Abstract
This work proposes a locally conservative and less restrictive algorithm to solve the problem dealt with in [1], i.e. a two-phase flow in a homogeneous porous medium (water and CO2), with mass absorption between the fluid phases and reaction between the CO2 phase and the rock. The latter is modeled by two non-linear hyperbolic equations that represent the transport of the flowing phases for a given velocity field (equations of saturation and concentration). From the numerical point of view, we use the operator splitting technique to properly treat the time scale of each physical phenomenon and a high-order non-oscillatory central-scheme finite volume method for nonlinear hyperbolic equations proposed by [2] that was extended for a system of equations with source terms to treat the equations that govern the saturation and concentration of phases. In addition, with respect to source terms, the mass flux between fluid phases was handled using the flash methodology, whereas kinetic theory was applied for reproducing the changes in porosity and permeability that are caused by the reaction of CO2 with the rock. The same physical trends observed in [1] were obtained in our numerical results which indicate a good predictive capability. Furthermore, this method avoids the difficulties that arise when adopting small time steps enforced by CFL stability restrictions. Finally, the results obtained show that the applicability of the KT method is beyond just a single nonlinear conservation law with the absence of source terms.
Highlights
The results obtained show that the applicability of the KT method is beyond just a single nonlinear conservation law with the absence of source terms
The KT method proposed by Kurganov and Tadmor [2] was developed for the nonlinear conservation laws, given by Equation (6), to a field of constant porosity φ
During 20 years, the CO2 was injected in a homogeneous porous media and the saturation profiles were recorded after the injection stopped for three cases: 1) disregarding dissolution and reaction, the flow is due to advection and dispersion only, non reactive rock, such as quartz, is considered, 2) allowing dissolution but no reaction, and 3) both effects considered
Summary
Models of geological CO2 sequestration should consider multiphase flows, equilibrium and non-equilibrium reactions, and partition phases in reservoirs This is a prominent problem that has been investigated by several researchers: Meer [5] [6] [7], Holt et al [8], Weir et al [9], Law and Bachu [10], Lindberg [11], Johnson et al [12], Ennis-King and Paterson [13], Wellman et al [14], Pruess et al [15], Xu and Pruess [16] and Kumar et al [17]. With respect to source terms, the mass flux between fluid phases was treated using the flash methodology (see [27]) and the reaction of CO2 with rock which causes changes in porosity and permeability, was treated by applying principles of kinetic theory (see [14])
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