Modeling Tools for Environmental Engineers and Scientists

of mass M (M), applied at x = 0 and t = 0 to an initially pristine aquifer over anarea A (L 2 ), the solution to Equation (6.13) has been reported to be as follows: x – u tC =MR– exp – k R 2 t (6.14)2AπERt R 4 EtRStep input, 1-D flow with first-order consumptive reactionA continuous steady release of a biodegradable chemical originating att = 0 into an initially pristine aquifer can also be described adequately by thesimplified Equation (6.13). For example, leakage of a biodegradable chemicalinto the aquifer from an underground storage tank can be simulated bytreating it as a step input load. The appropriate boundary and initial conditionsfor such a scenario can be specified as follows:BC: C(0, t) = C o for t > 0 and ∂ C = 0∂xIC: C(x,0) = 0 for x ≥ 0for x = ∞Under the above conditions, assuming first-order biodegradation of the dissolvedconcentration, C, the solution to Equation (6.13) has been reported tobe as follows:C C o2 exp (u – ) (Rx – t)x2Derf 2DRt + C o2 exp (u – )2Dx erf (6.15)where = u 1 + 4 kD2u Additional numerical solutions for other special cases are included inAppendix 6.1 at the end of this chapter.Worked Example 6.5(Rx – t)2DRt An underground storage tank at a gasoline station has been found to beleaking. Considering benzene as a target component of gasoline, it is desiredto estimate the time it would take for the concentration of benzene to rise to10 mg/L at a well located 1000 m downstream of the station. Hydraulic conductivityof the aquifer is estimated as 2 m/day, effective porosity of theaquifer is 0.2, the hydraulic gradient is 5 cm/m, and the longitudinal dispersivityis 8 m. Assume the initial concentration to be 800 mg/L.© 2002 by CRC Press LLC