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

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.


C s
The amount of adsorption of benzene to the soil particles (

Introduction
Soil and groundwater contamination by volatile chemical substances (VCSs), such as benzene (C 6 H 6 ), has become more apparent in recent years.As shown in Fig. 1, these compounds tend to permeate into the pore space in the surface soil (in the region defined as the unsaturated zone) through advection and dispersion and can subsequently transfer to either groundwater or the ambient atmosphere with changes in mass and composition based on several phenomena.A portion of the discharged VCSs may subsequently reach aquifers (saturated zone), leading to widespread contamination through groundwater flow.Additionally, the transfer of VCSs to the atmosphere at the ground surface due to their high volatility cannot be ignored, and there are concerns about health risks due to the inhalation of volatile components for residents living near contaminated sites.It is essential to minimize the effects of contamination and to take appropriate remediation countermeasures [1] based on the prediction of the long-term behavior of discharged VCSs in the surface soil and groundwater.Predicting this long-term behavior requires numerical analysis of complex phenomena, such as advection and dispersion consisting of three-phase non-aqueous phase liquids (NAPL)-water-gas volatilization/condensation and the distributions between each phase due to adsorption/desorption and elution/precipitation.Several numerical analyses of soil and groundwater contamination by specific VCSs have been reported that examined the diffusion through the soil of volatilized VCSs under unsaturated conditions.Some studies attempted to optimize a set of parameters to evaluate the advection and diffusion of volatile organic compounds through comparison with experimental data [2][3][4][5][6], whereas others attempted to predict the distribution of volatile organic compounds by targeting soil gas extraction as a remediation process or risk assessment [7][8][9][10][11][12][13][14][15].However, quantitative predictions of unsteady variations in the volatilization flux near the ground surface based on the permeation of rainfall into the surface soil and changes in the distribution of contaminants over time and space have not yet been reported.Therefore, these studies are insufficient because only the steady-state flow behavior in the gas phase with a constant VCS concentration as a boundary condition was considered, ignoring the changes in the saturation distribution in the pore spaces.
To quantify the human health risk derived from the exposure of volatile components, it is important to establish a highly accurate prediction method for the generation of volatilization fluxes at the ground surface.In our previous study [16], a numerical model for the prediction of volatilization flux was developed considering a series of physical phenomena, as shown in Fig. 1.In our previous paper, the generation mechanisms of volatilization flux targeting benzene as a model substance for VCSs were revealed using the developed model.In addition, we quantitatively evaluated the correlation between atmospheric pressure, temperature, moisture content, and the amount of VCSs in pore spaces on the generation behavior of the volatilization flux.The following findings were obtained: (1) The volatilization flux of benzene decayed over time because the amount of VCSs at the ground surface decreased with the permeation of rainfall into the surface soil, whereas the gas volume flux (GVF) changed periodically depending only on weather variations.(2) The volatilization flux of benzene became much larger at lower soil moisture content levels, in addition to the effect of an increase in the calculated GVF at higher temperatures and lower air pressures.(3) In the absence of rainfall, increases in GVF and high mole fractions of benzene in the gas phase produced a very large increase in the volatilization flux.
Because soil properties have a large effect on the distribution of VCSs owing to transport phenomena in unsaturated soil, it is supposed that the generation behavior of volatilization flux significantly changes depending on the soil properties.In this study, we aimed to evaluate the effects of soil properties on the generation of volatilization flux.A parameter study targeting benzene as a model substance for VCSs was conducted, changing the soil permeability, porosity, and distribution coefficient between the water and solid phases based on the results of the previous paper [16].Based on the calculated results, the effects of soil properties on the transport phenomena of VCSs and the generation behavior of volatilization flux under unsteady conditions were revealed, and the correlation between the amount of volatilization flux and each parameter was quantitatively evaluated.

Numerical Model for Multi-phase
Multi-component Flow of VCSs with Various Reactions in Unsaturated Contaminated Soil

Governing Equation
A numerical model was constructed based on the threephase flow of a gas/NAPL/water system resulting from the discharge of an undiluted solution of VCSs, defined as NAPL, and permeation of rainfall into the surface soil, as described in our previous paper [16].This model aims to quantitatively evaluate the generation of volatilization flux at the ground surface and the transfer of VCSs into the aquifer simulating a series of phenomena, as shown in Fig. 1. Figure 2 summarizes the relationship between each phase in the numerical model and each VCS component.The porous media flow of each phase was primarily defined by Darcy's law, and the changes in the composition of each phase were considered using mole fractions ( w g,k , x w,k , and y n,k ) as vari- ables.Elution/precipitation was considered depending on the octanol/water partition coefficient and solubility in the water phase between NAPL-water systems, and dissolved components in the water phase move throughout the soil by advection and dispersion.Volatilization/condensation dependent on the mole fractions and saturated vapor pressure of the VCS components in the water phase was considered to determine the distribution between the water and gas phases, and the volatile components in the gas phase were transferred throughout the soil by advection and dispersion.Additionally, adsorption/desorption dependent on the distribution coefficient and concentration of VCSs in the water phase was considered to determine the distribution between the water and solid phases.The mass conservation equations for each phase and each component are defined below.
The equation for the NAPL phase (corresponding to an undiluted solution of the VCSs) is The equation for the water phase is The equation for the gas phase is The equation for the VCS components in the NAPL phase is The equation for the dissolved components in the water phase is The equation for the gaseous components in the gas phase is The relationship between each saturation, defined as the volume ratio of the pore fluid, is expressed as In Eqs. ( 4) to (6), the suffix k indicates the component number, and, as shown in Fig. 2, k values of 1, 2, and 3 correspond to VCSs, water, and air, respectively.The sum of the mole fractions in each phase ( w g,k , x w,k , and y n,k ) must always be equal to t .
(7) S n + S w + S g = 1. 1.Because the NAPL phase corresponds to a one-component system constituted only from VCSs and with k equal to 1, y n,1 is also always 1, meaning that Additionally, the dissolution of air into the water phase was not considered in the numerical analysis.Therefore, the dissolved components in the water phase consist of VCSs and water, such that k is equal to 2 and The gas phase consists of three components (VCSs, water, and air), meaning that k is equal to 3 and In this numerical model, for the quantitative evaluation of the volatilization flux at the ground surface, the volatilization and condensation rates were defined based on the gas-liquid equilibrium in the pore spaces according to Raoult and Dalton's law.When the mole fraction of component k in the water phase and saturated vapor pressure of k component are defined as y l,k and P sat,k , respectively, the vapor-liquid equilibrium in the pore spaces is expressed as y l,k P sat,k = w g,k P , where w g,k P is the partial pressure of the k component in the gas phase.The volatilization and condensation rates ( R vnc,k , R vwc,k , and R vsc,k ) of component k in each phase can be classified according to either y l,k P sat,k > w g,k P or y l,k P sat,k < w g,k P .In the case of y l,k P sat,k > w g,k P , com- ponent k volatilizes from the liquid phase and is distributed into the gas phase.However, in the case of y l,k P sat,k < w g,k P , component k condenses from the gas phase and is distributed into the liquid phase.
The total volatilization (or condensation) rates for each phase, expressed as R vn , R vw , and R vs (kmol/m3/s) as in Eqs.
(1) to (3), were defined as the sum of each component ( R vnc,k , R vwc,k , and R vsc,k ), as follows, and introduced into the mass conservation equations expressed from Eqs. (1) to (3).The volatilization rate from the NAPL phase/condensation rate from the gas phase is determined as while the volatilization rate from the water phase/condensation rate from the gas phase is and the volatilization rate derived from the adsorbed VCSs on the soil particle surfaces is (8) y n,1 = 1.
In this numerical model, the pressure of the gas phase P g is treated as the system pressure P when the flow potential of the gas phase, Φ g , is defined by ∇Φ g = ∇P g − M g g g .The system pressure P , saturation values ( S g , S n , and S w ), and mole fractions ( w g,k , x w,k , and y g,k ) in each phase were initially obtained based on flow calculations.As a solution for the numerical analysis, after discretization of each conservation equation using the finite difference method, the implicit method for pressure and an explicit method for saturation and mole fraction were applied as the solving methods.Following this, the elution/precipitation and adsorption/ desorption of these components were considered to update each value in the same time step based on the solubility and distribution coefficients.Therefore, the terms for elution and adsorption were not included in the conservation equations.For details on the numerical model, see the authors' previous paper [16].See the abbreviations in the appendices for the respective variables in the governing equations.

Analytical Mesh Zone and Boundary Conditions
In surface soils, the vertical transfer of fluid and contaminants resulting from the permeation of rainfall and capillary pressure is dominant; therefore, each mass conservation equation (Eqs.( 1)-( 6)) was discretized in the x-z twodimensional coordinate system.The x-z two-dimensional analytical mesh zone employed in this study is shown in Fig. 3. Boundary blocks corresponding to the air on the ground were arranged at the top edge of the mesh zone.The porosity, , and absolute permeability, K , in the horizontal direction for these blocks were set to 1.00 and 98.7 μm 2 (= 100 Darcy), respectively.Each residual saturation ( S wi , S nr , S gr , and S lr ) was given a value of 0, and the effect of capillary pressure was not considered so as to facilitate fluid flow compared to the inside of the pore spaces.Changes in temperature, air pressure, and rainfall level were applied to these blocks as boundary conditions, and only diffusion in the gas phase was considered for the boundary surface at the top edge.In addition, it was assumed that the gaseous components derived from the volatilization present in these blocks diffused instantaneously into the atmosphere.
Each block at the bottom edge of the mesh corresponds to the boundary of the aquifer.The water saturation, S w , at the boundary surface with the aquifer was set to 1, and a change in air pressure equal to the ground level was applied to each block as a boundary condition because the first aquifer located just below the surface soil was not pressurized.Seasonal variations in the temperature distribution within the surface soil were considered based on the temperature gradient between the ground surface and the water table, while the temperature of the aquifer remained constant at Fig. 3 Analytical mesh zone and boundary conditions for the x-z two-dimensional system employed in the numerical analysis 15 °C.Temperatures within the soil blocks without the top and bottom edges were calculated based on the temperature gradient between the surface and the aquifer.The lateral boundary conditions were determined through preliminary calculations comprising three steps, and these conditions were subsequently introduced into the numerical analysis.In step 1, the steady-state distributions of pressure and saturation considering only the rise of the water table due to suction without rainfall were estimated.In step 2, the distributions of pressure and saturation obtained in step 1 were applied as constant lateral boundary conditions, and calculations were performed by considering weather variations as a boundary condition for each block corresponding to air on the ground.Finally, in step 3, the seasonal variations in the vertical distributions of pressure and saturation at the central part obtained in step 2 were introduced as the lateral boundary conditions during the actual calculation process.

Result and Discussions
Table 1 summarizes the basic parameters of the surface soil and the physical parameters for benzene as a model VCS contaminant in the numerical analysis.Based on the analytical mesh zone shown in Fig. 3, the lengths in the x-and y-directions and the thickness in the z-direction were set to 10.0, 1.00, and 4.00 m, respectively.The weather conditions applied as boundary conditions to the air on the ground, including temperature, air pressure, and rainfall level, were based on a series of data acquired in Ibaraki prefecture in 2017, as reported by the Japan Meteorological Agency [17], and introduced for 10 years of calculation in 1-year cycles.The initial total petroleum hydrocarbon (TPH) was set to 1.00 × 10 4 mg/kg, and the depth range initially contaminated by benzene was set from − 0.10 to − 1.00 m from the ground level.TPH is commonly used as an indicator for evaluating soil contamination by various hydrocarbons, such as oil and VOCs, without distinguishing between undiluted, dissolved, and adsorbed components.In this numerical analysis, TPH (mg/kg) was used to correlate the change in volatilization flux with the total amount of benzene in the soil, defined as In this calculation, we aimed to evaluate the effect of soil properties on the generation behavior of volatilization flux and changed the average diameter D A (m) of soil par- ticles, absolute permeability K (m 2 ), porosity (-), and the distribution coefficient between soil and water K d,k (m 3 / kg) as calculation parameters.The parameters for the reference conditions in a series of calculations were set to D A =5.00 × 10 −5 m, K =2.95 × 10 −2 mm 2 , =0.50, and K d,1 =5.89 × 10 −2 m 3 /kg.Details of each parameter are described in Sects.3.1 to 3.4.

Transport Phenomena of VCSs as Contaminants in Unsaturated Soils and Generation Behavior of Volatilization Flux
Figure 4 summarizes the changes in the distributions of TPH (mg/kg); NAPL saturation, S n (-); the concentration of benzene dissolved in the water phase, C w (mg/L); and the amount of benzene adsorbed on the soil particles, C s (mg/kg), in the vertical direction over time obtained under reference conditions.Although these results were already described in our previous paper, we display them again here to enable readers to easily interpret the results of the parameter studies.Whereas the initial TPH was set to 10,000 mg/ kg, equivalent to an undiluted solution of benzene, defined as the NAPL phase, the subsequent distribution of TPH shown in Fig. 4 corresponds to the total amount of benzene at each position based on elution into the water phase and adsorption onto the soil particles, in addition to the undiluted solution.Initially, the mole fractions for the NAPL and water phases ( x w,k and y n,k ) at each location were cal- culated by solving the advection-dispersion equations (see Eqs. ( 4) and ( 5)), after which x w,k , y n,k , and the adsorp- tion concentration, x s,k , were updated in the same time step based on the octanol/water partition coefficient of benzene, ( 14) K ow,1 (m 3 /m 3 ), and the distribution coefficient of benzene, K d,1 (m 3 /kg).
Expressing the block lengths in each direction as Δx , Δy , and Δz (m), the total moles, N mol,k (kmol), of benzene (k = 1) per block are calculated as Because the mole fraction of benzene ( y n,1 , x w,1 ) is converted into a concentration in each phase (kmol/m 3 ) by multiplying by the molar density ( n , w ), the elution equilibrium between the NAPL and water phases can be obtained using K ow,1 as In addition, K d,1 and x w,1 are related to x s,1 according to the equation By substituting the right-hand side of Eqs. ( 16) and (17) into Eq.( 15), the value of x w,1 can be updated by considering the effects of elution and adsorption as Although the S n value corresponding to the initial TPH was 0.04, the amount present in the pore spaces as the NAPL (15) phase after considering each partitioning associated with elution and adsorption, based on Eqs. ( 15)-(18), was estimated to be approximately 0.015 in terms of S n .In this case, because the pore space was below the residual NAPL saturation S nr , benzene, as the undiluted solution, did not have mobility depending on the relative permeability to the NAPL phase k rn .At this time, owing to the effect of the capillary pressure, the pressure of the water phase P w in the pore space was always below 1 atm, which corresponds to the air pressure.
In this case, a pressure gradient from the air on the ground to the inside of the surface soil occurs, allowing rainfall to easily permeate into the surface soil owing to the effects of gravity and capillary pressure, depending on the permeability of the soil.When j = 2 and j = 3 are defined as the block numbers in the z-direction corresponding to the air on the ground and ground surface, respectively, the permeation rate (PR) (kmol/m 2 /s) of rainfall into the surface soil is expressed by the following equation according to Darcy's law: As shown in Fig. 4, S n gradually decreased over time, beginning from the side of the ground surface, as the elution of benzene into the water phase was accelerated by the permeation of rainfall based on Eq. ( 19), and the elution process was complete after 5 years, when S n reached 0. In 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 addition, whereas a high C w value was maintained (corre- sponding to a solubility of 1.75 × 10 3 mg/L) as long as the undiluted benzene remained in the pore spaces, C w after the completion of the elution process decreased to approximately 1.30 × 10 2 mg/L, and benzene in the water phase spread downwards owing to the effect of advection and dispersion while maintaining this concentration level.The saturated adsorption of benzene, x s,sat,1 , in this case was tentatively set to 1.00 × 10 −4 kmol/kg, corresponding to 7.81 × 10 3 mg/kg, and C s remained at this value regardless of variations in C w because benzene was highly adsorptive onto the soil particles.The maximum TPH was maintained at 10,000 mg/kg, which was equal to the initial condition, until 2 years later, when an undiluted solution of benzene remained.Subsequently, the maximum TPH was estimated to be approximately 6000 mg/ kg, and the data showed that the majority of TPH was derived from adsorption because C w decreased.Based on the distri- bution of TPH, we confirmed that the spread of benzene as a contaminant after 10 years did not exceed a depth of 2 m, reflecting the high adsorption of benzene on the soil.Although the mobility of benzene in the surface soil was relatively low, the TPH at the ground surface decreased because of the progress of elution into the water phase over time.
Figure 5 shows the changes in TPH, GVF, volatilization flux of benzene (VFB), and cumulative VFB at the ground surface over time.GVF (m 3 /m 2 /s) results from the pressure gradient of the gas phase from the ground surface to the air on the ground, according to Darcy's law, which is defined as The occurrence of GVF was confirmed to be dependent on weather variations, such as atmospheric pressure, temperature, and rainfall, and to change periodically, as shown in Fig. 5.As described in the previous paper, GVF increases due to the increase of the relative permeability to the gas phase when water saturation decreases after rainfall especially in the summer season with high temperature and was estimated to peak at approximately 1.4 SL/m 2 / day under the present conditions.In addition, VFB occurs according to the gradients of pressure and concentration from the ground surface to the air on the ground and is defined as the mass flow rate (kmol/m 2 /s) of benzene in the gas phase per unit area of the ground surface.This value was calculated as the sum of the benzene outflow resulting from both advection and dispersion from the ground surface into the air on the ground, defined as: Multiplying Eq. ( 21) by the mole mass of benzene, M c,1 (kg/ kmol), the number of seconds per day (= 86,400 s) is converted (wg,1) i,3 −(w g,1 ) i,2
to (mg/m 2 /day) as the dimension of the vertical axis in Fig. 5.
The volatilization and condensation rates in the mass conservation equations are based on the gas-liquid equilibrium in the pore spaces, represented by y l,1 P sat,1 = w g,1 P .The mole fraction of benzene y l,1 in the liquid phase is related as a func- tion of TPH as follows: Since the estimated value of the average gas saturation at the ground surface S g,ave (-) under these conditions is only 8.27 × 10 −2 and the elution of benzene into the water phase is completed, then S n had reached 0 after 0.5 years, so in Eq. ( 22), assuming that S n = S g = 0 , y l,1 can be simplified as: As shown in Fig. 5, the value of TPH at the ground surface decreased from an initial value of 10,000 mg/kg to 1800 mg/ kg after 10 years, and the elution into the water phase and vertical transport of benzene proceeded with the permeation of rainfall.As referring to Eq. ( 23), the decrease in TPH corresponds directly to the decrease in y l,1 , and the saturated vapor pressure in the multi-component system y l,k P sat,k was lowered, resulting in a decrease in the mole fraction of benzene in the gas phase w g,1 over time.Based on Eq. ( 21), since the amount of the generation of VFB derived from both advection and dispersion is highly dependent on the w g,1 at the ground sur- face, the VFB gradually decayed over time, showing a maximum value of 133.2 mg/m 2 /day at 0.56 years, whereas the GVF changed periodically depending only on weather variations.The cumulative VFB after 10 years was estimated to be 107.8g/m 2 , equal to just 6.72 × 10 −1 % of the initial TPH.This result indicates that almost all of the benzene initially present was not discharged from the ground surface as a volatilization flux and remained in the pore spaces.

Comparison of Transport Phenomena of VCSs and Generation Behavior of VFB for Different Soil Particle Sizes
According to the classification of ground material based on soil particle size by the Japanese Geotechnical Society [18], the ranges of particle size for each ground material correspond to clay: below 5.00 × 10 −6 m; silt: 5.00 × 10 −6 to 7.50 × 10 −5 m; ( ⋅ TPH 1 . (23) and sand: 7.50 × 10 −5 to 2.00 × 10 −4 m.The actual distribution of soil particle size ranges widely, whereas the average particle size D A =5.00 × 10 −5 m under reference condition corresponds to silt in a series of calculations.It is supposed that the difference in soil particle size has a large effect on the permeability characteristics of VCSs in the soil; therefore, we conducted a series of numerical analyses by changing D A in the range of 1.00 × 10 −5 to 2.00 × 10 −4 m, including that of reference condition, and discussed the effects on the transport phenomena of VCSs in unsaturated soil and the generation behavior of VFB.The value of absolute permeability K (m 2 ) for different D A was estimated by Matsuo and Kogure's equation [19] as below and introduced to each condition: where w,15 • C is the viscosity of water at 15 °C (= 1.14× 10 −3 Pa⋅s).The absolute permeability K=2.95 × 10 −2 µm 2 as the reference condition ( D A = 5.00 × 10 −5 m), as shown in Table 1, was calculated using Eq. ( 24), and the values of K for D A in the range of 1.00 × 10 −5 to 2.00 × 10 −4 m varied from 1.45 × 10 −4 to 2.86 × 10 0 µm 2 .
(24) K = 0.5×(D A ×10 3 ) As D A decreased, the amount of water retained in the pore space increased owing to the effect of the capillary pressure.Therefore, it was assumed that the change in the amount of retained water had a large effect on the mobility of each phase and the generation of VFB.Based on the results of laboratory experiments, we formulated the residual saturations of water phase S wi as a function of D A , in the range of 0.00 to 2.00 × 10 −4 m, based on the S wi0 (= 0.230) obtained for Toyoura sand ( D A = 2.00 × 10 −4 m) [20,21] and introduced into the numerical analysis model, using the equation The relative permeabilities ( k rn , k rw , k rg ) and capillary pressures ( P c,gw , P c,nw ) of three-phase systems consisting of NAPL, water, and gas are based on formulations that consider the continuity and hysteresis of the respective curves of relative permeability and capillary pressure due to transitions from three-phase to two-phase and two-phase to single-phase [16].Note that although D A was treated as the dimension of meter in the numerical analysis, subsequent descriptions and figures are described in the dimension of micrometer.The changes in the TPH distribution in the vertical direction over time for different D A values obtained from a series of calculations are compared in Fig. 6.The behaviors of elution into the water phase and adsorption of benzene onto soil particles of benzene were common regardless of the difference in D A , as explained in Fig. 4.Where the position where TPH exceeded 1 mg/kg in the vertical direction was defined as the spread edge of contamination, specifically, each spread edge was located at − 1.35 m (10 µm), − 1.75 m (30 µm), − 2.15 m (50 µm corresponding to reference condition), − 2.35 m (100 µm), and − 2.35 m (200 µm).Therefore, it was confirmed that the spread of contamination differed significantly depending on D A , in the range of 10-50 µm.On the other hand, based on Eq. ( 19), although the amount of permeation of rainfall at the ground surface was proportional to the absolute permeability of the soil in vertical direction K z , and K z increased to 10 and 100 times to 2.90 × 10 −1 and 2.86 × 10 0 µm 2 at 100 and 200 µm compared to that at 50 µm, a significant difference was not observed in the spread of contamination in vertical direction.
Comparisons of the permeation ratio of rainfall into the surface soil, residual ratio of TPH (RTPH), and average water saturation at the ground surface in the different cases of D A are shown in Fig. 7.The permeation ratio of rain- fall was estimated by dividing the cumulative value of the permeation amount based on Eq. ( 19) for each condition after 10 years based on the total amount of rainfall.In addition, RTPH corresponds to the value of TPH after 10 years to the initial value (10,000 mg/kg).The permeation ratio at 10 µm was estimated to be 2.32 × 10 −2 even though the pressure gradient at the ground surface indicated the highest condition owing to the effect of capillary pressure.Therefore, because the K z value was very small, it was assumed that most of the rainfall spreads along the ground surface by surface run-off without permeation into the surface soil.Hence, we interpreted that the vertical benzene transport shown in Fig. 6 was principally due to dispersion, rather than advection.From this figure, in the range of 10-50 µm, the permeation ratio increased significantly with increasing D A , as 30 µm: 3.44 × 10 −1 and 50 µm: 8.49 × 10 −1 .However, when D A was greater than 75 µm, the permeation ratio reached almost 1.We confirmed that the entire rainfall permeated into the soil owing to the effect of gravity and capillary pressure before the occurrence of surface run-off, and these behaviors were less independent of the K z value.Therefore, it was interpreted that when the permeation ratio was equal to 1 under identical conditions of rainfall, the TPH distribution did not show significant differences because the spread due to advection in surface soil was almost the same under the condition of 50-200 µm.Additionally, the following Fig. 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 correlation between the permeation ratio and RTPH was observed: The RTPH remained at approximately 0.6 under the condition of 10-20 µm without any permeation of rainfall.On the other hand, the vertical transport of benzene was enhanced owing to a significant increase in permeation from 20 µm: Correspondingly, the RTPH decreased significantly.Furthermore, under the condition of larger than 50 µm, while the residual ratio ranged from 0.1-0.2, the ratio tended to increase from 0.115 at 100 µm.We interpreted these changes in the RTPH as follows: Corresponding to the change in the irreducible water saturation S wi based on Eq. ( 25), the aver- age water saturation decreased from 0.982 at 10 µm to 0.495 at 200 µm.Consequently, the total weight of the soil for the calculation of TPH decreased because the weight of water per unit volume of soil decreased as D A increased.
In Sect.3.1, the correlation between the transport of benzene in surface soils and the generation behavior of VFB was discussed using Figs. 4 and 5, and it was confirmed that TPH decreased with the permeation of rainfall and VFB decayed with time due to a decrease in the mole fraction of benzene in the liquid phase y l,1 .Whereas this series of behaviors was similar under the condition of different D A shown in Fig. 8, a significant increase in the amount of VFB generation was observed as D A became larger.For example, the maximum VFB around 0.50 years and cumulative VFB after 10 years were estimated to be 3637 mg/m 2 / day and 2089 g/m 2 at 200 µm, compared to 30.0 mg/m 2 /day and 50.8 g/m 2 at 10 µm.The changes in S g,ave , maximum GVF, total VFB, and VFB derived from dispersion after 10 years with respect to D A are shown in Fig. 9, and the differences in the generation behavior of VFB depending on D A are discussed.As shown in Eq. ( 21), VFB genera- tion is derived from advection and dispersion between the surface air and ground surface and is defined as the mass velocity of benzene per unit area of the ground surface.The advection term as the first one in Eq. ( 21) was expressed by multiplying g by w g,1 at the ground surface and GVF.Whereas w g,1 depends on the TPH at the ground surface, Fig. 7 Estimation of absolute permeability as a function of average diameter of soil particle D A and dependence of D A on permeation ratio of rainfall into surface soil, residual ratio of TPH, and average water saturation at the ground surface Fig. 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 GVF is proportional to the gas permeability in the soil and the pressure gradient between the air on the ground and the ground surface.On the other hand, assuming that the dispersion coefficient D g,1 and the porosity are constant regard- less of any conditions in the dispersion term as the second one in Eq. ( 21), VFB is proportional to the concentration gradient between the air on the ground and the ground surface ( Δw g,1 ∕Δz ) and the gas saturation at the ground surface S g .In this case, whereas the concentration gradient depends on the TPH at the ground surface, S g changes depending on the difference in permeability characteristics of the soil due to D A .According to Eq. ( 25), the amount of water retained in the pore space due to the capillary pressure decreases at a larger D A . Figure 9 shows that S g,ave tended to increase as D A increased, being estimated at 5.05 × 10 −1 at 200 µm, which was about 30 times higher than the 1.82 × 10 −2 at 10 µm, reflecting the changes in the amount of retained water.The absolute amount of benzene distributed to the gas phase by volatilization increased with higher S g , resulting in an increased amount of VFB being emitted from the ground surface as VFB is derived from dispersion (VFBD) at larger D A .Additionally, GVF generation increased when D A exceeded 100 µm, reaching 9.04 × 10 2 SL/m 2 /day at 200 µm.Because absolute permeability K z increases in addition to higher S g,ave and higher relative permeability to the gas when D A increases, the amount of GVF generated due to pressure gradients caused by changes in atmospheric pressure increased, resulting in an increase in VFB derived from advection.In the change in cumulative VFB and VFBD after 10 years with respect to D A , both VFB and VFBD increased with the same trend when D A was smaller than 75 µm, which is interpreted as the generation of VFB derived mostly from dispersion.In this case, as the S g,ave was maintained at a lower level, the absolute amount of benzene distributed in the gas phase decreased.For example, the cumulative VFB at 75 µm was estimated to be 219 g/m 2 , which was approximately 1/10 of the 2089 g/m 2 at 200 µm.
On the other hand, the trends of the increases of cumulative VFB and VFBD diverged from 100 µm because the generation of GVF increased.As D A increased past 100 µm, the Fig. 9 Change in average gas saturation at the ground surface ( S 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 contribution of advection to the generation of VFB increased, in addition to the increase in VFBD.These results suggest that when D A is large, there is a concern for increasing health risks to humans because of the increase in VFB generation caused by the effects of both advection and dispersion.

Correlation of Absolute Permeability to Averaged Gas Saturation S g, on the Generation of Volatilization Flux
The series of analyses in the previous section treated all parameters related to permeability characteristics in soil, consisting of absolute permeability K , relative perme- ability ( k rn , k rw , and k rg ), and capillary pressure ( P c,gw and P c,nw ), as functions of D A .The results showed that the fol- lowing two mechanisms have a large effect on the generation of VFB: (1) the generation of GVF, which depends mainly on absolute permeability, and (2) the difference in gas saturation at the ground surface, which varies significantly depending on the relative permeability and capillary pressure.Based on these results, we carried out additional calculations consisting of 146 cases, in which relative permeability and capillary pressure were treated virtually independent of absolute permeability, to clarify the correlation between absolute permeability and S g,ave on the generation of VFB.Specifically, with respect to the basic parameters shown in Table 1, whereas the parameters for multi-phase flow ( k rn , k rw , k rg , P c,gw , and P c,nw ) remained to be treated as a function of D A which varied stepwise from 25 to 200 µm, the values of K ranging from 1.00 × 10 −3 to 1.00 × 10 0 µm 2 were directly given for these calculations.
The relationship between the residual ratio of TPH (RTPH) at the ground surface and the decay rate of VFB obtained for a series of calculated conditions is shown in Fig. 10, prior to the interpretation of the correlation between K and S g,ave .The decay rate of VFB was estimated by divid- ing the average VFB value of the 10th year by that of the 1st year and subtracting the value from 1. RTPH and the decay rate of the VFB were shown to exhibit a good proportional relationship, with a correlation coefficient of 0.966.Hence, this relationship indicates that VFB decay is independent of differences such as permeability characteristics and the contribution of advection and dispersion to the mechanisms of VFB generation.Because VFB is predicted to behave in response to a decrease in TPH at the ground surface, decaying at the same ratio relative to the VFB value under the initial condition of contamination, it can be concluded that the amount of VFB generation changes is dependent on K and S g .
In addition, whereas the VFB decays by more than 80% after 10 years at RTPH of approximately 0.1 compared to the beginning of the contamination, the decay rate of VFB remained at approximately 40% at RTPH of approximately 0.5.This low decay rate suggests that VFB generation at a certain level continues for a long period.Figure 11 shows the correlation between K and S g,ave with respect to the total amount of VFB generated after 10 years.In this figure, the total amount of VFB generation is expressed as a relative value by dividing by the value obtained from reference conditions (107.8 g/m 2 ), and the RTPH according to Fig. 10 and the distribution of the contribution ratio of advection to total amount of VFB generation are shown by overlaying on the figure.The figure shows that the reason for the increase in the amount of VFB generation at a higher S g,ave was the increase in the absolute amount of benzene distributed to the gas phase by volatilization, as interpreted in Sect.3.2.1.
Furthermore, the dependence of S g,ave on the changes in RTPH and VFB was observed to be relatively small.In this case, the RTPH decreased owing to the increase in rainfall permeation with K , and conversely, the contribution ratio of advection increased with increasing GVF generation.On the other hand, a unique trend in which the amount of VFB generation increased toward low permeability on the left side of the diagram was confirmed, and the overall behavior can be interpreted as follows: 1. On the low-permeability side near log K= − 2.75 (1.77 × 10 −3 µm 2 ), the VFB was mainly derived from dispersion.Because the effect of rainfall permeation was relatively small and the RTPH remained above 0.4, the VFB decay decreased, resulting in an increase in the amount of VFB generated.2. At around log K= − 1.50 (3.16 × 10 −2 µm 2 ), the con- tribution ratio of advection was not large due to the small amount of GVF generated.In addition, the RTPH decreased to approximately 0.15.In this case, VFB decay was remarkable, resulting in a significant decrease in the amount of VFB generation.3. On the high-permeability side near log K= − 0.25 (5.62 × 10 −1 µm 2 ), the RTPH decreased to approximately 0.15; however, as the amount of GVF increased, the effect of advection became more significant than the VFB decay, resulting in turning an increase in the amount of VFB generation again.
Note that the total amount of VFB generation after 10 years was approximately 10 times higher than that of the reference condition for both low-permeability and high-gas saturation conditions on the top-left side and high-permeability and high-gas saturation conditions on the top-right side.In comparison, the low-permeability and high-gas saturation conditions, which were present at a higher RTPH, were concluded to continue the generation of VFB at high levels due to lower VFB decay, as shown in Fig. 10.In this case, there may be concerns that the health risk derived from exposure is the highest.

Effect of Soil Porosity on VFB Generation
The generation of VFB derived from dispersion (VFBD), defined as the second term on the right-hand side of Eq. ( 21), is proportional to the porosity , as well as to the gas saturation S g , as was discussed in Sects. 3.1 and 3.2.As varies widely with soil type and the degree of compaction, it is necessary to clarify the effect of on the distribution of VCSs in the soil and VFB generation.In this section, the model relationship by changing the value of across the range of 0.300-0.700was determined, as compared to 0.500 under reference conditions.The variation over time of the vertical TPH distribution for different values obtained for a series of calculations is compared in Fig. 12.The distribution mechanism of benzene in each phase due to elution into the water phase and adsorption onto the soil particles is based on the interpretation described in Fig. 4, independent of the porosity .As shown in Fig. 12, the elution of benzene was complete after 5 years.In this case, because the number of moles distributed into the water phase depending on the solubility of benzene is small compared to the amount of adsorption, the maximum value of TPH after 5 years in each condition is generally derived from adsorption.Under these conditions, the distribution coefficient K d,1 and saturated adsorption x s,sat,1 were set at 5.89 × 10 −2 m 3 /kg and 1.00 × 10 −4 kmol/kg, respectively.Because the weight of the solid phase (soil particles) per unit volume of soil decreases as increases, the absolute amount of benzene distributed in the solid phase decreases.The maximum TPH values after 10 years were estimated at 0.300: 6840 mg/kg, 0.400: 6380 mg/ Fig. 10 Correlation between residual ratio of TPH at the ground surface and decay of volatilization flux of benzene (VFB) kg, 0.500 (reference condition): 5640 mg/kg, 0.600: 5160 mg/ kg, and 0.700: 4310 mg/kg, respectively, and were observed to decrease as increases.In addition, the spread edge of contamination defined as the location beyond 1 mg/kg of TPH was located at 0.300: − 2.05 m, 0.400: − 2.05 m, 0.500 (reference condition): − 2.15 m, 0.600: − 2.45 m, and 0.700: − 2.85 m, respectively, after 10 years.Therefore, it was concluded that the vertical transport of dissolved benzene due to advection and dispersion was promoted corresponding to a decrease in the amount of retention in the soil as an adsorbent when increased.Figure 13 shows the variations in TPH, VFB, and cumulative VFB at the ground surface over time for different porosities .Although the behavior that VFB decays gradually as TPH decreases with time is common, independent of any condition, reflecting the difference in the amount of adsorption of benzene to the soil described above, the TPH value after 10 years was estimated to be 859 mg/kg at =0.700, compared to 3395 mg/kg at =0.300, and confirms a decrease with increasing .When is large, according to Eq. ( 21), the mechanism to increase VFB generation owing to the increase in the absolute amount of benzene distributed to the gas phase is supposed to be caused by the volume occupied by the gas in the pore space increasing.However, the maximum VFB remained only 77.5 mg/m 2 /day at =0.700, corresponding to about one-third of the 208.0 mg/m 2 /day at =0.300.The maximum VFB achieved is observed to decrease as increases.The cumulative VFB after 10 years was estimated as 192.9 g/ m 2 for =0.300 and 77.5 g/m 2 for =0.700 and showed the same tendency as the change of maximum VFB, which is contrary to the above interpretation of Eq. (21).Therefore, under conditions where is different, it is assumed that the dependence on the TPH value for the generation of VFB is relatively high.In the case of high , it is interpreted that the amount of VFB generation decreases the mole fraction y l,1 of benzene in the liquid phase due to a decrease in the amount of water occupied per unit volume in addition to the decrease in TPH.On the other hand, in the range of 0.300-0.700 in these analyses, a higher RTPH at lower would be expressed due to the continued higher levels of VFB, thus increasing the health risk due to exposure.

Effect of the Distribution Coefficient Between
Water and Soil Particles on VFB Generation Section 3.3 indicated that differences in the amount of benzene adsorbed onto soil particles, depending on the porosity , have a large effect on VFB generation.The distribution coefficient K d,1 =5.89 × 10 −2 m 3 /kg applied for these condi- tions is based on the literature [22].However, independent of , most of the benzene remained at a position shallower than 2 m of the surface soil even after 10 years, as shown in Fig. 13, and the adsorptive of benzene to soil was relatively high.In Fig. 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 Fig. 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 ◂ addition, because it is assumed that the adsorption behavior onto soil varies significantly depending on differences such as the specific surface area of soil particles and the organic matter content, we discuss the effect on the transport phenomena of VCSs and the behavior of VFB generation by changing the distribution coefficient, K d,1 , as a calculation parameter.
Figure 14 compares the adsorption isotherms when the saturated adsorption x s,sat,1 is set equal to 1.00 × 10 −4 kmol/kg in any case and K d,1 is changed in the range from 5.89 × 10 −4 to 1.00 × 10 0 m 3 /kg.The figure shows that if the concentration of benzene dissolved in the water phase C w reaches its solubility (1.75 × 10 3 mg/L), the amount of adsorbed C s does not reach saturated adsorption (7.81 × 10 3 mg/kg).Therefore, the distribution between the water and solid phases in this case was determined only by K d,1 .On the other hand, because C s reached saturated adsorption even in C w lower than its solubility, the adsorption onto soil particles in this case was maintained at saturated adsorption independent of C w .Furthermore, benzene was distributed to the NAPL phase as undiluted solutions as C w and C s were maintained at solubility and saturated adsorption in the region exceeding solubility and saturated adsorption on the right side of the figure.The changes in the vertical TPH distribution over time when these adsorption isotherms were applied are compared in Fig. 15.In the case of K d,1 =5.89 × 10 −4 m 3 /kg, because an undiluted solution of benzene existed in the pore space Fig. 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 due to the low amount of elution from the NAPL phase due to the low amount of adsorption onto the soil particle, the TPH remained at 10,000 mg/kg corresponding to the maximum value even after 5 years.In addition, according to the adsorption isotherm shown in Fig. 14, the TPH at a position deeper than − 1 m remained at a low level of 1225 mg/kg because the adsorption equilibrium was established without reaching saturation adsorption.In this case, it was confirmed that vertical benzene transport was consistent with rainfall permeation, and discharged benzene had reached the bottom edge of the surface soil corresponding to the boundary to the groundwater table after 5 years.On the other hand, the positions of the spread edge of the contamination defined as that beyond 1 mg/kg were estimated to be K d,1 =5.89 × 10 −3 m 3 /kg: − 3.55 m, 5.89 × 10 −2 m 3 /kg (reference condition): − 2.15 m, 5.89 × 10 −1 m 3 /kg: − 1.85 m, 5.89 × 10 0 m 3 /kg: − 1.85 m, respectively.Therefore, the tendency of benzene to remain in the upper part of the surface soil increased with a larger K d,1 and no difference in vertical distribu- tion was observed for conditions above 5.89 × 10 −1 m 3 /kg.Figure 16 shows the changes in the residual ratio of the TPH (RTPH) at the ground surface and the outflow ratio of benzene at the bottom of the surface soil after 10 years obtained in the range of K d,1 from 1.00 × 10 −5 to 1.00 × 10 1 m 3 /kg.The outflow ratio of benzene was estimated by dividing the number of moles of benzene corresponding to the amount of cumulative outflow by that corresponding to the initial TPH, which could be replaced by the inflow ratio into the aquifer (saturated zone).From this figure, bordering around on K d,1 = 1.00 × 10 −2 m 3 /kg, the contrary behavior was confirmed, and in the cases below K d,1 = 1.00 × 10 −2 m 3 /kg, benzene did not remain inside the surface soil, and vertical transport of benzene was promoted with rainfall permeation.As a result, in this case, it is estimated that up to 50% of the initial TPH flowed out from the bottom of the surface soil and transferred to the aquifer.Conversely, for conditions greater than K d,1 =1.00 × 10 −2 m 3 /kg, RTPH increased with a larger K d,1 , and we confirmed that 50% of the initial TPH remained inside the surface soil, especially at K d,1 =1.00 × 10 0 m 3 /kg.
Figure 17 shows the variation in TPH, VFB, and cumulative VFB at the ground surface over time for different K d,1 .Since the maximum values of VFB were detected around 0.5 years, when benzene sufficiently remained at the ground surface, maximum values ranged from 121.1 to 133.9 mg/m 2 /day, and significant differences depending on K d,1 were not recognized.However, there was a rapid decrease in TPH at the ground Fig. 15 Comparison of changes in the distribution of total petroleum hydrocarbons (TPH) (mg/ kg) in the vertical direction over time for different distribution coefficient surface with rainfall permeation, reflecting the different mobility of benzene under the conditions of 5.89 × 10 −4 and 5.89 × 10 −3 m 3 /kg, and TPH decreased to approximately onehundredth of the 10,000 mg/kg as the initial value after 2.5 and 5.8 years, respectively.Corresponding to this decrease in TPH, the determined VFB decay was significant, VFB generation after 10 years was in the state of convergence or very low level, and the cumulative VFB was only 19.7 g/m 2 for 5.89 × 10 −4 m 3 /kg and 32.0 g/m 2 for 5.89 × 10 −3 m 3 /kg, compared to 107.8 g/m 2 in the reference condition.On the other hand, the TPH after 10 years under the conditions of K d,1 =5.89 × 10 −1 m 3 /kg and 5.89 × 10 0 m 3 /kg was estimated as 4368 mg/kg and 4913 mg/kg, respectively, and benzene remained at the ground surface.As a result, the VFB did not decay significantly, and the discharge of benzene from the ground surface due to volatilization continued at high levels; in this case, health risk concerns would occur due to exposure associated with inhalation around the contaminated site.In addition, while VFB was significantly decayed for smaller K d,1 , which means that the risk associated with inhalation is relatively small, benzene can easily reach the aquifer, raising concerns about widespread contamination due to groundwater flow.In this paper, we discussed the effects of soil properties on the generation of volatilization flux through a parameter study by changing permeability, porosity, and distribution coefficient between water and solid phases based on our previous modeling, targeting benzene as a model substance for VCSs.In summary, the following conclusions were drawn: 1.The effect of the permeability characteristics of benzene in surface soil depending on the difference in soil properties was significant and was concluded to correspond to the amount of rainfall permeation into surface soil and the associated changes in the amount of TPH. 2. The average gas saturation in the soil increases with the larger average diameter of soil particle D A depending on the relative permeability, and the generation of VFB derived from dispersion (VFBD) increased because of the larger volume of pore spaces occupied by the gas phase.Furthermore, when D A became larger, the contribution of advection due to an increase in absolute permeability increased the total amount of VFB generation, in addition to the effect of dispersion, and there may be concerns regarding increased health risks due to inhalation.Notably, the residual ratio of TPH (RTPH) at the ground surface had a large direct effect on VFB generation, and the delay of TPH decay indicated the potential for VFB generation to continue for a long period.In particular, the conditions of low permeability and high-gas saturation produced the highest risk due to continued VFB generation.3. When the porosity was high, the VFB generation is observed to decrease due to the decrease in the TPH.In this case, it was supposed that the VFB generation is more dependent on the RTPH rather than the dispersion due to the increase in the volume occupied by the gas phase.In particular, at a smaller , the VFB generation will continue at a high level due to the higher RTPH, resulting in an increased health risk.4. The value of the distribution coefficients K d,1 is con- firmed to affect the degree of VFB generation and the transport phenomena of benzene in the surface soil.As the distribution coefficient K d,1 is increased, the majority of the discharged benzene is observed to remain in the upper part of the surface soil; consequently, VFB gen-eration was determined to continue at high levels.In this case, there may be increased concern regarding adverse health risks due to the potential inhalation around the contaminated site.On the other hand, at smaller K d,1 , the VCS did not remain inside the surface soil and was transferred to the aquifer by the permeation of rainfall.In this case, although there may be less risk of inhalation due to the low VFB generation, there may be concerns about widespread contamination due to groundwater flow because benzene easily reaches the aquifer.
As described above, the authors extracted specific parameters under which health risks may occur based on soil properties and the contaminated conditions under which health risks may occur.This study can provide information to evaluate the potential health risks and determine the optimal countermeasures required, based on an understanding of the transport phenomena of their respective VCS for contaminated sites, where the permeability characteristics, porosity, and distribution coefficients are well known.

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. 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 Fig. 19 Correlations between 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 Fig. 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 Fig. 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 Fig. 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

g
Viscosity of gas phase (Pa⋅s) n Viscosity of NAPL phase (Pa⋅s) w Viscosity of water phase (Pa⋅s) w,15 • C Viscosity of water phase at 15 °C (Pa⋅s) g Mole weight of gas phase (kmol/m 3 ) n Mole weight of NAPL phase (kmol/m 3 ) s Density of soil particle (kg/m 3 ) w Mole weight of water phase (kmol/m 3 ) Φ g Flow potential of gas phase (Pa) Φ n Flow potential of NAPL phase (Pa) Φ w Flow potential of water phase (Pa) Porosity (dimensionless)

Fig. 1
Fig. 1 Schematic illustration of soil and groundwater contamination by volatile chemical substances (VCSs)

Fig. 2
Fig. 2 Relationship between each phase and component in the present numerical model for soil and groundwater contamination by volatile chemical substances (VCSs)

Fig. 5
Fig.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

Fig. 11
Fig.11Correlation between absolute permeability in surface soil and average gas saturation at the ground surface ( S g,ave ) and the volatilization flux of benzene (VFB)

Fig. 16 Fig. 17 4
Fig.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

Table 1
Basic parameters of the surface soil and physical parameters for benzene (C6H6) as a model volatile chemical substance (VCS) for numerical analysis * These values corresponded to those for reference calculation condition and were changed as calculation parameter for a series of parametric study Basic parameter of surface soil for numerical analysis Length of x-direction (m)