Compositional formulation based on piece-wise linear representation in tie-simplex space

Compositional formulations are necessary for numerical simulation of EOR (Enhanced Oil Recovery) processes, such as gas and steam injection. The coupling of the nonlinear conservation laws of multiphase flow and transport with the thermodynamic equilibrium relations poses significant challenges for compositional simulation. We describe a new framework, in which the thermodynamic phase behavior is cast in tie-simplex space as a function of composition, pressure and phase fraction. This parameter space is then used to specify the base nonlinear variables for fully-implicit compositional simulation. The compositional space is discretized using tie-lines. Thus, all the thermodynamic properties become piecewise linear functions in this space. The numerical implementation employs multilinear interpolation of the phase behavior using adaptively constructed tie-line tables. The computation of the phase behavior in the course of a compositional simulation then becomes an iteration-free procedure and does not require any EoS (flashes or phase-stability tests) computations. The efficiency and accuracy of the method are demonstrated for several multidimensional compositional problems for both miscible and immiscible displacements. For the tested problems, the proposed method reduces the computational cost of the thermodynamic calculations significantly compared with standard EOS-based approaches. Moreover, the method shows better nonlinear convergence behavior for nearmiscible gas injection displacements.