New analytical models of subsurface reactive transport with transient flow field, time-dependent source concentration, and arbitrary initial condition

Abstract

Flow velocity, source concentration, or initial condition is treated as constant in previous advection–diffusion-reaction (ADR) analytical models for subsurface reactive transport. Such parameters may vary temporally and spatially, and therefore constants limit the application of ADR models. In this study, an ADR model is developed, considering transient flow fields, time-dependent source concentrations, and arbitrary initial conditions. A general analytical solution is derived by Green’s function method, where the flow velocity, source concentration, and initial condition are described by arbitrary continuous functions. The specific solutions are presented under three types of flow velocity models represented by the linear, exponential, and trigonometric functions. The new analytical models of this study are the extensions of many previous ones, and the robustness is tested by the laboratory-controlled experimental data. When compared with previous analytical solutions, findings from this study indicate that flow velocity, initial conditions, and source concentrations produce profoundly different model results of subsurface reactive transport, indicating that the transient properties of these model parameters should not be treated as constant. Similar to many previous analytical solutions, the limitation of the new analytical model is to use the temporally-dependent model to approximate the spatiotemporal variation of flow velocity. To test the influence of such assumptions on breakthrough curves (BTCs), the finite-element solution of the transient subsurface flow and reactive transport models is employed. Results show that the temporally-dependent model could be used to approximate the spatiotemporally-dependent velocity variation when the hydraulic diffusivity is greater than 5×105 m2d-1. Sensitivity analysis demonstrates that the most sensitive parameter on the output BTCs is the retardation factor, followed by parameters related to chemical reactions, dispersion, flow velocity, and the source concentration.