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Numerical Analysis on the Effect of Soil Properties on the Generation of Volatilization Flux from Unsaturated Soil Contaminated by Volatile Chemical Substances

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Abstract

For the assessment of human health risks from soil contaminated by volatile chemical substances (VCSs), it is important to quantitatively estimate the volatilization fluxes that occur at the ground surface due to the upward transport of VCS components in unsaturated soil. The model constructed by the authors is based on the quantitative evaluation of advection–dispersion behavior associated with the volatilization of VCSs and allows detailed consideration of soil properties and the boundary conditions between the atmosphere-ground surface and unsaturated soil-aquifer compared to existing models. This study focuses on the evaluation of the effect of soil properties on the generation of volatilization flux through numerical analyses by changing the permeability characteristics of surface soil depending on the difference in soil particle size, porosity, and distribution coefficient between the water and soil phases, targeting benzene as a model substance of VCSs. A series of calculated results can be classified into cases dominated by either an increase of volatilization flux or transport to the aquifer, depending on soil properties, indicating the necessity of appropriate countermeasures for remediation and risk assessment. For the reduction of health risks derived from the generation of volatilization flux, removal of contaminants existing in the surface soil, including the ground surface, is essential. However, it is necessary to prevent the spread of contamination into the aquifer when the contaminants have high mobility in surface soil.

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Abbreviations

\({C}_{\mathrm{s}}\) :

The amount of adsorption of benzene to the soil particles (mg/kg)

\({C}_{\mathrm{w}}\) :

Dissolved concentration of benzene in water phase (mg/L)

\({D}_{\mathrm{A}}\) :

Average grain diameter (m)

\({D}_{\mathrm{A0}}\) :

Average grain diameter of Toyoura sand as a standard value (m)

\({D}_{{\mathrm{g}},k}\) :

Dispersion coefficient of component k in gas phase (m2/s)

\({D}_{{\mathrm{w}},k}\) :

Dispersion coefficient of component k in water phase (m2/s)

\(g\) :

Gravity, (m/s2)

\(K\) :

Absolute permeability, (m2)

\({K}_{z}\) :

Absolute permeability for z-axis, (m2)

\({K}_{{\mathrm{d}},k}\) :

Distribution coefficient between soil and water of component k, (m3/kg)

\({K}_{\mathrm{ow},k}\) :

Octanol–water partition coefficient of component k, (m3/m3)

\({k}_{\mathrm{rg}}\) :

Relative permeability to gas phase (dimensionless)

\({k}_{\mathrm{rn}}\) :

Relative permeability to NAPL phase (dimensionless)

\({k}_{\mathrm{rw}}\) :

Relative permeability to water (dimensionless)

\({M}_{{\mathrm{c}},k}\) :

Molar mass of total benzene (kg/kmol)

\({M}_{\mathrm{g}}\) :

Molar mass of gas phase of benzene (kg/kmol)

\({M}_{\mathrm{n}}\) :

Molar mass of NAPL phase (undiluted solution) of benzene (kg/kmol)

\({M}_{\mathrm{w}}\) :

Molar mass of water phase of benzene (kg/kmol)

\(P\) :

System pressure (Pa)

\({P}_{i,k}\) :

System pressure of component k at i block (Pa)

\({P}_{\mathrm{c,gw}}\) :

Capillary pressure operating between gas and water phases (Pa)

\({P}_{\mathrm{c,nw}}\) :

Capillary pressure operating between NAPL and water phases (Pa)

\({P}_{\mathrm{g}}\) :

Pressure of gas phase (Pa)

\({P}_{\mathrm{sat},k}\) :

Saturated vapor pressure of component k (Pa)

\({R}_{\mathrm{vn}}\) :

Volatilization/condensation rate of NAPL phase (kmol/m3/s)

\({R}_{\mathrm{vnc},k}\) :

Volatilization/condensation rate of component k in NAPL phase (kmol/m3/s)

\({R}_{\mathrm{vs}}\) :

Volatilization rate derived from all of adsorption component (kmol/m3/s)

\({R}_{\mathrm{vsc},k}\) :

Volatilization rate derived from each adsorption component (kmol/m3/s)

\({R}_{\mathrm{vw}}\) :

Volatilization/condensation rate of water phase (kmol/m3/s)

\({R}_{\mathrm{vwc},k}\) :

Volatilization/condensation rate of component k in water phase (kmol/m3/s)

\({S}_{\mathrm{g}}\) :

Gas saturation (dimensionless)

\({S}_{\mathrm{gr}}\) :

Residual gas saturation (dimensionless)

\({S}_{\mathrm{lr}}\) :

Residual liquid saturation (dimensionless)

\({S}_{\mathrm{n}}\) :

NAPL saturation (dimensionless)

\({S}_{\mathrm{nr}}\) :

Residual NAPL saturation (dimensionless)

\({S}_{\mathrm{w}}\) :

Water saturation (dimensionless)

\({S}_{\mathrm{wi}}\) :

Irreducible water saturation (dimensionless)

\({S}_{\mathrm{wi}0}\) :

Irreducible water saturation obtained for Toyoura sand as a standard value (dimensionless)

\(t\) :

Time (s)

\({w}_{{\mathrm{g}},k}\) :

Molar fraction of component k in gas phase (dimensionless)

\({x}_{{\mathrm{w}},k}\) :

Molar fraction of component k in water phase (dimensionless)

\({x}_{{\mathrm{s}},k}\) :

Adsorption concentration of component k (kmol/kg)

\({x}_{\mathrm{s,sat}, k}\) :

Saturated adsorption of component k (kmol/kg)

\(\Delta x\) :

Block length in x-direction (m)

\({y}_{{\mathrm{n}},k}\) :

Molar fraction of component k in NAPL phase (dimensionless)

\({y}_{{\mathrm{l}},k}\) :

Molar fraction of component k in liquid phase (dimensionless)

\(\Delta y\) :

Block length in y-direction (m)

\(\Delta z\) :

Block length in z-direction (m)

\({\mu }_{\mathrm{g}}\) :

Viscosity of gas phase (Pa⋅s)

\({\mu }_{\mathrm{n}}\) :

Viscosity of NAPL phase (Pa⋅s)

\({\mu }_{\mathrm{w}}\) :

Viscosity of water phase (Pa⋅s)

\({\mu }_{{\mathrm{w}},15^\circ \mathrm{C}}\) :

Viscosity of water phase at 15 °C (Pa⋅s)

\({\rho }_{\mathrm{g}}\) :

Mole weight of gas phase (kmol/m3)

\({\rho }_{\mathrm{n}}\) :

Mole weight of NAPL phase (kmol/m3)

\({\rho }_{\mathrm{s}}\) :

Density of soil particle (kg/m3)

\({\rho }_{\mathrm{w}}\) :

Mole weight of water phase (kmol/m3)

\({\Phi }_{\mathrm{g}}\) :

Flow potential of gas phase (Pa)

\({\Phi }_{\mathrm{n}}\) :

Flow potential of NAPL phase (Pa)

\({\Phi }_{\mathrm{w}}\) :

Flow potential of water phase (Pa)

\(\phi\) :

Porosity (dimensionless)

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Acknowledgements

This study was conducted as part of an international joint research program programmed at the GP-RSS, Tohoku University, Japan.

Funding

The present study was supported by Japan Society for the Promotion of Science (JSPS) grants 23KJ0120. This research was performed by the Environment Research and Technology Development Fund, grant number 5–1905 (JPMEERF20195005), of the Environmental Restoration and Conservation Agency provided by the Ministry of Environment of Japan. And it was also supported by JST SPRING, Grant Number JPMJSP2114.

Author information

Authors and Affiliations

  1. Tohoku University, 6-6-20 Aramaki, Aoba-Ku, Sendai, Miyagi, 980-8579, Japan

    Monami Kondo, Takeshi Komai & Noriaki Watanabe

  2. National Institute of Advanced Industrial Science and Technology (AIST), 1-1-1, Higashi, Tsukuba, Ibaraki, 305-8567, Japan

    Yasuhide Sakamoto & Yoshishige Kawabe

Authors
  1. Monami Kondo
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  2. Yasuhide Sakamoto
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  3. Yoshishige Kawabe
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  4. Takeshi Komai
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  5. Noriaki Watanabe
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Contributions

All authors contributed to the study conception and design. Model simulations were carried out by Y.S. The first draft of the manuscript was written by M.K. and Y.S., and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

Corresponding author

Correspondence to Monami Kondo.

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Appendix A

Appendix A

Supplementary figures, not mentioned in the result and discussions, are added to provide increased understanding of the study, as follows: Figs. 18, 19, 20, 21, 22.

Fig. 1
figure 1

Schematic illustration of soil and groundwater contamination by volatile chemical substances (VCSs)

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Fig. 2
figure 2

Relationship between each phase and component in the present numerical model for soil and groundwater contamination by volatile chemical substances (VCSs)

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Fig. 3
figure 3

Analytical mesh zone and boundary conditions for the x–z two-dimensional system employed in the numerical analysis

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Fig. 4
figure 4

Changes in distributions of total petroleum hydrocarbon (TPH) (mg/kg), NAPL saturation, \({S}_{n}\) (-), dissolved concentration of benzene in the water phase, \({C}_{w}\) (mg/L), and amount of adsorption of benzene on soil particles, \({C}_{w}\) (mg/kg), in the vertical direction over time for reference calculation conditions

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Fig. 5
figure 5

Variations in the total petroleum hydrocarbon (TPH), gas volume flux (GVF), volatilization flux of benzene (VFB), and cumulative VFB at the ground surface over time under reference condition

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Fig. 6
figure 6

Comparison of changes in the distribution of total petroleum hydrocarbon (TPH) (mg/kg) in the vertical direction over time for different average diameters of soil particles

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Fig. 7
figure 7

Estimation of absolute permeability as a function of average diameter of soil particle \({D}_{\mathrm{A}}\) and dependence of \({D}_{\mathrm{A}}\) on permeation ratio of rainfall into surface soil, residual ratio of TPH, and average water saturation at the ground surface

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Fig. 8
figure 8

Comparison of changes in total petroleum hydrocarbon (TPH), volatilization flux of benzene (VFB), and cumulative VFB at the ground surface over time for different average diameters of soil particles

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Fig. 9
figure 9

Change in average gas saturation at the ground surface (\({S}_{\mathrm{g,ave}}\)) and maximum gas volume flux and comparison of contribution of advection and dispersion to the generation of volatilization flux of benzene (VFB) for different diameters of soil particles

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Fig. 10
figure 10

Correlation between residual ratio of TPH at the ground surface and decay of volatilization flux of benzene (VFB)

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Fig. 11
figure 11

Correlation between absolute permeability in surface soil and average gas saturation at the ground surface (\({S}_{\mathrm{g,ave}}\)) and the volatilization flux of benzene (VFB)

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Fig. 12
figure 12

Comparison of changes in the distribution of total petroleum hydrocarbon (TPH) (mg/kg) in the vertical direction over time for different porosities in surface soil

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Fig. 13
figure 13

Comparison of changes in total petroleum hydrocarbon (TPH), volatilization flux of benzene (VFB), and cumulative VFB at the ground surface over time in the case of different porosities in surface soil

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Fig. 14
figure 14

Relationship between equilibrium concentration of benzene in the water phase and the amount of adsorption onto soil particles based on adsorption isotherm by linear adsorption model

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Fig. 15
figure 15

Comparison of changes in the distribution of total petroleum hydrocarbons (TPH) (mg/kg) in the vertical direction over time for different distribution coefficient

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Fig. 16
figure 16

Dependence of the distribution coefficient on the residual ratio of TPH at the ground surface and outflow ratio of the VCS component to the initial TPH at the bottom of the surface soil

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Fig. 17
figure 17

Comparison of changes in total petroleum hydrocarbon (TPH), volatilization flux of benzene (VFB), and cumulative VFB at the ground surface over time for different distribution coefficient

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Fig. 18
figure 18

Correlations between absolute permeability in surface soil and porosity at the ground surface to the generation of volatilization flux of benzene (VFB), overlaying with residual ratio of TPH and average gas saturation at the ground surface and contribution ratio of advection to total volatilization flux

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Fig. 19
figure 19

Correlations between average gas saturation and porosity at the ground surface to the generation of volatilization flux of benzene (VFB), overlaying with residual ratio of TPH at the ground surface and contribution ratio of advection to total volatilization flux

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Fig. 20
figure 20

Correlations between distribution coefficient and absolute permeability in surface soil to the generation of volatilization flux of benzene (VFB), overlaying with residual ratio of TPH and average gas saturation at the ground surface and contribution ratio of advection to total volatilization flux

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Fig. 21
figure 21

Correlations between distribution coefficient and average gas saturation at the ground surface to the generation of volatilization flux of benzene (VFB), overlaying with residual ratio of TPH at the ground surface

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Fig. 22
figure 22

Correlations between distribution coefficient and porosity at the ground surface to the generation of volatilization flux of benzene (VFB), overlaying with residual ratio of TPH at the ground surface

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Kondo, M., Sakamoto, Y., Kawabe, Y. et al. Numerical Analysis on the Effect of Soil Properties on the Generation of Volatilization Flux from Unsaturated Soil Contaminated by Volatile Chemical Substances. Environ Model Assess 28, 1055–1081 (2023). https://doi.org/10.1007/s10666-023-09914-0

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