Reservoir recovery processes involve complex mass and heat transfer between the injected fluid and the resident rock-fluid system. Thermal-compositional reservoir simulators can be used to plan such displacement processes, in which the phase behavior is computed with an Equation of State (EoS). These thermodynamic-equilibrium computations include phase-stability tests and flash calculations, and can consume a significant fraction of the total simulation time, especially for highly detailed reservoir models and a large number of components. Here, we propose a general Compositional Space Parameterization (CSP) method for complex mixtures, especially those where more than two fluid phases can coexist in parts of the parameter space. For a given pressure (P), temperature (T) and overall composition, a unique tie-simplex (tie-line for two phases, tie-triangle for three phases, etc.) can be defined. For a particular composition at P and T, the tie-simplex provides the necessary phase equilibrium information (i.e., phase state and phase compositions). For compositional flow simulation, a set of tie-simplexes can be calculated in a preprocessing step, or adaptively constructed during the simulation. The tie-simplex representation can be used to replace standard phase-equilibrium calculations completely, or it can be used as an initial guess for standard EoS calculations. Challenging examples with two and three phases are presented to validate this tie-simplex CSP approach. Standard EoS methods, which are widely used in industrial compositional simulators, are compared with CSP-based simulations for problems with large numbers of components and complex two- and three-phase behaviors spanning wide ranges of pressure and temperature. The numerical experiments indicate that our multi-dimensional tie-simplex representation combined with linear pressure and temperature interpolation in tie-simplex space, which is implemented as an adaptive tabulation strategy, leads to highly robust and efficient computations of the phase behavior associated with compositional flow simulation.

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