Model commercial greenhouse seasonal doublet well hydraulics, Darcy drawdown, VDI 4640 seasonal heat pump COP, and German BEW (Bundesförderung für effiziente Wärmenetze) / US IRA 48C decarbonization economics.
Groundwater flow and seasonal heat recovery obey the coupled Darcy groundwater potential and energy conservation laws:
Aquifer Thermal Energy Storage (ATES) utilizes saturated geological formations (predominantly unconsolidated sand and gravel aquifers confined by clay aquicludes) as seasonal thermal energy buffers. During the summer cooling cycle, chilled groundwater ($6\text{--}9^\circ\text{C}$) is extracted from the Cold Well, routed through plate heat exchangers to absorb excess greenhouse sensible heat and fan-coil loads, and re-injected into the Warm Well at $16\text{--}22^\circ\text{C}$. In winter, the flow direction reverses: warm water is pumped from the Warm Well into the evaporator of industrial ammonia ($\text{NH}_3$/R717) or hydrocarbon heat pumps, lifting heat to $45\text{--}55^\circ\text{C}$ for pipe-rail heating networks while returning chilled water to recharge the cold reservoir.
For a fully penetrating well in a confined aquifer of thickness $H_{\text{aq}}$ and hydraulic conductivity $k_f$, steady-state radial drawdown $s_w$ at well radius $r_w$ under volumetric extraction $\dot{V}$ is governed by the Dupuit-Theis formulation:
To prevent catastrophic hydraulic jamming and borehole screen siltation, Darcy entry velocity must not exceed $v_{\text{crit}} = \sqrt{k_f} / 30 \text{ m/s}$ (Sichardt criteria).
Under radial advective transport, the seasonal thermal radius $R_{\text{th}}$ of injected warm or cold water within a porous matrix having volumetric heat capacity $c_{\text{aq}} = (1-\phi)c_{\text{solid}} + \phi c_{\text{water}}$ is calculated as:
According to VDI 4640 guidelines, well separation distance $L_{\text{well}}$ must strictly satisfy $L_{\text{well}} \ge 2.5 \cdot R_{\text{th}} + v_{\text{regional}} \cdot \tau_{\text{seasonal}}$ to prevent early thermal breakthrough, which degrades seasonal coefficient of performance (COP) over multi-decade lifecycles.
An unconsolidated sand or gravel aquifer with transmissivity $T = k_f \cdot H_{\text{aq}} > 50\text{ m}^2/\text{day}$, natural hydraulic gradient $< 0.005$ to avoid plume drift, low dissolved iron ($< 0.2\text{ mg/L}$) and manganese to prevent well screen clogging, and confining upper/lower clay aquicludes to isolate potable drinking water aquifers.
For commercial facilities exceeding 1 hectare (heating loads $> 1.5\text{ MW}_{\text{th}}$), ATES achieves $40\text{--}60\%$ lower capital expenditure per kilowatt installed compared to drilling hundreds of 100m U-tube boreholes, while offering significantly higher flow rates ($100\text{--}300\text{ m}^3/\text{h}$) and direct free cooling capacities.
Under BEW Modul 2, innovative deep and shallow geothermal installations, industrial heat pumps, and aquifer doublet wells qualify for up to $40\text{--}45\%$ non-dilutive capital grants, shortening commercial payback periods from 6.8 years to under 3.5 years.
Nitrogen gas blanketing in buffer tanks, pressurized closed-loop hydraulic loops keeping water above $\text{CO}_2$ outgassing pressure, seasonal regenerative backwashing, and continuous redox potential monitoring prevent calcium carbonate precipitation and ferric hydroxide scaling.