- Email: [email protected]
Exergoeconomic analysis with reliability and availability considerations of a nuclear energy-based combined cycle power plant
Energy 96 (2016) 187e196
Contents lists available at ScienceDirect
Energy journal homepage: www.elsevier.com/locate/energy
Exergoeconomic analysis with reliability and availability considerations of a nuclear energy-based combined cycle power plant V. Zare* Faculty of Mechanical Engineering, Urmia University of Technology, Urmia, Iran
a r t i c l e i n f o
a b s t r a c t
Article history: Received 30 June 2015 Received in revised form 15 October 2015 Accepted 16 December 2015 Available online xxx
The reliability and availability considerations are introduced in the exergoeconomic investigation of a combined cycle power plant in which an organic Rankine cycle is employed to recover the waste heat from a GT-MHR (Gas Turbine Modular Helium Reactor) power plant. The SPECO (specific exergy costing) theory is employed to investigate the exergoeconomic performance of the system and assess the specific cost of the output power. For the reliability analysis, however, the SSM (state-space method) along with the probabilistic analysis of Markov processes is employed. After conducting a parametric analysis, the performance of the cycle is optimized with respect to the specific cost of output power, with and without reliability considerations. The effects of the system failure and repair rates are examined on the cost of power and availability of the combined cycle by the sensitivity analysis. The optimization results show that, the specific cost of output power for the combined cycle is around 12% lower than that for the stand alone GT-MHR. However, availability of the combined cycle is lower than that of the GT-MHR as the former has more components and a complicated system. © 2015 Elsevier Ltd. All rights reserved.
Keywords: Availability Exergoeconomics GT-MHR (Gas Turbine Modular Helium Reactor) Organic Rankine cycle Reliability
1. Introduction Industrial plants as well as energy conversion systems are made from a large number of components, with multiple interactions and functional dependencies. Failure of a component may result in failure of a sub-system or the whole system with various detrimental consequences which necessitates the consideration of systems' reliability and availability characteristics in the design and implementation stages [1]. To increase competitiveness and market value of energy conversion systems, analyzing the influence on the generated power cost of equipment reliability is of major importance that leads to achieving more realistic and rational results for the system designers. Recently, some efforts have been devoted in literature to incorporate reliability and availability considerations in investigation of energy-related technologies and systems [2e5]. However, a few research works are reported to date in inclusion of reliability considerations in thermoeconomic (exergoeconomic) analysis of energy conversion systems. For a combined power and multi stage flash desalination plant, equipment reliability is incorporated in
* Tel.: þ98 4431980228. E-mail address: [email protected]. http://dx.doi.org/10.1016/j.energy.2015.12.060 0360-5442/© 2015 Elsevier Ltd. All rights reserved.
thermoeconomic analysis using the state space and continuous Markov method by Hosseini et al. [6]. They concluded that, the produced power and fresh water costs is increased by 4.1% and 6.4%, with reliability considerations. Incorporation of reliability and availability considerations in thermoeconomic modeling of a cogeneration of power and steam plant is presented by Frangopoulos et al. [1], who reported that the profit values are overestimated when reliability considerations are ignored. El-Nashar [7] incorporated equipment reliability considerations in the optimal design of cogeneration systems for power and desalination. In recent years, among the new options in power generation arena, a lot of attention has been paid to GT-MHR (Gas Turbine Modular Helium Reactor) in which a helium-cooled nuclear reactor is coupled with a high efficiency closed Brayton cycle. With a helium temperature of 850 C at the turbine inlet, the thermal efficiency of the GT-MHR cycle can reach 48% [8]. The huge amount (about 300 MW) of waste heat rejected via the pre-cooler of the GTMHR power plant is an ideal energy source to produce power employing suitable thermodynamic cycles. The waste heat from the large fossil and nuclear power plants, depending on its temperature level, can be utilized for different purposes. The high or medium temperate waste heat can be directly used for power generation and seawater desalination while low temperature waste heat has other usages such as space heating, water heating, heating of
188
V. Zare / Energy 96 (2016) 187e196
Nomenclature A C_ c E_ h ir m_ P Pre Q_ r Rec s T Z_
availability cost rate ($ h1) specific exergy cost ($ GJ1) exergy rate (kW) specific enthalpy (kJ kg1) interest rate mass flow rate (kg s1) pressure (bar) pre-cooler heat transfer rate (kW) pressure ratio recuperator specific entropy (kJ kg1 K1) temperature ( C or K) investment cost rate of components ($ h1)
Subscripts and abbreviations 0 ambient CBC closed Brayton cycle C compressor ch chemical
greenhouses and drying processes. For power generation from the waste heat the organic Rankine and Kalina cycles are the best alternatives. In the context of GT-MHR waste heat utilization, some research works are recently reported by the author [9e13] and others [14e18], none of which includes reliability and availability considerations. The idea of GT-MHR waste heat utilization was first proposed by Nisan et al. [15,16] who suggested employing the waste heat for desalination purposes. Utilizing the GT-MHR waste heat, other attempts are made to produce power and/or cooling by means of appropriate thermodynamic cycles. Comparing three ORC (organic Rankine cycle) configurations (simple ORC, regenerative ORC and ORC with internal heat exchanger) for GT-MHR waste heat recovery, Yari and mahmoudi [18] showed that the simple ORC performs better than regenerative ORC and ORC with internal heat exchanger. The utilization of GT-MHR waste heat for power and cooling cogeneration, using an ammonia-water cogeneration cycle, is proposed and analyzed by Zare et al. [9,10]. They showed that, at the optimum operating conditions, the unit cost of product for the combined cycle is 5.4% lower than that for the stand alone GT-MHR [10]. The utilization of GT-MHR waste heat for power production and water purification is proposed and analyzed by Zare et al. [11]. Zare and Mahmoudi [12] concluded that employing the ORC for GTMHR waste heat recovery leads to a higher first and second law efficiencies than the Kalina cycle. The performance of the stand alone GT-MHR with the proposed combined GT-MHR/Kalina cycle is compared by Zare et al. [13] from the exergoeconomic perspective. Their results indicate that the efficiency and the unit cost of product for the combined cycle is 8.2% higher and 8.8% lower than the corresponding values for the GT-MHR. In the present paper, the performance of a combined GT-MHR/ ORC is investigated and compared with that of the stand alone GT-MHR cycle. Both thermodynamic and economic analyses are performed where the SPECO (specific exergy costing) method is employing for exergoeconomic modeling. In most of the related publications, it is assumed that the system equipments are available for operation at any instant of time and reliability and availability aspects have been given less importance, if any at all. In the
CI CRF CD D Eva GT OM ORC RC ph pp Sup
capital investment capital recovery factor condenser destruction evaporator gas turbine operation and maintenance organic Rankine cycle reactor core physical pinch point superheater
Greek symbols ε effectiveness t annual plant operation hours hs,p pump isentropic efficiency hs,t turbine isentropic efficiency hP,C compressor polytropic efficiency l failure rate m repair rate hP,GT gas turbine polytropic efficiency
present work however, the reliability and availability considerations are incorporated in the analysis to account for the consequences of occurring failures and subsequent time for repairs. 2. System description Fig. 1 shows the schematic diagrams of the stand alone GT-MHR cycle and the combined GT-MHR/ORC, in which the GT-MHR waste heat is recovered by an organic Rankine cycle. In the GT-MHR cycle (Fig. 1(a)), the helium, as the reactor coolant and the Brayton cycle working fluid, is heated in the nuclear reactor to a temperature of 850 C and then is expanded in the turbine to generate power to drive the compressor and the electric generator. From the turbine exhaust (stream 2), the helium flows through the hot side of the recuperator before entering the pre-cooler where it is cooled from 150 to 200 C (stream 3), to about 30 C (stream 4), to reduce the power consumed by the compressor. The rejected heat from the helium in the pre-cooler is utilized to generate power employing an ORC, in the combined cycle as illustrated in Fig. 1 (b). Referring to Fig. 1(b), the helium flows through the superheater and the evaporator of the ORC before entering the pre-cooler, so that some part of the waste heat from the GT-MHR is recovered by the ORC. In the present work, among various ORC configurations, the simple one is employed due to its better performance compared to the other configurations for GT-MHR waste heat recovery [18]. Also, four candidate working fluids, namely n-pentane, R245fa, R123 and R141b are selected for the ORC and the performance of the combined cycle is examined for each of them. The following assumptions are made in the present study: 1. The systems operate in steady state conditions and changes in kinetic and potential energies are ignored. 2. For the GT-MHR cycle components, appropriate values (as given in Table 3) are assumed for pressure losses while the pressure losses in the ORC are neglected. 3. Polytropic efficiencies (as given in Table 3) are assumed for the compressor and turbine in the GT-MHR cycle.
V. Zare / Energy 96 (2016) 187e196
189
Other assumptions and input parameters for systems' analyses are provided in detail in Table 3. 3. Modeling and analysis 3.1. Thermodynamic analysis To perform a thermodynamic analysis, each system component is considered as a control volume for which the mass and energy conservation as well as the second law principles are applied. To simulate the performance of each cycle, these equations are solved using the computer programs developed by the EES (engineering equation solver) software. In evaluating the cycles' performances more attention is paid to the second law or exergy analysis as it provides rational understanding of the system performance. Considering the fact that, for the systems under consideration, the chemical exergy is canceled out in the exergy balance equations and ignoring the kinetic and potential exergies the flow exergy of a fluid stream can be written as:
_ h0 Þ T0 ðs s0 Þ E_ ¼ E_ ke þ E_ pe þ E_ ph þ E_ ch ¼ E_ ph ¼ m½ðh
(1)
In evaluating the systems' performances from the first law viewpoint, the first law or thermal efficiency may be expressed as:
hI ¼
_ net W _ net W ¼ _ _ Q in Q core
(2)
_ net is the net output power and Q_ core is the rate of thermal where W energy released from the nuclear fission and transferred to the helium in the reactor core. The second law or exergy efficiency of the considered cycles may be defined as:
hII ¼
_ net W E_
(3)
in
where E_ in is the total inflow exergy to the helium associated with the heat transfer in the nuclear reactor. Since the fission temperature is much higher than that of the environment, Tfission [T0 , the exergy transfer associated with heat transfer to the helium is approximately equal to the heat released from the nuclear fission, i.e. E_ in ¼ Q_ core [20]. Therefore, the second law efficiency can be expressed as:
hII ¼
_ net W _ net W ¼ _ E_ in Q core
(4)
Regarding the recent equations, it can be concluded that for both of the cycles (stand alone GT-MHR and the combined cycle) the first and second law efficiencies are the same. 3.2. Exergoeconomic analysis
Fig. 1. Schematic diagrams of the investigated cycles: a) GT-MHR cycle; b) combined GT-MHR/ORC.
4. Isentropic efficiencies (as given in Table 3) are assumed for the pump and turbine in the ORC. 5. Constant failure and repair rates are considered for the subsystems as they are often quite adequate even though a system or some of its components may exhibit moderate early failures or aging effects [19].
In evaluating thermal systems' performances the most efficient system is not always the optimal one in terms of cost. To incorporate both the technical and economical aspects in the analysis, thermal systems should be investigated from the exergoeconomic perspective. Exergoeconomics provides a procedure to reveal the cost formation process and calculate the specific exergy cost of the system product streams. The specific exergetic cost of the products obtained from this procedure can be used as a criterion for which the cycle performance is optimized. To perform an exergoeconomic analysis, a cost balance equation along with sufficient number of auxiliary equations, are applied to
190
V. Zare / Energy 96 (2016) 187e196
each system component. For the k th component, the cost balance equation can be expressed as [21]:
X
C_ out;k ¼
X
C_ in;k þ Z_ k
cP;total
(5)
3.3. Reliability modeling Reliability can be defined as the probability that a system performs properly for a specified period of time under a given set of operating conditions. A system is said to be failed when it ceases to perform its intended function. The failure of a system means the termination of the system's ability to perform its required function. In reliability and availability modeling accurate assessment and prediction of failures is essential for more accurate reliability evaluation. However, in order to take into account the different kinds of failure it is necessary to define failure quantitatively [25]. In addition to failure rate, repair rate is another important parameter in modeling the systems' reliability. Failure rate (l) is the expected number of failures in a specific time period such as one year and repair rate (m) determines the frequency of repair in that year. These are expressed as follows [26]:
(6)
The total cost rate for the k th component can be expressed as [22,23]: CI OM Z_ k ¼ Z_ k þ Z_ k
(7)
The annual levelized capital investment, for the k th component, may be expressed as [22]: CI Z_ k ¼
CRF Zk t
(8)
Number of component failures in a given period of time Total period of time the component was operating 1 ¼ MTTF (11)
l¼
where CRF and t are the capital recovery factor and the annual plant operation hours, respectively. The CRF is a function of the interest rate, ir, and the number of years of the plant operation, n [21]:
CRF ¼
ir ð1 þ ir Þn ð1 þ ir Þn 1
(10)
It should be noted that, for the stand alone GT-MHR cycle the value of cP,total given by the above relation, is equal to the specific cost of net output power i. e.: c10.
where C_ is the cost rate associated with the outlet and inlet exergy streams and Z_ k is the total cost rate associated with capital investment and operation and maintenance costs for the k th component. The cost rates associated with the stream of matter, power and heat can be expressed as a function of specific exergy costs as follows [21]:
C_ i ¼ ci E_ i _ C_ w ¼ cw W _ _ C q ¼ cq Eq
Pnf _ Pnk _ Z þ i¼1 Z fi i¼1 k ¼ cpi ¼ Pnp _ E i¼1 i¼1 Pi np X
(9) Number of component repaires in a given period of time Total period of time the component was being repaired 1 ¼ MTTR (12)
m¼
The cost balance and auxiliary equations, for each component of the considered cycles, are given in Table 1. In evaluating the systems' performances from the exergoeconomic viewpoint in the present work, the specific cost of net output power is considered as the performance criterion. This parameter is also selected as the objective function on which the systems' performances are optimized. Such an objective function includes all the capital investment, operation and maintenance and the fuel costs as follows [24]:
where MTTF and MTTR denote the mean time to failure and the mean time to repair. Different methodologies are developed for reliability analysis during the past few years. An important method which has
Table 1 Cost balance and auxiliary equations for each system component. Component
Cost balance and auxiliary equations Stand alone GT-MHR
Combined cycle C_ 7 ¼ C_ 6 þ C_ 20 þ Z_ Compressor C_ 6 þ C_ 15 ¼ C_ 5 þ C_ 14 þ Z_ Precooler c14 ¼ 0 C_ þ C_ ¼ C_ þ C_ þ Z_
Gas turbine
C_ 5 ¼ C_ 4 þ C_ 9 þ Z_ Compressor C_ 4 þ C_ 8 ¼ C_ 3 þ C_ 7 þ Z_ Precooler c7 ¼ 0 C_ 3 þ C_ 6 ¼ C_ 2 þ C_ 5 þ Z_ Recuperator c3 ¼ c2 C_ þ C_ þ C_ ¼ C_ þ Z_
Reactor
c1 ¼ c2, c9 ¼ c10 C_ 1 ¼ C_ 6 þ Z_ Reactor þ Z_ fuel
Evaporator
e
Superheater
e
ORC turbine
e
C_ 11 þ C_ 5 ¼ C_ 10 þ C_ 4 þ Z_ Evaporator c4 ¼ c5 C_ 12 þ C_ 4 ¼ C_ 3 þ C_ 11 þ Z_ SuperHeater c4 ¼ c3 C_ þ C_ ¼ C_ þ Z_
e
þ C_ 13 þ Z_ Condenser
Compressor Pre-cooler Recuperator
Condenser Pump
2
e
9
10
1
Turbine
3
8
7
2
Recuperator
c3 ¼ c2 C_ 2 þ C_ 21 þ C_ 20 ¼ C_ 1 þ Z_ Turbine c1 ¼ c2, c20 ¼ c21 C_ ¼ C_ þ Z_ Reactor þ Z_ 1
13
8
19
c12 ¼ c13 C_ þ C_ ¼ C_ 9
17
fuel
12
16
Turbine
c16 ¼ 0 C_ 10 ¼ C_ 18 þ C_ 9 þ Z_ Pump c18 ¼ c19
V. Zare / Energy 96 (2016) 187e196
received more attention is known as the Markov approach by which many component failure interactions can be modeled effectively. In the present work the state space method, which is based on the probabilistic analysis of Markov model, is selected as it is suitable for large, complex repairable systems and is appropriate for quantitative analysis [6]. In order to assess the continuous Markov processes the appropriate state space diagram is constructed and all the possible states for the system are incorporated in such a diagram. For the reliability modeling of the considered combined cycle in the present study, the cycle is divided into three sub-systems including: reactor core (i ¼ 1), closed Brayton cycle (i ¼ 2) and
2 6 6 6 6 6 M¼ 6 6 6 6 6 4
191
multiplication method, differential equation method, frequency balance method and stochastic transitional probability matrix method [2]. The last method is employed in the present work due to its simplicity. In this approach, the steady state probabilities can be found from Ref. [26]:
aM ¼ a
(13)
where a and M represent the steady state probability vector and the stochastic transitional probability matrix, respectively. For the considered combined cycle the transitional probability matrix may be expressed as follows:
3 1ðl1 þl2 þl3 Þ l1 l2 l3 0 0 0 0 7 1ðm1 þl2 þl3 Þ 0 0 l2 0 l3 0 m1 7 7 0 1ðm2 þl1 þl3 Þ 0 l1 l3 0 0 m2 7 7 0 0 1ðm3 þl1 þl2 Þ 0 l2 l1 0 m3 7 7 m1 0 1ðm2 þm1 þl3 Þ 0 0 l3 0 m2 7 7 0 0 m3 m2 0 1ðm2 þm3 þl1 Þ 0 l1 7 5 0 m3 0 m1 0 0 1ðm1 þm3 þl2 Þ l2 0 0 0 0 m3 m1 m2 1ðm3 þm1 þm2 Þ (14)
organic Rankine cycle (i ¼ 3). Considering two situations (operating or failed) for each sub-system, there will be a total number of 23 ¼ 8 possible states for the combined GT-MHR/ORC as illustrated by the state space diagram in Fig. 2. It is worth mentioning that, for the case of stand alone GT-MHR, the cycle is divided into two subsystems (reactor core and closed Brayton cycle) and the related state space diagram comprises of 22 ¼ 4 possible states. The probabilities of each system state are determined using the continuous Markov process by certain solution methods. Some of existing methods for evaluating state probabilities are: Matrix
Once the i'th state probability, Pi , for all 8 states for the combined cycle (and 4 states for the stand alone GT-MHR) are determined, they can be used to evaluate the specific cost of output power with reliability considerations as follows [6]:
cP ¼
X
Pi cPi
(15)
where, the state probabilities are used as weights for every operating state. As will be shown, the effect of equipment reliability inclusion in the analysis is to increase the power cost due to the unexpected equipment downtime as a result of system failures and the subsequent repairs. From the above mentioned definition of reliability, it is evident that it relates to the ability of a system to continue functioning without failure. This interpretation of the reliability, however, is an unsuitable measure for continuously operating systems that can tolerate failures. For these systems another criterion referred to as availability is suitable to be used. The availability can be interpreted as the probability of finding the component/system in the operating state at some time into the future [26]. The availability of the considered combined cycle, consisting of three sub-systems (RC (reactor core), CBC (closed Brayton cycle) and ORC), can be expressed as [6]:
A¼
mRC mCBC mORC ðlRC þ mRC ÞðlCBC þ mCBC ÞðlORC þ mORC Þ
(16)
4. Results and discussion
Fig. 2. State space diagram for the combined cycle.
In this section parametric studies are performed to assess the influence of decision variables on exergoeconomic performance of the stand alone GT-MHR and the combined cycle. The cycles are then optimized from the exergoconomic viewpoint. To evaluate the effect of reliability considerations in the exergoeconomic analysis the optimization is performed for two cases; one with incorporation of reliability considerations into the analysis and the other without considering the reliability aspects in the analysis.
192
V. Zare / Energy 96 (2016) 187e196
Table 2 Performance parameters for the GT-MHR cycle and the ORC; (a) present work, (b) Ref. [27] (c) Ref. [28]. Stand alone GT-MHR cyclea
(a)
(b)
ORCb
(a)
(c)
Turbine power (MW) Compressor power (MW) Pre-cooler heat load (MW) Recuperator heat load (MW) Helium mass flow rate (kg/s)
552.8 248.3 295.6 970.7 401.1
538.8 243.8 310.2 966.5 401.0
Net work output (kJ/kg) First law efficiency (%) Second law efficiency (%)
48.65 12.68 47.38
48.57 12.6 46.8
a b
T1 ¼ 900 C, rc ¼ 2.10. TEvaporator ¼ 120 C, TCondenser ¼ 40 C.
Table 3 The input data assumed in the simulation. Parameter
Symbol
Value
Ambient (dead state) pressure Ambient (dead state) temperature Heat released from the nuclear fission
P0 (bar) T0( C) Q_ ðMWÞ
1 15 600a
Reactor outlet temperature Pressure loss in reactor Pressure loss in pre-cooler Pressure loss in recuperator (high pressure side) Pressure loss in recuperator (low pressure side) Pressure loss in evaporator Pressure loss in superheater Gas turbine polytropic efficiency Compressor polytropic efficiency Pump isentropic efficiency ORC turbine isentropic efficiency Pinch point temperature difference Recuperator and pre-cooler effectiveness Interest rate ORC economic life GT-MHR economic life Fuel cost CBC failure rate CBC repair rate Reactor core failure rate Reactor core repair rate ORC failure rate ORC repair rate a b c d e
core
T1( C) DPcore(bar) DPPre(bar) DPRec, HP(bar) DPRec, LP(bar) DPEva(bar) DPSup(bar)
hP,GT hP,C hs,P (%) hs,T (%) DTPP ( C)
ε (%) ir (%) n (year) n (year) Zf ($/MWh) l (per day) m (per day) l (per day) m (per day) l (per day) m (per day)
850a 1b 0.4b 0.8b 0.5b 0.4b 0.2b 0.9160.0175 ln(rc)a 0.9320.0117 ln(rT)a 85 85 5 95c 10 20 60d 7.4d 0.00274e 0.1e 0.00274 0.0833 0.00274 0.14
[27]. [9]. [29]. [30]. [7].
4.1. Verification of simulation models To verify the thermodynamic simulation and modeling of the investigated cycles the results of the present work are compared with those reported in the literature [27,28] as shown in Table 2. Also verification of the exergoeconomic modeling is performed by comparing the results obtained from the present study with those published previously by the author [13]. The figures given in Table 2 indicate a good agreement between the values of parameters calculated in the present study and those reported in the literature. The considered assumptions and input parameters in investigating the considered cycles are summarized in Table 3. A parametric study is performed to examine the effects on the performance of the GT-MHR and the combined cycle of the decision variables. For the parametric study n-pentane is assumed as the ORC working fluid, however, for optimizing the combined cycle performance four working fluids are considered, as mentioned before. For the stand alone GT-MHR cycle, the only decision variable is the compressor pressure ratio (rc), keeping in mind that the other parameters of Brayton cycle (such as helium turbine inlet temperature) are assumed to be constant as given in Table 3. For the combined cycle, however, there exist three decision variables, namely; rc, TEva and DTsup.
Fig. 3 shows the effects on the efficiency (note that hI ¼ hII) of the compressor pressure ratio, for the GT-MHR and the combined cycle. Referring to Fig. 3, higher efficiency values are observed for the combined cycle compared to the standalone GT-MHR. For the
Fig. 3. Effects on the efficiency of compressor pressure ratio.
V. Zare / Energy 96 (2016) 187e196
combined cycle at some pressure ratios (for example rc < 2) the efficiency values are not shown in Fig. 3, as these rc values lead to T4 < TEva which is not practical. The variation of the specific cost of output power (cP,total) for both the cycles with the compressor pressure ratio is shown in Fig. 4. The cost values are calculated for two cases: with incorporation of reliability considerations and without it. Referring to Fig. 4, it is seen that for rc > 2.1 the cost of power for the combined cycle is lower than that for the standalone GT-MHR. Also, the power cost values obtained with incorporation of the reliability considerations are around 4.2% higher than those without reliability considerations. The higher power cost obtained with reliability considerations is due to the unexpected equipment downtime as a result of system failures and the subsequent repairs. Fig. 5 shows the variations of the efficiency and specific cost of power for the combined cycle with the evaporator temperature, TEva. Referring to Fig. 5, there exist optimum values for evaporator temperature with which the efficiency is maximized or the specific cost of power is minimized. The variation of the efficiency and specific cost of power of the combined cycle with respect to the superheating degree at the ORC turbine inlet is shown in Fig. 6. The figure indicates that, as DTsup increases, the efficiency decreases while the cP,total goes up. These trends are partly due to the reduction of GT-MHR output power as a result of helium pressure loss occurred in the superheater. In addition, an increase of DTsup, causes a decrease in ORC working fluid mass flow rate (because of a lower heat recovery in the
Fig. 4. Effects on the specific cost of power of compressor pressure ratio.
193
Fig. 6. Effects on the efficiency and the specific cost of power of superheating degree at the ORC turbine inlet.
evaporator) and consequently reduces the output power of the ORC. A reduction in net output power of the combined cycle results in a higher specific cost of power values as presented in Fig. 6. Referring to Figs. 4e6, it is evident that the power cost with and without reliability considerations are always in parallel with a constant value of difference. This trend can be justified considering Eq. (15) by which the cost of power is calculated when the reliability considerations are taken into account. It should be noted that the specified values for state probabilities corresponds only to the given values of failure and repair rates and are not affected by thermodynamic variables (such as compressor pressure ratio and/ or evaporator temperature). The effects of the system's failure rate and repair rate on the specific cost of power and system availability for the combined cycle are presented in Figs. 7 and 8. Fig. 7 indicates that as system failure rate increases, the power cost is increased (due to the increase in system downtime associated with repair actions) and the system availability is decreased. The opposite trend is observed as the system repair rate increases, as expected and shown in Fig. 8. In order to optimize the performances of the stand alone GTMHR and the combined cycle, the specific cost of output power (cP,total) is considered as the objective function. The minimum value of the objective function can be found by the solution to the following optimization problem considering the restrictions on decision variables as follows:
Minimize cP;total ðrc Þ ðfor stand alone GT MHR cycleÞ Minimize cP;total rc ; TEva ; DTsup ðfor combined cycleÞ
(17)
Subject to:
Fig. 5. Effects on the efficiency and the specific cost of power of evaporator temperature.
Fig. 7. Effects on the specific cost of power and system availability of system failure rate for the combined cycle.
194
V. Zare / Energy 96 (2016) 187e196
Fig. 8. Effects on the specific cost of power and system availability of system repair rate for the combined cycle.
around 4.3% and 4.4e4.7% for the stand alone GT-MHR and the combined cycle, respectively. The values of decision variables and important performance parameters for the two cycles, with reliability considerations at the optimized conditions, are outlined in Table 4. Also, the values of P k _ cost rate for overall system (Z_ Overall system ¼ nk¼1 Z k ) and the availability of the cycles are given in this Table. The figures in the Table indicate that, the combined cycle efficiency is higher than that of the GT-MHR by around 11.9e13.5% for different ORC working fluids among which R245fa yields the highest efficiency. Table 4 shows another interesting result which is the fact that the overall system cost rate for the combined cycle is just slightly higher than that for the stand alone GT-MHR, meaning that the efficiency enhancement and the cP,total reduction is achieved at the expense of just a negligible increase in the overall system cost rate (for instance 7860.9 $/h compared to 7787.2 $/h for n-pentane) when the ORC is combined with the GT-MHR. A close value of Z_ Overall system
for the combined cycle and the stand alone GT-MHR is in turn due to a significantly lower helium mass flow rate in the combined cycle that brings about lower components' size and cost regarding the relations given in Table A.1. Considering the availability values given in Table 4 for two cycles, it is revealed that availability of the combined cycle is lower than that of the GT-MHR as a result of having a complicated system which increases the probability of failures in the involved components and subsequent repair time. From the economic point of view, the expected loss in revenue due to system failure and downtime can be considered as an important index which can be estimated using the results of availability analysis. For the combined cycle in the present study the yearly produced energy, with and without reliability considerations, can be calculated as: Fig. 9. Specific cost of power at the optimized conditions with and without reliability considerations.
_ net 8760 ¼ 315:06 8760 W ¼ 2759926 MWh ðwithout reliability consideratiosÞ (19)
1:5 < rc < 5 100 < TEva < 170 0 < DTsup < 15
(18) _ net 8760 A ¼ 315:06 8760 0:9246 W
The values of cP,total at the optimized conditions (i.e. its minimum values) for the investigated cycles are shown in Fig. 9, for two cases of including and excluding reliability considerations. Referring to Fig. 9, it is revealed that the cP,total value for the combined cycle is around 12% lower than that for the stand alone GT-MHR and the lowest value is obtained when R141b is employed as the ORC working fluid. Fig. 9 also shows that the cP,total value obtained with taking reliability considerations into account is higher than the case when the equipment reliability is not considered. With inclusion of the reliability considerations the value of cP,total is increased by
¼ 2551827 MWh ðwith reliability consideratiosÞ (20) Thus, when reliability considerations are taken into account a loss of produced energy of 208,099 MWh is expected in a year. If a value of $50/MWh is assumed for the average selling price of electricity in the market, a huge amount of 10,404,950 $/year is estimated for the loss in revenue. This value of loss in revenue is disregarded when the reliability and availability considerations are not taken into account in the analysis.
Table 4 The values of decision variables and objectives with reliability considerations at the optimized conditions. Combined cycle with different ORC working fluids
Parameter
Stand alone GT-MHR
Compressor pressure ratio Evaporator temperature ( C)
2.328
Degree of superheat ( C)
e
2.907 157.7
e 46.83 281.01
0
0
0
0
52.51 268.46
53.14 280.47
52.87 270.01
52.41 255.64
n-pentane
Efficiency (%) _ W net;GTMHR (MW) _ W (MW) net;ORC
_ W net; total (MW) m_ Helium (kg/s) cP,total ($/GJ) Cost rate of overall system ($/h) Availability
e e 385.06 10.887 7787.2 0.9424
R245fa 2.394 131.1
R123 2.852 151.6
R141b 3.347 187.6
46.60
38.35
47.18
58.81
315.06
318.82
317.19
314.44
322.74 9.679 7860.9 0.9246
379.28 9.818 8019.3 0.9246
327.38 9.647 7880.6 0.9246
293.17 9.558 7838.4 0.9246
V. Zare / Energy 96 (2016) 187e196
5. Reliability and availability analysis of sub-systems
Table 6 Failure and repair rates assumed for the ORC components.
In the combined cycle the three subsystems are operating in series, thus generating power by the cycle needs the upper subsystem (reactor core) to be in operating mode. To conduct an availability analysis for the sub-systems (the closed Brayton cycle and the ORC) it is assumed that the reactor core is reliable (works with 100% reliability). The CBC sub-system consists of four components; GT (gas turbine), recuperator (Rec), pre-cooler (Pre) and compressor (C). For this sub-system, there will be a total number of 24 ¼ 16 possible states and the 16 steady state probabilities; P ¼ [P1, P2, …, P16] can be found using frequency balance method. It is obvious that the only operating mode of the CBC is the case when all the four components are working properly for which the steady state probability can be expressed as [2,5]:
P1 ¼
mGT mRec mPre mC ðlGT þ mGT ÞðlRec þ mRec ÞðlPre þ mPre ÞðlC þ mC Þ
(21)
This value equals to the availability of the CBC sub-system. For given values of failure and repair rates of the CBC components the availability of this sub-system, assuming a reliable operation for the reactor core, can be assessed. For the given values in Table 5, the availability of the CBC is calculated as:
A ¼ P1 ¼ 0:9816
(22)
The ORC sub-system consists of five components; turbine (T), condenser (CD), pump (P), evaporator (Eva) and superheater (Sup). The results of exergoeconomic optimization (Table 4) revealed that at optimum operating conditions DTsup ¼ 0. Thus, omitting the superheater from the system, the ORC subsystem includes four major components. Similar to the case of CBC, for the ORC subsystem which is a series combination of four components, there will be a total number of 24 ¼ 16 possible states and the 16 steady state probabilities; P ¼ [P1, P2, …, P16]. The only operating mode of the ORC sub-system is the case when all the four components are working properly for which the steady state probability can be expressed as:
P1 ¼
mT mCD mP mEva ðlT þ mT ÞðlCD þ mCD ÞðlP þ mP ÞðlEva þ mEva Þ
(23)
Assuming a reliable operation for the reactor core and the CBC sub-systems, the availability of the ORC sub-system can be evaluated using Eq. (23) for given values of failure and repair rates of its components. For the given values in Table 6, the availability of the CBC is calculated as:
A ¼ P1 ¼ 0:9891
195
(24)
Component
Failure rate (per day)
Repair rate (per day)
Turbine Condenser Pump Evaporator
0.001096 0.000548 0.001096 0.000548
0.25 0.5 0.25 0.5
utilized in an organic Rankine cycle. The exergoeconomic performance assessment is extended to include the often-forgotten criteria in literature: reliability and availability. As it is expected, the thermodynamic efficiency of the combined cycle is higher than that of the stand alone GT-MHR due to the waste heat recovery. However, the results of exergoeconomic analysis revealed that, the thermodynamic performance enhancement is achieved by just a negligible increase in total investment cost rate, implying an attractive outcome. The parametric study showed that, decreasing system failure rate and/or increasing system repair rate, increases the availability of the combined cycle and decreases the cost of output power. At the optimum operating conditions, the following findings are obtained quantitatively when the ORC is combined with the GT-MHR: 1) The combined cycle efficiency is higher than that of the GT-MHR by around 11.9e13.5%. 2) The specific cost of output power for the combined cycle is about 12% lower than that for the stand alone GT-MHR. 3) The overall system cost rate for the combined cycle is higher than that of the GT-MHR by a negligible amount (for instance 7838.4 $/h compared to 7787.2 $/h for R141b). 4) When the reliability considerations are taken into account the specific cost of power is increased by around 4.3% and 4.4e4.7% for the stand alone GT-MHR and combined cycle, respectively. 5) As a result of having more components and complicated system, availability of the combined cycle is lower than that of the GTMHR (0.9246 compared to 0.9424).
Appendix A. Investment costs of the system components For an exergoeconomic analysis, the purchased equipment cost of each system component should be expressed as a function of thermodynamic variables. Some of these variables are: temperature, pressure or other related variables to these, such as; mass flow rate, generated or consumed power (for turbine and compressor) and heat transfer area (for heat exchangers). The cost functions for each component of the investigated cycles in the present study are listed in Table A.1.
6. Conclusions A comprehensive exergoeconomic analysis and optimization is presented for a combined cycle power plant in which the waste heat from GT-MHR (Gas Turbine Modular Helium Reactor) is
Table A.1Cost functions for system components [10,31,32]. System component Gas turbine Compressor
Table 5 Failure and repair rates assumed for the CBC components.
Cost function m_ He 479:34 0:93h lnðrT Þð1 þ e0:036T1 54:4 Þ GT m_ He 71:1 0:91h rc lnðrc Þ C
Reactor core
Component
Failure rate (per day)
Repair rate (per day)
Gas turbine Recuperator Pre-cooler Compressor
0.00137 0.000822 0.000822 0.00137
0.20 0.333 0.333 0.20
Recuperator Pre-cooler ORC Turbine Pump Heat exchangers of ORC
283 Q_ core 2681 A0.59 2143 A0.514 _ 0:7 4405 W _ 0:8 1120 W 2143 A0.514
196
V. Zare / Energy 96 (2016) 187e196
References [1] Frangopoulos C. Effect of reliability considerations on the optimal synthesis, design and operation of a cogeneration system. Energy 2004;29:309e29. http://dx.doi.org/10.1016/S0360-5442(02)00031-2. [2] Haghifam MR, Manbachi M. Reliability and availability modelling of combined heat and power (CHP) systems. Int J Electr Power Energy Syst 2011;33: 385e93. http://dx.doi.org/10.1016/j.ijepes.2010.08.035. [3] Eti MC, Ogaji SOT, Probert SD. Reliability of the Afam electric power generating station, Nigeria. Appl Energy 2004;77:309e15. http://dx.doi.org/ 10.1016/S0306-2619(03)00094-1. [4] Koeppel G, Andersson G. Reliability modeling of multi-carrier energy systems. Energy 2009;34:235e44. http://dx.doi.org/10.1016/j.energy.2008.04.012. [5] Wang JJ, Fu C, Yang K, Zhang XT, Shi GH, Zhai J. Reliability and availability analysis of redundant BCHP (building cooling, heating and power) system. Energy 2013;61:531e40. http://dx.doi.org/10.1016/j.energy.2013.09.018. [6] Hosseini SR, Amidpour M, Behbahaninia A. Thermoeconomic analysis with reliability consideration of a combined power and multi stage flash desalination plant. Desalination 2011;278:424e33. http://dx.doi.org/10.1016/ j.desal.2011.05.061. [7] El-Nashar AM. Optimal design of a cogeneration plant for power and desalination taking equipment reliability into consideration. Desalination 2008;229: 21e32. http://dx.doi.org/10.1016/j.desal.2007.07.024. [8] Baldwin D, Campbell M, Ellis C, Richards M, Shenoy A. MHR design, technology and applications. Energy Convers Manag 2008;49:1898e901. http:// dx.doi.org/10.1016/j.enconman.2007.07.048. [9] Zare V, Mahmoudi SMS, Yari M. Ammoniaewater cogeneration cycle for utilizing waste heat from the GT-MHR plant. Appl Therm Eng 2012;48:176e85. http://dx.doi.org/10.1016/j.applthermaleng.2012.05.009. [10] Zare V, Mahmoudi SMS, Yari M. An exergoeconomic investigation of waste heat recovery from the gas turbine-modular helium reactor (GT-MHR) employing an ammoniaewater power/cooling cycle. Energy 2013;61: 397e409. http://dx.doi.org/10.1016/j.energy.2013.09.038. [11] Zare V, Yari M, Mahmoudi SMS. Proposal and analysis of a new combined cogeneration system based on the GT-MHR cycle. Desalination 2012;286: 417e28. http://dx.doi.org/10.1016/j.desal.2011.12.001. [12] Zare V, Mahmoudi SMS. A thermodynamic comparison between organic Rankine and Kalina cycles for waste heat recovery from the gas turbinemodular helium reactor. Energy 2015;79:398e406. http://dx.doi.org/ 10.1016/j.energy.2014.11.026. [13] Zare V, Mahmoudi SMS, Yari M. On the exergoeconomic assessment of employing Kalina cycle for GT-MHR waste heat utilization. Energy Convers Manag 2015;90:364e74. http://dx.doi.org/10.1016/j.enconman.2014.11.039. [14] Nisan S, Benzarti N. A comprehensive economic evaluation of integrated desalination systems using fossil fuelled and nuclear energies and including their environmental costs. Desalination 2008;229:125e46. http://dx.doi.org/ 10.1016/j.desal.2007.07.031.
[15] Nisan S, Dardour S. Economic evaluation of nuclear desalination systems. Desalination 2007;205:231e42. [16] Dardour S, Nisan S, Charbit F. Utilisation of waste heat from GT e MHR and PBMR reactors for nuclear desalination. Desalination 2007;205:254e68. [17] Yari M. Waste heat recovery from closed Brayton cycle using organic Rankine cycle: thermodynamic analysis. In: Proceedings of ASME turbo expo, power for land, sea and air, World Marriott Resort, Orlando, FL USA; 2009 June 8e12. [18] Yari M, Mahmoudi SMS. A thermodynamic study of waste heat recovery from GT-MHR using organic Rankine cycles. Heat Mass Transf 2010;47:181e96. http://dx.doi.org/10.1007/s00231-010-0698-z. [19] Jesus F, Carazas G, Francisco G, Souza M De. Availability analysis of gas turbines used in power plants. Int J Thermodyn 2009;12:28e37. [20] Sayyaadi H, Sabzaligol T. Exergoeconomic optimization of a 1000 MW light water reactor power generation system. Int J Energy Res 2009:378e95. http:// dx.doi.org/10.1002/er. [21] Bejan A, Tsatsaronis G, Moran M. Thermal design and optimization. New York: John Wiley and Sons; 1996. [22] Zare V, Mahmoudi SMS, Yari M, Amidpour M. Thermoeconomic analysis and optimization of an ammoniaewater power/cooling cogeneration cycle. Energy 2012;47:271e83. http://dx.doi.org/10.1016/j.energy.2012.09.002. [23] Gürtürk M, Oztop HF, Hepbasli A. Comparison of exergoeconomic analysis of two different perlite expansion furnaces. Energy 2015;80:589e98. http:// dx.doi.org/10.1016/j.energy.2014.12.015. [24] Soltani S, Mahmoudi SMS, Yari M, Morosuk T, Rosen MA, Zare V. A comparative exergoeconomic analysis of two biomass and co-firing combined power plants. Energy Convers Manag 2013;76:83e91. http://dx.doi.org/ 10.1016/j.enconman.2013.07.030. [25] Lewis EE. Introduction to reliability engineering. John Wiley and Sons Inc; 1994. [26] Billinton R, Allan RN. Reliability evaluation of engineering systems: concepts and techniques. New York: Plenum Publishing; 1992. [27] El-Genk MS, Tournier J-M. Noble gas binary mixtures for gas-cooled reactor power plants. Nucl Eng Des 2008;238:1353e72. http://dx.doi.org/10.1016/ j.nucengdes.2007.10.021. [28] Yari M. Exergetic analysis of various types of geothermal power plants. Renew Energy 2010;35:112e21. http://dx.doi.org/10.1016/j.renene.2009.07.023. [29] Herranz LE, Linares JI, Moratilla BY. Power cycle assessment of nuclear high temperature gas-cooled reactors. Appl Therm Eng 2009;29:1759e65. http:// dx.doi.org/10.1016/j.applthermaleng.2008.08.006. [30] Labar MP. The gas turbine-modular helium reactor: a promising option for near term deployment. General Atom April 2002:GA-A23952. [31] Ghaebi H, Amidpour M, Karimkashi S, Rezayan O. Energy, exergy and thermoeconomic analysis of a combined cooling, heating and power (CCHP) system with gas turbine prime mover. Int J Energy Res 2011:697e709. http:// dx.doi.org/10.1002/er. [32] Guo-yan Z, En W, Shan-tung T. Techno-economic study on compact heat exchangers. Int J Energy Res 2008:1119e27. http://dx.doi.org/10.1002/er.
Contents lists available at ScienceDirect
Energy journal homepage: www.elsevier.com/locate/energy
Exergoeconomic analysis with reliability and availability considerations of a nuclear energy-based combined cycle power plant V. Zare* Faculty of Mechanical Engineering, Urmia University of Technology, Urmia, Iran
a r t i c l e i n f o
a b s t r a c t
Article history: Received 30 June 2015 Received in revised form 15 October 2015 Accepted 16 December 2015 Available online xxx
The reliability and availability considerations are introduced in the exergoeconomic investigation of a combined cycle power plant in which an organic Rankine cycle is employed to recover the waste heat from a GT-MHR (Gas Turbine Modular Helium Reactor) power plant. The SPECO (specific exergy costing) theory is employed to investigate the exergoeconomic performance of the system and assess the specific cost of the output power. For the reliability analysis, however, the SSM (state-space method) along with the probabilistic analysis of Markov processes is employed. After conducting a parametric analysis, the performance of the cycle is optimized with respect to the specific cost of output power, with and without reliability considerations. The effects of the system failure and repair rates are examined on the cost of power and availability of the combined cycle by the sensitivity analysis. The optimization results show that, the specific cost of output power for the combined cycle is around 12% lower than that for the stand alone GT-MHR. However, availability of the combined cycle is lower than that of the GT-MHR as the former has more components and a complicated system. © 2015 Elsevier Ltd. All rights reserved.
Keywords: Availability Exergoeconomics GT-MHR (Gas Turbine Modular Helium Reactor) Organic Rankine cycle Reliability
1. Introduction Industrial plants as well as energy conversion systems are made from a large number of components, with multiple interactions and functional dependencies. Failure of a component may result in failure of a sub-system or the whole system with various detrimental consequences which necessitates the consideration of systems' reliability and availability characteristics in the design and implementation stages [1]. To increase competitiveness and market value of energy conversion systems, analyzing the influence on the generated power cost of equipment reliability is of major importance that leads to achieving more realistic and rational results for the system designers. Recently, some efforts have been devoted in literature to incorporate reliability and availability considerations in investigation of energy-related technologies and systems [2e5]. However, a few research works are reported to date in inclusion of reliability considerations in thermoeconomic (exergoeconomic) analysis of energy conversion systems. For a combined power and multi stage flash desalination plant, equipment reliability is incorporated in
* Tel.: þ98 4431980228. E-mail address: [email protected]. http://dx.doi.org/10.1016/j.energy.2015.12.060 0360-5442/© 2015 Elsevier Ltd. All rights reserved.
thermoeconomic analysis using the state space and continuous Markov method by Hosseini et al. [6]. They concluded that, the produced power and fresh water costs is increased by 4.1% and 6.4%, with reliability considerations. Incorporation of reliability and availability considerations in thermoeconomic modeling of a cogeneration of power and steam plant is presented by Frangopoulos et al. [1], who reported that the profit values are overestimated when reliability considerations are ignored. El-Nashar [7] incorporated equipment reliability considerations in the optimal design of cogeneration systems for power and desalination. In recent years, among the new options in power generation arena, a lot of attention has been paid to GT-MHR (Gas Turbine Modular Helium Reactor) in which a helium-cooled nuclear reactor is coupled with a high efficiency closed Brayton cycle. With a helium temperature of 850 C at the turbine inlet, the thermal efficiency of the GT-MHR cycle can reach 48% [8]. The huge amount (about 300 MW) of waste heat rejected via the pre-cooler of the GTMHR power plant is an ideal energy source to produce power employing suitable thermodynamic cycles. The waste heat from the large fossil and nuclear power plants, depending on its temperature level, can be utilized for different purposes. The high or medium temperate waste heat can be directly used for power generation and seawater desalination while low temperature waste heat has other usages such as space heating, water heating, heating of
188
V. Zare / Energy 96 (2016) 187e196
Nomenclature A C_ c E_ h ir m_ P Pre Q_ r Rec s T Z_
availability cost rate ($ h1) specific exergy cost ($ GJ1) exergy rate (kW) specific enthalpy (kJ kg1) interest rate mass flow rate (kg s1) pressure (bar) pre-cooler heat transfer rate (kW) pressure ratio recuperator specific entropy (kJ kg1 K1) temperature ( C or K) investment cost rate of components ($ h1)
Subscripts and abbreviations 0 ambient CBC closed Brayton cycle C compressor ch chemical
greenhouses and drying processes. For power generation from the waste heat the organic Rankine and Kalina cycles are the best alternatives. In the context of GT-MHR waste heat utilization, some research works are recently reported by the author [9e13] and others [14e18], none of which includes reliability and availability considerations. The idea of GT-MHR waste heat utilization was first proposed by Nisan et al. [15,16] who suggested employing the waste heat for desalination purposes. Utilizing the GT-MHR waste heat, other attempts are made to produce power and/or cooling by means of appropriate thermodynamic cycles. Comparing three ORC (organic Rankine cycle) configurations (simple ORC, regenerative ORC and ORC with internal heat exchanger) for GT-MHR waste heat recovery, Yari and mahmoudi [18] showed that the simple ORC performs better than regenerative ORC and ORC with internal heat exchanger. The utilization of GT-MHR waste heat for power and cooling cogeneration, using an ammonia-water cogeneration cycle, is proposed and analyzed by Zare et al. [9,10]. They showed that, at the optimum operating conditions, the unit cost of product for the combined cycle is 5.4% lower than that for the stand alone GT-MHR [10]. The utilization of GT-MHR waste heat for power production and water purification is proposed and analyzed by Zare et al. [11]. Zare and Mahmoudi [12] concluded that employing the ORC for GTMHR waste heat recovery leads to a higher first and second law efficiencies than the Kalina cycle. The performance of the stand alone GT-MHR with the proposed combined GT-MHR/Kalina cycle is compared by Zare et al. [13] from the exergoeconomic perspective. Their results indicate that the efficiency and the unit cost of product for the combined cycle is 8.2% higher and 8.8% lower than the corresponding values for the GT-MHR. In the present paper, the performance of a combined GT-MHR/ ORC is investigated and compared with that of the stand alone GT-MHR cycle. Both thermodynamic and economic analyses are performed where the SPECO (specific exergy costing) method is employing for exergoeconomic modeling. In most of the related publications, it is assumed that the system equipments are available for operation at any instant of time and reliability and availability aspects have been given less importance, if any at all. In the
CI CRF CD D Eva GT OM ORC RC ph pp Sup
capital investment capital recovery factor condenser destruction evaporator gas turbine operation and maintenance organic Rankine cycle reactor core physical pinch point superheater
Greek symbols ε effectiveness t annual plant operation hours hs,p pump isentropic efficiency hs,t turbine isentropic efficiency hP,C compressor polytropic efficiency l failure rate m repair rate hP,GT gas turbine polytropic efficiency
present work however, the reliability and availability considerations are incorporated in the analysis to account for the consequences of occurring failures and subsequent time for repairs. 2. System description Fig. 1 shows the schematic diagrams of the stand alone GT-MHR cycle and the combined GT-MHR/ORC, in which the GT-MHR waste heat is recovered by an organic Rankine cycle. In the GT-MHR cycle (Fig. 1(a)), the helium, as the reactor coolant and the Brayton cycle working fluid, is heated in the nuclear reactor to a temperature of 850 C and then is expanded in the turbine to generate power to drive the compressor and the electric generator. From the turbine exhaust (stream 2), the helium flows through the hot side of the recuperator before entering the pre-cooler where it is cooled from 150 to 200 C (stream 3), to about 30 C (stream 4), to reduce the power consumed by the compressor. The rejected heat from the helium in the pre-cooler is utilized to generate power employing an ORC, in the combined cycle as illustrated in Fig. 1 (b). Referring to Fig. 1(b), the helium flows through the superheater and the evaporator of the ORC before entering the pre-cooler, so that some part of the waste heat from the GT-MHR is recovered by the ORC. In the present work, among various ORC configurations, the simple one is employed due to its better performance compared to the other configurations for GT-MHR waste heat recovery [18]. Also, four candidate working fluids, namely n-pentane, R245fa, R123 and R141b are selected for the ORC and the performance of the combined cycle is examined for each of them. The following assumptions are made in the present study: 1. The systems operate in steady state conditions and changes in kinetic and potential energies are ignored. 2. For the GT-MHR cycle components, appropriate values (as given in Table 3) are assumed for pressure losses while the pressure losses in the ORC are neglected. 3. Polytropic efficiencies (as given in Table 3) are assumed for the compressor and turbine in the GT-MHR cycle.
V. Zare / Energy 96 (2016) 187e196
189
Other assumptions and input parameters for systems' analyses are provided in detail in Table 3. 3. Modeling and analysis 3.1. Thermodynamic analysis To perform a thermodynamic analysis, each system component is considered as a control volume for which the mass and energy conservation as well as the second law principles are applied. To simulate the performance of each cycle, these equations are solved using the computer programs developed by the EES (engineering equation solver) software. In evaluating the cycles' performances more attention is paid to the second law or exergy analysis as it provides rational understanding of the system performance. Considering the fact that, for the systems under consideration, the chemical exergy is canceled out in the exergy balance equations and ignoring the kinetic and potential exergies the flow exergy of a fluid stream can be written as:
_ h0 Þ T0 ðs s0 Þ E_ ¼ E_ ke þ E_ pe þ E_ ph þ E_ ch ¼ E_ ph ¼ m½ðh
(1)
In evaluating the systems' performances from the first law viewpoint, the first law or thermal efficiency may be expressed as:
hI ¼
_ net W _ net W ¼ _ _ Q in Q core
(2)
_ net is the net output power and Q_ core is the rate of thermal where W energy released from the nuclear fission and transferred to the helium in the reactor core. The second law or exergy efficiency of the considered cycles may be defined as:
hII ¼
_ net W E_
(3)
in
where E_ in is the total inflow exergy to the helium associated with the heat transfer in the nuclear reactor. Since the fission temperature is much higher than that of the environment, Tfission [T0 , the exergy transfer associated with heat transfer to the helium is approximately equal to the heat released from the nuclear fission, i.e. E_ in ¼ Q_ core [20]. Therefore, the second law efficiency can be expressed as:
hII ¼
_ net W _ net W ¼ _ E_ in Q core
(4)
Regarding the recent equations, it can be concluded that for both of the cycles (stand alone GT-MHR and the combined cycle) the first and second law efficiencies are the same. 3.2. Exergoeconomic analysis
Fig. 1. Schematic diagrams of the investigated cycles: a) GT-MHR cycle; b) combined GT-MHR/ORC.
4. Isentropic efficiencies (as given in Table 3) are assumed for the pump and turbine in the ORC. 5. Constant failure and repair rates are considered for the subsystems as they are often quite adequate even though a system or some of its components may exhibit moderate early failures or aging effects [19].
In evaluating thermal systems' performances the most efficient system is not always the optimal one in terms of cost. To incorporate both the technical and economical aspects in the analysis, thermal systems should be investigated from the exergoeconomic perspective. Exergoeconomics provides a procedure to reveal the cost formation process and calculate the specific exergy cost of the system product streams. The specific exergetic cost of the products obtained from this procedure can be used as a criterion for which the cycle performance is optimized. To perform an exergoeconomic analysis, a cost balance equation along with sufficient number of auxiliary equations, are applied to
190
V. Zare / Energy 96 (2016) 187e196
each system component. For the k th component, the cost balance equation can be expressed as [21]:
X
C_ out;k ¼
X
C_ in;k þ Z_ k
cP;total
(5)
3.3. Reliability modeling Reliability can be defined as the probability that a system performs properly for a specified period of time under a given set of operating conditions. A system is said to be failed when it ceases to perform its intended function. The failure of a system means the termination of the system's ability to perform its required function. In reliability and availability modeling accurate assessment and prediction of failures is essential for more accurate reliability evaluation. However, in order to take into account the different kinds of failure it is necessary to define failure quantitatively [25]. In addition to failure rate, repair rate is another important parameter in modeling the systems' reliability. Failure rate (l) is the expected number of failures in a specific time period such as one year and repair rate (m) determines the frequency of repair in that year. These are expressed as follows [26]:
(6)
The total cost rate for the k th component can be expressed as [22,23]: CI OM Z_ k ¼ Z_ k þ Z_ k
(7)
The annual levelized capital investment, for the k th component, may be expressed as [22]: CI Z_ k ¼
CRF Zk t
(8)
Number of component failures in a given period of time Total period of time the component was operating 1 ¼ MTTF (11)
l¼
where CRF and t are the capital recovery factor and the annual plant operation hours, respectively. The CRF is a function of the interest rate, ir, and the number of years of the plant operation, n [21]:
CRF ¼
ir ð1 þ ir Þn ð1 þ ir Þn 1
(10)
It should be noted that, for the stand alone GT-MHR cycle the value of cP,total given by the above relation, is equal to the specific cost of net output power i. e.: c10.
where C_ is the cost rate associated with the outlet and inlet exergy streams and Z_ k is the total cost rate associated with capital investment and operation and maintenance costs for the k th component. The cost rates associated with the stream of matter, power and heat can be expressed as a function of specific exergy costs as follows [21]:
C_ i ¼ ci E_ i _ C_ w ¼ cw W _ _ C q ¼ cq Eq
Pnf _ Pnk _ Z þ i¼1 Z fi i¼1 k ¼ cpi ¼ Pnp _ E i¼1 i¼1 Pi np X
(9) Number of component repaires in a given period of time Total period of time the component was being repaired 1 ¼ MTTR (12)
m¼
The cost balance and auxiliary equations, for each component of the considered cycles, are given in Table 1. In evaluating the systems' performances from the exergoeconomic viewpoint in the present work, the specific cost of net output power is considered as the performance criterion. This parameter is also selected as the objective function on which the systems' performances are optimized. Such an objective function includes all the capital investment, operation and maintenance and the fuel costs as follows [24]:
where MTTF and MTTR denote the mean time to failure and the mean time to repair. Different methodologies are developed for reliability analysis during the past few years. An important method which has
Table 1 Cost balance and auxiliary equations for each system component. Component
Cost balance and auxiliary equations Stand alone GT-MHR
Combined cycle C_ 7 ¼ C_ 6 þ C_ 20 þ Z_ Compressor C_ 6 þ C_ 15 ¼ C_ 5 þ C_ 14 þ Z_ Precooler c14 ¼ 0 C_ þ C_ ¼ C_ þ C_ þ Z_
Gas turbine
C_ 5 ¼ C_ 4 þ C_ 9 þ Z_ Compressor C_ 4 þ C_ 8 ¼ C_ 3 þ C_ 7 þ Z_ Precooler c7 ¼ 0 C_ 3 þ C_ 6 ¼ C_ 2 þ C_ 5 þ Z_ Recuperator c3 ¼ c2 C_ þ C_ þ C_ ¼ C_ þ Z_
Reactor
c1 ¼ c2, c9 ¼ c10 C_ 1 ¼ C_ 6 þ Z_ Reactor þ Z_ fuel
Evaporator
e
Superheater
e
ORC turbine
e
C_ 11 þ C_ 5 ¼ C_ 10 þ C_ 4 þ Z_ Evaporator c4 ¼ c5 C_ 12 þ C_ 4 ¼ C_ 3 þ C_ 11 þ Z_ SuperHeater c4 ¼ c3 C_ þ C_ ¼ C_ þ Z_
e
þ C_ 13 þ Z_ Condenser
Compressor Pre-cooler Recuperator
Condenser Pump
2
e
9
10
1
Turbine
3
8
7
2
Recuperator
c3 ¼ c2 C_ 2 þ C_ 21 þ C_ 20 ¼ C_ 1 þ Z_ Turbine c1 ¼ c2, c20 ¼ c21 C_ ¼ C_ þ Z_ Reactor þ Z_ 1
13
8
19
c12 ¼ c13 C_ þ C_ ¼ C_ 9
17
fuel
12
16
Turbine
c16 ¼ 0 C_ 10 ¼ C_ 18 þ C_ 9 þ Z_ Pump c18 ¼ c19
V. Zare / Energy 96 (2016) 187e196
received more attention is known as the Markov approach by which many component failure interactions can be modeled effectively. In the present work the state space method, which is based on the probabilistic analysis of Markov model, is selected as it is suitable for large, complex repairable systems and is appropriate for quantitative analysis [6]. In order to assess the continuous Markov processes the appropriate state space diagram is constructed and all the possible states for the system are incorporated in such a diagram. For the reliability modeling of the considered combined cycle in the present study, the cycle is divided into three sub-systems including: reactor core (i ¼ 1), closed Brayton cycle (i ¼ 2) and
2 6 6 6 6 6 M¼ 6 6 6 6 6 4
191
multiplication method, differential equation method, frequency balance method and stochastic transitional probability matrix method [2]. The last method is employed in the present work due to its simplicity. In this approach, the steady state probabilities can be found from Ref. [26]:
aM ¼ a
(13)
where a and M represent the steady state probability vector and the stochastic transitional probability matrix, respectively. For the considered combined cycle the transitional probability matrix may be expressed as follows:
3 1ðl1 þl2 þl3 Þ l1 l2 l3 0 0 0 0 7 1ðm1 þl2 þl3 Þ 0 0 l2 0 l3 0 m1 7 7 0 1ðm2 þl1 þl3 Þ 0 l1 l3 0 0 m2 7 7 0 0 1ðm3 þl1 þl2 Þ 0 l2 l1 0 m3 7 7 m1 0 1ðm2 þm1 þl3 Þ 0 0 l3 0 m2 7 7 0 0 m3 m2 0 1ðm2 þm3 þl1 Þ 0 l1 7 5 0 m3 0 m1 0 0 1ðm1 þm3 þl2 Þ l2 0 0 0 0 m3 m1 m2 1ðm3 þm1 þm2 Þ (14)
organic Rankine cycle (i ¼ 3). Considering two situations (operating or failed) for each sub-system, there will be a total number of 23 ¼ 8 possible states for the combined GT-MHR/ORC as illustrated by the state space diagram in Fig. 2. It is worth mentioning that, for the case of stand alone GT-MHR, the cycle is divided into two subsystems (reactor core and closed Brayton cycle) and the related state space diagram comprises of 22 ¼ 4 possible states. The probabilities of each system state are determined using the continuous Markov process by certain solution methods. Some of existing methods for evaluating state probabilities are: Matrix
Once the i'th state probability, Pi , for all 8 states for the combined cycle (and 4 states for the stand alone GT-MHR) are determined, they can be used to evaluate the specific cost of output power with reliability considerations as follows [6]:
cP ¼
X
Pi cPi
(15)
where, the state probabilities are used as weights for every operating state. As will be shown, the effect of equipment reliability inclusion in the analysis is to increase the power cost due to the unexpected equipment downtime as a result of system failures and the subsequent repairs. From the above mentioned definition of reliability, it is evident that it relates to the ability of a system to continue functioning without failure. This interpretation of the reliability, however, is an unsuitable measure for continuously operating systems that can tolerate failures. For these systems another criterion referred to as availability is suitable to be used. The availability can be interpreted as the probability of finding the component/system in the operating state at some time into the future [26]. The availability of the considered combined cycle, consisting of three sub-systems (RC (reactor core), CBC (closed Brayton cycle) and ORC), can be expressed as [6]:
A¼
mRC mCBC mORC ðlRC þ mRC ÞðlCBC þ mCBC ÞðlORC þ mORC Þ
(16)
4. Results and discussion
Fig. 2. State space diagram for the combined cycle.
In this section parametric studies are performed to assess the influence of decision variables on exergoeconomic performance of the stand alone GT-MHR and the combined cycle. The cycles are then optimized from the exergoconomic viewpoint. To evaluate the effect of reliability considerations in the exergoeconomic analysis the optimization is performed for two cases; one with incorporation of reliability considerations into the analysis and the other without considering the reliability aspects in the analysis.
192
V. Zare / Energy 96 (2016) 187e196
Table 2 Performance parameters for the GT-MHR cycle and the ORC; (a) present work, (b) Ref. [27] (c) Ref. [28]. Stand alone GT-MHR cyclea
(a)
(b)
ORCb
(a)
(c)
Turbine power (MW) Compressor power (MW) Pre-cooler heat load (MW) Recuperator heat load (MW) Helium mass flow rate (kg/s)
552.8 248.3 295.6 970.7 401.1
538.8 243.8 310.2 966.5 401.0
Net work output (kJ/kg) First law efficiency (%) Second law efficiency (%)
48.65 12.68 47.38
48.57 12.6 46.8
a b
T1 ¼ 900 C, rc ¼ 2.10. TEvaporator ¼ 120 C, TCondenser ¼ 40 C.
Table 3 The input data assumed in the simulation. Parameter
Symbol
Value
Ambient (dead state) pressure Ambient (dead state) temperature Heat released from the nuclear fission
P0 (bar) T0( C) Q_ ðMWÞ
1 15 600a
Reactor outlet temperature Pressure loss in reactor Pressure loss in pre-cooler Pressure loss in recuperator (high pressure side) Pressure loss in recuperator (low pressure side) Pressure loss in evaporator Pressure loss in superheater Gas turbine polytropic efficiency Compressor polytropic efficiency Pump isentropic efficiency ORC turbine isentropic efficiency Pinch point temperature difference Recuperator and pre-cooler effectiveness Interest rate ORC economic life GT-MHR economic life Fuel cost CBC failure rate CBC repair rate Reactor core failure rate Reactor core repair rate ORC failure rate ORC repair rate a b c d e
core
T1( C) DPcore(bar) DPPre(bar) DPRec, HP(bar) DPRec, LP(bar) DPEva(bar) DPSup(bar)
hP,GT hP,C hs,P (%) hs,T (%) DTPP ( C)
ε (%) ir (%) n (year) n (year) Zf ($/MWh) l (per day) m (per day) l (per day) m (per day) l (per day) m (per day)
850a 1b 0.4b 0.8b 0.5b 0.4b 0.2b 0.9160.0175 ln(rc)a 0.9320.0117 ln(rT)a 85 85 5 95c 10 20 60d 7.4d 0.00274e 0.1e 0.00274 0.0833 0.00274 0.14
[27]. [9]. [29]. [30]. [7].
4.1. Verification of simulation models To verify the thermodynamic simulation and modeling of the investigated cycles the results of the present work are compared with those reported in the literature [27,28] as shown in Table 2. Also verification of the exergoeconomic modeling is performed by comparing the results obtained from the present study with those published previously by the author [13]. The figures given in Table 2 indicate a good agreement between the values of parameters calculated in the present study and those reported in the literature. The considered assumptions and input parameters in investigating the considered cycles are summarized in Table 3. A parametric study is performed to examine the effects on the performance of the GT-MHR and the combined cycle of the decision variables. For the parametric study n-pentane is assumed as the ORC working fluid, however, for optimizing the combined cycle performance four working fluids are considered, as mentioned before. For the stand alone GT-MHR cycle, the only decision variable is the compressor pressure ratio (rc), keeping in mind that the other parameters of Brayton cycle (such as helium turbine inlet temperature) are assumed to be constant as given in Table 3. For the combined cycle, however, there exist three decision variables, namely; rc, TEva and DTsup.
Fig. 3 shows the effects on the efficiency (note that hI ¼ hII) of the compressor pressure ratio, for the GT-MHR and the combined cycle. Referring to Fig. 3, higher efficiency values are observed for the combined cycle compared to the standalone GT-MHR. For the
Fig. 3. Effects on the efficiency of compressor pressure ratio.
V. Zare / Energy 96 (2016) 187e196
combined cycle at some pressure ratios (for example rc < 2) the efficiency values are not shown in Fig. 3, as these rc values lead to T4 < TEva which is not practical. The variation of the specific cost of output power (cP,total) for both the cycles with the compressor pressure ratio is shown in Fig. 4. The cost values are calculated for two cases: with incorporation of reliability considerations and without it. Referring to Fig. 4, it is seen that for rc > 2.1 the cost of power for the combined cycle is lower than that for the standalone GT-MHR. Also, the power cost values obtained with incorporation of the reliability considerations are around 4.2% higher than those without reliability considerations. The higher power cost obtained with reliability considerations is due to the unexpected equipment downtime as a result of system failures and the subsequent repairs. Fig. 5 shows the variations of the efficiency and specific cost of power for the combined cycle with the evaporator temperature, TEva. Referring to Fig. 5, there exist optimum values for evaporator temperature with which the efficiency is maximized or the specific cost of power is minimized. The variation of the efficiency and specific cost of power of the combined cycle with respect to the superheating degree at the ORC turbine inlet is shown in Fig. 6. The figure indicates that, as DTsup increases, the efficiency decreases while the cP,total goes up. These trends are partly due to the reduction of GT-MHR output power as a result of helium pressure loss occurred in the superheater. In addition, an increase of DTsup, causes a decrease in ORC working fluid mass flow rate (because of a lower heat recovery in the
Fig. 4. Effects on the specific cost of power of compressor pressure ratio.
193
Fig. 6. Effects on the efficiency and the specific cost of power of superheating degree at the ORC turbine inlet.
evaporator) and consequently reduces the output power of the ORC. A reduction in net output power of the combined cycle results in a higher specific cost of power values as presented in Fig. 6. Referring to Figs. 4e6, it is evident that the power cost with and without reliability considerations are always in parallel with a constant value of difference. This trend can be justified considering Eq. (15) by which the cost of power is calculated when the reliability considerations are taken into account. It should be noted that the specified values for state probabilities corresponds only to the given values of failure and repair rates and are not affected by thermodynamic variables (such as compressor pressure ratio and/ or evaporator temperature). The effects of the system's failure rate and repair rate on the specific cost of power and system availability for the combined cycle are presented in Figs. 7 and 8. Fig. 7 indicates that as system failure rate increases, the power cost is increased (due to the increase in system downtime associated with repair actions) and the system availability is decreased. The opposite trend is observed as the system repair rate increases, as expected and shown in Fig. 8. In order to optimize the performances of the stand alone GTMHR and the combined cycle, the specific cost of output power (cP,total) is considered as the objective function. The minimum value of the objective function can be found by the solution to the following optimization problem considering the restrictions on decision variables as follows:
Minimize cP;total ðrc Þ ðfor stand alone GT MHR cycleÞ Minimize cP;total rc ; TEva ; DTsup ðfor combined cycleÞ
(17)
Subject to:
Fig. 5. Effects on the efficiency and the specific cost of power of evaporator temperature.
Fig. 7. Effects on the specific cost of power and system availability of system failure rate for the combined cycle.
194
V. Zare / Energy 96 (2016) 187e196
Fig. 8. Effects on the specific cost of power and system availability of system repair rate for the combined cycle.
around 4.3% and 4.4e4.7% for the stand alone GT-MHR and the combined cycle, respectively. The values of decision variables and important performance parameters for the two cycles, with reliability considerations at the optimized conditions, are outlined in Table 4. Also, the values of P k _ cost rate for overall system (Z_ Overall system ¼ nk¼1 Z k ) and the availability of the cycles are given in this Table. The figures in the Table indicate that, the combined cycle efficiency is higher than that of the GT-MHR by around 11.9e13.5% for different ORC working fluids among which R245fa yields the highest efficiency. Table 4 shows another interesting result which is the fact that the overall system cost rate for the combined cycle is just slightly higher than that for the stand alone GT-MHR, meaning that the efficiency enhancement and the cP,total reduction is achieved at the expense of just a negligible increase in the overall system cost rate (for instance 7860.9 $/h compared to 7787.2 $/h for n-pentane) when the ORC is combined with the GT-MHR. A close value of Z_ Overall system
for the combined cycle and the stand alone GT-MHR is in turn due to a significantly lower helium mass flow rate in the combined cycle that brings about lower components' size and cost regarding the relations given in Table A.1. Considering the availability values given in Table 4 for two cycles, it is revealed that availability of the combined cycle is lower than that of the GT-MHR as a result of having a complicated system which increases the probability of failures in the involved components and subsequent repair time. From the economic point of view, the expected loss in revenue due to system failure and downtime can be considered as an important index which can be estimated using the results of availability analysis. For the combined cycle in the present study the yearly produced energy, with and without reliability considerations, can be calculated as: Fig. 9. Specific cost of power at the optimized conditions with and without reliability considerations.
_ net 8760 ¼ 315:06 8760 W ¼ 2759926 MWh ðwithout reliability consideratiosÞ (19)
1:5 < rc < 5 100 < TEva < 170 0 < DTsup < 15
(18) _ net 8760 A ¼ 315:06 8760 0:9246 W
The values of cP,total at the optimized conditions (i.e. its minimum values) for the investigated cycles are shown in Fig. 9, for two cases of including and excluding reliability considerations. Referring to Fig. 9, it is revealed that the cP,total value for the combined cycle is around 12% lower than that for the stand alone GT-MHR and the lowest value is obtained when R141b is employed as the ORC working fluid. Fig. 9 also shows that the cP,total value obtained with taking reliability considerations into account is higher than the case when the equipment reliability is not considered. With inclusion of the reliability considerations the value of cP,total is increased by
¼ 2551827 MWh ðwith reliability consideratiosÞ (20) Thus, when reliability considerations are taken into account a loss of produced energy of 208,099 MWh is expected in a year. If a value of $50/MWh is assumed for the average selling price of electricity in the market, a huge amount of 10,404,950 $/year is estimated for the loss in revenue. This value of loss in revenue is disregarded when the reliability and availability considerations are not taken into account in the analysis.
Table 4 The values of decision variables and objectives with reliability considerations at the optimized conditions. Combined cycle with different ORC working fluids
Parameter
Stand alone GT-MHR
Compressor pressure ratio Evaporator temperature ( C)
2.328
Degree of superheat ( C)
e
2.907 157.7
e 46.83 281.01
0
0
0
0
52.51 268.46
53.14 280.47
52.87 270.01
52.41 255.64
n-pentane
Efficiency (%) _ W net;GTMHR (MW) _ W (MW) net;ORC
_ W net; total (MW) m_ Helium (kg/s) cP,total ($/GJ) Cost rate of overall system ($/h) Availability
e e 385.06 10.887 7787.2 0.9424
R245fa 2.394 131.1
R123 2.852 151.6
R141b 3.347 187.6
46.60
38.35
47.18
58.81
315.06
318.82
317.19
314.44
322.74 9.679 7860.9 0.9246
379.28 9.818 8019.3 0.9246
327.38 9.647 7880.6 0.9246
293.17 9.558 7838.4 0.9246
V. Zare / Energy 96 (2016) 187e196
5. Reliability and availability analysis of sub-systems
Table 6 Failure and repair rates assumed for the ORC components.
In the combined cycle the three subsystems are operating in series, thus generating power by the cycle needs the upper subsystem (reactor core) to be in operating mode. To conduct an availability analysis for the sub-systems (the closed Brayton cycle and the ORC) it is assumed that the reactor core is reliable (works with 100% reliability). The CBC sub-system consists of four components; GT (gas turbine), recuperator (Rec), pre-cooler (Pre) and compressor (C). For this sub-system, there will be a total number of 24 ¼ 16 possible states and the 16 steady state probabilities; P ¼ [P1, P2, …, P16] can be found using frequency balance method. It is obvious that the only operating mode of the CBC is the case when all the four components are working properly for which the steady state probability can be expressed as [2,5]:
P1 ¼
mGT mRec mPre mC ðlGT þ mGT ÞðlRec þ mRec ÞðlPre þ mPre ÞðlC þ mC Þ
(21)
This value equals to the availability of the CBC sub-system. For given values of failure and repair rates of the CBC components the availability of this sub-system, assuming a reliable operation for the reactor core, can be assessed. For the given values in Table 5, the availability of the CBC is calculated as:
A ¼ P1 ¼ 0:9816
(22)
The ORC sub-system consists of five components; turbine (T), condenser (CD), pump (P), evaporator (Eva) and superheater (Sup). The results of exergoeconomic optimization (Table 4) revealed that at optimum operating conditions DTsup ¼ 0. Thus, omitting the superheater from the system, the ORC subsystem includes four major components. Similar to the case of CBC, for the ORC subsystem which is a series combination of four components, there will be a total number of 24 ¼ 16 possible states and the 16 steady state probabilities; P ¼ [P1, P2, …, P16]. The only operating mode of the ORC sub-system is the case when all the four components are working properly for which the steady state probability can be expressed as:
P1 ¼
mT mCD mP mEva ðlT þ mT ÞðlCD þ mCD ÞðlP þ mP ÞðlEva þ mEva Þ
(23)
Assuming a reliable operation for the reactor core and the CBC sub-systems, the availability of the ORC sub-system can be evaluated using Eq. (23) for given values of failure and repair rates of its components. For the given values in Table 6, the availability of the CBC is calculated as:
A ¼ P1 ¼ 0:9891
195
(24)
Component
Failure rate (per day)
Repair rate (per day)
Turbine Condenser Pump Evaporator
0.001096 0.000548 0.001096 0.000548
0.25 0.5 0.25 0.5
utilized in an organic Rankine cycle. The exergoeconomic performance assessment is extended to include the often-forgotten criteria in literature: reliability and availability. As it is expected, the thermodynamic efficiency of the combined cycle is higher than that of the stand alone GT-MHR due to the waste heat recovery. However, the results of exergoeconomic analysis revealed that, the thermodynamic performance enhancement is achieved by just a negligible increase in total investment cost rate, implying an attractive outcome. The parametric study showed that, decreasing system failure rate and/or increasing system repair rate, increases the availability of the combined cycle and decreases the cost of output power. At the optimum operating conditions, the following findings are obtained quantitatively when the ORC is combined with the GT-MHR: 1) The combined cycle efficiency is higher than that of the GT-MHR by around 11.9e13.5%. 2) The specific cost of output power for the combined cycle is about 12% lower than that for the stand alone GT-MHR. 3) The overall system cost rate for the combined cycle is higher than that of the GT-MHR by a negligible amount (for instance 7838.4 $/h compared to 7787.2 $/h for R141b). 4) When the reliability considerations are taken into account the specific cost of power is increased by around 4.3% and 4.4e4.7% for the stand alone GT-MHR and combined cycle, respectively. 5) As a result of having more components and complicated system, availability of the combined cycle is lower than that of the GTMHR (0.9246 compared to 0.9424).
Appendix A. Investment costs of the system components For an exergoeconomic analysis, the purchased equipment cost of each system component should be expressed as a function of thermodynamic variables. Some of these variables are: temperature, pressure or other related variables to these, such as; mass flow rate, generated or consumed power (for turbine and compressor) and heat transfer area (for heat exchangers). The cost functions for each component of the investigated cycles in the present study are listed in Table A.1.
6. Conclusions A comprehensive exergoeconomic analysis and optimization is presented for a combined cycle power plant in which the waste heat from GT-MHR (Gas Turbine Modular Helium Reactor) is
Table A.1Cost functions for system components [10,31,32]. System component Gas turbine Compressor
Table 5 Failure and repair rates assumed for the CBC components.
Cost function m_ He 479:34 0:93h lnðrT Þð1 þ e0:036T1 54:4 Þ GT m_ He 71:1 0:91h rc lnðrc Þ C
Reactor core
Component
Failure rate (per day)
Repair rate (per day)
Gas turbine Recuperator Pre-cooler Compressor
0.00137 0.000822 0.000822 0.00137
0.20 0.333 0.333 0.20
Recuperator Pre-cooler ORC Turbine Pump Heat exchangers of ORC
283 Q_ core 2681 A0.59 2143 A0.514 _ 0:7 4405 W _ 0:8 1120 W 2143 A0.514
196
V. Zare / Energy 96 (2016) 187e196
References [1] Frangopoulos C. Effect of reliability considerations on the optimal synthesis, design and operation of a cogeneration system. Energy 2004;29:309e29. http://dx.doi.org/10.1016/S0360-5442(02)00031-2. [2] Haghifam MR, Manbachi M. Reliability and availability modelling of combined heat and power (CHP) systems. Int J Electr Power Energy Syst 2011;33: 385e93. http://dx.doi.org/10.1016/j.ijepes.2010.08.035. [3] Eti MC, Ogaji SOT, Probert SD. Reliability of the Afam electric power generating station, Nigeria. Appl Energy 2004;77:309e15. http://dx.doi.org/ 10.1016/S0306-2619(03)00094-1. [4] Koeppel G, Andersson G. Reliability modeling of multi-carrier energy systems. Energy 2009;34:235e44. http://dx.doi.org/10.1016/j.energy.2008.04.012. [5] Wang JJ, Fu C, Yang K, Zhang XT, Shi GH, Zhai J. Reliability and availability analysis of redundant BCHP (building cooling, heating and power) system. Energy 2013;61:531e40. http://dx.doi.org/10.1016/j.energy.2013.09.018. [6] Hosseini SR, Amidpour M, Behbahaninia A. Thermoeconomic analysis with reliability consideration of a combined power and multi stage flash desalination plant. Desalination 2011;278:424e33. http://dx.doi.org/10.1016/ j.desal.2011.05.061. [7] El-Nashar AM. Optimal design of a cogeneration plant for power and desalination taking equipment reliability into consideration. Desalination 2008;229: 21e32. http://dx.doi.org/10.1016/j.desal.2007.07.024. [8] Baldwin D, Campbell M, Ellis C, Richards M, Shenoy A. MHR design, technology and applications. Energy Convers Manag 2008;49:1898e901. http:// dx.doi.org/10.1016/j.enconman.2007.07.048. [9] Zare V, Mahmoudi SMS, Yari M. Ammoniaewater cogeneration cycle for utilizing waste heat from the GT-MHR plant. Appl Therm Eng 2012;48:176e85. http://dx.doi.org/10.1016/j.applthermaleng.2012.05.009. [10] Zare V, Mahmoudi SMS, Yari M. An exergoeconomic investigation of waste heat recovery from the gas turbine-modular helium reactor (GT-MHR) employing an ammoniaewater power/cooling cycle. Energy 2013;61: 397e409. http://dx.doi.org/10.1016/j.energy.2013.09.038. [11] Zare V, Yari M, Mahmoudi SMS. Proposal and analysis of a new combined cogeneration system based on the GT-MHR cycle. Desalination 2012;286: 417e28. http://dx.doi.org/10.1016/j.desal.2011.12.001. [12] Zare V, Mahmoudi SMS. A thermodynamic comparison between organic Rankine and Kalina cycles for waste heat recovery from the gas turbinemodular helium reactor. Energy 2015;79:398e406. http://dx.doi.org/ 10.1016/j.energy.2014.11.026. [13] Zare V, Mahmoudi SMS, Yari M. On the exergoeconomic assessment of employing Kalina cycle for GT-MHR waste heat utilization. Energy Convers Manag 2015;90:364e74. http://dx.doi.org/10.1016/j.enconman.2014.11.039. [14] Nisan S, Benzarti N. A comprehensive economic evaluation of integrated desalination systems using fossil fuelled and nuclear energies and including their environmental costs. Desalination 2008;229:125e46. http://dx.doi.org/ 10.1016/j.desal.2007.07.031.
[15] Nisan S, Dardour S. Economic evaluation of nuclear desalination systems. Desalination 2007;205:231e42. [16] Dardour S, Nisan S, Charbit F. Utilisation of waste heat from GT e MHR and PBMR reactors for nuclear desalination. Desalination 2007;205:254e68. [17] Yari M. Waste heat recovery from closed Brayton cycle using organic Rankine cycle: thermodynamic analysis. In: Proceedings of ASME turbo expo, power for land, sea and air, World Marriott Resort, Orlando, FL USA; 2009 June 8e12. [18] Yari M, Mahmoudi SMS. A thermodynamic study of waste heat recovery from GT-MHR using organic Rankine cycles. Heat Mass Transf 2010;47:181e96. http://dx.doi.org/10.1007/s00231-010-0698-z. [19] Jesus F, Carazas G, Francisco G, Souza M De. Availability analysis of gas turbines used in power plants. Int J Thermodyn 2009;12:28e37. [20] Sayyaadi H, Sabzaligol T. Exergoeconomic optimization of a 1000 MW light water reactor power generation system. Int J Energy Res 2009:378e95. http:// dx.doi.org/10.1002/er. [21] Bejan A, Tsatsaronis G, Moran M. Thermal design and optimization. New York: John Wiley and Sons; 1996. [22] Zare V, Mahmoudi SMS, Yari M, Amidpour M. Thermoeconomic analysis and optimization of an ammoniaewater power/cooling cogeneration cycle. Energy 2012;47:271e83. http://dx.doi.org/10.1016/j.energy.2012.09.002. [23] Gürtürk M, Oztop HF, Hepbasli A. Comparison of exergoeconomic analysis of two different perlite expansion furnaces. Energy 2015;80:589e98. http:// dx.doi.org/10.1016/j.energy.2014.12.015. [24] Soltani S, Mahmoudi SMS, Yari M, Morosuk T, Rosen MA, Zare V. A comparative exergoeconomic analysis of two biomass and co-firing combined power plants. Energy Convers Manag 2013;76:83e91. http://dx.doi.org/ 10.1016/j.enconman.2013.07.030. [25] Lewis EE. Introduction to reliability engineering. John Wiley and Sons Inc; 1994. [26] Billinton R, Allan RN. Reliability evaluation of engineering systems: concepts and techniques. New York: Plenum Publishing; 1992. [27] El-Genk MS, Tournier J-M. Noble gas binary mixtures for gas-cooled reactor power plants. Nucl Eng Des 2008;238:1353e72. http://dx.doi.org/10.1016/ j.nucengdes.2007.10.021. [28] Yari M. Exergetic analysis of various types of geothermal power plants. Renew Energy 2010;35:112e21. http://dx.doi.org/10.1016/j.renene.2009.07.023. [29] Herranz LE, Linares JI, Moratilla BY. Power cycle assessment of nuclear high temperature gas-cooled reactors. Appl Therm Eng 2009;29:1759e65. http:// dx.doi.org/10.1016/j.applthermaleng.2008.08.006. [30] Labar MP. The gas turbine-modular helium reactor: a promising option for near term deployment. General Atom April 2002:GA-A23952. [31] Ghaebi H, Amidpour M, Karimkashi S, Rezayan O. Energy, exergy and thermoeconomic analysis of a combined cooling, heating and power (CCHP) system with gas turbine prime mover. Int J Energy Res 2011:697e709. http:// dx.doi.org/10.1002/er. [32] Guo-yan Z, En W, Shan-tung T. Techno-economic study on compact heat exchangers. Int J Energy Res 2008:1119e27. http://dx.doi.org/10.1002/er.