Analytical and numerical solutions for carbonated waterflooding

We develop a Riemann solver for transport problems including geochemistry related to oil recovery. The example considered here concerns one-dimensional incompressible flow in porous media and the transport for several chemical components, namely H₂O, H⁺, OH⁻, CO₂, (Formula presented.), (Formula presented.), and decane; they are in chemical equilibrium in the aqueous and oleic phases, leading to mass transfer of CO₂ between the oleic and aqueous phases. In our ionic model, we employ equations with zero diffusion coefficients. We do so because it is well known that for upscaled equations, the convection terms dominate the diffusion terms. The Riemann solution for this model can therefore be applied for upscaled transport processes in enhanced oil recovery involving geochemical aspects. In our example, we formulate the conservation equations of hydrogen, oxygen, hydrogen, and decane, in which we substitute regression expressions that are obtained by geochemical software. This can be readily done because Gibbs phase rule together with charge balance shows that all compositions can be rewritten in terms of a single composition, which we choose to be the hydrogen ion concentration (pH). In our example, we use the initial and boundary conditions for the carbonated aqueous phase injection in an oil reservoir containing connate water with some carbon dioxide. We compare the Riemann solution with a numerical solution, which includes capillary and diffusion effects. The significant new contribution is the effective Riemann solver we developed to obtain solutions for oil recovery problems including geochemistry and a variable total Darcy velocity, a situation in which fractional flow theory does not readily apply. We thus obtain an accurate solution for a carbonated waterflood, which elucidates some mechanisms of low salinity carbonated waterflooding.