PROCEEDINGS OF ECOS 2018 - THE 31TH INTERNATIONAL CONFERENCE ON

EFFICIENCY, COST, OPTIMIZATION, SIMULATION AND ENVIRONMENTAL IMPACT OF ENERGY SYSTEMS

JUNE 17-22, 2018, GUIMARÃES, PORTUGAL

Design-stage assumptions for good off-design performance of a binary geothermal power plant

Sarah Van Erdeweghea,e

, Johan Van Baelb,e

, Ben Laenenc and William D’haeseleer

d,e

a University of Leuven (KU Leuven), Applied Mechanics and Energy Conversion Section,

Celestijnenlaan 300 – Box 2421, B-3001 Leuven, Belgium, sarah.vanerdeweghe@kuleuven.be (CA) b Flemish Institute for Technological Research (VITO),

Boeretang 200, B-2400 Mol, Belgium, johan.vanbael@vito.be c Flemish Institute for Technological Research (VITO),

Boeretang 200, B-2400 Mol, Belgium, ben.laenen@vito.be d University of Leuven (KU Leuven), Applied Mechanics and Energy Conversion Section,

Celestijnenlaan 300 – Box 2421, B-3001 Leuven, Belgium, william.dhaeseleer@kuleuven.be e EnergyVille, Thor Park, Poort Genk 8310, B-3600 Genk, Belgium

Abstract:

In the literature, several studies exist on the design of a binary geothermal power plant. However, most of them do not (properly) account for its off-design operation. Even for a baseload geothermal power plant, frequent off-design operation occurs due to the changing environment conditions. Therefore, in this work, we propose a two-step optimization methodology which allows optimizing the design of an air-cooled binary geothermal power plant as well as the operating conditions during a typical year. In the first step, the design of the shell-and-tube heat exchangers and the air-cooled condenser are optimized towards maximal Net Present Value (NPV). The NPV is chosen as the optimization objective since it accounts for the size of the components, the economic parameters and the time value of money. However, assumptions have to be made regarding the economic parameters, such as the electricity price, and the environment conditions. In the second step, we optimize the operating conditions (temperatures and flow rates) of the binary power plant during a typical year towards maximal net electrical power output. Here, we take into account the Belgian hourly weather data and electricity prices for 2016. If we calculate the NPV in a post-processing step, accounting for the real hourly electricity prices and weather conditions, the value is different from the value in step 1. The real NPV is the highest for an ORC which was designed for the average electricity price (of 36.57 EUR2016/MWh). The electricity prices are not a priory known, but for a design assumption close to the average electricity price (30-60 EUR2016/MWh), the NPV is not more than 10% lower than the optimal value. The influence of the environment temperature assumption on the real NPV is small (

off-design ORC performance for source temperatures of 130-180°C and ambient conditions of 0-

30°C. They neither have included an economic analysis. Usman et al. [9] have compared the off-

design behavior of air-cooled and water-cooled ORCs based on monthly-averaged data for the

environment conditions. They have considered two sets of geothermal source conditions (set 1:

130°C and 9.16kg/s, set 2: 145°C and 6.57kg/s) and they did include an economic analysis;

however, they have used monthly-averaged data which are not that accurate.

Calise et al. [10] have made a combined design and off-design analysis. They have first optimized

the heat exchanger design (tube length, tube number and shell diameter) of a solar-fueled ORC

starting from an initial plant design, towards minimal yearly plant cost. Furthermore, they have

investigated the off-design performance of this power plant for source temperatures (thermal oil) of

155-185°C and flow rates of 18-24kg/s. They have assumed constant cooling water inlet

temperatures.

In this work we present a two-step optimization methodology which allows optimizing the (heat

exchanger and condenser) design of a binary geothermal plant, and the optimization of the net

electrical power output during off-design (real operation) as given in Table 1. There are some

differences with the mentioned literature. We focus on an air-cooled condenser since then no

cooling water is needed, and on shell-and-tube heat exchangers because of the high (thermal)

powers and operating pressures. For the off-design optimization we use hourly data for the

electricity price observed in a real market environment and for the environment conditions. From

our model results it follows that it is important to take the hourly variability into account, rather

than using daily- or monthly-averaged data. Besides, we investigate the thermoeconomics (net

present value – NPV) of the geothermal power plant since the decision to build a power plant is

generally based on economics, not on thermodynamics.

Table 1: Objective, variables and parameter values for steps 1 and 2 of the optimization framework.

objective variables note on some parameter values

Step 1: design NPV ORC design & op. cond. Tenv = Tenvav 2016, pel = pel

av 2016

Step 2: off-design electrical power operating conditions hourly data for Tenv, pel

Changing the parameter assumptions for 𝑇𝑒𝑛𝑣 and 𝑝𝑒𝑙 in the design stage (step 1) and making the design and off-design optimization calculations, we can get some insights in the influence of these

parameter assumptions on the real NPV of the project. So the feedback between steps 2 and 1

allows us to make proper assumptions for 𝑇𝑒𝑛𝑣 and 𝑝𝑒𝑙 in the design stage for a good performance and high revenues during the plant lifetime. Furthermore, a big advantage of our two-step

optimization methodology is that the same models for the design and off-design optimizations are

used, but another optimization objective is imposed (NPV versus net electrical power) and the

constraints are slightly different.

2. Model

2.1. ORC set-up

Fig. 1 shows a standard ORC, and the most important states are indicated. However also

recuperated ORCs have been considered; but only the standard ORC is shown for clarity reasons. In

a recuperated ORC, an extra heat exchanger – also called recuperator – is added to use the outlet

superheated vapor of the turbine (state 4) for heating the fluid at the pump outlet (state 2). We

consider 1 pass / 1 pass TEMA E shell&tube heat exchangers with a 30° tube layout and the brine

flowing through the tubes. The wall thickness is 2.5mm and the thermal conductivity is 18W/mK

[11]. Other design parameters will be optimized. Besides, we consider an A-frame air-cooled

condenser (ACC) with flat tubes of 19mm x 200mm and a fin thickness of 0.25mm [1], [12]. The

fin spacing Sfin, fin height Hfin and the number of tubes ntube will be optimized.

2.2. Thermoeconomic model

Detailed thermodynamic models are used for the

heat exchangers and the air-cooled condenser.

The shell-and-tube heat-exchangers geometry is

modeled following the TEMA standards [13]–

[15]. We consider an economizer, an evaporator

and a superheater, but assume the same geometry

for the three parts – the three parts together are

called EES in Fig. 1. This eases the heat-

exchanger fabrication and allows us to make off-

design calculations without big numerical issues.

The Bell-Delaware method is used for the shell

side heat transfer and pressure drop modeling

[14], [15]. The working fluid flows through the

shell. For the one phase ideal heat transfer and

pressure drop calculations, we use the correlations

of Shah et al. in [15] and for the two-phase heat

transfer modeling, the correlations as given by

Hewitt in [14]. The brine flows through the tubes

and the correlation of Bhatti and Shah [16] and

the correlation of Petukhov and Popov [17] are

used for the friction factor and heat transfer

coefficient calculations, respectively. The same

modeling approach for the heat exchangers is

followed as in Walraven et al. [11]. For more

info, the reader is referred to [11].

An A-frame air-cooled condenser is considered and the model equations from Yang [1], [12] are

implemented for the air-side heat transfer and friction factor calculations. The working fluid heat

transfer coefficient and friction factor in single phase (desuperheater) are calculated using the

calculations of Gnielinski [18] and Petukhov and Popov [17], respectively. For the two-phase heat

transfer in the condensing part, the CISE correlation [19], the Chisholm correlation [20] and the

correlation of Shah [21] are used for the void fraction, pressure drop and heat transfer coefficient

calculations. The same modeling approach for the air-cooled condenser is followed as in Walraven

et al. [1]. For more info, the reader is referred to [1], [12].

The turbine efficiency is calculated using the widely used correlation of Macchi and Perdichizzi

[22]. A curve-fit has been derived by Walraven et al. in [1]. The off-design turbine performance is

calculated using the Stodola Ellipse Law [23] and the according off-design efficiency is calculated

using the Keeley correlation [24].

All ORC component costs are calculated following the same procedure as in our previous ECOS

contribution [25]. The bare equipment cost for the heat exchangers is corrected for high

temperatures (𝑓𝑇 = 1.6), high pressures (𝑓𝑝 = 1.5) and the need for stainless steel (𝑓𝑀 = 1.6) [26]. An installation factor of 0.6 is considered based on [27]. The chemical engineering index is used to

convert the costs to 2016-values and a euro-to-dollar conversion of 1.2$/EUR is assumed.

2.3. Model parameters

The brine conditions are based on the expected conditions of the Balmatt geothermal site (Mol

Belgium) [28]. The brine temperature, pressure and flow rate are 𝑇𝑏 = 130°𝐶, 𝑝𝑏 = 40𝑏𝑎𝑟 and �̇�𝑏 = 150𝑘𝑔/𝑠. The average environment temperature and pressure for 2016 are 𝑇𝑒𝑛𝑣

𝑎𝑣 2016 =10.85°𝐶 and 𝑝𝑒𝑛𝑣

𝑎𝑣 2016 = 1.01678𝑏𝑎𝑟. Some assumptions are made for the component efficiencies of the pump, motor, generator and fan: 𝜂𝑝 = 80%, 𝜂𝑚 = 98%, 𝜂𝑔 = 98% and 𝜂𝑓 = 60% [1]. The

Fig. 1: Schematic presentation of the standard

ORC, with indication of the most important

states.

fan efficiency includes both the mechanical and electrical efficiencies. The economic parameter

assumptions for the discount rate, the yearly electricity-price increase, the plant lifetime and the

plant availability are 𝑑𝑟 = 5%, 𝑑𝑒𝑙 = 1.25%/year, 𝐿 = 30years and 𝑁 = 98%, respectively. The average electricity price for 2016 is 𝑝𝑒𝑙

𝑎𝑣 2016 = 36.57𝐸𝑈𝑅/𝑀𝑊ℎ. Furthermore, the well pumps power consumption is 500kW and the well drilling costs are 15MEUR [29].

2.4. Working fluid

Isobutane (R600a) is chosen as the working fluid because of its low environmental impact [30],

good ORC performance for the considered brine conditions and the low cost of hydrocarbons [31].

The thermodynamic and environmental properties of Isobutane are summarized in Table 2.

Table 2: Thermodynamic and environmental properties of Isobutane (R600a) [30].

MW, g/mole 𝑇𝑐𝑟𝑖𝑡, °𝐶 𝑝𝑐𝑟𝑖𝑡, 𝑀𝑃𝑎 ODP GWP Isobutane (R600a) 58.12 134.66 3.63 0 20

3. Optimization methodology We have developed a two-step optimization methodology. In the first step we calculate the optimal

design of the shell-and-tube heat exchangers and the air-cooled condenser for assumed parameter

values (also assuming a fixed electricity price and fixed environment conditions). In the second step

we calculate the performance of an installed ORC in off-design operation. In this work, we focus on

the ORC off-design operation caused by changing environment conditions and we study the effect

on the net present value (NPV). The real NPV value depends on the electrical power output – which

depends on the (changing) environment conditions – on the one hand and on the fluctuating

electricity prices throughout the year, on the other hand.

3.1. Design optimization

Fig. 2 shows the flowchart of the design-optimization methodology. The input parameters and the

working fluid have been discussed in Section 2.3 and 2.4.

Fig. 2: Flowchart of the design optimization program.

The NPV is taken as the optimization objective since it takes into account the performance, the

component costs, the economics and the time value of money:

NPV = −Iwells − IORC + ∑ [Ẇnetpel(1+del)

iN 8760

106 − 0.025IORC

(1+dr)i]Li=1 [EUR2016] (1)

The operation and maintenance costs are estimated as 2.5% of the total ORC cost [32]. The

variables of the optimization problem and their bounds are shown in Table 3. The ORC cost IORC

and the net electrical power output Ẇnet depend on the values of the variables. The well costs Iwells and the economic parameters do not depend on the variables. The bounds on the variables related to

heat exchangers (shell diameter Dshell, tube diameter Dtube, tube pitch ptube, baffle cut Bc and length

between baffles Lbc) are based on the TEMA standards [13], the variable bounds related to the ACC

are based on the validity of the correlations of Yang [12]. Tt, Tevap and Tcond are the turbine inlet

temperature, the evaporator temperature and the condenser temperature, respectively; vair is the air

flow velocity. The operational constraints are chosen to ensure a proper ORC operation ( minimum

ΔTpinch=1°C) and the structural bound for the length of the ACC LACC is based on the report of

Zammit [33]. No constraint has been considered for the brine injection temperature Tb,inj.

Table 3: Variable bounds and operational & structural constraints of the optimization problem.

variables of the optimization process additional constraints

variable lower bound upper bound constraint lower bound upper bound

Tcond, °C Tenv min (Tb, Tupper) Dtube/Dshell, - 0 0.1

Tevap, °C Tenv min (Tb, Tupper) Tt – Tevap, °C 1 Tupper – Tenv

Tt, °C Tenv + 10 min (Tcrit, Tupper) Tevap – Tcond, °C 10 2 (Tupper – Tenv)

ε, - 0.01 0.9 Tb,inj °C 25 Tb

�̇�𝑤𝑓/�̇�𝑏, - 0.01 5 ΔTpinch, °C 1 100

Dshell, m 0.3 2 LACC, m 0 15

Dtube, mm 5 50

ptube/Dtube, - 1.2 2.5

Bc/Dshell, - 0.25 0.45

Lbc, m 0.3 5

Sfin, mm 1.14 3.04

Hfin, mm 14.25 23.75

vair, m/s 1.5 10

ntube, - 500 10000

The direct result of the design optimization problem are the heat exchanger design, the ACC design

and the optimal operation conditions corresponding to the highest NPV for the given parameter

values. From these results, other performance indicators like the net electrical power output, the

brine injection temperature, the size of the heat exchangers, the turbine and self-consumption power

and the component costs can be calculated.

The models have been implemented in Python [34], using the CasADi [35] optimization framework

and the IpOpt [36] non-linear solver. Fluid properties are calculated from the REFPROP 8.0

database [37].

3.2. Power optimization during off-design operation

Whereas the goal in the previous section was the optimal ORC design for given brine, environment

and economic conditions, here the goal is to optimize the revenues from an installed ORC. Due to

the changing environment conditions, the net electrical power output is different from the nominal

power. Combined with the fluctuating electricity prices this leads to changing revenues during the

plant operation. For the installed ORC we want to maximize the revenues, hence we want to

maximize the NPV over the plant lifetime. Therefore, the operating conditions (Tt, Tevap, Tcond,

�̇�𝑤𝑓/�̇�𝑏 and vair) are changed to maximize the electrical power output. Since now the total cost IORC of the installed ORC is fixed, the optimization objective (1) reduces to maximizing the net

electrical power output Ẇnet: max 𝑁𝑃𝑉 → max Ẇnet (2) The same optimization model is used as for the design optimization problem, however the variables

are reduced to the operational variables only and some extra constraints are imposed. The design

and size of the heat exchangers and ACC are fixed, and the turbine operation has to satisfy

Stodola’s Ellipse law in off-design [23].

Table 4 summarizes the variables and constraints of the off-design optimization problem1. The

direct results are the optimized operational variables and the value of the net electrical power output

for given brine, environment and economic parameters. We focus on the effect of the environment

conditions and electricity prices so only these values might be different from the values which were

used in the design optimization procedure (Section 3.1).

Table 4: Variable bounds and constraints of the off-design optimization problem.

variables of the optimization process additional constraints

variable lower bound upper bound constraint lower bound upper bound

Tcond, °C Tenv min (Tb, Tupper) Tt – Tevap, °C 1 Tupper – Tenv

Tevap, °C Tenv min (Tb, Tupper) Tevap – Tcond, °C 10 2 (Tupper – Tenv)

Tt, °C Tenv + 10 min (Tcrit, Tupper) Tb,inj °C 25 Tb

�̇�𝑤𝑓/�̇�𝑏, - 0.01 5 ΔTpinch, °C 0.75 100

ε, - 0.01 0.9 ΔPStodola, Pa -5 5

vair, m/s 1.5 10 LACC, m LACC,design LACC,design

AHEx, m² AHEx,design AHEx,design

Arecup, m² Arecup,design Arecup,design

4. Results for standard ORC

4.1. ORC design

In this step, we report on the results for the optimization of the design of the heat exchanger and the

air-cooled condenser. We consider the parameter values of Section 2.3 and Isobutane as a working

fluid. If we follow the flowchart of Fig. 2, we get the following ORC design:

1. Evaporator design: Dshell = 0.70m, Dtube = 5.98mm, pt = 1.2Dtube, Bc = 0.25DShell and Lbc = 2.35m;

2. ACC design: Sfin = 3.04mm, Hfin = 23.75mm and ntube = 714.57;

3. Operating conditions: Tt = 101.54°C, Tevap = 100.54°C, Tcond = 41.75°C, �̇�𝑤𝑓 = 0.54�̇�𝑏 and vair = 7.33m/s.

The design value for the isentropic turbine efficiency is 88.94%. The exergetic plant efficiency is

19.85%, whereas the cycle efficiency is 11.14%2. These values are rather low because the incentive

for building a well-performing and expensive ORC is low at low electricity prices (𝑝𝑒𝑙 =36.57𝐸𝑈𝑅/𝑀𝑊ℎ was considered). The net electrical power output is 2.46MW and the brine injection temperature is 82.09°C. The optimal ΔTpinch = 2.11°C, the heat transfer area of the

evaporator is AHEx = 1192.64m² and the length of the condenser is LACC = 15m. The total ORC cost

is 8.16MEUR from which 70% is allocated to the condenser and the total project cost including

well costs is 23.16MEUR. The specific costs are 9416 EUR2016/kWinstalled including well costs and

3318EUR2016/kWinstalled without well costs. The prospected 𝑁𝑃𝑉 = −12.09MEUR for the assumed parameter values of 𝑇𝑒𝑛𝑣 = 𝑇𝑒𝑛𝑣

𝑎𝑣 2016 = 10.85°𝐶 and 𝑝𝑒𝑙 = 𝑝𝑒𝑙𝑎𝑣 2016 = 36.57𝐸𝑈𝑅/𝑀𝑊ℎ. Note that

the project is economically unfeasible without any kind of feed-in tariff.

4.2. Hourly electricity prices and environment conditions for 2016

The real NPV is different from the estimated one in the design step due to changing environment

conditions and fluctuating electricity prices throughout the year. Fig. 3 shows hourly data for the

environment temperature [38] and the electricity price [39]. We consider data for Mol (Belgium) in

1 The ΔTpinch lower bound has been changed

with respect to the design stage (Table 3) to allow proper convergence.

2 Exergetic plant efficiency: ratio of the net electrical power output (incl. well pumps power and self-consumption by

ORC pump and fan) and the exergy content of the brine at the production state.

Energetic cycle efficiency: ratio of the mechanical turbine power minus the mechanical ORC pump power, and the heat

addition in the evaporator.

2016. The average environment temperature is 𝑇𝑒𝑛𝑣𝑎𝑣 2016 = 10.85°𝐶 and the average wholesale

electricity price is 𝑝𝑒𝑙𝑎𝑣 2016 = 36.57𝐸𝑈𝑅/𝑀𝑊ℎ.

Fig. 3: Hourly profiles for the environment temperature [38] and the electricity price [39] for Mol

in 2016. The dashed dotted lines indicate the average values.

4.3. Off-design operation

During operation, the goal is to maximize the net electrical power output at every moment in time

for the designed ORC. In contrast to the design optimization step (first step of the optimization

procedure – Section 4.1) where we used a constant value for the electricity price and for the

environment conditions, in this section we take into account real hourly weather data and electricity

prices. However, we want to reduce the number of data points to speed up the optimization

procedure without losing too much accuracy. Since the net electrical power output of an installed

ORC depends on the environment temperature, our data reduction is based on the monotonic

duration curve of the environment temperature. The original monotonic temperature duration curve

is shown on the left-hand side of Fig. 4 and results from the hourly data which were given in Fig. 3.

We reduce the number of data points to 100 by considering the temperatures at [0.5, 1.5, …, 99.5%]

of the original temperature duration curve. Thereby we reduce the peaks – which has a very small

impact on the overall result – and we still have satisfying accuracy. The resulting environment

temperatures which we use in the simulations are given on the right-hand side of Fig. 4.

Fig. 4: Left: Original temperature duration curve of the environment temperature (red dashes:

spline approximation) with 8784 data points, derived from the hourly environment temperature

data given in Fig. 3. Right: used temperature duration curve consisting of 100 data points.

For the real environment temperature during all 8784 operating hours, we check what the closest

value of Tenv on the reduced temperature duration curve is at that time. We average the electricity

prices for moments with that environment temperature and hence become the averaged electricity

price corresponding to every data point. The averaged electricity prices are given on the left-hand

𝑇𝑒𝑛𝑣𝑚𝑎𝑥 = 33.19°𝐶

𝑇𝑒𝑛𝑣𝑚𝑖𝑛 = −8.13°𝐶

𝑇𝑒𝑛𝑣𝑚𝑎𝑥 = 33.19°𝐶

𝑇𝑒𝑛𝑣𝑚𝑖𝑛 = −8.13°𝐶

𝑇𝑒𝑛𝑣𝑚𝑎𝑥 = 29.07°𝐶

𝑇𝑒𝑛𝑣𝑚𝑖𝑛 = −4.28°𝐶

side of Fig. 5 and the price is generally higher at low values of the environment temperatures, which

can be expected. The net electrical power output only depends on the environment temperature, so

for every value of the reduced temperature duration curve (right-hand side of Fig. 4) we optimize

the operating conditions towards maximal net electrical power output. The resulting net electrical

power output for every data point is shown on the right-hand side of Fig. 5.

Fig. 5: Left: Average electricity price for all data points of the reduced temperature duration curve

(right-hand side of Fig. 4). Right: Optimized electrical power output for every data point on the

reduced temperature duration curve (right-hand side of Fig. 4).

The real NPV is calculated as follows:

NPV = −Iwells − IORC + ∑ [∑ [Ẇnet,jpel,j𝑠𝑗]

100𝑗=1 (1+del)

iN 8760

106 − 0.025IORC

(1+dr)i]Li=1 [EUR2016] (3)

sj is the share of the year that a certain value of the environment temperature, out of the 100

considered data points (right-hand side of Fig. 4), occurs. pel,j is the corresponding averaged

electricity price (left-hand side of Fig. 5). We assume the same profiles for the environment

conditions and for the electricity price in every year of the plant lifetime. The real 𝑁𝑃𝑉 =−11.74MEUR, which is different from the estimated NPV in the design stage. This is due to the changing net electrical power output corresponding to changing environment temperatures

(opposite correlation) on the one hand, and the fluctuating electricity prices on the other hand. The

off-design results are better than the design results. Note that we used here 30 times the same annual

profiles for the environment temperature and electricity price.

Note on the accuracy: The electrical power output Ẇnet depends on the environment temperature Tenv. By reducing the number of points to 100, we do not account for the highest and the lowest value of the environment temperature (see Fig. 4). Within one interval on the reduced temperature

duration curve (right-hand panel of Fig. 4), the difference in net electrical power output is smaller

than 1.5%, and the higher and lower values compensate each other. However, the largest errors

occur at the lowest and the highest values of 𝑇𝑒𝑛𝑣. Instead of the correct minimum and maximum values 𝑇𝑒𝑛𝑣

𝑚𝑖𝑛 = −8.13°𝐶 and 𝑇𝑒𝑛𝑣𝑚𝑎𝑥 = 33.19°𝐶, we use the values 𝑇𝑒𝑛𝑣

𝑚𝑖𝑛 = −4.28°𝐶 and 𝑇𝑒𝑛𝑣𝑚𝑎𝑥 =

29.07°𝐶. The corresponding electrical power outputs are Ẇnet = 3.53𝑀𝑊 instead of Ẇnet =3.81𝑀𝑊 for 𝑇𝑒𝑛𝑣

𝑚𝑖𝑛, and Ẇnet = 1.40𝑀𝑊 instead of Ẇnet = 1.19𝑀𝑊 for 𝑇𝑒𝑛𝑣𝑚𝑎𝑥. So, the real electrical

power output at the lowest environment temperature is ∆Ẇnet = 3.81 − 3.53 = 0.28𝑀𝑊 (or 7.93%) higher than the value we consider in our simulations, and for the highest environmental

temperature the real electrical power output is ∆Ẇnet = 1.40 − 1.19 = 0.21𝑀𝑊 (or 15%) lower than the value we consider. 𝑇𝑒𝑛𝑣

𝑚𝑖𝑛 = −8.13°𝐶 occurs during an hour with a corresponding electricity price of 𝑝𝑒𝑙 = 65.61𝐸𝑈𝑅/𝑀𝑊ℎ and the corresponding electricity price at 𝑇𝑒𝑛𝑣

𝑚𝑎𝑥 = 33.19°𝐶 is 𝑝𝑒𝑙 = 34.55𝐸𝑈𝑅/𝑀𝑊ℎ (see Fig. 3). The real income is ∆Ẇnet𝑝𝑒𝑙=18.37EUR higher for the hour with the lowest environment temperature and 7.26EUR lower for the hour with the highest

environment temperature than what we consider in our simulations (by considering only the values

of the right-hand side panel of Fig. 4). So, our results are a bit conservative.

5. Discussion: Parameter assumptions in the design stage

5.1. Electricity price assumption The revenues of the power plant depend on the electricity prices. For higher electricity prices, a

better and more expensive ORC can be installed which leads to a higher net electrical power output

and a higher NPV. This is illustrated in Fig. 6. The figure on the left-hand side corresponds to the

design stage where a certain constant value for the electricity price is assumed. The ORC is

designed for this electricity price assumption. If the electricity price would be constant throughout

the year, the NPV of the left-hand side figure would be the real NPV. We can see that the

geothermal power plant becomes feasible (NVP=0) for electricity prices around 65EUR/MWh.

However, the real electricity prices were given in Fig. 3.

The right-hand side figure shows the real NPV, accounting for off-design, for an installed ORC

with the assumed constant electricity price in the design stage on the x-axis. The highest NPV is

reached for an ORC design based on the assumption of 𝑝𝑒𝑙 = 𝑝𝑒𝑙𝑎𝑣 2016 = 36.57𝐸𝑈𝑅/𝑀𝑊ℎ, the

average price for electricity over the year. However, in the design stage the average electricity price

is not known. But we see that in the close environment around 𝑝𝑒𝑙𝑎𝑣 2016 – say for 𝑝𝑒𝑙 = 30 −

60𝐸𝑈𝑅/𝑀𝑊ℎ (indicated by the dotted box) – the real NPV is almost equally high. However, for an electricity price assumption which was too high/too low, the real NPV might be significantly lower.

Furthermore, from the right-hand side figure of Fig. 6 follows that the NPV for the recuperated

ORC (orange line) and the standard ORC (blue line) are almost equal: 𝑁𝑃𝑉𝑟𝑒𝑐𝑢𝑝𝑒𝑟𝑎𝑡𝑜𝑟 =−11.52 𝑀𝐸𝑈𝑅 and 𝑁𝑃𝑉𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑 = −11.74𝑀𝐸𝑈𝑅. In general, a cheaper cooling system can be installed in the recuperated cycle due to the internal heat recuperation. The total ORC cost is

slightly higher for the recuperated ORC – partly due to the extra heat exchanger – but also the net

electrical power output is higher than for the standard ORC.

Fig. 6: Left: NPV if 𝑝𝑒𝑙would be constant throughout the year (assumption in the design stage). The blue and orange lines indicate the standard and recuperated ORC, respectively, the dashed green

line is the difference in NPV between the recuperated and the standard ORC and the dashed-dotted

black line is the line for ΔNPV=0. Right: Real NPV accounting for off-design (Fig. 3) as a function

of the electricity price assumed in the design stage of the ORC. 𝑇𝑒𝑛𝑣 = 𝑇𝑒𝑛𝑣𝑎𝑣 2016 = 10.85°𝐶.

5.2. Environment temperature assumption

The ORC revenues also depend on the environment temperature. For a higher environment

temperature, the net electrical power output is lower, which is shown on the left-hand side of Fig. 7.

The left-hand side panel shows the NPV for various environment temperatures according to

different design points, but for each design assuming that the real environment temperature remains

constant over the year.

The right-hand side panel takes off-design into account and shows the real NPV, accounting for the

changing environment conditions. The NPV is presented as a function of the environment

temperature for which the ORC was designed. The real NPV is maximal for a temperature

assumption in the design stage of 𝑇𝑒𝑛𝑣 = 14°𝐶 and is 𝑁𝑃𝑉𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑 = −11.70𝑀𝐸𝑈𝑅 for the

standard cycle and 𝑁𝑃𝑉𝑟𝑒𝑐𝑢𝑝𝑒𝑟𝑎𝑡𝑜𝑟 = −11.47𝑀𝐸𝑈𝑅 for the recuperated ORC. We see that the optimal design temperature 𝑇𝑒𝑛𝑣 = 14°𝐶 is different from the average environment temperature 𝑇𝑒𝑛𝑣

𝑎𝑣 2016 = 10.85°𝐶. If we design the ORC for a higher environment temperature, we benefit from the higher electrical power output which can be reached at moments of lower environment

temperatures. However, the real NPV only weakly depends on the environment temperature

assumption in the design stage.

Fig. 7: Left: NPV if 𝑇𝑒𝑛𝑣 would be constant throughout the year (assumption in the design stage). Right: Real NPV accounting for off-design (Fig. 3) as a function of the environment temperature

assumed in the design stage of the ORC. 𝑝𝑒𝑙 = 𝑝𝑒𝑙𝑎𝑣 2016 = 36.57𝐸𝑈𝑅/𝑀𝑊ℎ. The blue and orange

lines indicate the standard and recuperated ORC, respectively, the dashed green line is the

difference in NPV between the recuperated and the standard ORC.

6. Conclusions In this work, we have presented a two-step optimization methodology for calculating the optimal

(heat exchanger and air-cooled condenser) design of a binary geothermal ORC, on the one hand,

and for calculating the optimal operating conditions to reach maximal electrical power output of an

installed ORC during off-design, on the other hand. We use the same models for the design and off-

design optimization calculations. However, a different objective (NPV versus net electrical power)

is imposed and the constraints are slightly different. We have calculated the optimal design for a

binary geothermal plant based on the geological conditions of the Balmatt site (Mol, Belgium). In a

second step we have analyzed the performance of the designed power plant during real operation.

Therefore, we consider hourly data for the environment conditions and electricity prices for Mol

(Belgium) in 2016. In real operation, the plant mostly operates in off-design conditions due to

changing environment temperatures and the electrical power output is maximized at every moment.

From the results follows that the electricity price assumption in the ORC design stage might have a

big impact on the real revenues of the power plant. However, for an electricity price assumption in

the design stage of the project close enough to the (future) real average price, the real NPV will be

close to its maximum possible value. The environment temperature assumption in the design stage

of the ORC has a small impact on the real operation and revenues of the ORC. In general, the

recuperated ORC has slightly higher NPV than the basic cycle, but the difference is small (~2%).

Acknowledgments This project receives the support of the European Union, the European Regional Development

Fund ERDF, Flanders Innovation & Entrepreneurship and the Province of Limburg.

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