Hyperbolic Reformulation Approach to Enable Efficient Simulation of Groundwater Flow and Reactive Transport

Abstract

We apply Cattaneo's relaxation approach to the one-dimensional coupled Boussinesq groundwater flow and advection-diffusion-reaction equations, commonly used in engineering applications to simulate contaminant transport in the subsurface. The diffusion-type governing equations are reformulated as a hyperbolic system, augmented by an equation that can be interpreted as a momentum balance. The hyperbolization enables an efficient unified computation of the primary variable and its gradients, for example piezometric head and unit discharge in the Boussinesq equation. An augmented Roe scheme is used to solve the hyperbolic system. The hyperbolized system of equations is studied in a set of steady state and transient test cases with idealized geometry. These test cases confirm the equivalence of the hyperbolic system to its original formulation. The larger time step size of the hyperbolic equation is verified theoretically by means of a stability analysis and numerically in the test cases. Finally, a reach-scale application of flow and transport across a river meander is considered. This application case shows that the performance of the hyperbolic relaxation approach holds for more realistic groundwater flow and transport problems, relevant to water resources management.

Modeling reactive flow dynamics of gelled acid in fracture-vuggy carbonates: a coupled thermal-hydrological-chemical simulation

“…Reactive flow within porous media is a critical phenomenon exerting significant influence on a diverse array of geological and chemical processes, as well as engineering applications [1]. It lies at the core of comprehending processes such as diagenesis [2][3][4], karstification [5][6][7], geologic sequestration of carbon dioxide [8][9][10][11], contaminant transport in groundwater resources [12][13][14], safe disposal of nuclear waste [15], and the acidizing treatment of reservoir [16][17][18]. To investigate the reaction-dissolution mechanism of acid in porous media, researchers have conducted numerous experimental studies [19][20][21][22][23].…”