Question 5 of 7: Parameters and Modelling Relationships for DNAPL Infiltration After a Tanker-Car Derailment

Question A-5: Parameters and Modelling Relationships for DNAPL Infiltration After a Tanker-Car Derailment (20 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

A dense non-aqueous phase liquid (DNAPL — a common example is trichloroethylene or a chlorinated solvent) behaves very differently from a floating LNAPL: it is denser than water and, once past the water table, continues to sink under gravity until it reaches a low-permeability layer or is fully retained by residual saturation, so both the volume of information needed and the model itself differ from a standard fuel-spill infiltration calculation.

Parameters needed from the first responder. (1) Chemical identity/product — the specific DNAPL (from the shipping manifest/placard), since infiltration behaviour depends on its density, viscosity, interfacial tension with water, and solubility, all of which vary substantially between compounds. (2) Release volume or rate — how much has leaked and over what time, from tank capacity and observed leak rate/duration. (3) Release footprint — the surface area over which the DNAPL is spreading/pooling at the four car locations, needed to convert a volume into an infiltrating depth. (4) Soil type/texture at the derailment site (visual classification — sand, silt, clay, or a mixed fill typical of a rail bed/ballast), the minimum information needed to assign literature-typical hydraulic parameters when no site-specific testing is possible in an emergency. (5) Site topography and drainage — slope, any nearby ditches or waterbodies, and whether the rail bed itself (ballast) creates a preferential lateral pathway, as in the airport-spill scenario above. (6) Depth to water table, if known or estimable from regional data, since it sets the maximum vertical travel distance for the model and marks the transition to saturated-zone (dense-plume sinking) behaviour. (7) Weather/temperature, affecting both viscosity and, for a partly volatile DNAPL, vapour losses that reduce the infiltrating mass.

Mathematical relationships needed. A gravity-driven infiltration model — conceptually the Green–Ampt equation or an equivalent Darcy's-law-based wetting-front advance model — describes the depth of penetration versus time as a function of the soil's saturated hydraulic conductivity, porosity, and capillary/matric suction at the wetting front, and the density and viscosity of the infiltrating fluid. Because the fluid here is a DNAPL rather than water, every fluid-property term in the model (density, kinematic viscosity, and the fluid–soil interfacial tension controlling capillary pressure) must be substituted with the DNAPL's own values rather than water's — a DNAPL with higher density and lower viscosity than water infiltrates and sinks faster than an equivalent water infiltration model would predict, while the opposite is true for a viscous DNAPL. The residual saturation left behind in the pore space as the plume advances (governed by the soil's retention/capillary-pressure–saturation relationship, e.g., Brooks–Corey or van Genuchten parameters) also needs to be estimated, since it determines how much of the released volume is retained above the water table versus how much continues to advance as mobile free product.

Challenges in obtaining these parameters. DNAPL-specific fluid properties (viscosity, interfacial tension, residual saturation in the specific soil) are compound-specific and are rarely available for immediate field use — they typically require either laboratory measurement or literature values for the identified chemical, and an emergency responder in the field cannot measure them directly. Soil hydraulic conductivity and retention-curve parameters are similarly almost never measured on the spot; the practical field solution is to classify the soil texturally (sand/silt/clay, or "rail ballast fill") and assign literature-typical parameter ranges for that class, which introduces significant uncertainty into the resulting travel-time estimate. Real subsurface conditions beneath a rail bed are commonly layered and heterogeneous (engineered ballast over native soil, possibly over a buried utility trench), which a simple 1-D infiltration model does not represent, so the model output should be treated as an order-of-magnitude screening estimate to guide the urgency of the emergency response (e.g., how quickly to intercept before groundwater is reached), not a precise prediction.