Compositional Simulation Using an Advanced Peng-Robinson Equation of State
- Yizheng Wei (U. of Calgary) | Zhangxin John Chen (U. of Calgary) | Marco Satyro (University of Calgary) | Chao Charlie Dong (U. of Calgary) | Hui Deng (U. of Calgary)
- Document ID
- Society of Petroleum Engineers
- SPE Reservoir Simulation Symposium, 21-23 February, The Woodlands, Texas, USA
- Publication Date
- Document Type
- Conference Paper
- 2011. Society of Petroleum Engineers
- 5.5.1 Simulator Development, 5.2.2 Fluid Modeling, Equations of State, 5.2.1 Phase Behavior and PVT Measurements, 5.5 Reservoir Simulation, 4.1.1 Process Simulation, 5.4.9 Miscible Methods, 5.3.1 Flow in Porous Media, 5.3.2 Multiphase Flow
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During compositional reservoir simulations where underground fluid composition strongly affects the modeling of recovery processes, flash calculations are commonly employed to help determine the correct number of equilibrium phases, the corresponding compositions, and the phase amount of each phase.
Cubic equations of state (EOS) are widely used in the representation of volumetric and phase equilibria due to their simplicity and solvability. Commonly used cubic EOS such as Peng-Robinson (PR) and Soave-Redlich-Kwong (SRK) have well known limitations in predicting liquid phase properties for polar compounds.
In this paper, we present a compositional reservoir simulator equipped with the advanced Peng-Robinson EOS and an efficient and robust multiphase flash algorithm that can accurately predict the phase equilibrium. This method utilizes Michelsen's stability test (Michelsen, 1982) and a combination of accelerated successive substitution and a minimum-variable Newton-Raphson (MVNR) method for fast convergence.
The advanced Peng-Robinson (APR) EOS adds volume translation and a flexible attractive temperature-dependent term to the original PR EOS for accurate PVT and saturation property correlation for polar compounds. Examples of pure compounds and mixtures are tested. Computational results show that the developed simulator provides a more detailed description and better understanding of complex dynamic underground fluid phase behavior that may occur during oil recovery processes.
Compositional models are commonly used to simulate complex multiphase flow in a reservoir where phase compositions at equilibrium change with space and time, and an equation of state (EOS) is employed in the models to determine the correct number of equilibrium phases and the corresponding compositions in each phase in each grid block.
Since the late 1970s, many isothermal compositional models using cubic equations of state and taking into account up to three phases (water, gas and oil) have been developed. They are different in how the primary equations and unknowns are selected (Cao, 1999). Fussell and Fussell (1979) published a technique which used a minimum variable Newton-Raphson method to solve a system consisting of fugacity equations and a saturation constraint equation for primary variables: pressure, liquid phase mole fraction, liquid phase composition or pressure, vapor phase mole fraction, and vapor phase composition. Coats (1980) described a fully implicit compositional model which solved material balance equations for hydrocarbon components and water simultaneously. Nghiem et al. (1981) developed an implicit-pressure, explicit-composition, and explicit-saturation model with an EOS. These equations were solved using an iterative-sequential method. Pressure was first obtained by solving a material balance equation and the other unknowns were updated thereafter. Young and Stephenson (1983) presented a more efficient Newton-Raphson method-based procedure which differed from Fussell and Fussell's in the ordering of the equations and unknowns. In summary, a fully implicit model provides better stability; it, however, requires higher computational cost. For a partially implicit model, the implicitness varies with the selection of primary unknowns to be solved for and the choice of reasonable time steps becomes the key point in controlling convergence of the Newton-Raphson iteration and accelerating simulation process (Chen et al., 2006).
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