# Experimental study of a geothermal rainwater tank concept

Striegel Lucas, Bouvenot Jean-Baptiste, Edouard Walther, Hossein Nowamooz

► To cite this version:

Striegel Lucas, Bouvenot Jean-Baptiste, Edouard Walther, Hossein Nowamooz. Experimental study of a geothermal rainwater tank concept. Energy and Buildings, 2025, 343, pp.115887. 10.1016/j.enbuild.2025.115887. hal-04875534v2

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Submitted on 17 Jul 2025

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# Experimental study of a geothermal rainwater tank concept

Lucas Striegel ID a,b,*, Jean-Baptiste Bouvenot ID a,b, Edouard Walther ID a,b, Hossein Nowamooz c

<figure><img src="image_3.png" /></figure>

## ARTICLE INFO

### Keywords:

Geothermal rainwater tank

Geocooling

Passive cooling

Long-term experimental study

Water stratification

Rainwater temperature

Kendall analysis

## ABSTRACT

With increasingly frequent and severe heatwaves and droughts, the building sector need to develop solutions to ensure summer comfort and water management. This paper presents a concept of hybrid geothermal rainwater tanks. It consists of a buried rainwater tank and an immersed coiled heat exchanger that harvests shallow geothermal energy. It is a solution for passive cooling of buildings and water management. The paper investigates the thermal potential of the concept through the study of two in-situ experimental prototypes over more than two years with a fine-grained data acquisition (10 min time step). The behaviour of this “free-surface” water storage is described in detail, in particular the variation of the water stratification throughout the year: from no stratification in winter to a maximum of 2.5°C/m at the beginning of summer. The influence of rainwater entering the tank is studied: the influence of precipitation is positive in winter, autumn and spring. In summer, the influence is at least neutral, at best positive, because the rain temperature is close to the wet bulb temperature. The system managed to produce between 330 and 450 kWh (3 kWh/m² of buildings) of cooling energy with power peaks of 1 kW. Thanks to the system, the buildings remained comfortable (< 26°C) throughout the summer. Geothermal rainwater tanks can also substitute electrical anti-frost heater in winter. The performances are similar to climatic wells but the advantages of the system lies in its hybrid nature: it fulfills two functions and has a low ground surface area.

## 1. Context of the study

In the well-known context of climate change, characterized by increasingly frequent and severe heatwaves [1], the building sector (residential and tertiary) is in great need of resilience in terms of summer thermal comfort and reduction of CO₂ emissions. Around the world, according to IEA [2], about 20 % of the buildings electricity consumption is devoted to cooling. Because of climate change, this demand for cooling will increase leading to a rise in electricity consumption that could reach the current Chinese electricity demand by 2050 (a third of the world electricity demand - 9 000 TWh).

Near-surface and low-temperature geothermal energy is emerging as a promising solution to increase the cooling production but with greater efficiency in terms of electricity consumption. It offers higher coefficient of performance (COP) for heat pumps (HP), with up to 40 % energy savings compared to conventional air-source systems according to Lemale [3]. Geothermal energy also mitigates the urban heat island effect generated by the latter [4].

Shallow geothermal energy is harvested on the top one to two hundreds of meters by closed- or open-loop systems [5].

Horizontal water loop systems require a large available surface area with 40 W/m² as average heat extraction coefficient [6]. Hou et al. [7] classified these heat exchangers as “linear-loops, slinky-coils, helical-coils and others”. His review concluded that the helical coils provided better heat exchange but at a higher cost than the horizontal loop.

Vertical borehole heat exchangers' heat extraction rates ranges from 20 to 80 W/m [3]. The production increases with depth but as counterpart, the COP decreases slightly due to higher auxiliary energy consumption [8]. This type of system also may have been banned in certain hydrothermal zones, but the need to develop more geothermal solutions has led Viesi et al. [9] to challenge these restrictions through experimental monitoring of a borehole field. The high investment costs may also be an obstacle to the development of the system [10]. These systems are widely documented, with experimental studies and models for a wide case of application (from residential to large tertiary buildings) during winter or summer operation [11].

Santamouris [12] report recent knowledge on the synergy between increasing heatwaves and urban heat island and its impact on buildings consumption, outdoor air quality or health. Concerning the building consumption studies mention higher electricity consumption, higher

<footnote>aICube Laboratory, University of Strasbourg, CNRS, INSA Strasbourg, UMR 7357, 300 Boulevard Sébastien Brant, Illkirch, CS 10413- F-67412, France</footnote>

<footnote>bNational Institute of Applied Sciences of Strasbourg, Thermal, Energy and Environmental Engineering Department, 24 Boulevard de la Victoire, Strasbourg, 67000, France</footnote>

<footnote>cLaboratoire de Génie Civil et Génie Mécanique (LGCGM), 20 Avenue des Buttes de Coesmes, Rennes, 35700, France</footnote>

<footnote>* Corresponding author.
E-mail address: lucas.striegel@insa-strasbourg.fr (L. Striegel).</footnote>
Nomenclature

<table><tr><td>DD</td><td>degree days, °C.days</td></tr><tr><td>DH</td><td>DH index - stand for Degree Hour, °C.h</td></tr><tr><td>E</td><td>energy, Wh or kWh</td></tr><tr><td>h</td><td>hour</td></tr><tr><td>HR-air</td><td>relative humidity in the tank, %</td></tr><tr><td>HR_out</td><td>outside relative humidity, %</td></tr><tr><td>HX</td><td>heat exchanger</td></tr><tr><td>NE</td><td>North-East</td></tr><tr><td>P</td><td>power, W or kW</td></tr><tr><td>RW</td><td>rainwater</td></tr><tr><td>SE</td><td>South-East</td></tr><tr><td>SW</td><td>South-West</td></tr><tr><td>sgn()</td><td>the sign function</td></tr><tr><td>τ</td><td>Kendall coefficient, [-1; 1]</td></tr><tr><td>T</td><td>temperature, °C</td></tr><tr><td>T-air</td><td>air temperature in the tank, °C</td></tr><tr><td>T-air.blown</td><td>air temperature at the AAHX outlet, °C</td></tr><tr><td>Tair_in</td><td>air temperature at the AAHX inlet, °C</td></tr><tr><td>Tair_out</td><td>air temperature at the AAHX outlet, °C</td></tr><tr><td>T_bot</td><td>water temperature at the bottom of the tank, °C</td></tr><tr><td>Tin_helicoHX</td><td>water temperature at the WWHX inlet, °C</td></tr><tr><td>T_out</td><td>outside air temperature, °C</td></tr><tr><td>Tout_helicoHX</td><td>water temperature WWHX outlet, °C</td></tr><tr><td>T_filter</td><td>temperature in the filter, °C</td></tr><tr><td>T_w_Xm</td><td>water temperature at X meter from the bottom, °C</td></tr><tr><td>TW</td><td>tap water</td></tr><tr><td>W_level</td><td>water level, m</td></tr></table>

Subscript and exponent

<table><tr><td>avg</td><td>average</td></tr><tr><td>amb</td><td>ambient</td></tr><tr><td>in</td><td>inlet</td></tr><tr><td>max</td><td>maximum</td></tr><tr><td>min</td><td>minimum</td></tr><tr><td>op</td><td>operative</td></tr><tr><td>out</td><td>outside or outlet</td></tr></table>

peak demand but also a reduction of the electricity supply capacity due to losses of efficiency of the production and increase of losses in the distribution and substations. Elnagar et al. [13] points out the importance of developing cooling technologies with low electricity consumption, in particular thermal energy-driven systems (sorption systems) or passive systems.

Shallow geothermal energy can be used as a passive heat source, i.e. without the use of refrigerant and compressors, resulting in lower CO₂ emissions and electricity consumption [14,15]. In France, according to the AFPG (Association française des professionnels de la géothermie), the ADEME (Agence de la transition écologique) and the BRGM (Bureau de Recherches Géologiques et Minières), geothermal systems in general and ground-coupled heat exchangers for passive cooling of buildings in particular are promising solutions that need to be developed [16,17].

These passive shallow geothermal energy systems include long-known earth-air heat exchangers. Models, influential parameters [18] and its possible contribution to design buildings with high performance [19] are well established. Latest studies includes exergetic analysis [20] but also evaluating performance for cooling production depending on the climate, depth and air speed in the exchanger [21]. It can vary from 2 to 10 kWh/m² of energy savings. Ahmad et al. [22] investigated experimentally the possibility to use earth-air heat exchangers with or without fan to reduce energy consumption.

The ground heat-exchanger technologies presented earlier can also be used as passive systems. Latest studies includes the right sizing of

ground heat exchangers and the influence terminal units (active chilled beam, thermally activated building system) on the sizing [23]. Lyu et al. [24] proposed an integrated system that use shallow geothermal energy in pipe-embedded windows and walls to take advantage of the different temperatures of the envelope, indoor and fresh air and soil.

Climate change is responsible for not only a rise in temperature but also in more frequent and heavy precipitations and paradoxically ecological drought [25]. Water management is therefore a critical point. Buildings sector along with urban planners have to develop systems allowing water collection and storage. Prince George's County [26] mentions the low impact development approach to manage rainwater (RW). This method includes various tools, such as limiting run-off or developing infiltration. However, those solutions require a certain amount of land surface. Solutions like RW tanks (generally buried) spare land use.

In this context, this project aims to develop a new passive system using buried rainwater tanks - a standard solution for water management - as geothermal probes by immersing a water-to-water heat exchanger (HX). This hybrid geothermal rainwater tank concept will be referred to "Rainergy" (a contraction of Rain and Energy) [27] in the rest of this article. This article focuses on the experimental study of a full-scale experimental prototype and its performance comparison with other technologies of passive cooling systems. Data logging is a crucial step in validating a concept, especially for model establishment and validation, which will be the subject of other specific publication. The novelty of the system lies in the combined use of a water management system as a source of passive cold production. Sharing the use of the system saves space, resources and installation work.

The subject of water tank for cooling purposes has been studied by a number of authors. Upshaw et al. [28] modeled the peak load shift of an air-source chiller with a rainwater thermal storage tank. The conclusions showed that for both peak load and municipal water consumption reduction, right sizing is crucial with no benefit after a certain size of tank. However the authors did not use the tank as heat sink and pointed out that experimental studies would be needed to validate the model. Gan et al. [29], Marigo et al. [30] and Eu et al. [31] worked on coupling a ground-source heat pump with a RW tank as heat source and heat sink. Gan et al. [29] experimentally tested the optimal shape of HXs connecting a small rainwater tank (200 L) to the surrounding ground, but the limited volume of the storage did not enable its use for water supply. Marigo et al. [30] carried out simulations of a helical shape HX inside a rainwater tank as heat source. The depth and soil thermal characteristics seem to be the most influential parameters but the model was only validated over one day and only for heating application. Eu et al. [31], in a recent study (2024), experimented the performance of a heat pump with a 100 m³ reservoir as heat source. COP were not very high (2.4 to 3.4) but the authors demonstrated that higher level of water could improve the performances. In a similar way, studies [32,33] presented the coupling of solar thermal and heat pump systems with an ice storage. The ice storage can then be used as cooling source for the buildings. Compared to Rainergy, this system does not offer an alternative water supply -its level is constant - and is often presented as complex in terms of interactions between the different components (HP, solar collector, tank) and in terms of HX design, as the exchanger has to manage the change of state of the water.

The number of studies focused on passive mode is limited. Sodha et al. [34] conducted a summery estimation (monthly calculation, constant volume and temperature of water) of the performance of a buried rainwater tank directly connected to a fan coiled unit and cooled thanks to an evaporative HX. Choorapulakkal and Noguchi [35] tested to enhance climatic well by immersing a 45 m air pipe (diameter 5 cm) inside a buried 110 m³ rainwater tank. The experimental study over 4 days showed good results with a drop of up to 8°C of the outside air temperature. At a ventilation rate of 140 m³/h, the maximum cooling capacity was around 400 W. However the water level of the tank was low (75 cm out of 4.2 m) and constant. Kalz et al. [36] monitored during two years a thermo-active building system with 11 m³ cistern cooling the
<table><caption>**Table 1**
Synthesis of the systems resembling Rainergy.</caption><thead><tr><th>Sources</th><th>Passive or HP</th><th>RW or Water</th><th>Free-Surface</th><th>Summer or Winter</th><th>Model or Expe</th></tr></thead><tbody><tr><td>Upshaw et al. [28]</td><td>HP</td><td>Water</td><td>No</td><td>Summer</td><td>Model</td></tr><tr><td>Gan et al. [29]</td><td>HP</td><td><strong>RW</strong></td><td>No</td><td>Both</td><td>Both</td></tr><tr><td>Marigo et al. [30]</td><td>HP</td><td><strong>RW</strong></td><td>No</td><td>Winter</td><td>Both</td></tr><tr><td>Eu et al. [31]</td><td>HP</td><td><strong>RW</strong></td><td>Yes</td><td>Both</td><td>Expe</td></tr><tr><td>Sodha et al. [34]</td><td><strong>Passive</strong></td><td>Water</td><td>No</td><td>Summer</td><td>Model</td></tr><tr><td>Choorapulakkal and Noguchi [35]</td><td><strong>Passive</strong></td><td><strong>RW</strong></td><td>No</td><td>Summer</td><td>Expe</td></tr><tr><td>Kalz et al. [36]</td><td>Both</td><td><strong>RW</strong></td><td>No</td><td>Both</td><td>Expe</td></tr><tr><td>Rainergy (present study)</td><td>Passive</td><td><strong>RW</strong></td><td>Yes</td><td>Both</td><td>Both</td></tr></tbody></table>

<figure><img src="image_4.png" /><figcaption>**Fig. 1.** Data-sheet of a conventional rainwater tank - Source: PLUVIEAU (translated).</figcaption></figure>

building's structure during summer. The cooling power vary between 0.5 and 1 kW with a production of 1 000 kWh. The size and principle of this system is similar to our concept but three differences remains. The tank is "just" a buffer tank, i.e. the water inside the tank is just water (not rainwater - no water management) and the volume is therefore constant. However a second tank, used as heat source for a HP, serves also as an alternative water supply. The emitters are also different: Rainergy uses the air from the ventilation system whereas Kalz et al. [36]'s system uses a thermo-active building system.

The specificity of the present system is that the water inside the tank remains at atmospheric pressure and its level varies. Most of the articles dealing with buried water tanks do not study free-surface water storage. Additionally, the studies often focus on coupling the rainwater tank to a heat pump and do not study passive operation, see Table 1 (WW and AW mean water-to-water HX and air-to-water HX respectively, studies sharing characteristics with Rainergies are highlighted in bold fond).

This papers addresses the following questions:

* Is the concept of geothermal rainwater harvesting viable in terms of energy production?

* How does the stratification of the tank behave and how does it interact with the rainwater inflow?

## 2. Geothermal rainwater tanks concept

The basis of our solution consists in a new or existing buried rainwater tank, initially used to collect rainwater for non-potable use and to

relieve the sewage system (Fig. 1). In France, the water resources management legislation locally enforces on-site water management which could make the use of such rainwater tanks the new standard [37]. The collected rainwater is mainly used for gardening but also for flushing toilets. A water-to-water heat exchanger (WWHX) is placed in the tank in order to take advantage of the heat storage capacity of water as a by-product. Using an air-to-water heat exchanger (AWHX) connected to the ventilation supply duct, the tank provides cooling energy to the building during summer (Fig. 2). The heat exchanger in the double-flow mechanical unit can obviously be bypassed if not useful.

The rainwater can only be used for non-potable purposes (thanks to a pump) - it is only a supplement. The level in the tank varies between a minimum and a maximum level. When the maximum level is reached, the rainwater is discharged through the overflow outlet. An overflow regulator and a non-return valve ensure that the water is diverted into the sewage network. In general, the minimum level is the submersion level of the pump, but here it is set to keep the WWHX immersed (with a float valve). When the tank is at the minimum level, the water demands are filled with tap water from the city water supply network. The reservoir is only filled with rainwater.

The idea is to use the same installation for three purposes (rainwater harvesting, water management, cooling the building), which, in theory, allows savings in terms of costs and materials (to be quantified), for example by avoiding the need to drill boreholes for geothermal probes or the construction of a climatic well.
<figure><img src="image_5.png" /><figcaption>Fig. 2. Scheme of the Rainergy concept.</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>Fig. 3. Rainfall amount - annual average - France (ref. 1991-2020) and the prototypes location - Météo-France.</figcaption></figure>

# 3. Experimental set-ups

## 3.1. Description of the in-situ experimental prototypes

Three geothermal rainwater tank prototypes are installed in different locations in Alsace [38], France, in a semi-continental climate (see Fig. 3). Alsace is a region rather dry in France with an average rainfall amount (600–800 mm per year) under the national average or the world average (934 and 1 176 mm respectively) [39]. Its continental climate is characterised by cold winters and hot summers. The Rainergy system will therefore be tested in at least non-advantageous conditions. No consolidated data is available for the Saverne prototype, so it will not be presented.

### 3.1.1. Haguenau

The first prototype, with the most complete data set, is installed in Haguenau, in a 150 m² family house built in the 1930's but recently renovated to comply with the current French Energy Performance of

Buildings Code. This corresponds to a minimum performance of 50 kWh of primary energy per m². The external walls are made of hollow clay bricks (27 cm) with an additional layer of mineral wool insulation (16 cm). The windows have also been replaced with high performance double glazing windows (U = 1.3 W·m⁻²·K⁻¹). The building is heated by a wood pellet boiler (10 kW) and the domestic hot water is produced by a air-source heat pump water heater (780 W).

The 11 m³ rainwater tank (height: 3 m and diameter: 2.5 m) is made of precast concrete with a hundred-meter-long copper coiled HX (external diameter of 22 mm). It is buried at 30 cm just beneath the surface. The surrounding ground is dry sand. The coil has a diameter of 1 m and a pitch of approximately 4 cm (height of 65 cm). For visual reason (difficult to see under the water of a full tank), Fig. 4(a) shows two water-to-water HXs installed in Saverne. The Haguenau HX is very similar.

The HX is then connected to a 2 kW air-to-water heat exchanger (Zehnder ConfoFond-L), upstream of the double-flow mechanical unit (Fig. 4(b)). The ventilation rate is 240 m³/h and the water flow rate is 500 L/h. The double-flow ventilation unit is a Maico WS470 BET that
<figure><img src="image_7.png" /><figcaption>(a) Water-to-water heat exchanger inside a rainwater tank (Saverne)</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>(b) Air-to-water heat exchanger before the mechanical ventilation unit (Haguenau)</figcaption></figure>

<caption>**Fig. 4.** Main heat exchangers of the Rainergy concept.</caption>

<table><caption>**Table 2**

Synthesis of the two installed prototypes.</caption><thead><tr><th></th><th>Volume</th><th>Type of soil</th><th>HX material</th><th>Water usage</th><th>Control</th><th>Air flow rate</th></tr></thead><tbody><tr><td>Haguenau</td><td>11 m<sup>3</sup></td><td>sand</td><td>copper</td><td>garden, laundry, WC</td><td>Continuous</td><td>240 m<sup>3</sup>·h<sup>-1</sup></td></tr><tr><td>Eschbourg</td><td>9 m<sup>3</sup></td><td>sandstone and clay</td><td>PEHD</td><td>garden, WC</td><td>Depend. on T<sub>out</sub></td><td>180 m<sup>3</sup>·h<sup>-1</sup></td></tr></tbody></table>

includes a countercurrent heat exchanger in plastic (PS). The ventilation rate can be “boosted” up to 400 m³/h to increase the cooling power. The electrical consumption of the pump is 11 W.

The water stored inside the tank is used for gardening, flushing toilets and laundry. The behaviour of the (four) occupants is standard (tenants are out of the house during office hours of week days and present on week-ends, which is taken into account for occupancy schedule and internal gains, ...).

### 3.1.2. Eschbourg

The Eschbourg installation is very similar, with also a family house (passivHaus standard). The tank is from the same manufacturer, but a smaller model (9 m³ - height: 2.6 m and diameter: 2.5 m) and is buried at the same depth. The AWHX and the ventilation unit are also a Zehnder ConfoFond-L and a Maico WS470 BET. The air flow rate is lower than in Haguenau with 180 m³/h. However the soil is composed of sandstone and clay and the WWHX is in HDPE (100 m long). As the Passive House standard requires a heating demand of less than 15 kWh/m², the house only needs a small amount of heating support, provided by a wood-burning stove.

Moreover the controls strategy is slightly different, with a control based on the outside air temperature whereas the Haguenau system runs continuously and will be illustrated in the Section 4.4. The water stored inside the tank is only used for gardening and flushing the toilet.

The behaviour of the (four) occupants is also standard (tenants are out of the house during office hours of week days and present on week-ends, which is taken into account for occupancy schedule and internal gains, ...).

With the aim of having as complete a data set as possible, a limited number of sensors and more responsive interlocutors, a greater effort has been made on the Haguenau prototype. This will result in more incomplete data for Eschbourg, with a complete set only available in the summer of 2021 - see Table 2 which sums up the similarities and differences of the two prototypes.

### 3.2. Measurement plans

The Haguenau prototype is monitored with more than 25 sensors connected to data-loggers, with a minimum time-step of 10 min (see Fig. 5). The devices were installed in the summer of 2021 and consolidated data has been available since the beginning of 2022. The main measured data with their sensor references are:

* Water temperature stratification thanks to 5 fixed data-loggers (ref. HOBO MX2203 - ±0.2°C) evenly distributed over the height of the tank (0 m, 0.5 m, 1 m, 1.5 m, 2 m) (5 min time-step).

* Water level through total pressure at the bottom of the tank (ref. HOBO U20L-04 - ±1 cm).

* Air temperature and humidity inside the tank (ref. HOBO U23-002A-±0.25°C and ±2.5% from 10 to 90%, ±5% below and under this range).

* Temperature inside the filter (ref. HOBO MX2203 - ±0.2°C) to determine rainwater temperature (5 min time-step).

* Temperatures at the air-to-water heat exchanger limits (both air: ref. HOBO U23-002A - ±0.25°C and ±2.5% from 10 to 90%, ±5% below and under this range - and water: type K thermocouple - ±1°C).

* Meteorological data including rainfall, global solar radiation, air temperature and humidity (ref. Davis Vantage Pro 2) (1 min time-step).

* Temperatures inside the buildings (at air vent and in the room: ref. HOBO UX100-01 ±0.2°C)

After two years of data acquisition and with the goal of gaining a more detailed understanding of certain physical phenomena, the measurement plan has been adjusted.

The water level varies according to rainwater inflows and water withdrawals for uses within the building. To better understand the temperature stratification in the water and to prevent the emergence of a sensor designed to measure water temperature, the fixed sensors inside the tank were removed and then attached to a weighted wire on a float, allowing a constant immersion and image of the stratification
<figure><img src="image_9.png" /><figcaption>Fig. 5. Scheme of the location of the different sensors.</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>Fig. 6. Floating logging system of the water temperature stratification.</figcaption></figure>

regardless of the volume of water. As the volume decreases, the sensors fixed deeper than the water level go down to the bottom and measure the same temperature. The space between the sensors has been reduced to 30 cm for a finer record of the temperature stratification (instead of 50 cm). With 8 sensors (ref. HOBO MX2203 - ±0.2°C) the water temperature is logged from 0 to 2.4 m (see Fig. 6) with a 5 min time-step.

The temperature of the rain entering inside the tank is also an important data, especially to estimate its benefits (or drawbacks) on the water temperature and energy stored in the tank. Rainfall is an on-off event that can be very short and varied. Taking these criteria into account, we chose to install two thermocouples (Thcpl) (K-type - ±1°C) inside and after the filter with a 10 sec time-step. The loss of accuracy of the sensor is compensated by its quasi-instantaneous response time.

The soil thermal conductivity has also been measured sporadically thanks to the thermal properties analyser KD2 Pro from Decagon Devices (see Fig. 7). Measurement is not easy due to the contact resistance created when drilling the measurement hole. This

resistance is minimized with thermal grease. A careful measurement leads to an accuracy of ±20% from 0.2 to 4 W/(m·K). The four different measurements taken in Haguenau give conductivities of 1.36, 2.42, 1.79 and 2.67 W/(m·K). These are consistent with the values found in literature on sandy soil (water content between 3% and more than 2%) [40]. Unfortunately the water content has not been determined for the different readings.

# 4. Measurement results

## 4.1. *Analysis through a Kendall matrix*

The data was first analysed through the raw prism of the popular Kendall's correlation matrix [41] as can be found in recent publication [42,43]. This tool is integrated into the pandas library from Python.

This test is a well-known statistical tool used for pattern recognition, time-series analysis or image processing. The Kendall coefficient, also
<figure><img src="image_11.png" /><figcaption>Fig. 7. KD2 Pro analyser for thermal conductivity measurement.</figcaption></figure>

known as $\tau$ coefficient is calculated for pairwise quantities and takes value between -1 et 1. A value close to 1/-1 indicates high positive/negative correlation between the two quantities meaning they progress in the same/counter trend, respectively.

Most researchers would agree that a coefficient less than 0.1 indicates a negligible relationship and a coefficient greater than 0.9 indicates a very strong relationship. However, values in-between are controversial [44]. According to Schober et al. [44], “the coefficient should be interpreted as the measure of the strength of relationship in the context of the posed scientific question”. For values between 0.8 and 0.2, it is safer to rather analyse the correlation as a stronger/weaker one than the other.

Let us use two series of observation x and y of n elements. We have $(\frac{n}{2}) = \frac{n(n-1)}{2}$ pairs of $(x_i; y_i)$. The Kendall coefficient can be calculated as follows:

$$ \tau = \frac{(\text{concordant pairs}) - (\text{ discordant pairs})}{(\text{total of pairs})} \quad (1) $$

$$ = \frac{2}{n(n-1)} * \sum sgn(x_i - x_j)sgn(y_i - y_j) \quad (2) $$

A pair is said to be concordant if either both $x_i < x_j$ and $y_i < y_j$ holds or both $x_i > x_j$ and $y_i > y_j$, i.e. the order is preserved. Otherwise the pairs are discordant. sgn(x) is the sign function: if x is strictly positive (resp. negative), sgn(x) = 1 (resp -1). If x is null, it yields 0.

In terms of robustness regarding missing data, outliers values or nonlinear data, the Kendall coefficient performs better than other correlation coefficients (Spearman for example) [45]. In case of missing values, the coefficient is not evaluated. Moreover the missing value rate in the data is relatively low at 16%.

The aim here is to use an objective and easy to understand indicator that can summarize a big quantity of data (around a million over a year) and confirm - or deny - intuitive feelings about the system operation.

Results are presented on Fig. 8.

One can observe that the water temperature is negatively influenced by the water level (i.e. the volume of water), which makes a lot of sense. There are plenty of such obvious observations and time and words will not be used here for them. However, other remarks seem worthwhile:

* As a proof of the interest of this tool, one can observe that the water temperature at the bottom of the tank is less negatively impacted by the outdoor relative humidity and precipitations than other water temperature, which is consistent with the fact that the rainwater is injected at the bottom of the tank and has therefore a influence on that temperature.

* Noticeably, the outside air temperature has a greater effect on the water temperature than on the air temperature inside the tank. This air temperature variation is more in adequation with the water temperatures variation than with the outside air variations. This could indicate that the water heats up or cools down first (e.g. when the system starts up or due to increased geothermal transfer to the ground) and then the air in the tank. The model will help understand this phenomenon.

* Concerning the ambient conditions of the tank (relative humidity and temperature): the relative humidity is poorly correlated with all other variables and the air temperature is more correlated with the water temperature than with the outside air temperature. This indicates a rather isolated volume, more influenced by the internal conditions than the external ones. This isolation is reflected in the data by a relative humidity measured as constant throughout the year with a value close to 100%. The air inside the tank is therefore saturated, which is an important hypothesis when it comes to modelling the phenomenon inside the tank.

* The blown air temperature is more correlated to the outside air temperature than the water temperature. This means that the performance of the system (the blowing air temperature is representative of the performance) will be more dependent on the meteorological data than on the heat storage.

The analysis has also been conducted over the summer period from the 15th of May to the 1st of October to focus more on the summer operation. There is no trend reversal in the coefficients but two remarks can be made. Firstly, the rainfall and the outside relative humidity have less impact on the water temperature during summer (from -0.25 to -0.02). Section 4.3 will detail and confirm this observation. Secondly the relative humidity inside the tank impacts more (negatively) the water temperature (from -0.08 to -0.26). Intuitively, this could be explained by evaporative cooling of the water: with evaporation, the water cools down and the relative humidity rises up. However, a deeper analysis is needed to validate this hypothesis.

## 4.2. Water stratification analysis

The temperature of the heat sink is an important parameter for passive systems as it is the limiting parameter -i.e. in summer/winter mode the temperature of the working fluid can not fall below/exceed this value. It will also be used as a basis for numerical validation in further communication.

On Figs. 9 and 10, one can observe the variation of water temperature during a part of summer 2023 and winter 2023 at each level of the tank. Tw_X means the water temperature at X metres from the bottom of the tank. During summer operation (left-side of the Figure), the water stratification can reach more than 2.4°C/m whereas in winter (right-side), it is almost zero. In summer (Fig. 9), the lower temperature (Tw_0) varies between 18.1 and 20.5°C, while the upper temperature (Tw_1.5) varies between 19.2 and 22.5°C. This natural stratification of the tank (the coldest water is at the bottom) improves the performance of the coil, which is precisely positioned at the bottom of the tank.

Specifically, the stratification is well defined when the system is not operating (from the 04/08 to the 10/08) with an almost constant temperature gradient over the height of the tank (from 0.4 to 1°C/m). The stratification is imposed by the ground temperature gradient. When it is operating, 2 types of stratification can be distinguished. Whenever the outside temperature is rather high (i.e. high cooling power), a low and narrow thermocline forms (from the 11/08 to the 21/08). The
<figure><img src="image_12.png" /><figcaption>**Fig. 8.** Correlation plot of the measured data using Kendall's coefficient (positive/negative values imply a positive/negative correlation with 1/-1 being a total correlation for the two series).</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>**Fig. 9.** Water temperature variations in the tank during summer operation (2023 - Weeks 31 to 33 - Haguenau).</figcaption></figure>

gradient at the bottom of the tank, between $Tw_0$ and $Tw_{0.5}$, is large ~2.4°C/m - whereas none is observed at the top (the three temperatures at the top are the same). High outside temperatures cause more heat to be rejected into the tank. The temperature in the heat exchanger rises and spreads to the upper layers by conduction and convection. At lower heat extraction, from the 31/07 to the 04/08, the thermocline is wider, the gradients ranging from 1.4°C to 0.6°C at the bottom and top, respectively. The temperature at 0.5 m (and to a lesser extent, at 1 m) is influenced by the coil and fluctuates between the temperature at bottom and the top water.

Thanks to the floating water temperature acquisition system, it is possible to trace the evolution of the thermocline in a finer way. Fig. 11 shows the evolution of the thermocline every 15 days from the installation of the float (February 2024) until June 2024. The temperatures, averaged over the day, are only water temperatures under the float. The water level is indicated.

The stratification is greater at the beginning of the summer (15 May and 15 June: around 5°C between the top and bottom, which is 2.5°C/m). The bottom temperature increases rapidly after the 15/06 (because of the use of the HX). The temperatures at the top increase as well but slowly due to outside temperatures. At the end of the summer, the stratification measured is 1.7 to 1.8°C/m and the temperatures start decreasing rather uniformly. The available data end in September, but the decline has already begun and the stratification pattern should be closer to that of the early months of the year, as observed for September temperatures, which are close to August temperatures, with equivalent extremes and gradients.

The water stratification will be used as a criterion for the model validation. Work on said validation has already started [46] and will be carried on.

Overall, the water temperature of the tank is between 5 and 25°C. The temperatures are presented in Table 3. The averaged water
<figure><img src="image_14.png" /><figcaption>Fig. 10. Water temperature variations in the tank during winter operation (2023 - Weeks 48 to 51 - Haguenau).</figcaption></figure>

<figure><img src="image_15.png" /><figcaption>Fig. 11. Water stratification evolution (February to September 2024 - Haguenau).</figcaption></figure>

temperature is the average of every data logger, at each depth. The tem-
perature at the top has been taken according to the water level. Due to
loss of data of certain loggers during winter 2021-2022, the minimal
value at the top and averaged value was removed.

4.3. Influence of rainwater on the water temperature

Depending on its temperature, the rain entering the tank will either
cool or heat the water in the tank. Therefore it is important to well assess
the rain temperature. A very complete study by Byers et al. [47] high-
lights three types of rainy event and details the associated temperature
at the ground. During Type-I rain, the most common, the rain temper-
ature decreases rapidly to reach the wet bulb temperature. Type-II rain

presents a greater temperature difference between air and rain and is
associated to hail. Finally, Type-III rain temperature is very close to air
temperature, which occurs when the air has already been cooled and is
more humid than type-I rain (less evaporative cooling).

On top of this analysis, the Rainergy setups present some additional
complexities for water inlet temperature calculation. Namely: the catch-
ment area (roof) that can be heated by the sun, and the evaporative
cooling that can occur in the gutter downspouts.

As mention previously, the rain temperature or at least the inlet tem-
perature inside the tank has been recorded by two sensors placed inside
the filter: a thermocouple K and a Hobo logger MX2203. In the end,
the 2 sensors gave similar dynamic responses during intense, one-off,
rainfall events.
<caption>**Table 3**</caption>

Average, minimum and maximum temperature of water (averaged, top and bottom) and the date of the occurrence in the tank for the years 2022 and 2023 - Haguenau.

<table><thead><tr><th>Water temperature [°C]</th><th>T<sub>min</sub></th><th>T<sub>max</sub></th><th>T<sub>avg</sub></th></tr></thead><tbody><tr><td colspan="4">Top</td></tr><tr><td>2022</td><td>no data</td><td>24.8 (02/09)</td><td>no data</td></tr><tr><td>2023</td><td>7.4 (18/02)</td><td>24.1 (15/07)</td><td>14.4</td></tr><tr><td colspan="4">Bottom</td></tr><tr><td>2022</td><td>5.1 (27/01)</td><td>21.1 (05/08)</td><td>12.9</td></tr><tr><td>2023</td><td>6.5 (08/03)</td><td>20.8 (21/08)</td><td>13.4</td></tr><tr><td colspan="4">Averaged</td></tr><tr><td>2022</td><td>no data</td><td>23.0 (02/09)</td><td>13.3</td></tr><tr><td>2023</td><td>7.4 (13/02)</td><td>22.7 (22/06)</td><td>14.0</td></tr></tbody></table>

Fig. 12 shows the temperatures recorded during the month of July 2023, just after the deployment of the sensor.

The analysis of the data shows that Byers' rain behaviour (rain of type I,II and III, see above) is suitable for most of the rainy events during summer. As shown on Fig. 13, type I rain can be observed at 18:00 with the rain temperature falling to the wet bulb temperature, then the curve is flat until the next rainy event around 23:00, where it falls down again to the wet bulb temperature. This behaviour is typical of two type I rain events. The influence of the roof or solar radiation before a rain event is negligible a priori.

On the 15th of July (see Fig. 14) the same phenomenon occurs: at 21:00 and 00:00, the temperature falls down to the wet bulb temperature. However, some small precipitations (around 23:00 and 7:00) have little to no influence on the temperature filter. The rise of the filter temperature after the end of the rainfall tends to meet the air temperature inside the tank. Here the second rainfall is more like a rain III-type event because the outside temperature has already been sufficiently cooled by the first event (on Fig. 13 two drops from 35 to 25°C then from 25 to 20°C, versus on Fig. 14 one drop from 28°C to 20°C).

During fall or winter, the outside dry temperature is closer to the wet bulb temperature, resulting in almost exclusively type III rain. Fig. 15 illustrates that all three temperatures are equivalent: rain, outside and wet bulb. A certain amount of rain is necessary to meet the outside temperature.

The influence of the rain temperature on the water temperature can be seen at the bottom of the tank, where the rain comes in (see Fig. 16).

<figure><img src="image_16.png" /><figcaption>**Fig. 12.** Water temperature in the filter and precipitation amount (juilly 2023 - Haguenau).</figcaption></figure>

To take advantage of the cooling effect of the rain, the rain temperature should be below the water temperature inside the tank. The cooling effect of the precipitations is therefore mainly effective outside summer because the summer wet bulb temperature is around 20°C, which is very close to the tank temperature. At the end of the summer, when the tank reaches its maximum (around 23°C, see Section 4.2), the rain could help to extend the use of Rainergy. The influence is therefore at least positive and at worst neutral.

During fall or spring (and obviously winter), the rainfalls have a positive impact on the water temperature.

On Figs. 12 and 16, the positive rainfalls have been marked with a blue circle and those with no influence have been marked with a green circle. In addition, when the tank is full and the stratification is well established, the piston effect during rainfall pushes the hotter surface water into the overflow. Those events have been marked with a blue arrow on Fig. 16.

The final conclusion of the analysis made on these measurements is that the rain temperature can be modelized with the wet bulb temperature. Indeed, during rain I event, even if, at first, the dry outside air cools quickly to that temperature, taking the outside temperature would neglect the positive impact of the rain (the outside air being hotter than the water.) This assumption may not stand in certain cases like horizontal roofs or in dense urban area.

<figure><img src="image_17.png" /><figcaption>**Fig. 13.** Water temperature in the filter and precipitation amount: 2 type I rain events (11 juilly 2023 - Haguenau).</figcaption></figure>

<figure><img src="image_18.png" /><figcaption>**Fig. 14.** Water temperature in the filter and precipitation amount: type I into type III rain (15 July 2023 - Haguenau).</figcaption></figure>
<figure><img src="image_19.png" /><figcaption>**Fig. 15.** Water temperature in the filter and precipitation amount: type III rain (16 november 2023 - Haguenau).</figcaption></figure>

<figure><img src="image_20.png" /><figcaption>**Fig. 16.** Water temperature at the bottom of the tank and precipitation amount (Haguenau 2023/2024).</figcaption></figure>

## 4.4. Summer operation: production performances

As a preamble, we need to take a closer look at the climate balances for the summers of 2022 and 2023 in Haguenau and 2021 in Eschbourg, which will be studied below. According to the french meteorological service (Météo-France), the summer of 2021 was a “dull summer”. Despite a hot June (2.0°C above the norm ref.1991-2020), July and August were below the norm (-0.1 and -0.5°C respectively) [48]. Summer 2022 was the 2nd hottest summer ever (behind 2003). The average temperature of 22.7°C was 2.3°C above the norm, the rainfall deficit reached 25% and there was an excess of 10-30% of sunshine duration [49]. The summer 2023 was also hot (4th hottest) with an average temperature of 21.8°C, (+1.4°C above normal). However, 2023 was “less consistent in terms of heat” than 2022, with milder weather from mid-July to mid-august. Moreover, rainfall and sunshine duration were within the norm [50].

Cooling Degree Days (DD\_cooling) can be a key indicator of the intensity of summer weather. Degree days are calculated daily, as the difference between the mean temperature and a reference (18°C). They are integrated over a given period (e.g. year or summer with June, July and August, see Table 4).

As mentioned in Section 3.2, the two sites were instrumented with a weather station providing several weather data, including outside air

temperature courses. Average, minimum and maximum outdoor air temperature are also indicated in the Table 4.

### 4.4.1. Haguenau

When operating in summer, the Rainergy system can decrease the supply temperature of the ventilation by up to 13°C. On Fig. 17, during the hottest week of 2022, the outside temperature dropped from 37°C to 25°C, corresponding to a cooling power peak of around 1 kW (considering a constant ventilation flow rate of 240 m³/h). The distribution of cooling power is shown on Fig. 20. In Haguenau, the energy production is 450 and 400 kWh in 2022 and 2023 respectively. The 2023 energy production was lower than in 2022 mostly because of a lower operating duration due to a milder summer. Considering the consumption of the circulating pump (11 W), the averaged COP of the installation is higher than 30, which is within the order of magnitude of passive system installations [20].

The water-to-water heat exchanger has been designed to an efficiency of 0.9, which is verified by measurements: the efficiency exhibits a mean value of 0.82, in a range between 0.64 and 0.88. Fig. 18 shows the efficiency variation during the hottest week of 2022 in Haguenau. Due to forced convection, its variation is limited.

### 4.4.2. Eschbourg

In Eschbourg, the system managed to produce 332 kWh in the summer of 2021 for 1050 h of operation. The cooling power is also smaller with an average of 320 W. Several differences could explain this differences: the volume of the tank is smaller than in Haguenau (9 m³ vs 11 m³), the heat exchanger is in PEHD instead of copper and the type of soil is different. The difference in terms of climate is also an important factor.

### 4.4.3. Summary

The main results of the Rainergy system in Haguenau and Eschbourg are summarized in the Table 5.

The production of both prototypes is similar in terms of distribution (see Fig. 20), but the 2022 production in Haguenau is 1.35 higher than the 2021 production in Eschbourg. This difference is partly due to the lower flow rate in the Eschbourg system (180 m³/h compared to 240 m³/h in Haguenau). For a given temperature difference, this difference in flow rate results in a 25% reduction in cooling power.

The experimental nature of the study makes it difficult to isolate one factor and quantify its contribution to explaining this difference. Models will be needed to perform sensitive analysis or parametric variation. However, in Haguenau, the size of the tank, the type of soil and the HX material are the same. Differences remain: the volume stored varies according to rainfall and water use, and the weather data are not the same as above. In the three cases, the water level was high with very few variations as illustrated in Fig. 19. The averaged water levels are 1.9 m (82%) and 2.1 m (91%) out of 2.3 m during the production period in 2022 and 2023 for Haguenau and 1.8 m (90%) out of 2 m in Eschbourg. As a rough hypothesis, we can estimate that the variation in volume will have less impact on production over the 3 years.

In Haguenau, the cooling production in 2022 is 50 kWh higher than in 2023 (12.5% higher). It should also be noted that the tank was fuller in 2023. Given the previous comments, this difference would be due to the weather data. The DD in summer was 13% higher in 2022.

As comparison, the DD in 2022 (Haguenau) were 1.6 time higher than 2021's DD (Eschbourg) for a 35% production surplus.

The production clearly depends on the climate but no correlation could be drawn from the collected data, although it spans over summers: the ratios of production to DD computed during these cooling periods are 1.23, 1.01 and 1.02 kWh/DD.

However it shows that the system is efficient and performed well in this 3 cases.
<table><caption>**Table 4**
Cooling degree days for Strasbourg (S) and specific weather data in Eschbourg (E - 2021) and Haguenau (H - 2022 and 2023).</caption><thead><tr><th></th><th>DD<sub>cooling</sub><br>year (S)</th><th>DD<sub>cooling</sub><br>summer (S)</th><th>T<sub>min</sub><br>(E/H)</th><th>T<sub>av</sub><br>(E/H)</th><th>T<sub>max</sub><br>(E/H)</th></tr></thead><tbody><tr><td>2021 (S & E)</td><td>348.0</td><td>271.4</td><td>-6.3</td><td>12.3</td><td>35.5</td></tr><tr><td>2022 (S & H)</td><td>599.7</td><td>447.2</td><td>-12.4</td><td>13.5</td><td>39.1</td></tr><tr><td>2023 (S & H)</td><td>574.3</td><td>394.7</td><td>-6.2</td><td>13.1</td><td>37.3</td></tr></tbody></table>

<figure><img src="image_21.png" /><figcaption>**Fig. 17.** Air and water temperature at the AWHX limits (summer 2022 - Haguenau).</figcaption></figure>

<figure><img src="image_22.png" /><figcaption>**Fig. 18.** Cooling power produced by and efficiency of the AWHX during summer operation (summer 2022 - Haguenau).</figcaption></figure>

<table><caption>**Table 5**
Main production values for the summers of 2021 (Eschbourg), 2022 (Haguenau) and 2023 (Haguenau).</caption><thead><tr><th></th><th>H<sub>op</sub><br>h</th><th>ΔT<sub>max</sub><br>K</th><th>T<sub>blowvmax</sub><br>°C</th><th>P<sub>max</sub><br>W</th><th>P<sub>mean</sub><br>W</th><th>COP<sub>mean</sub><br>-</th><th>E<sub>prod</sub><br>kWh</th><th>E<sub>cons</sub><br>kWh</th></tr></thead><tbody><tr><td>22/05 to 01/10 2021</td><td>1050</td><td>11.7</td><td>24.5</td><td>954</td><td>320</td><td>28.8</td><td>332</td><td>11.6</td></tr><tr><td>11/05 to 15/09 2022</td><td>1338</td><td>13.1</td><td>25.6</td><td>1071</td><td>384</td><td>30.6</td><td>450</td><td>14.7</td></tr><tr><td>01/06 to 03/10 2023</td><td>1189</td><td>13.3</td><td>24.5</td><td>1085</td><td>336</td><td>30.5</td><td>400</td><td>13.1</td></tr></tbody></table>
<figure><img src="image_23.png" /><figcaption>Fig. 19. Water level for the three cases (Haguenau 2022 & 2023 and Eschbourg 2021).</figcaption></figure>

<figure><img src="image_24.png" /><figcaption>Fig. 20. Distribution of cooling capacity for the summers 2021 (Eschbourg), 2022 (Haguenau) and 2023 (Haguenau).</figcaption></figure>

### 4.4.4. Control strategy

The control is also a key point of the systems operation. It is different in Eschbourg and Haguenau. On Fig. 21, one can observe that the Eschbourg system shuts down when the outside temperature is lower than 15°C. The outlet air temperature in the AWHX drops to get closer to the outside air temperature. The system is then switched on when the outside air temperature exceeds 19°C. On Fig. 17, the system in Haguenau operates continuously: the outlet air temperature follows the water temperatures. Consequently, during night-time, when the outside air temperature is below the water temperature, it is “preheated” and blown at a higher temperature. This implies that the outside air cools the tanks and the energy is stored.

Intuitively, the best control for the system should be the first one, because the second does not permit freecooling. However one could argue that a good night ventilation (windows opening, which is around 4 vol.h⁻¹ for a house of 150 m² × 2.5 m height = 375 m³ and a ΔT of 10°C, representing around 15 kW) would largely exceed the preheating (maximum power of 400 W assuming ΔT = 5 K on the air side). Moreover, as

mentioned above, the energy stored inside the tank during night-time could be used when outside air temperature are higher. This issue will be investigated thanks to the numerical model in order to optimize the system operation.

### 4.5. Buildings temperature

Temperatures inside the building in Haguenau were monitored on three different locations (Bedroom - first floor (R+1), NE -, Kitchen - ground floor, SW -, Living - ground floor, SE -). During the hottest week of 2022 (see Fig. 22), the temperature did not exceed 27°C for any of the 3 sensors. In France, the DH index [° C.h] measures the summer thermal comfort of buildings (French Energy Performance of Buildings Code - RE2020). It is defined by:

$$DH = \sum_{op}^{h} T_{op} - T_{comfort} \quad \text{when } T_{op} > T_{comfort}$$
<figure><img src="image_25.png" /><figcaption>Fig. 21. Air and water temperature at the AWHX limits (summer 2021 - Eschbourg).</figcaption></figure>

The operative temperature *T*op is compared to a comfort temperature *T*comfort which is between 26 and 28°C. To take into account the adaptive comfort of the human body, the comfort temperature depends on the outside air temperature and increases as the latter rises over a long period. Here the analysis is based on a simpler and more conservative index *DH*<sub>simple</sub>:

$$DH_{\text{simple}} = \sum_{amb}^{h} T_{amb} - 26 \quad \text{when } T_{amb} > 26$$

Instead of a fluctuating comfort temperature, the ambient air (read by the sensors) is compared to a fixed value of 26°C. The summary of the DH index and maximum temperature are presented on Table 6.

In the RE2020, a building is said to be comfortable if DH < 350, which is largely the case in Haguenau (considering a conservative index). It is important to note that these performances were achieved with good building management from the occupants (sun protections, night ventilation, ...).

## 4.6. Winter operation: production performances

Besides geocooling, the Rainergy system can also be used for winter operation by using the water higher temperature to pre-heat the air before entering the mechanical ventilation. The experimental setup allows the use of Rainergy to avoid the use of an anti-frost electrical heater, which is necessary to protect ventilation elements. Fig. 23 shows how the air is heated before entering the air handling unit. Yet, the energy savings are moderate: during winter 2021–2022, the Haguenau prototype saved 39 kWh. Noticeably, this operating mode cools the water in the tank, which is beneficial for the coming summer. However, such an amount of energy transferred to the tank has almost zero influence on its temperature. Models will allow to test different operating modes to save more energy (by switching on the system as soon as the outside air is cooler than the water in the reservoir).

<caption>Table 6</caption>

Maximal temperature and the date of the occurrence and the DH index for the 3 temperatures of the building for the years 2022 and 2023 - Haguenau.

<table><thead><tr><th></th><th>Bedroom</th><th>Living room</th><th>Kitchen</th></tr></thead><tbody><tr><td>max 2022 [°C]</td><td>26.9 (05/08)</td><td>26.6 (05/08)</td><td>28.6 (30/08)</td></tr><tr><td>max 2023 [°C]</td><td>26.6 (21/08)</td><td>26.8 (20/08)</td><td>28 (20/08)</td></tr><tr><td>DH 2022 [°C.h]</td><td>34.5</td><td>0.8</td><td>91.9</td></tr><tr><td>DH 2023 [°C.h]</td><td>16.6</td><td>1.1</td><td>37.7</td></tr></tbody></table>

<figure><img src="image_26.png" /><figcaption>Fig. 22. Air temperature inside the building (hottest week of summer 2022 - Haguenau).</figcaption></figure>

<figure><img src="image_27.png" /><figcaption>Fig. 23. Air and temperature variations in the AWHX, winter operation (2021 - Week 51 - Haguenau).</figcaption></figure>

## 4.7. Impact of the system on water management

This study focuses mainly on the cooling function of the Rainergy system. However, its initial function is rainwater storage and management, which will be discussed here.

The tenants provided their water meter readings between November 2021 and October 2022. During this period, they used 59 m³ of tap water (TW) and 43 m³ of rainwater (RW). The amount of rainwater used was also obtained from the water level data, by taking into account the water level drops and converting them into the extracted volume. It appears that rainwater met about 40% of the total water demand, which is significant.

Meanwhile, the rainfall amount during this period was 813 mm. The amount of rainwater that can be harvested is given by:

$$RW_{harv} = C_f \cdot A_{roof} \cdot Rainfall$$

where $C_f$ is a dimensionless run-off coefficient, $A_{roof}$ is the catchment area in m² and Rainfall is the rainfall depth in m (which is a standard approach [51]).

Given the roof area - 120 m² - and a run-off coefficient of 0.9, the harvested rainwater volume is 87.8 m³. Therefore the system managed about 50% of the rainwater (ratio between harvested and used RW, assuming that the surplus was evacuated through the overflow outlet.).

This analysis was also conducted for the years 2022 and 2023 and is presented in the Table 7. The tenants did not provide the water meter
<table><caption>**Table 7**
Water management analysis for the Haguenau prototype.</caption><thead><tr><th></th><th>Used RW (readings)<br>m³</th><th>Consumed TW (readings)<br>m³</th><th>Used RW (calculated)<br>m³</th><th>Captured RW<br>m³</th><th>RW managed</th></tr></thead><tbody><tr><td>11/2021 - 10/2022</td><td>43</td><td>59</td><td>43,8</td><td>87,8</td><td>50%</td></tr><tr><td>01/2022 - 12/2022</td><td>-</td><td>-</td><td>56,7</td><td>90,9</td><td>62%</td></tr><tr><td>01/2023 - 12/2023</td><td>-</td><td>-</td><td>27,1</td><td>91,1</td><td>30%</td></tr></tbody></table>

readings for those years. The “used RW” refers to the rainwater used in the building (gardening, toilet flushing, etc...), the “captured RW” refers to the rainwater harvested on the roof and the “RW managed” represents the ratio between “used RW” and the “captured rainwater”.

Over the two years, the harvested rainwater remained stable but the rainwater used varied from 56 to 27 m³. This is probably due to differences in occupant behavior (e.g., less gardening). Overall the system contributes between 1/3 and 2/3 to rainwater management and can supply up to 40% of the total water used in a building which is significant.

To reduce the proportion of rainwater directly evacuated through the overflow outlet, the tank's volume should be increased. However, this would lead to higher installation cost and greater land surface requirements, with no improvement in the ratio of rainwater used to total water consumption.

# 5. Discussion

## 5.1. Comparison to other geothermal passive systems

Based on the previous promising analysis, it is legitimate to ask: how does this new system compare with other passive geothermal systems? Three case studies of four different systems have been selected and compared with the result described above. A comparison is also made with two conventional systems (air-to-water and water-to-water heat pumps) whose data are taken from several technical data sheets of HP manufacturers. Table 8 summarises generic values from the literature for each technology. The selected indicators are:

* The excavated volume, $V_{exc}$, as a measure of the space required for the system (and more or less investment cost, depending on the drilling/excavation technique).

* The temperature range of the heat sink, as this determines the minimum operating temperature of the system (in the summer case study).

* The maximum cooling power produced.

* The average COP, $COP_{avg}$, which is an important indicator for passive systems because the auxiliary consumption can be a limiting factor.

The energy produced is not studied because it is too dependent on the duration of operation and meteorological data.

In 2005, Hollmuller et al. [15] carried out a study for the Swiss Federal Office of Energy that established design rules for geocooling technologies based on 10 experimental at-scale installations. They investigated the free cooling potential of common vertical ground heat exchangers (VGHE), EAHE, but also geothermal pile foundations (GPF) and horizontal ground heat exchangers (HGHE). The latter was also coupled to an EAHE. The GPF and VGHE presented here are large installations with total borehole lengths exceeding one kilometre. However, the maximum linear power and cooling production of these systems are similar: 40 W/m and 30 kWh/(m.year). The data for the selected indicators are supplemented by literature data from several articles and are summarised in Table 8.

In terms of excavated volume, the trend shows that GPF are reserved for large projects, while EAHE and Rainergy are more likely to be used for single-family houses. VGHE and HGHG are suitable for all types of projects, from individual buildings to large blocks of flats. Cooling capacity is highly dependent on the size of the system.

Logically, the operating temperature ranges are very similar for passive systems and wider for heat pumps, demonstrating their advantage over passive systems, namely their controllability (at the cost of a lower COP but higher cooling power).

The Rainergy system performs well compared to other passive geocooling systems. Its COP of more than 30 is a bit higher than climatic wells (usual COP around 20 [20,21]) as the water is a better heat carrier than the air. Other shallow geothermal technologies such as borehole or horizontal heat exchangers exchange heat directly with the ground. The length of the heat exchanger is generally greater which creates more pressure drop and can contribute to higher auxiliary energy consumption [15,23].

One specificity of the Rainergy system is that the cooling energy produced is injected in the building through the ventilation system, i.e. through a small air flow (around 200 – 300 m³/h). To increase the cooling power, it could be possible to increase the air flow. In that case, the system is closer to a “forced air system” - no longer a ventilation system, which provide fresh air. These systems are less effective than water-loop systems. However, they are easier to implement, especially in renovation projects. The investigation of coupling the tank to a water-loop system could be interesting.

An other key distinguishing feature of the Rainergy system is its dual functionality: it serves both as a cooling system and a water management solution. Unlike other passive geothermal technologies that focus only on heat exchange with the ground, Rainergy incorporates a rainwater storage component. This aspect affects cost-benefit considerations. A conventional passive cooling system would require additional infrastructure to manage rainwater, leading to higher installation costs. In contrast, Rainergy consolidates both functions within a single excavation, optimizing resource use and potentially reducing overall investment. However, this dual-purpose design makes direct comparisons with other passive systems challenging, as their scope of application differs.

## 5.2. Limits of the in-situ study

The Rainergy system performs well, however the water level was high during both 2022 and 2023 (1.9 and 2.2 m in average respectively - which is close to the maximum value of 2.3). The system operation was not stressed as its two uses (water supply and cooling) were not put in competition. Eu et al. [31] pointed out that low water level is detrimental to system performances. It should be noted that the catchment area of the two buildings (120 m² and 180 m² for Haguenau and Eschbourg, respectively) allows the tank to be replenished quickly. In Alsace, the average rainfall is 8 mm (800 mm/year and 100 rainy days per year - source: Meteo France), which corresponds to a water input of about 1 m³ (10% of the total volume) per rainy day. The sizing the tank volume is therefore a question that needs to be resolved.

The heat exchange between the soil and the water could not be measured because the prototypes were already in operation at the start of the research project. However it is possible to estimate it using an energy balance and the following assumption:

* The energy stored in the tank is retrieved from the measured volume and averaged temperature.

* The energy variation is due to four mechanisms: volume change, HX operation, geothermal heat exchange and heat exchange with the air above.
<table><caption>**Table 8**
Comparison of different technologies using geocooling.</caption><thead><tr><th></th><th>Sources</th><th>V<sub>exc</sub><br>m<sup>3</sup></th><th>T<sub>source</sub><br>°C</th><th>P<sub>max</sub><br>kW</th><th>COP<sub>avgd</sub><br>—</th></tr></thead><tbody><tr><td>Geothermal rainwatertank (this study)</td><td>RW</td><td>~ 20</td><td>5–23</td><td>1.1</td><td>30</td></tr><tr><td>Climatic well [18,20,22]</td><td>Ground</td><td>33–70</td><td>2–25</td><td>1.2–7.1</td><td>14–20</td></tr><tr><td>Vertical Borehole [8,15,23,52,53]</td><td>Ground</td><td>85–3700</td><td>2–20</td><td>8–300</td><td>12–24</td></tr><tr><td>Geothermal pile foundation [15,54]</td><td>Ground</td><td>2000–31000</td><td>7–17</td><td>313–370</td><td>20–40</td></tr><tr><td>Horizontal water loop [15,53]</td><td>Ground</td><td>180–2000</td><td>16–27</td><td>2.6–5</td><td>18.4–20</td></tr><tr><td>Conventionnal chiller (AW HP)</td><td>Air</td><td>—</td><td>~20–48</td><td>5–1000</td><td>3–4</td></tr><tr><td>Conventionnal chiller (WW HP)</td><td>Ground</td><td>—</td><td>15–45</td><td>2–2500</td><td>4–5</td></tr></tbody></table>

* The latter can be neglected: the air is saturated which limits the evaporation and the exchange surface is smaller compared to geothermal exchange surfaces.

* The analysis focuses on the moment when the volume is constant leaving only heat exchanges through the wall or the heat exchanger.

In addition, as a simple macro analysis, the temperature of the tank increases during the summer, rising from 8.5°C to 22.4°C (on average) in 2023, from 10 March to 24 August. This energy increase of 165 kWh is calculated for a constant average volume (little variation). By comparing this value with measurements of the energy exchanged by the heat exchanger, we can deduce the impact of geothermal losses.

At Haguenau, the exchanger operates continuously, so its production heats up the reservoir during the day and cools it at night. The heating part (cooling energy for the building) during this period is 340 kWh and the cooling part is -107 kWh. Part of this energy (165 kWh) is absorbed: the tank temperature rises, reflecting the buffer effect of the tank. The overall balance is a cooling energy of -67 kWh for the geothermal part. 29% of the energy rejected by the heat exchanger is therefore dissipated by the geothermal effect and 71% is absorbed by the buffer effect.

However, the main benefit of the geothermal exchange occurs in winter, when the tank cools down to its minimum value (about 200 kWh to cool 10 m³ from 22.5 to 8°C).

In order to evaluate more precisely the different heat exchanges or to assess the performances at low water levels or over a wider operating range (extreme outdoor temperatures, different types of soil, ...), models need to be built. The main scientific hurdle will be the modelling of variable levels of the tank, which study in the literature is lacunary.

The model will also help to optimise the control of the system. Is it better to run the system all the time or to switch it on only during the day ? Is it worth turning it on at the beginning of the summer, when the outside temperature is not very high, or should the system's energy reserves be kept for the period of heat waves?

The composition of the soil tested in this study tends to favour heat exchange with the soil (high thermal conductivity). Models are needed to assess the performance of the system installed in a soil with a lower thermal conductivity. A third prototype will be studied in the future, in a location (Saverne, France) where the rainwater tank sits in an underground waterflow. It will be interesting to study the impact, probably positive, of such a flow on Rainergy's performance.

## 6. Conclusion

In conclusion, this paper introduced the concept of a geothermal rainwater tank with an experimental study conducted over two years on two different locations. This concept is scarcely studied in the literature, especially concerning its passive and hybrid operation. Providing an alternative water supply (i.e. being at variable levels) competes with the geothermal use.

The system managed to produce between 330 and 450 kWh a year, with averaged cooling power between 320 and 384 W and peaks reaching 1 kW, maintaining a blowing temperature below 26°C with outside

temperatures close to 38°C. The magnitude of the production is then of the order of 50 Wh/L. The air-to-water heat exchangers are well designed with efficiencies higher than 0.8.

The COP are around 30. These performances are comparable to other more traditional passive systems, such as climatic wells or horizontal water loop operating in geocooling mode. It is therefore a viable solution, at least with the tested conditions. Moreover, compared to other technologies, the system is compact due to its higher exchanger coefficient. This limits the footprint of the system, allowing its installation even in urban area (e.g. under a parking space).

Specific features of the system were investigated. In particular, the temperature of the rainwater entering the tank follows the rainwater temperature models found in the literature. This demonstrates the negligible effect of the roof or guttering. The rainwater entering the tank can therefore be modelled with the wet bulb temperature, which has a positive or neutral effect on the water temperature. Stratification of the water temperature in the system up to 2.5°C/m has also been observed and should therefore be included in the said modelling of the system.

Regarding water management, the Rainergy system can cover up to 40% of a building's water needs, which is significant. Its efficiency in managing rainwater varies with occupant behaviour, ranging from 30% to 60%. To improve this efficiency, larger tanks would be required, leading to additional costs and constraints without necessarily enhancing overall performance.

Rainergy concept does not aim at supplanting air conditioning systems but can help to reduce or avoid its use by improving the summer thermal comfort of the buildings. The in-situ experimental study evaluated the buildings' comfort: the maximum temperature reached 28.6°C and the maximum DH (degree hours) index is 92°C.h, showing the buildings good comfort (below the threshold of 350°C.h).

The in-situ study does not allow to control a large number of variable parameters, therefore, in perspective, the concept, experimentally validated, needs to be generalized and theoretically validated. Models are necessary to test the system behaviour in more extreme conditions: how does the system operates when the water levels are low (during droughts for example), will it still be effective in future climates when temperatures are higher and rainfall alternately abundant and scarce, how does soil type affect the performance ? The geometry (size, material, depth, ...) and the control strategy could then be improved to increase the system performance. The experimental data will be used as a validation dataset.

In order to continue this experimental work, the stored water will also be used in the Saverne prototype as an alternative water supply for an evaporative heat exchanger, which would improve the performance of the system. Such system and its integration with Rainergy needs to be further investigated.

Finally, in the longer term, the system will have to undergo a change of scale. The aim would be to test the feasibility of this system for larger buildings (apartment blocks) or buildings with a higher cooling demand (commercial buildings). It might also be interesting to follow up on the literature by coupling the system with a heat pump.
Declaration of generative AI and AI-assisted technologies in the
writing process

During the preparation of this work the authors used Deel Write and ChatGPT in order to improve readability and language. After using this tool/service, the authors reviewed and edited the content as needed and take full responsibility for the content of the publication.

CRediT authorship contribution statement

**Lucas Striegel:** Writing – review & editing, Writing – original draft, Visualization, Validation, Methodology, Investigation, Formal analysis, Data curation, Conceptualization; **Jean-Baptiste Bouvenot:** Writing – review & editing, Validation, Supervision, Project administration, Investigation, Funding acquisition, Conceptualization; **Edouard Walther:** Writing – review & editing, Formal analysis, Conceptualization; **Hossein Nowamooz:** Project administration.

Data availability

Data will be made available on request.

Declaration of competing interest

The authors declare the following financial interests/personal rela-
tionships which may be considered as potential competing interests:
STRIEGEL Lucas reports financial support was provided by The French
Agency for Ecological Transition. STRIEGEL Lucas reports financial sup-
port was provided by Greater Eastern France Region. BOUVENOT Jean-
Baptiste reports financial support was provided by Carnot Institutes Net-
work. If there are other authors, they declare that they have no known
competing financial interests or personal relationships that could have
appeared to influence the work reported in this paper.

Acknowledgment

The authors address many thanks to the Gasnier and Schneider fam-
ily for kindly lending us their Rainergy system and their availability.
Airbee and Damien Marcel for their ideas. And thanks to the ADEME,
the Région Grand Est and InterCarnot as well for their financial support.
Thanks to Nat and Lisa for taking the time to make this manuscript more
readable in English.

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