Three‐phase compositional modeling of CO₂ injection by higher‐order finite element methods with CPA equation of state for aqueous phase

Abstract

.[1] Most simulators for subsurface flow of water, gas, and oil phases use empirical correlations, such as Henry's law, for the CO 2 composition in the aqueous phase, and equations of state (EOS) that do not represent the polar interactions between CO 2 and water. Widely used simulators are also based on lowest-order finite difference methods and suffer from numerical dispersion and grid sensitivity. They may not capture the viscous and gravitational fingering that can negatively affect hydrocarbon (HC) recovery, or aid carbon sequestration in aquifers. We present a three-phase compositional model based on higher-order finite element methods and incorporate rigorous and efficient three-phase-split computations for either three HC phases or water-oil-gas systems. For HC phases, we use the Peng-Robinson EOS. We allow solubility of CO 2 in water and adopt a new cubic-plus-association (CPA) EOS, which accounts for cross association between H 2 O and CO 2 molecules, and association between H 2 O molecules. The CPA-EOS is highly accurate over a broad range of pressures and temperatures. The main novelty of this work is the formulation of a reservoir simulator with new EOS-based unique three-phase-split computations, which satisfy both the equalities of fugacities in all three phases and the global minimum of Gibbs free energy. We provide five examples that demonstrate twice the convergence rate of our method compared with a finite difference approach, and compare with experimental data and other simulators. The examples consider gravitational fingering during CO 2 sequestration in aquifers, viscous fingering in water-alternating-gas injection, and full compositional modeling of three HC phases.Citation: Moortgat, J., Z. Li, and A. Firoozabadi (2012), Three-phase compositional modeling of CO 2 injection by higher-order finite element methods with CPA equation of state for aqueous phase, Water Resour. Res., 48, W12511,

Numerical Modeling of Methane Leakage from a Faulty Natural Gas Well into Fractured Tight Formations

“…Discrete fractures are represented by a cross-flow equilibrium (CFE) approach, which is discussed in more detail later. The powerful features of this combination of finite-element methods has been demonstrated extensively in previous works (Moortgat and Firoozabadi 2010, 2013cMoortgat et al 2011Moortgat et al , 2012Shahraeeni et al 2015;Nasrabadi et al 2016).…”

“…The powerful features of this combination of finite-element methods has been demonstrated extensively in previous works (Moortgat and Firoozabadi 2010, 2013cMoortgat et al 2011Moortgat et al , 2012Shahraeeni et al 2015;Nasrabadi et al 2016). Specifically, the Mixed Hybrid Finite-Element (MHFE) method guarantees globally continuous pressure and velocity fields, even for highly heterogeneous and fractured media, discretized by unstructured hexahedral grids.…”

“…Here, we develop numerical models that utilize the cubic-plus-association equation of state (CPA-EOS, Li and Firoozabadi 2009;Moortgat et al 2012), which accounts for the self-association of water and the polar-induced cross-association between water and methane molecules. This approach is more accurate than those based on Henry's law, or alternatives such as the widely used Peng-Robinson EOS, and has not been used to model this type of problem before.…”

“…We model the thermodynamic phase behavior of hydrocarbon water mixtures with the accurate CPA-EOS, which takes into account the polar nature of water molecules, its self-association, and the polar-induced cross-association between water and methane molecules (Li and Firoozabadi 2009;Moortgat et al 2012). Other hydrocarbons do not associate with water.…”

Solutal convection in porous media: Comparison between boundary conditions of constant concentration and constant flux

“…The aqueous phase viscosity is insensitive to pressure and CO 2 compositions and is assumed to only depend on temperature T (K). We use the correlation µ(cP) = 0.02141 × 10 247.8/(T (K)−140) ∼ 0.3654 [25]. The Boussinesq approximation originally expresses that (i ) density fluctuations result principally from thermal effects-analogous to dissolution here-rather than pressure effects, and (ii ) density variations are neglected except when they are coupled to gravity (i.e., in the buoyancy force, −ρ g) [38,39].…”