Abstract:
A coupled continuum pipe-flow (CCPF) model has been developed for groundwater flow and solute transport in a karst aquifer with conduits. Groundwater flow in conduits is simulated through a pipe flow model and flow in fissured matrix rock is described by Darcy’s law. Water mass exchange between the two domains is modeled by a firstorder exchange rate method. In this study, we investigate mathematical well-posedness (mathematical term, which means solution existence and uniqueness) of the CCPF model, develop a finite elementary method to numerically approximate the mathematical model and study the convergence of the numerical method. The study results prove the modeling approach is mathematically well posed and numerically converged. To study the accuracy of the CCPF model, a recently developed Stokes-Darcy (SD) model and CCPF model are compared with laboratory experimental results. It was found that the SD model simulations match well with experimental results, but the CCPF model overestimates the hydraulic head in the matrix, especially around the matrix and conduit interface. The model underestimates solute transport in the conduit and does not capture the plume distribution in the matrix. In comparison with the SD model, the CCPF model requires an additional parameter, the first-order mass exchange rate, and the parameter is normally obtained through inverse method curve fitting. The SD method may provide an approach to directly estimate the parameter value.