Borehole Thermal Energy Storage (BTES)

• BTES is an underground sensible heat storage technology that stores and recovers thermal energy via borehole heat exchangers for seasonal balancing.
• Its design integrates vertical borehole heat exchangers, detailed thermal modeling, and control strategies to optimize heat injection and recovery.
• Performance depends on managing thermal interactions, groundwater advection, and drilling uncertainties to ensure effective long-term storage.

Searching arXiv for recent BTES literature to support the article. Borehole Thermal Energy Storage (BTES) is an underground sensible heat storage technology in which thermal energy is stored via a borehole heat exchanger in the ground. In thermal-energy-storage taxonomies, BTES is most naturally placed under Underground Thermal Energy Storage (UTES), itself a subset of Sensible Heat Storage (SHS); within that framing it is associated most strongly with long-term or seasonal balancing, including district heating, district cooling, industrial applications, and residential applications (Randenborgh et al., 28 Jul 2025, Maruf et al., 2021). BTES sits at the intersection of subsurface heat transport, borehole heat exchanger (BHE) design, thermal storage modeling, and building or district energy operation. Its central technical questions concern how heat is injected into and recovered from the subsurface, how boreholes interact thermally over timescales from seconds to decades, and how control, geometry, groundwater, and uncertainty alter usable storage performance.

1. Definition, scope, and classification

Within the classification reviewed in “Classification, potential role, and modeling of power-to-heat and thermal energy storage in energy systems” (Maruf et al., 2021), thermal energy storage is divided into Sensible Heat Storage, Latent Heat Storage, Thermochemical Heat Storage, and Thermo-mechanical Storage. UTES is listed as one of the promising sensible heat storage technologies and is defined as a technology that “uses geological strata made up of soil, sand or solid bedrock, or water in artificial pits or aquifers.” BTES is not named separately in that review, but the taxonomy implies the nested relation

$$\text{BTES} \subset \text{UTES} \subset \text{SHS} \subset \text{TES}.$$

The same review distinguishes short-term TES, which can provide stored heat during nighttime, from long-term TES, which can provide heat during winter; BTES is most naturally aligned with the latter interpretation (Maruf et al., 2021).

A recurring boundary issue is the distinction between BTES proper and borehole fields used primarily as ground heat exchangers. The UC Berkeley campus study “Application Potential of a Hybrid Ground Source Heat Pump Array for the UC Berkeley Campus Business and Law Node Energy System: A Preliminary Study” explicitly treats the subsurface system primarily as a ground heat exchanger for a hybrid GSHP system rather than as a canonical seasonal store (Chen et al., 2023). The reasons given are precise: no intentional seasonal charging/discharging strategy is designed, no explicit storage objective is formulated, no long-duration interseasonal state-of-charge analysis is presented, and the hybrid system is designed to reduce borefield size and control operating temperatures rather than to maximize seasonal thermal storage utilization. That distinction is important because BTES literature often overlaps with GSHP-field literature while pursuing different objectives (Chen et al., 2023).

This classification issue also clarifies a common misconception: not every multi-borehole geothermal field is a BTES system in the strict sense. A borefield may be BTES-relevant because it addresses annual thermal imbalance, cumulative thermal buildup, or seasonal buffering, yet still remain a load-serving GSHP field rather than an explicitly operated seasonal thermal store (Chen et al., 2023).

2. Physical configuration and storage mechanism

The control-oriented BTES model introduced in “A lightweight numerical model for predictive control of borehole thermal energy storages” (Randenborgh et al., 28 Jul 2025) describes a BTES as a field of vertical BHEs connected to a building through an auxiliary power unit (APU). Its physical components are the BHEs, pipes inside each borehole carrying a process fluid such as a water-glycol mixture, backfill or grout in the annulus, the surrounding ground, and the building-side thermal interface. The paper states that BHEs are typically vertical boreholes with lengths between 20 m and 300 m. The ground is the actual thermal storage medium, while the borehole wall is the thermal interface through which heat enters or leaves the storage (Randenborgh et al., 28 Jul 2025).

The storage mechanism is the temperature rise or fall of the subsurface. In the same model, heat propagates in the ground by conduction and, when groundwater flow is included, also by advection. This point is not merely a refinement of heat-transfer physics. It determines whether the stored thermal body remains spatially coherent, whether the thermal plume becomes asymmetric, and whether charge and discharge remain locally recoverable or are transported away from the borefield (Randenborgh et al., 28 Jul 2025).

The exchanger configurations treated across the cited literature are not uniform. “A combined thermal-resistance-capacity and finite-element model for very fast and accurate short- and medium-term simulations of single U-tube borehole heat exchangers” considers single U-tube BHEs with a triangular resistance network and a corrected transient resistance model (Zanchini et al., 16 Oct 2025). By contrast, “Quantification of Bore Path Uncertainty in Borehole Heat Exchanger Arrays” models double-U BHEs through a 1D line source/sink embedded in a 3D FEM domain and coupled to a thermal resistance and capacity model (Steinbach et al., 2021). The BRGM thermal-response-test study likewise uses 60 m deep double-U tube BHEs and emphasizes that grouting continuity must be verified before anomalous temperature behavior can be attributed to hydrogeology rather than completion defects (Voirand et al., 13 May 2025).

Field geometry is structurally important. The uncertainty study notes that in extraction arrays excessive proximity causes thermal “cannibalization,” whereas BTES relies on thermal interaction between BHEs and thus on mostly constant BHE spacings (Steinbach et al., 2021). This suggests that BTES requires neither minimal interaction nor uncontrolled interaction, but predictable interaction: storage efficiency, charge/discharge symmetry, thermal front development, and long-term recoverability depend on how the realized borehole geometry structures the accessible rock volume (Steinbach et al., 2021).

3. Modeling hierarchy

BTES modeling in the cited literature spans at least four abstraction levels: generic storage formulations for system optimization, semi-analytical bore-field response models, transient single-borehole models, and control-oriented numerical models.

At the coarsest level, the TES review gives the generic storage balance

$$s(t)=(1-L_S)\,s(t-1)+(1-L_D)\,q^C(t)-(1-L_D)\,q^D(t),$$

with bounds

$$s(t)\le S^{cap}, \qquad q^C(t)\le Q^{FLOW}, \qquad q^D(t)\le Q^{FLOW}.$$

These equations were introduced “notably for hot water tanks,” not for BTES specifically; treating BTES as a lumped sensible TES asset in this form is therefore an adaptation rather than a BTES-validated physical model (Maruf et al., 2021). The benefit is LP/MILP compatibility; the cost is omission of subsurface diffusion, field geometry, and geology.

At the field-response level, “A fast and accurate semi-analytical method to determine the thermal response of bore fields” (Zanchini et al., 2024) computes both the g-function, defined through the mean temperature of the external surface of the BHEs, and the ftg-function, the thermal response of the mean fluid temperature. The method divides boreholes into segments, computes finite-line-source segment-to-segment interactions, imposes the real operating condition of boreholes fed in parallel with equal inlet fluid temperature, and uses the 3D borehole thermal resistance $R_{b3D}(t)$ to relate fluid and wall temperatures. The paper concludes that, with constant $R_{b3D}$, the method yields an accurate g-function from minutes to thousands of years and a reasonably accurate ftg-function from hours to thousands of years; with supplied time-dependent $R_{b3D}(t)$, it yields accurate g- and ftg-functions from seconds to thousands of years (Zanchini et al., 2024).

At the single-borehole transient scale, “A combined thermal-resistance-capacity and finite-element model for very fast and accurate short- and medium-term simulations of single U-tube borehole heat exchangers” (Zanchini et al., 16 Oct 2025) fills the range from $10^{-2.5}$ h to $10^3$ h. Its base TRCM discretizes the BHE into horizontal slices and concentric ground annuli, while a time-dependent correction coefficient derived from 54 finite-element simulations adjusts the 3D borehole thermal resistance: $$C_{coeff} = \frac{R_{b3D,\;COMSOL}}{R_{b3D,\;TRCM}}.$$ The corrected model returns $T_{in}$, $$s(t)=(1-L_S)\,s(t-1)+(1-L_D)\,q^C(t)-(1-L_D)\,q^D(t),$$0, $$s(t)=(1-L_S)\,s(t-1)+(1-L_D)\,q^C(t)-(1-L_D)\,q^D(t),$$1, $$s(t)=(1-L_S)\,s(t-1)+(1-L_D)\,q^C(t)-(1-L_D)\,q^D(t),$$2, $$s(t)=(1-L_S)\,s(t-1)+(1-L_D)\,q^C(t)-(1-L_D)\,q^D(t),$$3, and $$s(t)=(1-L_S)\,s(t-1)+(1-L_D)\,q^C(t)-(1-L_D)\,q^D(t),$$4 within about 2 s runtime and can be easily connected to long-term simulation tools to obtain the full-time-scale thermal response of a bore field (Zanchini et al., 16 Oct 2025).

At the control scale, “A lightweight numerical model for predictive control of borehole thermal energy storages” assembles a 2D finite-volume ground model, a vertically discretized TRC model for each BHE, and an APU model into one affine discrete-time state-space system,

$$s(t)=(1-L_S)\,s(t-1)+(1-L_D)\,q^C(t)-(1-L_D)\,q^D(t),$$5

In the numerical study the total state dimension is $$s(t)=(1-L_S)\,s(t-1)+(1-L_D)\,q^C(t)-(1-L_D)\,q^D(t),$$6, the sampling time is $$s(t)=(1-L_S)\,s(t-1)+(1-L_D)\,q^C(t)-(1-L_D)\,q^D(t),$$7, and the prediction horizon is $$s(t)=(1-L_S)\,s(t-1)+(1-L_D)\,q^C(t)-(1-L_D)\,q^D(t),$$8, corresponding to 20 minutes (Randenborgh et al., 28 Jul 2025). This model preserves transient BHE dynamics, multi-borehole spatial interaction, and groundwater advection while yielding a quadratic program suitable for MPC.

4. Design, optimization, and operational control

BTES design is constrained by outlet-fluid temperature limits, thermal interference, land geometry, and long-term thermal accumulation. “Optimization of Closed-Loop Shallow Geothermal Systems Using Analytical Models” (Heinzel et al., 26 Mar 2026) formalizes one representative problem as

$$s(t)=(1-L_S)\,s(t-1)+(1-L_D)\,q^C(t)-(1-L_D)\,q^D(t),$$9

subject to

$$s(t)\le S^{cap}, \qquad q^C(t)\le Q^{FLOW}, \qquad q^D(t)\le Q^{FLOW}.$$0

with borehole positions first distributed heuristically inside a polygonal domain through a modified Lloyd / centroidal Voronoi tessellation and uniform depth then optimized with SLSQP (Heinzel et al., 26 Mar 2026). In the presented 25-borehole cases, the optimized depth is $$s(t)\le S^{cap}, \qquad q^C(t)\le Q^{FLOW}, \qquad q^D(t)\le Q^{FLOW}.$$1 m for a small $$s(t)\le S^{cap}, \qquad q^C(t)\le Q^{FLOW}, \qquad q^D(t)\le Q^{FLOW}.$$2 rectangle, $$s(t)\le S^{cap}, \qquad q^C(t)\le Q^{FLOW}, \qquad q^D(t)\le Q^{FLOW}.$$3 m for a medium rectangle, $$s(t)\le S^{cap}, \qquad q^C(t)\le Q^{FLOW}, \qquad q^D(t)\le Q^{FLOW}.$$4 m for a large $$s(t)\le S^{cap}, \qquad q^C(t)\le Q^{FLOW}, \qquad q^D(t)\le Q^{FLOW}.$$5 rectangle, and $$s(t)\le S^{cap}, \qquad q^C(t)\le Q^{FLOW}, \qquad q^D(t)\le Q^{FLOW}.$$6 m for an L-shape with an exclusion zone. The paper’s design interpretation is explicit: smaller area leads to a denser field, stronger thermal interference, and greater required depth (Heinzel et al., 26 Mar 2026).

The same paper is not a seasonal BTES paper in the strict sense; its objective is heat-pump feasibility rather than stored-energy maximization. Even so, its treatment of 20-year thermal buildup, heating/cooling imbalance, and layout optimization transfers directly to low-temperature BTES preliminary design (Heinzel et al., 26 Mar 2026).

Operationally, the MPC-oriented BTES model in (Randenborgh et al., 28 Jul 2025) demonstrates a tracking controller over 24 hours, with demand varying between $$s(t)\le S^{cap}, \qquad q^C(t)\le Q^{FLOW}, \qquad q^D(t)\le Q^{FLOW}.$$7 W and $$s(t)\le S^{cap}, \qquad q^C(t)\le Q^{FLOW}, \qquad q^D(t)\le Q^{FLOW}.$$8 W, state bounds of $$s(t)\le S^{cap}, \qquad q^C(t)\le Q^{FLOW}, \qquad q^D(t)\le Q^{FLOW}.$$9 K to $R_{b3D}(t)$0 K, and input bounds $R_{b3D}(t)$1 W. Using Gurobi on a Debian 12 machine with an Intel Core i5-4690 and 16 GB RAM, the average solve time is $R_{b3D}(t)$2 s, well below the 15 s sampling time (Randenborgh et al., 28 Jul 2025). The paper therefore places BTES not only in the domain of long-term storage planning but also in real-time supervisory control.

A BTES-adjacent design strategy appears in the UC Berkeley hybrid GSHP/ASHP study, where annual cooling dominance motivates offloading part of the load from the ground to avoid long-term ground temperature rise and borefield performance degradation (Chen et al., 2023). The optimization reports an optimum with 88% of cooling load and 98% of heating load served by GSHP, 231 boreholes each 200 m deep, and a 20-year total cost of \$19.1 million. The authors further report that the GSHP+ASHP case with 231 boreholes reduces electricity use by 14% versus ASHP-only (Chen et al., 2023). Because the study has no explicit storage objective, it is not canonical BTES; its importance lies instead in showing how hybridization can ration the use of the ground as a limited thermal resource under annual imbalance (Chen et al., 2023).

5. Uncertainty, groundwater, and site heterogeneity

BTES performance depends not only on nominal design but also on realized bore paths and hydrogeological structure. “Quantification of Bore Path Uncertainty in Borehole Heat Exchanger Arrays” (Steinbach et al., 2021) models uncertain drilling trajectories with 18 random variables for a 9-borehole array and propagates them with an adaptive anisotropic stochastic collocation method based on the generalized Smolyak algorithm of Gerstner and Griebel. In the 5-year seasonal extraction case study, the deterministic no-deviation average-fluid-temperature metric $R_{b3D}(t)$3 is approximately $R_{b3D}(t)$4 for the 12 m layout, $R_{b3D}(t)$5 for the 20 m layout, and $R_{b3D}(t)$6 for the 28 m layout. The key planning result is that the 20 m layout suggested by Earth Energy Designer is robust: even in the strongest tested uncertainty scenario, 95% of all geometries are not more than 6.32% worse than planned in terms of $R_{b3D}(t)$7 (Steinbach et al., 2021).

The same paper, however, explicitly warns against directly transferring that robustness to BTES. Its discussion states that deeper BHE arrays used for BTES rely on thermal interaction between BHEs and thus on mostly constant BHE spacings, and it identifies storage coefficient as a more natural BTES quantity of interest for future work (Steinbach et al., 2021). A plausible implication is that geometric uncertainty may matter differently in BTES than in pure extraction arrays because interaction is a design target rather than solely a loss mechanism.

Hydrogeological heterogeneity produces an equally strong challenge. “Evidence of localized groundwater flow during thermal response test using distributed thermal sensing” (Voirand et al., 13 May 2025) reports four 60 m BHEs at the BRGM Shallow Geothermal Research Facility in Orléans, with about 8 m spacing, and shows that two boreholes exhibit a localized interval of enhanced heat transfer between 25 m and 40 m depth while neighboring boreholes do not. Classical conductive TRT interpretation gives apparent conductivities of $R_{b3D}(t)$8 and $R_{b3D}(t)$9 for the anomalous boreholes, whereas inversion with the depth-discretized SAMBA model gives $R_{b3D}$0 and $R_{b3D}$1 together with effective Darcy velocities of $R_{b3D}$2 and $R_{b3D}$3 in the 25–40 m interval (Voirand et al., 13 May 2025). The paper’s central warning is that a standard depth-integrated TRT can mistake localized advection for high effective conductivity.

For BTES, the hydrogeological consequence is sharper than for a purely conductive exchange field. The BRGM study states that groundwater flow can be potentially beneficial for systems seeking strong instantaneous heat rejection or extraction with no need to retain heat locally, but potentially detrimental for BTES because it transports stored heat out of the target storage volume (Voirand et al., 13 May 2025). This directly contradicts the simplistic view that a higher apparent TRT conductivity is always favorable.

6. Field performance, common misconceptions, and research trajectory

The most consequential field-scale misconception addressed by the recent literature is that simplified bore-field assumptions are accurate enough for long-term storage design. The University of Bologna semi-analytical bore-field study shows the opposite (Zanchini et al., 2024). For realistic parallel-fed fields, the assumption of uniform heat rate per unit BHE length overestimates the thermal response, whereas the assumption of uniform borehole wall temperature underestimates it. In a 10×10 field for BHE U94 1.6, the overestimation from assuming uniform heat rate reaches 32.9% at $R_{b3D}$4 and 58.4% at $R_{b3D}$5, while the underestimation from assuming uniform surface temperature is 4.27% and 5.95% at the same times (Zanchini et al., 2024). The same paper also shows that central BHEs in compact large fields become thermally ineffective over long durations; in an 8×8 field in a 60 m × 60 m plot, the mean load of the central boreholes becomes very low for $R_{b3D}$6, i.e. after about 11.5 years (Zanchini et al., 2024).

That result links directly to BTES layout strategy. For a fixed land area of 60 m × 60 m and a fixed total field length of 8000 m, the paper compares 10×10, 9×9, and 8×8 square fields and finds that the 8×8 field with $R_{b3D}$7 m yields the lowest ftg-function over $R_{b3D}$8 (Zanchini et al., 2024). The performance advantage of fewer, longer, more widely spaced boreholes over more numerous, shorter, more compact boreholes is therefore not an anecdotal observation but an explicit outcome of a realistic field-response calculation.

Across the cited literature, limitations are equally consistent. The generic TES equations of the review are deliberately simple and omit subsurface thermodynamics (Maruf et al., 2021). The UC Berkeley hybrid GSHP study addresses annual thermal imbalance but does not compute storage efficiency, recovery factor, or multi-year state-of-charge behavior (Chen et al., 2023). The analytical field optimizer is conduction-only, assumes homogeneous ground, and fixes uniform heat rate per borehole (Heinzel et al., 26 Mar 2026). The MPC-oriented BTES model includes groundwater advection and transient BHE dynamics, but its building representation is reduced to an APU interface and its field study is not tied to a measured installation (Randenborgh et al., 28 Jul 2025). The corrected TRCM provides near-FE single-borehole fidelity from about 11 s to 1000 h, but it does not itself resolve field-scale seasonal accumulation (Zanchini et al., 16 Oct 2025).

A plausible synthesis is that BTES has no single universally sufficient model. Long-term field interaction, short-term borehole transients, groundwater transport, drilling uncertainty, and supervisory control are currently resolved by complementary rather than unified frameworks. The recent direction of travel is therefore modular: semi-analytical or analytical field solvers for decades-scale interference (Zanchini et al., 2024), corrected transient submodels for single-borehole short and medium terms (Zanchini et al., 16 Oct 2025), control-oriented affine state-space formulations for real-time MPC (Randenborgh et al., 28 Jul 2025), and site characterization workflows that expose groundwater and geometric uncertainty before those effects are collapsed into misleading effective parameters (Steinbach et al., 2021, Voirand et al., 13 May 2025).