Compositional space parameterization methods for thermal-compositional simulation [electronic resource]
Keywords: Energy Resources Engineering.

Compositional simulation is necessary for the modeling of complex Enhanced Oil Recovery processes (EOR), such as gas and steam injection. Accurate simulation of these EOR processes involves coupling the nonlinear conservation laws for multicomponent, multiphase flow and transport with the equations that describes the phase behavior of the mixture at thermodynamic equilibrium. Phase-behavior modeling requires extensive computations and consumes significant time. The computational cost associated with the phase-behavior calculations increases significantly for systems where three or more fluid phases coexist at equilibrium. We present a family of methods for the computation of the thermodynamic phase-behavior associated with multicomponent, multiphase flow in porous media. These methods are based on concepts developed in the analytical theory of one-dimensional gas-injection processes. For two-phase compositional simulation, we present a Compositional Space Parameterization (CSP) framework, in which the thermodynamic phase-behavior is reformulated in the tie-simplex space as a function of composition, pressure, and phase fractions. This tie-simplex space is then used to specify the base nonlinear variables for fully-implicit compositional simulation. The tie-simplex space is discretized, and multilinear interpolation of the thermodynamic relations is employed. Thus, all the thermodynamic properties become piece-wise linear functions in the tie-simplex space. The computation of the phase behavior in the course of a compositional simulation then becomes an iteration-free procedure and does not require any Equation of State (EoS) computations (flash computations or phase-stability tests). We demonstrate that the proposed CSP method reduces the computational cost of the thermodynamic calculations significantly compared with standard EoS-based approaches. Moreover, the proposed framework is promising not only for acceleration of phase-behavior computations, but more importantly as a new thermodynamically consistent approximation for general-purpose compositional simulation. Next, for the general case of multiphase (three, and more phases) simulation, we study the importance of using EoS-based modeling for thermal reservoir simulation. Here, the EoS-based approach is compared with the industry standard K-values method. The analysis employs simple one-dimensional thermal displacements of heavy oil by a mixture of steam and solvent. This analysis shows that three-phase EoS-based computations may be necessary for accurate modeling of certain types of thermal EOR processes. Finally, we develop an extension of the CSP framework for multicomponent, multiphase thermal-compositional simulation. In particular, we present a strategy for phase-state identification that can be used to bypass the need for full three-phase EoS computations. The method uses information from the parameterized extensions of the `key' tie-simplexes and is based on the adaptive discretization of the extensions of these tie-simplexes. We demonstrate the efficiency and robustness of the developed bypass strategy for the simulation of flow and transport in thermal, three-phase compositional models of heterogeneous reservoirs.