4. DEVELOPMENT OF MICROPOLLUTANT MODEL
4.2 PAH fate and transport model
The model considered the air-soil exchange of both particulate and gaseous phases of PAHs, which included deposition (dry, wet, and dry gaseous) and volatilization. The dry deposition flux of particulate PAH, Fdry,p[ng m-2d-1], was determined by the following equation:
, = × , (5)
where, Vd is the dry deposition velocity [m d-1] while, Cair,p is the particle-bound concentration per volume of air [ng m-3].
The wet deposition fluxes for the gaseous and particulate PAHs, Frain,g[ng m-2d-1] and Frain, p[ng-m-2-d-1] respectively, were calculated using the following equations (Bergknut et al., 2010):
, = , × × , (6)
, = , × × , (7)
where, Wrainis the washout ratio [-], GRis the precipitation rate [m d-1], and Cairis the concentration of PAH in air [ng m-3of air].
The fugacity method was then implemented to calculate air-soil exchange fluxes of the gaseous PAH compounds. Fugacity (f[Pa]) is the tendency of a chemical to escape from a phase and can be related to concentration using a fugacity capacity constant Z [mol m-3Pa-1] (Donald Mackay & Paterson, 1981). The fugacity-driven concentration, C[mol m-3], was computed using the equation (Don MacKay, 2004):
= × (8)
Since chemicals tend to establish equilibrium with their environment, the equilibrium status of PAH between the air and soil phases in this study can be assessed by determining their fugacity fractions, ff:
= /( + ) (9)
On the other hand, Zvalues of air (Za) and soil (Zs) can be determined from the physical-chemical properties of the compound and were calculated using the following equations (Bergknut et al., 2010):
= 1/ (10)
= × × × (11)
= 1/ (12)
= 0.35 (13) where, Ris the ideal gas constant [Pa m3mol-1 K-1], T is the temperature in Kelvin, focis the organic carbon fraction in soil, Kocis the organic carbon-water partition coefficient [L kg-1], ρis the soil density [kg L-1], Zwis the fugacity capacity for water [mol m-3Pa-1], His the Henry’s Law constant [Pa m3mol-
1], and Kowis the octanol-water partition coefficient.
The fugacity approach incorporated the dry gaseous deposition and volatilization processes of PAH.
The net diffusive flux N [mol m-2 h-1] from soil to air was calculated using the following equations (Bergknut et al., 2010):
= ( − ) (14)
where, Dvis the D-value for PAH transport across the air-soil interface [mol Pa-1h-1], respectively; fsis the fugacity of PAH in soil (from Eq. 4); and fais the fugacity of PAH in air (from Eq. 4). D-values are similar to rate constants that describe the rates of transport and transformation of chemicals (Sweetman, Cousins, Seth, Jones, & Mackay, 2002). Dry gaseous deposition and volatilization were represented by the D-values across air to soil and soil to air, respectively. The direction of the flux for each day was determined by the fugacity threshold; if ff (from Eq. 1) is less than 0.5, the direction for the D-value will be from air to soil (deposition) else, the direction will be from soil to air (volatilization). The appropriate daily D-value of each compound was determined in order to calculate for the net flux of the compound.
4.2.2 Air-Water Interaction
The same fugacity method was applied for the air-water exchange fluxes of the PAH compounds.
Eq. 5and Eq. 10were used to compute for ffand Nawof the air-water interface.
4.2.3 Soil-Water Interaction
The PAH compounds on the soil that were transported to the channel were assumed as the concentration of the exported suspended particles of PAHs from the saturated soils of the TR watershed to the river. The suspended particles concentrations were estimated using the three-phase partitioning model that included the freely dissolved PAHs and the PAHs adsorbed on dissolved organic carbon (DOC, described as the organic carbon particle that has a particle size between 0.22 and 0.45 μm (Ogura, 1970)) and particles. Runoff and degradation of PAH compounds were also considered and incorporated in the three-phase partitioning model which are discussed in detail in this section.
The total PAH and dissolved PAH concentrations in the bulk saturated soil, Cbst and Cbsd
respectively [kg L-1bulk soil], are defined by the following equations (Bergknut et al., 2010):
= + (15)
= + (16) where, Cbstis the total PAH concentration in the bulk soil [kg L-1bulk soil], Cbsp is the concentration of particle-bound PAH [kg L-1 bulk soil], Cbsfd is the freely-dissolved PAH, and CbsDOC is the DOC- associated PAH. Combining both equations will yield:
= + + (17)
Cbsp and CbsDOCcan be related to the freely-dissolved PAH and are expressed by (Bergknut et al., 2010):
= × × (18)
= [ ] × × (19)
[ ] = × (20)
where, rswis the soil-to-water ratio [kg L-1], Kswis the soil-water distribution coefficient [L kg-1], KDOCis the dissolved organic carbon-water partition coefficient [L kg-1], fDOCis the fraction of DOC, and OMis the concentration of the organic matter (kg L-1). Using SWAT parameters, OM was determined by dividing the mass of the soil carbon in the soil organic matter with the water yield. The ratio and the coefficient are given by the equations (Bergknut et al., 2010):
= × (21)
= × (22)
where, ρis the density of the solid matrix [kg m-3], ϕis the porosity, and focis the organic carbon fraction.
Cbsp, Cbsfd, and CbsDOC from Eq. 8 can also be determined by using the PAH bulk in soil fractions (Bergknut et al., 2010):
= × × exp − (23)
= × × exp − (24)
= × × exp(− ) (25)
where, fp[-], Wcp[kg L-1bulk soil], and μp[s-1] are the fraction, washoff load, and rate constant of particle- bound PAH, fd f[-], Wcf[kg L-1bulk soil], and μf[s-1] are the fraction, washoff load, and rate constant of freely-dissolved PAH, and fdDOC[-], Wcf[kg L-1bulk soil], and μDOC[s-1] are the fraction, washoff load,
and rate constant of DOC-bound PAH. The washoff loads (Eqs. 18-20) and fractions (Eqs. 21-24) of the PAHs are discussed below.
Considering the runoff of suspended particles to the main river, the PAH loading that ended up in the river was determined using the equation:
= × × (26)
= × × (27)
= × × (28)
where, Wcp, Wcf, and WcDOC are the washoff loads of the particle-bound, free-dissolved, and DOC- associated PAHs exported to the river via runoff [kg L-1bulk soil]; Cp1, Cf1, and CDOC1are the washoff coefficients for the particle-bound, free-dissolved, and DOC-associated PAHs [-],qis the runoff rate per unit area; and Cp2, Cf2, and CDOC2are the washoff exponents for the particle-bound, free-dissolved, and DOC-associated PAHs [-], respectively.
The sum of the fractions in Eq. 23-25 above is 1 and they can be calculated by the following equations (Bergknut et al., 2010):
= [ ] (29)
= [ ] (30)
= [ ][ ] (31)
+ + = 1 (32)
Degradation of PAH compounds was also considered in the model and is represented in Eqs. 15-17 above as a temperature-dependent rate constant, μ. The equations observed a first-order reaction for the particle-bound (p), freely-dissolved (f), and DOC-associated (DOC) PAH compounds. The rate constant for each phase was determined by the equation:
= × ( ) (33)
where, μiis the initial rate constant for the PAH compounds [s-1], θis the temperature adjustment factor for PAH compounds [-], and T is the temperature [°C]. μ and θ were then calibrated for the particle- bound, free-dissolved, and DOC-associated PAHs.
PAH loadings of the model were computed by (Bergknut et al., 2010):
= , (34)
= + , (35)
= , × ( ) , (36)
where, Cpand Cware the PAH loadings in soil (PAH per solid mass) and in water (PAH per fluid mass), respectively; Cbs,out p is the concentration of the particle-bound PAH in the bulk soil that will be transported to the channel [kg L-1bulk soil]; Cwfinalis the concentration of PAH transported from the soil to the water body after enrichment; and the two coeffenratioare the enrichment ratio coefficients (Neitsch et al., 2011).
4.2.4 PAH in Water
The PAH compounds are subjected to advection, dispersion, photodegradation, and settling upon reaching the channel. These processes were considered in calculating each PAH concentration in water.
The advection-dispersion equation was modified by adding the photodegradation term (aI) and the net diffusive flux between the air and water interface (Naw). The following describes the modified advection-dispersion equation used for the model:
+ = − ( + ) + (37)
where, Cis the PAH concentration in water [g m-3], tis time [second], x is distance [m], uis the water velocity [m s-1], DLis the dispersion coefficient [m2s-1] , fis the fraction of the particulate PAH in water [-], vs is the settling velocity [m s-1], h is the depth of the channel [m], a is the photodegradation coefficient [m2MJ-1s-1], and Iis the solar intensity [MJ m-2]. Nawis the water-air exchange of PAH [g- m-3s-1]. u was the SWAT simulated flow velocity from 2011 to 2012 of the Taehwa River Stations while vswas a fixed value of 4.16E-6 m-s-1(Beck, 1973; Cho et al., 2010).
Eq. 37was simulated at a spatial increment (dx) of 100 meters along the channel and a time step (dt) of 1 hour. Considering the increment of 100 meters, the channel was segmented into 300 cells. The initial condition was the first simulation of PAH concentration at the upstream boundary of the channel.
The lateral input of PAH to each cell was exported from the soil to water (Cwfinal) resulting from Eq. 36.
The Crank-Nicolson method, which can solve partial differential equations, was then used to obtain the PAH concentration in water. To achieve a more accurate result, a stability analysis was performed using the condition (Isaacson & Keller, 1994):
×∆
(∆ ) < 0.5 (38)
where DLis the dispersion coefficient (m2s-1), tis the time (s), and xis the distance (m).
4.3 Pesticide fate and transport model