New insight into advection of organic contaminate plume at drain outlet areas

Abstract To provide insight to optimize organic contaminants treatment at the drain outlet areas due to the discharge from the industrial plants, the fate and transport of variety kinds of organic contaminants were investigated. By taking the chemical properties (molecular weight (MW), Henry’s law constant (H), vapor pressure (Pv), organic carbon normalized soil-water partition coefficient for organic compounds (Koc), water solubility (S), air diffusivity (Da), and water diffusivity (Dw)) of 56 kinds of organic chemical into account, we studied the general transport equation (GTE) regarding the mass balance for the steady-state analysis of the accumulation of a chemical over time by the plume advection. We found that Koc has significant relationship with S and MW of the chemicals. Furthermore, higher organic carbon-water partitioning coefficient of the chemical will make it easier to stay at the drain outlet area, which gives us hints for next research of nanoscale particles for in situ remediation.


Introduction
As a result of industrial practices, organic contaminants have been detected in many drain outlet areas, resulting in contaminant in crop growth, water ecological environment, clean water resource and human health, which is lack of enough concern in some developing countries (Ávila et al., 2015, Honkonen and Rantalainen, 2012, Huang et al., 2015. The need to understand the fate and transport of the organic contaminants has led to numerous studies that used various techniques including dye-and chemical tracer studies (Barns et al., 2015, Subedi et al., 2015, and simple to more complex digital or numerical transport models (Georgi et al., 2015, Simon et al., 2013. However, all of them still did not solve the movement of particular organic contaminant problems with the determination of what happens to them (e.g. when does it end up? What does it transform to? How long does it persist? etc.) by the processes of definition, model, monitor and quantifying.
Obviously, the non-uniform/non-steady-state has more problems of interest. Most of the fate and transport phenomenon of the contaminants in natural or man-made systems are non-uniform and non-steady-state (Ramšak et al., 2013). However, it is difficult to define them and make models to quantify due to their un-directional concentration distribution. Moreover, the real and complex system includes solids and voids and there are lack of detailed data on its configuration within the void space (Yao et al., 2013). Thus, under some conditions, researchers just make it simple and assume it steady-state to do qualitative analysis. Luckily, researchers still could validate the model at a point within the void space by both recognizing the porous medium domain as a whole visualized as a continuum, and each of the phases and components as a continuum (Chabauty et al., 2015, Cheng and Saiers, 2015, Essaid et al., 2015. Sincerely, what more important is to win the public's concern like (Robles-Morua et al., 2012) did before. They showed that the regions in the river are in noncompliance with fresh water pathogen norms. It was shown that these risks are highly sensitive to spatiotemporal variability in river discharges and uncertainty in pathogen removal rates. Thus, the local government and people could be conscious of this series problem.
In this study, we derived the general transport equation (GTE) with the mass balance equation for the 56 kinds of organic chemicals. After solving the problem about GTE, we could get the accumulation of a substance over time within the defined control volume with the independent variables of the flux that we should assume. Specific information about chemical parameters that is needed includes molecular weight (MW), Henry's law constant (H), vapor pressure (Pv), organic carbon normalized soil-water partition coefficient for organic compounds (Koc), water solubility (S), air diffusivity (Da), and water diffusivity (Dw).

Methodology
In order to investigate the consistency between the tabulated values in Table S1, we firstly calculated the estimated Henry's law constant H(cal) using the following equation (Lesser et al., 2008, Luo, 2009: where R is the gas constant of 0.082 L-vapor atm mol −1 K −1 , T is the absolute temperature (K), Pv is the vapor pressure (atm), S is the solubility (g/L-water) and M is the molecular weight of the chemical (g/mol).
Furthermore, Koc has been correlated with the aqueous solubility and the solubility gives a good first approximation of adsorption when logKoc is plotted against logS for a group of organic compounds as the following equation (Shea, 1989): The expressions for fraction of total mass in dissolved phase, fraction of total mass in sorbed phase, and fraction of total mass in vapor phase are shown as follows and the derivative details are included in SI: where, in our study, Cm, Cs, Cv, and CT are dissolved concentration (g/L 3 -water), sorbed concentration (g/L 3 -soil), vapor concentration (g/L 3 -vapor), and total concentration (g/L 3 ), respectively, soil bulk density ρ=1.5 kg-soil/cm 3 -soil, Φv = 0.2 L-vapor/cm 3 -total voids, Φm = 0.2 cm 3 -water/cm 3 -total voids, Ks = foc*Koc with fraction of organic carbon foc = 0.01 g-OC/g-soil.
Using the advection model schematically illustrated in Fig. 1, the following mass balance equation could be obtained to derive the transient concentration curve (Cavanagh et al., 2014, Lundegard andJohnson, 2004): where M is the mass of the chemical (g), t is the time (day), C0 is the source concentration (g/L 3 ), qm is the specific discharge (L 3 /day/m 2 ), C600 is the concentration at 600 cm (g/L 3 ), A is the cross area (m 2 ), and Re is the reaction term (g/day). With the assumption of steady-state and no reaction, we can obtain the following equations: With another control volume cutting at x, another mass balance equation could be obtained: So at steady-state C = C0 over x.
In this case, we divided the control volume into two control volumes when the plume reaches a with the moving of the plume, then So we can get C = C0 when x < a or x = a, and C = 0 when x > a.
For problems, where diffusion, dispersion, and reduction are negligible in comparison with advection, there are stationary vapor and solid phases with the moving bulk water along the x direction and the geometry is such that the problem can be treated as one-dimensional (Lundegard and Johnson, 2004), the GTE can be reduced from to: where D eff and D disp are diffusion and dispersion coefficient, respectively.
We will look into the solution for the case where chemical is not present initially at the model domain boundaries, the concentration suddenly is increased and remains relatively constant at one boundary (x = 0). In this case, the boundary and initial conditions are: C = C0 at x = 0 and all t, and C = 0 at t = 0 and all x.

Results and discussion
Regarding the chemical properties of the 56 kinds of chemicals from Fig. 2a-d (diffusion coefficient in water vs. molecular weight see Fig. S1), as molecular weights of the chemicals increase, the solubility, vapor pressure, and diffusion coefficient in air or water decrease while organic carbon-water partitioning coefficient increases. Using the molecular weights of 56 kinds of organic chemicals as the reference variables, among them, Fig. 2a, d and Fig. S1 show that there are only several kinds of chemicals that deviate from the trend by more than one order of magnitude from the average, note that we define one order of magnitude as the level of correlation, which suggests that there is a strong correlation between molecular weight and the organic carbon-water partitioning coefficient/diffusion coefficient in water/air. However, a lot of chemicals have vapor pressures and solubilities that are above or below one order of magnitude from the average, which would suggest that there is no significant correlation between molecular weight and solubility/vapor pressure.  Table S1, most of them have vapor pressures that are positioned at the bottom 20% of all chemicals in the database. Moreover, Most of them have solubilities that are located within the bottom 20% of all chemicals in the database. It can be concluded that smaller solubility or vapor pressure makes the estimation less reliable. For example, for 3,3dichlorobenzidine, the estimated H using equation 1 has more than one order of magnitude greater than that of H value from table S1. Since 3,3-dichlorobenzidine is a sparingly soluble chemical, some of this chemical staying in the liquid phase might not be dissolved in water, which resulted in the overestimation of H using the equation 1. Similarly, for benzo(b)fluoranthene, the estimated H has more than one order of magnitude smaller than that of H value from table S1. Since benzo(b)fluoranthene is a low vapor pressure chemical, some of this chemical staying in the gas phase might not vaporized, which resulted in the underestimation of H using the equation 1. However, unlike Henry's law constant, organic carbon-water partitioning coefficient Koc has good agreement with that of the tabled values as shown in Fig.  S2, indicating that Koc is well correlated with water solubility S (Shiflett et al., 2006).  Fractions in different phases for the 56 kinds of organic chemicals have been plotted in Fig. 4. It indicates that fraction-sorbed is the largest while fraction-vapor is the smallest for all of the chemicals. Especially, the fraction-sorbed of some chemicals is close to 1. From the Eqs (3)-(5), the magnitude of fraction-sorbed, fraction-dissolved and franction-vapor have relationship with ρ, Ks, H, Φv and Φm, respectively. Among them, the H and Koc of chemicals basically determine the fraction distribution in different phases (Liu et al., 2013). Generally, higher H gives rise to relatively higher fraction in vapor, while lower Koc caueses higher fraction in water and lower fraction sorbed in soil. Based on this observation and trend, a rough estimated fractions in different phases can be initially figured out by observing these chemical properties, e.g. higher Koc indicates more fraction sobbed in soil and lower fraction dissolved in water; and higher H indicates bigger fraction in vapor than those with lower H, which could help to determine what kind of phases of the chemicals will present in the drain outlet areas. Since for organic contaminants with higher Koc, nanoscale particles for in situ remediation could be applied in solid phase resulted from effective subsurface dispersion. To study the accumulation of a chemical over time, the steady-state here describes the state of the system when a variable, e.g. concentration, remains constant with time changing. Note that equilibrium can exist where it is not necessary to be steady-state while steady-state can also be reached where equilibrium might not be reached (Paces, 1973). Table 1 shows 4 groups of the steady-state time reaching 6 m for the 56 kinds of organic chemicals according to the plume moving from the source with water flow. The four groups of chemical are plotted and shown in Fig. S3-S6 based on the steady-state time of 1 day (group A), 1-10 days (group B), 10-100 days (group C) and more than 100 days (group D), respectively. We selected one representative chemical from each of the four groups for a further comparison and discussion, such as Methyl bromide (Fig. 5a), Hexachloroethane (Fig. 5b), Fluroranthene ( Fig. 5c), and Benzo(a)pyrene (Fig. 5d). Fig. 5a-d show the concentration change from 0 to C0 from x = 0 to 6 m with the plume moving and Fig. 5e shows the plume can reach 1 m in y direction within 6 m for the 56 kinds of chemicals. All of the four chemicals show the similar shape of the steady-state concentration profiles. Since lower H and Koc could make the chemical more hydrophilic and stay with the bulk liquid, lower H and koc give rise to shorter time to reach steady-state as Methyl bromide did. However, it will need much more time for Benzo(a)pyrene to reach steady-state within 6 m. Basically, the largest factor affecting advections is Koc, since Koc increases, advection decreases, while the change of H does not significantly affect advection due to that the flow moves as a wall from the beginning to the end of the region of interest if without reaction or significant dispersion/diffusion terms. Therefore, the concentration is best represented by a step function, where concentration is either fully encountered or not yet encountered. And the chemical with high Koc, e.g. Benzo(a)pyrene, will be easy to stay at the drain outlet area. Moreover, for in situ remediation, the reactions between nanoscale particles and organic contaminants involving sorption, desorption, aggregation will help to study the longterm fate of nanoscale particle, which has been rarely reported, according to the fate and transport of organic contaminants.

Conclusion
For the 56 kinds of chemicals we researched, organic carbon-water partitioning coefficient Koc has significant relationship with water solubility and molecular weight. Our calculation indicates that higher organic carbon-water partitioning coefficient results in more fraction sorbed in soil and lower fraction dissolved in water. More importantly, chemicals with high Koc will be easier for them to stay at the drain outlet area. It suggests that more effort should be taken to focus on this kind of chemicals when applying the nanotechnology removal for the drain outlet area.