Streamline simulation of a reactive advective flow with discontinuous flux function

Abstract

Reactive transport in porous media with dissolution and precipitation has important applications in oil and gas industry and groundwater remediation. In this work, we present a simulation method for reactive flow in porous media of two salts that share an ion. The method consists of a front-tracking solver that uses the Riemann solutions of the underlying set of hyperbolic partial differential equations. In addition to the discontinuities stemming from the nonlinearities of the flux function, the flux function for the corresponding advection reaction equation also admits discontinuities for a heterogeneous medium. Here, we solve the Riemann problem for the governing nonlinear hyperbolic system with a discontinuous flux function. We use mass balance across the interface and the non-decreasing sequence of velocity of waves to seek the unique solution for this problem. Furthermore, a model is provided for mixing of streamlines at the well to estimate the amount of precipitate. In the use of streamline methods, we have modified the definition of time-of-flight to allow the model to be easily utilised for the heteregeneous case. The simulation method is applied to model dissolution through injection of an unsaturated fluid. It is shown that the first dissolution shock, which causes induced precipitation due to the co-ion effect, results in accumulation of precipitate at the well.