Xylene and ethanol present in contaminated soil (benzene) in the unsaturated zone, resulting from a spill.
Write the appropriate concentration equation PDE in the form of CDKd and list the appropriate initial and boundary conditions (See question 2 below). Similar to the analogous heat conduction case in Caraw and Jager 1959, p.100, Eq2), the concentration profile in the pore water is given by:
C(z,t) = C0 * exp(-z/δ) * erfc((z - v*t)/(2*sqrt(D*t)))
where:
C(z,t) is the concentration at depth z and time t,
C0 is the initial concentration,
δ is the depth of penetration of the concentration front,
v is the velocity of the concentration front, and
D is the diffusion coefficient.
At all times, including at t=0, concentrations are in equilibrium (NAPL vapor, water, and soil for each of the compounds). This was developed from our mass conservation equation for diffusion only (Fick's 2nd law) with initial and boundary conditions for various phases.
Boundary Conditions:
B.C.1: C(L) - C(L/K) = 0
B.C.2: C0 * sqrt(t) = 0
Note the boundary condition 2. This is due to the no-flux boundary condition at the groundwater surface.
The length-averaged concentration at any time is given by:
C(t) = (1/δ) * ∫[0 to δ] C(z,t) dz
where δ is the depth of penetration of the concentration front.
Given values:
Ct = 0.38 cm pores/cm^3
D = 16 cm^2/s
v = 0.05 cm/s
δ = 0.70 cm
C0 = 0.75 g/cm^3
K = 100 g/cm^3
T = 298 K
z = 0
Unsaturated Zone:
m-Ttplenel 3.1 NAPL (0MAPL 2.0E-05 020 2.0E-04 = 0.05) 4360 0.026 0.096 0.12 Vapor0 = 0.70) 1.02E-05 0.84E-05 3.4E-05 2.2E-05 Water0 = 0.25
Calculate the fractional mass loss for 0.10, 0.25, 0.56, 0.75, 0.90, 0.95, and 0.99 for each compound. Then make a plot with these curves (benzene, m-xylene, and ethanol) of fractional mass loss vs. time.
(cm^3-w/cm^3) (cm^3/hec) (cm^3/hec)
0.096 1.02E-05 3.4E-05
Solve for the fractional mass loss:
1 - C1 - (n/C - 1 - Cn)
4. How long would it take to deplete 99% of the benzene and m-xylene in the pores for C = 0.95, C = 0.05?
z = 0
Mass flux = 0 groundwater
