Radon Transport

Radon transport through porous media is governed by two independent mechanisms that act simultaneously: molecular diffusion and advective (bulk) flow.

Diffusion is the random thermal motion of radon atoms down a concentration gradient, analogous to a drop of dye spreading in still water. It requires no bulk air movement — only a concentration difference.

Advection is the transport of radon by bulk movement of soil gas, driven by pressure gradients. When soil gas flows toward a low-pressure zone (like a building foundation), it carries radon with it, analogous to a river carrying sediment.

Both mechanisms contribute, but their relative importance depends on soil permeability, pressure gradients, and distance. In undisturbed, unpressurized soil, diffusion dominates. Near buildings with induced negative pressure, advection typically accounts for 70–95% of radon entry.

Radon diffuses through air-filled soil pores according to Fick's first law: the diffusive flux J (atoms per area per time) is proportional to the concentration gradient ∂C/∂x. The proportionality constant is the effective diffusion coefficient D_eff.

In open air, the radon diffusion coefficient is D₀ ≈ 1.1 × 10⁻⁵ m²/s at 20°C. In soil, the effective diffusion coefficient D_eff is reduced by tortuosity (pores are not straight tubes), porosity (less cross-sectional area for diffusion), and moisture (water blocks diffusion).

A common empirical model is the Millington-Quirk equation: D_eff = D₀ × (n_air^(10/3) / n²), where n is total porosity and n_air is air-filled porosity. Water saturation drastically reduces D_eff — at 80% saturation, D_eff can drop to 1–5% of the dry value.

Diffusion length: The characteristic distance radon can diffuse before decaying is L = √(D_eff / λ), where λ = 2.1×10⁻⁶ s⁻¹ is the radon decay constant. For dry soil with D_eff = 2×10⁻⁶ m²/s, L ≈ 1.0 meter. For wet soil (D_eff = 5×10⁻⁸ m²/s), L drops to ~0.15 m.

Advective flow occurs when pressure differences exist across soil. The volumetric flow rate (Darcy flux) is given by Darcy's law: q = -(k/μ) × ∂P/∂x, where k is soil permeability (m²), μ is dynamic viscosity of air (~1.8×10⁻⁵ Pa·s), and ∂P/∂x is the pressure gradient.

Soil permeability spans many orders of magnitude: gravels may have k ~ 10⁻¹⁰ m², sands 10⁻¹² to 10⁻¹¹ m², silts 10⁻¹⁴ to 10⁻¹³ m², and clays <10⁻¹⁶ m². A factor of 100 in permeability can change radon entry rates by 100-fold.

Pressure sources: building depressurization (stack effect, exhaust fans, HVAC imbalances) creates 1–10 Pa negative pressure at the slab, pulling soil gas inward. Barometric pressure changes (0.1–1 kPa over days) pump soil gas. Wind creates pressure fluctuations on building exteriors. Temperature gradients drive thermal convection in highly permeable soils.

Advection dominance: Even small pressure differences (1 Pa) over permeable soil can generate advective radon fluxes 10–100 times larger than diffusion. Field measurements show advection accounts for 70–95% of radon entry in typical residential basements.

The steady-state transport of radon in soil is described by the advection-diffusion-decay equation:

D_eff × (∂²C/∂x²) - v × (∂C/∂x) - λ × C + S = 0

Where: D_eff is effective diffusion coefficient, C is radon concentration, v is advective velocity (Darcy flux / porosity), λ is decay constant (2.1×10⁻⁶ s⁻¹), and S is radon source term (generation from radium).

This equation balances diffusion (first term), advection (second term), radioactive decay (third term), and generation (fourth term). Solving it requires boundary conditions (e.g., concentration at depth, flux or concentration at the surface).

Simplified 1D solutions exist for special cases (pure diffusion with constant source, or advection-dominated flow), but real geometries near buildings require numerical modeling.

Buildings create depressurization due to stack effect (warm indoor air rises, pulling replacement air from below), mechanical ventilation (exhaust fans, clothes dryers), and HVAC systems. Typical basement depressurizations: 1–5 Pa winter, 0.5–2 Pa summer.

Radon enters through: floor-wall joints (largest contributor in most homes), cracks in concrete slabs, gaps around utility penetrations (pipes, wires), sump pits and floor drains (direct soil gas pathways), porous concrete (especially in block foundations), and crawlspaces and dirt floors.

A 1 mm wide crack around a 10 m × 10 m basement perimeter provides ~0.01 m² of opening. With 2 Pa depressurization and permeable soil, this can admit 10–50 m³/day of soil gas carrying 10,000–100,000 Bq/m³ radon, enough to raise indoor radon to 100–500 Bq/m³.

Soil permeability is as important as radium content in determining radon potential. High-radium soil that is wet or clay-rich may yield low indoor radon because radon cannot migrate efficiently. Moderate-radium soil that is dry, sandy, and permeable can yield very high indoor radon.

Field radon potential assessments measure both soil gas radon concentration (reflects radium, emanation, and decay) and soil permeability (reflects transport capacity). The product of the two correlates better with indoor radon than either alone.

Permeability can be estimated in the field using air permeability tests (measure flow rate vs applied vacuum in a soil probe). ASTM C1402 provides a protocol.

Radon entry rates vary by 2–10× over seasons and days due to changing transport conditions.

Stack effect: Stronger in winter (larger indoor-outdoor temperature difference) → higher depressurization → more advection → higher indoor radon. Radon levels in cold climates are often 2–3× higher in January than July. (Learn more about seasonal variations.)

Soil moisture: Spring snowmelt and rain saturate surface soil, blocking diffusion and sometimes reducing radon entry. Dry summer soil can increase diffusion slightly but reduces advection if cracks self-seal. Frozen winter soil acts as a low-permeability cap, forcing deeper radon upward.

Barometric pressure: Falling pressure (before a storm) pulls soil gas out of the ground, temporarily increasing radon. Rising pressure suppresses it. Diurnal pressure cycles cause 10–30% radon variation.

Wind: Creates positive pressure on windward walls and negative on leeward, modulating foundation depressurization by ±1 Pa.