Injection

Low-arsenic water was pumped from a deep well and injected into a shallower well with high arsenic concentrations after the addition of bromide as a tracer. Water was then withdrawn and dissolved arsenic was measured. This injection-withdrawal test was modeled by a finite difference approximation of the radial advective-dispersive transport equation, including rate-limited Langmuir or linear sorption:

where C [M/L3]is the dissolved concentration; S is the sorbed concentration [M/Ms]; alphar [L] is the radial dispersivity; r is the radial distance from the well; and v is the steady state velocity related to the pumping rate Q [L3/T] (positive for injection and negative for extraction); b [L] is the screened well thickness; and theta [-] is the porosity. A constant solute flux boundary condition was applied at the well during injection, and a zero gradient boundary condition was used during withdrawal.
Sorption-desorption was modeled both with rate-limited linear and Langmuir isotherms:

where  [T-1] is the rate coefficient, Kd [-] is the dimensionless distribution parameter for the linear isotherm; and k1 [-] and k2 [nMol As/gs] are the Langmuir isotherm constants.
The numerical simulation employed a centrally weighted Crank-Nicholson finite difference scheme including iterations for the non-linear Langmuir isotherm, and the spatial and temporal discretization was adjusted to assure that grid Peclet and Courant criteria (Pe < 2 and Cr< 1) were satisfied. The sum of squared errors between the modeled response and the observed response was minimized to estimate the following model parameters: kr, k, Kd (for the linear case), k1, k2,. Different initial guesses confirmed that the parameters converged to a unique value. The best-fit parameters were: Langmuir coefficients, k1 = 0.09, k2= 10 nMol As/gs; rate-coefficient = 0.009 hr-1; and dispersivity =2.8 cm.
Surface sorption sites appeared to be saturated with arsenic where dissolved concentrations are high. Measured dissolved arsenic concentrations were closely fit by a model that incorporates a Langmuir isotherm describing saturation of surface sites, but not by a linear isotherm. The fitted Langmuir isotherm agrees remarkably well with dissolved and sorbed arsenic concentrations measured at different depths. These results suggest that sorption sites saturate when dissolved arsenic concentrations exceed 100 ppb, and imply that, when aqueous concentrations are high, little additional arsenic can be sorbed. Further arsenic inputs would likely be manifest as increased dissolved concentrations that are readily transported by flowing groundwater. High concentrations of phosphate and silicate (approximately 50 and 700 M, and nearly uniform with depth) as well as carbonate may contribute to the limited capacity to sorb arsenic oxyanions. Iron phosphates and amorphous silica were both calculated to be supersaturated from measured aqueous concentrations, and were observed by scanning electron microscopy as rims on host grains.

Oxidant Injections (2006)
(Kai Udert supervising)