# Design and optimization of a geothermal absorption cooling system in a tropical climate

Charles Maragna, Amín Altamirano, Brice Tréméac, Florent Fabre, Laurène Rouzic, Pierre Barcellini

► To cite this version:

Charles Maragna, Amín Altamirano, Brice Tréméac, Florent Fabre, Laurène Rouzic, et al. Design and optimization of a geothermal absorption cooling system in a tropical climate. Applied Energy, 2024, 364, pp.123102. 10.1016/j.apenergy.2024.123102. hal-04536943

HAL Id: hal-04536943

https://brgm.hal.science/hal-04536943

Submitted on 8 Apr 2024

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<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
# Design and optimization of a geothermal absorption cooling system in a tropical climate

Charles Maragna, Amín Altamirano, Brice Tremeac, Florent Fabre, Laurène Rouzic, Pierre Barcellini

► To cite this version:

Charles Maragna, Amín Altamirano, Brice Tremeac, Florent Fabre, Laurène Rouzic, et al. Design and optimization of a geothermal absorption cooling system in a tropical climate. Applied Energy, 2024, 364, pp.123102. 10.1016/j.apenergy.2024.123102. hal-04536943

HAL Id: hal-04536943

https://brgm.hal.science/hal-04536943v1

Submitted on 8 Apr 2024

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
<figure><img src="image_2.png" /></figure>

# Design and optimization of a geothermal absorption cooling system in a tropical climate

Charles Maragna<sup>a, *</sup>, Amín Altamirano<sup>b</sup>, Brice Tréméac<sup>b</sup>, Florent Fabre<sup>c</sup>, Laurène Rouzic<sup>c</sup>, Pierre Barcellini<sup>c</sup>

## HIGHLIGHTS

* A geothermal absorption chiller in tropical climate is modelled.

* The influence of design parameters on electricity consumption is investigated.

* The system undergoes multi-objective optimization.

* The well proximity and geothermal temperature are keys to the system relevance.

## ARTICLE INFO

Keywords:

Air conditioning

Tropical climate

Absorption chiller

Geothermal energy

Surrogate modelling

Energy system optimization

## ABSTRACT

The electricity required for air conditioning is soaring worldwide. Absorption chillers represent an alternative to classical vapor compression systems, using heat instead of electricity. However, absorption chillers powered by renewable geothermal heat have received little attention so far. This paper introduces a system using a hot geothermal fluid (typically in the range of 80–110 °C) to produce cooling through a single-effect absorption chiller, and Domestic Hot Water (DHW) through a heat exchanger. It considers a hotel located in Martinique, a French Caribbean island. The electric consumption of every subsystem has been thoroughly estimated. The originality of this paper is twice: i) the system is modelled in TRNSYS software considering dynamic conditions, ii) the system undergoes surrogate modelling and multi-objective optimization to minimize both the cost and the CO₂ content of the delivered thermal energy. Several scenarios are considered, depending upon the geothermal temperature, mass flow rate, well remoteness, and demand size. The studied system appears to be systematically more expensive than a combination of a classical vapor compression chiller and a boiler for DHW. However, it can significantly decrease the CO₂ content of the provided energy, especially in an island where most electricity is generated from fossil fuels. The proximity of the geothermal well and the use of the warm water leaving the absorption generator (here for DHW production) appear to be key factors for system relevance, along with a hotter geothermal fluid (e.g., 110 °C instead of 80 °C).

## 1. Introduction

In 2016, the International Energy Agency estimated that the use of Air Conditioners (AC) and electric fans to keep buildings cool accounted for 2000 TWh·y⁻¹, i.e., nearly 20% of the total electricity used in buildings around the world; this number may soar to 6200 TWh·y⁻¹ by 2050 [1]. The Global Warming Potential (GWP) over the whole lifecycle of an AC installation (including electricity consumption) is especially

high in Caribbean Islands, where most electricity is generated through fossil fuels combustion, though geothermal resources have been proved to exist. For instance, a recent energy audit of 55 office buildings in Martinique, a French Caribbean island, showed that 47% of their electricity consumption is used for air conditioning [2]. Meanwhile, in 2023, the only geothermal power plant operated in the Caribbean is located in Bouillante, Guadeloupe [3]. The 15 MWe plant is fed by a 250 °C geothermal fluid and covers 6% of the electricity demand of the island. Besides, indirect measurements suggest that geological formations in

<footnote><sup>a</sup> BRGM, F-45060 Orléans, France</footnote>

<footnote><sup>b</sup> Laboratoire du froid et des systèmes énergétiques et thermiques (Lafset), Conservatoire national des arts et métiers, HESAM Université, F-75003 Paris, France</footnote>

<footnote><sup>c</sup> Etamine, F-44000 Nantes, France</footnote>

<footnote>* Corresponding author at: BRGM, 3 av. Claude-Guillemin BP 36009, 45060 Orléans Cedex 2, France.
E-mail address: c.maragna@brgm.fr (C. Maragna).</footnote>
<figure><img src="image_2.png" /></figure>

# Design and optimization of a geothermal absorption cooling system in a tropical climate

Charles Maragna<sup>a, *,</sup>, Amín Altamirano<sup>b</sup>, Brice Tréméac<sup>b</sup>, Florent Fabre<sup>c</sup>, Laurène Rouzic<sup>c</sup>, Pierre Barcellini<sup>c</sup>

## HIGHLIGHTS

* A geothermal absorption chiller in tropical climate is modelled.

* The influence of design parameters on electricity consumption is investigated.

* The system undergoes multi-objective optimization.

* The well proximity and geothermal temperature are keys to the system relevance.

## ARTICLE INFO

Keywords:

Air conditioning

Tropical climate

Absorption chiller

Geothermal energy

Surrogate modelling

Energy system optimization

## ABSTRACT

The electricity required for air conditioning is soaring worldwide. Absorption chillers represent an alternative to classical vapor compression systems, using heat instead of electricity. However, absorption chillers powered by renewable geothermal heat have received little attention so far. This paper introduces a system using a hot geothermal fluid (typically in the range of 80–110 °C) to produce cooling through a single-effect absorption chiller, and Domestic Hot Water (DHW) through a heat exchanger. It considers a hotel located in Martinique, a French Caribbean island. The electric consumption of every subsystem has been thoroughly estimated. The originality of this paper is twice: i) the system is modelled in TRNSYS software considering dynamic conditions, ii) the system undergoes surrogate modelling and multi-objective optimization to minimize both the cost and the CO₂ content of the delivered thermal energy. Several scenarios are considered, depending upon the geothermal temperature, mass flow rate, well remoteness, and demand size. The studied system appears to be systematically more expensive than a combination of a classical vapor compression chiller and a boiler for DHW. However, it can significantly decrease the CO₂ content of the provided energy, especially in an island where most electricity is generated from fossil fuels. The proximity of the geothermal well and the use of the warm water leaving the absorption generator (here for DHW production) appear to be key factors for system relevance, along with a hotter geothermal fluid (e.g., 110 °C instead of 80 °C).

## 1. Introduction

In 2016, the International Energy Agency estimated that the use of Air Conditioners (AC) and electric fans to keep buildings cool accounted for 2000 TWh·y⁻¹, i.e., nearly 20% of the total electricity used in buildings around the world; this number may soar to 6200 TWh·y⁻¹ by 2050 [1]. The Global Warming Potential (GWP) over the whole lifecycle of an AC installation (including electricity consumption) is especially

high in Caribbean Islands, where most electricity is generated through fossil fuels combustion, though geothermal resources have been proved to exist. For instance, a recent energy audit of 55 office buildings in Martinique, a French Caribbean island, showed that 47% of their electricity consumption is used for air conditioning [2]. Meanwhile, in 2023, the only geothermal power plant operated in the Caribbean is located in Bouillante, Guadeloupe [3]. The 15 MWe plant is fed by a 250 °C geothermal fluid and covers 6% of the electricity demand of the island. Besides, indirect measurements suggest that geological formations in

<footnote><sup>a</sup> BRGM, F-45060 Orléans, France</footnote>

<footnote><sup>b</sup> Laboratoire du froid et des systèmes énergétiques et thermiques (Lafset), Conservatoire national des arts et métiers, HESAM Université, F-75003 Paris, France</footnote>

<footnote><sup>c</sup> Etamine, F-44000 Nantes, France</footnote>

<footnote>* Corresponding author at: BRGM, 3 av. Claude-Guillemin BP 36009, 45060 Orléans Cedex 2, France.
E-mail address: c.maragna@brgm.fr (C. Maragna).</footnote>
Nomenclature<fnref n="1" />

Latin letters

c intensive cost (e.g. per energy)

C cost [€]

E energy [MWh]

L length of the buried twin pipes [m]

M mass [kg]

ṁ mass flow rate [kg · h⁻<fnref n="1" />]

r radius [m]

t time [h]

T temperature [°C]

Ψ pressure per unit length of pipe [Pa · m⁻<fnref n="1" />]

Ψ pressure [Pa]

Q heat transfer [MWh]

Q̇ heat transfer rate [W]

ν speed [m · s⁻<fnref n="1" />]

W work transfer [MWh]

Ẇ power [W]

Greek letters

δT temperature pinch of a heat exchanger [°C]

λ thermal conductivity [W · K⁻<fnref n="1" /> · m⁻<fnref n="1" />]

ρ density [kg · m⁻³]

ρCₚ volumetric heat capacity [J · K⁻<fnref n="1" /> · m⁻³]

γ intensive Global Warming Potential (e.g. per energy)

Γ Global Warming Potential [kgCO₂eq]

Subscripts

b borehole

GTH geothermal

demand total demand (cooling + DHW)

el electric

ev evaporator

ext external

gen generator

in inlet

int intermediate temperature source of the absorption chiller

nom nominal condition

out outlet

p pipe (of the buried twin pipes)

sorp absorption chiller

Superscripts

ū time derivative of u

u* dimensionless quantity u

E* energy normalized by the total demand E* = E/Q<sub>cooling</sub> + Q<sub>DHW</sub>

E~ energy normalized by the cooling demand E~ = E/Q<sub>cooling</sub>

Abbreviations

AC air conditioner

ACC air-cooled chiller

COP coefficient of performance

CT cooling tower

DHW domestic hot water

EER energy efficiency ratio

GP Gaussian process

GWP global warming potential

HX heat exchanger

KPI key performance indicator

ldb lower dead band of a logical processor

ORC organic Rankine cycle

PE polyethylene

PV photovoltaic

RMSE root mean square error

SDR standard dimensional ratio

udb upper dead band of a logical processor

Lamentin sector, Martinique, may contain geothermal fluids at 400–800 m depth at a temperature in the range 80–110 °C. Such a fluid may be used in a sorption chiller to produce cooling.

Sorption cooling systems represent an alternative to the classical vapor compression systems since they use heat instead of electricity to produce the cooling effect. They can run on renewable heat (e.g., solar, geothermal and biomass) or waste heat, thereby decreasing the CO₂ emissions related to cooling [4,5]. These chillers can be divided into two broad categories: closed-cycle (when the refrigerant fluid is not in direct contact with the cooled air, e.g., absorption and adsorption chillers) and open-cycle (when the refrigerant fluid is in direct contact with the cooled air, e.g., Desiccant Evaporative Cooling or DEC systems). A previous review study by the authors indicated that DEC and adsorption systems possess the smallest market share of commercial sorption chillers (7% and 9–11%, respectively) given their drawbacks related to either elevated costs, variable cooling power, low COP, ambient condition limitations, sanitary risks, or low cooling power density [4]. On the other hand, absorption chillers (with a market share of 82–84%), are the most popular given their performance, compactness, and investment cost [4,5]. For this reason, the present study focuses on the absorption chiller technology.

A typical single-stage absorption chiller (Fig. 1) consists of an evaporator, a condenser, an absorber, a generator (also referred to as desorber), a circulation pump, a liquid-to-liquid exchanger (also referred to as a solution heat exchanger), and two expansion valves. The chiller operates as follows: heat is applied to the solution in the generator (Q<sub>gen</sub>), causing it to release refrigerant vapor (i.e., water vapor) through desorption. This vapor then moves to the condenser where it

releases heat (Q<sub>con</sub>) and is condensed into liquid form. The liquid water then flows through a throttle valve and is vaporized again at low pressure and temperature in the evaporator. This evaporation process absorbs heat from the cold source (Q<sub>ev</sub>). The created vapor is then absorbed by the solution (poor in refrigerant) in the cooled absorber (Q<sub>abs</sub>). The solution, now rich in refrigerant, is then pumped from the absorber to the generator to start the cycle again. A solution exchanger (SHX) is placed between the absorber and the generator to recover internal heat, thereby improving the chiller's efficiency. Finally, if a volatile solution such as ammonia-water is used, a vapor purification system (commonly called a "rectifier") must be installed between the generator and the condenser to increase the purity of the refrigerant circuit. The excess heat produced at an intermediary temperature is Q<sub>int</sub> = Q<sub>cond</sub> + Q<sub>abs</sub>.

Regarding the working fluids in commercial systems, only two options are available: Ammonia/Water (NH₃/H₂O, being ammonia the refrigerant and water the absorbent), preferred when temperatures below 0 °C are needed, and Water/Lithium Bromide (H₂O/LiBr, being water the refrigerant and water the absorbent), preferred for building AC or applications where positive cooling is required since this working pair exhibits higher thermal Coefficient of Performance (COP<sub>th</sub>) [6]. Overall, the H₂O/LiBr seems like the predominant working fluid on the market [7] and has been considered for this study.

The use of geothermal energy to produce cooling through absorption chillers has already received some attention in recent times. For instance, Wang et al. performed a detailed economic viability analysis of a geothermal absorption chiller for a university in Western Australia, though they did not investigate to which extent the chiller performance

<footnote n="1">¹ The units between brackets are to be used for the numerical applications throughout the paper.</footnote>
Nomenclature<fnref n="1" />

Latin letters

c intensive cost (e.g. per energy)

C cost [€]

E energy [MWh]

L length of the buried twin pipes [m]

M mass [kg]

ṁ mass flow rate [kg · h⁻<fnref n="1" />]

r radius [m]

t time [h]

T temperature [°C]

Ψ pressure per unit length of pipe [Pa · m⁻<fnref n="1" />]

Ψ pressure [Pa]

Q heat transfer [MWh]

Q̇ heat transfer rate [W]

ν speed [m · s⁻<fnref n="1" />]

W work transfer [MWh]

Ẇ power [W]

Greek letters

δT temperature pinch of a heat exchanger [°C]

λ thermal conductivity [W · K⁻<fnref n="1" /> · m⁻<fnref n="1" />]

ρ density [kg · m⁻³]

ρCₚ volumetric heat capacity [J · K⁻<fnref n="1" /> · m⁻³]

γ intensive Global Warming Potential (e.g. per energy)

Γ Global Warming Potential [kgCO₂eq]

Subscripts

b borehole

GTH geothermal

demand total demand (cooling + DHW)

el electric

ev evaporator

ext external

gen generator

in inlet

int intermediate temperature source of the absorption chiller

nom nominal condition

out outlet

p pipe (of the buried twin pipes)

sorp absorption chiller

Superscripts

ū time derivative of u

u* dimensionless quantity u

E* energy normalized by the total demand E* = E/Q<sub>cooling</sub> + Q<sub>DHW</sub>

E~ energy normalized by the cooling demand E~ = E/Q<sub>cooling</sub>

Abbreviations

AC air conditioner

ACC air-cooled chiller

COP coefficient of performance

CT cooling tower

DHW domestic hot water

EER energy efficiency ratio

GP Gaussian process

GWP global warming potential

HX heat exchanger

KPI key performance indicator

ldb lower dead band of a logical processor

ORC organic Rankine cycle

PE polyethylene

PV photovoltaic

RMSE root mean square error

SDR standard dimensional ratio

udb upper dead band of a logical processor

Lamentin sector, Martinique, may contain geothermal fluids at 400–800 m depth at a temperature in the range 80–110 °C. Such a fluid may be used in a sorption chiller to produce cooling.

Sorption cooling systems represent an alternative to the classical vapor compression systems since they use heat instead of electricity to produce the cooling effect. They can run on renewable heat (e.g., solar, geothermal and biomass) or waste heat, thereby decreasing the CO₂ emissions related to cooling [4,5]. These chillers can be divided into two broad categories: closed-cycle (when the refrigerant fluid is not in direct contact with the cooled air, e.g., absorption and adsorption chillers) and open-cycle (when the refrigerant fluid is in direct contact with the cooled air, e.g., Desiccant Evaporative Cooling or DEC systems). A previous review study by the authors indicated that DEC and adsorption systems possess the smallest market share of commercial sorption chillers (7% and 9–11%, respectively) given their drawbacks related to either elevated costs, variable cooling power, low COP, ambient condition limitations, sanitary risks, or low cooling power density [4]. On the other hand, absorption chillers (with a market share of 82–84%), are the most popular given their performance, compactness, and investment cost [4,5]. For this reason, the present study focuses on the absorption chiller technology.

A typical single-stage absorption chiller (Fig. 1) consists of an evaporator, a condenser, an absorber, a generator (also referred to as desorber), a circulation pump, a liquid-to-liquid exchanger (also referred to as a solution heat exchanger), and two expansion valves. The chiller operates as follows: heat is applied to the solution in the generator (Q<sub>gen</sub>), causing it to release refrigerant vapor (i.e., water vapor) through desorption. This vapor then moves to the condenser where it

releases heat (Q<sub>con</sub>) and is condensed into liquid form. The liquid water then flows through a throttle valve and is vaporized again at low pressure and temperature in the evaporator. This evaporation process absorbs heat from the cold source (Q<sub>ev</sub>). The created vapor is then absorbed by the solution (poor in refrigerant) in the cooled absorber (Q<sub>abs</sub>). The solution, now rich in refrigerant, is then pumped from the absorber to the generator to start the cycle again. A solution exchanger (SHX) is placed between the absorber and the generator to recover internal heat, thereby improving the chiller's efficiency. Finally, if a volatile solution such as ammonia-water is used, a vapor purification system (commonly called a "rectifier") must be installed between the generator and the condenser to increase the purity of the refrigerant circuit. The excess heat produced at an intermediary temperature is Q<sub>int</sub> = Q<sub>cond</sub> + Q<sub>abs</sub>.

Regarding the working fluids in commercial systems, only two options are available: Ammonia/Water (NH₃/H₂O, being ammonia the refrigerant and water the absorbent), preferred when temperatures below 0 °C are needed, and Water/Lithium Bromide (H₂O/LiBr, being water the refrigerant and water the absorbent), preferred for building AC or applications where positive cooling is required since this working pair exhibits higher thermal Coefficient of Performance (COP<sub>th</sub>) [6]. Overall, the H₂O/LiBr seems like the predominant working fluid on the market [7] and has been considered for this study.

The use of geothermal energy to produce cooling through absorption chillers has already received some attention in recent times. For instance, Wang et al. performed a detailed economic viability analysis of a geothermal absorption chiller for a university in Western Australia, though they did not investigate to which extent the chiller performance

<footnote n="1">¹ The units between brackets are to be used for the numerical applications throughout the paper.</footnote>
<figure><img src="image_3.png" /><figcaption>Fig. 1. Single-effect absorption chiller.</figcaption></figure>

depends upon the geothermal fluid temperature [8]. Han et al. studied a H₂O/LiBr double-effect absorption cooling system powered by a geothermal fluid at 150 °C. They estimated the thermal COP to be above 1.0 [9]. Tetemke et al. designed an NH₃/H₂O absorption chiller to cool down drinking water from 37.8 °C to 16.0 °C [10]. They reported a thermal COP of 0.30, a typical value according to the authors for the NH₃/H₂O working fluid with relatively low geothermal source temperature (83 °C) [6]. Saucedo-Velázquez et al. simulated the retrofit of deep boreholes in closed-loop (Borehole Heat Exchangers) to produce cooling through a half-effect, a single-effect, a double-effect, or a triple-effect absorption chiller [11]. For geothermal driving temperatures in the range of 59–80 °C, 77–110 °C, 135–162 °C, and 180–187 °C, respectively, the cooling systems could deliver chilled water temperatures around 8 °C. In 2006, an NH₃/H₂O chiller was installed in Chena, Alaska, to produce cooling at –29 °C with a geothermal resource at 74 °C; a river at +4 °C cooled down the sorption chiller [12]. Finally, Gado et al. reviewed hybrid sorption-vapor compression cooling systems, classifying the systems as cascade, partially integrated and fully integrated systems [13]. They reported that this combination would allow an electricity consumption reduction of about 45–88% in comparison with conventional vapor compression systems.

Innovative architectures to produce cooling, heating, electricity, soft water or even hydrogen with solar and geothermal energy have been designed and modelled (see Table 1). However, these simulations are often carried out under steady-state conditions, though the performances of a single-effect absorption chiller are impacted by the fluctuating operative conditions. To the authors’ knowledge, the dynamic behavior of a single-effect geothermal absorption chiller has been poorly studied.

This paper intends to fill this knowledge gap in the Caribbean context. The present work is organized as follows (see Fig. 2): Section 2.1 describes the system and its dynamic modelling. Section 2.2 gives further insight of the system components for a preliminary, non-optimal sizing, while section 2.3 introduces the key performance indicators considered throughout the paper. Section 3 reports the results of the simulations for the preliminary sizing and a sensitivity analysis in the vicinity of this sizing, changing one or two parameters at a time. Section 4 discusses the multi-objective optimization of the system for several technical and economic scenarios.

## 2. Materials and methods

### 2.1. System modelling

#### 2.1.1. Overall system description

The designed system encompasses two geothermal wells (one for pumping, one for reinjection), a single-effect absorption chiller, a backup Air-Cooled Chiller (ACC), a Cooling Tower (CT), three-way valves (diverters and mixers), pumps, heat exchangers, and additional tanks (see Fig. 3).

The geothermal fluid extracted from a geothermal well (point 1) enters the source side of the heat exchanger HX_1 (point 2 in Fig. 3). It transfers heat to water entering the load side of HX_1 (points 6 and 4). The load side is connected to a buffer tank Tank_1 through a buried pipe, and then to the generator inlet of the absorption chiller (point 14). Tank_1 adds inertia to the model, making its numerical convergence easier.

The cooled water leaving the generator (point 15) flows to a buffer tank Tank_2 (point 18) and transfers heat through HX_2 for Domestic Hot Water (DHW) preparation.

When operated, the flow rates in pumps 3 and 5 (P_3 and P_5, respectively) are $\dot{m} = 5 \langle \dot{m}_{DHW} \rangle$, where $\langle \dot{m}_{DHW} \rangle$ is the daily mean of the required DHW flow rate and $\dot{m}_{DHW}$ the instantaneous required DHW flow rate (see §2.1.2). If the water temperature exiting the DHW tank Tank_3 (point 57) does not reach the setpoint $T_{59} = T_{sp DHW} = 40$ °C, then an electrical backup heater is turned on, consuming $\dot{Q}_{DHW}^{backup}$. Meanwhile, the intermediate temperature source of the absorption chiller is connected to a buffer tank (Tank_4) that leads to a Cooling Tower (CT).

The evaporator of the absorption chiller and the ACC are connected to the cooling tank (Tank_5), from which cooled water is distributed into the building (point 47). The set point departure in the cooling emitters is $T_{47} = 7$ °C, with water flowing back at $T_{48} = 12$ °C.

The role of the valves mix_i and div_i (i = 1 to 5) will be further explained in §2.2.7.

The system is modelled in TRNSYS v18 [23,24]. TRNSYS is a program for the dynamic simulation of transient systems. At every time step, TRNSYS iteratively solves the temperature and flow rate of every node of the system. Its modular structure and graphical interface allows the user to easily connect so-called “Types”, i.e. modules describing the
<figure><img src="image_3.png" /><figcaption>Fig. 1. Single-effect absorption chiller.</figcaption></figure>

depends upon the geothermal fluid temperature [8]. Han et al. studied a H₂O/LiBr double-effect absorption cooling system powered by a geothermal fluid at 150 °C. They estimated the thermal COP to be above 1.0 [9]. Tetemke et al. designed an NH₃/H₂O absorption chiller to cool down drinking water from 37.8 °C to 16.0 °C [10]. They reported a thermal COP of 0.30, a typical value according to the authors for the NH₃/H₂O working fluid with relatively low geothermal source temperature (83 °C) [6]. Saucedo-Velázquez et al. simulated the retrofit of deep boreholes in closed-loop (Borehole Heat Exchangers) to produce cooling through a half-effect, a single-effect, a double-effect, or a triple-effect absorption chiller [11]. For geothermal driving temperatures in the range of 59–80 °C, 77–110 °C, 135–162 °C, and 180–187 °C, respectively, the cooling systems could deliver chilled water temperatures around 8 °C. In 2006, an NH₃/H₂O chiller was installed in Chena, Alaska, to produce cooling at –29 °C with a geothermal resource at 74 °C; a river at +4 °C cooled down the sorption chiller [12]. Finally, Gado et al. reviewed hybrid sorption-vapor compression cooling systems, classifying the systems as cascade, partially integrated and fully integrated systems [13]. They reported that this combination would allow an electricity consumption reduction of about 45–88% in comparison with conventional vapor compression systems.

Innovative architectures to produce cooling, heating, electricity, soft water or even hydrogen with solar and geothermal energy have been designed and modelled (see Table 1). However, these simulations are often carried out under steady-state conditions, though the performances of a single-effect absorption chiller are impacted by the fluctuating operative conditions. To the authors’ knowledge, the dynamic behavior of a single-effect geothermal absorption chiller has been poorly studied.

This paper intends to fill this knowledge gap in the Caribbean context. The present work is organized as follows (see Fig. 2): Section 2.1 describes the system and its dynamic modelling. Section 2.2 gives further insight of the system components for a preliminary, non-optimal sizing, while section 2.3 introduces the key performance indicators considered throughout the paper. Section 3 reports the results of the simulations for the preliminary sizing and a sensitivity analysis in the vicinity of this sizing, changing one or two parameters at a time. Section 4 discusses the multi-objective optimization of the system for several technical and economic scenarios.

## 2. Materials and methods

### 2.1. System modelling

#### 2.1.1. Overall system description

The designed system encompasses two geothermal wells (one for pumping, one for reinjection), a single-effect absorption chiller, a backup Air-Cooled Chiller (ACC), a Cooling Tower (CT), three-way valves (diverters and mixers), pumps, heat exchangers, and additional tanks (see Fig. 3).

The geothermal fluid extracted from a geothermal well (point 1) enters the source side of the heat exchanger HX_1 (point 2 in Fig. 3). It transfers heat to water entering the load side of HX_1 (points 6 and 4). The load side is connected to a buffer tank Tank_1 through a buried pipe, and then to the generator inlet of the absorption chiller (point 14). Tank_1 adds inertia to the model, making its numerical convergence easier.

The cooled water leaving the generator (point 15) flows to a buffer tank Tank_2 (point 18) and transfers heat through HX_2 for Domestic Hot Water (DHW) preparation.

When operated, the flow rates in pumps 3 and 5 (P_3 and P_5, respectively) are $\dot{m} = 5 \langle \dot{m}_{DHW} \rangle$, where $\langle \dot{m}_{DHW} \rangle$ is the daily mean of the required DHW flow rate and $\dot{m}_{DHW}$ the instantaneous required DHW flow rate (see §2.1.2). If the water temperature exiting the DHW tank Tank_3 (point 57) does not reach the setpoint $T_{59} = T_{sp DHW} = 40$ °C, then an electrical backup heater is turned on, consuming $\dot{Q}_{DHW}^{backup}$. Meanwhile, the intermediate temperature source of the absorption chiller is connected to a buffer tank (Tank_4) that leads to a Cooling Tower (CT).

The evaporator of the absorption chiller and the ACC are connected to the cooling tank (Tank_5), from which cooled water is distributed into the building (point 47). The set point departure in the cooling emitters is $T_{47} = 7$ °C, with water flowing back at $T_{48} = 12$ °C.

The role of the valves mix_i and div_i ($i = 1$ to 5) will be further explained in §2.2.7.

The system is modelled in TRNSYS v18 [23,24]. TRNSYS is a program for the dynamic simulation of transient systems. At every time step, TRNSYS iteratively solves the temperature and flow rate of every node of the system. Its modular structure and graphical interface allows the user to easily connect so-called “Types”, i.e. modules describing the
<table><caption>**Table 1**
Some systems using geothermal heat for cooling through absorption chillers</caption><thead><tr><th rowspan="2">Reference</th><th colspan="3">Source</th><th colspan="7">Use</th><th rowspan="2">System</th><th rowspan="2">Location</th><th rowspan="2">Findings</th><th rowspan="2">Simulation (a)</th></tr><tr><th>Geothermal</th><th>PV</th><th>Solar thermal</th><th>Dehumidification</th><th>Cooling</th><th>Heating</th><th>Electricity</th><th>Desalinization</th><th>Hydrogen</th></tr></thead><tbody><tr><td>[14]</td><td>x</td><td></td><td></td><td></td><td>x</td><td></td><td>x</td><td>x</td><td></td><td></td><td></td><td>Better prediction of KPIs with improved machine learning techniques</td><td>S</td></tr><tr><td>[15]</td><td>x</td><td></td><td>x</td><td></td><td>x</td><td>x</td><td>x</td><td></td><td>x</td><td></td><td></td><td>Payback period of 6 years</td><td>S</td></tr><tr><td>[16]</td><td>x</td><td></td><td>x</td><td></td><td>x</td><td>x</td><td>x</td><td></td><td></td><td></td><td></td><td>Overall energetic and exergetic efficiencies 53% and 37% respectively</td><td>S</td></tr><tr><td>[17]</td><td>x</td><td></td><td></td><td></td><td>x</td><td></td><td></td><td></td><td></td><td></td><td></td><td>COP ≈ 0.44; Payback period between 6 and 9 years</td><td>S</td></tr><tr><td>[18]</td><td>x</td><td></td><td></td><td>x</td><td>x</td><td>x</td><td></td><td></td><td></td><td></td><td></td><td>Heating capacity decreases by 50% with the reinjection temperature increasing from 70 to 80 °C</td><td>S</td></tr><tr><td>[19]</td><td>x</td><td></td><td></td><td></td><td>x</td><td>x</td><td>x</td><td></td><td></td><td></td><td></td><td>Maximization of exergy efficiency or minimization of exergy destruction</td><td>S</td></tr><tr><td>[20]</td><td>x</td><td>x</td><td>x</td><td></td><td>x</td><td>x</td><td>x</td><td></td><td></td><td></td><td></td><td>Lower payback with PV compared with solar thermal</td><td>D</td></tr><tr><td>[21]</td><td>x</td><td></td><td></td><td></td><td></td><td></td><td></td><td>x</td><td></td><td></td><td></td><td>Power output increased by 41%, cost decreased by 10%</td><td>S</td></tr><tr><td>[22]</td><td>x</td><td></td><td></td><td></td><td>x</td><td></td><td>x</td><td></td><td></td><td></td><td></td><td>Cost 13-20% lower than Kalina Cycle separated from absorption cooling system</td><td>S</td></tr></tbody></table>

<footnote>a : S: Under static conditions; D: under dynamic conditions</footnote>
<table><caption>**Table 1**
Some systems using geothermal heat for cooling through absorption chillers</caption><thead><tr><th rowspan="2">Reference</th><th colspan="3">Source</th><th colspan="7">Use</th><th rowspan="2">System</th><th rowspan="2">Location</th><th rowspan="2">Findings</th><th rowspan="2">Simulation (a)</th></tr><tr><th>Geothermal</th><th>PV</th><th>Solar thermal</th><th>Dehumidification</th><th>Cooling</th><th>Heating</th><th>Electricity</th><th>Desalinization</th><th>Hydrogen</th></tr></thead><tbody><tr><td>[14]</td><td>x</td><td></td><td></td><td></td><td>x</td><td></td><td>x</td><td>x</td><td></td><td></td><td></td><td>Better prediction of KPIs with improved machine learning techniques</td><td>S</td></tr><tr><td>[15]</td><td>x</td><td></td><td>x</td><td></td><td>x</td><td>x</td><td>x</td><td></td><td>x</td><td></td><td></td><td>Payback period of 6 years</td><td>S</td></tr><tr><td>[16]</td><td>x</td><td></td><td>x</td><td></td><td>x</td><td>x</td><td>x</td><td></td><td></td><td></td><td></td><td>Overall energetic and exergetic efficiencies 53% and 37% respectively</td><td>S</td></tr><tr><td>[17]</td><td>x</td><td></td><td></td><td></td><td>x</td><td></td><td></td><td></td><td></td><td></td><td></td><td>COP ≈ 0.44; Payback period between 6 and 9 years</td><td>S</td></tr><tr><td>[18]</td><td>x</td><td></td><td></td><td>x</td><td>x</td><td>x</td><td></td><td></td><td></td><td></td><td></td><td>Heating capacity decreases by 50% with the reinjection temperature increasing from 70 to 80 °C</td><td>S</td></tr><tr><td>[19]</td><td>x</td><td></td><td></td><td></td><td>x</td><td>x</td><td>x</td><td></td><td></td><td></td><td></td><td>Maximization of exergy efficiency or minimization of exergy destruction</td><td>S</td></tr><tr><td>[20]</td><td>x</td><td>x</td><td>x</td><td></td><td>x</td><td>x</td><td>x</td><td></td><td></td><td></td><td></td><td>Lower payback with PV compared with solar thermal</td><td>D</td></tr><tr><td>[21]</td><td>x</td><td></td><td></td><td></td><td></td><td></td><td></td><td>x</td><td></td><td></td><td></td><td>Power output increased by 41%, cost decreased by 10%</td><td>S</td></tr><tr><td>[22]</td><td>x</td><td></td><td></td><td></td><td>x</td><td></td><td>x</td><td></td><td></td><td></td><td></td><td>Cost 13–20% lower than Kalina Cycle separated from absorption cooling system</td><td>S</td></tr></tbody></table>

<footnote>a : S: Under static conditions; D: under dynamic conditions</footnote>
<figure><img src="image_4.png" /><figcaption>Fig. 2. Flowchart of the research reported in this paper.</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>Fig. 3. Hydraulic diagram of the studied system. “0” or “1” close to div_3 indicates the effective outlet depending on the status of microprocessor #3 (see 2.2.7).</figcaption></figure>

physical behavior of the system components, and to define control strategies. The software comes with dozens of standard Types, additional Types from the Ground Heat Pump and Storage Tank libraries edited by TESS have been used for this work [25]. As pointed out in [26], the main limitations of TRNSYS are high development costs of user-defined Types and its incapability to natively deal with hydraulics (i.e. TRNSYS computes flow rates rather than pressures and resulting flow rates). Modelica/Dymola is widely used as an alternative, though the computational costs are reported to be higher [27]. Here the time step is

$\Delta t = 7.5$ min and the system is simulated for 1 year, after a simulated few days have been discarded to account for the initial transient behavior of the building. Note that all Types except the buried pipes (Type951) and tanks (Type1534) assume the components have no inertia, and internal transient phenomena are overlooked.

### 2.1.2. Thermal energy requirement

A 5173 m² (floor area) hotel located in Fort-de-France, Martinique, France, welcoming up to 365 guests was considered (see Supplementary
<figure><img src="image_4.png" /><figcaption>Fig. 2. Flowchart of the research reported in this paper.</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>Fig. 3. Hydraulic diagram of the studied system. “0” or “1” close to div_3 indicates the effective outlet depending on the status of microprocessor #3 (see 2.2.7).</figcaption></figure>

physical behavior of the system components, and to define control strategies. The software comes with dozens of standard Types, additional Types from the Ground Heat Pump and Storage Tank libraries edited by TESS have been used for this work [25]. As pointed out in [26], the main limitations of TRNSYS are high development costs of user-defined Types and its incapability to natively deal with hydraulics (i.e. TRNSYS computes flow rates rather than pressures and resulting flow rates). Modelica/Dymola is widely used as an alternative, though the computational costs are reported to be higher [27]. Here the time step is

$\Delta t = 7.5$ min and the system is simulated for 1 year, after a simulated few days have been discarded to account for the initial transient behavior of the building. Note that all Types except the buried pipes (Type951) and tanks (Type1534) assume the components have no inertia, and internal transient phenomena are overlooked.

### 2.1.2. Thermal energy requirement

A 5173 m² (floor area) hotel located in Fort-de-France, Martinique, France, welcoming up to 365 guests was considered (see Supplementary
Material for further description). The tropical climate consists of two main seasons: a relatively mild and dry season from January to mid-April, and a hot and wet season from July to November (see Fig. 4). The hotel was modelled in TRNSYS considering weather data forecast by 2050 and the RCP4.5 scenario of the Intergovernmental Panel on Climate Change. The cooling requirement was estimated to $Q_{cooling} = 570.5$ MWh/y with a peak load $Q_{cooling}^{max}$ of 104.3 kW. The monthly cooling need is minimum in January at 43.6 MWh and reaches a maximum of 56.3 MWh in August. The Domestic Hot Water (DHW) need was estimated to $Q_{DHW} = 90.0$ MWh/y, assuming every guest requires 125 L/day (that is $\langle \dot{m}_{DHW} \rangle = 5.2$ kg.h$^{-1}$) at $T_{sp} = T_{59} = 40$ °C, with hourly modulations, provided that the mains water varies between 30.0 °C in January and 33.3 °C in August. The need for cooling ($Q_{cooling}$) in 2050 is expected to be 9% higher than that of 2020, whereas the need for DHW ($Q_{DHW}$) is expected to decrease by 11.2% in the same period of time.

## 2.2. Components

The constitutive parameters of the components are reported in Table 2. Altogether, the values reported in Table 2 define a “preliminary sizing” whose simulation is reported in section 3.1. The preliminary sizing might not be optimal, but illustrate the system behavior. The system optimization is addressed in section 4.

### 2.2.1. Geothermal resource

The geothermal resource is characterized by an available (constant) mass flow rate $\dot{m}_{GTH} = \dot{m}_1 = \dot{m}_2$ and a temperature $T_{GTH} = T_1 = T_2$, assuming a volumetric fluid heat capacity of

4.15 MJ.K$^{-1}$.m$^{-3}$ [28]. The counterflow heat exchanger HX_1 couples the geothermal mass flow rate $\dot{m}_{GTH}$ (the source side) from the generator mass flow rate $\dot{m}_{gen}$ (the load side). For a given geothermal flow rate, an increase in the cold stream mass flow rate ($\dot{m}_{gen}$) leads to an increase in the exchanger heat rate (see Fig. 5a). This, however, leads to a decrease in the temperature of the fluid stream that goes back to the generator (as illustrated in Fig. 5b), causing a decrease in the absorption chiller’s thermal COP. For this reason, there is an optimal ratio $\dot{m}_{GTH}/\dot{m}_{gen}$, as discussed in sections 3.2 and 4. Note that in Fig. 5a, the heat losses through the buried pipe are overlooked so that $T_4 = T_{14}$ and $T_6 = T_{15}$. As $\dot{m}_{GTH}/\dot{m}_{gen}$ varies, the heat transfer coefficient of the exchanger is computed with the NTU-$\epsilon$ method to ensure a pinch of $\delta T = 2$ °C [29], a typical value for geothermal heat exchangers. The inequality $\dot{m}_{GTH} \le \dot{m}_{gen}$ implies that $T_3 - T_6 = \delta T$. A cold stream temperature difference $T_4 - T_6 = 5$ °C is applied, as this is typical for the generator of the absorption chiller considered in 2.2.3.

<figure><img src="image_6.png" /><figcaption>Fig. 4. Monthly boxplots forecast of (a) dry bulb and (b) wet bulb temperatures at Fort-de-France in 2050 according to RCP4.5 scenario of the IPCC</figcaption></figure>

### 2.2.2. Buried pipes

Insulated twin pipes of length L are buried at a depth of 1.0 m (see Fig. 6). These pipes convey hot water from the geothermal heat exchanger to the absorption chiller. Prior to the simulation, the inner diameter of the pipes $d_{int,p}$ is dimensioned to ensure a linear pressure drop $\Delta \rho$ (see Eq. (1)) per pipe of 100 Pa.m$^{-1}$.

$$ \Delta \rho' = \frac{\Delta \rho}{L} = \frac{f \rho}{2 d_{int,p}} v^2 \quad (1) $$

With $v = \frac{\pi \dot{m}_{4-2}}{4 \rho}$, $d_{int,p} = \frac{\pi \dot{m}_{3-5}}{4 \rho}$, $d_{ext,p} = \frac{\pi \dot{m}_{5-7}}{4 \rho}$ the fluid velocity [m.s$^{-1}$], $\rho$ the fluid density [kg.m$^{-3}$] and $f$ the friction factor [-]. The friction factor depends on the liquid’s flow regime, determined by the Reynolds number $Re$ (see Eq. (2)). If $Re < 3000$, the friction factor can be calculated using Eq. (3), otherwise, it can be calculated using Eq. (4).

$$ Re = \frac{\rho v d_{int,p}}{\mu} \quad (2) $$

$$ f_{lam} = \frac{64}{Re} \quad (3) $$

$$ \frac{1}{\sqrt{f_{nurb}}} = -2\log\left(\frac{\epsilon}{3.7 d_{int,p}} + \frac{2.51}{Re \sqrt{f_{nurb}}}\right) \quad (4) $$

The Standard Dimensional Ratio (SDR), i.e., the ratio of the outside pipe diameter $d_{ext,p}$ to the wall thickness $e_p$, is assumed to be 11. Therefore, $d_{ext,p} = \frac{d_{int,p}}{1 - \frac{d_{int,p}}{SDR}}$ and $e_p = \frac{d_{ext,p} - d_{int,p}}{2}$. Besides, the casing diameter $d_{casing}$ and the center-to-center pipe spacing $a_p$ are derived from geometric ratios as $d_{casing} = d_{casing}^* \cdot d_{ext,p}$ and $a_p = a^* \cdot d_{ext,p}$ with $d_{casing}^* = 3$ and $a^* = 1.5$ (see Fig. 6). The thermal conductivities of the pipe material and the fill insulation are 0.4 W.K$^{-1}$.m$^{-1}$ and 0.04 W.K$^{-1}$.m$^{-1}$, respectively. The soil thermal conductivity and heat capacity are assumed to be 1.8 W.K$^{-1}$.m$^{-1}$ and 2.10 MJ.K$^{-1}$.m$^{-1}$ [30]. For the preliminary sizing, a negligible pipe length of 1.0 m is considered. In other words, the absorption chiller is right at the edge of the geothermal well.

As the variations of monthly median values of $T_{dry bulb}$ are only about 3 °C, it is assumed that the annual temperature variations at a depth of 1.0 m are damped. Type951 considers that the pipe is encompassed in an equivalent cylinder of soil whose diameter equals the pipe depth and that a temperature is applied on the cylinder boundary, emulating the temperature at the ground surface. Here a constant temperature of 26 °C has been applied, which is somehow lower than the air dry bulb temperature used for the building simulation (see Fig. 4). However, the discrepancy shall not significantly affect the heat losses from the buried pipe since the heat-carrier fluid is much warmer than the air (typically, the temperature of the heat-carrier fluid is a few °C below the

<figure><img src="image_7.png" /></figure>
Material for further description). The tropical climate consists of two main seasons: a relatively mild and dry season from January to mid-April, and a hot and wet season from July to November (see Fig. 4). The hotel was modelled in TRNSYS considering weather data forecast by 2050 and the RCP4.5 scenario of the Intergovernmental Panel on Climate Change. The cooling requirement was estimated to $Q_{cooling} = 570.5$ MWh/y with a peak load $Q_{cooling}^{max}$ of 104.3 kW. The monthly cooling need is minimum in January at 43.6 MWh and reaches a maximum of 56.3 MWh in August. The Domestic Hot Water (DHW) need was estimated to $Q_{DHW} = 90.0$ MWh/y, assuming every guest requires 125 L/day (that is $\langle \dot{m}_{DHW} \rangle = 5.2$ kg.h$^{-1}$) at $T_{sp} = 59 = 40$ °C, with hourly modulations, provided that the mains water varies between 30.0 °C in January and 33.3 °C in August. The need for cooling ($Q_{cooling}$) in 2050 is expected to be 9% higher than that of 2020, whereas the need for DHW ($Q_{DHW}$) is expected to decrease by 11.2% in the same period of time.

## 2.2. Components

The constitutive parameters of the components are reported in Table 2. Altogether, the values reported in Table 2 define a “preliminary sizing” whose simulation is reported in section 3.1. The preliminary sizing might not be optimal, but illustrate the system behavior. The system optimization is addressed in section 4.

### 2.2.1. Geothermal resource

The geothermal resource is characterized by an available (constant) mass flow rate $\dot{m}_{GTH} = \dot{m}_1 = \dot{m}_2$ and a temperature $T_{GTH} = T_1 = T_2$, assuming a volumetric fluid heat capacity of

4.15 MJ.K$^{-1}$.m$^{-3}$ [28]. The counterflow heat exchanger HX_1 couples the geothermal mass flow rate $\dot{m}_{GTH}$ (the source side) from the generator mass flow rate $\dot{m}_{gen}$ (the load side). For a given geothermal flow rate, an increase in the cold stream mass flow rate ($\dot{m}_{gen}$) leads to an increase in the exchanger heat rate (see Fig. 5a). This, however, leads to a decrease in the temperature of the fluid stream that goes back to the generator (as illustrated in Fig. 5b), causing a decrease in the absorption chiller’s thermal COP. For this reason, there is an optimal ratio $\dot{m}_{GTH}/\dot{m}_{gen}$, as discussed in sections 3.2 and 4. Note that in Fig. 5a, the heat losses through the buried pipe are overlooked so that $T_4 = T_{14}$ and $T_6 = T_{15}$. As $\dot{m}_{GTH}/\dot{m}_{gen}$ varies, the heat transfer coefficient of the exchanger is computed with the NTU-$\epsilon$ method to ensure a pinch of $\delta T = 2$ °C [29], a typical value for geothermal heat exchangers. The inequality $\dot{m}_{GTH} \le \dot{m}_{gen}$ implies that $T_3 - T_6 = \delta T$. A cold stream temperature difference $T_4 - T_6 = 5$ °C is applied, as this is typical for the generator of the absorption chiller considered in 2.2.3.

<figure><img src="image_6.png" /><figcaption>Fig. 4. Monthly boxplots forecast of (a) dry bulb and (b) wet bulb temperatures at Fort-de-France in 2050 according to RCP4.5 scenario of the IPCC</figcaption></figure>

### 2.2.2. Buried pipes

Insulated twin pipes of length L are buried at a depth of 1.0 m (see Fig. 6). These pipes convey hot water from the geothermal heat exchanger to the absorption chiller. Prior to the simulation, the inner diameter of the pipes $d_{int,p}$ is dimensioned to ensure a linear pressure drop $\Delta\rho$ (see Eq. (1)) per pipe of 100 Pa.m$^{-1}$.

$$ \Delta\rho' = \frac{\Delta\rho}{L} = \frac{f\rho}{2d_{int,p}}v^2 \quad (1) $$

With $v = \frac{\pi \dot{m}_{4-2}}{4 \rho}$, $\frac{d_{int,p}^2}{4} = \frac{\pi \dot{m}_{3-5}}{4 \rho}$, $\frac{d_{int,p}^2}{4}$ the fluid velocity [m.s$^{-1}$], $\rho$ the fluid density [kg.m$^{-3}$] and $f$ the friction factor [-]. The friction factor depends on the liquid’s flow regime, determined by the Reynolds number $Re$ (see Eq. (2)), if $Re < 3000$, the friction factor can be calculated using Eq. (3), otherwise, it can be calculated using Eq. (4).

$$ Re = \frac{\rho v d_{int,p}}{\mu} \quad (2) $$

$$ f_{lam} = \frac{64}{Re} \quad (3) $$

$$ \frac{1}{\sqrt{f_{nurb}}} = -2\log\left(\frac{\varepsilon}{3.7d_{int,p}} + \frac{2.51}{Re\sqrt{f_{nurb}}}\right) \quad (4) $$

The Standard Dimensional Ratio (SDR), i.e., the ratio of the outside pipe diameter $d_{ext,p}$ to the wall thickness $e_p$, is assumed to be 11. Therefore, $d_{ext,p} = \frac{d_{int,p}}{1 - \frac{d_{int,p}}{SDR}}$ and $e_p = \frac{d_{ext,p} - d_{int,p}}{2}$. Besides, the casing diameter $d_{casing}$ and the center-to-center pipe spacing $a_p$ are derived from geometric ratios as $d_{casing} = d_{casing}^* \cdot d_{ext,p}$ and $a_p = a^* \cdot d_{ext,p}$ with $d_{casing}^* = 3$ and $a^* = 1.5$ (see Fig. 6). The thermal conductivities of the pipe material and the fill insulation are 0.4 W.K$^{-1}$.m$^{-1}$ and 0.04 W.K$^{-1}$.m$^{-1}$, respectively. The soil thermal conductivity and heat capacity are assumed to be 1.8 W.K$^{-1}$.m$^{-1}$ and 2.10 MJ.K$^{-1}$.m$^{-1}$ [30]. For the preliminary sizing, a negligible pipe length of 1.0 m is considered. In other words, the absorption chiller is right at the edge of the geothermal well.

As the variations of monthly median values of $T_{dry bulb}$ are only about 3 °C, it is assumed that the annual temperature variations at a depth of 1.0 m are damped. Type951 considers that the pipe is encompassed in an equivalent cylinder of soil whose diameter equals the pipe depth and that a temperature is applied on the cylinder boundary, emulating the temperature at the ground surface. Here a constant temperature of 26 °C has been applied, which is somehow lower than the air dry bulb temperature used for the building simulation (see Fig. 4). However, the discrepancy shall not significantly affect the heat losses from the buried pipe since the heat-carrier fluid is much warmer than the air (typically, the temperature of the heat-carrier fluid is a few °C below the

<figure><img src="image_7.png" /></figure>
<table><caption>**Table 2**

Constitutive parameters of the components and values used for the preliminary sizing.</caption><thead><tr><th>Component</th><th>TRNSYS Type</th><th>Parameter</th><th>Value</th></tr></thead><tbody><tr><td rowspan="4">Geothermal resource</td><td rowspan="4">Equation</td><td>Temperature (T<sub>GTH</sub>)</td><td>80 °C</td></tr><tr><td>Mass flow rate (ṁ<sub>GTH</sub>)</td><td>25.84 × 10<sup>3</sup> kg·h<sup>-1</sup></td></tr><tr><td>Specific mass flow rate (ṁ<sub>GTH</sub>·Q<sub>sorp</sub><sup>max</sup>)</td><td>68.57 kg·MJ<sup>-1</sup></td></tr><tr><td>Length (L)</td><td>1 m</td></tr><tr><td rowspan="7">Buried pipes</td><td rowspan="7">951</td><td>Nominal linear pressure drop (Δγ<sub>p</sub>) per pipe</td><td>100 Pa·m<sup>-1</sup></td></tr><tr><td>Inner diameter of pipes (d<sub>int,p</sub>)</td><td>6.67 cm</td></tr><tr><td>Outer diameter of pipes (d<sub>ext,p</sub>)</td><td>8.15 cm</td></tr><tr><td>Center-to-center pipe spacing (a<sub>p</sub>)</td><td>10.90 cm</td></tr><tr><td>Diameter of casing material (d<sub>casing</sub>)</td><td>24.45 cm</td></tr><tr><td>Normalized center-to-center pipe spacing (a<sup>*</sup> = a/d<sub>ext,p</sub>)</td><td>1.5</td></tr><tr><td>Normalized casing diameter (d<sub>casing</sub><sup>*</sup> = d<sub>casing</sub>/d<sub>ext,p</sub>)</td><td>3.0</td></tr><tr><td rowspan="4">Absorption chiller</td><td rowspan="4">127</td><td>Nominal cooling capacity Q<sub>sorp</sub><sup>ev</sup></td><td>104.3 kW</td></tr><tr><td>Normalized nominal cooling power (Q<sub>sorp</sub><sup>ev</sup> = Q<sub>sorp</sub><sup>max</sup>/Q<sub>cooling</sub>)</td><td>1</td></tr><tr><td>Auxiliary electrical consumption (Q<sub>sorp</sub><sup>elec</sup> (see eq. (9)))</td><td>0.32 kW</td></tr><tr><td>Chiller's total mass M<sub>sorp</sub> (see eq. (10))</td><td>1430 kg</td></tr><tr><td rowspan="6">Cooling tower</td><td rowspan="6">162</td><td>Mass flow rate at generator (ṁ<sub>sorp</sub><sup>gen</sup>)</td><td>25.84 × 10<sup>3</sup> kg·h<sup>-1</sup></td></tr><tr><td>Mass flow rate at the evaporator (ṁ<sub>sorp</sub><sup>ev</sup>)</td><td>16.43 × 10<sup>3</sup> kg·h<sup>-1</sup></td></tr><tr><td>Mass flow rate at the chiller's heat sink (ṁ<sub>air,CT</sub><sup>max</sup>)</td><td>54.93 × 10<sup>3</sup> kg·h<sup>-1</sup></td></tr><tr><td>Mass transfer constant (c)</td><td>1.3</td></tr><tr><td>Mass transfer exponent (n)</td><td>0.6</td></tr><tr><td>Maximum air mass flow rate (ṁ<sub>air,CT</sub><sup>max</sup>)</td><td>54.93 × 10<sup>3</sup> kg·h<sup>-1</sup></td></tr><tr><td rowspan="5">Air-cooled chiller</td><td rowspan="5">118</td><td>Water mass flow rate (ṁ<sub>w,CT</sub>)</td><td>54.93 × 10<sup>3</sup> kg·h<sup>-1</sup></td></tr><tr><td>Fan electrical consumption at maximum air flow (W<sub>el,fan</sub><sup>max</sup>)</td><td>4.23 kW</td></tr><tr><td>Pump power (W<sub>pump,CT</sub>)</td><td>1.66 kW</td></tr><tr><td>Nominal cooling capacity Q<sub>ACC</sub><sup>ev</sup></td><td>104.3 kW</td></tr><tr><td>Volume (V<sub>1</sub>)</td><td>12.92 m<sup>3</sup></td></tr><tr><td rowspan="2">Tank_1</td><td rowspan="2">1534</td><td>Equivalent storage duration (Δt<sub>1</sub>)</td><td>0.25 h</td></tr><tr><td>Volume (V<sub>3</sub>)</td><td>0.48 m<sup>3</sup></td></tr><tr><td rowspan="2">Tank_3</td><td rowspan="2">1534</td><td>Equivalent storage duration (Δt<sub>3</sub>)</td><td>0.25 h</td></tr><tr><td>Volume (V<sub>4</sub>)</td><td>27.34 m<sup>3</sup></td></tr><tr><td rowspan="2">Tank_4</td><td rowspan="2">1534</td><td>Equivalent storage duration (Δt<sub>4</sub>)</td><td>0.25 h</td></tr><tr><td>Volume (V<sub>5</sub>)</td><td>8.18 m<sup>3</sup></td></tr><tr><td rowspan="2">Tank_5</td><td rowspan="2">1534</td><td>Equivalent storage duration (Δt<sub>5</sub>)</td><td>0.5 h</td></tr><tr><td></td><td></td></tr></tbody></table>

geothermal fluid temperature, see Fig. 10c).

### 2.2.3. Absorption chiller

A black box model is used to characterize the absorption chiller's behavior. Data from the Yazaki manufacturer's catalogues for their SC series (nominal cooling capacities ($\dot{Q}_{sorp}^{ev}$) from 35.2 kW to 175 kW) was used for the model fitting [31]. The entire dataset includes 832 operating conditions in the temperature ranges of 5°C ≤ T<sub>ev,out</sub> ≤ 13°C, 24°C ≤ T<sub>int,in</sub> ≤ 32°C, and 70°C ≤ T<sub>gen,in</sub> ≤ 95°C. The nominal condition of these models is defined at T<sub>nom ev,out</sub> = 7°C, T<sub>nom int,in</sub> = 31°C, and T<sub>nom gen,in</sub> = 88°C for a thermal COP<sub>th</sub> of 0.700. Note that at these nominal conditions, the thermal COP reaches 38.0% of the maximum theoretical COP

(Carnot COP), defined in Eq. (5) [32]:

$$ COP_{th}^{Carnot} = \left( \frac{T_{gen,in}^{nom} - T_{int,in}^{nom}}{T_{gen,in}^{nom}} \right) \cdot \left( \frac{T_{ev,out}^{nom}}{T_{int,in}^{nom} - T_{ev,out}^{nom}} \right) \quad (5) $$

With the numerical application of Eq. (5) being $COP_{th}^{Carnot} = (\frac{88-31}{273.15+88} \cdot (\frac{273.15+7}{31-7}) = 1.84$. In order to regroup the different commercial models in a single dataset, the heat rate at the evaporator $\dot{Q}_{sorp}^{ev}$ and generator $Q_{sorp}^{gen}$ were normalized for their respective values at the nominal conditions ($\dot{Q}_{sorp}^{ev}$) and ($\dot{Q}_{sorp}^{gen}$). Finally, a Gaussian Process (GP) regression technique was used to model the cooling rate as a function of T<sub>ev,out</sub>, T<sub>int,in</sub> and T<sub>gen,in</sub> (see Appendix A for theoretical background). The model results are in reasonably good agreement with the dataset (see Fig. 7a), as indicated by the 5-fold cross-validation Root Mean Square Errors (RMSE) of 0.055 and 0.061 for the evaporator and generator normalized powers, respectively.

Using a subset of the dataset restricted to machines with ($Q_{sorp}^{ev}$)$_{nom}$ = 35.2 kW, the authors had previously derived linear fits of $Q_{sorp}^{ev}$ and $\dot{Q}_{sorp}^{gen}$ as functions of T<sub>ev,out</sub>, T<sub>int,in</sub> and T<sub>gen,in</sub> [33]. After elementary manipulations, they can be expressed as:

$$ \frac{\dot{Q}_{sorp}^{ev}}{(\dot{Q}_{sorp}^{ev})_{nom}} = -0.0795 + 0.0170 \cdot T_{ev,out} - 0.0883 \cdot T_{int,in} + 0.0414 \cdot T_{gen,in} \quad (6) $$

$$ \frac{\dot{Q}_{sorp}^{gen}}{(\dot{Q}_{sorp}^{gen})_{nom}} = -0.0157 + 0.0160 \cdot T_{ev,out} - 0.0832 \cdot T_{int,in} + 0.0390 \cdot T_{gen,in} \quad (7) $$

In Eq. (6) and (7), temperatures are expressed in °C. The RMSE calculated over the full dataset are then respectively 0.135 for eq. (6) and 0.101 for eq. (7). In other words, the newly fitted GPs outperform the linear fits.

When activated, the absorption chiller (Type 127) modulates the cooling heat rate $\dot{Q}_{sorp}^{ev}$ to ensure it meets the desired set point (see section 2.2.7). The resulting partial load decreases the thermal COP of the chiller, as observed in Fig. 7b.

Crystallization is a common risk in H₂O/LiBr systems. In order to prevent any crystallization risk in the simulated system, Eq. (8) was developed to indicate the maximum inlet generator temperature (function of the chilled water and intermediate temperatures) that can be employed. This equation has been derived from a thermodynamic model of the absorption chiller (assuming steady-state, thermodynamic equilibrium conditions, and a pinch of 5 °C between the internal fluids and the heat transfer fluids) [34], the equilibrium thermodynamic properties of the H₂O/LiBr couple [35] and the crystallization limit of the solution [36]:

$$ T_{gen,in}^{max} = \min(95, 58.67 + 0.121 \cdot T_{ev,out} + 1.215 \cdot T_{int,in}) \quad (8) $$

The inlet generator temperature is modulated by the recirculation valves mix_1 and div_1. Besides, the following equations for the electric power required by the absorption chiller ($\dot{W}_{sorp}^{el}$) and the chiller's mass $M_{abs}$ are deduced from the manufacturer datasheets [31]:

$$ \dot{W}_{sorp}^{el} = 0.334 \cdot \dot{Q}_{sorp}^{ev} \quad (9) $$

$$ M_{abs} = 0.0162 \cdot \dot{Q}_{sorp}^{ev} \quad (10) $$

Note that Eq. (9) $\dot{W}_{sorp}^{el}$ accounts for the electric consumption of the internal solution circulation pump and electronic devices. The chiller's mass will be used to estimate the chiller's GWP and investment and
<table><caption>**Table 2**

Constitutive parameters of the components and values used for the preliminary sizing.</caption><thead><tr><th>Component</th><th>TRNSYS Type</th><th>Parameter</th><th>Value</th></tr></thead><tbody><tr><td rowspan="3">Geothermal resource</td><td rowspan="3">Equation</td><td>Temperature (T<sub>GTH</sub>)</td><td>80 °C</td></tr><tr><td>Mass flow rate (ṁ<sub>GTH</sub>)</td><td>25.84 × 10<sup>3</sup> kg·h<sup>-1</sup></td></tr><tr><td>Specific mass flow rate (ṁ<sub>GTH</sub>·Q<sub>sorp</sub><sup>max</sup>·Q<sub>cooling</sub>)</td><td>68.57 kg·MJ<sup>-1</sup></td></tr><tr><td rowspan="7">Buried pipes</td><td rowspan="7">951</td><td>Length (L)</td><td>1 m</td></tr><tr><td>Nominal linear pressure drop (Δ<sub>γ</sub>) per pipe</td><td>100 Pa·m<sup>-1</sup></td></tr><tr><td>Inner diameter of pipes (d<sub>int,p</sub>)</td><td>6.67 cm</td></tr><tr><td>Outer diameter of pipes (d<sub>ext,p</sub>)</td><td>8.15 cm</td></tr><tr><td>Center-to-center pipe spacing (a<sub>p</sub>)</td><td>10.90 cm</td></tr><tr><td>Diameter of casing material (d<sub>casing</sub>)</td><td>24.45 cm</td></tr><tr><td>Normalized center-to-center pipe spacing (a<sup>*</sup> = a/d<sub>ext,p</sub>)</td><td>1.5</td></tr><tr><td>Normalized casing diameter (d<sub>casing</sub><sup>*</sup> = d<sub>casing</sub>/d<sub>ext,p</sub>)</td><td>3.0</td></tr><tr><td rowspan="2">Absorption chiller</td><td rowspan="2">127</td><td>Nominal cooling capacity Q<sub>sorp</sub><sup>ev</sup></td><td>104.3 kW</td></tr><tr><td>Normalized nominal cooling power (Q<sub>sorp</sub><sup>ev</sup> = Q<sub>sorp</sub><sup>max</sup>/Q<sub>cooling</sub>)</td><td>1</td></tr><tr><td rowspan="10">Cooling tower</td><td rowspan="10">162</td><td>Auxiliary electrical consumption (Q<sub>sorp</sub><sup>elec</sup> (see eq. (9)))</td><td>0.32 kW</td></tr><tr><td>Chiller's total mass M<sub>sorp</sub> (see eq. (10))</td><td>1430 kg</td></tr><tr><td>Mass flow rate at generator (ṁ<sub>sorp</sub><sup>gen</sup>)</td><td>25.84 × 10<sup>3</sup> kg·h<sup>-1</sup></td></tr><tr><td>Mass flow rate at the evaporator (ṁ<sub>sorp</sub><sup>ev</sup>)</td><td>16.43 × 10<sup>3</sup> kg·h<sup>-1</sup></td></tr><tr><td>Mass flow rate at the chiller's heat sink (ṁ<sub>w,CT</sub><sup>max</sup>)</td><td>54.93 × 10<sup>3</sup> kg·h<sup>-1</sup></td></tr><tr><td>Mass transfer constant (c)</td><td>1.3</td></tr><tr><td>Mass transfer exponent (n)</td><td>0.6</td></tr><tr><td>Maximum air mass flow rate (ṁ<sub>air,CT</sub><sup>max</sup>)</td><td>54.93 × 10<sup>3</sup> kg·h<sup>-1</sup></td></tr><tr><td>Water mass flow rate (ṁ<sub>w,CT</sub>)</td><td>54.93 × 10<sup>3</sup> kg·h<sup>-1</sup></td></tr><tr><td>Fan electrical consumption at maximum air flow (W<sub>el,fan</sub><sup>max</sup>)</td><td>4.23 kW</td></tr><tr><td rowspan="2">Air-cooled chiller</td><td rowspan="2">118</td><td>Pump power (W<sub>pump,CT</sub>)</td><td>1.66 kW</td></tr><tr><td>Nominal cooling capacity Q<sub>ACC</sub><sup>ev</sup></td><td>104.3 kW</td></tr><tr><td>Tank_1</td><td>1534</td><td>Volume (V<sub>1</sub>)</td><td>12.92 m<sup>3</sup></td></tr><tr><td rowspan="2">Tank_3</td><td rowspan="2">1534</td><td>Equivalent storage duration (Δt<sub>1</sub>)</td><td>0.25 h</td></tr><tr><td>Volume (V<sub>3</sub>)</td><td>0.48 m<sup>3</sup></td></tr><tr><td rowspan="2">Tank_4</td><td rowspan="2">1534</td><td>Equivalent storage duration (Δt<sub>3</sub>)</td><td>0.25 h</td></tr><tr><td>Volume (V<sub>4</sub>)</td><td>27.34 m<sup>3</sup></td></tr><tr><td rowspan="2">Tank_5</td><td rowspan="2">1534</td><td>Equivalent storage duration (Δt<sub>4</sub>)</td><td>0.25 h</td></tr><tr><td>Volume (V<sub>5</sub>)</td><td>8.18 m<sup>3</sup></td></tr><tr><td></td><td></td><td>Equivalent storage duration (Δt<sub>5</sub>)</td><td>0.5 h</td></tr></tbody></table>

geothermal fluid temperature, see Fig. 10c).

### 2.2.3. Absorption chiller

A black box model is used to characterize the absorption chiller's behavior. Data from the Yazaki manufacturer's catalogues for their SC series (nominal cooling capacities ($\dot{Q}_{sorp}^{ev}$) from 35.2 kW to 175 kW) was used for the model fitting [31]. The entire dataset includes 832 operating conditions in the temperature ranges of 5°C ≤ T<sub>ev,out</sub> ≤ 13°C, 24°C ≤ T<sub>int,in</sub> ≤ 32°C, and 70°C ≤ T<sub>gen,in</sub> ≤ 95°C. The nominal condition of these models is defined at T<sub>nom ev,out</sub> = 7°C, T<sub>nom int,in</sub> = 31°C, and T<sub>nom gen,in</sub> = 88°C for a thermal COP<sub>th</sub> of 0.700. Note that at these nominal conditions, the thermal COP reaches 38.0% of the maximum theoretical COP

(Carnot COP), defined in Eq. (5) [32]:

$$ COP_{th}^{Carnot} = \left( \frac{T_{gen,in}^{nom} - T_{int,in}^{nom}}{T_{gen,in}^{nom}} \right) \cdot \left( \frac{T_{ev,out}^{nom}}{T_{int,in}^{nom} - T_{ev,out}^{nom}} \right) \quad (5) $$

With the numerical application of Eq. (5) being $COP_{th}^{Carnot} = (\frac{88-31}{273.15+88} \cdot (\frac{273.15+7}{31-7}) = 1.84$. In order to regroup the different commercial models in a single dataset, the heat rate at the evaporator $\dot{Q}_{sorp}^{ev}$ and generator $Q_{sorp}^{gen}$ were normalized for their respective values at the nominal conditions ($\dot{Q}_{sorp}^{ev}$) and ($\dot{Q}_{sorp}^{gen}$). Finally, a Gaussian Process (GP) regression technique was used to model the cooling rate as a function of T<sub>ev,out</sub>, T<sub>int,in</sub> and T<sub>gen,in</sub> (see Appendix A for theoretical background). The model results are in reasonably good agreement with the dataset (see Fig. 7a), as indicated by the 5-fold cross-validation Root Mean Square Errors (RMSE) of 0.055 and 0.061 for the evaporator and generator normalized powers, respectively.

Using a subset of the dataset restricted to machines with ($Q_{sorp}^{ev}$)$_{nom}$ = 35.2 kW, the authors had previously derived linear fits of $Q_{sorp}^{ev}$ and $\dot{Q}_{sorp}^{gen}$ as functions of T<sub>ev,out</sub>, T<sub>int,in</sub> and T<sub>gen,in</sub> [33]. After elementary manipulations, they can be expressed as:

$$ \frac{\dot{Q}_{sorp}^{ev}}{(Q_{sorp}^{ev})_{nom}} = -0.0795 + 0.0170 \cdot T_{ev,out} - 0.0883 \cdot T_{int,in} + 0.0414 \cdot T_{gen,in} \quad (6) $$

$$ \frac{\dot{Q}_{sorp}^{gen}}{(\dot{Q}_{sorp}^{gen})_{nom}} = -0.0157 + 0.0160 \cdot T_{ev,out} - 0.0832 \cdot T_{int,in} + 0.0390 \cdot T_{gen,in} \quad (7) $$

In Eq. (6) and (7), temperatures are expressed in °C. The RMSE calculated over the full dataset are then respectively 0.135 for eq. (6) and 0.101 for eq. (7). In other words, the newly fitted GPs outperform the linear fits.

When activated, the absorption chiller (Type 127) modulates the cooling heat rate $\dot{Q}_{sorp}^{ev}$ to ensure it meets the desired set point (see section 2.2.7). The resulting partial load decreases the thermal COP of the chiller, as observed in Fig. 7b.

Crystallization is a common risk in H<sub>2</sub>O/LiBr systems. In order to prevent any crystallization risk in the simulated system, Eq. (8) was developed to indicate the maximum inlet generator temperature (function of the chilled water and intermediate temperatures) that can be employed. This equation has been derived from a thermodynamic model of the absorption chiller (assuming steady-state, thermodynamic equilibrium conditions, and a pinch of 5 °C between the internal fluids and the heat transfer fluids) [34], the equilibrium thermodynamic properties of the H<sub>2</sub>O/LiBr couple [35] and the crystallization limit of the solution [36]:

$$ T_{gen,in}^{max} = \min(95, 58.67 + 0.121 \cdot T_{ev,out} + 1.215 \cdot T_{int,in}) \quad (8) $$

The inlet generator temperature is modulated by the recirculation valves mix_1 and div_1. Besides, the following equations for the electric power required by the absorption chiller ($\dot{W}_{sorp}^{el}$) and the chiller's mass $M_{abs}$ are deduced from the manufacturer datasheets [31]:

$$ \dot{W}_{sorp}^{el} = 0.334 \cdot \dot{Q}_{sorp}^{ev} \quad (9) $$

$$ M_{abs} = 0.0162 \cdot \dot{Q}_{sorp}^{ev} \quad (10) $$

Note that Eq. (9) $\dot{W}_{sorp}^{el}$ accounts for the electric consumption of the internal solution circulation pump and electronic devices. The chiller's mass will be used to estimate the chiller's GWP and investment and
<figure><img src="image_8.png" /><figcaption>Fig. 5. Illustration of (a) HX_1 Heat rate and (b) i/o fluid streams' temperatures as a function of the ratio of the geothermal mass flow rate $\dot{m}_{GTH}$ to the generator mass flow rate $\dot{m}_{gen}$. T$_{GTH}$ = 80 °C; T$_{3}$ – T$_{6}$ = 2 °C; T$_{4}$ – T$_{6}$ = 5 °C.</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>Fig. 6. Cross-sectional view of the twin pipes in the insulating casing.</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>Fig. 7. Yazaki SC series absorption chillers modelling results. (a) Comparison of the normalized evaporator and generator heat rates $\dot{Q}_{sorp}^{ev}$ and $\dot{Q}_{sorp}^{gen}$ and (b) effect of the partial load on the thermal COP.</figcaption></figure>
<figure><img src="image_8.png" /><figcaption>Fig. 5. Illustration of (a) HX_1 Heat rate and (b) i/o fluid streams' temperatures as a function of the ratio of the geothermal mass flow rate $\dot{m}_{GTH}$ to the generator mass flow rate $\dot{m}_{gen}$. T$_{GTH}$ = 80 °C; T$_{3}$ – T$_{6}$ = 2 °C; T$_{4}$ – T$_{6}$ = 5 °C.</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>Fig. 6. Cross-sectional view of the twin pipes in the insulating casing.</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>Fig. 7. Yazaki SC series absorption chillers modelling results. (a) Comparison of the normalized evaporator and generator heat rates $\dot{Q}_{sorp}^{ev}$ and $\dot{Q}_{sorp}^{gen}$ and (b) effect of the partial load on the thermal COP.</figcaption></figure>
maintenance costs (see Table 8).

### 2.2.4. Cooling tower

In a direct-contact wet Cooling Tower (CT), a hot water stream is in direct contact with an air stream. Water, which is injected at the top of the CT through an exchange surface enhancement distribution method (e.g., spray nozzles), flows downwards as it is cooled through sensible and latent heat transfers. The cooled water is collected into a sump before leaving the CT. The air may enter a CT in two different flow configurations: counterflow, in which it enters at the bottom, and crossflow, in which it enters at the side [37]. As extensively reported in the literature [37,38], the transfer capability of the CT can be characterized through the Merkel number and the NTU:

$$Me = c \left( \frac{\dot{m}_{w,CT}}{\dot{m}_{air,CT}} \right)^{-n} \quad (11)$$

$$NTU = \frac{\rho A_v V_{cell}}{\dot{m}_{air,CT}} = c \left( \frac{\dot{m}_{w,CT}}{\dot{m}_{air,CT}} \right)^{-n+1} \quad (12)$$

Where c and n are two constants, $\dot{m}_w$ and $\dot{m}_{air}$ the water and air mass flow rates respectively

[kg.s⁻¹], $h_D$ the mass transfer coefficient [kg.m⁻².s⁻¹], $A_v$ the surface area of water droplets per unit volume of the tower [m².m⁻³], $V_{cell}$ the volume of tower [m³]. In addition to Eqs. (11)–(12), the e-NTU equation developed by Jaber and Webb allows to find the thermal power retrieved from the air stream [39]. The electric power requirements of the fan and the water pump at the maximum air flow rate are estimated through Eq. (13) and Eq. (14) respectively, where the flow rates $\dot{m}$ are in kg.h⁻¹:

$$\dot{W}_{fan,max}^{el} = 0.0569 \cdot \dot{m}_{air,CT}^{max} \quad (13)$$

$$\dot{W}_{P-8}^{el} = \frac{\dot{m}_{gen} \Delta \mathcal{P}_{33-34}}{0.75 \cdot \rho} \quad (14)$$

With $\Delta \mathcal{P}_{33-34} = 15$ kPa a typical value for water pressure drop in CT [40]. Type162 accounting for the cooling tower operates the fan so that the water outlet targets a desired set point $T_{sp}^{CT} = T_{wet bulb} + dT_{sp}^{CT}$ with $dT_{sp}^{CT}$ the CT “approach”, without exceeding the maximum air flow rate. The fan electric power consumption is then given by the cubic law (Eq. (13)):

<table><caption>**Table 3**
Summary of the characterization of different Cooling Towers in the literature.</caption><thead><tr><th>Coefficient c</th><th>Exponent n</th><th>Investigated range</th><th>Geometry</th><th>Comments</th><th>Reference</th></tr></thead><tbody><tr><td>1.3</td><td>0.77</td><td>0.25-3</td><td>Counterflow</td><td>Designed for direct evaporative cooling in mild climate</td><td>[42]</td></tr><tr><td>1.42</td><td>0.43</td><td>Counterflow</td><td>Counterflow</td><td></td><td>[43]</td></tr><tr><td>1.3</td><td>0.6</td><td>Counterflow</td><td>Counterflow</td><td></td><td>[41]</td></tr><tr><td>0.855</td><td>0.480</td><td>0.25-2</td><td>Counterflow</td><td></td><td>Saravel manufacturer (a)</td></tr><tr><td>0.342</td><td>0.253</td><td>0.3-3</td><td>Counterflow</td><td>Vertical PVC corrugated packing</td><td>[44]</td></tr><tr><td>0.224</td><td>0.295</td><td>0.3-3</td><td>Counterflow</td><td>Horizontal PVC corrugated packing</td><td>[44]</td></tr><tr><td>0.10</td><td>2.12</td><td>0.333-0.856</td><td>Counterflow/parallel flow</td><td>Air intake at the CT top to avoid the emission of airborne particles to the atmosphere</td><td>[45]</td></tr><tr><td>0.491</td><td>0.344</td><td>0.209-0.734</td><td>Counterflow/parallel flow</td><td></td><td>[46]</td></tr><tr><td>0.557</td><td>0.516</td><td>0.2-2.0</td><td>Counterflow</td><td>No drift eliminator</td><td>[47]</td></tr><tr><td>0.518</td><td>0.516</td><td>0.3-2.0</td><td>Counterflow</td><td>Drift eliminator A</td><td>[47]</td></tr><tr><td>0.593</td><td>0.573</td><td>0.3-2.0</td><td>Counterflow</td><td>Drift eliminator B</td><td>[47]</td></tr><tr><td>0.522</td><td>0.463</td><td>0.3-2.0</td><td>Counterflow</td><td>Drift eliminator C</td><td>[47]</td></tr><tr><td>0.586</td><td>0.733</td><td>0.3-2.0</td><td>Counterflow</td><td>Drift eliminator D</td><td>[47]</td></tr><tr><td>0.669</td><td>0.6</td><td>0.8-3.0</td><td>Counterflow</td><td>Drift eliminator E</td><td>[47]</td></tr><tr><td>0.67</td><td>0.525</td><td>0.8-3.0</td><td>Counterflow</td><td>Drift eliminator F</td><td>[47]</td></tr></tbody></table>

$$\dot{W}_{fan}^{el} = \dot{W}_{fan,max}^{el} \times \left( \frac{\dot{m}_{air,CT}}{\dot{m}_{air,CT}^{max}} \right)^3 \quad (15)$$

Many CT characterizations have been reported in the literature (see Table 3). The authors have chosen those of [41] for the present work. For the preliminary sizing, the maximum air flow rate ($\dot{m}_{air,CT}^{max}$) and water flow rate $\dot{m}_{w,CT}$ are set equal to $\dot{m}_{int} = 54.93 \times 10^3$ kg.h⁻¹.

### 2.2.5. Air-cooled chiller (ACC)

The Energy Efficiency Ratio (EER) of the ACC is modelled with Eq. (16) based on the catalog data of the LG manufacturer [48] (see Fig. 8a)

$$\begin{aligned} EER &= \frac{\dot{Q}_{ACC}^{ev}}{\dot{W}_{ACC}^{el}} \\ &= 5.11 + 0.135 \cdot T_{sp outlet} - 0.0728 \cdot T_{dry bulb} - 0.00165 \cdot T_{dry outlet} \end{aligned} \quad (16)$$

In Eq. (16), $\dot{Q}_{ACC}^{ev}$ and $\dot{W}_{ACC}^{el}$ represent the cooling load and electric power consumption, respectively, whereas $T_{dry bulb}$ and $T_{sp outlet}$ represent the dry bulb and setpoint temperatures respectively. The ACC modulates its power to ensure it meets the desired setpoint $T_{sp outlet}$ (see section 2.2.7), resulting in lowered EER at partial load (see Fig. 8b).

If the absorption chiller and the ACC fail at meeting the cooling load, then some extra cooling $\dot{Q}_{cooling}^{missing}$ must be added to the system.

$$\dot{Q}_{cooling}^{missing} = \dot{Q}_{cooling} - \dot{Q}_{cooling}^{sorption} - \dot{Q}_{cooling}^{AC} \quad (17)$$

For all simulations, the missing cooling $\dot{Q}_{cooling}^{missing}$ is negligible (typically $\dot{Q}_{cooling}^{missing} \approx 10^{-3} \cdot \dot{Q}_{cooling}$).

### 2.2.6. Tanks, heat exchangers and pumps

All tanks are covered with an insulating layer ($\lambda= 0.04$ W.K⁻¹.m⁻¹ and $e= 10$ cm). The volume $V_i$ can be expressed as an equivalent storage duration $\Delta t_i$, i.e., the ratio of the mass of water $\rho V_i$ to the nominal flow rate (Eq. (18)):

$$\Delta t_1 = \frac{\rho V_1}{\dot{m}_{gen}}; \Delta t_3 = \frac{\rho V_3}{\langle \dot{m}_{DHW} \rangle}; \Delta t_4 = \frac{\rho V_4}{\dot{m}_{w,CT}}; \Delta t_5 = \frac{\rho V_5}{\dot{m}_{cooling}} \quad (18)$$

As $\Delta t_i$ is an intensive quantity, it makes the comparison of systems of different scales easier. The volume of tank_2 is negligible.

<footnote>a Derived from manufacturer datasheets (http://www.saravel.com/products.php?en&id=73).</footnote>
maintenance costs (see Table 8).

### 2.2.4. Cooling tower

In a direct-contact wet Cooling Tower (CT), a hot water stream is in direct contact with an air stream. Water, which is injected at the top of the CT through an exchange surface enhancement distribution method (e.g., spray nozzles), flows downwards as it is cooled through sensible and latent heat transfers. The cooled water is collected into a sump before leaving the CT. The air may enter a CT in two different flow configurations: counterflow, in which it enters at the bottom, and crossflow, in which it enters at the side [37]. As extensively reported in the literature [37,38], the transfer capability of the CT can be characterized through the Merkel number and the NTU:

$$Me = c \left( \frac{\dot{m}_{w,CT}}{\dot{m}_{air,CT}} \right)^{-n} \quad (11)$$

$$NTU = \frac{\rho A_v V_{cell}}{\dot{m}_{air,CT}} = c \left( \frac{\dot{m}_{w,CT}}{\dot{m}_{air,CT}} \right)^{-n+1} \quad (12)$$

Where c and n are two constants, $\dot{m}_w$ and $\dot{m}_{air}$ the water and air mass flow rates respectively

[kg.s⁻¹], $h_D$ the mass transfer coefficient [kg.m⁻².s⁻¹], $A_v$ the surface area of water droplets per unit volume of the tower [m².m⁻³], $V_{cell}$ the volume of tower [m³]. In addition to Eqs. (11)–(12), the e-NTU equation developed by Jaber and Webb allows to find the thermal power retrieved from the air stream [39]. The electric power requirements of the fan and the water pump at the maximum air flow rate are estimated through Eq. (13) and Eq. (14) respectively, where the flow rates $\dot{m}$ are in kg.h⁻¹:

$$\dot{W}_{fan,max}^{el} = 0.0569 \cdot \dot{m}_{air,CT}^{max} \quad (13)$$

$$\dot{W}_{P-8}^{el} = \frac{\dot{m}_{gen} \Delta \mathcal{P}_{33-34}}{0.75 \cdot \rho} \quad (14)$$

With $\Delta \mathcal{P}_{33-34} = 15$ kPa a typical value for water pressure drop in CT [40]. Type162 accounting for the cooling tower operates the fan so that the water outlet targets a desired set point $T_{sp}^{CT} = T_{wet bulb} + dT_{sp}^{CT}$ with $dT_{sp}^{CT}$ the CT “approach”, without exceeding the maximum air flow rate. The fan electric power consumption is then given by the cubic law (Eq. (13)):

<table><caption>**Table 3**
Summary of the characterization of different Cooling Towers in the literature.</caption><thead><tr><th>Coefficient c</th><th>Exponent n</th><th>Investigated range</th><th>Geometry</th><th>Comments</th><th>Reference</th></tr></thead><tbody><tr><td>1.3</td><td>0.77</td><td>0.25-3</td><td>Counterflow</td><td>Designed for direct evaporative cooling in mild climate</td><td>[42]</td></tr><tr><td>1.42</td><td>0.43</td><td>Counterflow</td><td>Counterflow</td><td></td><td>[43]</td></tr><tr><td>1.3</td><td>0.6</td><td>Counterflow</td><td>Counterflow</td><td></td><td>[41]</td></tr><tr><td>0.855</td><td>0.480</td><td>0.25-2</td><td>Counterflow</td><td></td><td>Saravel manufacturer (a)</td></tr><tr><td>0.342</td><td>0.253</td><td>0.3-3</td><td>Counterflow</td><td>Vertical PVC corrugated packing</td><td>[44]</td></tr><tr><td>0.224</td><td>0.295</td><td>0.3-3</td><td>Counterflow</td><td>Horizontal PVC corrugated packing</td><td>[44]</td></tr><tr><td>0.10</td><td>2.12</td><td>0.333-0.856</td><td>Counterflow/parallel flow</td><td>Air intake at the CT top to avoid the emission of airborne particles to the atmosphere</td><td>[45]</td></tr><tr><td>0.491</td><td>0.344</td><td>0.209-0.734</td><td>Counterflow/parallel flow</td><td></td><td>[46]</td></tr><tr><td>0.557</td><td>0.516</td><td>0.2-2.0</td><td>Counterflow</td><td>No drift eliminator</td><td>[47]</td></tr><tr><td>0.518</td><td>0.516</td><td>0.3-2.0</td><td>Counterflow</td><td>Drift eliminator A</td><td>[47]</td></tr><tr><td>0.593</td><td>0.573</td><td>0.3-2.0</td><td>Counterflow</td><td>Drift eliminator B</td><td>[47]</td></tr><tr><td>0.522</td><td>0.463</td><td>0.3-2.0</td><td>Counterflow</td><td>Drift eliminator C</td><td>[47]</td></tr><tr><td>0.586</td><td>0.733</td><td>0.3-2.0</td><td>Counterflow</td><td>Drift eliminator D</td><td>[47]</td></tr><tr><td>0.669</td><td>0.6</td><td>0.8-3.0</td><td>Counterflow</td><td>Drift eliminator E</td><td>[47]</td></tr><tr><td>0.67</td><td>0.525</td><td>0.8-3.0</td><td>Counterflow</td><td>Drift eliminator F</td><td>[47]</td></tr></tbody></table>

$$\dot{W}_{fan}^{el} = \dot{W}_{fan,max}^{el} \times \left( \frac{\dot{m}_{air,CT}}{\dot{m}_{air,CT}^{max}} \right)^3 \quad (15)$$

Many CT characterizations have been reported in the literature (see Table 3). The authors have chosen those of [41] for the present work. For the preliminary sizing, the maximum air flow rate ($\dot{m}_{air,CT}^{max}$) and water flow rate $\dot{m}_{w,CT}$ are set equal to $\dot{m}_{int} = 54.93 \times 10^3$ kg.h⁻¹.

### 2.2.5. Air-cooled chiller (ACC)

The Energy Efficiency Ratio (EER) of the ACC is modelled with Eq. (16) based on the catalog data of the LG manufacturer [48] (see Fig. 8a)

$$\begin{aligned} EER = \frac{\dot{Q}_{ACC}^{ev}}{\dot{W}_{ACC}^{el}} \\ = 5.11 + 0.135 \cdot T_{sp outlet} - 0.0728 \cdot T_{dry bulb} - 0.00165 \cdot T_{dry outlet} \end{aligned} \quad (16)$$

In Eq. (16), $\dot{Q}_{ACC}^{ev}$ and $\dot{W}_{ACC}^{el}$ represent the cooling load and electric power consumption, respectively, whereas $T_{dry bulb}$ and $T_{sp outlet}$ represent the dry bulb and setpoint temperatures respectively. The ACC modulates its power to ensure it meets the desired setpoint $T_{sp outlet}$ (see section 2.2.7), resulting in lowered EER at partial load (see Fig. 8b).

If the absorption chiller and the ACC fail at meeting the cooling load, then some extra cooling $\dot{Q}_{cooling}^{missing}$ must be added to the system.

$$\dot{Q}_{cooling}^{missing} = \dot{Q}_{cooling} - \dot{Q}_{cooling}^{sorption} - \dot{Q}_{cooling}^{AC} \quad (17)$$

For all simulations, the missing cooling $\dot{Q}_{cooling}^{missing}$ is negligible (typically $\dot{Q}_{cooling}^{missing} \approx 10^{-3} \cdot \dot{Q}_{cooling}$).

### 2.2.6. Tanks, heat exchangers and pumps

All tanks are covered with an insulating layer ($\lambda= 0.04$ W.K⁻¹.m⁻¹ and $e = 10$ cm). The volume $V_i$ can be expressed as an equivalent storage duration $\Delta t_i$, i.e., the ratio of the mass of water $\rho V_i$ to the nominal flow rate (Eq. (18))

$$\Delta t_1 = \frac{\rho V_1}{\dot{m}_{gen}}; \Delta t_3 = \frac{\rho V_3}{\langle \dot{m}_{DHW} \rangle}; \Delta t_4 = \frac{\rho V_4}{\dot{m}_{w,CT}}; \Delta t_5 = \frac{\rho V_5}{\dot{m}_{cooling}} \quad (18)$$

As $\Delta t_i$ is an intensive quantity, it makes the comparison of systems of different scales easier. The volume of tank_2 is negligible.

<footnote>a Derived from manufacturer datasheets (http://www.saravel.com/products.php?en&id=73).</footnote>
<figure><img src="image_11.png" /><figcaption>Fig. 8. Air-cooled chiller. (a) Energy Efficiency Ratio and (b) Fraction of EER at partial load.</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>**Table 4**</figcaption></figure>

Nominal conditions for the heat exchangers sizing. m<sub>c</sub>, T<sub>in,c</sub>, m<sub>b</sub>, T<sub>in,h</sub> are the mass-flow rates, and inlet temperatures at the cold and hot sides respectively.

<table><thead><tr><th></th><th>m<sub>hot</sub> [kg.s<sup>-1</sup>]</th><th>m<sub>cold</sub> [kg.s<sup>-1</sup>]</th><th>T<sub>in,hot</sub> [°C]</th><th>T<sub>in,cold</sub> [°C]</th><th>k [kW·K<sup>-1</sup>]</th></tr></thead><tbody><tr><td>HX_1</td><td>25.84</td><td>25.84</td><td>80</td><td>73</td><td>75.04</td></tr><tr><td>HX_2</td><td>9.50</td><td>9.50</td><td>60</td><td>30</td><td>154.47</td></tr></tbody></table>

All heat exchangers (HX) are in counterflow configuration and are sized for a temperature pinch of $\delta T = 2$ °C under the nominal conditions defined in Table 4. Note that to size HX_1, the inlet temperature in the cold side is estimated as:

$$T_{in,c} = T_6 = T_{GTH} - \frac{\dot{m}_{gen}}{\dot{m}_{GTH}} \delta T \qquad (19)$$

The pressure drop of every fluid in the different heat exchangers (i.e. HX_1, HX_2, and the internal HXs of the absorption chiller) is assumed to be $\Delta \mathcal{P}_{HX} = 50$ kPa.

The pumps efficiency is assumed to be $\eta_{pump} = 0.75$. Therefore, the pumping power through one hydraulic element is calculated using Eq. (20):

$$P_{pump} = \frac{\dot{m} \Delta \mathcal{P}}{\eta_{pump} \rho} \qquad (20)$$

With $\rho$ the water density. The electric power consumed by the pumps (P_1, P_2, P_3, P_4, P_5, P_6) are therefore:

$$\dot{W}_{P-1}^{el} = \frac{\dot{m}_{gen} (\Delta \mathcal{P}_{6-4} + 2\Delta \mathcal{P}_{pipe})}{\eta_{pump} \rho} = \frac{\dot{m}_{gen} (\Delta \mathcal{P}_{HX} + 2\Delta \mathcal{P}_{pipe})}{\eta_{pump} \rho} \qquad (21)$$

$$\dot{W}_{P-2}^{el} = \frac{\dot{m}_{gen} \Delta \mathcal{P}_{14-15}}{\eta_{pump} \rho} = \frac{\dot{m}_{gen} \Delta \mathcal{P}_{HX}}{\eta_{pump} \rho} \qquad (22)$$

$$\dot{W}_{P-3}^{el} = \frac{\dot{m}_{to\_DHW} \Delta \mathcal{P}_{23-28}}{\eta_{pump} \rho} = \frac{\dot{m}_{to\_DHW} \Delta \mathcal{P}_{HX}}{\eta_{pump} \rho} \qquad (23)$$

$$\dot{W}_{P-4}^{el} = \frac{\dot{m}_{ev} \Delta \mathcal{P}_{37-30}}{\eta_{pump} \rho} = \frac{\dot{m}_{ev} \Delta \mathcal{P}_{HX}}{\eta_{pump} \rho} \qquad (24)$$

$$\dot{W}_{P-5}^{el} = \frac{\dot{m}_{to\_DHW} \Delta \mathcal{P}_{25-26}}{\eta_{pump} \rho} = \frac{\dot{m}_{to\_DHW} \Delta \mathcal{P}_{HX}}{\eta_{pump} \rho} \qquad (25)$$

$$\dot{W}_{P-6}^{el} = \frac{\dot{m}_{inl} \Delta \mathcal{P}_{42-38}}{\eta_{pump} \rho} = \frac{\dot{m}_{inl} \Delta \mathcal{P}_{HX}}{\eta_{pump} \rho} \qquad (26)$$

The water viscosity is estimated in TRNSYS through the Pressure Drop Calculator (Type586) based on the fluid's temperature at each time step. Note that the consumption of P_7 is merged with the consumption of the ACC, and that the consumption of the cooling and DHW

distribution pumps P_9 and P_10 are neglected. The overall electric power consumption $\dot{W}_{el}$ of the system is then:

$$\dot{W}_{el} = \sum_{l=0}^{8} \dot{W}_{P-1,l}^{el} + \dot{W}_{sorp,l}^{el} + \dot{W}_{fan,l}^{el} + \dot{W}_{ACC,l}^{el} + \dot{Q}_{DHW}^{backup} \qquad (27)$$

### 2.2.7. Control strategy

Four microprocessors control the system, each microprocessor controlling one or several actuators. Microprocessors #1, #2 and #4, which are modelled using Type2, perform a single comparison between two temperatures to execute a single operating mode labelled as 1 (in addition to a mode "0" that accounts for stand-by). Microprocessor #3, on the other hand, is modelled with a modified Type 40 [49] and performs 5 comparisons to determine 4 possible modes of operation (labelled from 1 to 4) in addition to a stand-by mode (labelled as 0).

Each comparator C compares an upper input temperature $T_U$ to a lower one $T_L$. A lower dead band $ldb$ and an upper one $udb$ ensure hysteresis and prevent the controller from switching modes too often: If comparator C was previously true, C remains true if $(T_U - T_L) \ge ldb$ on the current time step but switches to false if $(T_U - T_L) < ldb$. Conversely, if comparator C was previously false, C remains false on the current time step if $(T_U - T_L) < udb$, but switches to true if $(T_U - T_L) \ge udb$. To foster the numerical convergence of the TRNSYS model, the input temperatures of all microprocessors are delayed by one time step before feeding the microprocessor.

**Microprocessor #1** decides if geothermal energy must be brought to the system. To do so, it compares the geothermal temperature $T_{GTH}$ with $T_9$ (the temperature at the top of Tank_1). It turns P_0 and P_1 on to feed Tank_1 when $T_{GTH}-T_9$ is greater than an upper dead band ($udb_1 = 3$ °C), and turns P_0 and P_1 off when the difference reaches a lower dead band ($ldb_1 = 2$ °C). The values of $udb_1$ and $ldb_1$ have been chosen to be in line with HX_1, which has been sized with a pinch of 2 °C (see section 2.2.6).

**Microprocessor #2** decides if cooling from the ACC is needed (in case the absorption chiller is unable to meet the cooling needs). To do so, it compares the temperature at the bottom of the cooling tank Tank_5 ($T_{40}$) with the cooling setpoint temperature ($T_{sp cooling}$). It turns the ACC on when ($T_{40} - T_{sp cooling}$) is higher than $udb_2$, which is equal to -1 °C (i.e., when $T_{40}$ is getting close to $T_{sp cooling}$), and stops the ACC when the difference reaches $ldb_2$, which is equal to -2 °C (i.e., when the tank has been sufficiently cooled down).

**Microprocessor #3** decides if the absorption chiller must produce cooling and if DHW must be prepared (see Table 5). Four modes are possible: absorption chiller producing cooling (modes #1 and #2), production of DHW only, bypassing the generator of the absorption chiller (mode #3) and cooling and by-production of DHW with the outlet fluid from the generator (mode #4). To determine the mode, microprocessor #3 relies on 5 comparators:
<figure><img src="image_11.png" /><figcaption>Fig. 8. Air-cooled chiller. (a) Energy Efficiency Ratio and (b) Fraction of EER at partial load.</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>Table 4</figcaption></figure>

Nominal conditions for the heat exchangers sizing. m<sub>c</sub>, T<sub>in,c</sub>, m<sub>h</sub>, T<sub>in,h</sub> are the mass-flow rates, and inlet temperatures at the cold and hot sides respectively.

<table><thead><tr><th></th><th>m<sub>hot</sub> [kg.s<sup>-1</sup>]</th><th>m<sub>cold</sub> [kg.s<sup>-1</sup>]</th><th>T<sub>in,hot</sub> [°C]</th><th>T<sub>in,cold</sub> [°C]</th><th>k [kW·K<sup>-1</sup>]</th></tr></thead><tbody><tr><td>HX_1</td><td>25.84</td><td>25.84</td><td>80</td><td>73</td><td>75.04</td></tr><tr><td>HX_2</td><td>9.50</td><td>9.50</td><td>60</td><td>30</td><td>154.47</td></tr></tbody></table>

All heat exchangers (HX) are in counterflow configuration and are sized for a temperature pinch of $\delta T = 2$ °C under the nominal conditions defined in Table 4. Note that to size HX_1, the inlet temperature in the cold side is estimated as:

$$T_{in,c} = T_6 = T_{GTH} - \frac{\dot{m}_{gen}}{\dot{m}_{GTH}} \delta T \qquad (19)$$

The pressure drop of every fluid in the different heat exchangers (i.e. HX_1, HX_2, and the internal HXs of the absorption chiller) is assumed to be $\Delta\mathcal{P}_{HX} = 50$ kPa.

The pumps efficiency is assumed to be $\eta_{pump} = 0.75$. Therefore, the pumping power through one hydraulic element is calculated using Eq. (20):

$$P_{pump} = \frac{\dot{m} \Delta\mathcal{P}}{\eta_{pump} \rho} \qquad (20)$$

With $\rho$ the water density. The electric power consumed by the pumps (P_1, P_2, P_3, P_4, P_5, P_6) are therefore:

$$\dot{W}_{P-1}^{el} = \frac{\dot{m}_{gen} (\Delta\mathcal{P}_{6-4} + 2\Delta\mathcal{P}_{pipe})}{\eta_{pump} \rho} = \frac{\dot{m}_{gen} (\Delta\mathcal{P}_{HX} + 2\Delta\mathcal{P}_{pipe})}{\eta_{pump} \rho} \qquad (21)$$

$$\dot{W}_{P-2}^{el} = \frac{\dot{m}_{gen} \Delta\mathcal{P}_{14-15}}{\eta_{pump} \rho} = \frac{\dot{m}_{gen} \Delta\mathcal{P}_{HX}}{\eta_{pump} \rho} \qquad (22)$$

$$\dot{W}_{P-3}^{el} = \frac{\dot{m}_{to\,DHW} \Delta\mathcal{P}_{23-28}}{\eta_{pump} \rho} = \frac{\dot{m}_{to\,DHW} \Delta\mathcal{P}_{HX}}{\eta_{pump} \rho} \qquad (23)$$

$$\dot{W}_{P-4}^{el} = \frac{\dot{m}_{ev} \Delta\mathcal{P}_{37-30}}{\eta_{pump} \rho} = \frac{\dot{m}_{ev} \Delta\mathcal{P}_{HX}}{\eta_{pump} \rho} \qquad (24)$$

$$\dot{W}_{P-5}^{el} = \frac{\dot{m}_{to\,DHW} \Delta\mathcal{P}_{25-26}}{\eta_{pump} \rho} = \frac{\dot{m}_{to\,DHW} \Delta\mathcal{P}_{HX}}{\eta_{pump} \rho} \qquad (25)$$

$$\dot{W}_{P-6}^{el} = \frac{\dot{m}_{inl} \Delta\mathcal{P}_{42-38}}{\eta_{pump} \rho} = \frac{\dot{m}_{inl} \Delta\mathcal{P}_{HX}}{\eta_{pump} \rho} \qquad (26)$$

The water viscosity is estimated in TRNSYS through the Pressure Drop Calculator (Type586) based on the fluid's temperature at each time step. Note that the consumption of P_7 is merged with the consumption of the ACC, and that the consumption of the cooling and DHW

distribution pumps P_9 and P_10 are neglected. The overall electric power consumption $\dot{W}_{el}$ of the system is then:

$$\dot{W}_{el} = \sum_{l=0}^{8} \dot{W}_{P-l}^{el} + \dot{W}_{sorp}^{el} + \dot{W}_{fan}^{el} + \dot{W}_{ACC}^{el} + \dot{Q}_{DHW}^{backup} \qquad (27)$$

### 2.2.7. Control strategy

Four microprocessors control the system, each microprocessor controlling one or several actuators. Microprocessors #1, #2 and #4, which are modelled using Type2, perform a single comparison between two temperatures to execute a single operating mode labelled as 1 (in addition to a mode "0" that accounts for stand-by). Microprocessor #3, on the other hand, is modelled with a modified Type 40 [49] and performs 5 comparisons to determine 4 possible modes of operation (labelled from 1 to 4) in addition to a stand-by mode (labelled as 0).

Each comparator C compares an upper input temperature $T_U$ to a lower one $T_L$. A lower dead band $ldb$ and an upper one $udb$ ensure hysteresis and prevent the controller from switching modes too often: If comparator C was previously true, C remains true if $(T_U - T_L) \ge ldb$ on the current time step but switches to false if $(T_U - T_L) < ldb$. Conversely, if comparator C was previously false, C remains false on the current time step if $(T_U - T_L) < udb$, but switches to true if $(T_U - T_L) \ge udb$. To foster the numerical convergence of the TRNSYS model, the input temperatures of all microprocessors are delayed by one time step before feeding the microprocessor.

**Microprocessor #1** decides if geothermal energy must be brought to the system. To do so, it compares the geothermal temperature $T_{GTH}$ with $T_9$ (the temperature at the top of Tank_1). It turns P_0 and P_1 on to feed Tank_1 when $T_{GTH}-T_9$ is greater than an upper dead band ($udb_1 = 3$ °C), and turns P_0 and P_1 off when the difference reaches a lower dead band ($ldb_1 = 2$ °C). The values of $udb_1$ and $ldb_1$ have been chosen to be in line with HX_1, which has been sized with a pinch of 2 °C (see section 2.2.6).

**Microprocessor #2** decides if cooling from the ACC is needed (in case the absorption chiller is unable to meet the cooling needs). To do so, it compares the temperature at the bottom of the cooling tank Tank_5 ($T_{40}$) with the cooling setpoint temperature ($T_{sp cooling}$). It turns the ACC on when ($T_{40} - T_{sp cooling}$) is higher than $udb_2$, which is equal to -1 °C (i.e., when $T_{40}$ is getting close to $T_{sp cooling}$), and stops the ACC when the difference reaches $ldb_2$, which is equal to -2 °C (i.e., when the tank has been sufficiently cooled down).

**Microprocessor #3** decides if the absorption chiller must produce cooling and if DHW must be prepared (see Table 5). Four modes are possible: absorption chiller producing cooling (modes #1 and #2), production of DHW only, bypassing the generator of the absorption chiller (mode #3) and cooling and by-production of DHW with the outlet fluid from the generator (mode #4). To determine the mode, microprocessor #3 relies on 5 comparators:
<table><caption>**Table 5**

Characteristics of the microprocessor #3. "-1" means that the comparator plays no role in the selection of this mode</caption><thead><tr><th rowspan="2"></th><th colspan="5">Comparators</th><th colspan="3">Outputs status</th></tr><tr><th>C1<br>T<sub>40</sub></th><th>C2<br>32 °C</th><th>C3<br>T<sub>9</sub></th><th>C4<br>T<sub>9</sub></th><th>C5<br>T<sub>sp</sub></th><th>chiller, P_4, P_6,<br>div_3</th><th>P_3,<br>P_5</th><th>P_2</th></tr></thead><tbody><tr><td>Upper input</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Lower output</td><td></td><td>T<sub>sp</sub>,<br>cooling</td><td>T<sub>36</sub></td><td>55 °C</td><td>T<sub>55</sub></td><td>T<sub>54</sub></td><td></td><td></td></tr><tr><td>Upper dead band [°C]</td><td></td><td>-1</td><td>0,25</td><td>0,25</td><td>3</td><td>-20</td><td></td><td></td></tr><tr><td>Lower dead band [°C]</td><td></td><td>-2</td><td>0</td><td>0</td><td>2</td><td>-18</td><td></td><td></td></tr><tr><td>Mode 1</td><td>Absorption chiller produces cooling</td><td>1</td><td>1</td><td>1</td><td>-1</td><td>0</td><td>1</td><td>0</td></tr><tr><td>Mode 2</td><td>Absorption chiller produces cooling</td><td>1</td><td>1</td><td>1</td><td>0</td><td>1</td><td>1</td><td>0</td></tr><tr><td>Mode 3</td><td>DHW production</td><td>0</td><td>-1</td><td>-1</td><td>1</td><td>1</td><td>0</td><td>1</td></tr><tr><td>Mode 4</td><td>Absorption chiller produces cooling, fluid leaving the generator is used for DHW production</td><td>1</td><td>1</td><td>1</td><td>1</td><td>1</td><td>1</td><td>1</td></tr></tbody></table>

- C1 compares $T_{40}$ with $T_{sp cooling}$ to decide if cooling is needed, in the same way the comparator of microprocessor #2 does,

- C2 compares $T_{36}$ (the temperature at the bottom of Tank_4) with 32 °C. According to manufacturer datasheets, 32 °C is the maximum recommended temperature at the intermediary source of the absorption chiller. Similarly, C3 compares $T_9$ (the temperature at the top of Tank_1) with 55 °C. C2 and C3 both enforces a tiny dead band of 0.25 °C. If C2 or C3 is false, then the absorption chiller is prevented to start.

- C4 compares $T_9$ (the temperature at the top of the geothermal tank Tank_1) with $T_{55}$ (the temperature at the top of the DHW tank Tank_3) to determine if Tank_1 is hot enough to warm up the DHW tank. It is used to avoid heat being transferred back from the DHW tank to Tank_1. As for the single comparator of microprocessor #1 for HX_1, the upper and lower dead bands of C4 have been chosen to be in line with the pinch of HX_2.

- C5 compares $T_{sp DHW}$ (the DHW setpoint temperature) to $T_{54}$ (the temperature at the top of the DHW tank Tank_3). It will be used to decide if DHW must be prepared. The upper dead band of -20 °C aims at maintaining $T_{54}$ higher than $T_{sp DHW}$ by 20 °C, so that Tank_3 is always hot enough to provide DHW.

Microprocessor #3 starts the cooling production if C1, C2 and C3 are true, and:

- If C5 is false (mode 1): $T_{54}$ is higher than $T_{sp DHW}$ by at least 20 °C, which means no DHW is immediately required and therefore, there is no reason to take the value of C4 into account.

- If C5 is true but C4 is false (mode 2): DHW is needed. However, given that $T_9$ is lower than the temperature at the top of the DHW tank ($T_{55} + 2$ °C), Tank_1 is too cold to warm Tank_3 up and therefore, no DHW is delivered.

Mode 3 (DHW production only) is selected if comparator C1 is false and both C4 and C5 are true, which means that the cooling tank is cold enough (no cooling is required immediately). C2 and C3 are not taken into account since the absorption chiller is not operated in this mode.

Mode 4 is for combined cooling and DHW production. All comparators must be true: cooling is needed (C1 is true), the operative conditions are in line with the absorption chiller specifications (C2 and C3 are true), the geothermal resource is warmer than the water in the DHW tank (C4 is true) and DHW is required (C5 is true).

Microprocessor #4 decides if the excess heat from the absorption chiller must be evacuated to the Cooling Tower. To do so, it compares $T_{32}$ (the temperature at the top of Tank_4) with the wet bulb temperature of the air ($T_{wet bulb}$). It starts the CT when the temperature at the top of the CT tank ($T_{32}$) is higher than ($T_{wet bulb} + udb_{4,1}$), with $udb_{4,1} = 5$ °C, and stops the CT when $T_{32}$ falls to ($T_{wet bulb} + ldb_{4,1}$), with $ldb_{4,1} = 4.5$ °C. The water is therefore injected into the CT at a temperature above the desired outlet temperature ($T_{sp}^{CT} = T_{wet bulb} + dT_{sp}^{CT}$), where $dT_{sp}^{CT}$ is the CT

approach set fixed to 3 °C (see §2.2.4).

The set points of the outlet temperature from the absorption chiller and the air-cooled chiller are respectively $T_{38} = T_{sp cooling} - dT_{sp}^{sorp}$ and $T_{45} = T_{sp cooling} - dT_{sp}^{ASHP}$ with $dT_{sp}^{sorp} = dT_{sp}^{ASHP} = 1$ °C. This ensures the cooling tank is always cold enough when cooling is required.

The valves mix_4 and div_4 ensure that the distributed DHW temperature (point 59) does not overreach $T_{sp DHW}$, redirecting some tap water into the distribution loop if needed (point 62) rather than towards the DHW tank (point 63). Similarly, mix_2 and div_2 prevents entering the load side of HX_2 (point 25) with a temperature higher than 80 °C. mix_5 and div_5 prevent sending undercooled water into the cooling loop (point 47) by redirecting some warmed water flowing back from the building (point 49). P_9 is operated so that $T_{48} - T_{47} = 12-7$ °C = 5 °C, therefore $\dot{m}_{cooling} = \frac{\dot{Q}_{cooling}}{C_p(T_{48}-T_{47})}$.

## 2.3. Key Performance Indicators (KPI)

Throughout the paper, two key indicators will be used for both economic and environmental assessment. The first KPI is the normalized electric consumption of the system $W_{el}^*$:

$$W_{el}^* = \frac{W_{el}}{\frac{Q_{demand}}{Q_{cooling} + Q_{DHW}}} = \frac{W_{el}}{Q_{cooling}} \qquad (28)$$

Another important indicator is $Q_{sorp}^{ev}$, the normalized amount of cooling produced by the absorption chiller relative to the total cooling load only:

$$Q_{sorp}^{ev} \sim \frac{Q_{sorp}^{ev}}{Q_{cooling}} \qquad (29)$$

Note that the exergy destruction rate is not analyzed in this paper.

# 3. Results

## 3.1. Preliminary sizing

For the preliminary sizing defined in Table 2, most of the cooling requirement is covered by the absorption chiller (see Fig. 9a). The yearly electricity consumption of the system is $W_{el} = 76.6$ MWh.y$^{-1}$ or $W_{el}^* = 76.6/(570.5 + 151.9) = 0.106$. The three main electricity consumers are the ACC, followed by the CT fans and the pump P_4 (see Fig. 9b). The absorption chiller delivers $Q_{sorp}^{ev} \sim 0.817$ on an annual basis. Note that the entire DHW need is covered by the geothermal fluid without any backup.

During the wet season (July to November), the simultaneous increase in the cooling demand and the wet bulb temperature decreases the capacity of the absorption chiller during daytime, leading to an overall increase of the ACC contribution (see Fig. 9c and d). This is illustrated by Fig. 10: the absorption chiller is constantly operated (microprocessor #3 in mode #1) with sporadic by-production of DHW when microprocessor
<table><caption>**Table 5**

Characteristics of the microprocessor #3. “-1” means that the comparator plays no role in the selection of this mode</caption><thead><tr><th rowspan="2"></th><th rowspan="2"></th><th colspan="5">Comparators</th><th colspan="3">Outputs status</th></tr><tr><th>C1<br>T<sub>40</sub></th><th>C2<br>32 °C</th><th>C3<br>T<sub>9</sub></th><th>C4<br>T<sub>9</sub></th><th>C5<br>T<sub>sp</sub></th><th>chiller, P_4, P_6,<br>div_3</th><th>P_3,<br>P_5</th><th>P_2</th></tr></thead><tbody><tr><td>Upper input</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Lower output</td><td></td><td>T<sub>sp</sub>,<br>cooling</td><td>T<sub>36</sub></td><td>55 °C</td><td>T<sub>55</sub></td><td>T<sub>54</sub></td><td></td><td></td><td></td></tr><tr><td>Upper dead band [°C]</td><td></td><td>-1</td><td>0,25</td><td>0,25</td><td>3</td><td>-20</td><td></td><td></td><td></td></tr><tr><td>Lower dead band [°C]</td><td></td><td>-2</td><td>0</td><td>0</td><td>2</td><td>-18</td><td></td><td></td><td></td></tr><tr><td rowspan="4">Mode</td><td>1 Absorption chiller produces cooling</td><td></td><td>1</td><td>1</td><td>1</td><td>-1</td><td>0</td><td>1</td><td>0</td><td>1</td></tr><tr><td>2 Absorption chiller produces cooling</td><td></td><td>1</td><td>1</td><td>1</td><td>0</td><td>1</td><td>1</td><td>0</td><td>1</td></tr><tr><td>3 DHW production</td><td></td><td>0</td><td>-1</td><td>-1</td><td>1</td><td>1</td><td>0</td><td>1</td><td>1</td></tr><tr><td>4 Absorption chiller produces cooling, fluid leaving the generator is used for DHW production</td><td></td><td>1</td><td>1</td><td>1</td><td>1</td><td>1</td><td>1</td><td>1</td><td>1</td></tr></tbody></table>

- C1 compares $T_{40}$ with $T_{sp cooling}$ to decide if cooling is needed, in the same way the comparator of microprocessor #2 does,

- C2 compares $T_{36}$ (the temperature at the bottom of Tank_4) with 32 °C. According to manufacturer datasheets, 32 °C is the maximum recommended temperature at the intermediary source of the absorption chiller. Similarly, C3 compares $T_9$ (the temperature at the top of Tank_1) with 55 °C. C2 and C3 both enforces a tiny dead band of 0.25 °C. If C2 or C3 is false, then the absorption chiller is prevented to start.

- C4 compares $T_9$ (the temperature at the top of the geothermal tank Tank_1) with $T_{55}$ (the temperature at the top of the DHW tank Tank_3) to determine if Tank_1 is hot enough to warm up the DHW tank. It is used to avoid heat being transferred back from the DHW tank to Tank_1. As for the single comparator of microprocessor #1 for HX_1, the upper and lower dead bands of C4 have been chosen to be in line with the pinch of HX_2.

- C5 compares $T_{sp DHW}$ (the DHW setpoint temperature) to $T_{54}$ (the temperature at the top of the DHW tank Tank_3). It will be used to decide if DHW must be prepared. The upper dead band of -20 °C aims at maintaining $T_{54}$ higher than $T_{sp DHW}$ by 20 °C, so that Tank_3 is always hot enough to provide DHW.

Microprocessor #3 starts the cooling production if C1, C2 and C3 are true, and:

- If C5 is false (mode 1): $T_{54}$ is higher than $T_{sp DHW}$ by at least 20 °C, which means no DHW is immediately required and therefore, there is no reason to take the value of C4 into account.

- If C5 is true but C4 is false (mode 2): DHW is needed. However, given that $T_9$ is lower than the temperature at the top of the DHW tank ($T_{55} + 2$ °C), Tank_1 is too cold to warm Tank_3 up and therefore, no DHW is delivered.

Mode 3 (DHW production only) is selected if comparator C1 is false and both C4 and C5 are true, which means that the cooling tank is cold enough (no cooling is required immediately). C2 and C3 are not taken into account since the absorption chiller is not operated in this mode.

Mode 4 is for combined cooling and DHW production. All comparators must be true: cooling is needed (C1 is true), the operative conditions are in line with the absorption chiller specifications (C2 and C3 are true), the geothermal resource is warmer than the water in the DHW tank (C4 is true) and DHW is required (C5 is true).

Microprocessor #4 decides if the excess heat from the absorption chiller must be evacuated to the Cooling Tower. To do so, it compares $T_{32}$ (the temperature at the top of Tank_4) with the wet bulb temperature of the air ($T_{wet bulb}$). It starts the CT when the temperature at the top of the CT tank ($T_{32}$) is higher than ($T_{wet bulb} + udb_{4,1}$), with $udb_{4,1} = 5$ °C, and stops the CT when $T_{32}$ falls to ($T_{wet bulb} + ldb_{4,1}$), with $ldb_{4,1} = 4.5$ °C. The water is therefore injected into the CT at a temperature above the desired outlet temperature ($T_{sp}^{CT} = T_{wet bulb} + dT_{sp}^{CT}$), where $dT_{sp}^{CT}$ is the CT

approach set fixed to 3 °C (see §2.2.4).

The set points of the outlet temperature from the absorption chiller and the air-cooled chiller are respectively $T_{38} = T_{sp cooling} - dT_{sp}^{sorp}$ and $T_{45} = T_{sp cooling} - dT_{sp}^{ASHP}$ with $dT_{sp}^{sorp} = dT_{sp}^{ASHP} = 1$ °C. This ensures the cooling tank is always cold enough when cooling is required.

The valves mix_4 and div_4 ensure that the distributed DHW temperature (point 59) does not overreach $T_{sp DHW}$, redirecting some tap water into the distribution loop if needed (point 62) rather than towards the DHW tank (point 63). Similarly, mix_2 and div_2 prevents entering the load side of HX_2 (point 25) with a temperature higher than 80 °C. mix_5 and div_5 prevent sending undercooled water into the cooling loop (point 47) by redirecting some warmed water flowing back from the building (point 49). P_9 is operated so that $T_{48} - T_{47} = 12-7$ °C = 5 °C, therefore $\dot{m}_{cooling} = \frac{\dot{Q}_{cooling}}{C_p(T_{48}-T_{47})}$.

## 2.3. Key Performance Indicators (KPI)

Throughout the paper, two key indicators will be used for both economic and environmental assessment. The first KPI is the normalized electric consumption of the system $W_{el}^*$:

$$W_{el}^* = \frac{W_{el}}{Q_{demand}} = \frac{W_{el}}{Q_{cooling} + Q_{DHW}} \qquad (28)$$

Another important indicator is $Q_{sorp}^{ev}$, the normalized amount of cooling produced by the absorption chiller relative to the total cooling load only:

$$Q_{sorp}^{ev} \sim \frac{Q_{sorp}^{ev}}{Q_{cooling}} \qquad (29)$$

Note that the exergy destruction rate is not analyzed in this paper.

# 3. Results

## 3.1. Preliminary sizing

For the preliminary sizing defined in Table 2, most of the cooling requirement is covered by the absorption chiller (see Fig. 9a). The yearly electricity consumption of the system is $W_{el} = 76.6$ MWh.y$^{-1}$ or $W_{el}^* = 76.6/(570.5 + 151.9) = 0.106$. The three main electricity consumers are the ACC, followed by the CT fans and the pump P_4 (see Fig. 9b). The absorption chiller delivers $Q_{sorp}^{ev} \sim 0.817$ on an annual basis. Note that the entire DHW need is covered by the geothermal fluid without any backup.

During the wet season (July to November), the simultaneous increase in the cooling demand and the wet bulb temperature decreases the capacity of the absorption chiller during daytime, leading to an overall increase of the ACC contribution (see Fig. 9c and d). This is illustrated by Fig. 10: the absorption chiller is constantly operated (microprocessor #3 in mode #1) with sporadic by-production of DHW when microprocessor
<figure><img src="image_13.png" /><figcaption>**Fig. 9.** Cooling sources and electricity consumption (a, b) on a monthly basis and (c, d) on an hourly basis for the 2nd of September 2050. Preliminary sizing defined in Table 2.</figcaption></figure>

#3 switches to mode #4. Microprocessors #1 and #4 follow microprocessor #3 by operating P_0, P_1 and the CT. From approximately 8:00 to 22:00, the absorption chiller is not able to maintain the bottom of the cooling tank (point 38 in Fig. 3) to the cooling set point (7 °C, see Fig. 10d), which makes the ACC to operate so that the cooling setpoint is maintained. Note that, for this rather unfavorable day, the maximum inlet intermediate temperature in the absorption chiller is 29.8 °C, while the mains water is about 32 °C. Therefore, in the studied case, the CT is systematically a better heat sink for the absorption chiller than the mains water. However, in milder climates with cooler mains water, the excess heat from the condenser and absorber of the absorption chiller could be used to pre-heat the mains water without a negative impact on the absorption chiller efficiency.

## 3.2. "Status quo" scenario

A "Status quo" will serve as a comparison with the geothermal absorption chiller. It is basically an ACC with a fuel boiler for DHW, as it is common in the French overseas. This system has been modelled by setting negligible values for $Q_{sorp}^{ev}$ and $\dot{m}_{GTH}$. All cooling is delivered by the ACC (i.e. $Q_{sorp}^{ev} \sim 0$). The electricity consumption is entirely tracked

back to the ACC operation with $W_{el} = 164.9$ MWh.y$^{-1}$ or $W_{el} \sim = W_{el}/Q_{cooling} = 0.228$. In other words, the Seasonal Performance Factor of the ACC over a whole year would be SPF $\approx 1/0.228 \approx 4.39$. The maximum thermal power provided by the DHW boiler is $Q_{DHW}^{max} = 28.3$ kW.

## 3.3. Sensitivity analysis around the preliminary sizing

A sensitivity analysis of $Q_{sorp}^{ev} \sim$ and $W_{el}^{*} \sim$ around the preliminary sizing was carried out, considering the TRNSYS parameters reported in Table 2 as variable. This enlightens the following trends:

- Geothermal resource (see Fig. 11): $Q_{sorp}^{ev} \sim$ increases with the geothermal temperature $T_{GTH}$ or flow rate $\dot{m}_{GTH}$. As explained in §2.2.1, a geothermal resource with a much lower available flow rate may only slightly affect the cooling delivered by the absorption chiller (e.g. for $T_{GTH}=80$ °C, $Q_{sorp}^{ev} \sim \approx 0.73$ for $\dot{m}_{GTH} = 0.5 \dot{m}_{gen}$ instead of $Q_{sorp}^{ev} \sim \approx 0.82$ for $\dot{m}_{GTH} = \dot{m}_{gen}$). Reversely, only a fraction of the geothermal flow rate considered in the preliminary sizing is
<figure><img src="image_13.png" /><figcaption>**Fig. 9.** Cooling sources and electricity consumption (a, b) on a monthly basis and (c, d) on an hourly basis for the 2nd of September 2050. Preliminary sizing defined in Table 2.</figcaption></figure>

#3 switches to mode #4. Microprocessors #1 and #4 follow microprocessor #3 by operating P_0, P_1 and the CT. From approximately 8:00 to 22:00, the absorption chiller is not able to maintain the bottom of the cooling tank (point 38 in Fig. 3) to the cooling set point (7 °C, see Fig. 10d), which makes the ACC to operate so that the cooling setpoint is maintained. Note that, for this rather unfavorable day, the maximum inlet intermediate temperature in the absorption chiller is 29.8 °C, while the mains water is about 32 °C. Therefore, in the studied case, the CT is systematically a better heat sink for the absorption chiller than the mains water. However, in milder climates with cooler mains water, the excess heat from the condenser and absorber of the absorption chiller could be used to pre-heat the mains water without a negative impact on the absorption chiller efficiency.

## 3.2. "Status quo" scenario

A "Status quo" will serve as a comparison with the geothermal absorption chiller. It is basically an ACC with a fuel boiler for DHW, as it is common in the French overseas. This system has been modelled by setting negligible values for $Q_{sorp}^{ev}$ and $\dot{m}_{GTH}$. All cooling is delivered by the ACC (i.e. $Q_{sorp}^{ev} \sim 0$). The electricity consumption is entirely tracked

back to the ACC operation with $W_{el} = 164.9$ MWh.y$^{-1}$ or $W_{el} \sim = W_{el}/Q_{cooling} = 0.228$. In other words, the Seasonal Performance Factor of the ACC over a whole year would be SPF $\approx 1/0.228 \approx 4.39$. The maximum thermal power provided by the DHW boiler is $Q_{DHW}^{max} = 28.3$ kW.

## 3.3. Sensitivity analysis around the preliminary sizing

A sensitivity analysis of $Q_{sorp}^{ev} \sim$ and $W_{el}^{*} \sim$ around the preliminary sizing was carried out, considering the TRNSYS parameters reported in Table 2 as variable. This enlightens the following trends:

- Geothermal resource (see Fig. 11): $Q_{sorp}^{ev} \sim$ increases with the geothermal temperature $T_{GTH}$ or flow rate $\dot{m}_{GTH}$. As explained in §2.2.1, a geothermal resource with a much lower available flow rate may only slightly affect the cooling delivered by the absorption chiller (e.g. for $T_{GTH}=80$ °C, $Q_{sorp}^{ev} \sim \approx 0.73$ for $\dot{m}_{GTH} = 0.5 \dot{m}_{gen}$ instead of $Q_{sorp}^{ev} \sim \approx 0.82$ for $\dot{m}_{GTH} = \dot{m}_{gen}$). Reversely, only a fraction of the geothermal flow rate considered in the preliminary sizing is
<figure><img src="image_14.png" /><figcaption>**Fig. 10.** Evolution of several variables with time for September 2, 2050. (a) Microprocessors' operating modes; (b) inlet and outlet temperatures of the fluids in the geothermal HX (HX_1), (c) absorption chiller's heat sink heat transfer fluid temperature at the inlet and outlet of the chiller and of the CT, and (d) chilled water temperature at the absorption chiller's outlet and at the bottom of the cold storage tank. Preliminary sizing defined in Table 2.</figcaption></figure>

necessary to power the absorption chiller if the temperature is higher than 80 °C.

- **Thermal demand and distribution** (see Fig. 12a-d): The maximum cooling power $\dot{Q}_{\text{cooling}}^{\text{max}}$ has a limited effect since all machines (absorption chiller, ACC, cooling tower) behave the same, no matter their nominal capacity. Increasing the cooling setpoint temperature $T_{\text{sp cooling}}$ [°C] significantly increases the cooling delivered by the absorption chiller and consequently decreases the use of the ACC. A larger Tank_5 allows the storage of chilled water produced by the absorption chiller under favorable conditions (e.g., low wet bulb temperature early in the morning, see parameter $\Delta t_5$). Decreasing the fraction of DHW $r_{\text{DHW}}$ (where $r_{\text{DHW}} = 0$ if there is no DHW demand and $r_{\text{DHW}} = 1$ if DHW is computed according to §2.1.2) increases $W_{\text{el}}^{\text{r}}$ as it removes the “free” heat from the generator outlet used for DHW preparation.

- **Absorption chiller** (see Fig. 12e): The delivered cooling increases with the nominal cooling power. For instance, $Q_{\text{sorp}}^{\text{ev}} \sim$ reaches 0.91 for a

chiller whose nominal power $\dot{Q}_{\text{sorp}}^{\text{ev}}$ equals twice the cooling demand $\dot{Q}_{\text{cooling}}^{\text{max}}$.

- **Cooling tower** (see Fig. 12f-i): The exponent $n$ in Merkel's correlation has little influence upon $Q_{\text{sorp}}^{\text{ev}} \sim$ and $W_{\text{el}}^{\text{r}}$ contrarily to the exchange coefficient $c$, as reported in [37,38]. Electric consumption can be slightly decreased if the CT water flow rate is slightly higher than the absorption chiller intermediary flow rate ($\dot{m}_{\text{int}} \approx 1.2 \dot{m}_{\text{w,CT}}$). A larger CT with a much higher air flow rate than water flow rate (e.g. $\dot{m}_{\text{air,CT}}^{\text{max}} \approx 3 \dot{m}_{\text{w,CT}}$) achieves a much lower electric consumption, since fans operate at lower speed on a more regular basis.

- **Control** (see Fig. 12j-n): Setting a low algebraic value to $\text{udb}_2$ causes the ACC to start more often, decreasing the operation range of the absorption chiller and increasing the overall electric consumption. Increasing $\text{udb}_1$ causes Tank_1 to be warmed up by the geothermal fluid on a less regular basis, decreasing the overall system efficiency, while $\text{udb}_{4,1}$ plays little role. For the preliminary sizing, a CT approach $dT_{\text{sp}}^{\text{CT}} \approx 3$ °C seems to be optimal, since a lower value causes
<figure><img src="image_14.png" /><figcaption>**Fig. 10.** Evolution of several variables with time for September 2, 2050. (a) Microprocessors' operating modes; (b) inlet and outlet temperatures of the fluids in the geothermal HX (HX_1), (c) absorption chiller's heat sink heat transfer fluid temperature at the inlet and outlet of the chiller and of the CT, and (d) chilled water temperature at the absorption chiller's outlet and at the bottom of the cold storage tank. Preliminary sizing defined in Table 2.</figcaption></figure>

necessary to power the absorption chiller if the temperature is higher than 80 °C.

- **Thermal demand and distribution** (see Fig. 12a-d): The maximum cooling power $\dot{Q}_{\text{cooling}}^{\text{max}}$ has a limited effect since all machines (absorption chiller, ACC, cooling tower) behave the same, no matter their nominal capacity. Increasing the cooling setpoint temperature $T_{\text{sp cooling}}$ [°C] significantly increases the cooling delivered by the absorption chiller and consequently decreases the use of the ACC. A larger Tank_5 allows the storage of chilled water produced by the absorption chiller under favorable conditions (e.g., low wet bulb temperature early in the morning, see parameter $\Delta t_5$). Decreasing the fraction of DHW $r_{\text{DHW}}$ (where $r_{\text{DHW}} = 0$ if there is no DHW demand and $r_{\text{DHW}} = 1$ if DHW is computed according to §2.1.2) increases $W_{\text{el}}^\text{r}$ as it removes the “free” heat from the generator outlet used for DHW preparation.

- **Absorption chiller** (see Fig. 12e): The delivered cooling increases with the nominal cooling power. For instance, $Q_{\text{sorp}}^{\text{ev}} \sim$ reaches 0.91 for a

chiller whose nominal power $\dot{Q}_{\text{sorp}}^{\text{ev}}$ equals twice the cooling demand $\dot{Q}_{\text{cooling}}^{\text{max}}$.

- **Cooling tower** (see Fig. 12f-i): The exponent $n$ in Merkel's correlation has little influence upon $Q_{\text{sorp}}^{\text{ev}} \sim$ and $W_{\text{el}}^\text{r}$ contrarily to the exchange coefficient $c$, as reported in [37,38]. Electric consumption can be slightly decreased if the CT water flow rate is slightly higher than the absorption chiller intermediary flow rate ($\dot{m}_{\text{int}} \approx 1.2 \dot{m}_{\text{w,CT}}$). A larger CT with a much higher air flow rate than water flow rate (e.g. $\dot{m}_{\text{air,CT}}^{\text{max}} \approx 3 \dot{m}_{\text{w,CT}}$) achieves a much lower electric consumption, since fans operate at lower speed on a more regular basis.

- **Control** (see Fig. 12j-n): Setting a low algebraic value to $\text{udb}_2$ causes the ACC to start more often, decreasing the operation range of the absorption chiller and increasing the overall electric consumption. Increasing $\text{udb}_1$ causes Tank_1 to be warmed up by the geothermal fluid on a less regular basis, decreasing the overall system efficiency, while $\text{udb}_{4,1}$ plays little role. For the preliminary sizing, a CT approach $dT_{\text{sp}}^{\text{CT}} \approx 3$ °C seems to be optimal, since a lower value causes
<figure><img src="image_15.png" /><figcaption>Fig. 11. (a) Share of cooling from the absorption chiller $Q_{sorp}^{ev}$; (b) Normalized electricity $W_{el}^* = W_{el}/Q_{demand}$ as a function of geothermal temperature $T_{GTH}$ and flow rate $\dot{m}_{GTH}$. The TRNSYS results are represented with black dots. The red star accounts for the preliminary sizing defined in Table 2. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

<figure><img src="image_16.png" /></figure>

the CT to run on a much more regular basis which increases the electric fan and overall consumption, though the absorption chiller delivers more cooling. Beyond this point, the CT ability to lower the intermediary temperature decreases, resulting in more cooling provided from the ACC instead of the absorption chiller.

- Buried twin pipes (see Fig. 12a-q): Longer buried pipes results in increased electric consumption of P-1 and the overall system, though it may be mitigated by decreasing the nominal pressure loss $\Delta\eta$ and increasing of the pipes diameter. Slightly increasing the normalized casing diameter $d_{casing}^*$ improves the insulation and decreases the heat loss along the pipes, resulting in hotter fluid delivered to the absorption chiller which, in turns, produces more cooling.

## 4. Discussion: System optimization

The sensitivity analysis shows that the 19 investigated parameters have an impact upon both $W_{el}^*$ and $Q_{sorp}^{ev}$ KPIs, though to different extents. The preliminary sizing introduced in Table 2 is devoted to illustrate the system behavior but might be far away from a technical and economic optima. Leaving apart the CT mass transfer constant and exponent left to c = 1.3 and n = 0.6 respectively, the combination of 17 parameters must be investigated to determine optima. If one wants to explore the effect of 3 values per parameter, then the overall number of TRNSYS simulations would be $3^{17} \approx 129 \times 10^6$, an unrealistic high value. To overcome this, one needs to build fast-to-run approximations of $W_{el}^*$ and $Q_{sorp}^{ev}$, also known as surrogates, through a statistical analysis of a limited number of TRNSYS simulations, and then use these surrogates in the optimization process. Surrogate modelling applied to energy in buildings has been a booming research domain for the past few years (see for example [50] for a comprehensive overview of challenges, techniques, applications and past successes).

### 4.1. Framework for multi-objective optimization

#### 4.1.1. Surrogate modelling of $W_{el}^*$ and $Q_{sorp}^{ev}$

The D = 17 parameters and their bounds are reported in Table 7. The problem is expressed as a function of a single extensive parameter ($\dot{Q}_{cooling}^{max}$) and a set of intensive parameters. Extensive parameters ($\dot{m}_{GTH}$, $\dot{m}_{air,CT}^{max}$, $\dot{m}_{w,CT}$, L) have been replaced with the intensive quantities $\dot{m}_{GTH}/\dot{Q}_{cooling}^{max}$, $\dot{m}_{air,CT}^{max}/\dot{m}_{w,CT}$, $\dot{m}_{w,CT}/\dot{m}_{int}$ and $q_{\ell}^{-1} = L/(5500 \cdot \dot{Q}_{cooling}^{max})$

respectively. Each model parameter $x_i$ ($i \le 1 \le D$) is transformed into $\chi_i$, a variable normalized in the range [0;1] (see Table 7) though linear (Eq. (30)) or concave transformations (Eq. (31)):

$$ \chi_i = \frac{x_i - x_{i-}}{x_{i+} - x_{i-}} \qquad (30) $$

$$ \chi_i = 0.5 \left( \frac{x_i - x_{i-}}{x_{i+} - x_{i-}} \right) + 0.5 \left( \frac{x_i^{0.25} - x_{i-}^{0.25}}{x_{i+}^{0.25} - x_{i-}^{0.25}} \right) \qquad (31) $$

The concave transformation ensures a higher sampling density close to the lower bound $x_{i-}$ and was preferentially used for the variables changing by at least one order of magnitude.

The authors have chosen regression through Gaussian Processes (GP), sometimes referred to as kriging, for its flexibility [51]. A GP is a non-parametric regression (or machine learning) technique, which means it does not rely on any a priori restrictive assumption about the structure of the function, such as a “linear” or “quadratic” regression. The GP “learns” the underlying structure of the data to make predictions. Though GP techniques have been developed for high dimensional datasets [52–54], standard GPs with constant basis (i.e. simple kriging) and Matérn3/2 kernels have been used for this work. One advantage of GP is their interpretability (see Appendix A for theoretical background and further discussion).

The quality of the surrogate is estimated through cross-validation [55], a procedure where a part $1/n$ of the data is randomly selected and left apart (here $n = 5$), acting as a test sample. A surrogate is fitted on a fraction $(1-1/n)$ of the sample and the procedure is repeated $n$ times by permuting the samples. The metric for the estimation of the quality of the surrogate of an output $f$ is the Root Mean Square Error (RMSE), defined by Eq. (32):

$$ \text{RMSE}(f) = \left( \sum_{i=1}^{N} \frac{[f(\text{TRNSYS}) - (f)_{\text{surrogate}}]^2}{N} \right)^{1/2} \qquad (32) $$

The surrogates of both KPI are built through the iterative generation of points $\chi$ ($\chi \in [0; 1]^D$) and subsequent evaluation of TRNSYS models, starting with $N = 170$ points at the first iteration. The points are generated with a Latin Hyper Square (LHS), a method with enhanced space filling properties [56]. They must fulfil the constraint (C1) to ensure that the heat evacuation to the CT is started only when the wet bulb temperature is above the CT approach by 1 °C (Eq. (33)).
<figure><img src="image_15.png" /><figcaption>Fig. 11. (a) Share of cooling from the absorption chiller $Q_{sorp}^{ev}$; (b) Normalized electricity $W_{el}^* = W_{el}/Q_{demand}$ as a function of geothermal temperature $T_{GTH}$ and flow rate $\dot{m}_{GTH}$. The TRNSYS results are represented with black dots. The red star accounts for the preliminary sizing defined in Table 2. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

<figure><img src="image_16.png" /></figure>

the CT to run on a much more regular basis which increases the electric fan and overall consumption, though the absorption chiller delivers more cooling. Beyond this point, the CT ability to lower the intermediary temperature decreases, resulting in more cooling provided from the ACC instead of the absorption chiller.

- Buried twin pipes (see Fig. 12a-q): Longer buried pipes results in increased electric consumption of P-1 and the overall system, though it may be mitigated by decreasing the nominal pressure loss $\Delta\eta$ and increasing of the pipes diameter. Slightly increasing the normalized casing diameter $d_{casing}^*$ improves the insulation and decreases the heat loss along the pipes, resulting in hotter fluid delivered to the absorption chiller which, in turns, produces more cooling.

## 4. Discussion: System optimization

The sensitivity analysis shows that the 19 investigated parameters have an impact upon both $W_{el}^*$ and $Q_{sorp}^{ev}$ KPIs, though to different extents. The preliminary sizing introduced in Table 2 is devoted to illustrate the system behavior but might be far away from a technical and economic optima. Leaving apart the CT mass transfer constant and exponent left to c = 1.3 and n = 0.6 respectively, the combination of 17 parameters must be investigated to determine optima. If one wants to explore the effect of 3 values per parameter, then the overall number of TRNSYS simulations would be $3^{17} \approx 129 \times 10^6$, an unrealistic high value. To overcome this, one needs to build fast-to-run approximations of $W_{el}^*$ and $Q_{sorp}^{ev}$, also known as surrogates, through a statistical analysis of a limited number of TRNSYS simulations, and then use these surrogates in the optimization process. Surrogate modelling applied to energy in buildings has been a booming research domain for the past few years (see for example [50] for a comprehensive overview of challenges, techniques, applications and past successes).

### 4.1. Framework for multi-objective optimization

#### 4.1.1. Surrogate modelling of $W_{el}^*$ and $Q_{sorp}^{ev}$

The D = 17 parameters and their bounds are reported in Table 7. The problem is expressed as a function of a single extensive parameter ($\dot{Q}_{cooling}^{max}$) and a set of intensive parameters. Extensive parameters ($\dot{m}_{GTH}$, $\dot{m}_{air,CT}^{max}$, $\dot{m}_{w,CT}$, L) have been replaced with the intensive quantities

$$ \dot{m}_{GTH}/\dot{Q}_{cooling}^{max}, \dot{m}_{air,CT}^{max}/\dot{m}_{w,CT}, \dot{m}_{w,CT}/\dot{m}_{int} \text{ and } q_{\ell}^{-1} = L/(5500 \cdot \dot{Q}_{cooling}^{max}) $$

respectively. Each model parameter $x_i$ ($i \le 1 \le D$) is transformed into $\chi_i$, a variable normalized in the range [0;1] (see Table 7) though linear (Eq. (30)) or concave transformations (Eq. (31)):

$$ \chi_i = \frac{x_i - x_{i-}}{x_{i+} - x_{i-}} \qquad (30) $$

$$ \chi_i = 0.5 \left( \frac{x_i - x_{i-}}{x_{i+} - x_{i-}} \right) + 0.5 \left( \frac{x_i^{0.25} - x_{i-}^{0.25}}{x_{i+}^{0.25} - x_{i-}^{0.25}} \right) \qquad (31) $$

The concave transformation ensures a higher sampling density close to the lower bound $x_{i-}$ and was preferentially used for the variables changing by at least one order of magnitude.

The authors have chosen regression through Gaussian Processes (GP), sometimes referred to as kriging, for its flexibility [51]. A GP is a non-parametric regression (or machine learning) technique, which means it does not rely on any a priori restrictive assumption about the structure of the function, such as a “linear” or “quadratic” regression. The GP “learns” the underlying structure of the data to make predictions. Though GP techniques have been developed for high dimensional datasets [52–54], standard GPs with constant basis (i.e. simple kriging) and Matérn3/2 kernels have been used for this work. One advantage of GP is their interpretability (see Appendix A for theoretical background and further discussion).

The quality of the surrogate is estimated through cross-validation [55], a procedure where a part $1/n$ of the data is randomly selected and left apart (here $n = 5$), acting as a test sample. A surrogate is fitted on a fraction $(1-1/n)$ of the sample and the procedure is repeated $n$ times by permuting the samples. The metric for the estimation of the quality of the surrogate of an output $f$ is the Root Mean Square Error (RMSE), defined by Eq. (32):

$$ \text{RMSE}(f) = \left( \sum_{i=1}^{N} \frac{[f(\text{TRNSYS}) - (f)_{\text{surrogate}}]^2}{N} \right)^{1/2} \qquad (32) $$

The surrogates of both KPI are built through the iterative generation of points $\chi$ ($\chi \in [0; 1]^D$) and subsequent evaluation of TRNSYS models, starting with $N = 170$ points at the first iteration. The points are generated with a Latin Hyper Square (LHS), a method with enhanced space filling properties [56]. They must fulfil the constraint (C1) to ensure that the heat evacuation to the CT is started only when the wet bulb temperature is above the CT approach by 1 °C (Eq. (33)).
<figure><img src="image_17.png" /></figure>

<figure><img src="image_18.png" /></figure>

<figure><img src="image_19.png" /></figure>

<figure><img src="image_20.png" /></figure>

<figure><img src="image_21.png" /></figure>

<figure><img src="image_22.png" /></figure>

<figure><img src="image_23.png" /></figure>

<figure><img src="image_24.png" /></figure>

<figure><img src="image_25.png" /></figure>

<figure><img src="image_26.png" /><figcaption>**Fig. 12.** One-at-a-time sensitivity analysis. The bolder points account for the preliminary sizing defined in Table 2. Thermal demand and distribution: (a) Maximum cooling power $\dot{Q}_{\text{cooling}}^{\text{max}}$; (b) Cooling set point temperature $T_{\text{sp cooling}}$; (c) Nominal storage duration of cooling tank $\Delta t_5$[h]; (d) Fraction of DHW $r_{\text{DHW}}$. Absorption chiller: (e) Normalized nominal cooling power $\dot{Q}_{\text{sorp}}^{\text{ev} *}$. Cooling Tower: (f) Coefficient c; (g) Exponent n; (h) Ratio of maximal air flow rate to water flow rate</figcaption></figure>
<figure><img src="image_17.png" /></figure>

<figure><img src="image_18.png" /></figure>

<figure><img src="image_19.png" /></figure>

<figure><img src="image_20.png" /></figure>

<figure><img src="image_21.png" /></figure>

<figure><img src="image_22.png" /></figure>

<figure><img src="image_23.png" /></figure>

<figure><img src="image_24.png" /></figure>

<figure><img src="image_25.png" /></figure>

<figure><img src="image_26.png" /><figcaption>**Fig. 12.** One-at-a-time sensitivity analysis. The bolder points account for the preliminary sizing defined in Table 2. Thermal demand and distribution: (a) Maximum cooling power $Q_{\text{cooling}}^{\text{max}}$; (b) Cooling set point temperature $T_{\text{sp cooling}}$; (c) Nominal storage duration of cooling tank $\Delta t_5$[h]; (d) Fraction of DHW $r_{\text{DHW}}$. Absorption chiller: (e) Normalized nominal cooling power $\dot{Q}_{\text{sorp}}^{\text{ev}}$. Cooling Tower: (f) Coefficient c; (g) Exponent n; (h) Ratio of maximal air flow rate to water flow rate</figcaption></figure>
$\dot{m}_{air,CT}^{max}/\dot{m}_{w,CT}$; (i) Ratio of CT water flow rate to the intermediary flow rate of the absorption chiller $\dot{m}_{w,CT}/\dot{m}_{int}$. Control strategy: (j) Upper dead band of micro-processor #1 udb1; (k) Upper dead band of microprocessor #2 udb2; (l) Upper dead band of comparator C1 of microprocessor #4 udb4,1; (m) Difference between the cooling setpoint and the absorption chiller outlet temperature $dT_{sp}^{sorp}$; (n) Cooling tower approach $dT_{sp}^{CT}$; Buried pipes: (o) Pipe length; (p) Normalized casing diameter $d_{casing}^*$ (L = 500 m); (q) Nominal linear pressure drop $\Delta p$ (L = 500 m).

<figure><img src="image_27.png" /><figcaption>Fig. 12. (continued).</figcaption></figure>

$$ (C1) : udb_{4,1} \geq dT_{sp,CT} + 1^{\circ}C \quad (33) $$

During the following iterations, a second constraint (C2) excludes the configurations with excessive electric consumption since they would be of no interest compared to the status quo (Eq. (34)):

$$ (C2) : W_{el}^{*}(\chi) < 0.3 \quad (34) $$

The refinement is stopped when $N = 4589$ TRNSYS models have been evaluated since a negligible improvement of the RMSE of $W_{el}^*$ GP is observed (see Fig. 13a). The RMSE of $W_{el}^*$ reaches 0.0115 and the GP is

in good agreement with the TRNSYS models outputs (see Fig. 13b). For 75 points on Pareto fronts reported in section 4, the RMSE of $W_{el}^*$ is equal to 0.116. As these points have not been used for the GP training, the similarity of both RMSE indicates the robustness of the surrogate. Note that a quadratic regression summing a constant term and all linear, quadratic and interactions terms (respectively $\chi_i$, $\chi_j^2$ and $\chi_i \cdot \chi_j$ with $i \neq j$) has an RMSE equal to 0.0274. In other words, the GP outperforms the quadratic regression when learning the underlying structure of the data.
$\dot{m}_{air,CT}^{max}/\dot{m}_{w,CT}$; (i) Ratio of CT water flow rate to the intermediary flow rate of the absorption chiller $\dot{m}_{w,CT}/\dot{m}_{int}$. Control strategy: (j) Upper dead band of micro-processor #1 udb1; (k) Upper dead band of microprocessor #2 udb2; (l) Upper dead band of comparator C1 of microprocessor #4 udb4,1; (m) Difference between the cooling setpoint and the absorption chiller outlet temperature $dT_{sp}^{sorp}$; (n) Cooling tower approach $dT_{sp}^{CT}$; Buried pipes: (o) Pipe length; (p) Normalized casing diameter $d_{casing}^*$ (L = 500 m); (q) Nominal linear pressure drop $\Delta p$ (L = 500 m).

<figure><img src="image_27.png" /></figure>

<figure><img src="image_28.png" /></figure>

<figure><img src="image_29.png" /></figure>

<figure><img src="image_30.png" /></figure>

<figure><img src="image_31.png" /></figure>

<figure><img src="image_32.png" /></figure>

<figure><img src="image_33.png" /><figcaption>Fig. 12. (continued).</figcaption></figure>

$$ (C1) : udb_{4,1} \geq dT_{sp,CT} + 1^{\circ}C \qquad (33) $$

During the following iterations, a second constraint (C2) excludes the configurations with excessive electric consumption since they would be of no interest compared to the status quo (Eq. (34)):

$$ (C2) : W_{el}^{*}(\chi) < 0.3 \qquad (34) $$

The refinement is stopped when $N = 4589$ TRNSYS models have been evaluated since a negligible improvement of the RMSE of $W_{el}^*$ GP is observed (see Fig. 13a). The RMSE of $W_{el}^*$ reaches 0.0115 and the GP is

in good agreement with the TRNSYS models outputs (see Fig. 13b). For 75 points on Pareto fronts reported in section 4, the RMSE of $W_{el}^*$ is equal to 0.116. As these points have not been used for the GP training, the similarity of both RMSE indicates the robustness of the surrogate. Note that a quadratic regression summing a constant term and all linear, quadratic and interactions terms (respectively $\chi_i$, $\chi_j^2$ and $\chi_i \cdot \chi_j$ with $i \neq j$) has an RMSE equal to 0.0274. In other words, the GP outperforms the quadratic regression when learning the underlying structure of the data.
<figure><img src="image_28.png" /><figcaption>Fig. 13. (a) Evolution of the RMSE during the construction of $W_{el}^*$ surrogate. (b) Quality of this surrogate: TRNSYS data vs GP predictions, for the datasets used for learning and for results of the optimization reported in §4 (three points per scenario: one trade-off and the two ends of each Pareto front). The dotted black lines $\delta W = \pm 0.02$ indicate an absolute error of $\pm 0.02$ on the prediction of $W_{el}^*$.</figcaption></figure>

<table><caption>**Table 6**
Cost and GWP of energies.</caption><thead><tr><th>Energy</th><th>Cost at year 1 as a function of delivered energy E [£.MWh<sup>-1</sup>] <sup>(a)</sup></th><th>Yearly increase [%.y<sup>-1</sup>]</th><th>GWP [kgCO<sub>2</sub>eq.MWh<sup>-1</sup>] <sup>(b)</sup></th></tr></thead><tbody><tr><td>Heating Oil</td><td>110.3 - <div style="display: inline-block; vertical-align: middle; text-align: center;"><div style="border-bottom: 1px solid black; padding-bottom: 1px;">87.8</div><div style="padding-top: 1px;">1 + exp(25.43 - 16.62log<sub>10</sub>(E) + 3.79(log<sub>10</sub>(E))<sup>2</sup> - 0.306(log<sub>10</sub>(E))<sup>3</sup>)</div></div></td><td>0.90</td><td>321</td></tr><tr><td>Electricity</td><td>192.5 - <div style="display: inline-block; vertical-align: middle; text-align: center;"><div style="border-bottom: 1px solid black; padding-bottom: 1px;">135.3</div><div style="padding-top: 1px;">1 + exp(13.72 - 11.8log<sub>10</sub>(E) + 3.32(log<sub>10</sub>(E))<sup>2</sup> - 0.325(log<sub>10</sub>(E))<sup>3</sup>)</div></div></td><td>1.20</td><td>840</td></tr></tbody></table>

<figure><img src="image_29.png" /><figcaption>Fig. 14. Correction factor $f_{CO_2(n)}$ according to the French thermal regulation RE2020 for the general case and the specific case of a refrigerant fluid.</figcaption></figure>

### 4.1.2. Definition of the optimization problem

Multi-objective optimization aims at finding all possible designs when two or more competing objectives are considered. The resulting set of designs is known as the *Pareto front*. No design points can be more favorable than the *Pareto front*: an improvement in one objective requires a degradation in all other objectives.

#### 4.1.2.1. Objectives.
The authors have considered the minimization of two objectives:

- the cost of energy $c$ (see Eq. (35)) expressed in £.MWh$^{-1}$ and computed on $N_{y,LCOE} = 25$ years,

- the Global Warming Potential (GWP) $\gamma$ (see Eq. (36)) of the energy, expressed in kgCO$_2$eq.MWh$^{-1}$.

$$c = \frac{1}{N_{y,LCOE} \cdot Q_{\text{demand}}} \left( C_0 + \sum_{n=1}^{N_{y,LCOE}} \sum_{i=1}^{N_{\text{expense}}} C_{1,i} \left( \frac{1 + \alpha_i}{1 + a} \right)^n \right) \quad (35)$$

<footnote>a Adapted from data provided by the French Ministry of Ecology and Sustainable Development [57,58]</footnote>

<footnote>b According to Base Carbone by French Energy Agency ADEME [62]. The electricity GWP is from Martinique.</footnote>
<figure><img src="image_34.png" /><figcaption>Fig. 13. (a) Evolution of the RMSE during the construction of $W_{el}^*$ surrogate. (b) Quality of this surrogate: TRNSYS data vs GP predictions, for the datasets used for learning and for results of the optimization reported in §4 (three points per scenario: one trade-off and the two ends of each Pareto front). The dotted black lines $\delta W = \pm 0.02$ indicate an absolute error of $\pm 0.02$ on the prediction of $W_{el}^*$.</figcaption></figure>

<table><caption>**Table 6**
Cost and GWP of energies.</caption><thead><tr><th>Energy</th><th>Cost at year 1 as a function of delivered energy E [£.MWh<sup>-1</sup>] <sup>(a)</sup></th><th>Yearly increase [%.y<sup>-1</sup>]</th><th>GWP [kgCO<sub>2</sub>eq.MWh<sup>-1</sup>] <sup>(b)</sup></th></tr></thead><tbody><tr><td>Heating Oil</td><td>110.3 - <div style="display: inline-block; vertical-align: middle; text-align: center;"><div style="border-bottom: 1px solid black; padding-bottom: 1px;">87.8</div><div style="padding-top: 1px;">1 + exp(25.43 - 16.62log<sub>10</sub>(E) + 3.79(log<sub>10</sub>(E))<sup>2</sup> - 0.306(log<sub>10</sub>(E))<sup>3</sup>)</div></div></td><td>0.90</td><td>321</td></tr><tr><td>Electricity</td><td>192.5 - <div style="display: inline-block; vertical-align: middle; text-align: center;"><div style="border-bottom: 1px solid black; padding-bottom: 1px;">135.3</div><div style="padding-top: 1px;">1 + exp(13.72 - 11.8log<sub>10</sub>(E) + 3.32(log<sub>10</sub>(E))<sup>2</sup> - 0.325(log<sub>10</sub>(E))<sup>3</sup>)</div></div></td><td>1.20</td><td>840</td></tr></tbody></table>

<figure><img src="image_35.png" /><figcaption>Fig. 14. Correction factor $f_{CO_2(n)}$ according to the French thermal regulation RE2020 for the general case and the specific case of a refrigerant fluid.</figcaption></figure>

### 4.1.2. Definition of the optimization problem

Multi-objective optimization aims at finding all possible designs when two or more competing objectives are considered. The resulting set of designs is known as the *Pareto front*. No design points can be more favorable than the *Pareto front*: an improvement in one objective requires a degradation in all other objectives.

#### 4.1.2.1. Objectives.
The authors have considered the minimization of two objectives:

- the cost of energy $c$ (see Eq. (35)) expressed in £.MWh$^{-1}$ and computed on $N_{y,LCOE} = 25$ years,

- the Global Warming Potential (GWP) $\gamma$ (see Eq. (36)) of the energy, expressed in kgCO$_2$eq.MWh$^{-1}$.

$$c = \frac{1}{N_{y,LCOE} \cdot Q_{\text{demand}}} \left( C_0 + \sum_{n=1}^{N_{y,LCOE}} \sum_{i=1}^{N_{\text{expense}}} C_{1,i} \left( \frac{1 + \alpha_i}{1 + a} \right)^n \right) \quad (35)$$

<footnote>a Adapted from data provided by the French Ministry of Ecology and Sustainable Development [57,58]</footnote>

<footnote>b According to Base Carbone by French Energy Agency ADEME [62]. The electricity GWP is from Martinique.</footnote>
<figure><img src="image_30.png" /><figcaption>Fig. 15. Cost of energy as a function of the delivered energy. Adapted from data provided by the French Ministry of Ecology and Sustainable Development [57,58].</figcaption></figure>

component making, distribution, installation, maintenance and end of life) and $\gamma_{e,i}$ is the GWP associated with energy $i$. According to the French environmental regulation of buildings RE2020 [59], the GWP is computed over $N_{y,GWP} = 50$ years, and the GWP at year $n$ is corrected by a function $f_{CO2}(n)$ (see Fig. 14). Discussing the relevance of the RE2020 framework is beyond the scope of this paper. Note that compared with continental France, the electricity GWP in French overseas is extremely high (here 840 vs. 79 kgCO2eq.MWh$^{-1}$) since electricity is mostly produced by fossil fuels combustion. The GWP of the oil boiler and air-cooled chiller are computed according to datasheets integrated in the RE2020 framework, while the GWP of the absorption chiller and Cooling Tower are derived from already published papers (see Table 8).

The electric consumption $W_{el}$ is estimated from the surrogate as

$$W_{el}(\chi) = W_{el}^{*}(\chi) \times Q_{demand} \left( Q_{cooling}^{max}, r_{DHW} \right) \quad \text{where} \quad Q_{demand} \left( Q_{cooling}^{max}, r_{DHW} \right)$$

[MWh.y$^{-1}$] is a simple quadratic regression (with coefficient of determination $R^2 \approx 1$):

$$Q_{demand} \left( \dot{Q}_{cooling}^{max}, r_{DHW} \right) = \left( 16.018 + 66.999 \cdot \dot{Q}_{cooling}^{max} + 1.6057 \cdot r_{DHW} + 4.5835 \cdot \dot{Q}_{cooling}^{max} \cdot r_{DHW} - 9.1558 \cdot \dot{Q}_{cooling}^{max}^2 - 0.19682 \cdot r_{DHW}^2 \right)^2 \quad (37)$$

$$\gamma = \frac{1}{N_{y,GWP} \cdot Q_{demand}} \sum_{n=1}^{N_{y,GWP}} \left( \sum_{i=1}^{N_{comp}} \Gamma_{comp} \cdot f_{CO2}(n) + \sum_{i=1}^{N_{energy}} \gamma_{e,i} \cdot E_{i} \cdot f_{CO2}(n) \right) \quad (36)$$

In Eq. (35), $C_0$ is the initial investment, $C_{1,i}$ is the cost of expense $i$ at year 1, $a_i$ is the yearly increase of this expense $i$ (in %.y$^{-1}$), and $a$ is the discount rate, assumed to be 3.55%.y$^{-1}$ (see Table 6). Furthermore, the maintenance cost is assumed to increase by 1.41% per year, and the assumptions regarding the cost and CO$_2$ content of oil and electricity are reported in Table 6 and Fig. 15. Note that the refurbishment of the tanks, absorption chiller, air-cooled chiller, and gas boiler is included in the cost, since their lifetime (20–22 years) is less than $N_{y,LCOE}$. The costs of energy (electricity and oil) are estimated based on a survey published by the French Ministry of Ecology and Sustainable Development on a yearly basis [57,58]. The evolution of the macroeconomic parameters (inflation, discount rate, electricity and oil costs) are in line with the French subsidy fund Fonds Chaleur Renouvelable. Discussing the relevance of the values of the macroeconomic parameters and their evolutions over 25 years is beyond the scope of this paper. The investment and maintenance costs of every component are derived from already published regressions or are established from datasets (see Table 8).

In eq. (36), $\Gamma_{comp,i}$ is the GWP of component $i$ (including the

4.1.2.2. Bounds and constraints. $\chi_i$ must be in the range $[0;1]^D$. The constraint (C1) applies.

4.1.2.3. Numerical resolution. The multi-objective optimization problem was solved using Matlab. As recommended by Matlab developers, the Pareto front is determined through a two-steps procedure with first an exploration of the design space by a global optimizer (paretosearch function) followed by a refinement with a local optimizer (fgoalattain function) [60,61]. Conventionally, a trade-off between the competing objectives is defined as the closest point to the unachievable simultaneous minimization of both cost $c$ and GWP $\gamma$. This point on the Pareto front $c(\gamma)$ minimizes the dimensionless distance $\ell = \sqrt{\left(\frac{c(\gamma) - \min(c)}{\min(c)}\right)^2 + \left(\frac{\gamma - \min(\gamma)}{\min(\gamma)}\right)^2}$:

$$\{c, \gamma\}_{\text{tradeoff}} = \min \left( \sqrt{\left(\frac{c(\gamma) - \min(c)}{\min(c)}\right)^2 + \left(\frac{\gamma - \min(\gamma)}{\min(\gamma)}\right)^2} \right) \quad (38)$$

## 4.2. Optimization of a baseline configuration

The configuration to be optimized is described in Table 7. The value of the fixed parameters reported in Table 7 are identical to the

<figure><img src="image_31.png" /><figcaption>Fig. 16. Comparison of the structures of the cost $c$ for (a) the tradeoff (baseline optimization) and (b) the status quo.</figcaption></figure>

<figure><img src="image_32.png" /></figure>
<figure><img src="image_36.png" /><figcaption>Fig. 15. Cost of energy as a function of the delivered energy. Adapted from data provided by the French Ministry of Ecology and Sustainable Development [57,58].</figcaption></figure>

component making, distribution, installation, maintenance and end of life) and $\gamma_{e,i}$ is the GWP associated with energy $i$. According to the French environmental regulation of buildings RE2020 [59], the GWP is computed over $N_{y,GWP} = 50$ years, and the GWP at year $n$ is corrected by a function $f_{CO2}(n)$ (see Fig. 14). Discussing the relevance of the RE2020 framework is beyond the scope of this paper. Note that compared with continental France, the electricity GWP in French overseas is extremely high (here 840 vs. 79 kgCO2eq.MWh$^{-1}$) since electricity is mostly produced by fossil fuels combustion. The GWP of the oil boiler and air-cooled chiller are computed according to datasheets integrated in the RE2020 framework, while the GWP of the absorption chiller and Cooling Tower are derived from already published papers (see Table 8).

The electric consumption $W_{el}$ is estimated from the surrogate as

$$W_{el}(\chi) = W_{el}^{*}(\chi) \times Q_{demand} \left( Q_{cooling}^{max}, r_{DHW} \right) \quad \text{where} \quad Q_{demand} \left( Q_{cooling}^{max}, r_{DHW} \right)$$

[MWh.y$^{-1}$] is a simple quadratic regression (with coefficient of determination $R^2 \approx 1$):

$$Q_{demand}(\dot{Q}_{cooling}^{max}, r_{DHW}) = \left( 16.018 + 66.999 \cdot \dot{Q}_{cooling}^{max} + 1.6057 \cdot r_{DHW} + 4.5835 \cdot \dot{Q}_{cooling}^{max} \cdot r_{DHW} - 9.1558 \cdot \dot{Q}_{cooling}^{max}^2 - 0.19682 \cdot r_{DHW}^2 \right)^2 \quad (37)$$

$$\gamma = \frac{1}{N_{y,GWP} \cdot Q_{demand}} \sum_{n=1}^{N_{y,GWP}} \left( \sum_{i=1}^{N_{comp}} \Gamma_{comp} \cdot f_{CO2}(n) + \sum_{i=1}^{N_{energy}} \gamma_{e,i} \cdot E_{i} \cdot f_{CO2}(n) \right) \quad (36)$$

In Eq. (35), $C_0$ is the initial investment, $C_{1,i}$ is the cost of expense $i$ at year 1, $a_i$ is the yearly increase of this expense $i$ (in %.y$^{-1}$), and $a$ is the discount rate, assumed to be 3.55%.y$^{-1}$ (see Table 6). Furthermore, the maintenance cost is assumed to increase by 1.41% per year, and the assumptions regarding the cost and CO2 content of oil and electricity are reported in Table 6 and Fig. 15. Note that the refurbishment of the tanks, absorption chiller, air-cooled chiller, and gas boiler is included in the cost, since their lifetime (20–22 years) is less than $N_{y,LCOE}$. The costs of energy (electricity and oil) are estimated based on a survey published by the French Ministry of Ecology and Sustainable Development on a yearly basis [57,58]. The evolution of the macroeconomic parameters (inflation, discount rate, electricity and oil costs) are in line with the French subsidy fund Fonds Chaleur Renouvelable. Discussing the relevance of the values of the macroeconomic parameters and their evolutions over 25 years is beyond the scope of this paper. The investment and maintenance costs of every component are derived from already published regressions or are established from datasets (see Table 8).

In eq. (36), $\Gamma_{comp,i}$ is the GWP of component $i$ (including the

4.1.2.2. Bounds and constraints. $\chi_i$ must be in the range $[0;1]^D$. The constraint (C1) applies.

4.1.2.3. Numerical resolution. The multi-objective optimization problem was solved using Matlab. As recommended by Matlab developers, the Pareto front is determined through a two-steps procedure with first an exploration of the design space by a global optimizer (paretosearch function) followed by a refinement with a local optimizer (fgoalattain function) [60,61]. Conventionally, a trade-off between the competing objectives is defined as the closest point to the unachievable simultaneous minimization of both cost $c$ and GWP $\gamma$. This point on the Pareto front $c(\gamma)$ minimizes the dimensionless distance $\ell = \sqrt{\left(\frac{c(\gamma) - \min(c)}{\min(c)}\right)^2 + \left(\frac{\gamma - \min(\gamma)}{\min(\gamma)}\right)^2}$:

$$\{c, \gamma\}_{\text{tradeoff}} = \min \left( \sqrt{\left(\frac{c(\gamma) - \min(c)}{\min(c)}\right)^2 + \left(\frac{\gamma - \min(\gamma)}{\min(\gamma)}\right)^2} \right) \quad (38)$$

## 4.2. Optimization of a baseline configuration

The configuration to be optimized is described in Table 7. The value of the fixed parameters reported in Table 7 are identical to the

<figure><img src="image_37.png" /><figcaption>Fig. 16. Comparison of the structures of the cost $c$ for (a) the tradeoff (baseline optimization) and (b) the status quo.</figcaption></figure>

<figure><img src="image_38.png" /></figure>
<figure><img src="image_33.png" /></figure>

<figure><img src="image_34.png" /></figure>

<figure><img src="image_35.png" /></figure>

<figure><img src="image_36.png" /></figure>

<figure><img src="image_37.png" /></figure>

<figure><img src="image_38.png" /><figcaption>**Fig. 17.** Influence of some parameters upon the Pareto front: (a) maximum cooling power $Q_{cooling}^{max}$; (b) buried pipe length $L$; (c) geothermal temperature $T_{GTH}$; (d) geothermal flow-rate $\dot{m}_{GTH}$; (e) ratio of DHW $r_{DHW}$; (f) and cooling set point temperature $T_{sp cooling}$. The trade-off is highlighted and the black arrows indicate the reference scenario defined in Table 7.</figcaption></figure>
<figure><img src="image_39.png" /></figure>

<figure><img src="image_40.png" /></figure>

<figure><img src="image_41.png" /></figure>

<figure><img src="image_42.png" /></figure>

<figure><img src="image_43.png" /></figure>

<figure><img src="image_44.png" /><figcaption>Fig. 17. Influence of some parameters upon the Pareto front: (a) maximum cooling power $Q_{cooling}^{max}$; (b) buried pipe length L; (c) geothermal temperature $T_{GTH}$; (d) geothermal flow-rate $\dot{m}_{GTH}$; (e) ratio of DHW $r_{DHW}$; (f) and cooling set point temperature $T_{sp cooling}$. The trade-off is highlighted and the black arrows indicate the reference scenario defined in Table 7.</figcaption></figure>
<figure><img src="image_39.png" /><figcaption>**Fig. 18.** Normalized share of cooling from the sorption chiller $Q_{\text{sorp}}^{\text{ev}}$ and electricity consumption $W_{\text{el}}^{*}$ for the trade-offs reported in Fig. 17, as re-computed by TRNYS. The bold lowercase letters refer to the subplots in Fig. 17. The TRNSYS computation for $r_{\text{DHW}} = 0$ did not converge and is not represented.</figcaption></figure>

<table><caption>**Table 7**

TRNSYS parameters explored for the construction of the surrogates (D = 17 variables)</caption><thead><tr><th>Component</th><th>TRNSYS parameters (Predictor variables of the surrogates)</th><th>Lower bound</th><th>Upper bound</th><th>Transform</th><th>Value used for the optimization reported in § 4.2 <sup>(a)</sup></th></tr></thead><tbody><tr><td rowspan="4">Thermal demand and distribution</td><td>Maximum cooling power Q<sub>cooling</sub><sup>max</sup> [kW]</td><td>50</td><td>2000</td><td>Concave</td><td>2000</td></tr><tr><td>Cooling set point temperature T<sub>sp cooling</sub> [°C]</td><td>7</td><td>12</td><td>Linear</td><td>7</td></tr><tr><td>Nominal storage duration of cooling tank Δt<sub>5</sub> [h]</td><td>0.25</td><td>3.0</td><td>Concave</td><td></td></tr><tr><td>Fraction of DHW r<sub>DHW</sub> [−] (= 0 if no DHW; = 1 if DHW computed in §2.1.2; varies linearly between bounds)</td><td>0</td><td>1</td><td>Linear</td><td>1</td></tr><tr><td rowspan="2">Geothermal resource</td><td>Geothermal temperature T<sub>GTH</sub> [°C]</td><td>60</td><td>110</td><td>Concave</td><td>80</td></tr><tr><td>Specific mass flow rate m&#775;<sub>GTH</sub>/Q<sub>cooling</sub><sup>max</sup> [kg.MJ<sup>-1</sup>]</td><td>1</td><td>100</td><td>Concave</td><td>13.9 <sup>(b)</sup></td></tr><tr><td rowspan="2">Absorption chiller</td><td>Normalized nominal cooling power Q&#775;<sub>sorp</sub><sup>ev</sup> = Q&#775;<sub>sorp</sub><sup>ev</sup>/Q<sub>cooling</sub><sup>max</sup> [−]</td><td>0.25</td><td>2.0</td><td>Concave</td><td></td></tr><tr><td>Ratio of maximal air flow rate to water flow rate m&#775;<sub>air CT</sub><sup>max</sup>/m&#775;<sub>w CT</sub> [−]</td><td>0.5</td><td>3.0</td><td>Linear</td><td></td></tr><tr><td rowspan="4">Cooling tower</td><td>Ratio of the CT water flow rate to the intermediary flow rate of the absorption chiller to m&#775;<sub>w CT</sub>/m&#775;<sub>int</sub></td><td>0.5</td><td>2.0</td><td>Linear</td><td></td></tr><tr><td>Upper dead band of microprocessor #2 udb<sub>2</sub> [°C]</td><td>−1.2</td><td>−0.5</td><td>Linear</td><td></td></tr><tr><td>Upper dead band of microprocessor #1 udb<sub>1</sub> [°C]</td><td>3</td><td>7</td><td>Linear</td><td></td></tr><tr><td>Difference between the cooling setpoint and the absorption chiller outlet temperature dT<sub>sp</sub><sup>cool</sup> [°C]</td><td>0</td><td>2</td><td>Linear</td><td></td></tr><tr><td rowspan="3">Control</td><td>Cooling tower approach dT<sub>sp</sub><sup>CT</sup> [°C]</td><td>2</td><td>4</td><td>Linear</td><td></td></tr><tr><td>Upper dead band of comparator C1 of microprocessor #4 udb<sub>4,1</sub> [°C]</td><td>3</td><td>6</td><td>Linear</td><td></td></tr><tr><td>Pipe length per estimated delivered energy</td><td>0</td><td>1</td><td>Linear</td><td>0</td></tr><tr><td rowspan="3">Buried twin pipes</td><td>q<sub>l</sub><sup>-1</sup> = L/ (5500 • Q&#775;<sub>cooling</sub><sup>max</sup>) [m.MWh<sup>-1</sup>] <sup>(c)</sup></td><td></td><td></td><td></td><td></td></tr><tr><td>Normalized casing diameter d<sub>casing</sub><sup>*</sup> [−]</td><td>2.5</td><td>5</td><td>Linear</td><td>2.5 <sup>(d)</sup></td></tr><tr><td>Nominal linear pressure drop Δ<sub>ll</sub> [Pa.m<sup>-1</sup>]</td><td>50</td><td>200</td><td>Linear</td><td>100 <sup>(d)</sup></td></tr></tbody></table>

<sup>a</sup> Empty elements indicate the design variables to be optimized.

<sup>b</sup> $\dot{m}_{GTH} = 100 \times 10^3 \text{ kg.h}^{-1}$

<sup>c</sup> District Heating Networks are often considered too expensive if the delivered energy density is below 1 MWh.m<sup>-1</sup>. t<sub>eq</sub> = 5500 h is the cooling duration at full cooling load.

<sup>d</sup> Fixed if the pipe length L is zero, left to the optimizer otherwise.

preliminary sizing values reported in Table 2, except the much higher maximum cooling power $Q_{\text{cooling}}^{\text{max}}$ (2 MW instead 104.3 kW) and the lower specific geothermal flow rate of $\dot{m}_{GTH}/Q_{\text{cooling}}^{\text{max}} = 13.9 \text{ kg.MJ}^{-1}$ (i.e. $\dot{m}_{GTH} = 100 \text{ ton.h}^{-1}$).

The cost c and GWP γ at the trade-off are 37.5 €.MWh<sup>-1</sup> and 103.1 kgCO<sub>2</sub>eq.MWh<sup>-1</sup>, and 33.2 €.MWh<sup>-1</sup> and 170.1 kgCO<sub>2</sub>eq.MWh<sup>-1</sup> for the status quo scenario. The Appendix C reports the values of the design variables at the trade-off. Though the nominal cooling power $\dot{Q}_{\text{sorp}}^{\text{ev}}$ equals $2.0 \times 0.77 = 1.54 \text{ MW}$, the absorption chiller covers only $\dot{Q}_{\text{sorp}}^{\text{ev}} \sim$

0.56 of the cooling load. An alternative design focusing on the GWP minimization leads to $\gamma = 94.7 \text{ kgCO}_2\text{eq.MWh}^{-1}$ at the expense of a higher cost ($c = 44.3 \text{ €.MWh}^{-1}$), as represented by the far right end of the Pareto fronts in Fig. 17. The larger absorption chiller ($\dot{Q}_{\text{sorp}}^{\text{ev}} = 2.29 \text{ MW}$) provides then more cooling ($\dot{Q}_{\text{sorp}}^{\text{ev}} \sim 0.70$).

The initial investment represents about one third of the total cost, so does the energy cost and the maintenance and refurbishment altogether (see Fig. 16a). The energy cost accounts for 78% of the total cost of the status quo, which exposes the status quo installation to the volatility of
<figure><img src="image_45.png" /><figcaption>**Fig. 18.** Normalized share of cooling from the sorption chiller $Q_{sorp}^{ev}$ and electricity consumption $W_{el}^{*}$ for the trade-offs reported in Fig. 17, as re-computed by TRNYS. The bold lowercase letters refer to the subplots in Fig. 17. The TRNSYS computation for $r_{DHW} = 0$ did not converge and is not represented.</figcaption></figure>

<table><caption>**Table 7**

TRNSYS parameters explored for the construction of the surrogates (D = 17 variables)</caption><thead><tr><th>Component</th><th>TRNSYS parameters (Predictor variables of the surrogates)</th><th>Lower bound</th><th>Upper bound</th><th>Transform</th><th>Value used for the optimization reported in § 4.2 <sup>(a)</sup></th></tr></thead><tbody><tr><td rowspan="4">Thermal demand and distribution</td><td>Maximum cooling power Q<sub>cooling</sub><sup>max</sup> [kW]</td><td>50</td><td>2000</td><td>Concave</td><td>2000</td></tr><tr><td>Cooling set point temperature T<sub>sp cooling</sub> [°C]</td><td>7</td><td>12</td><td>Linear</td><td>7</td></tr><tr><td>Nominal storage duration of cooling tank Δt<sub>5</sub> [h]</td><td>0.25</td><td>3.0</td><td>Concave</td><td></td></tr><tr><td>Fraction of DHW r<sub>DHW</sub> [−] (= 0 if no DHW; = 1 if DHW computed in §2.1.2; varies linearly between bounds)</td><td>0</td><td>1</td><td>Linear</td><td>1</td></tr><tr><td rowspan="2">Geothermal resource</td><td>Geothermal temperature T<sub>GTH</sub> [°C]</td><td>60</td><td>110</td><td>Concave</td><td>80</td></tr><tr><td>Specific mass flow rate m&#775;<sub>GTH</sub>/Q<sub>cooling</sub><sup>max</sup> [kg.MJ<sup>-1</sup>]</td><td>1</td><td>100</td><td>Concave</td><td>13.9 <sup>(b)</sup></td></tr><tr><td rowspan="2">Absorption chiller</td><td>Normalized nominal cooling power Q&#775;<sub>sorp</sub><sup>ev</sup> = Q&#775;<sub>sorp</sub><sup>ev</sup>/Q<sub>cooling</sub><sup>max</sup> [−]</td><td>0.25</td><td>2.0</td><td>Concave</td><td></td></tr><tr><td>Ratio of maximal air flow rate to water flow rate m&#775;<sub>air CT</sub><sup>max</sup>/m&#775;<sub>w CT</sub> [−]</td><td>0.5</td><td>3.0</td><td>Linear</td><td></td></tr><tr><td rowspan="4">Cooling tower</td><td>Ratio of the CT water flow rate to the intermediary flow rate of the absorption chiller to m&#775;<sub>w CT</sub>/m&#775;<sub>int</sub></td><td>0.5</td><td>2.0</td><td>Linear</td><td></td></tr><tr><td>Upper dead band of microprocessor #2 udb<sub>2</sub> [°C]</td><td>−1.2</td><td>−0.5</td><td>Linear</td><td></td></tr><tr><td>Upper dead band of microprocessor #1 udb<sub>1</sub> [°C]</td><td>3</td><td>7</td><td>Linear</td><td></td></tr><tr><td>Difference between the cooling setpoint and the absorption chiller outlet temperature dT<sub>sp</sub><sup>corp</sup> [°C]</td><td>0</td><td>2</td><td>Linear</td><td></td></tr><tr><td rowspan="3">Control</td><td>Cooling tower approach dT<sub>sp</sub><sup>CT</sup> [°C]</td><td>2</td><td>4</td><td>Linear</td><td></td></tr><tr><td>Upper dead band of comparator C1 of microprocessor #4 udb<sub>4,1</sub> [°C]</td><td>3</td><td>6</td><td>Linear</td><td></td></tr><tr><td>Pipe length per estimated delivered energy</td><td>0</td><td>1</td><td>Linear</td><td>0</td></tr><tr><td rowspan="3">Buried twin pipes</td><td>q<sub>el</sub><sup>-1</sup> = L/ (5500 • Q&#775;<sub>cooling</sub><sup>max</sup>) [m.MWh<sup>-1</sup>] <sup>(c)</sup></td><td></td><td></td><td></td><td></td></tr><tr><td>Normalized casing diameter d<sub>casing</sub><sup>*</sup> [−]</td><td>2.5</td><td>5</td><td>Linear</td><td>2.5 <sup>(d)</sup></td></tr><tr><td>Nominal linear pressure drop Δ<sub>η</sub> [Pa.m<sup>-1</sup>]</td><td>50</td><td>200</td><td>Linear</td><td>100 <sup>(d)</sup></td></tr></tbody></table>

<sup>a</sup> Empty elements indicate the design variables to be optimized.

<sup>b</sup> $\dot{m}_{GTH} = 100 \times 10^3 \text{ kg.h}^{-1}$

<sup>c</sup> District Heating Networks are often considered too expensive if the delivered energy density is below 1 MWh.m<sup>-1</sup>. t<sub>eq</sub> = 5500 h is the cooling duration at full cooling load.

<sup>d</sup> Fixed if the pipe length L is zero, left to the optimizer otherwise.

preliminary sizing values reported in Table 2, except the much higher maximum cooling power $Q_{cooling}^{max}$ (2 MW instead 104.3 kW) and the lower specific geothermal flow rate of $\dot{m}_{GTH}/Q_{cooling}^{max} = 13.9 \text{ kg.MJ}^{-1}$ (i.e. $\dot{m}_{GTH} = 100 \text{ ton.h}^{-1}$).

The cost c and GWP γ at the trade-off are 37.5 €.MWh<sup>-1</sup> and 103.1 kgCO<sub>2</sub>eq.MWh<sup>-1</sup>, and 33.2 €.MWh<sup>-1</sup> and 170.1 kgCO<sub>2</sub>eq.MWh<sup>-1</sup> for the status quo scenario. The Appendix C reports the values of the design variables at the trade-off. Though the nominal cooling power $\dot{Q}_{sorp}^{ev}$ equals $2.0 \times 0.77 = 1.54 \text{ MW}$, the absorption chiller covers only $Q_{sorp}^{ev} \sim$

0.56 of the cooling load. An alternative design focusing on the GWP minimization leads to $\gamma = 94.7 \text{ kgCO}_2\text{eq.MWh}^{-1}$ at the expense of a higher cost ($c = 44.3 \text{ €.MWh}^{-1}$), as represented by the far right end of the Pareto fronts in Fig. 17. The larger absorption chiller ($\dot{Q}_{sorp}^{ev} = 2.29 \text{ MW}$) provides then more cooling ($\dot{Q}_{sorp}^{ev} \sim 0.70$).

The initial investment represents about one third of the total cost, so does the energy cost and the maintenance and refurbishment altogether (see Fig. 16a). The energy cost accounts for 78% of the total cost of the status quo, which exposes the status quo installation to the volatility of
<table><caption>**Table 8**
Assumption related to cost and GWP of each system component. All powers are expressed in kW</caption><thead><tr><th rowspan="2">Component</th><th colspan="2">Cost C [€]</th><th rowspan="2">Global Warming Potential Γ [kgCO2eq]</th><th rowspan="2">Fabrication, installation, use (excluding energy) and dismantling</th><th rowspan="2">Lifetime [years]</th></tr><tr><th>Investment</th><th>Maintenance</th></tr></thead><tbody><tr><td>Oil boiler</td><td>C<sub>0</sub> = 2500 +<br>5000 • (1 - exp(-0.01381 • Q<sub>DHW</sub><sup>max</sup>))<sup>(a)</sup></td><td>C<sub>j</sub> = 200 +<br>600 • (1 - exp(-0.01612 • Q<sub>DHW</sub><sup>max</sup>))<sup>(a)</sup></td><td>Application of Ecopassport<br>UNIC-00022-V02.01-EN <sup>(b)</sup></td><td>22</td><td></td></tr><tr><td>Absorption<br>chiller</td><td>C<sub>0</sub> = 6671 • Q<sub>sorp</sub><sup>ev</sup> <sup>0.430</sup> + 3669 • Q<sub>sorp</sub><sup>ev</sup> <sup>0.730</sup> (gear &amp;<br>installation)<sup>(c)</sup></td><td>C<sub>j</sub> = 2.628 × 10<sup>-2</sup> • Q<sub>cooling</sub><sup>max</sup> <sup>0.490</sup> • t<sub>eq</sub><br>With t<sub>eq</sub> = Q<sub>cooling</sub><sup>max</sup> / Q<sub>cooling</sub><sup>ev</sup> duration of operation [h] <sup>(d)</sup></td><td>Γ = 217.3 • Q<sub>sorp</sub><sup>ev</sup> <sup>(e)</sup></td><td>20 <sup>(b)</sup></td><td></td></tr><tr><td>Air-cooled<br>chiller</td><td>C<sub>0</sub> = 1167.9 • Q<sub>ASHP</sub><sup>cond</sup> <sup>0.834</sup></td><td>C<sub>j</sub> = 250; C<sub>11</sub> = 704 + 105.73 • Q<sub>ASHP</sub><sup>cond</sup><br>(replacement of compressor at year 11) <sup>[63]</sup></td><td>Application of Ecopassport<br>UNIC-00039-V01.01-FR <sup>(b)</sup></td><td>22</td><td></td></tr><tr><td>Cooling<br>Tower</td><td>C<sub>0</sub> = 0.32 • m<sub>air,CT</sub><sup>max</sup> <sup>(f)</sup></td><td>C<sub>j</sub> = 0.03 • C<sub>0</sub></td><td>Γ = 0.76 • m<sub>air,CT</sub><sup>max</sup> <sup>(g)</sup></td><td>20</td><td></td></tr><tr><td>Buried twin<br>pipes</td><td>Cost of one pipe (SDR = 11) without insulation [€.m<sup>-1</sup>]<br>c<sub>p</sub> = 8.104 • e<sub>p</sub> + 1.081 • d<sub>int,p</sub> + 12584 • e<sub>p</sub> • d<sub>int,p</sub> +<br>274.1 • d<sub>int,p</sub><sup>2</sup></td><td>C<sub>j</sub> = 0</td><td>Only emissions related to the raw<br>material and manufacturing and casing<br>are considered.</td><td>50</td><td></td></tr><tr><td></td><td>Additional cost for insulation [€.m<sup>-1</sup>]<br>c<sub>insul</sub> = 9848 • π/4 • (d<sub>casing</sub><sup>2</sup> - 2d<sub>ext,p</sub><sup>2</sup>)</td><td></td><td>PE (one pipe) [kgCO2eq.m<sup>-1</sup>]<br>γ<sub>PE</sub> = γ<sub>PE,M</sub> • ρ<sub>PE</sub> • π • (d<sub>int,p</sub> • e<sub>p</sub> + e<sub>p</sub><sup>2</sup>)</td><td></td><td></td></tr><tr><td></td><td>Network layout, including pipe handling, ground<br>excavation and sand backfilling [€.m<sup>-1</sup>] (assuming a<br>trench section is 1 m<sup>2</sup>):<br>c<sub>layout</sub> = 55</td><td></td><td>Insulation (one pipe) [kgCO2eq.m<sup>-1</sup>]<br>(regression on data from <sup>[64]</sup>):<br>γ<sub>insul</sub> = 8330 • π/4 • (d<sub>casing</sub><sup>2</sup> - 2d<sub>ext,p</sub><sup>2</sup>)</td><td></td><td></td></tr><tr><td></td><td>Cost [€] of a section of length L [m]:<br>C<sub>0</sub> = L • (c<sub>layout</sub> + c<sub>insul</sub> + 2 • c<sub>pipe</sub>)</td><td></td><td>For a section of length L [m]:<br>Γ = L • (2γ<sub>PE</sub> + γ<sub>insul</sub>)</td><td></td><td></td></tr><tr><td>Geothermal<br>wells</td><td>I = 1.9 • 10<sup>6</sup> <sup>(i)</sup></td><td>C<sub>j</sub> = 50 • 10<sup>3</sup></td><td>ρ<sub>PE</sub> = 950 kg.m<sup>-3</sup>; PE density<br>γ<sub>PE,M</sub> = 3.90 kgCO2eq.kg<sup>-1</sup> <sup>(h)</sup></td><td></td><td></td></tr></tbody></table>

energy costs (see Fig. 16b). Note that the difference of cost between the geothermal system and the status quo could be cleared by a subsidy s defined by Eq. (39):

$$s = \frac{c - c_{statu quo}}{\gamma_{statu quo} - \gamma} \qquad (39)$$

Here $s = \frac{37.5-33.2}{170.1-103.1} = 70$ € per avoided ton CO₂eq. This is a relatively low value since, for example, the advisory board of the French Prime Minister sets a reference value for the CO₂eq ton (in € of 2018) at 54€ in 2018, 250€ in 2030, then 500€ in 2050, and finally 775€ in 2050 [70]. For both the geothermal system and the status quo, the energy represents 90 to 95% of the GWP.

### 4.3. Influence of the scenario parameters upon the trade-off

Several alternative scenarios have been considered to investigate the influence of the input parameters upon the Pareto front (see Fig. 17a-e). For every scenario, the system undergoes multi-objective optimization. The normalized share of cooling from absorption chiller $Q_{sorp}^{ev}$ ~ and electricity consumption $W_{el}^*$ at the trade-off (defined by Eq. (38)) are reported in Fig. 18. Note that both values originate from the TRNSYS model evaluated after the optimization. There are little discrepancies between the predictions and the “true” values of $W_{el}^*$ as computed by TRNSYS, both values being in good agreement (see Fig. 13b). At the

trade-off points, the following trends appear:

- **Thermal demand** (see Fig. 17a): Decreasing the cooling demand to 1.5 MW (and the DHW demand accordingly) results in an increase of the cost, as illustrated by the Pareto front moving to the right. A lower demand increases the capital-intensive equipment costs (mainly sorption machine and geothermal wells), maintenance, and equipment per amount of delivered energy.

- **Buried pipe length** (see Fig. 17b): The remoteness of the end consumer dramatically increases both the cost and GWP, even for relatively small distances, e.g., $L = 1650$ m ($q_c^{-1} = 0.15$ m.MWh⁻¹). The total cost c reaches 41.9 €.MWh⁻¹. The cost of the buried pipes including its installation reaches 1310 €.ml⁻¹ and accounts for 16% of c. The remoteness drastically increases the electricity consumption, due to an increased consumption of the ACC rather than the circulation pumps P_1 and P_2. Meanwhile, $Q_{sorp}^{ev}$ ~ is almost halved compared to the reference scenario. Remoteness appears as a major obstacle to the system deployment. Only a subsidy as defined in eq. (39) reaching 220 € per avoided ton CO₂eq could make the system profitable compared to the status quo.

- **Geothermal temperature** (see Fig. 17c): Increasing $T_{GTH}$ dramatically increases the amount of cooling (and the absorption chiller's COP) provided by the absorption chiller, decreasing both the cost and GWP at the trade-off. A similar behavior is observed for solar-driven

<footnote>a Source: regressions established on the data provided by http://www.prix-construction.info</footnote>

<footnote>b Refers to *Profils Environnementaux de Produits* (PEP) Ecopassport, available at https://register.pep-ecopassport.org/pep/consult</footnote>

<footnote>c Regression on 45 machine costs. Personal communications from manufacturers.</footnote>

<footnote>d Source: Adapted from [65]</footnote>

<footnote>e Source: [66], for a LiBr-H₂O single-effect absorption chiller, similar to the chiller considered in this paper.</footnote>

<footnote>f Typical investment cost is often assumed to be 150 € per “cooling tower ton” (i.e. per 4.396 kW).</footnote>

<footnote>g Source: [67] studied a CT operating 8760 h/y in Germany for 20 years. The electricity in usage stage accounted for 90% of the total GWP. Based on the paper, the GWP of the Raw material and manufacturing per air flow rate is estimated to be 0.76 kgCO₂eq/(kg·h⁻¹). The energy for the wastewater treatment and the fresh water demand is not taken into account here, neither the demand for freshwater.</footnote>

<footnote>h Source: Base Carbone by French Energy Agency ADEME (https://base-impacts.ademe.fr)</footnote>

<footnote>i Source: [68] p 104. The investment estimated in 2011 has been increased by 19% to take into account inflation [69].</footnote>
<table><caption>**Table 8**
Assumption related to cost and GWP of each system component. All powers are expressed in kW</caption><thead><tr><th rowspan="2">Component</th><th colspan="2">Cost C [€]</th><th rowspan="2">Global Warming Potential Γ [kgCO2eq]</th><th rowspan="2">Fabrication, installation, use (excluding energy) and dismantling</th><th rowspan="2">Lifetime [years]</th></tr><tr><th>Investment</th><th>Maintenance</th></tr></thead><tbody><tr><td>Oil boiler</td><td>C<sub>0</sub> = 2500 +<br>5000 • (1 - exp(-0.01381 • Q<sub>DHW</sub><sup>max</sup>))<sup>(a)</sup></td><td>C<sub>j</sub> = 200 +<br>600 • (1 - exp(-0.01612 • Q<sub>DHW</sub><sup>max</sup>))<sup>(a)</sup></td><td>Application of Ecopassport<br>UNIC-00022-V02.01-EN <sup>(b)</sup></td><td>22</td><td></td></tr><tr><td>Absorption<br>chiller</td><td>C<sub>0</sub> = 6671 • Q<sub>sorp</sub><sup>ev</sup> <sup>0.430</sup> + 3669 • Q<sub>sorp</sub><sup>ev</sup> <sup>0.730</sup> (gear &amp;<br>installation)<sup>(c)</sup></td><td>C<sub>j</sub> = 2.628 × 10<sup>-2</sup> • Q<sub>cooling</sub><sup>max</sup> <sup>0.490</sup> • t<sub>eq</sub><br>With t<sub>eq</sub> = Q<sub>cooling</sub><sup>max</sup> / Q<sub>cooling</sub><sup>ev</sup> duration of operation [h] <sup>(d)</sup></td><td>Γ = 217.3 • Q<sub>sorp</sub><sup>ev</sup> <sup>(e)</sup></td><td>20 <sup>(b)</sup></td><td></td></tr><tr><td>Air-cooled<br>chiller</td><td>C<sub>0</sub> = 1167.9 • Q<sub>ASHP</sub><sup>cond</sup> <sup>0.834</sup></td><td>C<sub>j</sub> = 250; C<sub>11</sub> = 704 + 105.73 • Q<sub>ASHP</sub><sup>cond</sup><br>(replacement of compressor at year 11) <sup>[63]</sup></td><td>Application of Ecopassport<br>UNIC-00039-V01.01-FR <sup>(b)</sup></td><td>22</td><td></td></tr><tr><td>Cooling<br>Tower</td><td>C<sub>0</sub> = 0.32 • m<sub>air,CT</sub><sup>max</sup> <sup>(f)</sup></td><td>C<sub>j</sub> = 0.03 • C<sub>0</sub></td><td>Γ = 0.76 • m<sub>air,CT</sub><sup>max</sup> <sup>(g)</sup></td><td>20</td><td></td></tr><tr><td>Buried twin<br>pipes</td><td>Cost of one pipe (SDR = 11) without insulation [€.m<sup>-1</sup>]<br>c<sub>p</sub> = 8.104 • e<sub>p</sub> + 1.081 • d<sub>int,p</sub> + 12584 • e<sub>p</sub> • d<sub>int,p</sub> +<br>274.1 • d<sub>int,p</sub><sup>2</sup><br>Additional cost for insulation [€.m<sup>-1</sup>]<br>c<sub>insul</sub> = 9848 • π/4 • (d<sub>casing</sub><sup>2</sup> - 2d<sub>ext,p</sub><sup>2</sup>)<br>Network layout, including pipe handling, ground<br>excavation and sand backfilling [€.m<sup>-1</sup>] (assuming a<br>trench section is 1 m<sup>2</sup>):<br>c<sub>layout</sub> = 55<br>Cost [€] of a section of length L [m]:<br>C<sub>0</sub> = L • (c<sub>layout</sub> + c<sub>insul</sub> + 2 • c<sub>pipe</sub>)</td><td>C<sub>j</sub> = 0</td><td>Only emissions related to the raw<br>material and manufacturing and casing<br>are considered.</td><td>50</td><td></td></tr><tr><td>Geothermal<br>wells</td><td>I = 1.9 • 10<sup>6</sup> <sup>(i)</sup></td><td>C<sub>j</sub> = 50 • 10<sup>3</sup></td><td>PE (one pipe) [kgCO2eq.m<sup>-1</sup>]:<br>γ<sub>PE</sub> = γ<sub>PE,M</sub> • ρ<sub>PE</sub> • π • (d<sub>int,p</sub> • e<sub>p</sub> + e<sub>p</sub><sup>2</sup>)<br>Insulation (one pipe) [kgCO2eq.m<sup>-1</sup>]<br>(regression on data from <sup>[64]</sup>):<br>γ<sub>insul</sub> = 8330 • π/4 • (d<sub>casing</sub><sup>2</sup> - 2d<sub>ext,p</sub><sup>2</sup>)<br>For a section of length L [m]:<br>Γ = L • (2γ<sub>PE</sub> + γ<sub>insul</sub>)<br>ρ<sub>PE</sub> = 950 kg.m<sup>-3</sup>; PE density<br>γ<sub>PE,M</sub> = 3.90 kgCO2eq.kg<sup>-1</sup> <sup>(h)</sup><br>Not taken into account since the GWP is<br>site-specific.</td><td></td><td>50</td><td></td></tr></tbody></table>

energy costs (see Fig. 16b). Note that the difference of cost between the geothermal system and the status quo could be cleared by a subsidy s defined by Eq. (39):

$$s = \frac{c - c_{statu quo}}{\gamma_{statu quo} - \gamma} \qquad (39)$$

Here $s = \frac{37.5-33.2}{170.1-103.1} = 70$ € per avoided ton CO₂eq. This is a relatively low value since, for example, the advisory board of the French Prime Minister sets a reference value for the CO₂eq ton (in € of 2018) at 54€ in 2018, 250€ in 2030, then 500€ in 2050, and finally 775€ in 2050 [70]. For both the geothermal system and the status quo, the energy represents 90 to 95% of the GWP.

### 4.3. Influence of the scenario parameters upon the trade-off

Several alternative scenarios have been considered to investigate the influence of the input parameters upon the Pareto front (see Fig. 17a-e). For every scenario, the system undergoes multi-objective optimization. The normalized share of cooling from absorption chiller $Q_{sorp}^{ev}$ ~ and electricity consumption $W_{el}^*$ at the trade-off (defined by Eq. (38)) are reported in Fig. 18. Note that both values originate from the TRNSYS model evaluated after the optimization. There are little discrepancies between the predictions and the “true” values of $W_{el}^*$ as computed by TRNSYS, both values being in good agreement (see Fig. 13b). At the

trade-off points, the following trends appear:

- **Thermal demand** (see Fig. 17a): Decreasing the cooling demand to 1.5 MW (and the DHW demand accordingly) results in an increase of the cost, as illustrated by the Pareto front moving to the right. A lower demand increases the capital-intensive equipment costs (mainly sorption machine and geothermal wells), maintenance, and equipment per amount of delivered energy.

- **Buried pipe length** (see Fig. 17b): The remoteness of the end consumer dramatically increases both the cost and GWP, even for relatively small distances, e.g., $L = 1650$ m ($q_c^{-1} = 0.15$ m.MWh⁻¹). The total cost c reaches 41.9 €.MWh⁻¹. The cost of the buried pipes including its installation reaches 1310 €.ml⁻¹ and accounts for 16% of c. The remoteness drastically increases the electricity consumption, due to an increased consumption of the ACC rather than the circulation pumps P_1 and P_2. Meanwhile, $Q_{sorp}^{ev}$ ~ is almost halved compared to the reference scenario. Remoteness appears as a major obstacle to the system deployment. Only a subsidy as defined in eq. (39) reaching 220 € per avoided ton CO₂eq could make the system profitable compared to the status quo.

- **Geothermal temperature** (see Fig. 17c): Increasing $T_{GTH}$ dramatically increases the amount of cooling (and the absorption chiller's COP) provided by the absorption chiller, decreasing both the cost and GWP at the trade-off. A similar behavior is observed for solar-driven

<footnote>a Source: regressions established on the data provided by http://www.prix-construction.info</footnote>

<footnote>b Refers to *Profils Environnementaux de Produits* (PEP) Ecopassport, available at https://register.pep-ecopassport.org/pep/consult</footnote>

<footnote>c Regression on 45 machine costs. Personal communications from manufacturers.</footnote>

<footnote>d Source: Adapted from [65]</footnote>

<footnote>e Source: [66], for a LiBr-H₂O single-effect absorption chiller, similar to the chiller considered in this paper.</footnote>

<footnote>f Typical investment cost is often assumed to be 150 € per “cooling tower ton” (i.e. per 4.396 kW).</footnote>

<footnote>g Source: [67] studied a CT operating 8760 h/y in Germany for 20 years. The electricity in usage stage accounted for 90% of the total GWP. Based on the paper, the GWP of the Raw material and manufacturing per air flow rate is estimated to be 0.76 kgCO₂eq/(kg·h⁻¹). The energy for the wastewater treatment and the fresh water demand is not taken into account here, neither the demand for freshwater.</footnote>

<footnote>h Source: Base Carbone by French Energy Agency ADEME (https://base-impacts.ademe.fr)</footnote>

<footnote>i Source: [68] p 104. The investment estimated in 2011 has been increased by 19% to take into account inflation [69].</footnote>
absorption chillers [71], for which it is more a problem to overcome
since the solar irradiation drives the temperature level of the driving
source temperature [72]. Indeed, for these systems, the low driving
temperature available in the morning limits the cooling generation
capacity, which might be a problem for some applications. In the
case of the present work, the increased cooling capacity available at
high driving temperatures decreases the need of the ACC, also
decreasing the electricity consumption. To avoid LiBr crystallization,
the generator inlet temperature is not allowed to exceed a critical
value in the range 85–95 °C (see eq. (8)). Warmer fluid is recircu-
lated. Consequently the marginal gain in $Q_{sorp}^{ev}$ tends to decrease
when the geothermal temperature increases (see Fig. 18). Note that a
previous economical assessment of geothermal absorption chiller by
Wang et al. did not investigate the effect of the temperature [8],
though it appears to be a significant parameter.

- Geothermal flow-rate (see Fig. 17d): A similar trend than for the driving heat temperature is observed when $\dot{m}_{GTH}$ increases from 100 ton.h$^{-1}$ to 200 ton.h$^{-1}$, though the effect on $Q_{sorp}^{ev}$ and $W_{el}$ is much smaller. This is mainly due to the limited impact of the heat transfer fluid flow rate on the heat transfer coefficient of the generator, while the maximum heat transfer rate is limited by the temperature of the heat transfer fluid [73].

- Ratio of DHW (see Fig. 17e): The energy cost of the status quo de-creases when the ratio of DHW $r_{DHW}$ decreases since a smaller amount of rather expensive oil is used (for DHW preparation) in the final energy mix. By contrast, the cost of the geothermal sorption system increases with a decrease of DHW $r_{DHW}$ since the equipment and maintenance costs are no more allocated to the DHW needs. Regarding the GWP, since less fuel per MWh is burned when $r_{DHW}$ decreases, the relative advantage of cooling and DHW cogeneration from the geothermal absorption chiller decreases.

- Cooling set point temperature $T_{sp cooling}$ (see Fig. 17f): The GWP and cost of the system is highly sensitive to the setpoint cooling tem-perature. Indeed, even a small increase of $T_{sp cooling}$ (e.g., 2–3 °C) dramatically increases the absorption chiller production (and the sorption chiller’s COP), decreasing both the electricity consumption and the energy cost.

Finally, from Fig. 17, one can clearly observe the trends highlighted
through Fig. 16. Indeed, one can see that a higher driving temperature is
ideal to increase the cooling capacity (and reduce the electricity con-
sumption that a backup ACC would demand). On the other hand,
increasing the geothermal heat transfer fluid flow rate and the setpoint
cooling temperature also increases the cooling capacity while
decreasing the electricity consumption. Furthermore, the most of the
electricity consumed in the studied configurations comes from the
backup ACC. Even though the variation of the different studied pa-
rameters impact the normalized electricity consumption, their impact
remains small compared with the consumption of the ACC, which
dominates the trend.

## 5. Conclusions

This paper has introduced a system combining a geothermal single-effect absorption chiller and a heat exchanger for cooling and Domestic Hot Water production in tropical climates. The dynamic simulation of the system shows that the cooling production of the absorption chiller depends upon the weather conditions. Furthermore, the temperature of the geothermal resource, its flow rate, and the nominal capacity of the absorption chiller are the most significant parameters impacting the electricity consumption of the system and the share of cooling delivered

by the absorption chiller.

After a stage of surrogate modelling, the system undergoes a multi-objective optimization to minimize both the cost and the Global Warming Potential of the delivered thermal energy. Several scenarios are considered taking into account the energy mix and economic context of a French Caribbean Island where most electricity is generated from fossil fuels. The following trends are observed:

a) Without any subsidy, the system turns out to be systematically more expensive than a combination of a classical vapor compression chiller and a boiler for DHW preparation. However, the GWP of the provided energy can be significantly diminished.

b) The proximity of the geothermal well, large cooling powers (here 2 MWth), and the use of the warm water leaving the sorption generator (here for DHW production) appear to be key factors for the system relevance.

c) Even though a single-stage absorption chiller can operate with a geothermal fluid as low as 70 °C, hotter geothermal resources (e.g., 100–110 °C) dramatically increase the economic viability and should be therefore looked for. The cost and GWP, however, are less sensitive to the geothermal flow rate.

d) The equipment of buildings with cooling emitters operating at 10 °C instead of 7 °C can increase the system profitability as well.

It should be emphasized that a hotel has been considered for this study. This building exhibits a high cooling requirement throughout the year since cooling is required day and night; the equivalent duration of cooling is as high as $t_{eq cooling} = Q_{cooling} / Q_{cooling}^{max} = 570,500/104.3 = 5470$ h.y$^{-1}$. In-situ monitoring of office buildings shows they tend to exhibit much lower, or even zero, cooling needs at night and large cooling peaks, which decreases $t_{eq cooling}$ [2]. The supply of those buildings, though not investigated in this paper, may lead to a high initial investment per amount of delivered thermal energy and subsequent high energy costs.

Further research may focus on integrating solar thermal collectors to
warm the geothermal fluid before feeding the absorption chiller. Bes-
sides, it would be relevant to compare the system with an Organic
Ranking Cycle generating electricity directly from the geothermal
resource.

## CRediT authorship contribution statement

**Charles Maragna:** Writing – review & editing, Writing – original draft, Validation, Supervision, Methodology, Investigation, Formal analysis, Conceptualization. **Amín Altamirano:** Writing – review & editing, Writing – original draft, Validation, Investigation, Formal analysis. **Brice Tréméac:** Writing – review & editing. **Florent Fabre:** Investigation. **Laurène Rouzic:** Investigation. **Pierre Barcellini:** Investigation.

## Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

## Data availability

Data will be made available on request.
absorption chillers [71], for which it is more a problem to overcome
since the solar irradiation drives the temperature level of the driving
source temperature [72]. Indeed, for these systems, the low driving
temperature available in the morning limits the cooling generation
capacity, which might be a problem for some applications. In the
case of the present work, the increased cooling capacity available at
high driving temperatures decreases the need of the ACC, also
decreasing the electricity consumption. To avoid LiBr crystallization,
the generator inlet temperature is not allowed to exceed a critical
value in the range 85–95 °C (see eq. (8)). Warmer fluid is recircu-
lated. Consequently the marginal gain in $Q_{\text{sorp}}^{\text{ev}}$ tends to decrease
when the geothermal temperature increases (see Fig. 18). Note that a
previous economical assessment of geothermal absorption chiller by
Wang et al. did not investigate the effect of the temperature [8],
though it appears to be a significant parameter.

- Geothermal flow-rate (see Fig. 17d): A similar trend than for the driving heat temperature is observed when $\dot{m}_{GTH}$ increases from 100 ton.h$^{-1}$ to 200 ton.h$^{-1}$, though the effect on $Q_{\text{sorp}}^{\text{ev}}$ and $W_{el}$ is much smaller. This is mainly due to the limited impact of the heat transfer fluid flow rate on the heat transfer coefficient of the generator, while the maximum heat transfer rate is limited by the temperature of the heat transfer fluid [73].

- Ratio of DHW (see Fig. 17e): The energy cost of the status quo de-
creases when the ratio of DHW r<sub>DHW</sub> decreases since a smaller
amount of rather expensive oil is used (for DHW preparation) in the
final energy mix. By contrast, the cost of the geothermal sorption
system increases with a decrease of DHW r<sub>DHW</sub> since the equipment
and maintenance costs are no more allocated to the DHW needs.
Regarding the GWP, since less fuel per MWh is burned when r<sub>DHW</sub>
decreases, the relative advantage of cooling and DHW cogeneration
from the geothermal absorption chiller decreases.

- Cooling set point temperature $T_{sp cooling}$ (see Fig. 17f): The GWP and cost of the system is highly sensitive to the setpoint cooling temperature. Indeed, even a small increase of $T_{sp cooling}$ (e.g., 2–3 °C) dramatically increases the absorption chiller production (and the sorption chiller’s COP), decreasing both the electricity consumption and the energy cost.

Finally, from Fig. 17, one can clearly observe the trends highlighted
through Fig. 16. Indeed, one can see that a higher driving temperature is
ideal to increase the cooling capacity (and reduce the electricity con-
sumption that a backup ACC would demand). On the other hand,
increasing the geothermal heat transfer fluid flow rate and the setpoint
cooling temperature also increases the cooling capacity while
decreasing the electricity consumption. Furthermore, the most of the
electricity consumed in the studied configurations comes from the
backup ACC. Even though the variation of the different studied pa-
rameters impact the normalized electricity consumption, their impact
remains small compared with the consumption of the ACC, which
dominates the trend.

5. Conclusions

This paper has introduced a system combining a geothermal single-
effect absorption chiller and a heat exchanger for cooling and Domes-
tic Hot Water production in tropical climates. The dynamic simulation of
the system shows that the cooling production of the absorption chiller
depends upon the weather conditions. Furthermore, the temperature of
the geothermal resource, its flow rate, and the nominal capacity of the
absorption chiller are the most significant parameters impacting the
electricity consumption of the system and the share of cooling delivered

by the absorption chiller.

After a stage of surrogate modelling, the system undergoes a multi-
objective optimization to minimize both the cost and the Global
Warming Potential of the delivered thermal energy. Several scenarios
are considered taking into account the energy mix and economic context
of a French Caribbean Island where most electricity is generated from
fossil fuels. The following trends are observed:

a) Without any subsidy, the system turns out to be systematically more
expensive than a combination of a classical vapor compression
chiller and a boiler for DHW preparation. However, the GWP of the
provided energy can be significantly diminished.

b) The proximity of the geothermal well, large cooling powers (here 2 MWth), and the use of the warm water leaving the sorption generator (here for DHW production) appear to be key factors for the system relevance.

c) Even though a single-stage absorption chiller can operate with a geothermal fluid as low as 70 °C, hotter geothermal resources (e.g., 100–110 °C) dramatically increase the economic viability and should be therefore looked for. The cost and GWP, however, are less sensitive to the geothermal flow rate.

d) The equipment of buildings with cooling emitters operating at 10 °C instead of 7 °C can increase the system profitability as well.

It should be emphasized that a hotel has been considered for this
study. This building exhibits a high cooling requirement throughout the
year since cooling is required day and night; the equivalent duration of
cooling is as high as $t_{eq cooling} = Q_{cooling} / Q_{cooling}^{max} = 570,500/104.3 = 5470$ h.y$^{-1}$. In-situ monitoring of office buildings shows they tend to exhibit
much lower, or even zero, cooling needs at night and large cooling
peaks, which decreases $t_{eq cooling}$ [2]. The supply of those buildings,
though not investigated in this paper, may lead to a high initial invest-
ment per amount of delivered thermal energy and subsequent high en-
ergy costs.

Further research may focus on integrating solar thermal collectors to
warm the geothermal fluid before feeding the absorption chiller. Be-
sides, it would be relevant to compare the system with an Organic
Ranking Cycle generating electricity directly from the geothermal
resource.

CRediT authorship contribution statement

**Charles Maragna:** Writing – review & editing, Writing – original draft, Validation, Supervision, Methodology, Investigation, Formal analysis, Conceptualization. **Amín Altamirano:** Writing – review & editing, Writing – original draft, Validation, Investigation, Formal analysis. **Brice Tréméac:** Writing – review & editing. **Florent Fabre:** Investigation. **Laurène Rouzic:** Investigation. **Pierre Barcellini:** Investigation.

Declaration of competing interest

The authors declare that they have no known competing financial
interests or personal relationships that could have appeared to influence
the work reported in this paper.

Data availability

Data will be made available on request.