Economic analysis of a combined power and desalination plant considering availability changes due to degradation

Desalination 414 (2017) 1–9

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Economic analysis of a combined power and desalination plant considering availability changes due to degradation Ahmad Mohammad Alizadeh Arani, Vahid Zamani, Ali Behbahaninia ⁎ Department of Energy System Engineering, Faculty of Mechanical Engineering, K.N.Toosi University of Technology, Iran

H I G H L I G H T S • • • • •

The paper presents a new economic analysis method for thermal systems. State space method with time-varying failure rate is used to estimate availability changes due to degradation and overhauls. The maintenance cost is calculated considering overhaul and number of components repairs. A combined gas turbine and multi-stage flash desalination plant is considered as the case study. The results are compared with conventional economic analysis method.

a r t i c l e

i n f o

Article history: Received 27 September 2016 Received in revised form 23 February 2017 Accepted 21 March 2017 Available online xxxx Keywords: Economic analysis Availability Time-varying failure rate Thermal system Multi-stage flash desalination plant

a b s t r a c t In a conventional economic analysis, the availability of system is considered as a constant value. However, some factors such as increasing components' failure rate due to degradation, reducing failure rates by replacement or repairing, and stops in operation because of overhauls change the availability during the lifetime of a system. Furthermore, due to overhauls and degradation, maintenance costs are not identical in different years. This paper presents a new approach for economic analysis of thermal systems in which change in the availability of system during its lifetime is considered. A combined gas turbine cycle and desalination is studied. The instantaneous availability of system is calculated using state space method with time-varying failure rates and considering overhauls. Then, the average availability of producing electricity and fresh water in each year of lifetime is applied to the economic analysis. In addition, maintenance costs are calculated according to the overhauls and the number of components repairs in each year. Finally, some economic indicators are compared in two cases of variable and constant availability, using the life cycle cost analysis method. Considering time-varying availability, increase in payback period is observed by 9 months and reduction in net present value by about $18 million. © 2017 Elsevier B.V. All rights reserved.

1. Introduction Economic analysis is one of the most important factors in selection and usage of thermal systems, in which indicators such as payback period, net present value, products unit cost, and benefit-cost ratio are studied by different methods. Life cycle cost analysis is one of the most widely used methods. Performing an economic analysis needs some predictions regarding economic and operational parameters. There are some works which consider uncertainties in various economic parameters. For example, Momen et al. considered uncertainty of economic parameters in the economic optimization of a cogeneration system using Monte Carlo method [1]. ⁎ Corresponding author. E-mail address: [email protected] (A. Behbahaninia).

http://dx.doi.org/10.1016/j.desal.2017.03.026 0011-9164/© 2017 Elsevier B.V. All rights reserved.

There are many researches on the economic analysis and feasibility study of energy systems. An economic analysis was carried out on a cogeneration system, and the present value of incomes and costs, payback period, and internal rate of return were calculated [2]. Petrillo et al. presented a life cycle cost analysis and life cycle assessment for a hybrid renewable system [3]. Rodriguez et al. assessed the performance of several designs of hybrid systems composed of photovoltaic panels, solar thermal collectors, and natural gas internal combustion engines using life cycle cost analysis [4]. Tadros performed an economic study on multi-stage flash (MSF) desalination combined with a variety of steam and gas turbines and discussed the optimum value of performance ratio and its effect on reducing the desalinated water cost in each scheme [5]. Gomar et al. carried out a techno-economic analysis to select the most economic desalination method for Assaluyeh combined cycle power plant [6]. Rautenbach and Arzt demonstrated the superiority of the multiple-

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Nomenclature A P W t i d n _f m cf cw ce N Z

Average availability Probability Power (kW) Time Inflation rate (%) Discount rate (%) Year Fuel consumption rate (kg/s) Fuel unit cost ($/GJ) Fresh water price ($/m3) Electricity price ($/kWh) Plant economic life (year) Investment cost (M$)

Greek letter λ Failure rate μ Repair rate α Weibull distribution scale parameter β Weibull distribution shape parameter

Abbreviation PV Present value OM Operation and maintenance cost LHV Lower heating value (kJ/kg) MTTR Mean time to repair ARC Average repair cost O&M Operation and maintenance GT Gas turbine HRSG Heat recovery steam generator MSF Multi-stage flash

Subscript TC TB f e w G H D

Total cost Total benefit Fuel Electricity Fresh water Gas turbine Heat recovery steam generator Desalination

effect stack (MES) process compared to the standard MSF process for a desalination plant to combine with a 10 MW gas turbine [7]. Sun studied energy efficiency and economic feasibility of a cogeneration system and concluded that using this combined system results in 37% energy saving and payback period reduction of 4.5 to 2.65 years [8]. Operation time of a system during its lifetime and, as a result, the amount of products plays a key role in its economic analysis. Thermal systems cannot operate continuously because of random failures and preventive maintenance at defined intervals which change the availability of a system. System availability depends on its components' failure and repair rates. However, if they are assumed to be constant with time, degradation of the system is ignored and, as a result, the availability is nearly constant. There are some researches on feasibility study and economic analysis of thermal systems, especially desalination plants coupled

with a gas turbine, assuming a constant value for the system availability without any availability analysis [9–12]. There are different methods for reliability and availability analysis; one of the most widely used methods is Markov state space [13–16]. These studies assume constant values for components' failure and repair rates. If time-varying failure rates are considered in the availability analysis, the economic evaluation results will be more accurate. There are few studies on availability analysis with time-varying failure rates [17–23], and the results of these analyses have not been used for economic evaluation. This paper presents a new method for the economic analysis of thermal systems considering time-varying availability. At first, instantaneous availability at any time is obtained using state space method with time-varying failure rates. Furthermore, periodic overhauls which stop production and decrease failure rates are considered. Then, the average availability in each year of system's lifetime is calculated and used for the economic analysis. The system studied in this research is an MSF desalination plant coupled with a gas turbine (GT) cycle. It is assumed that when the desalination plant or heat recovery steam generator (HRSG) is failed, the gas turbine can generate electricity. So, different availabilities are obtained for the electricity and fresh water production. Furthermore, maintenance costs in each year are calculated due to overhauls and the number of components' repairs. 2. System description Today, use of cogeneration systems, due to their higher efficiency, is significantly increasing. One kind of these systems is simultaneous production of electricity and desalinated water which is useful in coastal areas. These lands have significant energy sources and need fresh water. One of the most common systems, combining a gas turbine power plant with MSF desalination plant through an HRSG, produces desalinated water by recovering excess heat of gas turbine exhaust. Fig. 1 shows the schematic of this system. Power generation cycle consists of three main components of compressor, combustion chamber, and gas turbine. The compressor is connected axially to the gas turbine, and its power is provided by turbine during plant operation. After compressing, the fresh air enters the combustion chamber together with fuel. The produced high-temperature gas passes through the gas turbine where it expands to the atmospheric pressure, thus power is produced. Finally, the turbine exhausted gas enters an HRSG to give its heat to the MSF desalination plant. 3. Economic analysis Economic analysis of a designed system requires estimation of major costs considering various assumptions and predictions (e.g. lifetime, inflation, and discount rate) and use of engineering economics techniques. Life cycle cost analysis is a method commonly used for evaluating the profitability of alternative investments. This method is based on cash flow analysis, while time value of money is taken into account. Considering variable costs and benefits due to changes in the availability and maintenance cost of system during its lifetime, the present value of cash flows is calculated. Then, three common economic indicators including net present value, payback period, and internal rate of return are used to evaluate the GT-MSF combined system. 3.1. Costs The total cost of a system consists of investment, operation and maintenance costs. The investment costs include purchased equipment and land cost, installation, piping, designing, engineering, construction, and other costs before plant operation. Operation and maintenance (O&M) costs are incurred yearly, consisting of fixed O&M costs, variable O&M costs, and fuel cost [24].

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3

Fig. 1. Combined gas turbine cycle and desalination [11].

a) Fuel cost: With the assumption of a yearly increasing unit cost of consumed fuel, the present value of fuel cost in the nth year is calculated as follows:

where A is the average availability; MTTR is mean time to repair (hour/ repair), and ARC is average repair cost of the component ($/repair). So, the O&M cost in the nth year (OM(n)) is calculated by addition of these parts:


 n−1   _ f LHV  t =ð1 þ dÞn PV f ðnÞ ¼ c f 1 þ i f m

OM ðnÞ ¼ OMfixed ðnÞ þ OMoverhaul ðnÞ þ OMvariable ðnÞ

ð1Þ

where cf is the fuel unit cost in the first year ($/kJ); if is the fuel cost in_ f is fuel consumption rate (kg/s); LHV is the lower heating flation rate; m value of the fuel (kJ/kg); d is the discount rate, and t is the number of seconds in a year (s). b) Operation and maintenance cost: usually O&M cost is considered as a percentage of initial investment cost. However, in this study, it is assumed that the plant is subjected to planned major maintenance (overhaul) at 25000 h operating intervals, and other maintenance occurs annually. So, the O&M cost is considered in three parts: 1. OMfixed: Fixed part of O&M cost which equals 1% of initial investment annually. 2. OMoverhaul: Overhaul cost (only in years that it occurs). 3. OMvariable: Variable O&M cost calculated by (2) for each component:

OMvariable ¼

  1−A 8760 ARC MTTR

ð2Þ

ð3Þ

Finally, the present value of O&M costs in nth year is:   n PV OM ðnÞ ¼ OMðnÞð1 þ iOM Þn−1 =ð1 þ dÞ

ð4Þ

where iOM , d , and OM(n) are, respectively, the O&M cost inflation rate, the discount rate and the O&M costs in the nth year. 3.2. Benefits The GT-MSF combined system has two products: electricity and desalinated water. Thus, the present values of sold electricity and water in the nth year are respectively:    n PV e ðnÞ ¼ W  ce ð1 þ ie Þn−1 t =3600  ð1 þ dÞ

ð5Þ

   _ w  cw ð1 þ iw Þn−1 t =ð1 þ dÞn PV w ðnÞ ¼ m

ð6Þ

where ie and iw are electricity and water price inflation; W is the net generated power (W); ce is the electricity price in the first year ($/ _ w is the rate of producing water (m3/s); cw is the desalinated kWh); m water price in the first year ($/m3); d is the discount rate, and t is the number of seconds in a year (s). 3.3. Availability consideration To calculate costs and benefits through Eqs. (1), (5), and (6), it is assumed that the system works all the year, while the system's availability is not equal to 1 and changes through its lifetime. Furthermore, sometimes gas turbine may generate electricity, but no water is produced because of HRSG or desalination failure. Thus, the availability should be considered in the economic analysis. So, the present value of total cost and total benefit can be calculated by Eqs. (7) and (8), respectively: i N h PV TC ¼ Z þ ∑ PV f ðnÞ Ae ðnÞ þ PV OM ðnÞ

ð7Þ

i N h PV TB ¼ ∑ PV e ðnÞ Ae ðnÞ þ PV w ðnÞ Aw ðnÞ

ð8Þ

n¼1

Fig. 2. Typical bathtub curve [22].

n¼1

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Fig. 3. Gas turbine failure rate function: a) in the first 25,000 h, b) in the second time interval, and c) during lifetime.

A.M.A. Arani et al. / Desalination 414 (2017) 1–9 Table 1 Reliability assumptions.

Gas turbine HRSG Desalination

Weibul parameters

Constant failure rate (failure per hour)

Constant repair rate (repair per hour)

α = 2562.05 β = 0.95 α = 2551.8 β = 0.995 α = 2556.8 β = 0.98

0.0003578

0.006

0.0003886

0.037

0.0003779

0.016

5

To create a bathtub type failure rate, a combination of two or three distribution functions can be used. One of the most widely used distribution functions in reliability analysis is the Weibull distribution which can model a changing failure rate. Standard Weibull distribution has two constant parameters named α and β, which are the scale and shape parameters, respectively. It is given by the distribution function: "   # t β F ðt Þ ¼ 1− exp − α

where Ae ðnÞ and Aw ðnÞ are the average availability of electricity and water in the nth year, respectively. Z is the initial investment costs. Finally, the net present value is given by: NPV ¼ PV TB −PV TC

ð9Þ

The payback period and the internal rate of return are, respectively, the length of time (N) and the discount rate (i) that make the net present value zero. 4. Availability calculation Availability is the probability that a repairable system or component function at time t. However, for non-repairable systems or components, availability equals reliability [22]. Many reliability and availability analysis methods have been developed. In the present work, the state space method was selected since it is appropriate for quantitative analysis of availability and reliability of systems, especially in the case of large complex systems [14]. In the following section, reliability modeling, failure and repair rates of components, and system availability calculation are described.

λðt Þ ¼

  β t β−1 α α

ð11Þ

4.2. Assumptions Gas turbine manufacturers usually offer a schedule for preventive maintenance, inspections, and overhauls. So, in this study, it is assumed that after 25,000 operational hours, the gas turbine is submitted to a major overhaul. The intervention takes around 1000 h. In parallel to the gas turbine maintenance activities, the desalination plant and HRSG are also submitted to complex preventive maintenance tasks. So, it is assumed that both pieces of equipment are submitted to major maintenance after 25,000 operational hours. Fig. 3a shows that in the beginning of plant operation, its components' distribution function follows a complete bathtub; for 0 ≤ t b 25000: 







"

λG ¼ 0:5 0:00037

"

λH ¼ 0:5 0:00039



0:05   # t 25000−t 0:05 Þþ 2562:05 2562:05

λD ¼ 0:5 0:000383



# 0:005   t 25000−t 0:005 Þþ 2551:8 2551:8 0:02   # t 25000−t 0:02 Þþ 2556:8 2556:8

1

2

3

4

5

6

7

8

✓ ✓ ✓

Χ ✓ ✓

✓ Χ ✓

✓ ✓ Χ

✓ Χ Χ

Χ ✓ Χ

Χ Χ ✓

Χ Χ Χ

ð12Þ

ð13Þ

"

ð14Þ

Fig. 3b shows the next time interval, in which the failure rate is constant for 20,000 h and follows an increasing Weibull distribution

Table 2 Possible states in a three component system.

Gas turbine HRSG MSF Desalination

ð10Þ

So, the Weibull failure rate function is given by:

4.1. Failure rate and repair rate Failure rate and repair rate are two important parameters used for modeling the reliability and availability of multi-component systems. Failure rate (λ(t)) is the frequency at which a component or system fails, and repair rate (μ(t)) determines the frequency of the repair [14]. Generally, a non-repairable component or system has a bathtub shape failure rate function composed of three distinct regions, as shown in Fig. 2. At the initial period of operation, the failure rate is high but decreases over time. In this region, named infant mortality region, most failures are related to the inherent defects resulting from poor design, manufacturing, or assembly. A significant proportion of failures can also occur because of human errors during installation or operation. The high failure rate decreases with time due to reparation or replacement of defective components and also increasing the experience of operation personnel. In the middle region of the bathtub curve, the lowest failure rate can be achieved, which is nearly constant. This steady behavior is related to random failures which do not have a predictable pattern. During this period, referred to as the useful life, the probability of failure is independent of system's age. In the last region, the failure rate increases with time due to irreversible aging effects. Scheduled replacement of components or preventive maintenance is often necessary to reduce the failure rate [22].

t; α; βN0

Fig. 4. State space diagram for combined GT-MSF system.

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Fig. 5. The instantaneous availability of electricity.

function. It means that for 26000 ≤ t b 46000, λG = 0.0003578, λH = 0.0003886 and λD = 0.0003779 as three constant values; for 46000 ≤ tb 51000: λG ¼ 0:00037

  25000−t 0:05 2562:05

ð15Þ

λH ¼ 0:00039

  25000−t 0:005 2551:8

ð16Þ

λD ¼ 0:000383



25000−t 2556:8

After a major overhaul, the failure rate function will raise 5% in comparison to previous time interval. The failure rate function of gas turbine is presented in Fig. 3c. The repair rate assumptions of GT, HRSG, and desalination are 0.006, 0.037, and 0.016 repair per hour, respectively. Table 1 summarizes reliability assumptions of this study. 4.3. State space analysis

0:02 ð17Þ

For reliability and availability analysis, the GT-MSF combined system is considered as series system configuration. The maximum number of states in a three component system, where each component can exist in two states (operating or failed), is 23 (Table 2) [25].

Fig. 6. Average availability of producing electricity.

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7

Fig. 7. Average availability of producing fresh water.

In the initial state, the system is fully working. If one of the components GT, HRSG, or MSF fails, the system goes to the state 2, 3, or 4 respectively, and after repairing, it returns to the state 1. It may also be possible for both components to fail simultaneously, but this transition that implies a common mode or common cause failure is not considered in this study. Also, it is assumed that a component will not fail when it is not in use. For example, when the system is in state 3 and the HRSG is being repaired, the desalination plant is out of service and will not fail. So, the states 5 and 8 will not be possible. The state space diagram including the relevant transition rates is shown in Fig. 4. λ G and μ G , λ H and μ H , and λ D and μ D are failure rates and repair rates of the gas turbine, the HRSG, and the desalination plant respectively.

Table 3 Assumptions and technical specifications of studied system. Parameter

Unit

Value

GT net power output MSF desalination capacity Fuel consumption rate GT power plant initial investment cost Desalination plant initial investment cost Discount rate (i) Inflation rate (d) Plant economic life (N) lower heating value of the fuel The cost of natural gas at the beginning of the first year Electricity unit price Fresh water unit price

MW m3/day kg/s M$ M$ % % Year (kJ/kg)

30 14,055 1.61 28.6 14.5 12 5 30 50,000

$/GJ

4

$/kWh $/m3 Percent of initial investment Percent of initial investment M$/overhaul M$/repair M$/repair

0.07 1.1

M$/repair

0.025

O&M cost in the 1st method Fixed O&M cost in the 2nd method (OMfixed) Overhaul cost in the first year (OMoverhaul) GT average repair cost (ARCGT) HRSG average repair cost (ARCHRSG) Desalination plant average repair cost (ARCDesalination)

The probabilities of each state at any time t can be obtained by solving a set of differential equations: 3 2 −λG ðt Þ−λH ðt Þ−λD ðt Þ μ G P 1 ðt Þ 6 P 2 ðt Þ 7 6 −μ G λG ðt Þ 7 6 6 7 6 6 d 6 P 3 ðt Þ 7 6 λH ðt Þ 0 7¼6 λ ð t Þ 0 ð t Þ P dt 6 D 4 7 6 6 4 P 6 ðt Þ 5 4 0 0 0 0 P 7 ðt Þ 2

μH 0 −λG ðt Þ−μ H 0 0 λG ðt Þ

μD 0 0 −λG ðt Þ−μ D λG ðt Þ 0

0 μD 0 μG −μ G −μ D 0

32 3 0 P 1 ðt Þ 76 P 2 ðt Þ 7 μH 76 7 76 P 3 ðt Þ 7 μG 76 7 76 P 4 ðt Þ 7 0 76 7 54 P 6 ðt Þ 5 0 −μ G −μ H P 7 ðt Þ

ð18Þ It is difficult to obtain general time-dependent expressions for the probabilities. Therefore, solving the system by numerical techniques using MATLAB software gives the state probabilities at any time t. It is clear that only in states 1, 3, and 4, the system produces electricity. So, the instantaneous availability of electricity at any time can be obtained by addition of probabilities of these states at the same time. However, fresh water can be produced only in state 1. Fig. 5 shows the instantaneous availability of electricity at the first 130,000 h of the system's lifetime. Then, the average availabilities in each year of lifetime can be calculated by: Ae ðnÞ ¼

1 T ∫ n ½P 1 ðt Þ þ P 3 ðt Þ þ P 4 ðt Þdt T n −T n−1 T n−1

ð19Þ

Aw ðnÞ ¼

1 T ∫ n P 1 ðt Þdt T n −T n−1 T n−1

ð20Þ

Pj(t) is the probability of state j at time t, and Tn is the number of hours spent at the end of nth year. Figs. 6 and 7 show the average availabilities of producing electricity and fresh water. After every 25,000 operational hours, the system is submitted to a major overhaul which takes 1000 h and thus reduces availability.

5

5. Studied methods

1

In this study, the economic analysis of system is carried out through two approaches:

8.62 0.06 0.013

a) The conventional economic analysis with constant availability of 0.9 through system's lifetime and fixed total O&M cost as 5% of investment annually.

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Fig. 8. Present value of fuel costs.

b) The new method presented in this study, considering availability and maintenance cost changes due to degradation and overhauls. Table 3 summarizes the economic assumptions and technical specifications of the studied system. 6. Results Economic analysis is carried out in two cases of constant and timevarying availability. Fig. 8 shows the present value of fuel costs in the 30 years lifetime. Figs. 9 and 10 show the present value of sold electricity and fresh water incomes, respectively. It is clear that when an overhaul occurs and the system stops operation for 1000 h, its availability, and as a result, fuel cost, sold electricity, and water incomes decrease.

Table 4 shows the economic analysis results in two studied cases.

7. Conclusions The present study introduced a new method for economic analysis of thermal systems, considering changes in the system availability due to early failures, degradation, overhauls, and interruptions occurred because of overhauls. A combined gas turbine cycle and desalination plant was chosen as study case. The system was considered as a series configuration with time-varying failure rate, and its instantaneous availability at any time was obtained using state space method. Then, the average availability of producing electricity and fresh water in each year of system's lifetime was calculated. Finally, three economic indicators including net present value, payback period, and internal rate of return were compared in two cases of constant and time-varying availability.

Fig. 9. Present value of sold electricity.

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Fig. 10. Present value of sold fresh water.

Table 4 Results of economic analysis.

Present value of total sold electricity Present value of total sold water Present value of total fuel cost Present value of total maintenance cost Net present value Payback period Internal rate of return

Unit

Constant availability

Time-varying availability

M$ M$ M$ M$ M$ Year %

202.4 62.08 112.07 26.34 82.96 5.46 28.87

202.8 59.84 112.32 42.3 64.95 6.24 26.62

The results have shown that in thermal systems which have severe degradation and wearing-out and need multiple and long-lasting overhauls, it is better to estimate the availability of system in each year of lifetime in order to be used in the economic analysis. It could only be considered as a fixed value; however, the results will be imprecise, and the impact of time value of money will not be included. References [1] M. Momen, M. Shirinbakhsh, A. Baniassadi, A. Behbahani-nia, Application of Monte Carlo method in economic optimization of cogeneration systems - case study of the CGAM system, Appl. Therm. Eng. 104 (2016) 34–41. [2] M.V. Biezma, J.R. San Cristobal, Investment criteria for the selection of cogeneration plants- a state of the art review, Appl. Therm. Eng. 26 (2006) 583–588. [3] A. Petrillo, et al., Life cycle assessment (LCA) and life cycle cost (LCC) analysis model for a stand-alone hybrid renewable energy system, Renew. Energy 95 (2016) 337–355. [4] L.R. Rodríguez, et al., Analysis of the economic feasibility and reduction of a building's energy consumption and emissions when integrating hybrid solar thermal/PV/micro-CHP systems, Appl. Energy 165 (2016) 828–838. [5] S. Tadros, A new look at dual purpose, water and power, plants - economy and design features, Desalination 30 (1979) 613. [6] Z. Gomar, H. Heidary, M. Davoudi, Techno-economics study to select optimum desalination plant for Asalouyeh combined cycle power plant in Iran, Int. J. Electr. Comput. Energ. Electron. Commun. Eng. 5 (2011) 256–262.

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