Closure to 'Integral and Closed-Form Analytical Solutions to the Transport Contaminant Equation Considering 3D Advection and Dispersion' by Luan Carlos de S. M. Ozelim and Andre Luis Brasil Cavalcante

摘要

The writers thank the discussers for being interested in the writers' paper and for the useful comments presented. First, it is of interest to review the motivation behind the work of the writers.The mathematical representation of the transport of a solute subjected to linear retardation and first-order processes in a homogeneous and isotropic aquifer during three-dimensional (3D) steady state flow with 3D dispersion can be given asR ∂c/∂t=D_(xx)∂~2c/∂x~2+2D_(xy)∂~2c/∂x∂y+2D_(xz)∂~2c/∂x∂z-v_x ∂c/∂x+D_(yy)∂~2c/∂y~3 +2d_(yz)∂~2c/∂y∂z-v_y ∂c/∂y+D_(zz)∂~2c/∂z~2-v_z ∂c/∂z-λc (1) wherein where t = time; (x, y, z) = spatial variables; c = contaminant concentration; R = retardation factor; λ = first-order reaction coefficient; v_x, v_y, and v_z = components of the steady-state groundwater velocity vector whose norm is v; v =(v_x~2+v_y~2_v_x~2)~(1/2)D_d = molecular diffusion coefficient of the soil; and α_l and α_t, = longitudinal and transverse dispersivities, respectively.