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.
Highlights
Dissolution and precipitation of minerals in reactive flows are important phenomena in many industrial and natural processes
Water-flooding operations in oil and gas industry are one of these processes where evaluation of precipitation and dissolution of minerals plays a major role in reducing potential risks
We present a streamline method for flows with two chemical reactions involving dissolution and precipitation of two salts relevant to water-flooding
Summary
Dissolution and precipitation of minerals in reactive flows are important phenomena in many industrial and natural processes. Considering the fact that the flow is dominated by trasport in these type of problems [2], Comput Geosci (2019) 23:255–271 we can effectively model the problem using a hyperbolic system of partial differential equations This class of problems is a good candidate to be used in streamline simulators. It should be noted that numerical solutions for a class of more general problems including diffusion has been studied and developed [1, 23, 24] The models in these papers have been obtained from the work of [22]. The general solution for hyperbolic systems with discontinuous functions do not exist in a closed form [17] The structure of this manuscript is as follows: Section 2 describes the physical and chemical model.
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