Improvements and corrections to AT123D code.

Although based on exact analytical solutions, semi-analytical solute transport models can have significant numerical error in applications with high frequency oscillatory source terms and when parameter value combinations cause series solution approximations to converge slowly. Methods for correcting these numerical errors are presented and implemented in the AT123D code, which employs Green's functions to represent point, linear, and rectangular prismatic source zones. In order to increase its computational accuracy, a Romberg numerical integration scheme was added to AT123D with prespecified error criteria, variable time stepping, and partitioning of the integral to handle rapidly changing source terms. More rapidly converging series solution approximations for the Green's functions were also incorporated to improve both accuracy and computational efficiency for finite-depth aquifers. AT123D also has been modified to eliminate redundant calculations at points where approximate steady-state conditions have been reached to improve computational efficiency during numerical integration. These modifications help to decrease computer run times that can be excessive for three-dimensional problems with large numbers of computational points, small time steps, and/or long simulation time periods. Errors in the original AT123D code also were corrected in this modified version, AT123D-AT, in order to accurately simulate finite-duration (pulse) source releases.

Analytical models of steady-state plumes undergoing sequential first-order degradation.

An exact, closed-form analytical solution is derived for one-dimensional (1D), coupled, steady-state advection-dispersion equations with sequential first-order degradation of three dissolved species in groundwater. Dimensionless and mathematical analyses are used to examine the sensitivity of longitudinal dispersivity in the parent and daughter analytical solutions. The results indicate that the relative error decreases to less than 15% for the 1D advection-dominated and advection-dispersion analytical solutions of the parent and daughter when the Damköhler number of the parent decreases to less than 1 (slow degradation rate) and the Peclet number increases to greater than 6 (advection-dominated). To estimate first-order daughter product rate constants in advection-dominated zones, 1D, two-dimensional (2D), and three-dimensional (3D) steady-state analytical solutions with zero longitudinal dispersivity are also derived for three first-order sequentially degrading compounds. The closed form of these exact analytical solutions has the advantage of having (1) no numerical integration or evaluation of complex-valued error function arguments, (2) computational efficiency compared to problems with long times to reach steady state, and (3) minimal effort for incorporation into spreadsheets. These multispecies analytical solutions indicate that BIOCHLOR produces accurate results for 1D steady-state, applications with longitudinal dispersion. Although BIOCHLOR is inaccurate in multidimensional applications with longitudinal dispersion, these multidimensional multispecies analytical solutions indicate that BIOCHLOR produces accurate steady-state results when the longitudinal dispersion is zero. As an application, the 1D advection-dominated analytical solution is applied to estimate field-scale rate constants of 0.81, 0.74, and 0.69/year for trichloroethene, cis-1,2-dichloroethene, and vinyl chloride, respectively, at the Harris Palm Bay, FL, CERCLA site.