Numerical study of PFAS movement in soil:
influence of water uptake by roots and non-uniform organic carbon
distribution
Barbara Biesek1, Adam Szymkiewicz1, Jirka Šimůnek2
1 Gdańsk University of Technology

2 University of California – Riverside

PFAS – „forever” chemicals
Per- and Polyfluoroalkyl Substances• very persistent• negative effects on human health• common sources: firefighters training
grounds, military bases, airfields,
chemical factories• need for monitoring and modeling(www.deq.virginia.gov)

2Sorption at interfaces
Hydrophobic tailHydrophobic tailHydrophilic headFluorine
Hydrophilic head

CarbonPFOS = Perfluorooctane sulfonate(ITRC)

SulphurOxygen• PFAS tend to accumulate at air-waterinterface (AWI) and on soil organicHydrogen
PFOA = Perfluorooctanoate

carbon (SOC)3

PFAS in soils(Guo et al. 2020)• „historical” PFAS in soil can be a long-term source of ground water contamination• need for dedicated modeling approaches (AWI sorption)4Modeling tools• Guo, B., Zeng, J., & Brusseau, M. L. (2020). A mathematical model for the release, transport, and retention ofper‐and polyfluoroalkyl substances (PFAS) in the vadose zone. Water Resources Research, 56(2), e2019WR026667.
• new computer code, later extended to 2D/3D• Silva, J. A. K., Šimůnek, J., & McCray, J. E. (2020). A modified HYDRUS model for simulating PFAS transport in thevadose zone. Water, 12(10), 2758.
• extension of Hydrus-1D and 2D programs• Wallis, I., Hutson, J., Davis, G., Kookana, R., Rayner, J., & Prommer, H. (2022). Model-based identification of vadosezone controls on PFAS mobility under semi-arid climate conditions. Water Research, 225, 119096.
• extension of LEACHM program5Modeling studies• AWI vs. SOC sorption (Guo et al. 2020, Silva et al. 2020)• soil textural heterogeneities (Silva et al. 2020, Zeng and Guo 2021)• nonlinearities and kinetic effects in sorption (Brusseau et al. 2021)• sensitivity to flow and transport parameters (Zeng et al. 2021)• simplified solutions for screening (Guo et al. 2022, Silva et al. 2022)• application to site-specific conditions (Silva et al. 2022, Wallis et al. 2022)• most of the studies neglect the presence of root zone and the SOC distribution over depth

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Objectives• perform numerical simulations to investigate how PFAS movement invadose zone can be influenced by:• presence of root zone
• non-uniform distribution of soil organic carbon

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Contaminated site in Minnesota
Xiao, F., Simcik, M. F., Halbach, T. R., & Gulliver, J. S. (2015).
Perfluorooctane sulfonate (PFOS) and perfluorooctanoate (PFOA)
in soils and groundwater of a US metropolitan area:
migration and implications for human exposure.
Water Research, 72, 64-74.

• sandy loam soil
• depth to groundwater 14-20 m• fOC = 1.25% in the upper 30 cmof soil
• fOC = 0.034% in the aquifer• annual precipitation 850 mm• annual reference ET 1020 mm
8Richards’ equation∂θ w ( hw )
∂t

∂hw 
∂
−  K ( hw )+ U ( hw ) =0∂z ∂z θW – volumetric water content
hw – pore water pressure (negative)K – hydraulic conductivity

θw(hw) and K(hw) functions typical for sandy loam(van Genuchten model, parameters from Carsel and Parrish 1988)

U – water uptake by roots

9Water uptake by plant roots• relative density of plant roots• bare soil (no roots)• grassland & forest (Jackson et al. 1996)• stress function according to Feddes, Kowalik and Zaradny (1978) with typical parameters

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PFAS transport equation∂ (θ w c )∂t∂cSOC ∂c AWI ∂ ( v θ w c ) ∂ ∂c 
0+++− θw D  =∂t∂t∂z∂z ∂z c – concentration in pore waterθW – volumetric water content
cSOC – concentration in SOC (per soil volume)
cAWI – concentration at AWI (per soil volume)

different sorption models possible:
equilibrium vs. kinetic, linear vs. nonlinearv – unit discharge (Darcy velocity)
D – hydrodynamic dispersion coefficient(standard velocity-dependent formula)

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Sorption at AWI• linear equilibrium model (valid for low concentrations)

AAW=(θ w )1

θs

σ AW ∫θpc ( Θ w ) d Θ wc AWI = K AW AAW c(Zeng et al. 2021)

w

cAWI – concentration at the interface
KAW – partitioning coefficient wrt AWI
AAW – AWI area per volume of soilpC – capillary pressure

σAW – surface tension (air-water)θW – volumetric water content
θS – water content at saturation
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Sorption on SOC
Typical SOC distribution with depth• linear equilibrium model

Depth [cm]=cOC K=f OC K OC c
Dc

(Jobbagy and Jackson 2000)

cOC – concentration in the solid phase
KD – partitioning coefficient wrt soil
fOC – fraction of OC in soil

KD = 1.61 to 0.21 L/kg (PFOA)KD = 5.99 to 0.80 L/kg (PFOS)

KOC – partitioning coefficient wrt OC
KOC = 129 L/kg (PFOA)
KOC = 479 L/kg (PFOS)(Xiao et al. 2015)

Relative amount of SOC [-]13

Infiltration of contaminated water
infiltration

evaporation

z=0rootzone

z = -14 m

transpiration

top boundary:• atmospheric boundary condition• daily weather data 1979-2014• constant concentration in infiltrating water• PFOA = 1 µg/L, PFOS = 1 µg/L
initial condition:• pressure distribution from a warm-up simulation• concentration = 0bottom boundary:• water pressure = 0 (groundwater table)• concentration gradient = 014

Effect of variable SOC
PFOA breakthrough curves at 2 m depth, grass cover
Uniform SOC (low)Variable SOC

Uniform SOC (high)15Effect of variable SOC
PFOS breakthrough curves at 2 m depth, grass cover
Uniform SOC (low)Variable SOC

Uniform SOC (high)16Effect of plant roots
PFOA profiles, variable SOC, t = 730, 1095, 3300, 6600, 12987 days
Bare soil
average recharge 0.115 cm/day
max AWI area 228 cm2/cm3

Grassaverage recharge 0.065 cm/day
max AWI area 360 cm2/cm3

Forestaverage recharge 0.049 cm/day
max AWI area 360 cm2/cm3

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Effect of plant roots
PFOS profiles, variable SOC, t = 730, 1095, 3300, 6600, 12987 days
Bare soil
average recharge 0.115 cm/day
max AWI area 228 cm2/cm3

Grassaverage recharge 0.065 cm/day
max AWI area 360 cm2/cm3

Forestaverage recharge 0.049 cm/day
max AWI area 360 cm2/cm318

Leaching of „historical” PFOS

• initial condition approximating field measurements(no PFOS below 90 cm)• simulation time 100 years• repeating daily data of a single year representing average conditions• atmospheric BC with clean water infiltrating from the surface• groundwater table & zero concentration gradient at 24 m

Numerical study of PFAS movement in soil

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Effect of variable SOC
Total concentration profiles in 10 year intervals – grass cover
Uniform SOC (high)Variable SOC

Uniform SOC (low)20Effect of plant roots
Total concentration profiles in 10 year intervals – variable SOC
Bare soil

GrassForest21

Conclusion• variable SOC distribution in soil must be considered for realistic predictions• SOC estimates from shallow depths lead to overestimation of retardation effect• presence of plant roots significantly slows down PFAS movement• mostly due to increased actual ET, but AWI also increases• water uptake by plants lead to evapo-concentration of PFAS (Wallis et al. 2022)

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The XXV International Conference on
Computational Methods in Water Resources
will be held in Quebec City, Canada in June 2024
Numerical study of PFAS movement in soil