Injection of CO2 in water-flooded hydrocarbon reservoirs and in saline aquifers may require models based on high-order accurate numerical methods. For such applications, cubic equations of state (EOS) and Henry's law may not be sufficiently accurate. The association of water molecules and cross-association of water and CO2 molecules affects the phase behavior of CO2-water mixtures and requires a cubic-plus-association (CPA) equation of state (EOS). In this work, we present a new higher-order three-phase compositional model with the following features: 1) species transfer among the three phases, in particular CO2 solubility in water, 2) an implicit-pressure, explicit-composition scheme that uses the mixed hybrid finite element method to simultaneously solve for the pressure and the total volumetric flux, and a discontinuous Galerkin approximation to update mass transport, 3) Fickian diffusion, 4) efficient solution of the CPA-EOS, 5) advancement in the two-dimensional bisection method for robust phase amount computation, and 6) consistent boundary conditions for the three-phase fractional flow formalism. We present a number of numerical examples with broad applications in improved oil recovery in water-flooded oil reservoirs, and CO2 sequestration.

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