 3.96 4.33 4.61 4.87 5.13 5.39 5.67 6.04 6.64

3.45 4.01 4.36 4.64 4.90 5.15 5.41 5.71 6.08 6.75

3.52 4.05 4.39 4.67 4.92 5.18 5.44 5.74 6.13 6.88

3.59 4.08 4.42 4.69 4.95 5.20 5.47 5.77 6.18 7.05

3.66 4.12 4.45 4.72 4.97 5.23 5.50 5.81 6.23 7.33

and its value is function of the particular hazardous event [22]. A possible method to evaluate the fatality F of a hazardous event is represented by Probit functions [21,24]. Probit functions are an alternative way of expressing the probability of injury from accident and may show different forms according to the injury probability distribution of the specific hazard i. Frequent hazards in energy sector are leaks, emissions, dispersions, fires and explosions [21]. Hazards are related to specific injury factors x as indicated in Table 2. The probability distribution of injury factors usually considered first is the log-normal distribution [18]. Under this assumption, Probit functions assume the form:

Y i ¼ k1 þ k2 ln xi

ð2Þ

where Yi is the probit expressing the fatality F(Yi) from the hazard i,as shown in [21] and [24] and xi is the injury factor of i. k1 and k2 are defined constants that assume specific values according to the specific type of hazard. The relation between F and Y is extrapolated from Finney chart [21], represented in Table 3. Assuming individual risk in terms of acceptable risk as a cost for the society[25], this approach can produce an information equivalent to what Thermoeconomics does for monetary cost, where now the cost is the risk to ‘‘accept’’ in order to benefit from the product of the system (e.g. electricity, gas, heat for energy systems). The model hence is conceived to identifying the elements of highest impacts in terms of damage to human health. In this manner, it can be used to delineate specific indications for the system design and the identification of the safety measures required by international standards [26]. 5. Formulation of the model Here below the complete model proposed by the author is presented in details. The Combined Exergy and Risk Analysis stands on two main pillars which are below detailed: – Relation between individual risk and exergy. – Duality with the Thermoeconomics productive structure.

ð3Þ

where ua,k are a the independent operating parameters such as Pk, _ h;k , where h is the type of fluid used with its specific toxicoTk, or m logical profile. These parameters are evaluated in the point where the accident occurs and are therefore related to those of the stream of flow rates crossing the component k [22]. From Eqs. (2) and (3) therefore it is possible to suppose a direct relation between the probability of injury F(Yi) and the operating parameters of the system. From Eq. (1), being Rk function of Fi,k, it is possible hence to associate the risk of the k-th component Rk to the independent operating parameters of the system:

Rk ¼ f1 ðua;k Þ

ð4Þ

For the exergy balance, two considerations need to be added. Exergy associated to heat and work may depend on (some of) the parameters of the component k, while the exergy associated to a stream flow rate depends directly on the parameters of the stream itself entering or exiting component k [17]. These are necessarily related _ h;k . The exergy to the operating parameters of k such as Pk, Tk and m balance and thus E_ D;k depends on the same parameters and from the fuel- product allocation of Thermoeconomics (see par. 5.2) also E_ P;k comes to be linked to system operating parameters and therefore to Rk. On the consequence it is possible to state:

Ep;k ¼ f2 ðua;k Þ

ð5Þ

Therefore a link between Rk and E_ P;k is recognized, even if no functions, trend or tendency can be predictable a priori. 5.2. Duality with Thermoeconomics productive structure As mentioned, the formulation of the model descends from the fundamental system of Thermoeconomics. Considering the Fuel – Product formulation [13], the system of equations is:

C_ j ¼ cj E_ j

exergy costing principle for j-th stream

E_ F;k ¼ E_ P;k þ E_ L;k þ E_ D;K

exergy balance of component k

ð6:aÞ ð6:bÞ

C_ P;k ¼ C_ F;k þ Z_ k

cost balance of component k

ð6:cÞ

_ O&M Z_ k ¼ Z_ CI j þ Zj

cost of component k

ð6:dÞ

Eq. (6.a) represents the exergy costing principle correlating the monetary cost of the general stream j to its exergy content. C_ j and E_ j are correlated through the specific cost cj of j, calculated from Eq. (6.a). Eq. (6.b) is the exergy balance of the k-th component where: – the Fuel is the sum of all input exergy streams in the k-th component, – the Product is the sum of useful output exergy streams from the k-th component, net of losses E_ L;k and exergy destroyed E_ D;k . The cost balance of the k-th component (Eq. (6.c)) expresses the monetary cost of output exergy streams as the sum of the costs of

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fuel C_ F;k , investment costs Z_ CI j and operation & maintenance costs Z_ O&M (Eq. (6.d)) [12,13]. j By solving the system of Eq. (6), it is possible to evaluate the specific cost rate of the product cP,k:

cP;k ¼ C_ P;k =E_ P;k

ð7Þ

The design optimization of the system is performed by minimizing the specific cost rate of the product cP,k [13]. A similar system of equations is proposed in the model formulation, where costs are turned into risks and the information obtained can be useful for design optimization, where the current objective is risk minimization. 5.3. Combined Risk and Exergy Analysis (CRExA)

k-th component (Eq. (8.d)) and R_ F;k is the cumulated risk associated to the intermediate products to produce P in component k, which hence is the result of the risk analysis performed on the d upstream components (Eq. (8.e)). Finally it is possible to evaluate the specific risk of the product of k:

rP;k ¼ R_ P;k =E_ P;k

ð8:eÞ

The calculation of the R_ P function is necessary for the implementation of the model and the evaluation of specific risk rP is the ultimate parameter to minimize. When a defined EP is the supply requested by the society all the plants ki that contribute to meet this need have to be considered in order to understand the best set of configuration that minimize the specific global risk for the society associated to the amount of EP that is requested. Hence being:

The complete model is defined by the following system of equations to be applied to the k-th component of the system. The exergy costing principle is expressed in terms of risk and the cost balance is converted in a cumulated risk balance, obtained performing a quantitative risk analysis. The exergy costing principle can be therefore defined for the product as:

R_ P;ki ¼ r P;ki E_ P;ki

R_ P ¼ r P E_ P

we finally obtain:

Being R expressed in [hazardous events y1], the mathematical symbolism R_ is used. The system is hence:

rp ¼

R_ P ¼ rP E_ P the exergy costing equation of the product in terms of risk ð8:aÞ

E_ F;k ¼ E_ P;k þ E_ L;k þ E_ D;k

the exergy analysis of component k

ð8:bÞ

R_ P;k ¼ R_ F;k þ R_ k R_ F;k ¼

the cumulated risk balance in component k

c X R_ kd

ð8:cÞ ð8:dÞ

d¼1

In Eq. (8.a), the exergy costing is defined in terms of risk [16]: this assumption is here made only for the product E_ P and the risk R_ P to produce it. This assumption is possible since risk and exergy balance, connecting E_ D and E_ P , are demonstrated to be somehow correlated through the parameters of the system, through Eqs. (4) and (5). It is worth mentioning nonetheless that Eq. (8.a) does not state that RP is dependent from the specific exergy of E_ P , as also underlined in [3], but only that the risk R of producing a product is allocated to the product itself (see par. 5.4) Eq. (8.b) is the exergy balance at component k as Eq. (6.b), where E_ F;k is the exergy input (Fuel) in component k, E_ P;k is the exergy output (Product), E_ L;k is the eventual exergy loss and E_ D;k is the exergy destroyed in component k. The risk R of the product in Eq. (8.c) is given by two contributions (Fig. 3): R_ k is the result of the risk analysis performed on

Fig. 3. Risk balance at the k-th component and the k-th-1.

rP ¼

X

 R_ P;ki =E_ P

ð8:fÞ

and

X

ð8:gÞ

 r P;ki E_ P;ki =E_ P

ð8:hÞ

This is the real specific risk that needs to be minimised for the given production Ep. It is worth mentioning that due to the consideration made at the end of paragraph 5.1, rp is not necessary a constant and may depend on the same parameters on which E_ P and R_ P depend. 5.4. Main assumption of the formulation For the application of the Thermoeconomic approach, two further assumptions are required to the model: (1) the possibility of setting a cumulated risk balance, (2) the coherence of the exergy costing principle expressed in terms of risk (Eq. (8.a)). These two additional assumptions are addressed here in details. Cumulated risk balance: the assumption of Eq. (8.c) is enforced by the analysis of risk assessment procedures [24] according to which the total risk R of a system is given by the sum of all the different sources of risk existing in the system, so it is possible to write [17]:

R¼

n X m n X m X X Ri;k ¼ ðpi  F si Þ k¼1 i¼1

ð8:iÞ

k¼1 i¼1

where i represents the i-th hazard in the k-th component of the system. Eq. (8.c) therefore expresses the risk R_ P of the product E_ P of the system, as the sum of all the risks related to the processes required to produce E_ P . Exergy costing principle in terms of R: in pure Thermoeconomics the exergy costing principle [16] gives the correlation between the monetary cost of a stream and its exergy (Eq. (6.a)). This principle assigns the economic value of a general stream j to the effective utility (E_ j ) of j, rather than its energy. In the model a similar assumption is made by considering the risk as a cost to accept for the society, not expressed in terms of monetary cost, but in terms of possible damage on human health [25]. Hence the risk of the product of the system is assigned proportionally to the effective utility generated by the system. In this vision, the willingness to accept the risk associated to a process is function of the obtainable utility (e.g. the same idea behind the action of taking a flight despite the risk of accident).

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6. A Case study: correlation between exergy, operating parameters and exergy efficiency in a geothermal binary power plant In this paragraph a simple application of the model is presented with the main goal to clarify some of the assumptions made in the formulation. The example reported is a geothermal binary power plant using an Organic Rankine Cycle with R134a as refrigerant. The simulation has been performed with the tool Aspen Plus Ò and Microsoft ExcelÒ with the support of tool RefpropÒ to evaluate the fluids properties. The scheme is represented in Fig. 4. The plant produces a net power of 75 kW exploiting a geother_ geo rate of 17 kg/s at 77 °C. The Rankine cycle is mal water flow m supposed to be saturate and the condensation to perform through an air condenser. The refrigerant flow rate calculated assuming a _ R134a = 5.1 kg/s. reference temperature Tenv = 15 °C is m Risks identified in the system are supposed only related to R134a leakage from ORC, leading to toxic R134a release hazard, R_ ORC , and to accidental emission of H2S in drilling operation, as second hazard of toxic emission, R_ drill . The evaluation of risks is performed according to quantitative risk analysis as obtained from [17]. Exergy analysis of the system: In Table 4 the results of the exergy analysis of the system are represented. Risk Analysis of the ORC plant: The risk analysis of the system has been performed considering the following data: Values of FR134a and FH2S have been evaluated through Probit equation (Eq. (2)), considering the concentration of refrigerant and H2S respectively as injury factors xi. Applying Eq. (13) with data from Table 5 and considering a hazard in each component of the ORC cycle, the total risk of the ORC plant is given by:

Table 4 Exergy analysis of the geothermal power plant. E_ F E_ p

_ geo ðegeo;in  egeo;out Þ E_ Q_ in ¼ m E_ _ ¼ E_ _  E_ _

204 kW

E_ l E_ d

_ air ðeout;air  ein;air Þ E_ Q_ out ¼ m E_ _  E_ _  E_ _

52,6 kW

W

Q in E_ W_ E_ _

gII

WT

W

WP

Q out

75 kW

75.9 kW 0.37

Q in

Table 5 Data for risk analysis of the geothermal power plant. Hazardous events Injury factors

Release flow rate H2S content in geofluid Frequency P of releases of refrigerant from components

Frequency of release of geothermal fluid from pipe Shut down valve probability Exposure time Probability of injury from refrigerant release FR134a Probability of injury from accidental H2S emission FH2S

– R134a toxic release – Accidental H2S emission – Concentration of R134a released – H2S concentration in accidental emission _ R134a 100% m 15 mmol/kg geo [27] Turbine 0.011 y1 Evaporator and condenser 0.007 y1 Pump 0.007 y1 [28] 0.05 y1 [28] 1.4  105 y1 [28] 1s 0.97 [17,29] 0.19 [17,29]

R_ ORC ¼ R_ Turb þ R_ Evap þ R_ Cond þ R_ Pump ¼ 4:45  109 y1

The risk associated to the system k is therefore the risk of the ORC plant:

R_ drill ¼ 1:35  107 y1

R_ k ¼ R_ ORC ¼ 4:45  109 y1

Considering Eq. (8.c) of the model, the product of the system is the net power generated by the ORC, thus we can indicate the risk associated to the product as the cumulated:

R_ P ¼ R_ drill þ R_ ORC ¼ 1:39  107 y1

while the risk associated to upstream component R_ F;k is the risk of drilling:

R_ F ¼ R_ drill ¼ 13:5  108 y1 R_ F is much more relevant compared to the risk of the ORC cycle, as the probability of the event of geothermal fluid pipeline rupture is higher than the probability of components failures. The specific risk rP can be therefore evaluated:

rP ¼

R_ P ¼ 1:86  109 y1 J1 E_ P

At the variation of operating parameters of the system, risk evaluated and exergy balance are expected to change, according to Eq. (4) and (5). Three variations for the operative conditions of the plants are here presented to show the comprehensive set of information that can be obtained by the application of the model. 6.1. First case

Fig. 4. Scheme of ORC geothermal plant.

In the first case the reference temperature Tenv is modified and a variation of E_ P produced is observed. In Table 6 results are presented and we can observe that at lower Tenv the efficiency of the plant increases, producing higher E_ P . Configuration A is the base configuration previously introduced. In all the configurations R_ P re_ geo and m _ R134a do not experience any mains constant since m variation. Here we can see how the minimization of specific risk rP leads to the configuration characterized by higher E_ P , even if the three

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Table 6 Results of simulation 1: variable Tenv and E_ P . Configuration A B C

Tenv (°C) 15 10 20

gII 0.37 0.42 0.32

E_ P (kW) 75.0 87.5 62.9

Table 7 Results of simulation 2: variable DTPP and E_ P constant. rP (y1 J1)

R_ P (y1) 8

13.95  10 13.95  108 13.95  108

Configuration

DTPP (°C)

mr134a (kg/ s)

gII

R_ P (y1)

rP (y1 J1)

A B C

10 8 12

5.1 4.8 5.5

0.37 0.39 0.34

13.95  108 13.94  108 13.96  108

1.86  109 1.85  109 1.86  109

9

1.86  10 1.59  109 2.21  109

configurations present the same global RP. In Figs. 5 and 6 the values of rP for configurations A, B and C according to Tenv and gII are represented.

6.2. Second case In the second case the pinch point delta temperature in the evaporator is modified while E_ P is kept constant. On the _ R134a is modified and R_ P along with it. Results are consequence, m presented in Table 7. Also in this case we can see that the lowest value of rP is found in the configuration characterized by the highest efficiency gII, that corresponds to the configuration with the smallest pinch point temperature DTPP and lowest R_ P . Therefore, in this case, minimizing rP and R_ P leads to the same configuration since the product is constant. In Fig. 7 and 8, R_ P as a function of DTPP and rP as a function of gII are represented.

Fig. 7. Simulation 2: R_ P (y1) in configurations A, B and C according to DTPP (°C).

6.3. Third case In the last case we choose to modify DTPP and observe the variation of the power produced E_ P . In order to maintain the cycle _ R134a is modified. In Table 8 saturated the refrigerant flow rate m values obtained for this case are shown.

Fig. 8. Simulation 2: rP (y1 J1) in configurations A, B and C according to gII.

In Fig. 9 values of R_ P versus DTPP for the three configurations are represented. It is possible to evince that the configuration with the lowest total risk R_ P is the one characterized by the highest DTPP.

Fig. 5. Simulation 1: rP (y1 J1) in configurations A, B and C according to Tenv (°C).

The same configuration however reports the highest value of rP (Fig. 10). In this case therefore the minimization of the total risk R_ P and the specific risk rP brings to different favorite configurations. This situation is then more complex compared to the previous two for the decision maker, who has to select the final configuration. The favorite configuration for the society is generally the configuration that guarantees the lowest total risk R_ P , but in this case this means to accept a lower benefit, represented by E_ P . The decision maker has thus to evaluate which is the power supply that better fits the need of the society and decide on the consequence the configuration representing the best trade off. Value of rP can be helpful thus to operate the best decision taking into account that it represents the marginal risk per unit of power produced. 7. Discussion

Fig. 6. Simulation 1: rP (y1 J1) in configurations A, B and C according to gII.

Results of the case study lead to three relevant statements. First, since the highest contribution of R_ P;k is given by the risk associated to upstream component R_ F;k , corresponding to the risk of drilling R_ drill , it appears therefore the advantage to consider the cumulated

G. Cassetti, E. Colombo / Energy Conversion and Management 76 (2013) 874–882 Table 8 Results of simulation 3: variable DTPP and E_ P . Configuration

TPP (°C)

mr134a (kg/s)

gII

E_ P (kW)

R_ P (y1)

rP (y1 J1)

A B C

10 8 12

5.1 6.1 4.1

0.37 0.39 0.34

75 89.6 60.4

13.95  108 13.97  108 13.91  108

1.86  109 1.55  109 2.30  109

Fig. 9. Simulation 3: R_ P (y1) in configurations A, B and C according to DTPP (°C).

881

correlation between the design of system processes and their associated risk is proposed. The driving assumptions of the formulation are the validity of the cumulated risk balance (Eq. (8.c)), dual of cost balance in pure Thermoeconomics (Eq. (6.c)) and the validity of the exergy costing principle expressed in terms of risk (Eq. (8.a)) rather than in monetary cost (Eq. (6.a)). These assumptions are analyzed in detail: the definition of a cumulated risk balance is corroborated by procedure of classical risk analysis, according to which the total risk R associated to a system is given by the sum of all the different sources of risk existing in the system. The exergy costing principle is expressed in terms of risk since it is conceived as a cost for the society: not given in terms of monetary proxy, but in terms of adverse effect eventually generated by a risk source. The model can thus be used to assess the impact from major accidents in an energy system, and integrated to methodologies that evaluate impacts from other complementary perspectives, it can supply a more complete understanding of the global impact of a system. Results of the model may also be used to delineate specific indications for the system design and the identification of the safety measures required in line with the international standards. The model might also supply useful information in decision making process about the selection of the system configuration that best fits the needs of society compared to the risk to accept. Concluding, the present formulation refers to human health safety, but it might be extended to the ecological asset once provided that a proper indicator representing the risk for ecosystems and biosystems is identified and available, thus opening further opportunities for applying Combined Risk and Exergy Analysis modeling. References

Fig. 10. Simulation 2: rP (y1 J1) in configurations A, B and C according to gII.

risk rather than solely R_ k in system design. A relevant source of risk would not be otherwise properly addressed. Second, the application of the model might allow to understand the sensitivity of R_ P;k to evaluating whether or not the thermodynamic inefficiency causes a higher level of risk in the overall system, compared to a better efficient configuration. Third, results obtained in the case study show that for a given need from the society (the product E_ P ) the lowest risk R_ P can be associated with the most efficient configuration of the plant, but in other cases where E_ P is variable, the minimization of specific risk rP can supply additional information to the decision maker for selecting the final configuration that can differ from the choice of the lowest R_ P . Hence the model might finally give a contribution to the Risk Management of energy systems. 8. Conclusion The model presented in the paper integrates the exergy and the quantitative risk analysis of a system. The aim is to identify the elements of highest impacts in terms of damage to human health and evaluate the influence of exergy destruction and losses of the system. It is structured as a dual model to Thermoeconomics and the

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