KULeuven Energy Institute

TME Branch

WP EN2018-13

Design and off-design optimization procedure for low-temperature geothermal

organic Rankine cycles

Sarah Van Erdeweghe, Johan Van Bael, Ben Laenen and William D‘haeseleer

TME WORKING PAPER - Energy and Environment Last update: February 2019

An electronic version of the paper may be downloaded from the TME website:

http://www.mech.kuleuven.be/tme/research/

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

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

aUniversity of Leuven (KU Leuven), Applied Mechanics and Energy Conversion Section, Celestijnenlaan 300 - box2421, B-3001 Leuven, Belgium

bFlemish Institute for Technological Research (VITO), Boeretang 200, B-2400 Mol, Belgium

cEnergyVille, Thor Park 8310, B-3600 Genk, Belgium

Abstract

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 in-

vestigated 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 (-12.62MEUR) which indicates that the low-temperature (130◦C) geother-

mal electric power plant is not economically attractive for the investigated case. Nevertheless, and

demonstrated by the results of a detailed sensitivity analysis, a low-temperature geothermal power

plant might be economically feasible for geological sites with a higher brine temperature or in a coun-

try with a more favorable economic situation; e.g., with higher electricity prices (∼70EUR/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.

Keywords: ORC, geothermal energy, design optimization, off-design performance

∗Corresponding authorEmail address: william.dhaeseleer@kuleuven.be (William D’haeseleer)

Preprint submitted to Applied Energy February 18, 2019

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 low-temperature

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 set-ups 1 for application in a geothermal power plant (160◦C, 5kg/s). A Pareto front solution

has been shown for the specific investment cost (SIC) and the exergy efficiency (ηex)2, as they are

conflicting optimization objectives. The authors have found that the basic ORC has the lowest SIC

for ηex < 45% whereas the regenerative ORC has the lowest SIC for ηex > 45%.

Braimakis et al. [2] have performed a thermoeconomic optimization of the standard and the regen-

erative ORC. Heat source temperatures of 100, 200 and 300◦C and heat source capacities of 100,

500, 1000 and 2000kWth have been considered, representing different energy sources. They have

concluded that the expander type has a dominant role in the economic performance of ORCs. Fur-

thermore, 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 thermoeconomic optimization of differ-

ent types of ORCs for application to low- to medium-enthalpy geothermal brines (120 − 180◦C,

1In 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.2The 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).

2

200kg/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 re-

sults, 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 6MW power output) with a levelized cost of electricity (LCOE) of 88.5EUR/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 125EUR/MWh (for a 500kW

power 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, 20kg/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 optimization 3 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 ratein the range of 18− 24kg/s. The maximum net power generation of 335.4kW is obtained for a flowrate of 18kg/s and a source temperature of 185◦C, the lowest value of 269.3kW is obtained for a

source temperature of 185◦C and a flow rate of 24kg/s.

Kim et al. [6] have performed an off-design performance analysis for an ORC fueled by waste heat

3The mentioned optimization was rather a parameter search in this case.

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or residual heat from a combined heat-and-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, 10kg/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 3.6kg/s to 14.4kg/s, the cycle efficiency increases from 2.6% to 6.3% and the

net power increases from 16.7kW to 88.7kW. 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 low-enthalpy geothermal power plant

(100kg/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

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depends on the mass flow rate (by a power law). The authors 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 off-design 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 3500kW. 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

off-design analysis has been performed for every design point. The off-design 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 off-design 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, 12kg/s). Then the off-design 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 200kg/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

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a net present value (NPV) of 6.89MUSD. 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 9.16kg/s, the second is at a temperature of 145◦C

and has a flow rate of 6.57kg/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 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 off-design. Finally, the real NPV is calculated, taking the

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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 off-design 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

4This 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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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 site-dependency 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. Figure 1a shows a schematic presentation of the recuperated ORC with indication of

the states. The brine, at a temperature Tb,prod and flow rate ṁb, transfers heat to the working fluid

and is injected at a temperature Tb,inj . The working fluid is pumped to a higher pressure (1→ 2),gets subsequently heated in the recuperator (RECUP, 2 → 3), the economizer (ECO, 3 → 4), theevaporator (EVAP, 4 → 5) and the superheater (SUP, 5 → 6), expands over the turbine (6 → 7)which is connected to a generator to produce electrical power, transfers part of its heat in the

recuperator (7→ 8) and is finally condensed back to state 1 to close the cycle. The cooling mediumis 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 Figure

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

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(a) Recuperated ORC (b) T-s diagram

Figure 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.

9

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-stagehas 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 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

5The 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.6The 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.

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parameter component correlation

heat transfer and pressure drop shell HEx Bell-Delaware [23–25]

ideal heat transfer and pressure drop single-phase shell HEx Shah et al. [24]

ideal heat transfer and pressure drop two-phase shell HEx Hewitt et al. [23]

friction factor single-phase tube HEx Bhatti and Shah [26]

heat transfer coefficient single-phase tube HEx Petukhov and Popov [27]

heat transfer and friction factor air-side ACC Yang [19]

heat transfer coefficient single-phase wf ACC Gnielinski [28]

friction factor single-phase wf ACC Petukhov and Popov [27]

void fraction two-phase wf ACC CISE [29]

pressure drop two-phase wf ACC Chisholm [30]

heat transfer coefficient two-phase wf ACC Shah [31]

design efficiency turbine Macchi and Perdichizzi [32]

off-design efficiency turbine Keeley [33]

Table 1: Correlations used in the thermodynamic models. The abbreviation wf stands for working fluid.

expanded to be able to perform design as well as off-design 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 off-design 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 Ẇ . We assume correction factors to

account for high temperatures (> 100◦C), high pressures (> 7bar) and the need for stainless steel

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capacity measure size range cost correlation [USD] ref

shell&tube HEx A [m2] 80-4000m2 3.28 104(A/80)0.68 [34]

centr. pump (incl. motor) Ẇ [W ] 4-700kW 9.84 103(Ẇ/4000)0.55 [34]

turbine Ẇ [W ] 0.1-20MW −19000 + 820(Ẇ/1000)0.8 [36]ACC excl. fan A [m2] 200-2000m2 1.56 105(A/200)0.89 [34]

ACC fan incl. motor Ẇ [W ] 50-200kW 1.23 104(Ẇ/50000)0.76 [34]

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

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 fp 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.

2.4. Reference parameter values

Table 3 presents the reference parameter values. The brine is modeled as pure water and the

reference conditions (brine production temperature Tb,prod and pressure pb,prod, brine flow rate ṁb,

well investment costs Iwells and well pumps power Ẇwells) 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 ηp [42], generator and motor mechanical-to-electrical efficiencies ηg and ηm [42,

43], fan efficiency ηf [44], the minimum pinch-point-temperature difference over the heat exchangers

∆Tmin and the minimum degree of superheating ∆Tminsup . 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].

7ηf = 60% is the total fan efficiency, which includes the isentropic and mechanical-to-electrical conversion effi-

ciency.

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Brine & wells [37] Economic [38–41] Environment [45] Cycle [42–44]

Tb,prod = 130◦C pel = 60EUR/MWh Tenv = 10.85◦C ηp = 80%

pb,prod = 40bar del = 1.25%/year penv = 1.02bar ηg = 98%

ṁb = 150kg/s dr = 5% ηm = 98%

Iwells = 15MEUR L = 30years ηf = 60%7

Ẇwells = 500kW N = 90% ∆Tmin = 1◦C = ∆Tminsup

Table 3: Reference parameter values.

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 [21, 48]. The thermodynamic and environ-

mental properties of Isobutane are summarized in Table 4.

MW [g/mole] Tcrit [◦C] pcrit [MPa] ODP GWP

Isobutane (R600a) 58.12 134.7 3.63 0 20

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

3. Design optimization

3.1. Optimization strategy

The net present value (NPV) is considered as the objective and is defined as:

NPV = −Iwells − IORC +L−1∑

i=0

Ẇnetpel(1 + del)iN8760− 0.025IORC

(1 + dr)i(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

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variable lower bound upper bound variable lower bound upper bound

Dshell [m] 0.3 2 Lbc [m] 0.3 5

Dtube [mm] 5 50 Sfin [mm] 1.14 3.04

ptube/Dtube [-] 1.2 2.5 Hfin [mm] 14.25 23.75

Bc/Dshell [-] 0.25 0.45 ntube [-] 500 10000

T6 [◦C] Tenv + 10◦C min(Tcrit, Tupper) ṁwf/ṁb [-] 0.01 5

T4 [◦C] Tenv min(Tb,prod, Tupper) vair [m/s] 1.5 10

T1 [◦C] Tenv min(Tb,prod, Tupper) � [%] 0.01 90

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

conditions. The operating conditions are the turbine inlet temperature T6, the evaporator inlet

temperature T4, the condenser outlet temperature T1, the working fluid mass flow rate ṁwf , the

air speed vair through the condenser and the recuperator efficiency � (=T7−T8T7−T2 , with reference to

Figure 1) in case of the recuperated ORC. All 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 with the TEMA standards [22]. In addition, a minimal degree of superheating of

∆Tminsup 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.

3.2. Flowchart

Figure 2 shows the flowchart of the developed design optimization model. The black values be-

long to the design optimization flowchart. The flowchart will be extended with the red values

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constraint lower bound upper bound

Dtube/Dshell [-] 0 0.1

LACC [m] 0 15

T6 − T4 [◦C] ∆Tminsup Tupper − TenvT4 − T1 [◦C] 10 2(Tupper − Tenv)Tb,inj [

◦C] 25 Tb,prod

∆Tpinch [◦C] ∆Tmin 100

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

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 post-processing step,

all other performance indicators can be calculated.

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 optimiza-

tion results are trustworthy. There are no experimental results available to the authors. Never-

theless, 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 pre-

15

Figure 2: Flowchart of the optimization procedure. Black: design optimization framework, red: extension to the

design optimization framework (black) for off-design calculations.

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

3.4. Definition of the performance indicators

The following performance indicators are used:

• Levelized cost of electricity, LCOE =Iwells+IORC+

∑L−1i=0

0.025IORC(1+dr)i

∑L−1i=0

ẆnetN(1+del)i8760

(1+dr)i

;

• Specific investment cost, SIC = Iwells+IORCẆnet

;

• Specific work of the ORC 8, w = Ẇ∗net

ṁwf;

8In the definition of the specific work w, the well pumps power is not included in Ẇ ∗net since w is a property of

the ORC. Note that in the definition of the plant net electrical power output Ẇnet, the well pumps power has been

included.

16

standard recuperator recuperator

shell diameter Dshell [m]

EE

S

0.77 0.77

RE

CU

P

1.05

tube diameter Dtube [mm] 6.00 5.97 5.52

tube pitch ptube [mm] 7.20 7.16 8.69

baffle cut Bc [m] 0.19 0.19 0.26

length between baffles Lbc [m] 3.05 3.15 5.00

fin height Hfin [mm]

AC

C

23.75 23.75

fin spacing Sfin [mm] 3.04 3.04

number of tubes ntube 1060 1066

Table 7: Optimal design of the economizer, evaporator, superheater (called EES), the air-cooled condenser (ACC )

and the recuperator (RECUP) for the reference conditions of Table 3.

standard recuperator standard recuperator

NPV [MEUR] -3.74 -2.81 ηen [%] 11.45 12.44

Ẇnet [MW] 3.11 3.38 ηex [%] 25.12 27.28

w [kJ/kg] 38.91 41.50 Tb,inj [◦C] 73.53 74.52

IORC [MEUR] 11.48 (73.90%) 12.49 (68.28%) � [%] - 71.15

SIC [EUR/kW] 8509.51 8135.71 ηt [%] 89.07 88.86

LCOE [EUR/MWh] 68.20 65.67

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

• Energetic cycle efficiency, ηen =Ẇt−Ẇp

Q̇b, with Q̇b = ṁb(hb,prod − hb,inj);

• Exergetic plant efficiency, ηex = ẆnetĖxb,prodwith Ėxb,prod = ṁbexb,prod and exb,prod = hb,prod − henv − Tenv(sb,prod − senv).

3.5. Results for the reference conditions

The T-s diagrams of the optimized standard and recuperated ORCs for the reference conditions

were already shown in Figure 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.

17

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 ηt 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], whichcorresponds to 1 − 2% of the total investment costs (including the drilling costs) for the referenceconditions and a NPV which would be 0.2MEUR to 0.6MEUR 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 (68.20EUR/MWh for the standard ORC and 65.67EUR/MWh for the recu-

perated cycle) is higher than the assumed electricity price of 60EUR/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], electricity prices higher than 80USD/MWh

(≈ 67EUR/MWh) are possible for the 450 Scenario, which indicates that the low-temperaturegeothermal 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 Figure 4.

18

3.6. Sensitivity analysis

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 Ẇnet, the

SIC and the LCOE.

3.6.1. Brine conditions

We consider different brine temperatures and mass flow rates and investigate the effect on the

project feasibility. Figure 3 shows the results.

(a) Net present value (NPV) (b) Net electrical power output (Ẇnet)

(c) Levelized cost of electricity (LCOE) (d) Specific investment cost (SIC)

Figure 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.

From Figure 3a follows that the NPV increases for both the brine temperature and flow rate, which

19

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 ṁb = 200kg/s. For the reference brine

flow rate of 150kg/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 100kg/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.

Figure 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.

Figures 3c and 3d show that the LCOE and the SIC decrease with Tb,prod and ṁb. Also here,

the brine temperature has the highest impact. The LCOE can be as high as 176EUR/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 ṁb = 200kg/s and is 41EUR/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 23,315EUR/kW for

the standard ORC at Tb,prod = 110◦C and ṁb = 100kg/s, and 4,959EUR/kW for the recuperated

ORC Tb,prod = 150◦C and ṁb = 200kg/s.

3.6.2. Economic conditions

Figure 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 Figures 4a to 4d. The results are

shown for the standard ORC, however similar trends hold for the recuperated cycle.

From Figure 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 (Ẇwells).

If the electricity price would be 50% higher (pel = 90EUR/MWh instead of 60EUR/MWh),

the NPV would be 11.12MEUR instead of -3.74MEUR. This is a difference of almost 15MEUR

and makes the project economically attractive. Remark that NPV = 0 for an electricity price

20

(a) Net present value (NPV) (b) Net electrical power output (Ẇnet)

(c) Levelized cost of electricity (LCOE) (d) Specific investment cost (SIC)

Figure 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 Figure 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 Ẇwells. The results for a changing brine temperature

Tb,prod and flow rate ṁb are additionally shown. For every line, the corresponding parameter value is changed whilst

all other parameters are at their reference values of Table 3.

21

of pel = LCOE = 68.20EUR/MWh. From Figure 4b follows that Ẇnet is mostly affected by pel

followed by N , dr and Ẇwells. 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. Figure 4c shows that the LCOE is mostly affected byN 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 Figure 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 > 60EUR/MWh. The same reasoning

holds for the lifetime 9.

In addition to the economic conditions, also the sensitivity towards the brine conditions is included

in Figure 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.

Figure 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− 70EUR/MWh (and for reference values forthe 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.

9For 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.

22

(a) NPV as a function of pDel, for TDenv = 10.85

◦C (b) NPV as a function of TDenv, for pDel =

60EUR/MWh

Figure 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).

3.6.3. Environment conditions

Figure 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 Figure 6a, but our off-design model results are based on the duration curve for Tenv which

23

is shown in Figure 6b 10. Instead of using all 8784 data points (blue line, 8784 hours 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 of Tenv (Tmaxenv = 29.04

◦C is used

instead of the real maximum temperature 33.19◦C and Tminenv = −4.28◦C is used instead of the realminimum temperature −8.13◦C). The impact on the annual power production and the NPV isvery small, which will be discussed more in detail in Section 4.4.

Furthermore, the real hourly electricity prices are shown in Figure 6c. 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 Figure 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 Figure 6d.

4.2. Optimization strategy

The same models are used as in the design optimization framework, 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. Further-

more, 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 elec-

trical power output since all investments are made (and do not depend on the operating variables

anymore).

The flowchart of the off-design optimization framework was already given in Figure 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 (Figure 6b), the off-design

optimization model is run. The optimization results are the operational variables and the net

10The duration curve for Tenv shows for what percentage of the time during a year, the environment temperature

is above a certain value.

24

(a) Hourly environment temperature Tenv (b) Environment temperature duration curve

(c) Hourly electricity price pel (d) Average electricity price pavel for the 100 data

points of the reduced temperature duration curve

Figure 6: Real hourly data and reduced curves (considering 100 data points) for the environment temperature and

electricity price.

25

electrical power output for every data point. Taking the corresponding electricity prices into account

(Figure 6d) 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. Figure 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 Figure 7a it

follows that the turbine inlet temperature is almost constant for all values of Tenv. The minimum

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 Figure 7b. The air velocity

varies from −2.50% to 8.05% and from −1.72% to 6.89% for the standard and the recuperated cyclewith respect to its design value as Tenv varies from 29.07

◦C to −4.28◦C. So the fan power is higherat 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.

4.4. Note on the data reduction errors

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 10−2MW and 2.82 10−2MW for

the standard and the recuperated cycle, respectively. This corresponds to 0.85% and 0.83% of

26

(a) Working fluid temperatures (nomenclature of

Figure 1a)

(b) Net electrical power output (Ẇnet)

Figure 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 Figure 6b. The results for the

standard and the recuperated cycle are shown in blue and green dashed lines, respectively.

Tmaxenv [◦C] Ẇnet [MW] ∆Ẇnet [MW] T

minenv [

◦C] Ẇnet [MW] ∆Ẇnet [MW]

stan

d model 100 points 29.07 1.780.27 (+18%)

-4.28 4.40-0.34 (-7.1%)

reality 33.19 1.51 -8.13 4.74

recu

p model 100 points 29.07 1.940.29 (+18%)

-4.28 4.74-0.35 (-6.9%)

reality 33.19 1.65 -8.13 5.09

Table 9: Estimation of the errors due to the data reduction to 100 points, for the reference case.

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◦Cto 29.07◦C instead of the real range of occurring temperatures, from −8.13◦C to 33.19◦C (seeFigures 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.

27

Figure 8: Off-design model results for the net electrical power output as a function of the environment temperature

for the reference case (pDel = 60EUR/MWh and TDenv = 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 off-design model results.

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 under-prediction 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. Figure 8 shows the electrical power - environment tem-

perature dependency for the reference case. The dots are the results of the off-design optimization

process for the 100 data points, and the full lines indicate the spline approximations. The standard

deviation is 7.6 10−3MW , so the spline approximations are of satisfying accuracy.

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

5.1. Influence of the design-stage assumptions pDel and TDenv on the real NPV

Figure 9 shows the impact of a parameter assumption in the design step for the electricity price (pDel)

and for the environment temperature (TDenv) 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

28

(a) Real NPV as a function pDel (b) Real NPV as a function of TDenv

Figure 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.

parameters. In order to calculate the real NPV, we take into account the duration curve for Tenv

of Figure 6b and the corresponding electricity prices of Figure 6d. This is in contrast to the design

optimization procedure (Figure 5), where we have assumed a fixed parameter value for pDel and TDenv,

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 Figure 9a, the real NPV is given as a function of the parameter value assumption for pDel in

the design step, so for a power plant which is designed for an electricity price of pDel on the x-axis.

From the figure, it is clear that the highest NPV is reached for the average electricity price of pavel =

36.57EUR/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− 60EUR/MWh, the real NPV of the project stays within 10% of the design value. For a badelectricity price assumption, e.g. for pDel = 120EUR/MWh, the NPV might be 50% lower. This

emphasizes the importance of taking the off-design performance into account. In Figure 9b, the

real NPV is given as a function of the parameter value assumption for TDenv in the design step.

29

From the results follows that the design value of TDenv 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 Tenv ≈ 30◦C insteadof T avenv = 10.85

◦C.

5.2. Combined influence of pDel and TDenv 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 Figure 6). Figure 10 shows the net electrical power output and the NPV for a standard ORC

as a function of the parameter value assumption of pDel in the design stage and for multiple values

of the design environment temperature TDenv. 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 Figure 6).

From Figure 10a follows that for the reference value of TDenv = 10.85◦C = T avenv, the real average

power output (blue dashed) corresponds very well to the predicted values (blue full line). However,

the discrepancies for TDenv = 20◦C and 30◦C are higher 11. The installed 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 (Figure 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 highest for TDenv = 30◦C (red). So it is beneficial to design the ORC

for a higher than average value of the environment temperature.

Figure 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 design environment temperature (TDenv = 10.85◦C, 20◦C and 30◦C in blue, green

and red, respectively). We see that the NPV which is the result of the design optimization is in

11For the design values pDel = 30EUR/MWh and TDenv = 30

◦C, it is not worth it to produce electricity. The value

Ẇnet = −0.5MW corresponds to the well pumps power.

30

(a) Net electrical power output (b) Net present value

Figure 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 (dashed line), as a function of the design electricity price

assumption and for multiple design environment temperature assumptions (TDenv = 10.85◦C, 20◦C, and 30◦C 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 Figure 10b compared to Figure 9a.

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 corresponding optimal value for pDel is different for every line of TDenv. A higher value

of pDel and a lower value of TDenv in the design stage lead to a higher nominal electrical power output

and a more expensive ORC which is installed. So, there is a trade-off between pDel and TDenv which

causes that every line of TDenv reaches its optimal value for NPV at a different design value for

pDel . In this case—and for the real environment temperature and electricity price profiles of Figure

6—the optimal design of the ORC is the design which corresponds to pDel = 45EUR/MWh and

TDenv = 20◦C. The optimal point is reached for 45EUR/MWh = pDel > p

avel = 36.57EUR/MWh

and 20◦C = TDenv > Tavenv = 10.85

◦C. The average electrical power generation is 2.35MWe and the

real NPV = −12.75MEUR for the standard cycle. For the recuperated cycle, the average powerproduction is 2.53MWe and the real NPV = −12.62MEUR, which are slightly higher valuesthan for the standard ORC. Note that the optimal design parameter assumptions for pDel and T

Denv

are case-specific, and depend on the real profiles for the electricity price and for the environment

31

pDel [EURMWh

] TDenv [◦C] NPV [MEUR] Ẇnet [MW] Eyear [GWh]

reference 60 10.85 -3.74 -14.06 -14.01 3.11 3.13 3.13 24.60 24.74 24.74

Figure 9a 36.57 10.85 -13.23 -12.93 -12.90 2.29 2.31 2.31 18.13 18.25 18.25

Figure 9b 60 30 -13.70 -12.79 -12.75 1.40 2.43 2.43 11.06 19.19 19.19

optimal 45 20 -13.54 -12.75 -12.72 1.82 2.35 2.35 14.39 18.58 18.58

model D O O: spl D O O: spl D O O: spl

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.

temperature.

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 (Ẇnet) and the energy production during one year (Eyear)

for the reference case, for the optimal point of Figure 9a, for the optimal point of Figure 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 Figure 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, Figure 8) for calculating

the real hourly net electrical power output as a function of the environment temperature for all

8784 hours during the year. In this approach, all environment temperatures are considered (from

Tminenv = −8.13◦C to Tmaxenv = 33.19◦C). The spline approximation is a quick and accurate way ofcalculating the hourly electricity production profiles (see Figure 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 perfor-

mance results should be included!

• The spline approximation of the off-design model allows a quick and accurate calculation of

the hourly profiles of the real electricity production (and the operating variables) as a function

of the environment temperature.

32

pDel [EURMWh

] TDenv [◦C] NPV [MEUR] Ẇnet [MW] Eyear [GWh]

reference 60 10.85 -2.81 -14.04 -13.99 3.38 3.39 3.39 26.72 26.84 26.84

Figure 9a 36.57 10.85 -13.10 -12.80 -12.76 2.47 2.49 2.49 19.56 19.67 19.67

Figure 9b 60 30 -13.54 -12.67 -12.63 1.52 2.62 2.62 12.02 20.69 20.69

optimal 45 20 -13.40 -12.62 -12.58 1.97 2.53 2.53 15.57 20.02 20.02

model D O O: spl D O O: spl D O 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.

• Using the two-step optimization framework to calculate the optimal design and off-design

performance for multiple design parameter assumptions for TDenv and pDel 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 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 3.38MW, which is 8.68%

higher than for the standard ORC. The corresponding net present value (NPV) is -2.81MEUR,

which means that the project is not economically attractive for the investigated conditions. This

is also reflected in the levelized cost of electricity LCOE = 65.67EUR/MWh, which is higher

than the current wholesale electricity prices. However, according to the IEA [56], electricity prices

higher than 80USD/MWh (≈ 67EUR/MWh) are possible for the 450 Scenario, which indicatesthat 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

33

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 1.95MW to 4.74MW 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 -12.62MEUR

for design parameter values for the environment temperature and electricity price of 20◦C and

45EUR/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 -2.81MEUR. Since the real average

electricity price is only 36.57EUR/MWh instead of 60EUR/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 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 heat-and-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.

34

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 number 1510829. The authors also want to thank Sylvain Quoilin (KU Leuven

/ University of Liège) for the interesting discussion on the off-design turbine modeling.

Nomenclature

Abbreviations

symbol description

ACC air-cooled condenser

CHP combined heat-and-power

ECO economizer

EES economizer, evaporator, superheater

EVAP evaporator

GWP global warming potential

NW northwest

ODP ozone depletion potential

ORC organic Rankine cycle

RECUP recuperator

SUP superheater

35

Symbols

symbol description

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

Eyear [GWh] yearly energy production

Ė [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

ṁ [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

Q̇ [MWth] heat

S [mm] spacing

SIC [EUR/kW] specific investment cost

s [kJ/kgK] specific entropy

T [◦C] temperature

v [m/s] velocity

Ẇ [MWe] electrical power

w [kJ/kg] specific work

� [%] heat exchanger efficiency

η [%] efficiency

σ standard deviation

36

Subscripts & superscripts

symbol description

av average

b brine

crit critical point

D design conditions

el electricity

en energy

env environment

ex exergy

f ACC fan

fin ACC fin

g generator

inj injection state

M material

m motor

max maximum

min minimum

net net value

p pump

prod production state

shell heat exchanger shell

sup degree of superheating

t turbine

th thermal

tube heat exchanger tube

wf working fluid

wells well drillings

37

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:

ṁOwfṁDwf

=ρO6 c

O6

ρ6DcD6

with c =

√δp

δρ|s (A.1)

Herein is ρ 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 Figure 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]:

ηOt = ηDt sin

0.5π

(ṁOwfρ

D6

ṁDwfρO6

)0.1 (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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