An oxidant (lixiviant) is injected into an ore-bearing sandstone horizon and pulled toward extraction wells by a superposed potential-flow field — each well is a point source or sink, so the seepage velocity at any point is the vector sum of every well's radial contribution:
v(r) = Σ_wells Q_i / (2π·b·n·|r − r_i|) · (r − r_i)/|r − r_i|
∂C/∂t = −v·∇C + D∇²C − k·C·U (oxidant transport + consumption)
∂U/∂t = −k·C·U (ore grade depletion, first-order)
∂D/∂t = −v·∇D + D∇²D + k·C·U − sink(D) (dissolved U₃O₈ transport + well capture)
The oxidant plume (blue tint) advects and diffuses through the grid, oxidizing insoluble U(IV) to mobile uranyl-carbonate wherever it meets ore (the brown field fading pale as it depletes). The mobilized uranium (gold tint) is swept toward the extraction wells and captured there, accumulating as recovered U₃O₈.
- Flow ratio — real ISR wellfields deliberately extract slightly more fluid than they inject (a "bleed") so the hydraulic gradient stays inward; drop the ratio below 1.0 here and the field loses containment ("Excursion risk").
- Pattern — a 5-spot (one injector, four surrounding producers) sweeps radially; a line drive pushes the plume straight across the field between well rows.
- Reactivity — higher k leaches ore faster per unit of oxidant contact, but also depletes the oxidant plume closer to the injector, so sweep efficiency and reaction rate trade off exactly as they do in a real wellfield.