Managing High Groundwater Velocities in Aquifer Thermal Energy Storage Systems: A Three-Well Conceptual Model

Abstract

Aquifer Thermal Energy Storage (ATES) is a promising technology for the seasonal storage of heat, thereby bridging the temporal gap between summer surpluses and peak winter demand. However, the efficiency of conventional ATES systems is severely compromised in aquifers with high groundwater flow velocities, as advective heat transport leads to significant storage losses. This study explores a novel three-well concept that implements an active hydraulic barrier, created by an additional extraction well upstream of the ATES doublet. This well effectively disrupts the regional groundwater flow, thereby creating a localized zone of stagnant or significantly reduced flow velocity, to protect the stored heat. A comprehensive parametric study was conducted using numerical simulations in FEFLOW. The experiment systematically varied three key parameters: groundwater flow velocity, the distance of the third well and its pumping rate. The performance of the system was evaluated based on its thermal recovery efficiency and a techno-economic analysis. The findings indicate that the hydraulic barrier effectively enhances heat recovery, surpassing twice the efficiency observed in a conventional two-well configuration (100 m/a). The analysis reveals a critical trade-off between hydraulic containment and thermal interference through hydraulic short-circuiting. The techno-economic assessment indicates that the three-well concept has the potential to generate significant cost and CO₂e savings. These savings greatly exceed the additional capital and operational costs in comparison to a traditional doublet system in the same conditions. In conclusion, the three-well ATES system can be considered a robust technical and economic solution for expanding HT-ATES to sites with high groundwater velocities; however, its success depends on careful, model-based design to optimize these competing effects.

1. Introduction

Decarbonizing the heating sector has become a critical priority in the global energy transition. In regions like Europe, the heating and cooling of buildings account for a large share of total energy use—for example, in Germany this sector represents roughly 50% of final energy consumption, yet only ~19% of its heating demand is currently met by renewables [1,2]. Achieving climate targets will require transitioning this thermal demand away from fossil fuels towards sustainable sources. District heating networks are seen as a key enabler in this shift, as they can integrate diverse renewable heat sources (solar thermal, geothermal, industrial waste heat) and distribute them efficiently to consumers. A major challenge, however, is the temporal mismatch between heat supply and demand—particularly the surplus of renewable heat in summer vs. high demand in winter [3,4,5]. In this context, thermal energy storage (TES) plays a vital role by bridging seasonal gaps [5]; long-term underground thermal energy storage (UTES) systems are especially promising for decoupling supply and demand in the heating sector [4,6,7]. Among UTES options, aquifer thermal energy storage (ATES) has gained growing attention due to its large storage capacity and minimal surface footprint [8]. ATES systems store heat (or cold) by injecting heated groundwater into a suitable aquifer for later recovery, typically on a seasonal cycle, making them well-suited for supplying district heating and cooling networks with renewable thermal energy [6,9,10]. ATES technology is already proven in low-flow, low-temperature settings—for instance, thousands of ATES installations in the Netherlands provide sustainable heating/cooling for buildings [6,11].

The basic ATES configuration employs well doublets (paired extraction and injection wells) to create warm and cold storage zones in the aquifer [12]. Over operational cycles, a thermal plume of heated groundwater develops around the warm well (and a cold plume around the cold well) as heat is injected and later extracted. In ideal conditions (homogeneous aquifer, negligible ambient flow), these thermal plumes remain relatively stationary around the well, and a high fraction of the injected heat can be recovered in subsequent seasons. However, heterogeneous or advective hydrogeologic conditions can significantly impact ATES performance. In particular, aquifers with high ambient groundwater flow velocities pose a serious challenge: natural advection can carry the stored heat (or cold) away from the well, causing increased thermal losses and reduced recovery [11,13,14,15,16]. The moving groundwater effectively migrates the thermal plume down-gradient, expanding the heated volume beyond the intended storage zone and potentially dissipating useful heat into the surrounding environment or into other wells. This issue of thermal plume migration under high-flow conditions has become a focal point in recent ATES research [11,13,14,16,17,18]. In essence, beyond a certain flow threshold, the aquifer starts to “flush” the stored heat away before it can be used, greatly undermining the storage.

Researchers have been actively exploring new ATES configurations and management approaches to overcome the challenges of high-flow aquifers [14]. A noteworthy development is the concept of using multiple wells aligned with the flow direction to intercept and recapture migrating heat. Bloemendal and Olsthoorn first analyzed the use of multiple doublets in series along the groundwater flow path to counteract advective losses [11]. In their approach, two or more warm wells and an equal number of cold wells are placed sequentially in the direction of ambient flow. During operation, an upstream well injects heat into the aquifer, and a downstream well (aligned down-gradient) is used to extract that heat after it has drifted with the groundwater. By storing heat via the up-gradient well and recovering via the down-gradient well, the natural advection is no longer purely a loss mechanism but is partially harnessed to move heat from injection to extraction. Similarly Silvestri et al. developed a uni-directional ATES in which injection of heat and cold is fixed in an upstream well and recovered from the downstream well [13]. They showed heat recovery efficiencies of about 55–75% (for LT-ATES) despite strong ambient flow, whereas conventional open-loop systems would suffer much lower recovery. Moreover, this uni-directional pumping scheme was found to significantly mitigate the thermal impact downstream of the system compared to a standard bidirectional (seasonally reversing) ATES. These findings underscore that intelligently reconfiguring the ATES operation to work with the natural flow (rather than against it) can turn a challenging hydrogeologic setting into a viable storage opportunity.

A fundamentally different approach is not to adapt to the ambient groundwater flow and instead impose engineering control on the subsurface environment, by actively counteracting it. This philosophy is embodied by the concept of an active hydraulic barrier or capture zone [19,20]. Rather than using physical, impermeable barriers like slurry walls, which are common in contaminant hydrogeology but impractical for the scale of ATES, a hydraulic barrier can be created by continuous pumping from one or more strategically placed wells [21,22,23,24]. The extraction and injection of water creates hydraulic capture zones that can locally stagnate, slow, or redirect the regional groundwater flow, a principle commonly applied to prevent seawater intrusion in coastal aquifers [21,23,25].

Building on this established principle this paper proposes and investigates a novel application of active hydraulic containment specifically for high-temperature ATES (HT-ATES) systems. The central idea is to protect the thermal plume by manipulating the local flow field. We hypothesize that by positioning a single, continuously extracting well strategically upstream of the ATES doublet, a hydraulic capture zone can be created that intercepts the ambient groundwater flow before it reaches the thermal storage area. This action is intended to create a localized zone of stagnated or significantly reduced advective flow around the ATES wells, thereby preserving the stored heat. Although an ATES system with three wells has already been proposed [26], the approach fundamentally differs from the system described in this study, since the third well is not used as an additional storage well.

This study uses detailed numerical modeling to evaluate this “ATES with hydraulic barrier” configuration (see Figure 1). We quantify the improvement in thermal recovery compared to a conventional two-well system by systematically varying groundwater velocities, third-well pumping rates, and well spacing. The analysis investigates the underlying hydraulic containment mechanisms and the critical trade-off with thermal interference. Furthermore, we assess the techno-economic viability and environmental benefits of the system compared to reference cases. The paper proceeds by detailing the methodology, presenting the results, and discussing their implications for expanding the applicability of ATES technology.

2. Materials and Methods

To investigate the performance of the proposed three-well hydraulic barrier system, a detailed numerical modeling approach was employed. A conceptual model was created in the finite element software FEFLOW (v. 10.0) [27] to simulate the coupled thermo-hydraulic processes within the aquifer. This model served as the basis for a comprehensive parameter study to quantify the system’s thermal recovery efficiency and techno-economic benefits across a wide range of operational and hydrogeological scenarios.

2.1. Groundwater Flow and Heat Transport Solver FEFLOW

All simulations for this study were performed using the commercial software FEFLOW, a widely-used finite element modeling environment for simulating fluid flow and heat transport in porous media. FEFLOW was selected due to its extensive use in prior ATES modeling studies [28,29,30,31] and its robust support for process automation via Python (3.12) and C++ (17) interfaces.

The simulations in this study are based on the fundamental principles of groundwater flow and heat transport in porous media. FEFLOW solves the governing partial differential equations for fluid flow and heat transport using the finite element method. The equation for saturated groundwater flow, which relates changes in hydraulic head to the movement of water through the porous medium, is given by:

$$\begin{array}{c}{S}_s{\displaystyle \frac{\partial h}{\partial t}}=\nabla \cdot (K\nabla h)+Q\end{array}$$

(1)

where:

• $S_s$ is the specific storage coefficient (${\mathrm{m}}^{-1}$).
• $h$ is the hydraulic head ($\mathrm{m}$).
• $t$ is time span of head change ($\mathrm{s}$).
• $K$ represents the hydraulic conductivity tensor ($\mathrm{m}\cdot {\mathrm{s}}^{-1}$).
• $Q$ is the source/sink term for fluid (${\mathrm{s}}^{-1}$).

The term on the left side of the equation represents the transient change in fluid storage, while the right side describes the flux of water according to Darcy’s law and any sources or sinks.

The transport of thermal energy within the model domain is described by the heat transport equation:

$$\begin{array}{c}{\left(\rho c_p\right)}_m{\displaystyle \frac{\partial T}{\partial t}}+{\rho }_w{c}_{p,w}v\cdot \nabla T=\nabla \cdot ({\lambda }_m\nabla T)+Q_T\end{array}$$

(2)

where:

• ${\rho }_m$ is the density of the porous medium ($\mathrm{k}\mathrm{g}\cdot {\mathrm{m}}^{-3}$).
• $c_{p,m}$ is the specific heat capacity of the porous medium ($\mathrm{J}\cdot {\mathrm{k}\mathrm{g}}^{-1}\cdot {\mathrm{K}}^{-1}$).
• $T$ is the temperature (°C).
• $t$ is time span ($\mathrm{s}$).
• ${\rho }_w$ is the density of the fluid ($\mathrm{k}\mathrm{g}\cdot {\mathrm{m}}^{-3}$).
• $c_{p,w}$ is the specific heat capacity of the fluid ($\mathrm{J}\cdot {\mathrm{k}\mathrm{g}}^{-1}\cdot {\mathrm{K}}^{-1}$).
• $v$ is the groundwater flow velocity ($\mathrm{m}\cdot {\mathrm{s}}^{-1}$).
• ${\mathsf{\lambda }}_m$ is the thermal conductivity tensor of the porous medium ($\mathrm{W}\cdot {\mathrm{m}}^{-1}\cdot {\mathrm{K}}^{-1}$).
• $Q_T$ is the source/sink term for heat ($\mathrm{W}\cdot {\mathrm{m}}^{-3}$).

In this equation, the first term on the left, ${\left(\rho c_p\right)}_m{\displaystyle \frac{\partial T}{\partial t}}$, describes the change in thermal energy stored in the bulk porous medium (both solid and fluid phases). The second term, ${\rho }_w{c}_{p,w}v\cdot \nabla T$, represents the advective heat transport, or the movement of heat carried by the flowing groundwater. On the right side, $\nabla \cdot ({\mathsf{\lambda }}_m\nabla T)$ accounts for conductive heat transport through the porous medium and hydrodynamic dispersion.

To accurately capture the thermo-hydraulic processes in the ATES system, the simulations accounted for the temperature-dependence of fluid properties. All models were simulated using a consistent set of equations of state. For fluid density, the full set of density variations was considered, including terms for buoyancy, gradient, rate of change, and fluid dispersion, rather than using the simplified Boussinesq approximation.

Furthermore, fluid viscosity was not treated as a constant. Instead, viscosity was modeled with a nonlinear dependency on temperature. This relationship is based on FEFLOW’s default polynomial coefficients, which provide a close fit to the National Institute of Standards and Technology (NIST) reference data for water between 0 and 100 °C at atmospheric pressure. This ensures that the changes in viscosity due to the injection and storage of heated water are realistically represented in the model.

2.2. Model Description and Setup

This section details the construction of the conceptual model, including the domain geometry, mesh generation, boundary conditions, and the operational scheme used for the transient simulations.

2.2.1. Conceptual Model and Mesh Generation

The numerical model consists of a three-dimensional rectangular domain with dimensions of 3000 m (x-direction) by 2000 m (y-direction), based and adapted from the conceptual model proposed by Silvestri et al. [13]. The simplified model stratigraphy includes a 30 m thick aquifer situated between two 30 m thick aquitards. The top of the model is located at an elevation of −80 m below sea level. The ambient groundwater flow is aligned with the x-axis, as depicted in Figure 2.

The entire model setup and meshing process was automated using the FEFLOW Python interface (IFM) and its PySMH module. A structured finite element mesh was generated using the Triangle algorithm [32]. To enhance accuracy while maintaining computational efficiency, local mesh refinement was applied in critical areas. Specifically, a higher element density was implemented around the well locations and in the downstream region where the thermal plume is expected to migrate. This approach ensures a fine resolution near points of high hydraulic and thermal gradients, with element sizes gradually increasing towards the model boundaries.

2.2.2. Boundary Conditions

Initial conditions for the transient simulations were established by running the model to a steady state. For groundwater flow, fixed hydraulic head (Dirichlet) boundary conditions were applied to the model faces perpendicular to the main flow direction (x-axis). The hydraulic head at the western boundary was calculated for each scenario using Darcy’s Law to achieve the desired ambient Darcy velocity. The corresponding average actual groundwater velocity, which represents the advection speed of the thermal plume, is related to the Darcy velocity by the aquifer’s effective porosity. For the remainder of this paper, the term “groundwater velocity” refers to the Darcy velocity unless otherwise specified. All other model boundaries were defined as no-flow (Neumann) boundaries.

For the heat transport, top and bottom boundaries were set to fixed Dirichlet conditions of 17.3 °C, which is the temperature at 210 m below sea level, assuming a geothermal gradient of 0.03 °C/m and a surface temperature of 11 °C. All other boundary layers are set to default Neumann no-flow boundary conditions. With a steady-state simulation, the initial conditions for the transient simulations are obtained. In the last step, time series for the operational scenarios of the wells are created. After this, multilayer well boundary conditions (MLW BC) were set for all three wells, applying the mentioned time series for the well flow rates. All these steps were realized using a single python script. By looping over the parameter variations, all 336 models were created at once, ready for the transient batch simulations.

A grid independence test was conducted to ensure that the simulation results were not depending on the mesh resolution. A refined model with a significantly higher element density was created, consisting of 563,940 elements and 290,960 nodes, compared to the 270,378 elements and 141,092 nodes used in the primary model. A comparative simulation was run for a key scenario (300 m third-well distance, 100 m/a groundwater velocity, 4000 m³/d pumping rate). After five operational cycles, the refined model yielded a cumulative heat budget of 75,331.8 MWh at the hot well. This result differs by less than 1% from the 74,709.2 MWh calculated with the primary model, confirming that the mesh resolution is sufficient, and that the numerical results are robust and independent of the grid density.

The thermal and hydraulic properties summarized in

Table 1. FEFLOW material properties and parameters.

Material Property	Value	Unit
Horizontal hydraulic conductivity aquifer (at reference temperature)	12.0	$\mathrm{m}\cdot {\mathrm{d}}^{-1}$
Vertical hydraulic conductivity aquifer (at reference temperature)	2.4	$\mathrm{m}\cdot {\mathrm{d}}^{-1}$
Horizontal hydraulic conductivity aquitard (at reference temperature)	0.05	$\mathrm{m}\cdot {\mathrm{d}}^{-1}$
Vertical hydraulic conductivity aquitard (at reference temperature)	0.01	$\mathrm{m}\cdot {\mathrm{d}}^{-1}$
Storage coefficient	0.0001	[-]
Thermal conductivity aquifer	2.0	$\mathrm{W}\cdot {\mathrm{m}}^{-1}\cdot {\mathrm{K}}^{-1}$
Thermal conductivity aquitard	1.5	$\mathrm{W}\cdot {\mathrm{m}}^{-1}\cdot {\mathrm{K}}^{-1}$
Density solid	2400	$\mathrm{k}\mathrm{g}\cdot {\mathrm{m}}^{-3}$
Density fluid	999.7	$\mathrm{k}\mathrm{g}\cdot {\mathrm{m}}^{-3}$
Specific heat capacity solid	1050	$\mathrm{J}\cdot {\mathrm{k}\mathrm{g}}^{-1}\cdot {\mathrm{K}}^{-1}$
Specific heat capacity fluid	4200	$\mathrm{J}\cdot {\mathrm{k}\mathrm{g}}^{-1}\cdot {\mathrm{K}}^{-1}$
Porosity	0.3	[-]
Longitudinal dispersivity	0.5	$\mathrm{m}$
Transversal dispersivity	0.05	$\mathrm{m}$

were selected to represent the general settings of quaternary and tertiary aquifers in the Upper Rhine Graben [33]. This ensures the model is representative of a for a generic geological environment for HT-ATES. Furthermore, the chosen parameters were aligned with values used in recent ATES modeling studies [11,13,31,34] to ensure that the results were comparable to and built upon the existing body of research.

2.2.3. Transient Simulations and Operational Scheme

The dynamic operation of the ATES wells was managed using a custom C++ plug-in developed for FEFLOW. This plug-in dynamically applies or removes thermal boundary conditions at well nodes based on the operational phase. During injection, the plug-in calculates the required heat rate to raise the water temperature from the ambient 17.3 °C to the target injection temperature of 85 °C. Conversely, during extraction, the thermal boundary condition is removed to allow the model to freely calculate the produced water temperature.

For scenarios during the extraction phase, in which both the hot well and the third well abstract from the aquifer simultaneously, a perfect mixing of the two water streams is assumed. The resulting mixing temperature ($T_{mix}$) is calculated using Equation (3). This approach ensures a realistic and dynamic representation of the fluid temperatures throughout the operational cycle, avoiding the need to impose artificial temperature constraints on the extraction wells.

$$\begin{array}{c}{T}_{mix}={\displaystyle \frac{T_1\times m_1+T_2\times m_2}{m_1+m_2}},\end{array}$$

(3)

The models are simulated using the operational scheme proposed by [35] and is shown in Figure 3. They proposed an idealized seasonal charging and discharging scheme based on four periods: 120 days of injections, 60 days of falloff/storage, 120 days of drawdown/extraction and 65 days of build-up/rest.

The simulations were performed using FEFLOW’s automatic time-step control, which adjusts the step size based on a predefined error norm to ensure numerical stability, with a maximum allowable time step of 5 days.

2.2.4. Parameter Study

To evaluate the effectiveness of the three-well system under a wide range of subsurface and operational conditions, a comprehensive parameter study was conducted. This study systematically varied key parameters to quantify their influence on the system’s hydraulic and thermal performance. We investigated various ambient groundwater flow scenarios, with background velocities ranging from 10 m/a to 250 m/a, to represent conditions from nearly stagnant to highly advective. The geometric configuration was also altered by adjusting the distance of the third well from the primary ATES doublet, with distances from 50 m up to 500 m. Furthermore, to understand the impact of the hydraulic barrier, we simulated various continuous pumping schemes for the third well, with extraction rates from 0 m³/d (representing a standard two-well ATES) up to 6000 m³/d. A full-factorial combination of these parameters resulted in a total of 336 unique simulation scenarios, which are summarized in

Table 2. Parameter variation for the analysis of various operational conditions.

Parameter	Values	Unit
Groundwater velocity	10, 25, 50, 75, 100, 250	$\mathrm{m}\cdot {\mathrm{a}}^{-1}$
Third well distance	50, 100, 150, 200, 250, 300, 400, 500	$\mathrm{m}$
Pumping rate	0, 250, 500, 1000, 2000, 4000, 6000	${\mathrm{m}}^3\cdot {\mathrm{d}}^{-1}$

.

2.3. Recovery Efficiency and Thermal Interference Factor

The thermal recovery efficiency ($R$) is the primary metric used in this study to evaluate and compare the performance of the different ATES configurations. It quantifies the fraction of stored heat that is successfully recovered during the extraction phase. The calculation is based on the energy fluxes at the wellbores over a full operational cycle.

For each time step in the transient simulations, FEFLOW calculates the heat rate at the well nodes by comparing the temperature and flow of the abstracted or injected water against the ambient groundwater temperature. To determine the total energy exchanged during an operational cycle, these instantaneous heat rates are integrated over time for the entire injection period to yield the total injected energy ($E_{injected}$), and similarly for the extraction period to yield the total produced energy ($E_{produced}$). The thermal recovery efficiency is then calculated as the ratio of the total energy produced to the total energy injected, as shown in Equation (4).

$$\begin{array}{c}R={\displaystyle \frac{E_{produced}}{E_{injected}}}={\displaystyle \frac{\int {\dot{Q}}_{produced}dt}{\int {\dot{Q}}_{injected}dt}}\end{array}$$

(4)

This approach provides a direct measure of the system’s ability to retain thermal energy between seasons, accounting for all heat loss mechanisms, including advection and conduction.

While the primary metric for performance is the thermal recovery efficiency, it is also crucial to quantify the degree of thermal interference, where the third well captures a portion of the stored heat. This “thermal short-circuiting” can negatively impact system performance, especially at close well spacings and high pumping rates. To measure this effect, the Thermal Interference Factor (TIF) is introduced. The TIF is defined as the ratio of the thermal energy captured by the third well to the total thermal energy injected into the hot well over a complete operational cycle:

$$TIF={\displaystyle \frac{E_{captured3rdwell}}{E_{injectedhotwell}}}$$

(5)

A TIF value much greater than zero indicates that thermal interference is occurring. An optimized system design should therefore seek to maximize thermal recovery efficiency while minimizing the TIF.

2.4. Economic and Environmental Assesement

To assess the potential cost and greenhouse gas emission reduction, the performance of the three-well system was compared against a conventional two-well system operating under the same hydrogeological conditions. The analysis is based on the increased annual thermal recovery (ΔQ), which is defined as the difference in thermal energy recovered by the optimal three-well scenario versus the baseline two-well scenario (i.e., where the third-well pumping rate is 0 m³/d).

For each groundwater velocity investigated (e.g., 10, 25, 50 m/a, etc.), the optimal three-well scenario was identified from the parameter study as the specific combination of the third-well pumping rate and distance that yielded the highest 5-year thermal recovery efficiency.

The annual operational expenditures (OPEX) for this optimal scenario were then calculated by selecting an appropriate submersible pump model for the third well (see Table 3). The choice of pump was based on its ability to provide the required pumping rate and overcome the necessary hydraulic head lift calculated in the FEFLOW simulations. This ensures that the costs are based on a realistic power consumption for that specific optimal scenario. It is assumed that all extra heat gained displaces heat from a single marginal technology, which is exemplified by using a natural gas boiler for a fossil fuel-based system and a river source heat pump for a more renewable system.

The net annual cost is calculated as:

$$\begin{array}{c}\mathsf{\Delta }C=CAPEX+OPEX-C_{avoid}\end{array}$$

(6)

where:

• $\mathsf{\Delta }C$: Net annual cost (EUR); a negative value indicates a cost reduction.
• $CAPEX$: Annualized capital expenditures (EUR).
• $OPEX$: Annual operational expenditures (EUR).
• $C_{avoid}$: Annual avoided costs (EUR).

Annualized capital expenditures are calculated as:

$$CAPEX={\displaystyle \frac{c_{drill}\times d_{aq}}{L}}+n_{sp}\times c_{sp}$$

(7)

where:

• $c_{drill}$: drilling costs (EUR/m).
• $d_{aq}$: depth of aquifer (m).
• $L$: Lifetime of well (30 years).
• $n_{sp}$: number of submersible pumps per year (0.5 items, equaling a replacement every two years).
• $c_{sp}$: cost of submersible pump (EUR/item).

Annual operational expenditures are calculated as:

$$OPEX=P_{sp}\times t_{sp}\times c_{el}$$

(8)

where:

• $P_{sp}$: average power consumption of submersible pump (MW).
• $t_{sp}$: operation time of submersible pump per year (8760 h, operation all year).
• $c_{el}$: cost of electricity (EUR/MWh).

Annual avoided costs are calculated as:

$$\begin{array}{c}{C}_{avoid}=\mathsf{\Delta }Q\times c_a\end{array}$$

(9)

where:

• $\mathsf{\Delta }Q$: increased thermal recovery (MWh).
• $c_a$: Variable costs of displaced technology (EUR/MWh).

Similarly, impacts of greenhouse gas emission are calculated as:

$$\begin{array}{c}\mathsf{\Delta }E=E_{CAPEX}+E_{OPEX}-E_{avoid}\end{array}$$

(10)

Emission factors are retrieved from the ecoinvent consequential database 3.11 [36], using the IPCC 2021 Life Cycle Impact Assessment (LCIA) method “Climate change: total (excl. biogenic CO₂)” [37].

Table 3. Costs and emission data.

	Cost	Source	Comment	Ecoinvent Dataset	Comment
CAPEX
Drilling	675 EUR/m	[38]		Deep well drilling, for deep geothermal power—DE	Cost is inflation adjusted (2019–2024) [39] and currency-converted (2024 average) [40]
Submersible Pump (SP)	EUR 3388.46 (SP 32-2) EUR 10,866.03 (SP 95-2) EUR 14,682.00 (SP 160-2) EUR 29,255.10 (SP 215-3)	[41]	Pumps used in ascending order of groundwater flow rate. SP 215-3 used for 75 m/a and 100 m/a	Water pump production, 22 kW—GLO	Dataset linearly scaled to rated pump power
OPEX
Electricity for SP	0.3052 EUR/kWh	[42]	Electricity price for commercial customer	Market for electricity, medium voltage—DE
Avoided
Heat from natural gas	0.1191 EUR/kWh	[42]	Natural gas price for commercial customer $0.1039\mathrm{EUR}/\mathrm{kWh}\times$ 1/boiler efficiency (~87%) from ecoinvent dataset	Heat production, natural gas, at boiler modulating >100 kW—Europe without Switzerland	Calorific value of natural gas: 11 kWh/m3
Heat from river source heat pump	0.1174 EUR/kWh	[42]	Electricity price for commercial customer	Market for electricity, medium voltage—DE	COP = 2.6

Table 3. Costs and emission data.

	Cost	Source	Comment	Ecoinvent Dataset	Comment
CAPEX
Drilling	675 EUR/m	[38]		Deep well drilling, for deep geothermal power—DE	Cost is inflation adjusted (2019–2024) [39] and currency-converted (2024 average) [40]
Submersible Pump (SP)	EUR 3388.46 (SP 32-2) EUR 10,866.03 (SP 95-2) EUR 14,682.00 (SP 160-2) EUR 29,255.10 (SP 215-3)	[41]	Pumps used in ascending order of groundwater flow rate. SP 215-3 used for 75 m/a and 100 m/a	Water pump production, 22 kW—GLO	Dataset linearly scaled to rated pump power
OPEX
Electricity for SP	0.3052 EUR/kWh	[42]	Electricity price for commercial customer	Market for electricity, medium voltage—DE
Avoided
Heat from natural gas	0.1191 EUR/kWh	[42]	Natural gas price for commercial customer $0.1039\mathrm{EUR}/\mathrm{kWh}\times$ 1/boiler efficiency (~87%) from ecoinvent dataset	Heat production, natural gas, at boiler modulating >100 kW—Europe without Switzerland	Calorific value of natural gas: 11 kWh/m3
Heat from river source heat pump	0.1174 EUR/kWh	[42]	Electricity price for commercial customer	Market for electricity, medium voltage—DE	COP = 2.6

3. Results

The numerical simulations demonstrate that the inclusion of a third extraction well significantly enhances the performance and viability of Aquifer Thermal Energy Storage (ATES) systems in environments with high ambient groundwater flow. This chapter presents the detailed results of the 336 simulated scenarios. First, the fundamental impact of the third well on the local hydraulic gradient and thermal plume containment is illustrated (Section 3.1). Following this, the thermal recovery efficiency is quantified across the full parameter space, highlighting the influence of groundwater velocity, third-well distance, and pumping rate (Section 3.2). Section 3.3 provides a direct comparison of the evolution of the heat budget and well temperatures over five years for scenarios with and without the hydraulic barrier. Subsequently, these thermal performance gains are translated into tangible economic and environmental benefits (Section 3.4). Finally, the effects of alternative operational strategies on long-term system efficiency are explored to assess opportunities for operational optimization (Section 3.5).

3.1. Thermal and Hydraulic Plume Migration

The following visualizations and analyses illustrate the significant influence of the third pumping well on groundwater flow and thermal plume distribution compared to a conventional two-well ATES.

In Figure 4, first the changes in the hydraulic head are compared. In a normal ATES operation, the pressures and hydraulic heads inside the aquifer are only changed to injection and extraction pressure changes, which do not affect the overall groundwater flow trend. With adding the third well upstream of the ATES doublet, the local hydraulic gradient is altered. The area of similar hydraulic head is expanded over the whole distance of the three wells, and the visible hydraulic plume shows enhanced confinement near the wells due to lowering and lifting of the third and cold well.

Similar effects can be observed for the temperature field and thermal plume of the simulations (Figure 5). With the active third well, the downstream thermal plume migration is highly reduced compared to the traditional ATES system. For the specific shown case of 50 m/a Darcy velocity, the thermal plume travels downstream and fully reaches the cold well within 5 years, effectively creating a thermal short cut, which would highly influence the effectiveness of the overall system. By applying the third well, the thermal plume is mostly contained around the well.

3.2. Comparison of Temperature and Heat Budget Evolution with and Without the Third Well

The effect of the third well comes clearly visible in the amount of heat stored and extracted. Though the same amount of heat is injected into the aquifer, only a fraction can be recovered when reversing the pumping direction because of heat losses that are predominately advective (Figure 6). With each cycle, the heat period budget—the cumulated injected and extracted energy—of the system without an additional pumping well deviates more from the one with a third well (Figure 6). This is more than 25 GWh higher than that of the hydraulic barrier system.

This becomes visible in the temperatures of the wells as well. While the injected temperatures are equal, extracted temperatures show a clear difference (Figure 7). Initially the temperature at the well rises to 85 °C and stays there for the injection period. Within the falloff, the temperature at the bottom well nodes decrease due to advection by the groundwater, density-driven flow (convection) and dispersive heat flux. Here, the decrease in temperature is much higher for the convectional ATES system (orange). When entering the drawdown phase, the temperatures shortly spike, because of the way FEFLOW models its MLW BC, sitting at the bottom of the well screen and the temperature at the top of the screen being higher due to buoyancy of the hot groundwater. When extracting and in the build-up phase, both scenarios show similar temperature behavior.

3.3. Recovery Efficiency

To assess the performance of the ATES with a hydraulic barrier, the different scenarios of how groundwater flow, third well distances and pumping rate effect the recovery efficiencies over multiple years are compared, and the effects are investigated. The 5-year thermal recovery efficiency (R), which quantifies the fraction of stored heat that is successfully recovered, was used as the primary metric to evaluate system performance. The results for groundwater velocities up to 100 m/a are presented in Figure 8. While simulations were also conducted for a velocity of 250 m/a, these scenarios resulted in near-zero recovery efficiencies (<9%) regardless of the third-well pumping rate and are therefore excluded from the figures for clarity.

A primary observation across all scenarios is the strong inverse relationship between groundwater velocity and thermal recovery. For instance, in a standard two-well configuration (0 m³/d pumping rate), the efficiency drops from over 65% at 10 m/a to approximately 11% at 100 m/a, demonstrating the severe impact of advective heat loss. The results clearly show that increasing the extraction rate of the third well effectively counteracts this loss. At a velocity of 100 m/a, implementing a hydraulic barrier with a 4000 m³/d pumping rate raises the recovery efficiency to over 30%, a nearly threefold improvement. However, this effect exhibits diminishing returns, as the efficiency gain from increasing the pumping rate from 4000 m³/d to 6000 m³/d is less pronounced than the gain from 2000 m³/d to 4000 m³/d.

The distance of the third well also proves to be a relevant design parameter. The heatmaps suggest an optimal distance range for the hydraulic barrier, which appears to be between 200 and 400 m. At very close distances (e.g., 50–100 m), particularly with high pumping rates, a slight reduction in efficiency is observed compared to intermediate distances. This is attributable to parasitic thermal drawdown, where the extraction well captures a portion of the heated water prematurely, an effect suggested by the temperature distribution in Figure 9.

To quantify the impact of well spacing on the system’s energy balance, a detailed analysis was performed for a high-stress scenario with a groundwater velocity of 75 m/a and a third-well pumping rate of 4000 m³/d. Figure 10 illustrates the heat period budget over five years for both the ATES hot well and the third extraction well at four different distances.

The results clearly demonstrate the trade-off between hydraulic containment and thermal interference. This effect can be quantified by the Thermal Interference Factor (TIF), which measures the fraction of injected heat that is captured by the third well. At distances of 250 m and 200 m, the TIF is negligible (7.9 ×∙10⁻⁸ and 0.0014, respectively), confirming that almost no thermal short-circuiting occurs, and the majority of heat is stored near the hot well. Consequently, the ATES hot well exhibits the best affordable performance at these distances, as shown by the solid green and blue lines.

However, as the third well is placed closer, thermal interference becomes a significant factor. At 150 m, the TIF rises to 0.088, quantifying the slight thermal capture observed in later cycles. This interference becomes severe at 100 m, where the TIF reaches 0.278, meaning that nearly 28% of the injected energy is captured by the third well over time. This directly corresponds to the visible reduction in the peak energy recovered by the ATES hot well (solid orange line).

This analysis is critical, as it reveals that while a close-in hydraulic barrier may effectively prevent plume migration, it can do so at the cost of capturing the stored heat itself. Therefore, optimizing the third well’s distance is paramount to balance the goals of hydraulic control (maximizing recovery) and thermal energy preservation (minimizing TIF), ensuring that the system is both effective and efficient.

3.4. Economic and Environmental Assessment

This section quantifies the potential cost and emission reductions by comparing the performance of the optimal three-well configuration against a standard two-well system for each groundwater velocity investigated. The optimal scenarios were chosen based on maximum recovery efficiency, that comes with minimum TIF and pumping rate. The results, shown in Figure 11, display a great potential in cost reduction and emission reduction, with increasing numbers from low to high groundwater flow velocity for a gas boiler as the marginal technology. The net annual emission reduction of river source heat pumps as the marginal technology is much lower.

CAPEX (Figure 11a, red bars) are small and almost irrelevant compared to OPEX and avoided costs (Figure 11a, orange and blue bars), with avoided costs of natural gas being about a magnitude larger than OPEX. Since the same submersible pump is used for the velocities 75 m/a and 100 m/a, OPEX for these are almost of same size. The higher the velocity, the higher the cost reduction, with 100 m/a reaching over EUR 1.1 million (Figure 11b). The net annual cost is in a similar range for river source heat.

Emissions in Figure 12 show similar results to costs, with emissions for capital investments being even more negligible than capital costs. Avoided emissions of natural gas are most important; the operation of submersible pumps has only a comparatively small impact. The net emission reduction shows a great potential for decarbonization of almost up to 2.9 million kg CO₂e annually when groundwater flow is 100 m/a. However, when river source heat pumps are considered the marginal technology, the situation changes. While emissions continue to be reduced, the magnitude of this reduction is considerably diminished.

3.5. Alternative Operational Schemes and Scenarios

While the base operational case (50 m/a GW flow, 400 m distance, 4000 m³/d pumping) proves effective, this section explores alternative operational strategies to assess potential optimizations for thermal efficiency and reductions in auxiliary energy consumption. Four scenarios were compared over a 5-year period: the ‘Base case’ used throughout this study, a ‘Longer injection/extraction’ case, a ‘Partial pumping’ case, and a ‘Combined scenario’. The results are shown in Figure 13.

The ‘Base case’ (blue line), which operates on a 120-day injection, 60-day storage, 120-day extraction, and 65-day rest schedule with continuous pumping from the third well, serves as the benchmark. It shows a steady increase in performance, reaching a stable recovery efficiency of approximately 65.5% by the fourth cycle.

The ‘Longer injection/extraction’ scenario (orange line) simplifies the cycle to two equal 182.5-day periods of injection and extraction (see e.g., [43]), while the third well also runs continuously. This strategy initially shows a higher recovery efficiency in the first year compared to the base case. However, its performance plateaus sooner and is eventually surpassed by the base case, suggesting that the lack of rest periods might lead to slightly higher thermal dispersion over multiple years.

The other two scenarios investigate the potential for reducing operational costs by running the third well intermittently. In the ‘Partial pumping’ scenario (green line), the operational timing is the same as in the base case, but the third well is inactive during the 120-day extraction phase. This results in a significantly lower recovery efficiency, which plateaus at around 57%. This shows that although the hydraulic barrier effectively protects the thermal plume during injection and storage operation, shutting it down during extraction causes the regional hydraulic gradient to re-establish itself almost immediately. Once the containment from the third well is removed, the natural ambient groundwater flow begins to flush the stored heat plume downstream away from the hot recovery well. As shown in the two-well comparison (Figure 5), this advective heat loss is rapid. Even though the extraction phase lasts just 120 days, this is sufficient time for a significant portion of the thermal energy to migrate beyond the capture zone of the hot well before it can be recovered, which severely impacting performance.

The ‘Combined scenario’ (red line) represents the worst-performing strategy. It combines the longer 182.5-day cycles with intermittent pumping from the third well (only during injection). The recovery efficiency in this case decreases after the second year, ending below 53%. This indicates that the system loses more residual heat year after year than it can build up.

Ultimately, these results highlight that for the three-well concept to be effective in high-velocity aquifers, the continuous operation of the hydraulic barrier is critical, particularly during the long storage and extraction phases. The significant loss in thermal recovery from intermittent pumping likely outweighs any potential savings in operational energy costs.

4. Discussion

The results of this study demonstrate that a three-well ATES configuration can be a technically and economically viable solution for implementing high-temperature heat storage in aquifers characterized by high ambient groundwater flow. The following sections interpret these findings in greater detail, discussing the effectiveness and underlying mechanics of the hydraulic barrier, the critical design trade-offs identified, the practical implications of the operational strategy and the limitations of this conceptual study.

4.1. Effectivenes of the Hydraulic Barrier

The primary objective of this study—to mitigate advective heat loss—was successfully achieved. The simulations confirm that the introduction of an upstream extraction well fundamentally alters the local hydraulic regime in a way that is favorable for thermal energy recovery. As shown in Figure 4, the pumping of the third well creates a broad zone of similar hydraulic head that effectively nullifies the regional hydraulic gradient in the vicinity of the ATES doublet. The direct consequence of this hydraulic containment is a dramatic reduction in the downstream migration of the thermal plume. In contrast to a conventional two-well system in which the heat plume is rapidly swept towards the cold well, the three-well system contains most of the thermal energy around the hot well, preserving it for seasonal recovery. This finding validates the core principle of the concept: that an engineered hydraulic barrier can transform an advection-dominated environment into one that is suitable for efficient thermal energy storage.

4.2. The Critical Trade-Off: Hydraulic Capture vs. Thermal Interference

While the hydraulic barrier is effective, one of the most significant findings of this study is the critical design trade-off between hydraulic containment and thermal interference [44]. The detailed energy balance analysis in Figure 10 reveals that well spacing is an important design parameter. At larger distances, the third well operates mostly without capturing any of the stored heat, resulting in the highest ATES performance. However, as the well spacing is reduced, this study demonstrates that the third well can begin to capture a portion of the stored thermal energy itself. This “thermal short-circuiting” becomes severe at distances of 50–100 m, where the third well captures a substantial and increasing amount of heat over subsequent cycles, which directly corresponds to a reduction in the energy recovered by the primary ATES well. This reveals that relying solely on the ATES recovery efficiency metric can be misleading. An optimized system design must therefore carefully balance the need for a strong hydraulic barrier with sufficient spacing to prevent this capture of heat.

4.3. Economic Viability and Environmental Impacts

The technical success of the three-well system is underpinned by a strong economic and environmental case. It is important to clarify that these benefits are calculated based on the increased thermal recoveries (ΔQ) by the optimal three-well configuration when compared to a basic two-well system operating under identical hydrogeological conditions. The analysis shows that the additional CAPEX and OPEX associated with the third-well are largely offset by the value of the increased recovered heat. A total cost reduction of over EUR 1.1 million per year at a groundwater velocity of 100 m/a (Figure 11) transforms the concept from a technical novelty into a financially appealing investment. Similarly, the potential to avoid nearly 2900 tons of CO₂e emissions annually (Figure 12) is a strong argument for the system’s role in decarbonizing fossil fuel-based heating systems. These benefits are most pronounced at the highest velocities, which are precisely the conditions where conventional ATES fails.

The example of a river source heat pump underlines the economic feasibility also in more renewable heating systems, but also shows that emission reduction is strongly dependent on the displaced technology. However, the economic and environmental model presented relies on a key assumption that warrants discussion. The method provides a static calculation approach, which is very sensitive to the single displaced technology. As district heating networks undergo a transition to low-temperature systems that include a variety of heating technologies, the actual displaced technology may vary time- and system-dependently. Therefore, while this study demonstrates an illustrative simplified example, detailed case studies should be conducted for any real-world application to identify the specific displaced technology and its corresponding costs and emissions under varying conditions.

4.4. Model Limitations and Future Research

It is important to acknowledge that this study was based on a conceptual model of a simplified, homogeneous aquifer. This approach was chosen to isolate and analyze the fundamental thermohydraulic principles of the three-well concept. However, real-world aquifers are inherently heterogeneous [45]. They have features such as preferential flow paths, layered stratigraphy, and—in hard rock systems—fractures that were not considered but that have a major influence on the hydraulic and thermophysical parameters of the geology. This geological complexity could significantly impact the system’s performance. For example, high-permeability layers or channels could alter the shape and effectiveness of the hydraulic capture zone, potentially enabling parts of the thermal plume to bypass the containment area. Conversely, low-permeability barriers could divide the reservoir into sections that could help or hinder the system depending on their location relative to the wells. Therefore, the uniform containment presented in our simulations is an idealization, and accurately predicting the behavior of the hydraulic barrier would require a detailed characterization of site-specific geological conditions. However, site knowledge is crucial to take any optimization measure.

Additionally, the study assumes that groundwater flow velocity and direction are constant, even though they could vary in reality. Future research should focus on incorporating this geological complexity. Investigating the system’s performance in models with layered structures, fractures or stochastically generated heterogeneity would provide critical insights into its real-world applicability and robustness. These studies would refine design guidelines for well placement and pumping rates, ensuring effective hydraulic control in heterogeneous subsurface environments. A key limitation is the assumption of a constant and perfectly known groundwater flow vector, which is subject to significant uncertainty in real-world field applications. The effectiveness of the three-well system is highly sensitive to this parameter; an error in assessing the flow direction or velocity could render the hydraulic barrier ineffective or inefficiently designed. Again, thorough site characterization is a prerequisite for implementation, and future work should include sensitivity analyses on the flow vector’s uncertainty to assess the systems robustness.

This study modeled only a linear well arrangement and used an idealized operational schedule with fixed 120-day cycle lengths to provide a consistent basis for comparing scenarios. However, real-world heat demand fluctuates seasonally and even daily. Therefore, future modeling work should incorporate dynamic, demand-driven energy loads to investigate the system’s performance and flexibility under more realistic operational conditions. This would provide deeper insights into the practical integration of the system with district heating networks.

Methodologically, the premise of the economic comparison also warrants discussion. The analysis calculates the benefit of the three-well system by comparing it to a standard two-well system that is, by design, not viable under high-flow conditions. A more conservative analysis might compare the entire three-well ATES system with a non-geothermal alternative system (i.e., the natural gas boiler). A more precise time dependent model could also identify a varying displaced technology, for example, based on a merit order. Similarly, investment decisions could be modeled dynamically using a net present value (NPV) framework, as proposed by Xiao et al. [46], to capture the time-dependent financial viability of projects. Future analyses could then explore a broader range of scenarios (e.g., varying fuel prices, demand patterns, and policy assumptions) and include additional environmental impact categories, enabling a comprehensive trade-off assessment between different system configurations.

This study generated a large parametric dataset that lends itself to advanced data analysis. Although a complete implementation was beyond the scope of this conceptual paper, future work could use regression or machine learning algorithms to create a predictive model of the system’s performance. Such a model would be highly valuable for optimization. For example, an optimization framework could balance the competing objectives of maximizing thermal recovery efficiency and minimizing the thermal interference factor (TIF). This would identify optimal operational modes for a given set of hydrogeological conditions.

A further consideration is the definition of the recovery efficiency metric itself, which was based solely on the ATES hot well. As shown in scenarios with close well spacing, a more holistic metric evaluating the total useful energy delivered by the overall system would provide a different and potentially more realistic perspective on performance.

From a practical standpoint, the economic analysis assumes continuous, year-round pumping of the third well, which represents a high-cost operational scenario that could potentially be optimized. Moreover, the study does not address the significant regulatory and legal frameworks that would govern a system designed to actively manipulate the local water table, nor does it consider detailed mechanical aspects such as heat exchanger and well clogging. These limitations highlight the need for future work that includes detailed sensitivity analyses and investigation of alternative system geometries. Ultimately, the design of the three-well hydraulic barrier system is strongly dependent on the real-world conditions regarding, geology, hydrogeology and available space and needs to be optimized based on these realistic conditions.

4.5. Comparison to Alternative ATES Configurations

This study compares the three-well concept to a conventional two-well doublet to quantify the performance gain under identical conditions. However, other advanced ATES configurations have been proposed to mitigate advective losses. Systems like the multi-doublet approach by Bloemendal and Olsthoorn [11] or the uni-directional ATES by Silvestri et al. [13] operate on a different principle: they are “flow-along” systems designed to intentionally let the thermal plume drift and recapture it downstream.

The fundamental difference lies in the approach to managing groundwater flow. Flow-along systems adapt to the regional flow, using it as a transport mechanism from an injection to an extraction well. In contrast, the three-well hydraulic barrier concept presented here is a “flow-control” system designed to actively counteract the regional flow, creating a localized zone of stagnant water to protect the thermal plume. While a detailed comparative modeling study is beyond the scope of this paper, the choice between these concepts would depend on site-specific factors. Flow control may offer higher recovery efficiencies but requires continuous energy for the third well, whereas flow-along systems may be more passive but could require larger land areas and potentially have lower recovery rates. Future work could include a direct techno-economic comparison of these competing design philosophies under various hydrogeological scenarios.

5. Conclusions

This study investigated the viability of a novel three-well ATES configuration to overcome the challenge of high ambient groundwater velocities. The detailed numerical modeling and techno-economic analysis led to the following principal conclusions:

• The addition of an upstream extraction well creates an effective hydraulic barrier that contains the thermal plume, transforming advection-dominated environments into locations suitable for efficient heat storage.
• The three-well system significantly increases thermal recovery, with the most pronounced benefits observed at the highest groundwater velocities, at which conventional ATES systems fail.
• The concept demonstrates strong performance for low to high groundwater velocities (up to 100 m/a); however, its effectiveness is limited at extremely high velocities (e.g., 250 m/a), where advective forces still dominate and lead to near-zero recovery.
• A critical design trade-off exists between hydraulic containment and thermal interference. Well spacing must be carefully optimized to prevent the hydraulic barrier from capturing the stored heat itself.
• The concept is economically robust, offering substantial annual cost and CO₂e emission reductions that justify the additional capital investment. Continuous operation of the third well is essential for achieving these results.

In summary, the three-well ATES system represents a promising and practical solution for expanding the application of high-temperature geothermal energy storage. Its successful implementation, however, is contingent on careful, model-based design that balances the competing hydraulic and thermal effects to ensure both effectiveness and efficiency.