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Thermodynamic equilibrium computations are usually the most time-consuming component in compositional reservoir flow simulation. A compositional space adaptive tabulation (CSAT) approach was developed as a preconditioner for equation of state (EOS) computations in isothermal compositional simulation. The compositional space is decomposed into sub-and supercritical regions. In the subcritical region, we adaptively parameterize the compositional space using a small number of tie-lines, which are assembled into a table. The critical surface is parameterized and used to identify supercritical compositions. The phase-equilibrium information for a composition is interpolated as a function of pressure using the tie-line table. We extend the CSAT approach to thermal problems. Given an overall composition at a fixed temperature, the boundary between sub-and supercritical pressures is represented by the critical tie-line and the corresponding minimal critical pressure (MCP). A small set of subcritical tie-lines is computed and stored for a given temperature. This process is repeated for the pressure and temperature ranges of interest, and a coarse (regular) tie-line table is constructed. Close to the critical boundary, a refined tie-line table is used. A combination of regular and refined interpolation improves the robustness of the tie-line search procedure and the overall efficiency of the computations. Several challenging problems, including an unstructured heterogeneous discrete fracture field model with 26 components, are used to demonstrate the robustness and efficiency of this general tie-line-based parameterization method.Our results indicate that CSAT provides accurate treatment of the near-critical region. Moreover, the computational efficiency of the method is at least an order of magnitude better than that of standard EOS-based reservoir simulation approaches. We also show the efficiency gains relative to standard techniques as a function of the number of gridblocks in the simulation model.

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A theoretical analysis is provided of the continuity of multiphase compositional space parameterization for thermalcompositional reservoir simulation. It is shown that the tie-simplex space changes continuously as a function of composition, pressure, and temperature, and this justifies the Compositional Space Adaptive Tabulation (CSAT) framework, in which a discrete number of tie-simplexes are constructed, tabulated, and reused in the course of a simulation. The CSAT is extended for thermal-compositional displacements for mixtures that can form an arbitrary number of phases. In particular, the construction is described of three-phase tie-simplex tables, and it is shown how the degeneration of multiphase regions can be accurately captured over wide ranges of temperature and pressure. Several challenging multiphase examples are used to demonstrate the accuracy and effectiveness of phase-state identification using tabulated tie-simplexes.

Summary Enhanced Oil Recovery (EOR) processes usually involve complex phase behavior between the injected fluid (e.g., steam, hydrocarbon, CO2, sour gas) and the in-situ rock-fluid system. Several fundamental questions remain regarding Equation-of-State (EOS) computations for mixtures that can form three, or more, phases at equilibrium. In addition, numerical and computational issues related to the proper coupling of the thermodynamic phase behavior with multi-component transport must be resolved to accurately and efficiently model the behavior of large-scale EOR processes. Previous work has shown that the adaptive tabulation of tie-simplexes in the course of a compositional simulation is a reliable alternative to the conventional EOS-based compositional simulation. In this paper, we present the numerical results of reservoir flow simulation with adaptive tie-simplex parameterization of the compositional space. We study the behavior of thermal-compositional reservoir displacement processes across a wide range of fluid mixtures, pressures, and temperatures. We show that our approach rigorously accounts for tie-simplex degeneration across phase boundaries. We also focus on the complex behavior of the tie-triangles and tie-lines associated with three-phase, steam injection problems in heterogeneous formations. Our studies indicate that the tie-simplex based simulation is a potential approach for fast EOS modeling of complex EOR processes.

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Thermodynamic equilibrium computations are usually the most time consuming component in compositional reservoir flow simulation. A Compositional Space Adaptive Tabulation (CSAT) approach has been developed as a preconditioner for Equation of State (EoS) computations in isothermal compositional simulation. The compositional space is decomposed into sub- and super-critical regions. In the sub-critical region, we adaptively parameterize the compositional space using a small number of tie-lines, which are assembled into a table. The critical surface is parameterized and used to identify super-critical compositions. The phase equilibrium information for a composition is interpolated as a function of pressure using the tie-boundary between sub- and super-critical tie-lines is computed and stored for a given temperature. This process is repeated for the pressure and temperature ranges of interest, and a coarse (regular) tie-line table is constructed. Close to the critical boundary, a refined tie-line table is used. A combination of regular and refined interpolation improves the robustness of the tie-line search procedure and the overall efficiency of the computations. Several challenging problems, including an unstructured heterogeneous discrete fracture field model with 26 components, are used to demonstrate the robustness and efficiency of this general tie-line based parameterization method. Our results indicate that CSAT provides very accurate treatment of the near-critical region. Moreover, the computational efficiency of the method is at least an order of magnitude better than that of standard EoS-based reservoir simulation approaches. We also show the efficiency gains relative to standard techniques as a function of the number of gridblocks in the simulation model. Introduction Thermal recovery and gas injection processes are among the most commonly used Enhanced Oil Recovery (EOR) methods. Due to the complexity of their models, accurate and efficient simulation of thermal-compositional processes is the target of active research. Farouq Ali and Abou-Kassem (1988) presented a detailed description of the complex physical mechanisms and various numerical models for thermal recovery processes. A comprehensive review of the numerical considerations in general-purpose reservoir simulation models was presented by Wong and Azia (1988). For a general thermal-compositional simulation model, the energy balance equation as well as species conservation equations must be discretized and solved. Simultaneous solutions of the energy and mass conservation equations was first demonstrated by Coats set al. (1974). Their numerical model solved the three-phase flow of oil, water, and steam for a stream-flooding problems. Their model assumed that only the water and steam phases exchange mass. Later, Coats (1976) extended this formulation by modeling steam distillation of oil and release of solution gas. In his model, a fixed number of conservation equations is solved, where oil is represented as a mixture of solution gas, as distillable portion and nonvolatile heavy ends. Moreover, Coats assumed that the phase equilibrium rations are functions of pressure and temperature only. Natural variables (pressure, temperature, phase saturations, and component mole fractions) were used in the formulation.