Off-design performance analysis of a novel hybrid binary geothermal-biomass power plant in extreme environmental conditions

Energy Conversion and Management 195 (2019) 210–225

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Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman

Off-design performance analysis of a novel hybrid binary geothermalbiomass power plant in extreme environmental conditions

T

Stefano Briolaa,b, , Roberto Gabbriellic, Aldo Bischib ⁎

a

German Engineering Research and Development Center LSTME Busan Branch, Affiliate Institute to FA Universität Erlangen, 1276 Jisa-Dong, Gangseo-Gu, 46742 Busan, Republic of Korea b Center for Energy Systems – Skolkovo Institute of Science and Technology, Nobel Street 3, 143026 Moscow, Russia c Department of Civil and Industrial Engineering (DICI), University of Pisa, Largo L. Lazzarino, 56126 Pisa, Italy

ARTICLE INFO

ABSTRACT

Keywords: Off-design performance analysis Hybrid geothermal biomass plant Extreme environmental conditions Organic Rankine cycle Aspen simulation model

A novel configuration of a hybrid binary geothermal biomass power plant is proposed that generates electricity through the Organic Rankine Cycle (ORC), which receives the thermal power provided by a biomass heat source through intermediate geothermal fluid. The plants are located in regions with extreme environmental conditions where water is not available, making the use of air-cooled condensers in the ORC necessary, and the seasonal variations of the ambient air temperature are remarkable. As a further novel aspect, the modification of the biomass mass flow rate is used to overcome the simultaneous harmful effects of a considerable reduction in the geothermal fluid temperature during the operative life of the plant and the more significant seasonal change of the ambient air temperature. Our original approach involves developing a simulation model of the proposed plant using the commercial software Aspen® to determine the energy performance in off-design conditions, i.e., in the presence of the simultaneous changes of the biomass flow rate, ambient air temperature and geothermal fluid temperature. The biomass flow rate is controlled to maximize the net electric power or net thermodynamic efficiency of the plant with varying ambient air and geothermal fluid temperatures. In comparison to the first operating mode, the second enables a saving of the biomass used annually in the range of 28.3%–42.6%, corresponding to the maximum and minimum geothermal fluid temperature, respectively, with the resulting detrimental effect on the yearly produced electric energy in the range of 9%–23.6%.

1. Introduction Geothermal energy originates from the Earth’s interior, and unlike other renewable sources (e.g., solar and wind energy) is not intermittent. It is widely applied in several energy conversion processes [1]. The performance of traditional geothermal plants hybrid systems can be improved through the effective integration and synergy of geothermal energy and different fossil fuels and/or other renewable sources [2], and various models have been proposed and analysed. Biomass has many widely distributed features, and can be effectively integrated with the geothermal source and is thus an attractive solution [3]. The integration of a biomass heat source in geothermal power plants can provide an effective strategy for managing two significant harmful effects. First, the temperature degradation of the geothermal source is due to the reinjection of geothermal fluid, which is particularly significant for applications in which its temperature is not high, i.e., lower than

200 °C. The second effect is the high yearly variations in the ambient air temperature, which are particularly critical in extreme environmental locations, such as arctic zones, where water can be scarce and thus the atmospheric air must be used as the heat sink. 1.1. Literature review Few original contributions in the scientific literature consider hybrid geothermal-biomass (HGB) plants, which integrate the geothermal source solely with biomass. However, HGB plants which have purposes other than solely generating electricity are:

• cogeneration: a ground source heat pump integrated with biomass

partial gasification [4], or a low-temperature geothermal source integrated with Organic Rankine Cycle (ORC) and biomass gasification [5];

⁎ Corresponding author at: German Engineering Research and Development Center LSTME Busan Branch, Affiliate Institute to FA Universität Erlangen, 1276 JisaDong, Gangseo-Gu, 46742 Busan, Republic of Korea. E-mail address: [email protected] (S. Briola).

https://doi.org/10.1016/j.enconman.2019.05.008 Received 8 December 2018; Received in revised form 2 April 2019; Accepted 2 May 2019 Available online 09 May 2019 0196-8904/ © 2019 Elsevier Ltd. All rights reserved.

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Nomenclature cp ΔTF-A h HHV I LHV M MW P R s T W x y

FAC FAP GF GFHS GFP GST gross HGB HP HS i in j k l LP m min max n net off OFP ORC OT out PEE ph PH Rr

heat capacity [J/(kg K)] condenser temperature difference (outlet working fluid, inlet air) [°C] specific enthalpy [J/kg] higher heating value of biomass [MJ/kg] exergy loss [kW] lower heating value of biomass [MJ/kg] mass flow rate [kg/s] molecular weight [kg/kmol] pressure [bar] universal gas constant [J/(mol K)] specific entropy [J/(kg K)] temperature [°C] thermal or electric power in i-th operative unit [MW] quality [-] mole fraction [-]

Greek symbols ε ζ η ρ Y Φ

specific exergy [kJ/kg] exergy loss ratio [%] efficiency [%] density [kg/m3] Stodola’s constant of turbine [m−2 s−2 K−1] mass flow coefficient (temperature form) at design point [m s K0.5]

Acronyms, subscripts 0 A AC AP BIO ch CON dp ECO EDR EP EVA EW

reference state air air-cooled condenser air preheater biomass chemical condenser design point condition economizer Aspen Exchanger Design & Rating extraction pump evaporator extraction well

Rc Rcc RH RW SH ST t TR UB VG

• a district energy system and hydrogen production facility using a hybrid lignite-geothermal plant [6]; • production of electric and cooling power, hot water, liquefied gas

fans of air-cooled condenser fan of air preheater geothermal fluid geothermal fluid heating subsystem geothermal fluid pump geothermal steam turbine gross quantity hybrid geothermal-biomass power plant high-pressure heat source or heat sink i-th unit operation inlet section j-th inlet section k-th outlet section l-th heat source or heat sink low-pressure mechanical power minimum value maximum value n-th chemical species net quantity off-design condition organic fluid pump organic Rankine cycle organic turbine outlet section produced electric energy [MWh] physical preheater intermediate part of the reactor (heat exchange to geofluid by radiation) rear part of the reactor (heat exchange to geofluid by convection) front part of the reactor (combustion chamber) reheater reinjection well superheater steam turbine thermal power thermal recuperator used biomass [t] vapour generator

and low-pressure (LP) SH, whereas the geothermal heat source is used for LP-PH and LP-EVA [9];

and heated drying air using geothermal power plant integrated with a biomass combustion cycle; a Linde Hampson liquefaction cycle, an absorption chiller, a water heating and air-dryer systems [7];

2) Geothermal fluid: a) A geothermal dry steam power plant, where the flue gas from the biomass combustion transfers thermal power to the geothermal steam in SH upstream of the geothermal steam turbine [10]. A HGB power plant was developed in 2015 in Larderello (Italy), using geothermal dry steam [1]; b) A variant of the previous configuration 2a), where a geothermal single flash power plant is used in lieu of a geothermal dry steam power plant [11]; c) A geothermal double flash power plant, where the biomass heat source is used both in SH and in the reheater (RH) [9];

The current proposed configurations of HGB plants used solely for the generation of electricity can be classified according to the typologies of the working fluid used in the production of electric power, as follows: 1) Water: a) A geothermal binary steam Rankine power plant, where the biomass heat source is used in the preheater (PH), evaporator (EVA) and superheater (SH), whereas the geothermal heat source his used in the economizer (ECO) [8]; b) A dual-pressure steam Rankine power plant, where the biomass heat source is used in the high-pressure (HP) circuit (from ECO to SH)

3) Water and geothermal fluid: A geothermal single flash power plant integrated with a dual211

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pressure steam Rankine power plant, where the former transfers thermal power to the latter for the thermal degassing process, located between the low-pressure and high-pressure water pumps. The biomass heat source is used in the SH of the geothermal single flash power plant and also in the HP circuit (from ECO to SH) and LP-RH of the dual-pressure steam Rankine power plant [9].

condenser is used in the bottom ORCs. The energy performance of the fifth and sixth configurations are evaluated at the design point condition. The above classification of the configurations of HGB plants used solely for the generation of electricity is summarized in Table 1. 1.2. Novelty of the article

4) Water and organic fluid:

The following shortcomings have been identified in the HGB power plants described above:

A top steam Rankine power plant integrated with a bottom geothermal binary ORC (the organic working fluid is R365mfc), where biomass is used in the former and geothermal heat sources in the latter. In particular, the geothermal heat exchanger in the bottom geothermal binary ORC is located upstream of the thermal cascade coming from the top steam Rankine power plant [8]. This type of configuration of a HGB power plant was installed in 1989 in Lassen County, USA. A thermal recuperator was used in the bottom geothermal binary ORC, where the organic fluid in the hot side (located downstream of the turbine) transfers thermal power to the same organic fluid in the cold side (located upstream of the geothermal heat exchanger) [12];

1) the water and geothermal fluids used as working fluids in the production of electric power in configurations 1–5 have technical and operational drawbacks. Steam turbines require accurate water treatment and control processes, deareators, and steam networks on site, and they have high maintenance and personnel costs [16]. The geothermal steam turbines require adequate design and materials, and their operational costs are high [17]. The thermal oils, which are used as intermediate thermal fluids between the biomass heat source and the ORC in the sixth configuration, have health, safety and environmental effects, and they also degrade with time [18]; 2) in the fifth and sixth configurations (i.e., air-cooled HGB power plants), the biomass is not used in off-design conditions, to counteract the simultaneous harmful effects due to the high reduction of the geothermal source temperature during the operative life of the plant, and the high annual changes of the ambient air temperature. The energy performance of air-cooled geothermal power plants significantly depends on these two uncontrollable parameters, particularly the high fluctuations in the ambient air temperature, which occur in extreme environmental conditions [19]. Thus, an analysis of off-design conditions is fundamental for air-cooled HGB power plants placed in extreme environments, because their operative conditions for most of their life are very different from those at the design point.

5) Geothermal and organic fluids: A top geothermal single flash power plant integrated with several bottom ORCs (the organic working fluid is normal pentane), where the former transfers thermal power in PH and EVA to the latter through the geothermal liquid and geothermal superheated vapor at the outlets of the flash and of the geothermal steam turbine, respectively. The biomass energy is used in SH of the geothermal single flash power plant [9]; 6) Organic fluid: A variant of the previous configuration 4), where the top steam Rankine power plant is substituted by a top ORC power plant. This is fed by the biomass heat source through an intermediate thermal oil. The top ORC power plant contains the thermal recuperator, where the organic fluid in the hot side (located downstream of the turbine) transfers thermal power to the same organic fluid in the cold side (located downstream of the pump). The organic working fluids are MDM and HFC-245fa in the top and bottom ORC, respectively [13]. The thermal oil is used as an intermediate thermal fluid between the biomass heat source and the organic fluid to avoid local overheating of the latter and the resulting thermal degradation [14,15].

The present article proposes a novel air-cooled HGB power plant suitable for extreme environmental conditions, which can overcome the shortcomings described above. It has the following characteristics: 1) the electricity generation takes place through the ORC turbine, avoiding the drawbacks of steam turbines, geothermal steam turbines and thermal oils. In particular, the ORC turbine receives thermal power provided by the biomass heat source through the intermediate geothermal fluid; 2) the control of the biomass mass flow rate is realized to maximize the plant energy performances at off-design conditions in the presence of the high fluctuations in the atmospheric air temperature and the large reduction of the geothermal source temperature during the entire operative plant life. In particular, the optimum values of the biomass mass flow rate are determined through an extensive

Of the six categories of configurations of the HGB power plants described above, only the fifth and sixth satisfy their cooling demands through atmospheric air in lieu of water, which is not available in extreme environmental conditions. In both configurations, an air-cooled Table 1 HGB power plant classification. Layout

Process

Heat sources

Cooling

1a [8]

Geothermal binary steam Rankine

Water

1b [9]

Dual-pressure steam Rankine

2a [10] 2b [11] 2c [9] 3 [9]

Geothermal dry steam Geothermal single flash Geothermal double flash Geothermal single flash + dual-pressure steam Rankine

4 [8] 5 [9] 6 [13]

Top steam Rankine + bottom geothermal binary ORC Top geothermal single flash + bottom ORCs Top ORC + bottom geothermal binary ORC

GF: in ECO BIO: in PH ÷ SH GF: in LP-PH and LP-EVA BIO: in HP-ECO ÷ HP-SH and LP-SH BIO: in SH BIO: in SH BIO: SH, RH GEO: in degassing of Rankine BIO: in SH of geothermal single flash, in HP-ECO ÷ HP-SH and LP-RH of Rankine GEO: in ORC upstream heat from Rankine BIO: in Rankine GEO: in PH and EVA of ORCs BIO: in SH of geothermal single flash GEO: in bottom ORC BIO: in top ORC

212

Water Water Water Water Water Water Air Air

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sensitivity analysis of off-design conditions, considering the simultaneous variations of the geothermal source temperature, air temperature and biomass mass flow rate. Of these three process parameters, only the biomass flow rate can be controlled by the enduser of the HGB power plant.

working fluid are chosen to maximize the performances of the exploitation of the geothermal source considered in the present analysis [23]. The R134a shows thermal stability up to 368 °C [24,25], allowing thermal exchange with the geothermal fluid in VG to occur without thermal degradation.

The configuration of the proposed HGB power plant is described in Section 2, and its simulation model is then explained in Section 3. The investigation of the design point conditions is presented in Section 4. In Sections 5 and 6, the main assumptions and results related to the sensitivity analysis at the off-design conditions are given, and conclusions and future remarks are provided in Section 7.

3. Aspen simulation model description We developed a simulation model of the proposed power plant (Fig. 1) using the commercial software Aspen Plus and Aspen Exchanger Design & Rating (EDR) V9® [26]. The detailed geometry of the abovementioned five heat exchangers (i.e. AP, Rc, VG, TR and AC) is determined to accurately simulate the heat exchange with varying operative conditions. The main assumptions, both in the investigation of the design point conditions (Section 4) and in the sensitivity analysis of the off-design conditions (Section 5), are listed below:

2. Configuration of the proposed hybrid binary geothermal biomass power plant Fig. 1 is the process flow diagram of the proposed hybrid binary geothermal biomass power plant. The atmospheric air mass flow rate (stream 1) is first preheated in a heat exchanger (AP) by the exhaust gas upstream of the stack (stream 5). The fan of the preheater (FAP) increases the pressure of the atmospheric air at the inlet of AP (stream 2) so that the pressure of the exhaust gas at the stack (stream 6) is equal to the atmospheric pressure. Then, the preheated air (stream 3) enters the reactor where the combustion of the biomass (stream 4) takes place in the front part (Rcc). The flue gas transfers thermal power to the geothermal fluid (stream 9), from the extraction well (EW) through the extraction pump (EP), by radiation in the intermediate part of the reactor (Rr) and by convection in the rear part of the reactor (Rc). The geothermal fluid is transported by EP from the bottom (stream 7) to the head of the geothermal well (stream 8) at the same pressure as the geothermal reservoir. The geothermal fluid is then pressurized in the geothermal fluid pump (GFP) so that it remains in a saturated liquid phase at the outlet of Rc (stream 10), thus avoiding its phase change. This implies an increase in the geothermal fluid temperature at the outlet of Rc with a resulting increase of the temperature of the organic working fluid at the outlet of the vapor generator (VG) of the ORC (stream 13), where the organic working fluid is heated by the geothermal fluid. The latter is the intermediate thermal fluid between the biomass heat source and the ORC and is reinjected at the outlet of VG (stream 11) into the reinjection well (RW). The reinjection process takes place without a reinjection pump, due to the pressure of the geothermal fluid at the outlet of VG, which is slightly lower than that at the outlet of GFP. The ORC is built up in sequence (from stream 12 to stream 17) by the VG, the organic turbine (OT), the thermal recuperator (TR) the thermal recuperator (TR), the air-cooled condenser (AC) and finally the organic fluid pump (OFP). In AC, the fans (FAC) move the atmospheric air as a cooling medium (from stream 18 to stream 20). The working fluid at the outlet of OT flows through the hot side of TR (inlet stream 14, outlet stream 15), where it transfers thermal power to the same working fluid circulating in the cold side of TR (inlet stream 17, outlet stream 12). The plant is assumed to be located in a region with extreme environmental conditions, specifically Mutnovsky (Kamchatka, Russia). Here, the geothermal fluid at the outlet of the EW has a maximum temperature of TGF,max = 160 °C at the starting of the well exploitation, and a pressure of PGF = 20 bar and a mass flow rate MGF = 15 kg/s, both of which are constant throughout the plant’s operative life [20]. Due to the reinjection, the geothermal fluid temperature decreases by 1 °C per year with a resulting minimum temperature of the geothermal fluid TGF,min = 130 °C at the end of the plant’s operative life (30 years) [19]. In Mutnovsky, very significant seasonal fluctuations of the ambient air temperature (TA) take place. Specifically, TA is in the range TA,max = 30 °C (summer) and TA,min = −30 °C (winter) [21]. In the Mutnovsky area the AC is necessary for satisfying the cooling demand of power plants due to the unavailability of water [22]. The supercritical configuration of the ORC and R134a as the organic

1) the atmospheric air is composed of 0.767 nitrogen and 0.233 oxygen by mass. The air mass flow rate at the inlet of AP is calculated so that the flue gas produced by the biomass combustion contains 6% oxygen by mass, which is the minimum value commonly used in the industry to ensure complete biomass combustion [27]; 2) the biomass is untreated wood pine, which is a widespread species in Kamchatka [28], and whose properties are shown in Table 2 (as received) [29]; 3) the biomass combustion process is simulated through a series of two reactors available in the Aspen Plus library: a yield-reactor model (“RYield” block) and a Gibbs-reactor model (“RGibbs” block). The RYield block is used to describe endothermic reactions relative to the biomass devolatilization process with the production of the following chemical species: H2, N2, H2O, Cl2, S, CO, CO2, CH4, char and ash. The RGibbs block simulates the subsequent oxidative exothermic reactions between O2 and the above chemical species [30]; 4) Rr is modelled by the “HeatX” block. The outlet temperature of the flue gas is 840 °C, below which the radiation can be considered negligible [31]; 5) Rc, VG, TR and AP are shell and tube heat exchangers. The BEM configuration is used for the first three heat exchangers and the BXM for the final one, and both configurations are according to the standards of the Tubular Exchangers Manufacturers Association [32]. In each, the hot fluid circulates in the tube side, which has a plain surface. The AC is modelled as a forced air-cooled condenser, where the hot fluid circulates inside the tubes, which are externally finned. Each of these five heat exchangers is modelled in Aspen

Fig. 1. Proposed hybrid binary geothermal biomass power plant. 213

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where hGF,VG,in and hGF,VG,out [J/kg] are the specific enthalpy of the geothermal fluid at the inlet and at the outlet of VG, respectively. In particular, hGF,VG,in coincides with hGF,Rc,out. The gross and net thermodynamic efficiencies of the proposed HGB power plant are defined as:

Table 2 Biomass (untreated wood pine as received) properties. Proximate analysis (dry basis)

Ultimate analysis (dry basis)

LHVBIO HHVBIO

6)

7)

8) 9)

10) 11)

12)

Moisture [%]

5.82

Fixed carbon [%] Volatile matter [%] Ash [%] Ash [%] C [%] H [%] N [%] Cl [%] S [%] O [%] [MJ/kg] [MJ/kg]

14.58 85.35 0.07 0.07 52.89 6.29 0.18 0.03 0.02 40.52 17.95 19.38

HGB, gross HGB, net

The Aspen Plus and EDR V9® simulation models of the power plant previously described (Section 3) are used for the investigation at the design point conditions to define the geometry of the heat exchangers and the main features of the organic turbine. Thus, using these features, the subsequent evaluation of the energy performance in the off-design conditions is carried out. The additional assumptions associated with the design point conditions are: 1) TA and TGF are equal to the minimum (−30 °C) and maximum (160 °C) allowable values for the location under consideration, respectively, and MBIO is 0.5 kg/s, to ensure a high value of ηHGB,net; 2) the pressure at the outlet of OFP is 70 bar, which is suitable for high energy performances of supercritical binary ORC power plants [23]; 3) for each Rc, VG and TR, the temperature difference between the hot fluid at the outlet and cold fluid at the inlet is 10 °C; 4) for AP, the exhaust gas temperature at the outlet is 120 °C, which is common in industrial practice, as it avoids water condensation on the tubes walls [36]; 5) the air mass flow of AC is calculated so that the air temperature difference between the inlet and outlet is 5 °C, allowing the organic working fluid to be obtained at the outlet in the saturated liquid phase and reducing the electric power absorbed by FAC. This is obtained by changing the cooling air mass flow by controlling the fan speed via the inverter; 6) the isentropic efficiency of OT is 0.85. In Table 3, the values of the mass flow rate and the inlet and outlet thermodynamic states for hot and cold fluids in each sized heat exchanger are reported. In Tables 4 and 5, the values of the main quantities for each sized shell and tube and air-cooled heat exchanger are reported, respectively. The detailed geometry of the heat exchangers used is in accordance with common industrial practices. The fluid velocities imply low pressure drops [37] and the overall heat transfer coefficients are consistent with the typical values reported in the literature for similar applications [38]. The absolute values of the thermal and electric powers for each operative unit at design point conditions are reported in Table 6. The

The gross and net produced electric power of the proposed HGB power plant are defined as:

WEP

Wnet = Wgross

WFAC

WGFP

WOFP

(1) (2)

WFAP

The thermodynamic efficiency of the geothermal fluid heating subsystem (ηGFHS) is defined as the overall enthalpy change of the geothermal fluid between the extraction well and the outlet of the reactor over the thermal power produced by the biomass combustion: GFHS

= MGF (hGF , Rc, out

hGF , EW )/(MBIO LHVBIO )

Table 3 Process data for each sized heat exchanger.

(3)

AP

where hGF,EW and hGF,Rc,out [J/kg] are the specific enthalpy of the geothermal fluid in the extraction well and at the outlet of Rc (i.e., at the inlet of VG), respectively. The gross and net thermodynamic efficiencies of the ORC are defined as: ORC , gross ORC , net

Wgross/[MGF (hGF , VG, in Wnet /[MGF (hGF , VG, in

hGF , VG, out )] hGF , VG, out )]

(7)

GFHS ORC , net

4. Investigation at design point conditions

Plus using the “HeatX” block, which is linked to the EDR simulation model; the R134a mass flow rate is calculated so that the geothermal fluid temperature in the reinjection well is 70 °C. This value is higher than the typical crystallization temperature of the geothermal brines to avoid the precipitation of salts such as Silica (SiO2) and Calcium Carbonate (CaCO3) [19,33]; the pressure at the outlet of OT is calculated so that the pressure of R134a at the outlet of AC is that of the wet saturated vapor corresponding to the condensation temperature. This is 10 °C (ΔTF-A) higher than that of the atmospheric air at the inlet of AC. The value of ΔTF-A is a compromise, because in correspondence to a specified atmospheric air temperature at the inlet, the electric power produced by OT increases with the decrease of ΔTF-A, whereas the electric power absorbed by FAC decreases with the growth of ΔTF-A; the geothermal fluid is modeled as water, thus neglecting any possible effects of salts and noncondensable gases that may be present in the fluid [34,35]; the Equation of State in each operative unit is Peng-Robinson, except for the operative units involving the geothermal fluid (i.e. GFP, the cold sides of Rr and Rc and the hot side of VG) where the steam tables STEAMNBS Equation of State is used; the efficiencies of EP, GFP and OFP are constantly equal to 0.85, and those of their electric motors are equal to 0.95; the electric consumption of EP, which is constant and equal to 80 kW, is associated with the Mutnovsky geothermal well depth, which is equal to 500 m, and the mass flow rate described above [20]; the mechanical efficiency of OT is 0.95.

Wgross = WOT

(6)

GFHS ORC , gross

Rc VG TR

(4)

AC

(5) 214

side

M [kg/s]

Pin [bar]

Tin [°C]

xin [-]

Pout [bar]

Tout [°C]

xout [-]

Hot Cold Hot Cold Hot Cold Hot Cold Hot Cold

4.8 4.3 4.8 15 15 40.7 40.7 40.7 40.7 1803.6

1.03 1.05 1.04 57.41 57.40 69.94 1.36 70 1.34 1.01

233.3 −30 840 223.3 271 60 111.6 −17.1 −7.1 −30

1 1 1 0 0 0 1 0 1 1

1.01 1.04 1.03 57.40 57.37 69.88 1.34 69.94 1.32 1.01

120 105.2 233.3 271 70 245.2 −7.1 60 −20 −25

1 1 1 0 0 1 1 0 0 1

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Table 4 Main quantities for each sized shell and tube heat exchanger.

Number of units (series, parallel) [-] Number of tubes [-] Number of tube passes [-] Tube length [mm] Tube external diameter [mm] Number of single segmental baffles [-] Shell external diameter [mm] Overall heat transfer area [m2] Overall heat transfer coefficient [W m−2 K−1] Effective mean temperature difference [°C]

Table 7 Gross and net thermodynamic efficiencies [%] at design point conditions.

AP

Rc

VG

TR

1, 1 852 1 1620 19.1 0 924 77.3 60 126.7

1, 1 2516 1 3809 19.1 4 1760 515.9 46.1 145.1

2, 1 5748 1 4755 19.1 10 2094 3042 194.1 22.7

2, 1 5821 1 3840 19.1 4 2090 2487.8 66.7 26.1

ηGFHS [%]

ηORC,gross [%]

ηORC,net [%]

ηHGB,gross [%]

ηHGB,net [%]

85.76

28.70

26.76

24.61

22.95

Table 5 Main quantities for the sized air-cooled heat exchanger.

6 2 368 1 9380 25.4 28,508 44 7.3

Y=

0.1]

(11)

6.1.1. Geothermal fluid at the inlet of the vapour generator In Figs. 2 and 3, the pressure (PGF,VG,in) and temperature (TGF,VG,in) of the geothermal fluid at the inlet of the vapour generator as functions of MBIO, TGF and TA are depicted, respectively:

• if T •

1) TA and TGF change according to the ranges related to the location under consideration, i.e., TA = −30 ÷ 30 °C in steps of 20 °C and TGF = 130 ÷ 160 °C in steps of 10 °C. MBIO also changes in the range 0 ÷ 1 kg/s with a step of 0.1 kg/s; 2) OT operates in a sliding pressure mode with a fixed nozzle area [33]. Thus, the pressure at the outlet of OFP is calculated so that the pressure at the inlet of OT changes in relation to the Stodola’s ellipse approach [39–41], which is expressed as:

GF and TA are fixed, both PGF,VG,in and TGF,VG,in increase with MBIO. In fact, the growth of the thermal power transferred by the biomass to the geothermal fluid implies increases of TGF,VG,in and of the pressure at the outlet of GFP. The latter is determined so that the geothermal fluid is in the saturated liquid phase at the outlet of Rc; both PGF,VG,in and TGF,VG,in increase with TGF (once the values of TA and MBIO are fixed) and with TA (once the values of TGF and MBIO are fixed), but only slightly. In fact, the change in quantities is similarly as that described above, with varying MBIO for fixed TGF and TA.

6.1.2. R134a at the inlet of the organic turbine In Figs. 4 and 5, the pressure (POT,in) and temperature (TOT,in) of the R134a at the inlet of the organic turbine as functions of MBIO, TGF and TA, respectively, are illustrated.

• for the generic couple of T

GF and TA, both pOT,in and TOT,in increase with MBIO. Indeed, the growth of TGF,VG,in (Section 6.1.1) implies that a higher thermal power is transferred in VG with resulting increases in both the R134a mass flow rate and TOT,in. In turn, this determines the increase of pOT,in due to the aforementioned

(8) 2 dp)

OT , in, dp /(MOT , dp OT , in, off ))

6.1. Results

A sensitivity analysis of the off-design conditions is conducted to analyze the energy performances of the proposed HGB power plant (Fig. 1), by simultaneously varying several process parameters, i.e., MBIO, TA and TGF, as described below. The Aspen Plus and EDR V9® simulation models of the power plant previously described (Section 3) are used together with the detailed geometry of the five heat exchangers determined above (Section 4). At off-design conditions, the following assumptions are made in addition to those related to the design point conditions (Section 4):

2 2 POT , out , dp )/(POT , in, dp

(MOT , off

6. Sensitivity analysis at off-design conditions: Results and discussion

5. Sensitivity analysis at off-design conditions: Main assumptions

2 (POT , in, dp

OT , dp sin[0.5

Finally, as in the design point conditions, the air mass flow of AC is calculated so that the organic working fluid at the outlet of AC is in the saturated liquid phase.

electric consumption of FAP is negligible compared to the other powers exchanged in the respective operative units. Finally, in Table 7, the gross and net thermodynamic efficiencies of the geothermal fluid heating subsystem, ORC and the proposed HGB power plant at design point conditions are reported.

=

=

4) for low values of MBIO, the low mass flow rate of the flue gas would be highly cooled in AP by the whole oxidizing air mass flow rate (MA). Thus, only a portion of MA circulates in AP to obtain the minimum value (120 °C) of the flue gas temperature at the outlet of AP, avoiding condensation on the tubes walls. The remaining portion of MA directly feeds the reactor. Conversely, for high values of MBIO, MA circulates in AP, obtaining a flue gas temperature at the outlet of AP equal or higher than 120 °C.

AC

2 MOT , dp TOT , in, dp /POT , in, dp

(10)

3) the isentropic efficiency of OT in the off-design conditions is approximated as [42]: OT , off

Number of bays in parallel [-] Number of bundles in parallel per bay [-] Number of tubes per bundle [-] Number of tube passes per bundle [-] Tube length [mm] Tube external diameter [mm] Overall heat transfer area [m2] Overall heat transfer coefficient [W m−2 K−1] Effective mean temperature difference [°C]

2 2 MOT , off TOT , in, off Y + POT , out , off

POT , in, off =

(9)

Table 6 Thermal [MWt] and electric [MWe] powers for operative units at design point conditions. WAP [MWt]

WRr [MWt]

WRc [MWt]

WVG [MWt]

WTR [MWt]

WAC [MWt]

WOT [MWe]

WGFP [MWe]

WOFP [MWe]

WFAC [MWe]

Wgross [MWe]

Wnet [MWe]

0.588

4.175

3.449

13.382

4.335

9.147

4.254

0.079

0.255

0.260

3.840

3.581

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Fig. 2. PGF,VG,in [bar] as a function of MBIO [kg/s], TGF and TA [°C].

Fig. 6. WOT [MW] as a function of MBIO [kg/s], TGF and TA [°C].

Stodola’s ellipse approach; OT,in and TOT,in increase with TGF (once the values of TA and MBIO are fixed) and with TA (once the values of TGF and MBIO are fixed), and with varying MBIO for fixed TGF and TA, as previously explained.

• both P

6.1.3. Electric power of the organic turbine In Fig. 6, WOT as a function of MBIO, TGF and TA is depicted:

• if T •

Fig. 3. TGF,VG,in [°C] as a function of MBIO [kg/s], TGF and TA [°C].

•

GF and TA are constant, WOT increases with MBIO. This implies an increase in the R134a mass flow rate, of TOT,in and of POT,in (Section 6.1.2), with a resulting increase of WOT; once TA and MBIO are fixed, WOT increases with TGF. The quantities change similarly to those described above with varying MBIO for fixed TGF and TA; considering constant TGF and MBIO, WOT decreases with the increase of TA. The reduction of the specific enthalpy change in OT is higher than the increase of the R134a mass flow rate, which is controlled to keep the temperature of the geothermal fluid at RW constant.

6.1.4. Overall electric power of the extraction pump, geothermal fluid pump and ORC pump In Fig. 7, the overall electric power absorbed by the pumps, i.e., WEP (which is constant and equal to 80 kW), and WGFP and WOFP as functions of MBIO, TGF and TA are reported:

• by fixing T

GF and TA, the overall electric power of the pumps increases with MBIO. In fact, the increase of WGFP is due to the growth of the geothermal fluid pressure at the outlet of GFP (Section 6.1.1). In addition, WOFP increases due to the growth of the R134a mass

Fig. 4. POT,in [bar] as a function of MBIO [kg/s], TGF and TA [°C].

Fig. 5. TOT,in [bar] as a function of MBIO [kg/s], TGF and TA [°C].

Fig. 7. Overall WEP, WGFP, WOFP [MW] as functions of MBIO [kg/s], TGF and TA [°C].

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flow rate (Section 6.1.2); A and MBIO, the overall electric power absorbed by the pumps increases with TGF. The quantities change similarly to those described above with varying MBIO for fixed TGF and TA; with the same values of TGF and MBIO, the overall electric power absorbed by the pumps increases with TA. WOFP increases due to the growth of the R134a mass flow rate (Section 6.1.3), which is higher than the reduction of the pressure difference between the inlet and outlet of OFP. The increase of WGFP is negligible.

first;

• with constant T •

• with constant T

GF and MBIO, Wnet decreases with the increase of TA, due to the reduction of Wgross and the growth of WFAC.

The maximum Wnet of the proposed HGB power plant with varying TA and TGF is reported in Table 8. In particular, Wnet,max is almost unaffected by TGF for each TA. 6.1.8. Thermodynamic efficiency of the geothermal fluid heating subsystem Fig. 11 depicts ηGFHS as a function of MBIO, TGF and TA, and here ηGFHS is not defined for MBIO = 0, as in the proposed HGB power plant it coincides with the traditional geothermal binary power plant, i.e., without biomass:

6.1.5. Gross electric power of the proposed HGB power plant In Fig. 8, Wgross as a function of MBIO, TGF and TA is shown. Due to the overall electric power absorbed by the pumps, the reduction of Wgross in comparison to WOT is slight for low values of MBIO, whereas it is more appreciable for high values of MBIO.

• when T

6.1.6. Electric power of the fans of the air-cooled condenser In Fig. 9, WFAC as a function of MBIO, TGF and TA is reported. When TA is equal to −30 °C and −10 °C, WFAC is associated with positive Wnet for each value of MBIO. Conversely, for the TA equal to 10 °C and 30 °C, the maximum value of WFAC (represented in Fig. 9) is associated with values of MBIO corresponding to Wnet = 0:

• When T

• •

GF and TA remain fixed, WFAC increases with MBIO, and at the inlet of AC, R134a is in the superheated vapour phase with an increasing temperature and a negligible pressure change. Thus, the thermodynamic state of R134a at the outlet of AC is practically constant and the resulting specific enthalpy change of R134a in AC increases with MBIO. However, the mass flow rate of R134a increases with MBIO (Section 6.1.2). Hence, the exchanged thermal power in AC increases, with a resulting higher air mass flow rate required. Finally, this determines the growth of WFAC; if TA and MBIO are fixed, WFAC increases with TGF. In fact, the quantities change similarly as described above with varying MBIO for fixed TGF and TA; for the generic couple of TGF and MBIO, WFAC increases with TA. In fact, the increase of the mass flow rate of R134a is higher than the reduction of the specific enthalpy change of R134a in AC. Thus, the thermal power exchanged in AC increases, with a resulting growth in the required air mass flow rate.

•

•

GF and TA are fixed, ηGFHS shows a maximum with varying MBIO, due to the following effects. The first effect, which is beneficial to ηGFHS, is an increase in the enthalpy change of the geothermal fluid between EW and the inlet of VG with MBIO due to the growth of its specific enthalpy at the inlet of VG (Section 6.1.1). The second effect, which is harmful to ηGFHS, is an increase in the thermal power produced by the biomass combustion with MBIO. For low values of MBIO, the first effect is higher than the second, whereas the opposite is true for high values of MBIO. In addition, for very low values of MBIO, ηGFHS is almost unaffected by MBIO; with constant TA and MBIO, ηGFHS increases and decreases with TGF for low and high values of MBIO, respectively, due to the increase in the specific enthalpy of the geothermal fluid both in EW and at the inlet of VG with the increase of TGF (Section 6.1.1). The former (which implies a harmful effect on ηGFHS) is larger for high values of MBIO, whereas the latter (which implies a beneficial effect on ηGFHS) is larger for low values of MBIO. For very low values of MBIO, ηGFHS is almost unaffected by TGF; with the same values of TGF and MBIO, ηGFHS increases with TA due to the growth of the specific enthalpy of the geothermal fluid at the inlet of VG (Section 6.1.1).

6.1.9. Gross and net thermodynamic efficiencies of the ORC In Fig. 12, ηORC,gross as a function of MBIO, TGF and TA is illustrated:

• when T

The maximum WFAC corresponding to a positive Wnet is equal to 4.69 MW for TA = −10 °C, TGF = 160 °C and MBIO = 1 kg/s. The minimum WFAC is 4.1 kW for TA = −30 °C, TGF = 130 °C and MBIO = 0. With varying TA, TGF and MBIO, the decrease of WFAC, in terms of the aforementioned maximum value, is obtained through the reduction in the number of active fans and/or their velocity. Similarly, in the design point conditions, the electric power absorbed by FAP is negligible compared to the other powers exchanged in the respective operative units.

•

GF and TA remain fixed, ηORC,gross increases with MBIO and is constant for high values of MBIO. This is due to the trends of Wgross and the specific enthalpy change of the geothermal fluid in VG. The increase in the former with MBIO is greater than that of the latter, except for high values of MBIO where both quantities similarly increase; for the generic couple of TA and MBIO, ηORC,gross increases with TGF for low values of MBIO, whereas it is practically independent of TGF for high values of MBIO. In the first case the increase of Wgross with TGF is greater than the specific enthalpy change of the geothermal fluid in VG. In the second case, the influence of TGF is negligible

6.1.7. Net electric power of the proposed HGB power plant Fig. 10 illustrates Wnet as function of MBIO, TGF and TA:

• if T

•

GF and TA are constant, Wnet shows a maximum with varying MBIO, due to the following effects. First is the increase of Wgross with MBIO, which is beneficial to Wnet. Second is the increase of WFAC with MBIO, which is harmful to Wnet. Specifically, for low values of MBIO, Wgross is considerably higher than WFAC and results in a prevailing beneficial effect. The opposite occurs for high values of MBIO; once TA and MBIO are fixed, Wnet increases with TGF with low values of MBIO, whereas it decreases with TGF with high values of MBIO. In fact, as described above for low MBIO, the first beneficial effect (i.e., the increase of Wgross with TGF) is significantly higher than the harmful second effect (i.e., the increase of WFAC with TGF). Conversely, with high MBIO, the second effect is greater than the

Fig. 8. Wgross [MW] as a function of MBIO [kg/s], TGF and TA [°C]. 217

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Fig. 9. WFAC [MW] as a function of MBIO [kg/s], TGF and TA [°C].

Fig. 12. ηORC,gross [%] as a function of MBIO [kg/s], TGF and TA [°C].

Fig. 10. Wnet [MW] as a function of MBIO [kg/s], TGF and TA [°C].

Fig. 13. ηORC,net [%] as a function of MBIO [kg/s], TGF and TA [°C].

Table 8 Maximum Wnet [MW] with varying TA and TGF [°C]. Wnet,max [MW]

TA [°C]

change of the geothermal fluid in VG, similar to those described above for ηORC,gross.

TGF [°C]

−30 −10 10 30

130

140

150

160

4.192 2.907 1.770 1.020

4.236 2.912 1.774 1.023

4.259 2.934 1.778 1.026

4.266 2.943 1.780 1.029

6.1.10. Gross and net thermodynamic efficiencies of the proposed HGB power plant Figs. 14 and 15 show ηHGB,gross and ηHGB,net as functions of MBIO, TGF and TA. The values of ηHGB,gross are much lower than those of ηORC,gross due to ηGFHS, and their trends are similar, except for MBIO = 0 where ηHGB,gross is not defined as well as ηGFHS. Similar considerations are also valid for ηHGB,net, which is related to ηORC,net. Table 9 gives the maximum ηnet of the proposed HGB power plant with varying TA and TGF. In particular, ηHGB,net,max is almost unaffected by TGF for each TA. 6.1.11. Exergy analysis of the proposed HGB power plant An exergy analysis aims to determine the amount of exergy lost in the units operation of an energy system, following the second law of thermodynamics. The exergy losses are internal, i.e., due to

Fig. 11. ηGFHS [%] as a function of MBIO [kg/s], TGF and TA [°C].

compared to that of MBIO; G and MBIO are constant, ηORC,gross decreases with the growth of TA due to the reduction of Wgross and the increase of the specific enthalpy change of the geothermal fluid in VG.

• if T

Fig. 13 depicts ηORC,net as a function of MBIO, TGF and TA. The trends of ηORC,net are determined by those of Wnet and of the specific enthalpy

Fig. 14. ηHGB,gross [%] as a function of MBIO [kg/s], TGF and TA [°C]. 218

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Fig. 15. ηHGB,net [%] as a function of MBIO [kg/s], TGF and TA [°C].

Fig. 17. TA [°C] as a function of time [h] in Mutnovsky during an entire representative year.

Table 9 Maximum ηHGB,net [%] with varying TA and TGF [°C]. ηHGB,net,max [%]

TA [°C]

TGF [°C]

−30 −10 10 30

130

140

150

160

22.87 18.80 14.71 10.02

22.89 18.85 14.75 10.05

22.92 18.89 14.79 10.09

22.95 18.94 14.83 10.12

irreversibility within the energy system, and external, i.e., due to unused exergy discharged by the energy system into the environment [43,44]. In this study, the exergy loss ratio of the i-th unit operation of the proposed HGB power plant is determined, which is the proportion of exergy loss in the i-th unit operation in terms of the overall exergy losses in the system (ζi [%]) [45,46]. The exergy balance equations in an open system in steady-state conditions are used for this (Appendix A2). The exergy losses in FAP, EP and GFP are negligible compared to the other losses related to the respective operative units. In addition, the exergy losses of AC include those associated with FAC. In Fig. 16, ζi is reported for each case corresponding to the maximum ηHGB,net with varying TA and TGF (Table 9). Exergy destruction mainly takes place in the combustion chamber and radiation part of the reactor (Rcc and Rr, respectively). For each operation unit, the respective exergy loss increases with the reductions of the ambient air temperature.

Fig. 18. Relative frequency histogram [%] of TA [°C] in Mutnovsky during an entire representative year.

6.2. Monthly produced electric energy and used biomass A general overview of the operative management of the proposed HGB power plant is provided in this section. The monthly produced electric energy and used biomass are determined according to two alternative operating modes. In both, MBIO is controlled to maximize Wnet and ηHGB,net with varying TA and TGF, respectively. The hourly trend of TA during an entire representative year for the location considered, i.e., Mutnovsky, and a relative frequency histogram are depicted in Figs. 17 and 18, respectively [21].

Fig. 16. ζi [%] corresponding to the ηHGB,net,max with varying TA and TGF [°C].

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In the first operating mode described above, the maximum Wnet (Table 8) and MBIO corresponding to the maximum Wnet are determined both as functions of the ambient air temperature and geothermal fluid temperature at the extraction well, i.e., Wnet,max(TA,TGF) and the related MBIO(TA,TGF) (Appendix A1). From the hourly trend of TA during an entire representative year, i.e., TA(h) in Fig. 16, the hourly trends of the maximum Wnet and corresponding MBIO are both determined as functions of TGF during an entire representative year, i.e., Wnet,max(h,TGF) and MBIO(h,TGF). These are used to determine the monthly levels of electric energy produced (PEE, [MWh]) and biomass used (UB, [t]) for different values of TGF, i.e., TGF = 160, 150, 140 and 130 °C (Figs. 19 and 20), respectively. From Fig. 19, it follows that: i) for each year (i.e., for each value of TGF), PEE is higher in the months where TA is lower; and ii) for each month, PEE is virtually unaffected by the reduction of TGF. From Fig. 20, it follows that: i) for each year, UB is lower in the months where TA is larger; ii) for each month, UB decreases due to the increase of TGF. The same approach is taken for the aforementioned second operating mode. Wnet and MBIO both corresponding to the maximum ηHGB,net (Table 9) are determined as functions of TA and TGF (Appendix A1). Then, due to TA(h) in Fig. 16, the hourly trends of Wnet and MBIO are both determined as functions of TGF over an entire representative year. Finally, the latter are used to determine PEE and UB for the above described values of TGF (Figs. 21 and 22), respectively. These figures show qualitative trends of PEE and UB that are similar to the homologous trends of Figs. 19 and 20, but with the following exceptions: i) for each year, the changes of PEE and UB are lower in comparison to those related to the first operating mode; ii) for each month, PEE decreases with the reduction of TGF whereas UB is almost unaffected by TGF. In both operating modes, the influence of TA on the performances of the proposed HGB power plant is higher than that of TGF. Table 10 reports the cumulative yearly PEE and UB corresponding to the two alternative operating modes. For each year, the PEE corresponding to the first operating mode is higher, whereas the second operating mode enables a decrease in UB. In particular, the percentage increase of PEE, calculated with respect to the first operating mode, is at a minimum (i.e., 9%) for TGF = 160 °C and a maximum (i.e., 23.6%) for TGF = 130 °C. The percentage reduction of UB, calculated with respect to the first operating mode, is at a minimum (i.e. 28.3%) for TGF = 160 °C and a maximum (i.e., 42.6%) for TGF = 130 °C. Thus, the first operating mode can be used for the maximization of associated electric energy revenues, whereas the second is useful for minimizing the operational cost associated with the biomass.

related to geothermal steam turbines and diathermic oil (Section 1.2), which are used in configurations 5 and 6, respectively. 6.4. Economic analysis To assess the practical value of the novel cycle’s energy performance, a simple economic analysis is conducted. The profitability of the installation and operation of the hybrid plant is evaluated by considering the net present value (NPV) and the levelized cost of the electricity (LCOE) [47] in the two operating modes described in Section 6.2. We used the cost functions for the assessment of the capital cost of the main plant equipment, and the cost factors for the evaluation of the total investment cost [47,48]. The economic scenario and the data for the analysis are: ○ the investment is fully funded with a 20-year bank loan and an interest rate of 4.5% ○ the life of the investment is equal to 30 years, in accordance with the thermal degradation of the geothermal source ○ rate of interest = 6% ○ tax rate = 20% ○ fiscal amortization = 11 years ○ cost of biomass supplied by the business’ own forest, from cutting and transportation to the hybrid plant = 25 €/t ○ maintenance cost = 2% of the total investment cost ○ three operators required for the operation of the plant with an annual wage of 20,000 €/year ○ the electricity is produced and supplied to customers in a remote village at a selling price of 90 €/MWh ○ the governmental incentive for the net renewable electricity supplied to the grid is 100 €/MWh ○ annual hours of operation = 7,900 h/y

6.3. Thermodynamic performance comparison between the novel and the current configurations of HGB power plants

The purchased and installed costs (PIC) of each plant equipment item have been calculated considering the following cost functions, based on the specific cost of each design feature: Specific cost of biomass stoker furnace, considering the maximum pressure of the superheated water: 820 €/kW (first operating mode) and 600 €/kW (second operating mode) [49,50] Specific cost of the ORC turbine = 19,000 + 820 WTurb0.80, where Wturb is the turbine power [kW] [50] Specific cost of the steam generator and air-cooled condenser of the ORC cycle = 1,397 S0.89, where S is the heat exchange surface [m2] [51] Cost function of the recuperator of the ORC cycle = 280.3 mwf0.67, where mwf is the working fluid mass flow [kg/s] [51] Cost function of the pumps of the geothermal fluid and ORC

In Table 11, the thermodynamic performance of the other configurations of HGB power plants described above (Section 1.1) are summarized and compared to those of the novel HGB power plant. If data for the quantities are not available, they are identified as “N.A.”, whereas those that are not relevant to a specific configuration are identified as ”-“. In the novel configuration, the quantities related to the maximum ηHGB,net (with varying MBIO) and TA = 30 °C are identified with apex (1) and those related to the maximum ηHGB,net (with varying MBIO) and TA = −30 °C with apex (2). Among the current configurations, layouts no. 5 and no. 6 have operating conditions closer to those of the novel configuration. In fact only these configurations satisfy their cooling demands with atmospheric air in lieu of water. The maximum ηHGB,net values of the novel configuration are aligned with those of configurations 5 and 6, although for the latter the energy performance is not evaluated in off-design conditions, due to fluctuations in the ambient air temperature. Finally, it is worth noting that the novel configuration avoids the drawbacks

Fig. 19. First operating mode: monthly PEE [MWh] for different values of TGF [°C]. 220

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cycle = 200 Wpump0.65, where Wpump [kW] is the electric power absorbed by the pump [52] Cost function of the fan of the air-cooled condenser = 12,400 (Wfan/ 50)0.76, where Wfan [kW] is the electric power absorbed by the fans [53] For each piece of equipment, the highest value of the cost function variables is used, considering that the equipment must be sized by considering the worst operative conditions in terms of temperature and pressure. Hence, the overall PIC has been calculated by adding the cost of each plant equipment item using the cost functions reported above and has been increased by a factor equal to 1.05 with the aim of including inside the PIC also the costs of the equipment that could have been eventually neglected in the analysis. Then, the process buildings cost (material equal to 10% PIC and labour equal to 5% material × 15 €/h as wage), the service building costs (material equal to 7.5% PIC and labour equal to 5% material × 15 €/h as wage) and the service systems cost (material equal to 10% PIC and labour equal to 2% material × 15 €/h as wage) (PSBC) have been calculated. The initial spare cost is added to obtain the total investment cost (TIC) considering 1.5% of the PIC of the novel hybrid plant. More details of the procedure are provided in [47,48]. The overall capital cost of the investment (Capex) is obtained adding the cost for the realization of the geothermal well to the TIC. So, the following cost function is used for the assessment of the well cost: Cost of the well in terms of depth (X) = 1.72⋅10−7⋅X2 + 2.3⋅10−3⋅X + 0.62 [M€] [54] In Table 12 the results of the economic analysis are summarized. The economic profitability of the novel hybrid plant can be considered satisfactory for an investor in both operating conditions. The goodness of the investment is assured by the presence of governmental incentive to the renewable electric energy. The two operating modes are economically equivalent in terms of NPV when the overall specific income from the electricity selling and incentive is equal to about 160 €/MWh.

Fig. 20. First operating mode: monthly UB [t] for different values of TGF [°C].

Fig. 21. Second operating mode: monthly PEE [MWh] for different values of TGF [°C].

7. Conclusions The main contributions to the field of knowledge, the meaningful results, the applicability and limitations of the study and further research possibilities follow. 7.1. Main contributions to the field of knowledge A novel configuration for a hybrid binary geothermal biomass power plant is proposed, for regions with extreme environmental conditions, where water is not available and where the seasonal variations in the ambient air temperature are remarkable. The electricity generation takes place through the turbine of the ORC, which receives thermal power provided by a biomass heat source through geothermal fluid. The biomass is effectively deployed in off-design conditions, to counteract the simultaneous harmful effects produced by the considerable reduction of the geothermal fluid temperature during the operative life of the plant, and significant seasonal changes in the ambient air temperature. Thus, the exploitation of the geothermal source can be effectively ensured, and a fully renewable power plant can be maintained.

Fig. 22. Second operating mode: monthly UB [t] for different values of TGF [°C]. Table 10 Two operating modes: cumulative yearly PEE [MWh] and UB [t]. Operating mode

1st (Wnet,max) 2nd (ηHGB,net,max)

Quantity

PEE [MWh] UB [t] PEE [MWh] UB [t]

7.2. Meaningful results

TGF [°C] 130

140

150

160

18,850 18,580 14,400 10,650

18,940 17,740 15,460 10,620

19,040 16,390 16,470 10,590

19,140 14,730 17,410 10,560

The energy performance (i.e., Wnet and ηHGB,net) in off-design conditions is determined by an extensive sensitivity analysis in the presence of simultaneous changes in three process parameters (i.e., TA, TGF and MBIO). The trends of Wnet and ηHGB,net are qualitatively similar. In particular, for each pair of values of TA and TGF, Wnet and ηHGB,net are maximized in correspondence to the respective value of MBIO. Hence, in

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Table 11 Current and novel HGB power plant configurations: thermodynamic performances. Layout

TGF,EW [°C]

TGST,in [°C]

TOT,in [°C]

TST,in [°C]

TCON,out [°C]

ηHGB,net [%]

1a [8] 1b [9] 2a [10] 2b [11] 2c [9] 3 [9] 4 [8] 5 [9] 6 [13]

80 ÷ 120 207 154 151.7 240 200 80 ÷ 120 220 110 ÷ 150

– – 370 372.3 400 350 – 450 –

230 400 – – – 450 230 – –

30 70 45 44 70 70 30 N.A. 30

22.9 ÷ 23.1 22.2 28 20.4 N.A. 36.3 24.9 ÷ 25.1 25.4 16.7 ÷ 24.3

novel

130 160

– –

– – – – – – TGF,EW − 5 N.A. 275 (top) 115 (bot) 152(1),232(2) 165(1),245(2)

– –

40(1),-20(2) 40(1),-20(2)

10(1) ÷ 22.9(2) 10.1(1) ÷ 22.9(2)

7.3. Applicability

Table 12 Results of the economic analysis.

ORC cost, M€ Biomass stoker furnace, M€ Geothermal wells, M€ PIC, M€ PSBC, M€ TIC First year operative costs, M€ Last year operative costs, M€ First year net annual income, M€ Last year net annual income, M€ Net present value, M€ LCOE, €/MWh

Operating modes 1st (Wnet,max)

2nd (ηHGB,net,max)

4.3 7.3 1.1 12.2 5.3 17.7 2.3 1.4 1.3 2.1 17.9 113

4.2 5.3 1.1 10.1 4.4 14.6 1.9 1.1 1.3 1.7 16.8 105

In general, the integration of biomass can be considered an effective strategy for controlling the performance of power plants, which are subject to external disturbances that are simultaneously variable with time. In this study the integration of biomass in an air-cooled ORC geothermal power plant is proposed, to mitigate the harmful effects on performance of remarkable high seasonal fluctuations in the ambient air temperature, combined with the annual degradation of the geothermal fluid temperature. This situation is associated with niche locations in regions with extreme environmental conditions, and where both geothermal and biomass heat sources are available. 7.4. Limitations and future studies To continue and extend the present investigation, future research should evaluate different operating modes for the ORC, such as an organic turbine with a constant inlet pressure, to optimize the energy performance with varying operative conditions. Furthermore, an economic assessment of the proposed HGB power plant, including the biomass supply chain, should be conducted. In regions with severe climates and ambient conditions, the supply and availability of biomass may be extremely challenging, and must therefore be carefully analysed.

the proposed power plant, the use of biomass appears to be an effective strategy, in relation to the specific operation requirements, as it can manage the effects of TA variability, which is the parameter that influences performances most, and TGF. Indeed, MBIO can be dynamically modified to maximize the annual electric energy production or to minimize the biomass used annually. Both operating modes are economically profitable. Appendix

A1. Net produced electric power and related biomass mass flow rate as functions of ambient air temperature and geothermal fluid temperature at the extraction well The maximum Wnet [MW] and related MBIO [kg/h] as functions of TA and TGF [°C] are: (A1)

Wnet , max (TA, TGF ) = aW + bW TA + cW TA2 + dW TA3 + eW TGF MBIO (TA, TGF ) = aM + bM TA +

cM TA2

+

dM TA3

+ eM / TGF +

(A2)

2 fM / TGF

where

•a •a

W = 2.1554,

bW = −5.7908·10−2, cW = 3.5203·10−4, dW = 4.8281·10−6, eW = 1.0975·10−3; bM = −42.3187, cM = 1.6312·10−1, dM = 1.3687·10−2, eM = 235.1743·104, fM = −146.8950·106

M = −7171.7531,

The Wnet [MW] and related MBIO [kg/h] corresponding to the maximum ηHGB,net as functions of TA and TGF [°C] are: 2 Wnet (TA, TGF ) = aW + bW TA + cW TGF + dW TA2 + eW TGF + fW TA TGF

(A3)

2 MBIO (TA, TGF ) = aM + bM TA + cM TGF + dM TA2 + eM TGF + fM TA TGF

(A4)

where

•a •a

−1 , bW = −1.5063·10−2, cW = 2.1956·10−2, dW = 1.8141·10−4, eW = −3.4375·10−5, fW = −1.7685·10−4; W = −5.2714·10 3 −1 , dM = −1.5625·10−4, eM = 6.2500·10−4, fM = 5.6500·10−3 M = 1.3334·10 , bM = −18.9030, cM = −5.5875·10

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A2. Exergy loss ratio of the i-th unit operation The exergy loss of the i-th unit operation (Ii [kW]) in an open system in steady-state conditions is expressed as [43,55]:

Ii =

Min, j

Mout , k

in, j

j

out , k

+

k

Wt , HS, l 1 l

T0 THS , l

± |Wm|

(A5)

where

• M = mass flow rate of the j-th stream in the respective inlet section [kg/s]; • M = mass flow rate of the k-th stream in the respective outlet section [kg/s]; • ε = specific exergy of the j-th stream in the respective inlet section [kJ/kg]; • ε = specific exergy of the k-th stream in the respective outlet section [kJ/kg]; • W = exchanged thermal power between the i-th unit operation and the l-th heat source or heat sink [MW]; • T = temperature of the reference state [K]. In particular, T is assumed equal to the air ambient temperature, i.e. T = T = −30 ÷ 30 °C; • T = temperature of the l-th heat source or heat sink [K]; • W = exchanged mechanical power between the i-th unit operation and the external environment [kW]. The negative sign is for the case in in,j

out,k

in,j

out,k

t,HS,l

0

0

0

A

HS,l m

which mechanical power is supplied from the i-th unit operation to the external environment, and the positive sign is for the opposite case.

In the absence of nuclear effects, magnetism, electricity and surface tension and if neglecting the kinetic and potential specific exergies, the specific exergy of a generic stream in the respective inlet or outlet section of the i-th unit operation consists of physical and chemical specific exergies (εph and εch, respectively) [43,55]:

=

ph

+

(A6)

ch

For a generic stream in a solid, liquid or vapour phase, εph [kJ/kg] is expressed as [43,55]: ph

= (h

(h0

T0 s )

(A7)

T0 s 0)

where

• h = specific enthalpy of the stream in the current thermodynamic state [J/kg]; • s = specific entropy of the stream in the current thermodynamic state [J/(kg K)]; • h = specific enthalpy of the stream in the reference state [J/kg], where P = 1 atm; • s = specific entropy of the stream in the reference state [J/(kg K)]. 0

0

0

For a generic stream in vapour phase, e.g., a gas mixture consisting of several chemical species, or an ideal liquid solution, εch [kJ/kg] is expressed as [43,56]: ch

=

(yn

0 ch, n

+ RT0 yn lnyn )/MW

(A8)

n

where

• y = mole fraction of the n-th chemical species [-]; • ε = standard chemical exergy of the n-th chemical species in correspondence to the reference state [kJ/kmol]; • R = universal gas constant [kJ/(kmol K)], R = 8.3144 kJ/(kmol K); • MW = molecular weight of the stream [kg/kmol]. n 0 ch,n

Finally, ζi [%] is expressed as [45,46]: i

= 100Ii /

Ii

(A9)

i

The exergy losses in each unit operation of the proposed HGB power plant are given as follows, according to the aforementioned exergy equations and numbered streams in Fig. 1.

IVG = M10 (h10

h11) + M12 (h12

h13)

T0 [M10 (s10

s11) + M12 (s12

s13)]

(A10)

ITR = M14 (h14

h15) + M17 (h17

h12)

T0 [M14 (s14

s15) + M17 (s17

s12)]

(A11)

IAC = M15 (h15

h16) + M18 (h18

h20)

T0 [M15 (s15

s16) + M18 (s18

s20 )] + |WFAC|

(A12)

IAP = M1 (h1

h3) + M5 (h5

IOT = M13 [(h13 IOFP = M16 [(h16

h14 ) h17)

h 6)

T0 (s13 T0 (s16

T0 [M1 (s1 s14 )]

s3) + M5 (s5

(A13)

s6 )]

(A14)

|WOT|

(A15)

s17)] + |WOFP|

The exergy destruction in the first part of the reactor (IRcc, [kW]) is: IRcc = M3 ( ph,3 + ch,3) + M4 ch,4 M4' ( ph,4' + ch,4') (A16) The specific physical and chemical exergy of the oxidizing air at the inlet of Rcc (εph,3 and εch,3, respectively [kJ/kg]), where εph,3 is approximately calculated with the perfect gas assumption, are [43,55]:

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S. Briola, et al.

cp,3 [(T3

ph,3

=

ch,3

T0)

(yn

0 ch, n

(A17)

T0 ln(T3/T0 )] + RT0 ln(P3/ P0)

+ RT0 yn lnyn )/

n = N 2, O2

(yn MWn)

(A18)

n = N 2, O2

The specific chemical exergy of the wet biomass at the inlet of Rcc (εch,4 [kJ/kg]) is [43]: ch,4

= (LHV + 2442w )

dry

= 1.0438 + 0.1882

dry

+ 9417s

h c

(A19)

0.2509 1 + 0.7256

h n + 0.0383 / 1 c c

0.3035

o c

(A20)

where w, h, o, c and s are the mass fraction of moisture, H, O, C and S in the biomass, respectively [-]. The specific physical and chemical exergy of the flue gas at the outlet of Rcc (εph,4′ and εch,4′, respectively [kJ/kg]) are:

cp,4' [(T4'

ph,4'

ch,4'

T0)

=

(A21)

T0 ln(T4'/ T0 )] + RT0 ln(P4'/ P0 )

(yn

0 ch, n

+ RT0 yn lnyn )/

n = H 2O, N 2, O2, CO2

(yn MWn)

(A22)

n = H 2O, N 2, O2, CO2

The main chemical species of the flue gas (mole composition) are yH2O = 0.09988, yN2 = 0.71834, yO2 = 0.05475 and yCO2 = 0.12703. The exergy destruction in the intermediate and rear part of the reactor (IRr and IRc, respectively [kW]) are:

IRr = M4' (h 4'

h4'') + M9 (h9

h 9')

T0 [M4' (s4'

s4'') + M9 (s9

s9')]

(A23)

IRc = M4' (h4''

h5) + M9 (h 9'

h10)

T0 [M4' (s4''

s5) + M9 (s9'

s10 )]

(A24)

The standard chemical exergies of the chemical species in the oxidizing air and flue gas in the reference state are approximately equal to the homologous one at TA = 298 K, which are reported in [57].

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