Accepted Manuscript Exergoeconomic evaluation and optimization of a novel combined augmented Kalina cycle/ Gas Turbine-Modular Helium Reactor S.M.S. Mahmoudi, A. Pourreza, A.D. Akbari, M. Yari PII: DOI: Reference:
S1359-4311(16)31357-6 http://dx.doi.org/10.1016/j.applthermaleng.2016.08.011 ATE 8810
To appear in:
Applied Thermal Engineering
Received Date: Revised Date: Accepted Date:
11 June 2016 21 July 2016 2 August 2016
Please cite this article as: S.M.S. Mahmoudi, A. Pourreza, A.D. Akbari, M. Yari, Exergoeconomic evaluation and optimization of a novel combined augmented Kalina cycle/ Gas Turbine-Modular Helium Reactor, Applied Thermal Engineering (2016), doi: http://dx.doi.org/10.1016/j.applthermaleng.2016.08.011
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Exergoeconomic evaluation and optimization of a novel combined augmented Kalina cycle/ Gas Turbine-Modular Helium Reactor S. M. S. Mahmoudi *1 , A. Pourreza, A. D. Akbari, M. Yari Faculty of Mechanical Engineering, University of Tabriz, Iran Abstract A new combined system including Gas Turbine-Modular Helium Reactor (GT-MHR) and an augmented Kalina cycle (AKC) is proposed, analyzed and optimized thermodynamically and economically. The simulation is performed using the conservation of energy, exergy balance and cost equations for each system component. For comparison purposes the previously published data for the combined cycle consisting of the GT-MHR and a conventional Kalina cycle (GTMHR/KCS34), are also presented. Parametric studies are carried out to show the influences on exergy efficiency and total product unit cost of such decision parameters as compressor pressure ratio, pump pressure ratio, ammonia concentrations at different state points and separator temperature. The results indicate that the maximum exergy efficiency of the proposed system is 8.7% and 0.64% higher compared to the corresponding values for the GT-MHR and GTMHR/KCS34, respectively. The results also show that the minimum total product unit cost for GT-MHR/AKC is 11.3% and 2.53% lower than the corresponding values for the GT-MHR and GT-MHR/KCS34, respectively. It is observed that, under optimized condition, the helium mass flow rate in GT-MHR is reduced as the system is combined with the AKC. This is significant in reducing the size of system and consequently having more economically efficient system.
1
* corresponding author :
[email protected]
Keywords: Augmented Kalina cycle; GT-MHR; Combined cycle; Exergoeconomic analysis; Optimization. 1. Introduction Effective use of energy is a challenge for thermal system designers as it is an important issue concerning the world development and environmental pollution. In this regard, a lot of attention has been paid to recovering waste heat from energy converting systems to produce more power, cooling, heating or distilled water. The Gas Turbine-Modular Helium Reactor (GT-MHR), among the new options for power production, attracts interest of investigators owning to its encouraging aspects such as better economics, safety and proliferation resistance. In order to reduce the compression work in the GT-MHR system, the working fluid should be cooled so that around 300 MWth low grade thermal energy is rejected in the pre-cooler of the system with an input energy of 600 MWth [1, 2]. In order to increase efficiency, attempts have been made in literature to utilize this energy for running some bottoming cycles. Utilization of waste heat from the GT-MHR was first suggested by Yari [3] who proposed an organic Rankin cycle (ORC) for recovering waste heat from the GT-MHR. He reported that the combined cycle efficiency is around 10% higher than that of the GT-MHR. Yari and Mahmoudi [4] proposed a combined cycle including the GT-MHR employing a two-stage compressor and two ORCs. They reported an enhancement of 3% points in the efficiency when the ORCs are combined with the GT-MHR cycle. These authors, in another work employed three different configurations of ORC to recover the waste heat from GT-MHR and reported that the simple ORC performs better that the other configurations [5]. Zare et al. [6] suggested using a combined ammonia-water power/cooling system for recovering waste heat from the GT-MHR. They reported that the energy utilization factor and second law efficiency of the GT-MHR cycle are
enhanced by 9-15% and 4-10%, respectively. These authors in another work [7] performed an exergoeconomic analysis and reported a reduction of 5.4% in the products unit cost as the ammonia-water power/cooling cycle is used for waste heat recovery from the GT-MHR. It is evaluated that the total investment cost rate is increased by 1% when the two cycles were combined. Zare et al. [8] also proposed utilization of waste heat for producing power and purifying water and concluded that the first law efficiency was enhanced by up to 7%. Soroureddin et al. [9] used the waste heat from GT-MHR to run an ejector refrigeration system as well as different configurations of ORC and reported an increase of about 2.6% in the exergy efficiency. Mohammadkhani et al. [10] performed a comprehensive exergoeconomic analysis for waste heat utilization from GT-MHR by means of two ORCs. They reported that the pre-cooler and condenser, among the other components, have the worst exergoeconomic performance. A comparative exergoeconomic performance was assessed for the GT-MHR coupled with three types of ORC by Shokati et al. [11] who claimed that the lowest and highest unit product cost of the ORC turbine is achieved by the GT-MHR/RORC and GT-MHR/HORC, respectively. Zare et al. [12] combined a Kalina cycle with the GT-MHR and concluded that the product unit cost is lowered by 8.8% and the efficiency is enhanced by 8.2% in using the Kalina for recovering the waste heat from GT-MHR. The variable boiling temperature of ammonia-water solution in a Kalina cycle brings about a good temperature matching in recovering the waste heat from GT-MHR so that less exergy is destructed in the waste heat recovery heat exchanger [13]. In recent years, a lot of attention has been paid to the Kalina cycle because of its peculiarities and different configurations have been proposed for this cycle to make it more convenient for being used for low, medium and high
temperature heat sources. Among these configurations the KCS34 and AKC are convenient for being combined with the GT-MHR as the heat rejected in pre-cooler of GT-MHR is at medium temperature. The use of KCS34 configuration for waste heat recovery from the GT-MHR has been reported previously by the authors [12]. To the best of our knowledge, the AKC performance has not been investigated using exergoeconmic analysis. This lack of information makes the exergoeconomic analysis of the combined GT-MHR/AKC system seem to be more interesting and this forms the basis of the current study. Beside this, exergoeconomic comparison of the two GT-MHR/KCS34 and GT-MHR/AKC systems is accomplished in the present work. A parametric study is carried out to identify the effects on GT-MHR/AKC system performance of some decision parameters. The proposed system performance is also optimized for maximum efficiency or minimum unit product cost, applying the Direct Search Method in the Engineering Equation Solver (EES) software [14].
Nomenclature C
E F H ir P Pre R S T X Z
cost rate ($ ) cost per exergy unit ($ ) total product unit cost exergy rate (kW) specific exergy (kJ ) exergoeconomic factor specific enthalpy (kJ ) interest rate mass flow rate (kg ) pressure (bar) precooler heat transfer rate (kW) pressure ratio specific entropy (kJ ) temperature (oC or K) power (kW) ammonia concentration capital cost ($) capital cost rate ($ )
Subscripts and abbreviations 0 environmental state
1, 2, 3, … AKC AWM C Ch CI COD CRF D Exe Kct KCS34 P HE SH T TOD
state points augmented Kalina cycle ammonia-water mixture compressor chemical capital investment cost optimal design capital recovery factor destruction exergetic Kalina cycle turbine Kalina cycle system 34 product, pump heat exchanger super heater turbine thermodynamic optimal design
Greek letters effectiveness annual operation hours efficiency
2. Systems description and assumption 2.1. GT-MHR/AKC Fig. 1 shows the schematic diagram of proposed combined GT-MHR/AKC system and the T-s diagram associated with the processes in the system. The system actually consists of a GT-MHR cycle and an augmented Kalina cycle so that the waste heat from pre-cooler of the GT-MHR cycle is utilized to run the Kalina cycle. Helium as working fluid in the GT-MHR cycle is heated in the reactor before flowing to the turbine (state point 1) where it is expanded and produce power. The helium exiting turbine (state point 2) passes to the recuperator to preheat the helium entering the reactor. The helium then (state point 3) flows to the superheater (SH) and heat
exchanger 6 (HE6) to heat the ammonia-water solution entering the Kalina turbine. The helium at the exit of HE6 (state point 5) is divided into two parts: one part (state point 7) flows to the heat exchanger 5 (HE5) and then to heat exchanger 3 (HE3) and the other part (state point 6) goes to the heat exchanger 4 (HE4). The two parts after passing the mentioned heat exchangers are mixed at the mixer 4 (MX4) and flows to the compressor after being cooled in the pre-cooler (state point 12). The helium exiting compressor (state point 13) then goes back to the recuperator to complete the GT-MHR cycle. The waste heat utilized in SH, HE6, HE5, HE4 and HE3 are input energy to run the Kalina cycle. Superheated basic ammonia solution enters the mixture turbine (MT) to expand and produce additional power before heating the stream 26 in the heat exchanger 2 (HE2). The basic ammonia solution (state point 17) then passes to the separator from which strong ammonia-water vapor (state point 19) and weak ammonia-water liquid (state point 18) exit. The latter is divided into two parts in the splitter 1 (SP1); one stream (state point 34) goes to HE4 via pump 1 (P1) and the other stream (state point 20) passes to mixer 1 (MX1) to get mixed with the strong ammoniawater vapor coming from the separator (state point 19). The ammonia-water solution exiting MX1 (state point 21) flows to heat exchanger 1 (HE1) before passing to the condenser (state point 22) where complete condensation occurs. The liquid ammonia-water solution at the condenser exit (state point 23) is pumped by pump 2 (P2) before flowing to HE1 (state point 24) and splitter 2 (SP2) where the solution is divided into two parts (state points 26 and 27). These two parts are heated in HE2 and HE3, as indicated in the figure, before getting mixed again in mixer 2 (MX2). The solution exiting MX2 (state point 30) passes to HE5 and mixer3 (MX3) where it is mixed with weak ammonia-water liquid coming from SP1 via P1 and HE4 (state point 36). The solution exiting MX3 (state point 32) is heated in the HE6 and SH to complete the
Kalina cycle. The idea of using separator in Kalina cycle is useful as the high temperature liquid exiting this component is sent back to turbine without getting cooled in the condenser and therefore, the Kalina cycle performance is enhanced [15].
[Fig. 1]
2.2. GT-MHR/KCS34 Another plant scheme has been proposed for the Kalina cycle for some other concern. The KCS34 configuration was first employed in a geothermal power plant named as the Húsavik plant [16]. Zare et al. [12] used this Kalina cycle to utilize the waste heat from GT-MHR as illustrated schematically in Fig. 2. For clarification purposes, the T-s diagram associated with the GT-MHR/Kalina cycle, KCS34 is also shown in Fig. 2. Referring to Fig. 2, the input heat to the KCS34 in this configuration is provided in the superheater and evaporator by the helium passing through these components. The detailed description of the GT-MHR/KCS34 system however, is provided in reference [12].
[Fig. 2]
3. Thermodynamic analysis Applying the principles of mass and energy conservations as well as the exergy balance to each system component as a control volume, the GT-MHR and proposed combined cycle
thermodynamic performances are simulated by computer programs using the EES software. More attention is paid to second law analysis as it provides useful information for economic evaluation of the system performance [18, 19]. A stream total exergy includes the physical and chemical exergies if the kinetic and potential exergies are neglected: (1) where the physical exergy is obtained as follows: )–
[(
(s
(2)
)]
For the GT-MHR cycle no chemical exergy is considered as it cancels out when exergy balance is applied to each system component. The chemical exergy for ammonia–water mixture in the Kalina cycle however, are considered as there is variation in the concentration as the mixture passes through some components in the Kalina cycle. The chemical exergy of ammonia-water mixture can be expressed as [20]: R where
and
respectively. The term
(3)
are the standard chemical exergies of ammonia and water, R
in Eq. (3) is associated with the mixing effect. It is
negligible in comparison with the other terms in the equation. For the GT-MHR as a standalone system and also for the proposed GT-MHR/AKC, the first law efficiency is expressed as [4]: (4) where AKC ( =
is the sum of net produced powers produced in the GT-MHR (
) and
): +
The net produced powers in the GT-MHR and AKC are calculated as follows:
(5)
(6) (7) The exergy efficiency for each system component is expressed as [10]:
(8) The fission energy,
, in the nuclear reactor is transferred to the helium by heat transfer
process, the exergy associated with this heat transfer is obtained as [21, 22]: = where
(
)
(9)
is the fission temperature. This temperature is very high compared to T o so that the
exergy input to helium in the reactor is almost equal to the fission energy [21, 22]:
(10) Therefore, the second law efficiency is similar to the first law efficiency [4]: (11)
In the present work, the following assumptions are made for simulation. 1. The system operates under steady state condition. 2. Changes in potential and kinetic energies are neglected. 3. The recuperator and the pre-cooler have an effectiveness of 0.95 [17]. 4. Polytropic efficiencies are considered for the turbine and compressor in the GT-MHR cycle [1]. 5. The turbine and pump in the KC have an isentropic efficiency of 0.85 [16].
6. The pressure losses in the Kalina cycle are neglected while some appropriate values are considered for pressure losses in the GT-MHR cycle [1]. 7. The ammonia–water solution leaves the condenser and separator as saturated. Table 1 summarizes the assumptions and input data used to simulate the proposed system performance from the viewpoints of thermodynamics and economics. As indicated in the table, the value of pressure loss for the helium stream in pre-cooler of the GT-MHR, as a standalone system, is 0.4 bar. For the proposed combined system however, this pressure loss is smaller, (
= 0.2 bar) because of the smaller size of this component.
[Table 1]
The capacity factor in Table 1 is defined as the ratio of actual produced power in a period of time, to the maximum possible output power. [27]. 3.1. Model validation In order to validate the developed thermodynamic models for proposed systems the available data in literature were used. The validation is performed for GT-MHR and the AKC, separately as presented in Tables 2 and 3, respectively. Referring to Tables 2 and 3, there are good agreements between the results.
[Table 2] [Table 3]
4. Exergoeconomic Analyses A major criterion in assessing performance of an energy converting system is the unit product cost. This cost is obtained by means of exergoeconomic analysis performed by applying appropriate cost balance equation along with the associated auxiliary equations for each system component as a control volume. In expressing the cost balance for each system component the sum of cost rates related to the exiting exergy streams is considered as equal to the sum of cost rates of entering exergies and the total cost rate required to accomplish the process [18].
+ where
=
+
+
is the output power cost rate,
(12) is the cost rate related to the heat transfer and
is
the total cost rate associated with capital investment and operating and maintenance for the kth component [18]. =
(13)
+
For each exergy stream, the cost per unit of exergy (c) can be expressed as [18]: (14) For the kth component, the cost rate associated with capital investment cost can be expressed as [18, 23]: (15) where CRF and
are the capital recovery factor and the annual plant operation hours,
respectively. The functions for calculating
of components are given in Appendix A. The
capital recovery factor is calculated as follows [23]: (16)
where n is the number of years of the plant operation and
is the interest rate.
For each component, the annual levelized operating and maintenance cost can be calculated as [18, 23]: (17) where
and
are associated with the fixed and variable operating and maintenance costs,
respectively, for the kth component and
accounts for all the other operating and maintenance
costs. The last two terms at the right side of Eq. (17) are very small and therefore neglected in the present work. The value of
is assumed to be 0.1 [24, 25].
In exergoeconomic analysis it is required to define properly the fuel and product for system components and the overall system in terms of exergy. The fuel is exergy required to produce product and the product is the required output generated by the system or system components. Table 4 represents the definitions of the fuel and product exergies, for the combined cycle components.
[Table 4]
Once the fuel and product exergy associated with a component is identified, the exergy cost rate and exergy unit cost for each stream is obtained by means of solving the system of equations given in Table 5 including the associated auxiliary costing equations and Eq. (14). It must be mentioned that the number of auxiliary costing equations required for a component with n exit streams is n-1.
[Table 5]
The total product unit cost (
) is considered as the objective function in optimizing the
system’s performance from the viewpoint of economics. This parameter is defined as [24]: (18) where
is the net output power and
is the rate of cost associated with the heat transfer
in the reactor core. 5. Exergoeconomic parameters In order to evaluate the performance of each system component as well as the overall system the following exergoeconomic parameters are used.
Exergy destruction ratio
Exergy destruction ratio is defined as [18]:
(19) where
is exergy destruction rate and
which is equal to
(600 MW), is the
exergy input to the system.
Cost of exergy destruction
Cost of exergy destruction doesn't appear in the cost balance equation and it can be referred as a hidden cost. It is associated with the exergy destruction as follows [18]:
(20) where
is the average unit cost of fuel for each system component; Exergoeconomic factor ( )
Exergoeconomic factor indicates the contribution of capital investment and operating and maintenance cost to the cost associated with the exergy destruction and loss in each component [18, 26].
(21) According to the Eq. (21), a lower value of
suggests an increase in the component efficiency
(a reduction in the exergy destruction) for reducing the overall cost in the system. Depending on the type of component, the value of
is generally between 35% and 75% for compressors and
turbines, lower than 55% for heat exchangers and above 70% for pumps [18]. 6. Results and discussion
The simulation results are presented in Table 6 which shows the thermodynamic properties and stream cost rate at each state point of the GT-MHR/AKC under a workable design condition. The values of decision parameters for the results in Table 6 are indicated at the bottom of the table.
[Table 6]
6.1. Parametric studies
In order to assess the effects of some decision parameters on the thermodynamic and thermoeconomic performance of proposed systems parametric studies are performed. Assuming a constant value for turbine inlet temperature, the compressor pressure ratio, , is the only decision variable for the GT-MHR as a standalone system. For the proposed combined system however, the decision variables are considered as: the compressor pressure ratio, the pump pressure ratio,
, the ammonia concentration in the solution entering Kalina cycle turbine,
and the condenser, and
, and the separator temperature,
[15]. In the figures associated with
the results for GT-MHR/KCS34, published by the authors previously [12], are also
presented for comparison purposes. The effects on the efficiency ( = cost,
,
) and total product unit
, are shown in Figs. 3(a) and (b) of the compressor pressure ratio, for the GT-MHR
and the combined GT-MHR/AKC and GT-MHR/KCS34systems. Referring to Fig. 3(a) and (b), higher efficiency and lower
values are obtained for the combined cycles compared to the
corresponding values for the GT-MHR. Fig. 3 also indicates that the GT-MHR/AKC performs better than the GT-MHR/KCS34 especially at higher compressor pressure ratios. Referring to Fig. 3, compared to the GT-MHR/KCS34, the GT-MHR/AKC performance is less sensitive to the variations in
so that the maximum value for efficiency and minimum value for
are
less projected for the case of GT-MHR/AKC. This point can be accounted as an advantage for the GT-MHR/AKC. However, the compressor pressure ratio for better performance in the GTMHR/AKC is higher than the corresponding value for the GT-MHR/KCS34. It should be pointed out that for compressor pressure ratios of less than some specific values the efficiency and for the combined cycles are not shown in the figure since these
values lead to a helium
temperature at the recuperator exit less than the ammonia-water solution temperature at superheater exit (T3
