(353d) Adaptive Interpolation in Compositional Space for Flow and Transport in Porous Media

We present a Compositional Space Parameterization (CSP) method for the computation of thermodynamic phase behavior associated with multiphase compositional flow simulation. The method is based on multilinear interpolation of thermodynamic properties, including compositions, densities, and viscosities of the phases, in the discretized tie-simplex space. Here, the Equation of State (EoS) related computations are employed only for grid (supporting) points and interpolation is used for the reconstruction of the properties inside a discretization cell. The discretization of an arbitrary dimensional tie-simplex space is performed adaptively, and is based on a generalized octree technique. The computation of phase behavior in CSP is an iteration-free procedure and does not require any solution of EoS.

We demonstrate that the errors associated with interpolations are bounded. We also show that, with several assumptions, the error decreases quadratically with the tie-simplex space grid refinement. That allows for the use of only a limited number of supporting points for accurate representation of a phase behavior. Moreover, in different regions of the compositional space we can use different types of EoS including direct results of laboratory or numerical experiments.

We employ the CSP approach for efficient modeling of multicomponent compositional flow simulation in porous media. CSP here is used for acceleration of EoS computations, namely, phase stability test and multiphase flash. The computational gains are demonstrated through several challenging miscible and immiscible gas injection problems. In additions, a generalization of the method for 3-phase thermal compositional simulations is proposed.