2.1 Soil Collection
Clayey soil and sandy soil were collected from a chemical plant in Shenyang city, China. The silty soil was collected from a contaminated site that was used as a gas chemical plant in Taiyuan city, China. Sandy soil is the soil that particles larger than 2 mm in diameter account for less than 50% of the total mass while the particles larger than 0.075 mm exceed 50% of the total mass. Silty soil is a type of soil that particles greater than 0.075 mm do not exceed 50% of the total mass while the plasticity index equals or less than 10. Soil with plasticity index greater than 10 is identified as clayey soil. This classification is based on the standard issued by Ministry of Housing and Urban-Rural Development of the People’s Republic of China in 2009 (MOHURD, 2009). Benzene was determined the only soil pollutant in the two sites by previous investigations. An SH-30 model rig method (a gravity impact drill) was applied to drill the soil cores at each site and we sampled from the middle of the original core after it was collected and cut open. It should be noted that soil samples were both collected from the polluted and non-polluted areas. The non-polluted soils were used for the static headspace experiment and the polluted soils were used for the equilibrium partitioning experiment. The group identified samples with labels like sampling date and boring number prior to transporting them. Then the group reserved and transported these samples in sealed wide-mouth bottles. The bottles were arranged into large plastic boxes and transported to laboratories subsequently. The preservation and transportation of soil samples were followed the standard practices released by ASTM in 2014 (ASTM, 2014).
2.2 Static Headspace Experiment
After air drying, sorting and sieving, the non-polluted soil was placed on a stainless steel tray and dried in an oven at 105 °C. Samples were taken at 24 h, 48 h and 72 h respectively during drying for background pollution analysis. The result showed that there was no background pollution after 48-hour drying. Then, the soil was quickly transferred to clean dry ground glass bottle and sealed with sealing film. The bottle was placed in a constant temperature dehumidification box (t = 25 °C).
Adding every 10 g of dried soil to empty brown headspace bottles, clean and dry inner tubes were placed upright in the bottle. The bottle caps were equipped with airtight valves which connected to the tubes. The empty bottles were weighed before and after the filling procedure, and the accurate mass of the soil samples in the bottle could be calculated by the difference method.
Benzene is the pollutant of concern in this study. A gradient mass of benzene was transferred through the tubes of the headspace bottles. After the addition the valves were quickly closed and the bottles were weighed again. The mass of benzene injected to the bottles could be calculated by the difference method. Headspace bottles were placed in a constant temperature oscillation box (t = 25 °C) for distribution reactions. The pre-experiment results showed that the partitioning of benzene in the headspace bottle could achieve equilibrium within 24 h. Therefore, the airtight headspace bottles were placed in the constant temperature oscillation box for more than 24 h. After opening the valve switch on the cap one by one, 0.1 mL of headspace gas was transferred to the gas chromatograph-mass spectrometer by a gas-tight syringe to determine the gas concentration in the headspace at equilibrium. The valve push rods were pushed to close the valves immediately after the gas-tight syringe probe completed the sampling. After an interval of 0.5 h, parallel samples were taken repeatedly. Then, the bottle caps were slowly unscrewed, and a precision pipette gun was used to quickly inject 10 mL of methanol to fully wet the soil in every bottle. An air pipe was used to inject high-purity nitrogen to purge the headspace gas in the bottles. After the air pipe was removed, the headspace bottles were sealed quickly and placed in an incubator (t = 25 °C) for 24 h.
A micro-liquid sampler was used to puncture through the silica gel spacers of the bottle caps, and 1 μL of the methanol supernatant was accurately measured and injected into the gas chromatograph-mass spectrometer to determine the benzene concentration in the extract liquor. After half an hour, parallel samples were taken repeatedly for analysis.
2.3 Equilibrium Partitioning Experiment
The benzene-polluted soil sample was moved from the refrigerator (t = 4 °C) and transferred in the incubator (t = 25 °C) for approximately 6 h. Empty headspace bottles were marked a serial number and weighed. A handle and non-disturbance sampler was used to transfer approximately 10 g of soil for every headspace bottle. The sampling and analysis steps were identical with the static headspace experiment.
2.4 Model Development
2.4.1 Adsorption on the Surface of Soil Particles. The adsorption of VOCs on the soil particles surface can be divided into adsorptions on the liquid-solid interface and vapor-solid interface. Liquid-solid interface adsorption by soil OM is expressed by the DED model as follows, which considers the irreversible adsorption of organic compounds on the soil surface and shows great agreement with the experimental data (Kan et al., 1998):
where Cs1 is the liquid-solid sorption concentration (mg/kg), CW is the aqueous-phase solute concentration (mg/L), KOC and K2nd oc represent the OC normalized partition coefficients for the first and second compartments (L/kg), respectively, ƒOC is the OC content of soil (g/g), q2nd max is the maximum sorption capacity of the second compartment (mg/kg), and ƒ represents the fraction of the second compartment that is saturated upon exposure (usually 0 ≤ f ≤ 1). The values and corresponding sources of the above parameters are given in Table A.7 of the supplementary material.
Brunauer, Emmett, and Teller extended the Langmuir model to include multilayer adsorption (Brunauer et al., 1938). The BET adsorption model assumes that the theory of the Langmuir equation applies to each adsorption layer and that the heat of adsorption of the first layer has a distinct value, while that of the second and higher layers are equivalent. The BET isotherm has been proven to have an excellent goodness of fit to the measured data of organic compounds adsorbed on soil (Brunauer et al., 1938, Chiou et al., 1985, Unger et al., 1996). The expression is as follows:
where Cs2 is the gas-solid sorption concentration of benzene in soil (mg/kg), P is the partial pressure of the sorbate in the gas phase (Pa), P0 is the saturation pressure of the compound (Pa), K is the affinity constant exponentially related to the heat of adsorption (unitless), and CMONO is the sorbed concentration (mg/kg).
When both sides of the equation are divided by P0 and M, the expression of the ideal gas law can be rewritten as:
where Csg is the vapor-phase concentration of organic compounds (mg/L), R is the gas constant (8.3145 J·mol-1·K-1), T is the system temperature (K), and M is the molecular mass of the compound (g/mol). A parameter µ is defined as follows:
Then, the expression of the BET isotherm can be rewritten as:
2.4.2 Mass balance. A mass balance accounts for solute in each phase of the system, including the mass of VOC in the vapor phase and the liquid phase, adsorbed at the solid-vapor interface and the solid-liquid interface and the gas-liquid interface, condensed in micro-pores. The quantitative relation of gas-liquid sorption can be expressed by the Gibbs absorption equation. However, this part has been hardly proven because the thickness of the effective interface is not more than a few molecules. Solute condensation is only significant when both RS=0 and P/P0 > 0.4, as determined by the Kelvin equation (Unger et al., 1996). Therefore, valid phases generally include four components.
where CT represents the total soil concentration (mg/kg), ρ represents the dry soil bulk density (kg/L), θair represents the volumetric air content, θwater represents the volumetric water content, and fv is the fraction of the soil surface exposed to the vapor phase and is given by N2-BET adsorption and mercury intrusion analysis of the soil (the results for each of the soils were showed in the section 3 of the supplementary material) (ISO, 2016, 2007, 2006). Based on the soil pore size distribution and soil moisture content, fv value can be calculated. The calculation was introduced by Unger before (Unger et al., 1996).
Compared to the existing models quantifying the partitioning of VOC in soil, a noteworthy superiority of this MPE model is that VOC adsorption at the soil gas-solid interface is involved. By integrating Henry's law, the DED model, the transformed BET isotherm and mass conservation equation, the proposed model contains all dominating and potential phases of VOC uptake by soil.
2.4.3 Form of Solution. Defining CT as the independent variable and Csg as the dependent variable, the solution becomes a mathematical problem of solving a quartic equation with one variable. Here, the Ferrari method was applied to solve the equation and the solutions are as:
The lowercases in the equation are assumed:
and the upper cases in equation (8) ~ (11) are assumed:
To a quartic equation there are four solutions which may include complex or negative solutions. It is necessary to take the solution with a real and positive number as the final solution. The form of the final expression is the Ferrari’s solution which contained a bulk of parameters relative to the pollutant and soil. The detailed solution process is given in the section 1 of the supplementary material.
2.5 Analytical Methods
The benzene in the soil gas was determined by gas chromatography with flame ionization detection (GC-FID) (7894A, Agilent, USA). The length, diameter and film thickness of the gas chromatography column were 30 m, 0.32 mm, and 0.25 mm, respectively (19091J-413, Agilent, USA). The inlet and detector temperatures were 200 °C and 250 °C, respectively. The gas sample injection volume was 1 mL with the split ratio of 10:1. Five-point calibration curves were prepared using a liquid phase standard before conducting gas sample analysis.
2.6 Quality Control
During the static headspace experiment, the headspace concentration was measured at equilibrium. The volume capacity of the glass bottle was known as well as the weight of the added soil, so the volume of the headspace could be calculated. After collecting the headspace gas samples, the sealing film on the glass bottle was opened, and the headspace gas in the bottle was rapidly expelled with a stream of nitrogen. The benzene was extracted from 10 mL of methanol, and this fraction of the mass plus the mass of benzene in the headspace gas was defined as the recovered mass. Compared to the mass initially added, the recovery rate was basically higher than 75% (arithmetic mean = 78.19%, median = 76.89%). In addition, the relative average deviations (RADs) of parallel samples collected during the static headspace experiment for determining the gas concentration of benzene were all in the range of -7% to 7%, and the RADs of parallel samples of methanol supernatant analysis were in the range of -14% to 14%. Detailed data are found in the section 2 of the supplementary material.