Thermo-economic optimization of heat recovery steam generator for a range of gas turbine exhaust temperatures

Accepted Manuscript Thermo-economic optimization of heat recovery steam generator for a range of gas turbine exhaust temperatures Mahmoud Nadir, Adel Ghenaiet, Carlo Carcasci PII: DOI: Reference:

S1359-4311(16)30938-3 http://dx.doi.org/10.1016/j.applthermaleng.2016.06.035 ATE 8446

To appear in:

Applied Thermal Engineering

Received Date: Revised Date: Accepted Date:

28 April 2015 21 April 2016 6 June 2016

Please cite this article as: M. Nadir, A. Ghenaiet, C. Carcasci, Thermo-economic optimization of heat recovery steam generator for a range of gas turbine exhaust temperatures, Applied Thermal Engineering (2016), doi: http:// dx.doi.org/10.1016/j.applthermaleng.2016.06.035

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Thermo-economic optimization of heat recovery steam generator for a range of gas turbine exhaust temperatures 1

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Mahmoud NADIR , Adel GHENAIET and Carlo CARCASCI

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Laboratory of Energetic Mechanics, Faculty of Engineering, University of Boumerdes, 35000, Boumerdes, Algeria [email protected] 2 Laboratory of Energetics and Conversion Systems, Faculty of Mechanical Engineering, University of Sciences and Technology, Houari Boumediene, BP32 El-Alia, Bab-Ezzouar, 16111, Algiers, Algeria [email protected] 3 Department of Industrial Engineering, University of Florence, Via Santa Marta, 3, Florence, Italy [email protected]

Abstract This paper illustrates the effect of selling price on the optimum design parameters of a heat recovery steam generator and selection of its ideal configuration for an outlet temperature range of 350°C - 650°C. The Particle Swarm Optimization (PSO) method was used, considering the steam cycle specific work as an objective to be maximized, the net present value as another objective to be maximized for the economic optimization and a combination of both of them. Three configurations of heat recovery steam generators are considered with one, two and three pressure levels with reheat. The results show that, the three pressure level system is the best configuration from a thermodynamic point of view, but with respect to the economical aspect the two pressure levels is the best configuration for the low and medium selling prices (0.04$/kWh, 0.08$/kWh and 0.2$/kWh), whereas the three pressure level configuration would only be interesting for a high selling price of 0.3$/kWh and a temperature range 450-600°C. For a temperature of 650°C, the high cost of the three level system leads to net present value decrease. As the selling price increases the optimized design parameters of the three pressure level HRSG based on an economic or a thermodynamic optimization are similar. The obtained results are used to elaborate a new correlation relating the net present value with the gas turbine outlet temperature, gas mass flow rate, number of levels of HRSG and the selling price.

Keywords: Combined cycle; HRSG; Exhaust gas temperature; Net present value; Thermo-economic optimization

Highlights  Thermo-economic optimization of HRSG configurations  The maximum value of the net present value was targeted for the economic optimization  Three level HRSG is the best option in respect of power output and high priced medium  Two level HRSG is the best for net benefit in low and intermediate priced mediums

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1 INTRODUCTION Today, combined cycles (CC) installations are considered as the favorite facilities for electricity power generation, and their bottoming steam cycle provides about 30-40 % of the overall generated power [1]. Any improvement could be done mainly through optimizing the heat recovery steam generator (HRSG) according to some manufacturing specifications or costumers economic requirements, contrary to gas turbines (GT) which are mass manufactured with imposed design parameters. Many studies concentrated on CC steam part, started with the optimization of a single pressure level HRSG such as Valdés and Rapuan [2]. Franco and Casarosa [3] and Franco and Russo [4] compared HRSG systems for one, two and three pressure levels with and without reheat and demonstrated that it is possible to reach an overall efficiency of 60% just by optimizing the steam cycle. Xiang and Chen [5] optimized a reheat three pressure levels HRSG both at a full and a part load, and suggested using a partial recovery of the exhaust gas energy for a temperature exceeding 590°C. Mohagheghi and Shayegan [6] optimized four types of HRSG of one, two and three pressure levels with a reheat adapted for the GT Siemens V94.2 for which the turbine outlet temperature (TOT) is equal to 550°C, and showed that by adding a pressure level always leads to improving the steam cycle performance. Bracco and Siri [7] considered several objective functions when optimizing a single pressure level HRSG adapted to four types of GTs present on the market, and outlined the influence of TOT and gas mass flow rate on the steam cycle performance. Kaviri et al. [8] optimized HRSG with two pressure levels and a supplementary firing designed to work with the gas turbine GE9171E having a TOT equal to 550°C. They fixed the optimized parameters and examined the effect of TOT variation on HRSG, and found that by increasing TOT to a value of 650°C leads to an increase in the steam cycle thermal and exergetic efficiencies, but above this temperature the thermodynamic performance improvement is lower. Bassily [9, 10] optimized the whole CC in which the steam cycle is reheated at two and three pressure levels, resulting in an efficiency enhancement by 1.9 - 2.1 % as compared to the design case. Godoy et al. [11] optimized a simple steam CC by maximizing its exergetic efficiency for a wide range of power with the determination of HRSG optimum surface. In order to increase the specific work of GT and TOT (due to its direct impact on the steam cycle performance), some studies suggested a reheated expansion and a blade cooling with the steam extracted from HRSG. Polyzakis et al. [12] optimized and compared between simple, intercooled, reheated and intercooled-reheated GT when adapted to a simple steam cycle, and concluded that the reheat is the most suitable solution. Khaliq and Kaushik [13] showed that the reheated expansion of GT improves the CC global performance, especially its specific work. Chiesa and Macchi [14] have demonstrated that an efficiency higher than 61% can be achieved when GT expansion is reheated and the turbine blades are cooled with the steam extracted from the bottoming cycle using a “closed loop” configuration. Also Sanjay et al. [15] have shown that with reheated expansion and steam turbine blade cooling, the thermal efficiency may reach 62

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%. Boyaghchi and Molaie [16] have suggested an advanced exergy and environmental analyses and a multi objective optimization of a CC plant with supplementary firing. Their results reveal that the optimum value of the total avoidable exergy destruction rate and CO2 emission indicates, respectively, 10.6% and 8.3% improvements comparatively to the basic case. The above mentioned studies have only addressed the thermodynamic analysis and optimization, but the maximization of performance may lead to a higher cost of investment and electricity [17, 18], and this is why other authors have considered the economical aspect. Casarosa et al. [19] made a thermo-economic optimization for TOT equal 700K, 773K and 823K, and have shown that the optimum pinch points are a consequence of a compromise between thermodynamic efficiency and investment costs. Bassily [20] optimized an objective function of net additional revenue for a triple pressure level reheat HRSG adapted to a GT reheated with exhaust gas recuperation. The optimization resulted in an annual saving of 33.7 million USD for a 481MW power plant. Kotowicz and Bartela [21] analyzed the influence of fuel price variation on the optimum values of the design parameters of the steam cycle parts, and found that an increase in fuel price requires higher optimum pressure in both high and intermediate pressure parts and lesser optimum pinch point and a higher optimum value of steam temperature in the intermediate pressure turbine. Ahmadi and Dincer [22] studied the effect of fuel cost on the optimum design variables of CC and concluded that by increasing the fuel price, the values of the decision variables in the thermo-economically optimum design tend to those of the thermodynamically optimum design. Carapellucci and Giordano [23] undertook a thermo-economic optimization of several types of HRSG adapted to three types of GT, and investigated the effect of fuel price and capacity factor on the electricity cost. Rovira et al. [24] considered the frequent off-design operation of CC and developed a thermoeconomic optimization model in order to minimize the electricity cost. Bakhshmand et al. [25] have optimized a CC with supplementary firing leading to 3% decrement in the power plant specific cost and consequently the cost of electricity. Rovira et al. [26] have optimized several configurations of CC using a partially recuperative gas turbine and an HRSG of two and three pressure levels, among their main conclusions: the optimum recuperative mass fraction is approximately 90% for both two and three pressure levels HRSG. By considering the exergo-economic and environmental aspects, Vandani et al. [27] have shown that the natural gas fuel leads to better performance comparing to diesel in operation of combined cycle power plants A synthesis of this review shows that most of previous studies addressed the optimization of one or several HRSG types intended to work with a specific gas turbine, but there is no study for both thermodynamic and economic aspects considering the effect of electricity selling price on the optimum design parameters and selection of the best HRSG configuration for a wide range of TOT. In fact, considering a range of TOT for several HRSGs and selling prices allows

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generalizing the results that can be correlated thereafter to get the NPV in relation with the selling price, which may in the case of preliminary. Accordingly, the main objectives of this study are as follows: 

A parametric analysis to illustrate the evolution of the net present value (NPV) according to the electricity selling price, interest rate and HRSG design variables.

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A thermodynamic optimization of three HRSG configurations namely: HRSG with one pressure level with reheat (1PRH), two pressure levels with reheat (2PRH) and three pressure levels with reheat (3PRH). The steam cycle specific work is considered as the objective function for a TOT range 350°C-650°C.

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An economic optimization of the three configurations for several selling prices considering NPV as an objective function

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A Thermo-economic optimization combining the thermodynamic objective function (steam cycle specific work) with the economic objective function (NPV). The highest TOTs which do not exceed 650°C are observed in the case of the most advanced gas turbines operating

under a high turbine inlet temperature (1500°-1600°C [28]). The following examples can be quoted: Westinghouse 501G (597°C) [21], Siemens SGT6-8000H (627°C) [29], GE S107FA (603°C) [30] and GE-P9371FB (644°C) [31]. For relatively low TOTs the conventional steam cycles do not operate suitably and other cycles are preferred such as the chemical recuperated gas turbine cycle (CRGT) and the organic Rankine cycle (ORC) [32], at a lower limit of 350°C is chosen. In this study the range of TOT 350°C-650°C is chosen to cover the majority of gas turbines.

2 THERMODYNAMIC MODELING An HRSG is used to recover the maximum of heat of a GT exhaust, through the optimization of the produced mass flow, temperature and pressure of steam taking into consideration some constraints such maximum pressure and temperature, minimal steam fraction at turbine outlet, minimum stack temperature and minimum pinch point. The simplest HRSG configuration that can be designed is the one pressure level without re-heat which destroys a considerable quantity of exergy. The transformation of one pressure level HRSG into two and three pressure levels HRSG with reheat allows the diminution of destroyed exergy, the recovery of more heat quantity and the reduction of exit gas temperature at the stack. However, by increasing the number of pressure levels increases the capital cost of steam cycle, and in this context both thermodynamic and economic aspects have to be considered. The quantity of steam to be produced and its temperature are more affected by the difference between the gas temperature leaving the evaporator and the temperature of the water leaving the economizer, and such a difference is composed of the sum of the approach point and the pinch point. The approach point is the difference between the temperature of saturated steam

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and the temperature of water at the exit of the economizer and the pinch point is the difference between the gas temperature leaving the evaporator and the temperature of saturated steam. The schematics of the three HRSG configurations are presented in Fig. 1, their temperature-transferred heat diagrams are given by Fig. 2. For an easy presentation, only the modeling of HRSG with three pressure levels and a reheat is shown. Each heat exchanger is modeled by means of mass and energy balance that can also be explained schematically by the Fig. 2. The energy balance for the evaporator, reheater and superheater of the third level, separately one by one, leads to the following equations respectively: (1) (2) (3) Through the sum on these three parts equations, the following expression is obtained: (4) The effectiveness of superheater and reheater is defined by: (5) (6) The definition of pinch point of the third level: (7) The temperature of gas leaving the economizer of third level (

) is obtained from energy balance: (8)

Equations from (3) to (8) represent a system of 6 equations with 6 unknowns:

and

, that

are solved by using a numerical method. The properties of water and steam and the determination of saturation temperatures are based on relations of the International Association of the Properties of Water and Steam (IAPWS) [33]. Contrary to the third level pressure (where the equations are coupled), the determination of the unknowns of the second level may be done explicitly. Knowing the steam temperature at evaporator exit (

wich is obtained

using the IAPWS relations), the steam temperature at the superheater exit is obtained from the definition of effectiveness: (9)

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Gas temperature at the outlet of second level evaporator (

is obtained by using the second level pinch point

definition: (10) It is now possible to determine the ratio of steam of the second pressure level from the energy balance across both evaporator and superheater: (11) The gas temperature at the outlet of economizer (

) is obtained from the second level economizer energy balance: (12)

For the first pressure level, similar relations as for the second level still apply. The exit temperature of superheater is obtained from the definition of effectiveness: (13) Gas temperature at the exit of the first level evaporator (

is obtained from the first level pinch point definition : (14)

The steam ratio of the first pressure level is determined from the energy balance across both evaporator and superheater: (15) The stack exit temperature (

) is obtained from the first level economizer energy balance: (16)

Once the system of equations is resolved, it is possible to determine the specific work produced by the three parts of the steam turbines (LP, IP, HP) and thus the total steam cycle specific work per 1kg of exhaust gas: (17) and

represent the ratios of steam for the first, second and third pressure level in relation to the gas mass flow

rate at the inlet of the HRSG. In general terms, the steady state exergy balance applied for a given control volume is written as follows:

For 1kg of exhaust and considering a control volume that corresponds to the whole steam cycle and by neglecting the exergy of heat transfer, equation (18) becomes: (19) The net exergy carried into the control volume: (20)

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The destroyed exergy can be deduced: (21) The destroyed exergy rate: (22) The validity of the proposed model is confirmed after comparing its results with the real data of three pressure levels and reheat steam cycle built around the GE-PG9371FB [31]. This comparison is presented in table 1 showing that the calculated values are close to the real data and the slight difference is due to other non-considered aspects by the present model such as the auxiliary equipments.

3 ECONOMICAL ASPECTS The net present value (NPV) is one of the most interesting criteria in the analysis of the economic performance because it represents the updated net income along the life of the project. Its mathematical formulation [21] is as the follows:

In equation (23)

represents the average service life,

is the annual interest rate and

is the cost operation and

maintenance. The assumed values of these three parameters in the case of economic optimization are given in table 2. is the capital charge factor defined as [34]:

The total annual income (

) is as follows: (25)

In equation (25),

is the electricity selling price in USD per kWh,

(obtained after a thermodynamic calculation) and The cost of the steam cycle (

is the steam cycle produced power in kW

is the yearly operating hours.

) is obtained by the sum of its components for which correlations are given in the table

3 [23, 35]. 4 OPTIMIZATION For a given GT the values of TOT and the specific work are fixed, and hence the maximization of the energetic or exergetic efficiency of CC requires only maximizing the specific work (per unit mass of exhaust gas) of the steam cycle which is considered as the objective function. Concerning the economic optimization, the NPV is chosen as the economic objective function that should be maximized. The pinch point of each pressure level, the superheater

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effectiveness and the pressures at different levels are the optimization variables of HRSG. The steam ratio at each level, the exit temperatures of superheaters and reheater in addition to the specific work and the NPV represent the optimization results.

4.1 Constraints analyses In order to avoid the mechanical and aerodynamic performance degradation of the last stages of the steam turbine, the steam fraction should be higher than 88% [36]. Ganjeh Kaviri et al. [37] have shown that from a thermo-economic and environmental point of view, the steam fraction at a turbine outlet should be higher than the value of 88%. The steam pressure and the temperature at exit of HRSG should not exceed 160 bar and 580°C, in order to maintain a good operation of HRSG and turbine material [38]. The condensed water in the exhaust gas could form a corrosive sulfuricacid, so the stack temperature should be higher than 80°C to avoid water condensation [39]. All these constraints are taken into account as summarized below:  Vapor fraction at exit of steam turbine should not drop below 88 %:

 Steam temperature at superheater exit or reheater should not exceed 580°C:

 Exhaust gases temperature must be higher than 80°C to avoid condensation and corrosion:

 Pressure of the third level should not exceed 160 bar:

 Pinch points:

 Superheaters and reheater effectiveness:

4.2 PSO Algorithm PSO method proposed by Eberhart and Kennedy [40] is inspired from the ability of groups of animals’ species to work as a whole, e.g. birds flocking to a food source, and this seeking behavior was associated with that of an optimization search for solutions to non-linear equations in a real-valued search space [41]. PSO algorithm starts with a population of solutions (taken randomly) and looks for an optimum for the problem, making population individuals

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evolving over generations and the research for the best solutions by moving the individuals from their previous positions (

) to better one (

) such as:

path towards their own previous best positions ( of the group (

. The role of the velocity (

) is to adjust the particles

), and towards the previous best position obtained by any member

), which is expressed as:

The performance of each particle is evaluated using the fitness function. In the case of the thermodynamic optimization, the fitness function is the steam cycle specific work per kg of exhaust gas (

, while for the economic optimization

the fitness function is the NPV. More details concerning this algorithm can be found in the reference [42]. An example, the objective function of 3PRH at TOT=600°C, in the case of thermodynamic and economic optimization, is shown (Fig. 3) to converge after about 40 iterations.

4.3 Thermo-economic optimization In order to consider simultaneously both thermodynamic and economic optimization, a bi-objective optimization is addressed in the present study. The two objective functions may be merged in a single one: (26) Since the orders of magnitude of the two objective functions are different, they were divided by their maximum values (

and

) obtained through the maximization of each objective. By varying

in the range 0-1

and maximizing , the Pareto front that gives a set of the best solutions is obtained. For instance, Fig.4 gives an example of Pareto front for TOT=600°C and a selling price of 0.04$/kWh. The Pareto front can be used for the determination of the equilibrium point, however in the present study an equitable influence between the two objectives was adopted and the weight was taken as

.

5 RESULTS AND DISCUSSION 5.1 Parametric analysis This section presents a parametric study in order to understand the evolution of NPV according to the electricity selling price, interest rate, HRSG design variables (pressure at HP turbine inlet, pinch points, superheaters and reheater effectiveness). The TOT, the gas mass flow rate and the pressure at HP turbine inlet are fixed at 600°C and 650 kg/s and 160 bar respectively.

a. Evaluation of NPV depending on the pinch point: Figure 5 shows NPV depending on the pinch point in the case of 3PRH configuration. The selling price and the interest rate are considered as parameters. It is well understood that the decrease of the pinch point makes the

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thermodynamic performance of the steam cycle increasing, but its impact on the net present value (NPV) is different. It depends greatly on the selling price and the interest rate. In fact, the decrease of the pinch point must ensure a compromise between the increase of the produced power and the over cost due to an increase in the exchange area caused by the decrease of the pinch point. The decrease of interest rate and increase of the selling price cause the reduction of the optimum pinch point. In the case of a relatively high selling price of 0.2$\kWh and a low interest rate of 0.04 (Fig. 5c), the optimum pinch point maximizing the NPV tends to its maximum value which corresponds, in fact, to the optimum thermodynamic pinch point. The increase of the interest rate till the value of 0.2 makes the optimum pinch point increase to reach a value of about 12°C. The optimum pinch point in the case of low interest rates is lower than the one of high interest rate values. For example, for a selling price of 0.08$\kWh, the optimum pinch point is about 7°C for i = 0.04 and about 22°C for i = 0.2 (Fig. 5b). The decrease of selling price till 0.04$\kWh, as shown by Fig. 5a, increases the optimum pinch point till 16°C for i = 0.04 and 31°C for i = 0.2. This is justified by the fact that the increase of “sp” and the decrease of “i” increase the net present value (NPV) and the over cost caused by the decrease of the pinch point is lower than the additional profit thanks to the surplus of power due to the same decrease of pinch point fostering the reduction of the optimum pinch point, and vice-versa. For the low selling prices and high interest rates, the profits decrease and consequently cannot overcome the over cost due to the reduction of pinch point that must increase its optimum value in order to reduce its exchange area and then reduce the steam cycle cost and finally allow the NPV to keep its maximum value.

b. Variation of NPV depending on superheater effectiveness: For the configuration 3PRH, Fig. 6 shows that the optimum effectiveness of the superheater depends on the selling price and the interest rate. It increases with the decrease of interest rate and the increase of selling price. In the case of a combination between a low selling price and a high interest rate, the optimum effectiveness does not tend to the highest value. As shown by Fig. 6a, if the selling price is 0.04$/kWhr and the interest rate is 0.2, the optimum effectiveness is approximately 0.75. By decreasing the interest rate till 0.04 it increases the optimum effectiveness to 0.85. On the other hand, by increasing the selling price also increases the optimum as shown by Figs.6b and 6c revealing that the combination between the high selling price and the low interest rate makes the optimum effectiveness to reach its maximum value.

c. NPV variation depending on inlet pressure of HP turbine: The optimum pressure at the inlet of HP turbine in the case of 3PRH configuration is influenced by the selling price and the interest rate, but only in the case of a combination between a low sp=0.04$/kWhr and a high interest rate of 0.2.

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Figure 7a shows that in this case the optimum pressure takes a value of 120 bar. For the same interest rate (i= 0.2), by increasing the selling price to sp=0.08$/kWhr, the optimum pressure is 140 bar (Fig. 7b). In the other cases, as shown by Figs. 7b and 7c, the NPV increases when the pressure at the inlet of HP turbine increases.

5.2 Thermodynamic optimization The optimum specific work obtained for three HRSG configurations is given by Fig. 8. As seen, for all TOT values, adding a pressure level is always interesting and an HRSG configuration of 3PRH leads to high values of the specific work than HRSG of 2PRH or 1PRH. This is due to the fact that by adding a pressure level this allows achieving higher pressures, destroying less exergy and producing more steam quantities. This explanation is argued according to Fig. 9 showing that at higher pressure level the optimum pressure becomes higher for a given TOT. For example, for TOT=450°C for 3PRH, the pressure at inlet HP turbine reaches 92 bar, while for 2PRH it is 48 bar and only 22 bar for 1PRH. It is also shown from this figure that the optimum pressure at the inlet of HP turbine cannot reach the limit of 160 bar for given values of TOT: 580°C for 1PRH, 530°C for 2PRH and 500°C for 3PRH, because a low value of TOT leads to a low superheated steam temperature and subsequently a low steam fraction which must remain above a value of 0.88. For the values of TOT higher than these latter, the optimum inlet pressure at the HP turbine reaches its limit and becomes constant due to imposed constraint on the maximum cycle pressure that must be under a value of 160bar as previously mentioned in section 4.1. This result is practically justified by the fact that the maximum pressure of a steam cycle is constrained by the steam fraction in the last stages of LP turbine which must be higher than 88 % for a given inlet turbine temperature. In addition, the use of a high pressure leads to a low steam fraction at the end of expansion. Consequently, there is recourse to reheat in order to increase the steam fraction (and the pressure at turbine inlet). On other hand, Fig. 9 shows that the steam temperature after a reheat in 3PRH is higher than for 2PRH or1PRH, which justifies the fact that for a given TOT, 3PRH pressure level allows reaching high pressures more than in the case of 2PRH or 1PRH. Also Fig. 9 gives the optimum total steam ratio obtained as a function of partial steam ratios of all levels. HRSG with 3PRH allows producing more steam as compared with 2PRH or 1PRH, which is valid for all values of TOT. For example, at TOT equal 600°C, the produced optimum total steam ratios are 13.3 %, 14.8 % and 16.4 % for 1PRH, 2PRH and 3PRH, respectively. Another thermodynamic aspect in the favor of configuration 3PRH, concerns the destroyed exergy. The evolution of destroyed exergy with TOT is illustrated by Fig. 10, showing that for an HRSG of 3PRH, the destroyed exergy is the lowest. Thus one may conclude from a thermodynamic point of view that for all TOT values the 3PRH is the best configuration since it allows achieving a high pressure, destroying less exergy, producing more steam quantities and more specific work. However, this causes an increase of the steam cycle cost.

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5.3 Economic optimization As shown by Fig. 11, for an exhaust gas mass flow rate of 650 kg/s, the cost of a configuration 3PRH is significantly higher than 2PRH or 1PRH. Also, this figure shows that the steam cycle cost for a given gas mass flow rate increases with TOT. Furthermore, for a TOT equal to 650°C and above, the cost of steam cycle marks relatively a rapid increase than for low TOTs. In order to decide between the three types of HRSG, the economical aspect should be considered. The design parameters maximizing

and NPV for several electricity selling prices will be determined.

Figure 12 plots the maximum values of NPV for different values of TOT considered in this study, and as revealed the selling price influences the optimum configuration. For a low selling price of 0.04 $/kWhr (Fig. 12a) an HRSG with 2PRH represents the best configuration and 1PRH is more profitable than 3PRH for all TOTs. The more the selling price increases the more the addition of another level of pressure becomes more interesting. Also, the 2PRH seems to be the best configuration for the relatively medium selling prices (Fig. 12b), but 3PRH leads to higher NPV than 1PRH whatever the value of TOT. Furthermore, even for a high selling price, for example 0.2 $/kWhr (Fig. 12c), the 2PRH allows having NPV values similar to those of the configuration 3PRH. For a selling price of 0.3 $/kWhr and values of TOT lower than 600°C, the configuration of 3PRH allows getting higher NPVs than for 2PRH. The optimization of the three HRSG configurations to operate with a specific gas turbine such as GE-PG9371FB (design parameters are listed in table 1) allows obtaining the results reported in table 4, which reveals that for prices lower than or equal to 0.2 $/kWh, the use of the configuration of 2PRH is more beneficial while the 3PRH is only interesting for a very high selling price of 0.3$/kWh. The configuration 1PRH is also better than 3PRH for prices equal 0.04 and 0.08 $/kWh while for a very high selling price, the configuration 1PRH gives the lowest NPV. For Sp=0.04 the net benefit obtained with 2PRH is higher than the one of 3PRH by 42.26 million USD which represents 13.2 % of the NPV obtained with 3PRH. Increasing the selling price till 0.08 or 0.2 $/kWh decreases the net benefit, respectively, at 4.97% and 2.11%, but 2PRH remains better than 3PRH. Furthermore, for a low price such as 0.04$/kWh, the NPV of 1PRH is higher than 3PRH by 31.47 million USD representing 9.82%. The results of Fig. 12 can be correlated to express the NPV in relation to TOT, gas mass flow rate and selling price, thus, the following correlations are suggested for 1PRH, 2PRH and 3PRH:

The mean absolute percentage error (MAPE) is 1.2 %, 1.04 % and 2.3 %, respectively for 1PRH, 2PRH and 3PRH. The MAPE is defined as follows:

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where

is the actual value (results of Fig. 12),

is the number of times for which

is the value obtained with the correlation and

is calculated.

The optimum economic design parameters maximizing the NPVs are compared to those of the optimum thermodynamic design parameters in Fig. 13, Fig. 14 and Fig. 15, plotting for several selling prices the optimum pressure at the inlet of HP turbine, the pinch point and the effectiveness of the superheater. The evaluated data of these curves are given in tables from 5 to 7.The analyses of these curves reveal the following aspects: Inlet pressure at HP turbine: For the configuration 3PRH (Fig. 13a), the more the selling price increases, the more the optimum economic design inlet pressure tends to the optimum thermodynamic design value, till reaching the constraint of 160 bar. For the 2PRH (Fig. 13b), even though the decrease in selling price leads to an optimum economic inlet pressure which is different from that of the optimum thermodynamic design value, but the difference is not as significant as in the case of 3PRH. This is also confirmed for the 1PRH, as shown by Fig. 13c, for which the optimum economic design inlet pressure coincides with the thermodynamic design value for all TOTs. It may be concluded that, in addition to the fact that a decrease in selling price brings the economic and the thermodynamic optimum values close, the reduction in pressure levels allows making the economic optimum independent of the selling price and close to the thermodynamic optimum owing to a lesser cost of steam cycle and subsequently an increase in NPV. Pinch points: Figure14 allows noticing that in case of 3PRH, the pinch point is clearly influenced by the selling price for which a reduced value moves the optimum thermodynamic design value away from the optimum economic design, but this is not the case for 2PRH and 1PRH which reveal a similarity between the optimum thermodynamic and the economic pinch point. For a relatively high selling price (0.2$/kWhr or 0.3$/kWhr), the optimum pinch point of 3PRH is identical to the thermodynamic optimum, except for TOT equal 650°C where the noticeable difference is attributed to a rapid increase in the cost of steam cycle for this temperature, as previously illustrated by Fig. 11. Superheater effectiveness: Figure 15 shows that for the thermodynamic optimization, the superheater effectiveness tends to its maximum value of 0.85 for all the TOTs except for 650°C, for which a drop is noticed. However, for TOT=650°C in the case of 3PRH and 2PRH, the reduction of selling price always tends to move the economic optimum away from the thermodynamic one, but for the 1PRH, as expected, there is no noticeable influence. In summary, the 3PRH allows destroying less exergy reaching higher optimum inlet pressure and producing more steam quantity and specific work, thus representing the best configuration from a thermodynamic point of view. However, with respect to the economic aspect, the results are different and the choice for the optimum configuration depends on the electricity selling price, when the NPV is chosen as a criterion for the economic performance. For low

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selling prices, the 2PRH represents the best configuration and 1PRH leads to higher NPV than 3PRH, whereas for a medium selling price, the 2PRH also represents the best configuration and 3PRH leads to a higher NPV than the case of 1PRH. For high selling prices and medium TOTs, the configuration 3PRH has the highest NPV, but for high TOTs the configuration 2PRH remains the best solution due to the high cost of 3PRH. Concerning the optimum design parameters, the selling price seems to impact much more on the 3PRH configuration and the more the selling price drops the more the parameters of the optimum economic design parameters move away from the parameters of the optimum thermodynamic design. The reduced selling price leads to a decrease in the optimum pressure at the inlet of HP turbine, an increase in pinch point and a decrease of superheater effectiveness. However, the influence for 2PRH is less than 3PRH, and it is almost insignificant for 1PRH. This can be explained by the fact that by reducing the number of pressure levels, this leads to a lesser cost of the steam cycle and therefore an increase in NPV.

5.4 Thermo-economic optimization As shown in the previous section, in the case of a configuration 3PRH, (when NPV is considered as the objective function to be maximized), the optimum pressure at HP turbine inlet increases with the selling price, especially for TOT lower or equal than 550°C, till reaching the optimum pressure of the thermodynamic optimization. For TOT higher than 550°C, the pressure reaches its limit which is constrained by the value of 160 bar, whatever the selling price. However, the combination of the two objectives reduces the sensitivity of the optimum pressure toward the selling price, as shown by Fig.16. For a price higher or equal than 0.08$/kWhr, the optimum pressures correspond practically to those of the thermodynamic optimization, except for sp=0.04$/kWh where the optimum pressure is different. Figure 17 reveals that the optimum pinch point of 3PRH shows a sensitivity toward the selling price only for a low value of 0.04$/kWhr and practically for all TOTs, except 350°C. For the selling price of 0.08$/kWhr, the change in the optimum values start from a TOT of 550°C, while for the economic optimization, changes are significant for all the TOTs. This increase in the pinch point may be explained by the increase of the steam cycle capital cost with TOT (as previously shown by Fig. 11). For the selling prices 0.2$/kWhr and 0.3$/kWhr, the optimum pinch points correspond to the results obtained in the thermodynamic optimization independently from TOT. For the configuration 2PRH the optimum pressure (which is slightly dependent on selling price) converges totally to the thermodynamic results, in the case of thermo-economic optimization, as illustrated by Fig. 16. For 1PRH, since both of the thermodynamic and the economic optimizations lead to the same parameters. The combination will also give the same results, thus by considering the two objectives simultaneously is not necessary. Concerning the superheater effectiveness, Fig. 18 shows that it has no significant effect on the optimum values and all of them take approximately the same value in both thermodynamic and thermo-economic optimizations.

14

6 CONCLUSION A thermo-economic parametric study and an optimization were undertaken for HRSG of configurations one, two and three pressure levels with a reheat, and considering several values of turbine outlet temperature, electricity selling prices and interest rate. The considered objective functions are the steam cycle specific work and the NPV for thermodynamic and economic optimizations, respectively. Correlations relating the NPVs of the three configurations HRSG in relation to TOT, gas mass flow rate and selling price are suggested. The main conclusions to be drawn are:  From the thermodynamic point of view, the steam cycle with 3PRH and reheat is the best configuration for all values of TOT because it allows producing more steam quantities, reaching higher pressures, destroying less exergy and producing more specific work.  Considering the economical aspect, for the low and medium selling prices (0.04-0.08$/kWh and 0.2$/kWh), 2PRH is the best configuration.  The configuration 3PRH would only be interesting for a high selling price of 0.3$/kWh and TOT range 450-600°C, while for a high TOT (650°C) the high cost of 3PRH leads to NPV decrease.  The electricity selling price impacts more the 3PRH and its influence on the design parameters of 2PRH is less than for 3PRH, and becomes almost insignificant for 1PRH.  For the configuration 3PRH, the less electricity selling price, the more the economic optimum moves away from the thermodynamic one.  The two objective functions steam cycle specific work and NPV show that, in the case of 3PRH, the selling price influences only the design parameters for a low value of 0.04$/kWh, whereas for 2PRH and 1PRH, their optimum parameters are non sensitive to the selling price variation.  The interest rate influence has revealed via the parametric analysis an important effect on NPV and on optimum design parameters. As a perspective to improve the NPV correlations a wide range of interest rate, system life and additional cost due to emissions will be included.

Funding This research has received no funding

Conflict of interest None declared.

15

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NOMENCLATURE

18

Heat transfert area [

]

Cost [US$] Specific heat capacity [kJ/kg K] Effectiveness of exchanger Ex

Exergy [kJ] Specific exergy [kJ/kg] Fitness function Global best solution Steam or water specific enthalpy [kJ/kg] Yearly operating hours Annual interest rate Total annual income Mass flow rate [kg/s] Condenser cooling water mass flow rate [kg/s] Number of particles in population Average service life Pressure [bar] Power [kW] Best solution for each particle Population Selling price Temperature [K] speed of particle vector Inertia weight Specific work [kJ/kg] Vapor fraction at turbine exit Optimization variables vector Logarithmic mean temperature difference [K] Pinch point [K] Efficiency

19

Isentropic efficiency Steam to gas mass ratio SUBSCRIPTS Condenser Exit Economizer Evaporator Gas High pressure Inlet Intermediate pressure Particle Low pressure Reheater Steam Steam cycle Superheater Steam turbine Thermal First level Second level Third level Gas station at different heat exchangers ABBREVIATION GT

Gas turbine

CC

Combined cycle

HRSG

Heat recovery steam generator

IAPWS

International Association for the Properties of Water and Steam

NPV

Net present value

TOT

Turbine outlet temperature

20

1PRH

Reheat one pressure level HSRG

2PRH

Reheat two pressures level HSRG

3PRH

Reheat three pressures level HSRG

21

(a)

(b)

(c) Figure 1: Three configurations of HRSG: a) 1PRH, b) 2PRH, c) 3PRH

(a)

(b)

22

(c) Figure 2: Temperature-transferred heat diagram: a) HRSG 1PRH, b) HRSG 2PRH, c) HRSG 3PRH

222

6.3x10

8

6.3x10

8

6.2x10

8

6.2x10

8

6.2x10

8

6.2x10

8

220

NPV ($)

Wsc (kJ/kg)

218 216 214 212 210 10

20

30

40

50

60

70

80

90

100

10

20

30

40

Iterations

50

(a)

70

80

90

100

(b)

Figure 3: Objective function convergence for 3PRH at TOT=600°C: a)

maximization, b) NPV maximization

280 278

NPV (Million US$)

60

iterations

276 274 272 270 207

208

209

210

211

212

213

214

215

Ws (kJ/kg)

Figure 4: Pareto front in the case of 3PRH, TOT=600°C and sp=0.04

23

112

106 104

258.5

102 258.0

100

i=0.04 i=0.2

257.5

NPV (million US$)

108 259.0

262.5

585.0

NPV (million US$)

NPV (million US$)

586.5

110

259.5

98

260.0

583.5

257.5

582.0

255.0

580.5

252.5

i=0.04 i=0.2

579.0

NPV (million US$)

260.0

250.0

96 3

6

9

12

15

18

21

24

27

30

3

6

9

Pinch point (K)

12

15

18

21

24

27

30

Pinch point (K)

(a)

(b)

1575

i=0.04 i=0.2

1570

726

722

1560 1555

720 1550 1545

NPV (million US$)

NPV (million US$)

724 1565

718 3

6

9

12

15

18

21

24

27

30

Pinch point (K)

(c) Figure 5: NPV variation for 3PRH versus pinch point, selling price (sp) and interest rate (i) as parameters: a) sp=0.04$/kWh, b) sp=0.08$/kWh, c) sp=0.2$/kWh

718

716

351 147.5 350 147.0

349

NPV (million US$)

148.0

NPV (million US$)

NPV (million US$)

352

320

i=0.04 i=0.2 319

714

712

318

710 317 708

348

146.5 0.4

0.5

0.6

0.7

0.8

0.4

0.9

0.5

0.6

0.7

0.8

Superheater effectiveness

Superheater effectiveness

(a)

(b)

24

0.9

NPV (million US$)

i=0.04 i=0.2

i=0.04 i=0.2

836

NPV (million US$)

1805

834

1800

832

1795

830

1790

828

NPV (million US$)

1810

826

1785 0.4

0.5

0.6

0.7

0.8

0.9

Superheater effectiveness

(c) Figure 6: NPV variation for 3PRH versus superheater effectiveness: a) sp=0.04$/kWh, b) sp=0.08$/kWh, c) sp=0.2$/kWh

353

319

715 147.5

351

146.5 347 146.0 345

317 705 315

700

i=0.04 i=0.2

344

710

145.5 40

60

80

100

120

140

i=0.04 i=0.2 40

160

60

80

100

120

140

NPV (million US$)

348

NPV (million US$)

147.0

NPV (million US$)

NPV (million US$)

318 350

314

160

Pressure at HP turbine inlet (bar)

Pressure at HP turbine inlet (bar)

(a)

(b) 1810

835

830 1790 825 1780 820

1770

i=0.04 i=0.2

1760 40

60

80

100

120

140

NPV (million US$)

NPV (million US$)

1800

815

160

Pressure at HP turbine inlet (bar)

(c) Figure 7: NPV variation for 3PRH versus the pressure at HP turbine inlet: a) sp=0.04$/kWh, b) sp=0.08$/kWh, c) sp=0.2$/kWh

25

1PRH 2PRH 3PRH

220 200 180

Wsc (kJ/kg)

160 140 120 100 80 60 40 350

400

450

500

550

600

650

TOT(°C)

Figure 8: Steam cycle specific work versus TOT

Pressure at HP turbine inlet (bar)

160

1PRH 2PRH 3PRH

140

18

500

16

450

14

400

12

350

120 100 80 60

pressure at HP turbine inlet (bar) steam ratio (%) steam temperature at inlet of reheater (°C)

40 20

10 8

300

250

0 350

400

450

500

550

600

650

TOT(°C)

Figure 9: Optimum pressure at inlet of HP turbine, optimum total steam ratio and steam temperature at exit of reheater versus TOT

50

1P 2P 3P

45

exdr (%)

40 35 30 25 20 350

400

450

500

550

600

650

TOT(C°)

Figure 10: Destroyed exergy of steam cycle

26

Steam cycle cost (Million US $)

130

3PRH 2PRH 1PRH

120 110 100 90 80 70 60 50 40 30 20 350

400

450

500

550

600

650

TOT

Figure 11: Steam cycle cost corresponding to the optimum thermodynamic parameters of steam cycle

8

1PRH 2PRH 3PRH

8x10

8

7x10

8

3.5x10

8

3.0x10

8

6x10

8

2.5x10

8

5x10

8

2.0x10

8

4x10

8

1.5x10

8

3x10

8

1.0x10

8

2x10

8

5.0x10

7

1x10

8

NPV ($)

NPV ($)

4.0x10

350

400

450

500

550

600

650

1PRH 2PRH 3PRH

350

400

450

TOT (°C)

1.6x10

9

1.4x10

9

1.2x10

9

1.0x10

9

8.0x10

8

6.0x10

8

4.0x10

8

3.0x10

1PRH 2PRH 3PRH

NPV ($)

NPV ($)

9

350

400

450

500

550

600

650

(b)

9

1.8x10

550

TOT (°C)

(a) 2.0x10

500

600

650

9

2.5x10

9

2.0x10

9

1.5x10

9

1.0x10

9

5.0x10

8

1PRH 2PRH 3PRH

350

400

450

500

550

600

TOT (°C)

TOT (°C)

(c)

(d)

Figure 12: Optimum NPVs versus TOT for several electricity selling price: a) sp=0.04$/kWhr, b) sp=0.08$/kWhr, c) sp=0.2$/kWhr, d) sp=0.3$/kWhr

27

650

160

Pressure at HP turbine inlet (bar)

Pressure at HP turbine inlet (bar)

160 140 120 100 80

sp=0.04 $/kWh sp=0.08 $/kWh sp=0.2 $/kWh sp=0.3 $/kWh Thermodynamic optimization

60 40 20 350

400

450

500

550

600

140 120 100 80

sp=0.04 $/kWh sp=0.08 $/kWh sp=0.2 $/kWh sp=0.3 $/kWh Thermodynamic optimization

60 40 20 350

650

400

450

550

600

650

TOT (°C)

TOT (°C)

(a) 160

Pressure at HP turbine inlet (bar)

500

(b) sp=0.04 $/kWh sp=0.08 $/kWh sp=0.2 $/kWh sp=0.3 $/kWh Thermodynamic optimization

140 120 100 80 60 40 20 350

400

450

500

550

600

650

TOT (°C)

(c)

20

20

18

18

16

16

Pinch point (°C)

Pinch point (°C)

Figure 13: Effect of selling price on optimum inlet pressure at HP turbine: a) 3PRH, b) 2PRH, c) 1PRH

14

sp=0.04 $/kWh, sp=0.08 $/kWh sp=0.2 $/kWh, sp=0.3 $/kWh Thermodynamic optimization

12 10 8

sp=0.04 $/kWh sp=0.08 $/kWh sp=0.2 $/kWh sp=0.3 $/kWh Thermodynamic optimization

14 12 10 8

6

6

4

4

350

400

450

500

550

600

650

350

400

450

TOT (°C)

500

550

600

650

TOT (°C)

(a)

(b)

Figure 14: Effect of electricity selling price on optimum pinch point: a) 3PRH, b) 2PRH and 1PRH

28

0.90

0.85

0.85

Superheater effectiveness

Effectiveness of superheater

0.90

0.80 0.75

sp=0.04 $/kWh sp=0.08 $/kWh sp=0.2 $/kWh sp=0.3 $/kWh Thermodynamic optimization

0.70 0.65

0.80 0.75

sp=0.04 $/kWh sp=0.08 $/kWh sp=0.2 $/kWh sp=0.3 $/kWh Thermodynamic optimization

0.70 0.65 0.60

0.60 350

400

450

500

550

600

350

650

400

450

500

550

600

650

TOT (°C)

TOT (°C)

(a)

(b) 0.90

Superheater effectiveness

0.85 0.80 0.75

sp=0.04 $/kWh sp=0.08 $/kWh sp=0.2 $/kWh sp=0.3 $/kWh Thermodynamic optimization

0.70 0.65 0.60 350

400

450

500

550

600

650

TOT (°C)

(c) Figure 15: Effect of selling price on optimum effectiveness: a) 3PRH, b) 2PRH, c) 1PRH

Pressure at HP turbine inlet (bar)

160 140

3PRH

120 100 80

sp=0.04$/kWh sp=0.08$/kWh sp=0.2$/kWh sp=0.3$/kWh Thermodynamic optimization

60 40

2PRH

20 350

400

450

500

550

600

650

TOT (°C)

Figure 16: Selling price effect on optimum

pressure at HP turbine inlet of 2PRH and 3PRH in case of thermo-

economic optimization. Dashed lines: 3PRH, continuous lines: 2PRH

29

20

Pinch point (°C)

15

sp=0.04 $/kWh, sp=0.2 $/kWh, Thermodynamic optimization

sp=0.08 $/kWh, sp=0.3 $/kWh,

400

550

10

5

0 350

450

500

600

650

TOT (°C)

Figure 17: Selling price effect on optimum pinch point of 3PRH in case of thermo-economic optimization

Effectiveness of superheater

0.88 0.84 0.80 0.76 0.72 0.68

sp=0.04 $/kWh sp=0.08 $/kWh sp=0.2 $/kWh sp=0.3 $/kWh Thermodynamic optimization

0.64 0.60 0.56 0.52 350

400

450

500

550

600

650

TOT (°C)

Figure 18: Selling price effect on optimum 3PRH superheater effectiveness in case of thermo-economic optimization

30

Table 1: Model validation Parameter (unit) Power ( MW) 1st level mass flow rate (kg/s) 2nd level mass flow rate (kg/s) 3rd level mass flow rate (kg/s) Maximum steam cycle temperature (°C) Stack temperature (°C)

Real data [31] 145.5 12.63 12.76 86.7 565 96

Model results 146.21 13.01 13.51 88.07 564.9 94.8

Table 2 : Economic assumptions Economic parameters Average service life ( ) Yearly operating hours ( ) The annual interest rate ( ) Electricity selling price ( ) Operation and maintenance cost (

Assumptions 12 years 8000 hours [16] 8% [19] 0.04 - 0.3 $/kWh 10% of [16]

)

Table 3: Steam cycle components costs [23, 35] Number of elements

Steam turbines

Cost correlations

3 corresponds to LP turbine, IP turbine and HP turbine

HRSG heat exchangers

10

( 1.2

990)500

0.8+17500.2 =1100.097 30+0.9

+1948.4

corresponds to the heat exchanger in the HRSG namely: 1st, 2nd and 3rd level economizers, evaporators and superheaters.

Condenser

Pumps

1 3

31

corresponds to the pump of each level (pump of 1st , 2nd and 3rd level).

Table 4: Optimized NPV in case of the gas turbine GE-PG9371FB Sp ($/kWh) 1PRH (million US$) 2PRH (million US$) 3PRH (million US$) 0.04 346.7046 362.565 320.306 0.08 701.339 727.842 693.406 0.2 1773.725 1863.937 1825.420 0.3 2667.792 2790.898 2809.531

Table 5: 3PRH optimum design variables TOT (°C)

350 400 450 500 550 600 650

Thermodynamic optimization (bar) 41.93 63.10 139.56 160 160 160 160

(K) 5 5 5 5 5 5 5

Economic optimization Sp=0.04

0.85 0.85 0.85 0.85 0.85 0.85 0.76

(bar) 31.35 50.05 78.66 102.72 160 160 160

(K) 14.19 14.28 14.35 14.39 15.83 17.62 19.04

Sp=0.08

0.85 0.85 0.85 0.85 0.85 0.85 0.64

(bar) 33.43 54.88 82.20 138.10 160 160 160

(K) 6.28 6.36 7.21 7.67 8.46 9.42 11.11

Sp=0.2

0.85 0.85 0.85 0.85 0.85 0.85 0.69

(bar) 33.44 55.30 92.80 160 160 160 160

(K) 5 5 5 5 5 5 6.02

Sp=0.03

0.85 0.85 0.85 0.85 0.85 0.85 0.75

(bar) 33.62 55.91 103.37 160 160 160 160

(K) 5 5 5 5 5 5 5.73

0.85 0.85 0.85 0.85 0.85 0.85 0.75

Table 6: 2PRH optimum design variables TOT (°C)

350 400 450 500 550 600 650

Thermodynamic optimization (bar) 21.34 36.34 55.69 95.00 160 160 160

(K) 5 5 5 5 5 5 5

Economic optimization Sp=0.04

0.85 0.85 0.85 0.85 0.85 0.85 0.76

(bar) 21.12 32.37 53.85 78.02 160 160 160

(K) 5 5 5 5 5 5 5

Sp=0.08

0.85 0.85 0.85 0.85 0.85 0.85 0.73

(bar) 21.20 32.85 54.59 87.52 160 160 160

(K) 5 5 5 5 5 5 5

Sp=0.2

0.85 0.85 0.85 0.85 0.85 0.85 0.75

(bar) 21.11 32.26 54.67 87.49 160 160 160

(K) 5 5 5 5 5 5 5

Sp=0.03

0.85 0.85 0.85 0.85 0.85 0.85 0.76

(bar) 21.90 32.94 54.013 87.04 160 160 160

(K) 5 5 5 5 5 5 5

0.85 0.85 0.85 0.85 0.85 0.85 0.76

Table 7: 1PRH optimum design variables TOT (°C)

350 400 450 500 550 600 650

Thermodynamic optimization (bar) 11.021 16.754 24.356 38.006 59.014 160 160

(K) 5 5 5 5 5 5 5

Economic optimization Sp=0.04

0.85 0.85 0.85 0.85 0.85 0.85 0.75

(bar) 11.022 16.754 24.354 38.006 59.014 160 160

(K) 5 5 5 5 5 5 5

Sp=0.08

0.85 0.85 0.85 0.85 0.85 0.85 0.75

(bar) 11.021 16.754 24.355 38.006 59.014 160 160

32

(K) 5 5 5 5 5 5 5

Sp=0.2

0.85 0.85 0.85 0.85 0.85 0.85 0.75

(bar) 11.022 16.754 24.356 38.008 59.034 160 160

(K) 5 5 5 5 5 5 5

Sp=0.03

0.85 0.85 0.85 0.85 0.85 0.85 0.75

(bar) 11.020 16.749 24.343 38.004 59.018 160 160

(K) 5 5 5 5 5 5 5

0.85 0.85 0.85 0.85 0.85 0.85 0.75

33

Highlights  Thermo-economic optimization of HRSG configurations  The maximum value of the net present value was targeted for the economic optimization  Three level HRSG is the best option in respect of power output and high priced medium  Two level HRSG is the best for net benefit in low and intermediate priced mediums

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