Design and off-design optimization procedure for low-temperature geothermal organic Rankine cycles

Design and off-design optimization procedure for low-temperature geothermal organic Rankine cycles

Applied Energy 242 (2019) 716–731 Contents lists available at ScienceDirect Applied Energy journal homepage: www.elsevier.com/locate/apenergy Desig...

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Applied Energy 242 (2019) 716–731

Contents lists available at ScienceDirect

Applied Energy journal homepage: www.elsevier.com/locate/apenergy

Design and off-design optimization procedure for low-temperature geothermal organic Rankine cycles

T

Sarah Van Erdeweghea,c, Johan Van Baelb,c, Ben Laenenb, William D’haeseleera,c,



a

University of Leuven (KU Leuven), Applied Mechanics and Energy Conversion Section, Celestijnenlaan 300 - box 2421, B-3001 Leuven, Belgium Flemish Institute for Technological Research (VITO), Boeretang 200, B-2400 Mol, Belgium c EnergyVille, Thor Park 8310, B-3600 Genk, Belgium b

HIGHLIGHTS

optimization tool for design and off-design of binary geothermal ORCs. • Two-step temperature and electricity price are most-influencing parameters. • Brine power output varies from 1.95 MW to 4.74 MW for T = 29.07 °C to −4.28 °C. • Net reduction and splines reduce off-design calculation time by a factor of 88. • Data • Optimal ORC design for a given location, including off-design performance. env

ARTICLE INFO

ABSTRACT

Keywords: ORC Geothermal energy Design optimization Off-design performance

In this paper, a two-step optimization methodology for the design and off-design optimization of low-temperature (110–150 °C ) geothermal organic Rankine cycles (ORCs) is proposed. For the investigated conditions—which are based on the Belgian situation—we have found that the optimal ORC design is obtained for design parameter values for the environment temperature and for the electricity price which are both higher than the respective yearly-averaged values. However, the net present value is negative (−12.62 MEUR) which indicates that the low-temperature (130 °C) geothermal electric power plant is not economically attractive for the investigated case. Nevertheless, and demonstrated by the results of a detailed sensitivity analysis, a lowtemperature geothermal power plant might be economically feasible for geological sites with a higher brine temperature or in a country with a more favorable economic situation; e.g., with higher electricity prices ( 70 EUR/MWh). The novelty of our paper is the development of a thermoeconomic design optimization strategy for low-temperature geothermal ORCs, accounting for the off-design behavior already in the design stage. The generic methodology is valid for low-temperature geothermal ORCs (with MW scale power output) and includes detailed thermodynamic and geometric component models, is based on hourly data rather than monthly-averaged data and accounts for economics.

1. Introduction Geothermal energy is readily available all over the world, as long as one is willing to drill deeply enough. Nevertheless, the available geothermal source temperature depends on the site-specific geological conditions. In this work, geothermal source (also called brine) temperatures of 110–150 °C are considered, which are typical for non-

volcanic regions like NW Europe. The organic Rankine cycle (ORC) is the most appropriate energy conversion cycle to effectuate this lowtemperature heat-to-electricity conversion. Some relevant thermodynamic and economic studies have already been performed in the literature and are briefly discussed. Imran et al. [1] have compared the basic, recuperated and regenerative ORC setups1 for application in a geothermal power plant (160 °C, 5 kg/s ). A

⁎ Corresponding author at: University of Leuven (KU Leuven), Applied Mechanics and Energy Conversion Section, Celestijnenlaan 300 - box 2421, B-3001 Leuven, Belgium. E-mail address: [email protected] (W. D’haeseleer). 1 In a recuperated ORC, a heat exchanger (the recuperator) is used the preheat the working fluid before it enters the economizer/evaporator with the heat of the turbine outlet vapor. In a regenerative ORC, part of the working fluid mass flow rate is extracted between two turbine stages to preheat the working fluid in direct contact before it enters the economizer/evaporator.

https://doi.org/10.1016/j.apenergy.2019.03.142 Received 6 September 2018; Received in revised form 18 February 2019; Accepted 13 March 2019 0306-2619/ © 2019 Elsevier Ltd. All rights reserved.

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Q [MWth] heat S [mm] spacing SIC [EUR/kW] specific investment cost s [kJ/kgK] specific entropy T [°C] temperature v [m/s] velocity W [MWe]electrical power w [kJ/kg]specific work [%] heat exchanger efficiency [%] efficiency standard deviation

Nomenclature Abbreviations ACC CHP ECO EES EVAP GWP NW ODP ORC RECUP SUP

air-cooled condenser combined heat-and-power economizer economizer, evaporator, superheater evaporator global warming potential northwest ozone depletion potential organic Rankine cycle recuperator superheater

Subscripts and superscripts av b crit D el en env ex f fin g inj M m max min net p prod shell sup t th tube wf wells

Symbols A [m2 ] heat transfer area Bc [m] heat exchanger baffle cut C [USD] equipment cost D [m] diameter del [%/year] electricity price increase dr [%] discount rate E year [GWh] yearly energy production E [MWth] flow exergy ex [kJ/kg] specific flow exergy H [mm] height h [kJ/kg] specific enthalpy I [MEUR] investment cost L [year] lifetime Lbc [m] heat exchanger baffle distance LCOE [EUR/MWh] levelized cost of electricity m [kg/s] mass flow rate MW [g/mole] molecular weight NPV [MEUR] net present value N [%] availability factor ntube ACC number of tubes pel [EUR/MWh] electricity price ptube [mm] tube pitch p [bar] pressure

Pareto front solution has been shown for the specific investment cost (SIC) and the exergy efficiency ( ex )2, as they are conflicting optimization objectives. The authors have found that the basic ORC has the lowest SIC for ex < 45% whereas the regenerative ORC has the lowest SIC for ex > 45%. Braimakis et al. [2] have performed a thermoeconomic optimization of the standard and the regenerative ORC. Heat source temperatures of 100, 200 and 300 °C and heat source capacities of 100, 500, 1000 and 2000 kWth have been considered, representing different energy sources. They have concluded that the expander type has a dominant role in the economic performance of ORCs. Furthermore, the authors do not recommend the use of a regenerative ORC for geothermal applications, because the performance benefits are found to be insignificant and the economic competitiveness inferior. Astolfi et al. [3] have performed a thermodynamic and

average brine critical point design conditions electricity energy environment exergy ACC fan ACC fin generator injection state material motor maximum minimum net value pump production state heat exchanger shell degree of superheating turbine thermal heat exchanger tube working fluid well drillings

thermoeconomic optimization of different types of ORCs for application to low- to medium-enthalpy geothermal brines (120–180 °C, 200 kg/s). The authors have found that the supercritical ORC, with a working fluid which has a critical temperature slightly lower than the brine temperature, leads to the lowest SIC and that the optimal operating conditions do not depend on the well costs. Furthermore, the results of the thermoeconomic optimization are significantly different from the thermodynamic optimization results, which highlights the importance of including economics. For the investigated case, the main effect of the economic optimization is a reduction of the total plant (−7%) and power block (−16%) specific costs, even if the net power output decreases. Fiaschi et al. [4] have compared the ORC, Kalina and CO2 cycles for geothermal heat sources based on an exergoeconomic analysis. Two cases are considered for the geothermal heat source: a medium-temperature source of 212 °C and a low-temperature source of 120 °C . The authors have found that an ORC with R1233zd has the best performance for the medium-temperature source (approximately 6 MW power output) with a levelized cost of electricity (LCOE) of 88.5 EUR/ MWh. For the low-temperature source, the Kalina cycle has shown the best performance. The electrical power output is 22–42% higher than for the ORC and the LCOE is 125 EUR/MWh (for a 500 kW power

2

The exergy efficiency has been based on the flow exergy which is transferred between the brine and the working fluid in the evaporator. In our case, however, the exergetic plant efficiency is based on the exergy content of the brine at the production state (so we consider the remaining brine flow exergy at the injection state as a loss for the system). 717

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output). Next to the design optimization, also the off-design performance of (geothermal) ORC plants has been studied in the literature. Calise et al. [5] have developed an off-design simulation model for recuperated ORCs powered by medium-temperature heat sources (solar, via diathermic oil at 160 °C, 20 kg/s). First, the authors have performed a parameter study to find the optimal values for the heat exchanger design parameters (tube length, tube number and shell diameter) for the lowest annualized total cost of the ORC plant. The authors have found that by optimization3 of the heat exchangers geometry, the economic benefit, the net power generation and the global efficiency can be increased with 21.06%, 20.01% and 33.60%, respectively. And second, the off-design performance has been calculated for a varying source temperature in the range of 155–185 °C and a flow rate in the range of 18–24 kg/s . The maximum net power generation of 335.4 kW is obtained for a flow rate of 18 kg/s and a source temperature of 185 °C, the lowest value of 269.3 kW is obtained for a source temperature of 185 °C and a flow rate of 24 kg/s . Kim et al. [6] have performed an off-design performance analysis for an ORC fueled by waste heat or residual heat from a combined heatand-power plant. The authors have concluded that off-design performance should be taken into account in the performance analysis. They have highlighted a case for which the ORC design based on the nominal operating conditions would not be economical because the actual source temperature and flow rate (during off-design) — and hence the electrical power output — are generally lower than the design values. A pure thermodynamic study has been performed without taking economics into account. Hu et al. [7] have developed a model for the design and off-design calculation of a geothermal power plant (90 °C , 10 kg/s). No cost models have been included but the net electrical power output and the cycle efficiency are used as the indicators. They have concluded that for an increase of the source flow rate from 3.6 kg/s to 14.4 kg/s, the cycle efficiency increases from 2.6% to 6.3% and the net power increases from 16.7 kW to 88.7 kW. The heat exchanger pressure drop in the design step is limited to 3%, from which the heat exchanger layout has been calculated. Astolfi et al. [8] have compared the performance of a dry-cooling system with the novel Emeritus cooling system for application in a low temperature (120 °C ) geothermal ORC. The Emeritus cooling system is a dry-cooler with additional adiabatic panels and water sprays. The variables of the optimization procedure are the cooling water temperature at the condenser inlet and the number and type of heat rejection units. The authors have concluded that the novel Emeritus cooling system is better than the dry-cooling system for the investigated desert climate and high electricity-to-water price ratio. However, for mild climates and low electricity prices, the dry-cooling system might perform better. Wang et al. [9] have performed an off-design analysis of a solar ORC plant. The ORC has been designed for the weather conditions on June 21st. As a result, the maximum net power output occurs in June or September because then the operating conditions are the closest to the design conditions. The exergy efficiency is the highest in December, and both the net power output and the exergy efficiency are the lowest in August. Manente et al. [10] have developed an off-design model for a lowenthalpy geothermal power plant (100 kg/s). The influence on the net power output by a varying heat source temperature (130–180 °C ) and a fluctuating environment temperature (0–30 °C ) has been studied. The pump speed, turbine capacity (using control valves) and the air-flow rate in the condenser are the control variables. The off-design modeling has been simplified by assuming that the overall heat transfer coefficient only depends on the mass flow rate (by a power law). The authors 3

have concluded that the environment temperature greatly influences the power output due to the air-cooled system and that the electrical power output increases with the geothermal source temperature. Other authors have investigated the design aspects as well as the offdesign performance. Lecompte et al. [11] have developed a thermoeconomic design methodology for an ORC, including off-design behavior. The methodology has been applied to internal combustion engine waste heat with a thermal power of 1800 to 3500 kW. In a first step, the number of plates and the length of the plate heat exchangers, and the number of tube rows and the frontal area of the condenser are optimized together with the operating conditions towards minimal SIC. This is repeated for multiple design values for the heat source thermal power and the environment temperature. In the second step, the offdesign analysis has been performed for every design point. The offdesign results are based on an hourly waste heat profile and hourly data for the environment temperature over one year. Using the off-design results, the real SIC has been calculated corresponding to every design point and the best design point (design values for the waste heat power and the environment temperature) is indicated. Petrollese et al. [12] have studied the optimal design of an ORC fueled by solar energy and a thermal storage tank, considering the offdesign performance. Different scenarios are defined based on the hot fluid mass flow rate and inlet temperature to the ORC, and the environment temperature. In the first step, a preliminary design of the components is calculated based on the thermodynamic cycle under design conditions (source conditions: 275 °C, 12 kg/s). Then the offdesign performance is calculated for the different scenarios and the respective LCOE is finally calculated (taking into account the probability of each scenario). The authors have concluded that the different scenarios should be considered together (a so-called multi-scenario approach) because this results in an ORC design with the lowest LCOE value. The optimal ORC has a lower performance under design conditions but is less sensitive to fluctuating heat source and ambient conditions. Budisulistyo et al. [13] have developed a lifetime design strategy for a geothermal power plant in New Zealand. The geothermal source temperature and flow rate decline over the plant’s lifetime of 40 years, starting from 131 °C and 200 kg/s. The authors have calculated the design of a standard ORC for the geothermal source conditions in years 1, 7, 15 and 30 and have found that the ORC design for year 7 (with partly degraded source conditions) shows the best overall performance, with a net present value (NPV) of 6.89 MUSD. Furthermore, they have concluded that two types of adaptations can be made to increase the performance at heat source degradation. The operating conditions (working fluid flow rate and air flow rate in the condenser) can be adapted or structural changes can be made such as installing a recuperator at the half-life or down-sizing the preheater and vaporizer at the half-life. Usman et al. [14] have compared the performance of an air-cooled and a cooling tower based ORC for different climate conditions. Two types of geothermal sources have been considered: the first one has a temperature and flow rate of 130 °C and 9.16 kg/s, the second is at a temperature of 145 °C and has a flow rate of 6.57 kg/s. During off-design, the heat sink is controlled to get maximum power output at different environment conditions. The ORC has been designed for summer conditions such that it can benefit from larger pressure ratios in winter. The authors have concluded that the environment conditions have significant effect on the power output. In summer, the drop in power output can be 62% of its winter capacity. Furthermore, the authors have found that the cooling tower based ORC is preferable for hot dry regions and that an air-cooled ORC can be implemented in other climates. In the aforementioned references, some assumptions have been made regarding the design and/or thermodynamic cycle: a fixed geometry for the heat exchangers [1,2,6] or a fixed heat transfer area [9], a fixed condenser temperature [1] or cooling water inlet temperature [2,7], a fixed pinch-point-temperature difference [1,7,8,13], a fixed

The mentioned optimization was rather a parameter search in this case. 718

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degree of superheating [9,11,14] and fixed (or neglected) temperature and/or pressure drops over the heat exchangers [3,5,7–9]. However, to properly calculate the economics of a geothermal ORC, these parameter values should be optimized. Furthermore, some off-design studies have been based on monthly-averaged data [9,13,14] but then the extreme weather conditions and the corresponding ORC operation are not considered. Note also that a variety of optimization/simulation tools have been used in the literature: Matlab [1–3,7,9–11,14], EES [4,5], Excel/VBA [8], Aspen Plus and EDR [13] and Aspen HYSYS [6]; which means that there is no clear best tool for this kind of simulations. In this paper, we propose a novel two-step optimization framework for low-temperature geothermal ORCs. In the first step, the design of the geothermal ORC is optimized towards maximal NPV. In a second step, the operating conditions are optimized towards maximal net power output depending on the real environment conditions during offdesign. Finally, the real NPV is calculated, taking the off-design performance—and thereby the real power production—into account. In general the real NPV differs from the value in the design stage because some parameter assumptions were made, e.g., for the environment temperature and electricity price. The design which corresponds to the highest real NPV is the optimal design of the power plant. In our work, the same optimization framework is used for the design and the offdesign optimization steps. The models for the heat transfer and pressure drop calculations hold for design and off-design conditions. Only for the turbine modeling, an off-design model for the turbine efficiency calculation has been added. Since the same computer tool is used for the design and off-design calculations, errors related to the use of different programming languages are avoided. The novelties of our paper are multiple. First, the assumptions which are commonly made in the literature regarding the design or the thermodynamic cycle (as mentioned before) are optimized in our optimization framework. This results in a more accurate estimation for the thermodynamic states and for the size and cost of the different components. Furthermore, the correlations used are valid for multiple working fluids such that a generic (non-linear) optimization tool has been obtained.4 Also, economics are included since the optimized values of the variables are different compared to a pure thermodynamic approach [3]. Furthermore, our off-design calculations are based on hourly data for the environment conditions instead of monthly-averaged values, such that the extreme operating conditions are taken into account. Together with the use of hourly data for the electricity price, this might result in large differences in total revenues compared to the use of monthly-averaged data. And finally, our optimization tool contains detailed models which are valid for an electrical power output in the MW scale, whereas most of the studies in the literature (including the study of Lecompte et al. [11], who have followed a similar optimization approach) consider lower power scales (and use different component models) or do not include detailed thermoeconomic models. Up to the authors’ knowledge, the implementation of all these aspects in an economic design optimization tool for low-temperature geothermal ORCs which also accounts for the off-design performance, has not been proposed in the literature so far. It is generally known that low-temperature geothermal power plants are hardly economically feasible in NW Europe without some kind of feed-in tariff [15]. Therefore, the first goal of this paper is to investigate under which (brine, environment and economic) conditions this type of power plant might become economically attractive. Due to the sitedependency of some model parameters, the aim is to give trends rather than a single numerical value for the optimization objective, variables and performance indicators. The second goal is to study the influence of varying environment conditions during off-design on the net power

output, and the impact of fluctuating electricity prices on the revenues and on the economic feasibility of the power plant. Finally, and based on the design and off-design results which are obtained by the proposed two-step optimization approach, the optimal ORC design will be calculated for the investigated conditions. 2. Methodology 2.1. ORC set-up Standard and recuperated organic Rankine cycles (ORCs) are considered for the electrical power production. Fig. 1a shows a schematic presentation of the recuperated ORC with indication of the states. The brine, at a temperature Tb, prod and flow rate mb , transfers heat to the working fluid and is injected at a temperature Tb, inj . The working fluid is 2 ), gets subsequently heated in the pumped to a higher pressure (1 3), the economizer (ECO, 3 4 ), the evarecuperator (RECUP, 2 5) and the superheater (SUP, 5 6), expands over porator (EVAP, 4 7 ) which is connected to a generator to produce the turbine (6 8) and electrical power, transfers part of its heat in the recuperator (7 is finally condensed back to state 1 to close the cycle. The cooling medium is air at the environment conditions (Tenv and penv ). In the standard ORC, there is no recuperator and this component is removed from the set-up (state 2 = state 3 and state 7 = state 8). The corresponding T-s diagram for the reference standard and recuperated ORC is shown in Fig. 1b. Shell-and-tube TEMA E type heat exchangers are used with the brine flowing through the tubes (which eases the cleaning processes). For the recuperator, the liquid (state 2 3) is in the tubes. Furthermore, we assume that the economizer, the evaporator and the superheater have the same geometry, which will be optimized in the design optimization procedure of Section 3. According to previous KU Leuven/VITO PhD research [16], a 30° tube layout leads to the highest electrical power output (if all heat exchangers have the same tube layout). The air-cooled condenser is the most general type of condenser since no water has to be on site [17]. The considered cooling system is a forced-draft air-cooled condenser (ACC). An A-frame ACC with flat tubes and corrugated fins has been implemented. Flat tubes are considered because the pressure drop is lower than for round tubes [18,19]. The legs of the A-frame make an angle of 60° with the horizontal. The considered fins do not have a perpendicular orientation with respect to each of the legs, but are vertically oriented in order to minimize fouling [19]. A single-stage axial turbine is chosen for the expander. The axial flow turbine is the most often applied in geothermal power plants with about 80% of the total global capacity installed, followed by the centripetal turbine ( 15%) and the centrifugal radial turbine (<5%) [17]. A single-stage has been considered to lower the investment costs [20]. A variable-speed multi-stage centrifugal pump is commonly used in geothermal ORCs [21]. However, because of the small contribution of the pump power with respect to the power output of the ORC, a constant pump efficiency has been assumed.5 The same reasoning holds for the fan of the ACC. 2.2. Thermodynamic models Table 1 summarizes the models and correlations which have been 5 The mechanical ORC pump power is 6.79% of the mechanical turbine power for the standard cycle and 6.67% for the recuperated cycle (for the reference parameter values). In absolute numbers, the ORC pump power is approximately half of the well pumps power. Therefore, the implementation of a more detailed off-design model for the pump efficiency has only a small impact on the overall economics of the plant. The implementation of a more detailed model for the pump efficiency might be considered for future work.

4 This is in contrast to some papers in the literature (for example in the paper of Astolfi et al. [3]) where a fit of manufacturer data has been used, but that approach is very case-specific.

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Fig. 1. Schematic presentation of the recuperated ORC and corresponding T-s diagram for the reference standard and recuperated cycle. For the standard ORC (without recuperator), state 2 = state 3 and state 7 = state 8. Table 1 Correlations used in the thermodynamic models. The abbreviation wf stands for working fluid. Parameter

Component

Correlation

Heat transfer and pressure drop Ideal heat transfer and pressure drop Ideal heat transfer and pressure drop Friction factor Heat transfer coefficient

Shell HEx Single-phase shell HEx Two-phase shell HEx Single-phase tube HEx Single-phase tube HEx

Bell-Delaware [23–25] Shah et al. [24] Hewitt et al. [23] Bhatti and Shah [26] Petukhov and Popov [27]

Heat transfer and friction factor Heat transfer coefficient Friction factor Void fraction Pressure drop Heat transfer coefficient

Air-side ACC Single-phase wf ACC Single-phase wf ACC Two-phase wf ACC Two-phase wf ACC two-phase wf ACC

Yang [19] Gnielinski [28] Petukhov and Popov [27] CISE [29] Chisholm [30] Shah [31]

Design efficiency Off-design efficiency

Turbine Turbine

Macchi and Perdichizzi [32] Keeley [33]

implemented. The models which are used in the design optimization step are based on previous PhD work of Walraven [15]6. The off-design models are newly implemented, and the optimization procedure has been adapted and expanded to be able to perform design as well as offdesign optimization calculations. The geometry of the heat exchangers is modeled following the TEMA standards [22–24]. Detailed thermodynamic models have been implemented for the calculation of pressure drops and heat transfer coefficients in the heat exchangers and the air-cooled condenser, and a correlation has been implemented for the turbine design efficiency calculation and for its offdesign performance. More information on the turbine efficiency modeling and off-design behavior is given in Appendix A. For the heat exchangers and the air-cooled condenser, the same heat transfer and

friction factor correlations hold for the off-design calculations as for the design optimization but the geometry is fixed. 2.3. Cost models The correlations for the bare equipment costs (CBE ) of all components are summarized in Table 2. They are based on the heat transfer area A or on the power W . We assume correction factors to account for high temperatures (> 100 °C), high pressures (>7 bar ) and the need for stainless steel in the heat exchangers: fT = 1.6, fp = 1.5 and fM = 1.7 [34]. Furthermore, an installation factor of fI = 0.6 has been assumed [35]. The equipment cost C thus becomes:

C = CBE (fT f p fM + fI )

(1)

The chemical engineering index has been used to convert the costs to 2016-based values and a conversion factor of EUR to USD = 1.2 has been assumed.

6

The reader is kindly reffered to the PhD work of Walraven [15] for more detailed information regarding the design models (implementation). Walraven [15] has also found that the Nusselt number which is given in the paper of Yang [19] is 10 times too big, so we have adapted the equation of the Nu number accordingly. Furthermore, we have divided the equation for the friction factor by 2, because the correlations of Yang were established for another type of fins.

2.4. Reference parameter values Table 3 presents the reference parameter values. The brine is 720

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outlet temperature T1, the working fluid mass flow rate m wf , the air speed vair through the condenser and the recuperator efficiency T T (= T7 T8 , with reference to Fig. 1) in case of the recuperated ORC. All 7 2 variable bounds are given in Table 5. The design variable bounds are based on the TEMA standards [22] for the heat exchangers and comply with the validity range of the correlations given by Yang [19] for the ACC. Tcrit and Tupper refer to the critical temperature and the temperature which corresponds to the maximal pressure in the fluid properties database, respectively. Some additional structural and operational constraints are set for the optimization problem and are summarized in Table 6. The constraint on the tube-to-shell ratio of the heat exchangers is in accordance

Table 2 Bare equipment costs. Table is adapted from [15].

Shell& tube HEx centr. pump (incl. motor) Turbine

ACC excl. fan ACC fan incl. motor

Capacity measure

Size range

Cost correlation [USD]

Ref.

A [m2 ]

80–4000 m2 4–700 kW

3.28 × 10 4 (A /80)0.68

[34]

9.84 × 103 (W /4000)0.55

[34]

0.1–20 MW

19000 + 820(W /1000)0.8

[36]

W [W] W [W] A [m2 ]

W [W]

200–2000 m2 50–200 kW

1.56 × 105 (A/200)0.89

1.23 × 10 4 (W /50000)0.76

[34] [34]

Table 3 Reference parameter values. Brine & wells [37]

Economic [38–41]

Environment [45]

Tb,prod = 130 °C

pel = 60 EUR/MWh

Tenv = 10.85 °C

pb, prod = 40 bar

del = 1.25%/year

penv = 1.02 bar

mb = 150 kg/s Iwells = 15 MEUR

dr = 5% L = 30 years

Wwells = 500 kW

N = 90%

a

f

p

= 80%

g

= 98%

m

= 98% = 60% a

f

min Tmin = 1°C = Tsup

= 60% is the total fan efficiency, which includes the isentropic and mechanical-to-electrical conversion efficiency.

with the TEMA standards [22]. In addition, a minimal degree of sumin perheating of Tsup has been assumed to ensure a proper turbine operation. From the well tests at the Balmatt geological site [37], no problems regarding salt sedimentation are expected around the optimized values so no constraint has been imposed on the brine injection temperature Tb, inj . The pinch-point-temperature difference over each of the heat exchangers is higher than the assumed minimal temperature difference Tmin .

modeled as pure water and the reference conditions (brine production temperature Tb, prod and pressure pb, prod , brine flow rate mb , well investment costs Iwells and well pumps power Wwells ) are based on the test parameters for the geological site of Balmatt (Mol, Belgium) [37]. The economic parameters are the yearly-averaged constantly assumed electricity price pel [38], yearly electricity price increase del [39], discount rate dr [40], lifetime L and availability factor N [41]. Furthermore, the cycle parameters are the pump isentropic efficiency p [42], generator and motor mechanical-to-electrical efficiencies g and m [42,43], fan efficiency f [44], the minimum pinch-point-temperature difference over the heat exchangers Tmin and the minimum degree of min superheating Tsup . Throughout the entire paper, the year 2016 is taken as the reference year. The reference environment conditions (Tenv and penv ) are the average values for Mol in 2016 [45].

3.2. Flowchart Fig. 2 shows the flowchart of the developed design optimization model. The black values belong to the design optimization flowchart. The flowchart will be extended with the red values for the off-design optimization (see Section 4.2). The parameter values for the brine, economic and environment conditions, the ORC working fluid, some parameter assumptions related to the cycle modeling and the costs of the wells and the well pumps power are input parameters for the optimization model (see Tables 3 and 4). The optimization model includes all geometric models, heat transfer coefficient and pressure drop correlations, the turbine efficiency correlation and the cost functions as defined in Tables 1 and 2. The objective in the design optimization step is the NPV, since it takes into account the component costs, the time value of money (as reflected by the discount rate) and the thermodynamic performance. The variable bounds are set (in Table 5) and some structural and operational constraints are defined (in Table 6). The results are the optimized ORC design (geometry of the heat exchangers and the ACC) and optimal operating conditions (temperatures and flow rates), and the value for the objective function. In a postprocessing step, all other performance indicators can be calculated.

2.5. ORC working fluid Isobutane (R600a) [46] is chosen as the working fluid because of its low environmental impact [47], high power output and the low cost of hydrocarbons [48,21]. The thermodynamic and environmental properties of Isobutane are summarized in Table 4. 3. Design optimization 3.1. Optimization strategy The net present value (NPV) is considered as the objective and is defined as: L 1

NPV =

Cycle [42–44]

Iwells

IORC + i=0

Wnet pel (1 + del )iN 8760 (1 + dr )i

0.025IORC (2)

According to the IEA [49], the maintenance costs can be estimated by 2.5% of the ORC investment costs. The design of the heat exchangers (shell diameter Dshell , tube diameter Dtube , tube pitch ptube , baffle cut Bc , length between baffles Lbc ) and the air-cooled condenser (height of the fins Hfin , spacing between the fins Sfin , number of tubes ntube ) are optimized together with the operating conditions. The operating conditions are the turbine inlet temperature T6 , the evaporator inlet temperature T4 , the condenser

Table 4 Thermodynamic and environmental properties of Isobutane (R600a) [47].

Isobutane (R600a)

721

MW [g/mole ]

Tcrit [°C ]

pcrit [MPa]

ODP

GWP

58.12

134.7

3.63

0

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Table 5 Variable bounds in the optimization procedure, based on [19,22]. Variable

Lower bound

Upper bound

Variable

Lower bound

Upper bound

Dshell [m] Dtube [mm]

0.3 5

2 50

14.25

5 3.04

0.25

2.5

0.3 1.14

Bc /Dshell [–]

Lbc [m] Sfin [mm] Hfin [mm]

T6 [°C ]

Tenv + 10 °C

min(Tcrit , Tupper )

mwf /mb [–]

0.01

ptube /Dtube [–]

T4 [°C ] T1 [°C ]

1.2

Tenv Tenv

0.45

ntube [–]

min(Tb,prod, Tupper ) min(Tb,prod, Tupper )

Lower bound

Upper bound

Dtube / Dshell [–] LACC [m] T6 T4 [°C ]

0 0

0.1 15

Tb,inj [°C ]

Tpinch [°C ]

min Tsup

10

25

Tmin

5

10

0.01

90

correlations used (optimization bounds in Tables 5 and 6).

Constraint

T1 [°C ]

10,000

1.5

vair [m/s ] [% ]

Table 6 Constraints to the optimization procedure, based on [19,22].

T4

23.75

500

Tupper

3.4. Definition of the performance indicators The following performance indicators are used:

Tenv

2(Tupper

• • Specific investment cost, SIC =

Iwells + IORC +

Levelized cost of electricity, LCOE =

Tenv )

Tb,prod 100

L 1 0.025IORC i = 0 (1 + dr )i

i L 1 Wnet N (1 + d el ) 8760 i=0 (1 + dr )i

;

Iwells + IORC ; Wnet

Fig. 2. Flowchart of the optimization procedure. Black: design optimization framework, red: extension to the design optimization framework (black) for off-design calculations.

• Specific work of the ORC, cycle • Energetic

3.3. Model implementation The thermodynamic and economic models are implemented in Python [50] and the CasADi [51] optimization framework together with the IpOpt [52] non-linear solver are used for the optimization. Fluid properties are called from the REFPROP 8.0 database [53]. Concerning the validation/verification of our obtained results, we are confident that our optimization results are trustworthy. There are no experimental results available to the authors. Nevertheless, the considered thermoeconomic optimization model is an extension of our thermodynamic optimization model, which has been discussed and verified against results in the literature in previous work [54]. The added heat transfer coefficient and pressure drop correlations and the turbine efficiency model (which were given in Table 1) are commonly used in the field of ORC modeling and are validated in the literature. We confirm that we stay within the range of validity for each of the

Qb = mb (hb, prod

7

henv

Wnet ; mwf

efficiency,

hb, inj ) ;

• Exergetic plant efficiency, exb, prod = hb, prod

w=

ex

=

Wnet with Exb, prod

Tenv (sb, prod

senv) .

en

=

Wt

Wp Qb

,

with

Exb, prod = mb exb, prod and

3.5. Results for the reference conditions The T-s diagrams of the optimized standard and recuperated ORCs 7 In the definition of the specific work w, the well pumps power is not included in Wnet since w is a property of the ORC. Note that in the definition of the plant net electrical power output Wnet , the well pumps power has been included.

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electricity prices higher than 80 USD/MWh ( 67 EUR/MWh ) are possible for the 450 Scenario, which indicates that the low-temperature geothermal power plant might become economically competitive in the future. The results of a detailed sensitivity analysis, including the influence of the electricity price on the NPV and LCOE, are given in Section 3.6.2 and Fig. 4.

Table 7 Optimal design of the economizer, evaporator, superheater (called EES), the aircooled condenser (ACC) and the recuperator (RECUP) for the reference conditions of Table 3.

Shell diameter Dshell [m] Tube diameter Dtube [mm] Tube pitch ptube [mm] Baffle cut Bc [m] Length between baffles Lbc [m]

EES

Fin height Hfin [mm]

ACC

Fin spacing Sfin [mm] Number of tubes ntube

Standard

Recuperator

0.77 6.00

0.77 5.97

7.20 0.19 3.05

7.16 0.19 3.15

23.75

23.75

1060

1066

3.04

Recuperator RECUP

1.05 5.52

3.6. Sensitivity analysis

8.69 0.26 5.00

In order to identify the parameters which affect the project feasibility the most, we perform a sensitivity analysis of the brine, economic and environment parameters on the NPV, the Wnet , the SIC and the LCOE.

3.04

3.6.1. Brine conditions We consider different brine temperatures and mass flow rates and investigate the effect on the project feasibility. Fig. 3 shows the results. From Fig. 3a follows that the NPV increases for both the brine temperature and flow rate, which was expected. Furthermore, we see that for the reference brine temperature of Tb, prod = 130 °C, the project only becomes feasible for the high flow rate of mb = 200 kg/s . For the reference brine flow rate of 150 kg/s, the project becomes feasible for a brine production temperature of 140 °C. For higher temperatures, the project is almost break-even at the lowest flow rate of 100 kg/s and has a positive NPV for higher brine flow rates. Besides, the NPV of the recuperated ORC is always (slightly) higher than for the standard ORC for all investigated conditions. Fig. 3b shows similar trends for the net electrical power output. The power production of the optimized cycles increases with the brine production temperature and the brine mass flow rate. The brine production temperature has the highest impact. Figs. 3c and d show that the LCOE and the SIC decrease with Tb, prod and mb . Also here, the brine temperature has the highest impact. The LCOE can be as high as 176 EUR/MWh for the standard ORC and the lowest investigated brine temperature and flow rate. The lowest value for the LCOE is at Tb, prod = 150 °C and mb = 200 kg/s and is 41 EUR/ MWh for the recuperated cycle. For comparison, the black dashed line indicates the electricity price which was assumed in the reference scenario. The corresponding highest and lowest values for the SIC are 23,315 EUR/kW for the standard ORC at Tb, prod = 110 °C and mb = 100 kg/s , and 4959 EUR/kW for the recuperated ORC Tb, prod = 150 °C and mb = 200 kg/s .

Table 8 Design optimization results for the reference conditions of Table 3.

NPV [MEUR]

Wnet [MW] w [kJ/kg]

IORC [MEUR] SIC [EUR/ kW] LCOE [EUR/ MWh]

Standard

Recuperator

−3.74 3.11

−2.81 3.38

11.48 (73.90%) 8509.51

12.49 (68.28%)

68.20

65.67

38.91

41.50

8135.71

en ex

[%] [%]

Tb,inj [°C] [%] t

[%]

Standard

Recuperator

11.45 25.12

12.44 27.28



71.15

89.07

88.86

73.53

74.52

for the reference conditions were already shown in Fig. 1b. The use of a recuperator leads to a higher cycle efficiency and the condenser can be cooled at a lower temperature. Furthermore, the optimal design for the reference parameter values is given in Table 7 and the general results are summarized in Table 8. Both, the standard and the recuperated geothermal ORC are not feasible (NPV < 0 ) for the investigated reference conditions without some kind of feed-in tariff. However, the recuperated ORC has a higher NPV than the standard ORC. Although the total investment costs are higher, the revenues from the higher electrical power production are higher. This also leads to a lower specific investment cost for the recuperated cycle and a lower LCOE. The use of a recuperator leads to a higher cycle efficiency, a higher specific work and a higher brine injection temperature. But due to the higher pressure ratio over the turbine, the turbine efficiency t is slightly lower for the recuperated ORC. Furthermore, the values between brackets in the row of IORC indicate the share of the ORC costs which is allocated to the ACC. The cost of the cooling system is the major investment cost, which is a direct consequence of the low brine temperature and the corresponding low cycle efficiency. This emphasizes the importance of a good cooling system design since getting a lower condensing pressure, at given environment conditions, results in a higher electrical power output. Note that the working fluid isobutane is a flammable fluid. Therefore, a fire protection system should be installed. The cost can be estimated as 2–5% of the total plant investment costs [55], which corresponds to 1–2% of the total investment costs (including the drilling costs) for the reference conditions and a NPV which would be 0.2 MEUR to 0.6 MEUR less. The fire protection system cost is rather unpredictable and small compared to the total investment costs, and is therefore not discussed further in this study. The LCOE in Table 8 (68.20 EUR/MWh for the standard ORC and 65.67 EUR/MWh for the recuperated cycle) is higher than the assumed electricity price of 60 EUR/MWh, which indicates that a higher electricity price is needed to have break-even (NPV = 0 ) of the geothermal power plant at the end of its lifetime. According to the IEA [56],

3.6.2. Economic conditions Fig. 4 shows the sensitivity analysis results of the standard ORC for changing economic parameter values with respect to their reference values (of Table 3). For the yearly electricity price increase (del ), only the case of a constant electricity price over the entire lifetime (del = 0%) has been additionally investigated and is indicated with the black arrow in Fig. 4a to d. The results are shown for the standard ORC, however similar trends hold for the recuperated cycle. From Fig. 4a follows that, from the economic parameters, the electricity price ( pel ) and the availability factor (N) have the highest impact on the NPV, followed by the discount rate (dr), the investment costs for the drillings (Iwells ), the lifetime (L) and the well pumps power (Wwells ). If the electricity price would be 50% higher ( pel = 90 EUR/MWh instead of 60 EUR/MWh ), the NPV would be 11.12 MEUR instead of − 3.74MEUR. This is a difference of almost 15 MEUR and makes the project economically attractive. Remark that NPV = 0 for an electricity price of pel = LCOE = 68.20 EUR/MWh . From Fig. 4b follows that Wnet is mostly affected by pel followed by N , dr and Wwells . The electrical power production is not influenced by Iwells because it is a constant cost which does not depend on the variables of the optimization process. For a higher pel , more revenues can be received from selling electricity and a more expensive ORC is installed which generates more power. Fig. 4c shows that the LCOE is mostly 723

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Fig. 3. Sensitivity analysis on the design optimization results for different brine conditions, for the standard and the recuperated ORC. Every bar is the result of a design optimization.

affected by N and L, followed by pel (on the negative side), dr and Iwells . In contrast to the electrical power output, the LCOE depends on the well investment costs. Finally, from Fig. 4d follows that the SIC is dominated by the well costs, since Iwells and IORC are of the same order of magnitude. The electrical power output strongly depends on the incentive to invest in an efficient (hence more expensive) ORC. For low values of pel , a cheap ORC will be installed which produces little power. For high values of pel , a more expensive ORC is installed, but the electrical power production increases as well. Therefore, the SIC is almost independent of the electricity price for pel > 60 EUR/MWh . The same reasoning holds for the lifetime.8 In addition to the economic conditions, also the sensitivity towards the brine conditions is included in Fig. 4. The project feasibility mostly depends on the brine conditions (especially the brine temperature), followed by the electricity price and the availability factor, the discount rate and the investment costs for the well drillings. The brine conditions are determined by the geological conditions, but the type of contract for electricity selling, the type of investor (discount rate) and the maturity of the well drilling company might have a big impact on the overall project feasibility. Well-considered assumptions have to be made in the design stage of the geothermal project. Fig. 5a shows the impact of the electricity price pel on the project feasibility. For a higher electricity price, a more efficient ORC can be installed which produces more electricity. The project becomes feasible for electricity prices higher than 65–70 EUR/MWh (and for reference values for the other parameters of Table 3), as was already indicated by the results for the LCOE in Table 8. The gray line indicates the difference between the NPV for the recuperated and the standard ORC. The

recuperated ORC has generally a higher NPV, and the difference increases for higher electricity prices. 3.6.3. Environment conditions Fig. 5b shows the impact of the environment temperature on the NPV. If the same installation would be installed in colder regions, the NPV is higher which could be expected. The opposite is true for hotter regions. Also here, the recuperated ORC has a slightly higher NPV than the standard cycle and the difference (gray line) increases for lower environment temperatures. 4. Off-design optimization 4.1. Hourly data for the environment temperature and electricity prices The off-design analysis is based on hourly data for the environment temperature in Mol and the wholesale day-ahead electricity prices in Belgium for 2016. The hourly environment temperature is given in Fig. 6a, but our off-design model results are based on the duration curve for Tenv which is shown in Fig. 6b9. Instead of using all 8784 data points (blue line, 8784 h in 2016), we reduce this curve to 100 data points (red dashed line) to speed up the calculation time. The 100 data points are defined as the points at 0.5%, 1.5%, …, 99.5% of the duration curve for Tenv . This data reduction leads to the elimination of the extreme values max = 29.04 °C is used instead of the real maximum temperaof Tenv (Tenv min = 4.28 °C is used instead of the real minimum ture 33.19 °C and Tenv temperature 8.13°C ). The impact on the annual power production and the NPV is very small, which will be discussed more in detail in Section

8 For low values of pel and L, the net electrical power output is too low to compensate for the investment costs which results in a higher SIC value.

9 The duration curve for Tenv shows for what percentage of the time during a year, the environment temperature is above a certain value.

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Fig. 4. Sensitivity analysis on the design optimization results for different economic and brine conditions, for the standard ORC. Every point is the result of a design optimization. The legend is shown in Fig. 4c. The economic conditions are the electricity price pel and yearly electricity price increase del , the lifetime L, the availability factor N, the well investment costs Iwells and the well pumps power Wwells . The results for a changing brine temperature Tb, prod and flow rate mb are additionally shown. For every line, the corresponding parameter value is changed whilst all other parameters are at their reference values of Table 3.

Fig. 5. Impact of the design electricity price and the design environment temperature assumptions on the design NPV value. All other parameter values are at their reference values of Table 3. Every point is the result of a design optimization. The results for the standard and the recuperated cycle are shown in blue and green dashed lines, respectively. The gray line indicates the difference between the NPV for the recuperated and the standard ORC (ordinate scale on the right-hand side).

4.4. Furthermore, the real hourly electricity prices are shown in Fig. 6a. The inset is a zoom of the y-axis to more moderate values. For each of the 100 data points on the duration curve for Tenv (red dashed line in Fig. 6b), the average electricity price is calculated for all hours during the year which correspond to that environment temperature. The resulting average electricity price for every data point is shown in Fig. 6b.

and the off-design models are added. Since the design is fixed (the ORC is installed and the investments are made), only the operational variables are considered in the operational optimization procedure. Some additional constraints are set for the fixed design geometry and for the off-design operation constraints. In order to allow convergence, Tmin = 0.75 °C instead of 1 °C in the design optimization. Furthermore, the brine parameters are kept constant at their reference values, which were given in Table 3. In the off-design case, the objective of maximizing the NPV reduces to maximizing the net electrical power output since all investments are made (and do not depend on the operating variables anymore).

4.2. Optimization strategy The same models are used as in the design optimization framework, 725

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Fig. 6. Real hourly data and reduced curves (considering 100 data points) for the environment temperature and electricity price.

The flowchart of the off-design optimization framework was already given in Fig. 2. The changes with respect to the design optimization framework are indicated in red. For each of the 100 data points on the reduced duration curve of Tenv (Fig. 6b), the off-design optimization model is run. The optimization results are the operational variables and the net electrical power output for every data point. Taking the corresponding electricity prices into account (Fig. 6b) and the number of hours that each value of Tenv occurs in the year, the real NPV can be calculated in a post-processing step.

4.3. Off-design performance for the reference conditions The optimal design for the standard and the recuperated ORC was already found in Section 3.5 as the result of the design optimization model. Fig. 7 shows the off-design optimization model results for the optimized (reference) ORC design. The optimized working fluid temperatures and the net electrical power output are shown for each of the 100 data points. First, from Fig. 7a it follows that the turbine inlet temperature is almost constant for all values of Tenv . The minimum

Fig. 7. Results of the off-design optimization model for the reference design and for the 100 data points. The dashed red line is the reduced duration curve of the environment temperature of Fig. 6b. The results for the standard and the recuperated cycle are shown in blue and green dashed lines, respectively.

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superheating degree of 1 °C is optimal for every point (so the optimal evaporator temperature is 1 °C lower than the turbine inlet temperature). The condenser temperature, however, has a big impact on the net electrical power production. T1 varies within a range of 22.01 °C to 53.47 °C and 18.29 °C to 51.05 °C for the standard and the recuperated cycle, respectively. We see that the condenser temperature is lower for the recuperated cycle (even more at low values of Tenv ), which directly results in a higher net electrical power output which is shown in Fig. 7b. The air velocity varies from −2.50% to 8.05% and from −1.72% to 6.89% for the standard and the recuperated cycle with respect to its design value as Tenv varies from 29.07 °C to −4.28 °C. So the fan power is higher at low environment temperatures. The working fluid mass flow rate slightly decreases with a lower Tenv but the variation is smaller than 0.3% from the design value. The recuperator efficiency stays within 0.75% of its design value, and slightly increases with a lower Tenv .

Fig. 8. Off-design model results for the net electrical power output as a function of the environment temperature for the reference case ( pelD = 60 EUR/MWh and D Tenv = 10.85 °C ). The dots indicate the off-design model results for the considered 100 data points, the lines indicate the spline approximation of the offdesign model results.

4.4. Note on the data reduction errors

5. Discussion: Optimal ORC design accounting for off-design performance

By using only 100 data points instead of performing the off-design optimization for every hour in the reference year, we reduce the number of times the optimization model has to run from 8784 to 100 and thereby reduce the calculation time. In this section we make an estimation of the errors we make by doing this. The off-design model is used for maximizing the net electrical power output for every data point as a function of the environment temperature. The average difference between the electrical power output of two consecutive data points is 2.64 × 10 2 MW and 2.82 × 10 2 MW for the standard and the recuperated cycle, respectively. This corresponds to 0.85% and 0.83% of the average electrical power production in one year for the standard and the recuperated cycle. Therefore, the step size results in a good accuracy of the data reduction to 100 points. The largest errors occur at the extreme values of Tenv since we only consider a range of 4.28 °C to 29.07 °C instead of the real range of occurring temperatures, from 8.13 °C to 33.19 °C (see Figs. 6a and 6b). Therefore, we calculate the off-design power output for the real extreme values of the environment temperature and compare them to the values we use in the 100 data points approximation. Table 9 shows the results. For the maximum temperature of 29.07 °C instead of 33.19 °C , the model predicts a 18% higher electrical power output than the real power would be in case of the highest environment temperature. For the lowest environment temperature, the model under-predicts the electrical power production by 6.9–7.1%. The errors are almost symmetric so they partly cancel each other. We end up with a slight underprediction of the real electrical power output, which justifies the data reduction to 100 data points and speeding up the off-design calculations with almost a factor 88. Furthermore, we will use spline approximations of the off-design optimization results for a quick calculation of the hourly power profiles. Fig. 8 shows the electrical power - environment temperature dependency for the reference case. The dots are the results of the offdesign optimization process for the 100 data points, and the full lines indicate the spline approximations. The standard deviation is 7.6 × 10 3 MW , so the spline approximations are of satisfying accuracy.

D on the real NPV 5.1. Influence of the design-stage assumptions pelD and Tenv

Fig. 9 shows the impact of a parameter assumption in the design step for the electricity price ( pelD ) and for the environment temperature D (Tenv ) on what we refer to as the real NPV of the geothermal power plant. In qualitative terms, the real, or actual, NPV is the appropriately discounted sum of costs and revenues occurring during actual operation i.e., subject to varying market and environment conditions, for a device that has already been invested in and that was optimized for the fixed design parameters. In order to calculate the real NPV, we take into account the duration curve for Tenv of Fig. 6b and the corresponding electricity prices of Fig. 6d. This is in contrast to the design optimization procedure (Fig. 5), where we have assumed a fixed parameter D value for pelD and Tenv , namely the values which were given in Table 3. In the off-design optimization, however, we are able to see the effect of these parameter assumptions on the real power production during operation (mostly in off-design) and on the real NPV of the power plant. In Fig. 9a, the real NPV is given as a function of the parameter value assumption for pelD in the design step, so for a power plant which is designed for an electricity price of pelD on the x-axis. From the figure, it is clear that the highest NPV is reached for the average electricity price of pelav = 36.57 EUR/MWh (which was the average value for the wholesales prices in 2016). However this electricity price cannot be predicted in advance; a good approximation is of the utmost importance for the plant feasibility and thus a reasonable guesstimate of the average wholesale price must be made for the entire expected lifetime of the plant. For a design value of the electricity price within 30–60 EUR/MWh , the real NPV of the project stays within 10% of the design value. For a bad electricity price assumption, e.g. for pelD = 120 EUR/MWh , the NPV might be 50% lower. This emphasizes the importance of taking the off-design performance into account. In Fig. 9c, the real NPV is given as a function of the parameter value asD sumption for Tenv in the design step. From the results follows that the

Table 9 Estimation of the errors due to the data reduction to 100 points, for the reference case. max Tenv [°C ]

Wnet [MW]

Wnet [MW]

min Tenv [°C ]

Wnet [MW]

Wnet [MW]

Stand

Model 100 points Reality

29.07 33.19

1.78 1.51

0.27 (+18%)

−4.28 −8.13

4.40 4.74

−0.34 (−7.1%)

Recup

Model 100 points Reality

29.07 33.19

1.94 1.65

0.29 (+18%)

−4.28 −8.13

4.74 5.09

−0.35 (−6.9%)

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Fig. 9. Real NPV as a function of the design value for the electricity price and the design environment temperature. Every point is the result of one design optimization and 100 runs of the off-design optimization model. The results for the standard and the recuperated cycle are shown in blue and green dashed lines, respectively.

Fig. 10. Average net electrical power output and NPV of the standard ORC for the design prediction (full line) and for the real results taking off-design into account D = 10.85 °C, 20 °C , and 30 °C (dashed line), as a function of the design electricity price assumption and for multiple design environment temperature assumptions (Tenv are shown in blue, green and red, respectively). Every data point on the full lines is the result of one design optimization. The data points on the dashed lines account for the off-design performance and are based on 100 additional runs of the off-design optimization model. Note the different ordinate scale used in Fig. 10b compared to Fig. 9b. D design value of Tenv has a smaller impact on the real NPV. The NPV can be improved by 9.76% by designing the ORC for a higher value of av = 10.85 °C . Tenv 30 °C instead of Tenv

ORC is cheaper and less-performing for higher design values of Tenv . However, during off-design operation, the environment temperature is mostly lower than the design value (Fig. 6a) and a higher electrical power output is reached than the power for which the ORC was designed (the dashed lines are above the full lines). The difference is the D = 30 °C (red). So it is beneficial to design the ORC for a highest for Tenv higher than average value of the environment temperature. Fig. 10b shows the predicted NPV in the design stage (full lines) and the real NPV (dashed lines) which takes off-design into account, as a function of the design electricity price and for multiple values of the D = 10.85 °C , 20 °C and 30 °C in design environment temperature (Tenv blue, green and red, respectively). We see that the NPV which is the result of the design optimization is in general very different from the real NPV value. This shows the importance of taking the off-design results into account. As been discussed in Section 5.1, there exists and optimum for every line. For every design value of the environment temperature, the real NPV reaches an optimal value. However the D corresponding optimal value for pelD is different for every line of Tenv .A D higher value of pelD and a lower value of Tenv in the design stage lead to a higher nominal electrical power output and a more expensive ORC D which which is installed. So, there is a trade-off between pelD and Tenv D causes that every line of Tenv reaches its optimal value for NPV at a different design value for pelD . In this case—and for the real environment temperature and electricity price profiles of Fig. 6—the optimal design of the ORC is the design which corresponds to pelD = 45 EUR/MWh and D Tenv = 20 °C . The optimal point is reached for 20 ° C= 45EUR/MWh = pelD > pelav = 36.57 EUR/MWh and

D 5.2. Combined influence of pelD and Tenv on the real NPV

Now the main goal is to find the optimal design, taking into account the off-design performance as a result of real varying environment conditions and fluctuating electricity prices (as was shown in Fig. 6). Fig. 10 shows the net electrical power output and the NPV for a standard ORC as a function of the parameter value assumption of pelD in the design stage and for multiple values of the design environment temD perature Tenv . The results for the recuperated cycle are similar. The full lines show the results of the design optimization model, based on the assumptions for the electricity price (x-axis) and for the environment temperature (multiple lines) in the design stage. The dashed lines indicate the real average net electrical power output and the real NPV when the off-design performance is taken into account (changing environment conditions and fluctuating electricity prices of Fig. 6). From Fig. 10a follows that for the reference value of D av Tenv = 10.85 ° C= Tenv , the real average power output (blue dashed) corresponds very well to the predicted values (blue full line). However, D = 20 °C and 30 °C are higher.10 The installed the discrepancies for Tenv 10 D = 30 °C , it is not worth it For the design values pelD = 30 EUR/MWh and Tenv to produce electricity. The value Wnet = 0.5 MW corresponds to the well pumps power.

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Table 10 Performance indicators of the design model results (D), the off-design model results (O) and the spline approximation based on the off-design model results (O: spl) for the standard geothermal ORC. pelD [ Reference Fig. 9a Fig. 9b Optimal Model

EUR ] MWh

60 36.57 60 45

NPV [MEUR]

D Tenv [°C ]

10.85 10.85 30 20

−3.74 −13.23 −13.70 −13.54 D

−14.06 −12.93 −12.79 −12.75 O

Eyear [GWh]

Wnet [MW] −14.01 −12.90 −12.75 −12.72 O: spl

3.11 2.29 1.40 1.82 D

3.13 2.31 2.43 2.35 O

3.13 2.31 2.43 2.35 O: spl

24.60 18.13 11.06 14.39 D

24.74 18.25 19.19 18.58 O

24.74 18.25 19.19 18.58 O: spl

Table 11 Performance indicators of the design model results (D), the off-design model results (O) and the spline approximation based on the off-design model results (O: spl) for the recuperated geothermal ORC. pelD [ Reference Fig. 9a Fig. 9b Optimal Model

EUR ] MWh

60 36.57 60 45

NPV [MEUR]

D Tenv [°C ]

10.85 10.85 30 20

−2.81 −13.10 −13.54 −13.40 D

−14.04 −12.80 −12.67 −12.62 O

−13.99 −12.76 −12.63 −12.58 O: spl

D av Tenv > Tenv = 10.85 °C. The average electrical power generation is 2.35 MWe and the real NPV = 12.75 MEUR for the standard cycle. For the recuperated cycle, the average power production is 2.53 MWe and the real NPV = 12.62 MEUR , which are slightly higher values than for the standard ORC. Note that the optimal design parameter assumptions D for pelD and Tenv are case-specific, and depend on the real profiles for the electricity price and for the environment temperature.

3.38 2.47 1.52 1.97 D

3.39 2.49 2.62 2.53 O

3.39 2.49 2.62 2.53 O: spl

26.72 19.56 12.02 15.57 D

26.84 19.67 20.69 20.02 O

26.84 19.67 20.69 20.02 O: spl

for the design and off-design performance optimization of a low-temperature geothermal organic Rankine cycle (ORC). The developed optimization tool can be used to design a binary geothermal power plant and to calculate the off-design performance over its lifetime. Based on the results, the optimal design parameters can be indicated, which correspond to the ORC design with the highest net present value. From the design results follows that the recuperated ORC has better economic performance than the standard cycle. For the investigated reference conditions, which are based on the Belgian conditions in 2016, the net power output of the recuperated cycle is 3.38 MW, which is 8.68% higher than for the standard ORC. The corresponding net present value (NPV) is −2.81 MEUR, which means that the project is not economically attractive for the investigated conditions. This is also reflected in the levelized cost of electricity LCOE = 65.67 EUR/MWh , which is higher than the current wholesale electricity prices. However, according to the IEA [56], electricity prices higher than 80 USD/MWh ( 67 EUR/MWh ) are possible for the 450 Scenario, which indicates that the low-temperature geothermal power plant might become economically competitive in the future. Next to the electricity price, also the brine temperature has a very large impact on the plant economics. Therefore, for other geographical locations, a binary geothermal power plant might be cost-competitive depending on the local climate and electricity prices. From the off-design results follows that the net power output strongly depends on the environment temperature. For the recuperated ORC, the net power increases from 1.95 MW to 4.74 MW for a decreasing environment temperature from 29.07 °C to −4.28 °C . A data reduction has been performed to improve the calculation time of the off-design model by a factor 88, and a spline approximation has been used for a quick calculation of the hourly net power profile as a function of the environment temperature. Both, the data reduction technique and the spline approximation are found to be of satisfying accuracy. Taking the off-design performance into account, the optimal ORC design has been calculated for the investigated conditions. The recuperated ORC reaches a maximum real NPV of −12.62 MEUR for design parameter values for the environment temperature and electricity price of 20 °C and 45 EUR/MWh, which are different from the yearly-averaged values. Note also the difference with the NPV which has been estimated in the design stage at −2.81 MEUR. Since the real average electricity price is only 36.57 EUR/MWh instead of 60 EUR/ MWh, which has been assumed in the design stage, the net power output and the corresponding revenues are overestimated. The impact of the environment temperature assumption in the design stage is

5.3. Summary Tables 10 and 11 summarize the results for the standard and the recuperated ORC, respectively. The NPV, the net electrical power output (Wnet ) and the energy production during one year (E year ) for the reference case, for the optimal point of Fig. 9a, for the optimal point of Fig. 9b and for the overall optimal design are given. The first column gives the value which is predicted by the design optimization model (D). The values of the second column take the off-design performance (O) into account—the environment temperature variation and electricity price fluctuations of Fig. 6. So, column 2 contains the results of the off-design model for the 100 data points. Column 3 uses the spline approximations of the off-design optimization model results (O:spl, Fig. 8) for calculating the real hourly net electrical power output as a function of the environment temperature for all 8784 h during the year. In this approach, all environment temperatures are considered (from min max Tenv = 8.13 °C to Tenv = 33.19 °C). The spline approximation is a quick and accurate way of calculating the hourly electricity production profiles (see Fig. 8). From Tables 10 and 11, the following conclusions are made:

• The design optimization model alone is not able to predict the real NPV. Off-design performance results should be included! • The spline approximation of the off-design model allows a quick and •

Eyear [GWh]

Wnet [MW]

accurate calculation of the hourly profiles of the real electricity production (and the operating variables) as a function of the environment temperature. Using the two-step optimization framework to calculate the optimal design and off-design performance for multiple design parameter D assumptions for Tenv and pelD allows finding the optimal design of the geothermal ORC for a given location, and accounting for off-design.

6. Conclusions In this paper, we have proposed a two-step optimization procedure 729

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smaller, but it is beneficial to design the ORC for a higher environment temperature than the average value. The proposed optimization procedure for the design optimization of a low-temperature geothermal organic Rankine cycle (MW scale) and accounting for the off-design performance already in the design stage, using hourly weather data and detailed thermoeconomic models is novel compared to the existing literature. In future work, we will investigate the potential of low-temperature geothermal combined heatand-power (CHP) plants where electricity will be generated via an ORC and, additionally, heat will be provided to a nearby district heating system. The idea is to improve the revenues by selling two products (heat and electricity). The study of geothermal CHP plants will be based on a similar two-step optimization methodology, for which the already developed ORC models will be used. The big advantages of our

optimization framework are that detailed thermoeconomic models are implemented, that the input parameters can be easily adapted (generic methodology), and that errors related to the use of multiple programming tools are avoided since the same models are used for the design and the off-design optimization procedure. Acknowledgments This project receives the support of the European Union, the European Regional Development Fund ERDF, Flanders Innovation & Entrepreneurship and the Province of Limburg, and is supported by the VITO PhD Grant No. 1510829. The authors also want to thank Sylvain Quoilin (KU Leuven/ University of Liège) for the interesting discussion on the off-design turbine modeling.

Appendix A. Turbine modeling In this section, we give some more details regarding the modeling of a single-stage axial turbine in design and off-design conditions. The isentropic efficiency calculation in the design stage is based on a curve-fit that Walraven et al. [57] have made for the correlation given by Macchi and Perdichizzi in [32]. Due to the high pressure ratio, the turbine nozzles are choked all the time and the following relation holds during off-design operation: O m wf D m wf

=

O O 6 c6 D 6D c6

with c =

p

|s

(A.1)

Herein is the density, c the speed of sound, p the pressure, and O and D indicate the off-design and the design conditions, respectively. Since we have to account for the real gas properties, the speed of sound has to be calculated and no further simplifications based on the ideal gas law are allowed. By using the turbine inlet conditions (state 6 from Fig. 1) instead of the throat conditions, we make an assumption which is justified for the purpose of this paper (system approach for the ORC rather than a detailed turbine design). The turbine efficiency in off-design conditions is calculated via the Keeley correlation [33]: O t

=

D t sin

0.5

D 0.1 6 D O m wf 6

O m wf

(A.2)

Since the turbine is in choking conditions, it can be justified that a correlation only based on the turbine inlet conditions and the mass flow rate is used.

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