Question

Contaminant sorption and flow in subsurface environment (12 points) An aquifer is contaminated due to a recent spill of a certain industrial solvent. The aquifer has a hydraulic head difference of 0.01 m as measured by two piezometers about 2 m apart along the direction of groundwater flow. The aquifer has a porosity of 0.3, organic carbon (foc) of 1.7%, soil particle density of 2.6 g/cm, and hydraulic conductivity (K) of 2.5 x 10-3 cm/sec The solvent has a log Koc of 2.1 mL/g. (Useful formula: Ka-foc Koc; ρ,-(1-n) ρ.) (a) Estimate distribution coefficient Kd in mL/g (b) Estimate the bulk density of the aquifer material in g/cm3 (c) Estimate the retardation factor R (d) Estimate the Darcy's velocity, groundwater flow velocity, and the traveling velocity of the solvent. Express your results in cm/day. (e) Estimate time needed for a cloud of solvent, dissolved in water, moves along a saturated porous medium 2 m in length. Express your result in years

Answer 1

According to the given data, log(K_oc) = 2.1 mL/g. Thus, K_oc = 125.9 mL/g
a) The distribution coefficient, K_d = f_oc * K_oc = 0.017 * 125.9 mL/g = 2.14 mL/g

b) Bulk density of the aquifer material, $\rho$_b = $\rho$_s(1-n) ; where $\rho$s: particle density and n: porosity
= 2.6 * (1-0.3) = 1.82 g/cm³

c) Retardation factor, R = 1 + ($\rho$_b /n)(K_d) = 1 + (1.82/0.3)(2.14) = 13.98

d) Darcy's velocity, V_D = K (Difference in hydraulic head between two lateral points / Length between two lateral points)
= 2.5 x 10^-3 x (0.01/2) cm/sec = 1.25 x 10^-5 cm/sec = 1.25 x 24 x 3600 x 10^-5 cm/day = 1.08 cm/day
Groundwater flow velocity = V_D/n = 1.08/0.3 = 3.6 cm/day
e) Time needed = 2 / (3.6 x 10^-2 ) = 55.55 days = 0.152 year