The Phase Envelope of Multicomponent Mixtures in the Presence of a Capillary Pressure Difference

Sandoval, Diego R.; Yan, Wei; Michelsen, Michael Locht; Stenby, Erling Halfdan

doi:10.1021/acs.iecr.6b00972

Cited by 61 publications

(58 citation statements)

References 22 publications

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“…Recently, capillary pressure is involved in the phase equilibrium at the NPT conditions [26,30,33,36,37] since capillarity can significantly change phase properties. However, there are very few contributions on the NVT-flash calculation incorporating capillarity effect.…”

Section: Accepted Manuscriptmentioning

confidence: 99%

A stable algorithm for calculating phase equilibria with capillarity at specified moles, volume and temperature using a dynamic model

Kou

Sun

2018

Fluid Phase Equilibria

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Section: Accepted Manuscriptmentioning

confidence: 99%

A stable algorithm for calculating phase equilibria with capillarity at specified moles, volume and temperature using a dynamic model

Kou

Sun

2018

Fluid Phase Equilibria

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“…11). In comparison with the previous formulation presented by Sandoval et al, 18 the number of equations remains the same after adding the capillary pressure effect. Moreover, if the simple parachor model for the interfacial tension in (Eq.…”

Section: Construction Of Phase Envelope With Capillary Pressurementioning

confidence: 95%

“…One such problem is equilibrium calculation involving capillary pressure effects, which has been investigated using P T -based thermodynamics. [16][17][18][19] One of the main advantages of using V T -based thermodynamics is that most of the interfacial tension models are explicit functions of V, T and n, and the derivatives w.r.t. V are simpler and more straightforward than w.r.t.…”

Section: Introductionmentioning

confidence: 99%

VT-Based Phase Envelope and Flash Calculations in the Presence of Capillary Pressure

Sandoval

Michelsen

Yan

et al. 2019

Ind. Eng. Chem. Res.

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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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“…F α i = P α ϕ α i ), instead of the fugacity coefficients ϕ α i alone to avoid undefined values during intermediate calculations. 18 After updating the capillary pressure, the K i values are calculated as follows:…”

Section: Direct Substitutionmentioning

confidence: 99%

Influence of Adsorption and Capillary Pressure on Phase Equilibria inside Shale Reservoirs

Sandoval¹,

Yan²,

Michelsen³

et al. 2018

Energy Fuels

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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.

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The Phase Envelope of Multicomponent Mixtures in the Presence of a Capillary Pressure Difference

Cited by 61 publications

References 22 publications

A stable algorithm for calculating phase equilibria with capillarity at specified moles, volume and temperature using a dynamic model

A stable algorithm for calculating phase equilibria with capillarity at specified moles, volume and temperature using a dynamic model

VT-Based Phase Envelope and Flash Calculations in the Presence of Capillary Pressure

Influence of Adsorption and Capillary Pressure on Phase Equilibria inside Shale Reservoirs

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