A borehole thermal energy store (BTES) is a cluster of vertical boreholes drilled into rock or clay that turns the ground itself into a giant seasonal heat battery: excess summer solar or waste heat is injected in summer and pulled back out to heat buildings in winter, instead of being wasted or generated fresh from fuel.
This model treats the store as N = 6 concentric cylindrical shells around a shared borehole axis, each with heat capacity Ci = ρc·Vi (rock density × specific heat × shell volume). Heat moves between neighbouring shells by conduction and the outermost shell loses heat to the undisturbed ambient ground:
dT_i/dt = [ Q_in,i − Q_out,i + k·A_i,i+1·(T_i+1 − T_i)/dr
− k·A_i-1,i·(T_i − T_i-1)/dr ] / C_i
Outer shell: extra loss term −U·A_outer·(T_N − T_ambient)
Q_charge → injected into the innermost shell when solar input > 0
Q_extract → withdrawn from the innermost shell for heating load
The seasonal solar and heating-demand curves are sinusoids matched to the northern-hemisphere calendar (solar charging peaks around day 172 / late June, heating draw peaks around day 355 / late December), scaled by your slider values in kW. Insulation quality sets the conduction coefficient U between the store and the surrounding ground — better insulation (higher value) keeps summer heat from bleeding away before winter.
- Time speed — advances the simulated calendar; the borehole ring colours (blue → deep red) track each shell's temperature live.
- Summer solar charge rate and winter heating draw — the peak power injected/extracted at the height of each season.
- Round-trip efficiency — energy withdrawn for heating this year ÷ energy injected last summer, once at least one full charge/discharge cycle has completed; conduction losses to the ambient ground are what keep this below 100%.
Real systems (Drake Landing, Canada; Vojens, Denmark) reach 40–70% seasonal efficiency and can cover the majority of a district's winter heating load from summer solar collectors — the same physics this model integrates numerically, just at engineering scale.