Confined fluids such as oil and gas mixtures inside tight reservoirs are systems that can experience high capillary pressure difference between the liquid and gas phases. This capillary pressure difference has an effect on the phase equilibrium and in some cases is considerably high. We presented an algorithm which can reliably compute the whole phase envelope for multicomponent mixtures when there is a capillary pressure difference. It uses an equation of state for the phase equilibrium and the Young−Laplace equation for the capillary pressure model. The algorithm proves to be robust and efficient for test mixtures with wide ranges of compositions at different capillary radii and vapor fractions. The calculation results show that the phase envelope changes everywhere except at the critical point. The bubble point and the lower branch of the dew point show a decrease in the saturation pressure, whereas the upper branch of the dew point shows an increase. The cricondentherm is shifted to a higher temperature. We also presented a mathematical analysis of the phase envelope shift due to capillary pressure based on linear approximations. The resulting linear approximation equations can predict the correct direction of the phase envelope shift. Combined with the multicomponent Clapeyron equation, the equations reveal why the shift changes direction for the saturation pressure at the cricondentherm and for the saturation temperature at the cricondenbar. The equations can be used to estimate the magnitude of shift, and the approximation is close for the change in the bubble point pressure.

Due to the small pore sizes and organic content of shale, capillary pressure and adsorption are two effects that should be taken into account in the study of phase equilibrium inside shale. The inclusion of both effects in the phase equilibrium modeling can shed light on how bulk phase composition inside the porous media changes with temperature and pressure, and how the phase equilibrium changes accordingly. In the long run, such a model can be used in reservoir simulation for more complicated analysis. In this study, we present a calculation method that can effectively include adsorption and capillarity. We propose to introduce an excess adsorbed phase and treat the remaining substance inside the pores as a bulk phase (gas, liquid, or both) in order to make the mass balance formulation simpler. The adsorbed phase is modeled by the Multicomponent Langmuir (ML) equation for its simplicity and computational efficiency. A more theoretical adsorption model, the multicomponent potential theory of adsorption (MPTA), is used to determine the parameters of the simpler ML equation. The liquid and gas phases are described by the Peng-Robinson equation of state and 1 the capillary pressure across their interface is taken into account. A flash algorithm by alternately updating the adsorbed phase amount and the fugacities in the bulk phases has been developed. The flash algorithm is used to analyze some representative systems (from binary, ternary to low-GOR and high-GOR model reservoir fluid systems) for the phase equilibrium inside porous media. The results show that adsorption and capillary pressure can significantly change the bulk phase composition and thus its corresponding phase envelope. Since the adsorption varies at different temperature and pressure conditions, the extent of change in the phase envelope is different. In general, a much shrunk phase envelope with a shifted critical point is observed. The heavier components are preferentially adsorbed in the whole pressure and temperature range studied here. At high pressure and low temperature, the selectivity towards heavier components is moderate in comparison to the that at low pressure and high temperature. The adsorption effects are stronger for the gas bulk phase region, leading to bigger changes in the gas phase composition and the shift of the dew point curve. PVT simulations of two model reservoir fluid systems show significant change in the results when capillary pressure and adsorption are included.

Phase envelope construction and isothermal flash are two widely used phase equilibrium calculations. Because of the increasing importance of oil and gas production from shale, there is a need to perform these calculations in the presence of capillary pressure. Such calculations are also important for other processes inside porous media. Classical phase equilibrium calculations usually use P T-based thermodynamics that requires the solution of the equation of state (EoS) for the molar volume or density to calculate the desired thermodynamic properties. An alternative to this formulation is V T-based thermodynamics where repeated molar volume or density solutions are avoided by co-solving the equality of phase pressures in the equilibrium calculation. The formulation is particularly advantageous for equilibrium calculation with capillary pressure. It can naturally handle the negative pressures in the wetting phase (usually the liquid) caused by the capillary pressure. Furthermore, the capillary pressure function usually has a high level of implicitness for the pressure variable which can be circumvented in the V T-formulation. We present the V T-based formulations for 1 phase envelope construction and isothermal flash with capillary pressure. The incorporation of capillary pressure actually does not increase the number of equations since the pressure equality equation is included in the V T-based formulations without capillary pressure. Using volume as an independent variable result in simpler derivatives for the interfacial tension models, which is more suitable for cases with large capillary pressures or with saturation dependent capillary pressures that account for pore size distribution. The developed algorithms are tested for multicomponent reservoir fluid examples, including natural gas, gas condensate, and black oil, down to extremely small pore sizes. The algorithms converge with only a few Newton iterations even for the extreme cases. For the cases where pore size distribution is considered and the capillary pressure is treated as saturation dependent, the same convergence behavior is kept. This feature is especially attractive for reservoir simulation cases in which saturation dependent capillary pressure curves are used.

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