Groundwater Seepage Velocity and Travel Time

Darcy's law gives a FLUX and not a speed, and the difference between the two is the single most consequential mistake in groundwater arithmetic. The Darcy velocity is the flow per unit of TOTAL cross-sectional area -- solids included -- and no water particle moves at it. Water only moves through the pores, so the actual particle speed is the Darcy velocity divided by the EFFECTIVE porosity, and since effective porosity is a fraction well under one, the seepage velocity is always SEVERAL TIMES the Darcy velocity. Using the Darcy velocity to estimate travel time overstates it by exactly the reciprocal of the porosity, and it overstates it in the dangerous direction: it says a plume takes thirteen years to reach a receptor it actually reaches in four, which is the difference between an urgent response and a monitoring plan. Both numbers are reported here for that reason. EFFECTIVE POROSITY IS NOT TOTAL POROSITY and the gap is largest exactly where it matters. Total porosity counts every void; effective porosity counts only the interconnected pore space that actually conducts flow, and in a clay the two differ enormously -- water held in dead-end pores and bound to particle surfaces is part of the total and conducts nothing. A total porosity used in this calculation gives a seepage velocity that is too slow. The gradient is the other input people take from a map without thinking: it is the head difference divided by the distance ALONG THE FLOW PATH, and on a contoured potentiometric surface the flow path is perpendicular to the contours rather than along the shortest line between two wells. RETARDATION IS THE LAST TERM AND IT ONLY EVER SLOWS THINGS DOWN. A sorbing contaminant partitions onto the aquifer solids and travels slower than the water by its retardation factor, so a conservative tracer -- chloride, bromide -- arrives first and defines the fastest possible arrival. Reporting a contaminant arrival without saying which factor was assumed is reporting an assumption as a result. One-dimensional steady flow through a homogeneous isotropic aquifer, which is what the arithmetic can carry and not what the ground is. Real aquifers are heterogeneous, and preferential pathways -- sand lenses, fractures, old utility trenches, abandoned borings -- carry water far faster than any bulk average, so a computed travel time is a central estimate around a distribution with a very fast tail. It does not model dispersion, which spreads arrival over a range rather than a date; degradation or attenuation, which reduce concentration along the way; density-driven flow; the unsaturated zone above the water table; or any transient behaviour from pumping, recharge, or tides. The hydrogeologist's conceptual model, the site's own measured conductivity and gradient, and the regulator govern.

gradient i = head difference / flow path length; Darcy velocity q = K i; seepage (particle) velocity v = q / effective porosity; travel time = distance / v, divided again by a retardation factor for a sorbing contaminant.

Darcy's law and the seepage velocity relation by name. EFFECTIVE porosity, not total porosity: only interconnected pore space conducts flow, and the gap between the two is largest in clay. One-dimensional steady flow through a homogeneous isotropic aquifer; no dispersion, degradation, density effects, or preferential pathways. The hydrogeologist's conceptual model, the site's own measured conductivity and gradient, and the regulator govern.

Two divisions on a conductivity and a gradient the reader measures; no aquifer data is reproduced.

Estimate. AHJ and licensed professional govern.

Field names used by the API: hydraulic_conductivity_ft_day, head_difference_ft, flow_path_ft, effective_porosity, travel_distance_ft, retardation_factor, gradient, darcy_velocity_ft_day, seepage_velocity_ft_day, travel_time_days, travel_time_years, darcy_travel_time_years, overstatement_x

• Effective porosity, not total dead-end pores and bound water are part of the total and conduct nothingthe hydrogeologist's conceptual model
• Homogeneous isotropic aquifer sand lenses, fractures and old trenches carry water far fasterthe site investigation
• No dispersion or degradation arrival is a range, not a date, and concentration falls along the waythe regulator