Discussion of “Integral and Closed-Form Analytical Solutions to the Transport Contaminant Equation Considering 3D Advection and Dispersion” by Luan Carlos de S. M. Ozelim and André Luís Brasil Cavalcante
where t 5 time; (x, y, z) 5 variables of the Cartesian coordinate system; c 5 contaminant concentration; R 5 retardation factor; l 5 first-order reaction coefficient; v5 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi vx 1 vy 2 1 vz p in which vx, vy, and vz are the components of the groundwater velocity v in the x, y, and z directions, respectively; Dd 5 molecular diffusion coefficient of the formation; al and at 5 longitudinal and transverse dispersivities, respectively; and the matrix defines the components of the dispersion coefficient tensor. The authors assumed that al=at 5 1 (i.e., al 5at) and the flow velocity is steady and uniform; therefore, Eq. (1) reduces to