The paper considers the problem of isothermal filtration of a binary hydrocarbon mixture in a porous medium, taking into account capillary pressure and the presence of retrograde regions of the phase diagram. The thermodynamic properties of the model mixture were calculated using the Peng – Robinson equations of state. The Lorentz – Bray – Clark relations were used to determine the viscosity of the phases, and the Gillespie – Lerberg equation was used to determine the chemical potentials. The functions of the relative phase permeability were specified in the form of empirical formulas of Chen Chzhun Xiang. The system of differential equations describing the modeled process was solved by the finite element method in the FlexPDE environment. It is shown that for given thermobaric conditions for filtering a binary mixture through a porous medium, time-varying changes in saturation, mixture composition, and mass flow rate of the liquid and vapor phases at the exit of the experimental model are possible. For the case of filtration of a model gas-condensate mixture of methane - butane, the problem was solved in an equilibrium and non-equilibrium formulation, and in both cases, the calculation results confirm the assumption about the cyclic formation of a liquid plug and its movement inside the simulated section. It is shown that taking into account nonequilibrium leads to a change in the pressure field along the filtration path, the amplitude and shape of the resulting self-oscillations in the flow rate of the vapor and liquid phases. These features must be taken into account when interpreting unsteady regimes of real (nonequilibrium) flows of reservoir fluids in the bottomhole formation zone. The proposed model can be used to assess the effectiveness of technologies for increasing the flow rate of gas condensate wells by affecting the bottomhole formation zone, as well as when calculating the flow rate of a well, taking into account the possibility of unsteady filtration modes.

References

1. Mitlin V.S., Self-oscillatory flow regimes of two-phase multicomponent mixtures through porous media (In Russ.), Doklady AN SSSR, 1987, V. 296, pp. 1323–1327.

2. Makeev B.V., Mitlin V.S., Self-oscillation in distributed systems: phase change filtering (In Russ.), Doklady AN SSSR, 1990, V. 310, no. 6, pp. 1315–1319.

3. Zaychenko V.M., Torchinskiy V.M., Sokotushchenko V.N., Kolebaniya i volny v gazokondensatnykh sistemakh (Oscillations and waves in gas condensate systems), Moscow: Publ. of Joint Institute for High Temperatures of the Russian Academy of Sciences, 2017, 146 p., ISBN 978-5-9500112-1-4.

4. Grigor'ev B.A., Zaychenko V.M., Molchanov D.A. et al., Math simulation of gas condensate mixture isothermal filtering for different flow patterns (In Russ.), Vesti gazovoy nauki. Aktual'nye voprosy issledovaniy plastovykh sistem mestorozhdeniy uglevodorodov, 2016, V. 28, no. 4, pp. 37–40.

5. Kachalov V.V., Molchanov D.A., Zaichenko V.M., Sokotushchenko V.N., Mathematical modeling of gas-condensate mixture filtration in porous media taking into account non-equilibrium of phase transitions, J. Phys.: Conf. Ser., 2016, V. 774, DOI:10.1088/1742-6596/774/1/012043.

6. Zemlyanaya E.V., Kachalov V.V., Volokhova A.V. et al., Numerical investigation of the gas-condensate mixture flow in a porous medium (In Russ.), Zhurnal komp'yuternye issledovaniya i modelirovanie, 2018, V. 10, no. 2, pp. 209–219.

7. Sokotushchenko V.N., Mathematical and experimental modeling filtration processes of hydrocarbons in a gas condensate reservoir (In Russ.), Vestnik Mezhdunarodnogo universiteta prirody, obshchestva i cheloveka “Dubna”. Ser. Estestvennye i inzhenernye nauki, 2018, no. 1 (38), pp. 32–38.

8. Basniev K.S., Kochina I.N., Maksimov V.M., Podzemnaya gidromekhanika (Underground hydromechanics), Moscow: Nedra Publ., 1993, 416 p.

9. PVTi referens manual, Schlumberger, 2009.1.

10. Peng D.Y., Robinson D.B., A new two-constant equation of state, Industrial and Engineering Chemistry Fundamentals, 1976, V. 15, pp. 59–64.

11. Krichevskiy I.R., Ponyatiya i osnovy termodinamiki (Thermodynamics concepts and basics), Moscow: Khimiya Publ., 1970, 440 p.

12. Gubaydullin D.A., Sadovnikov R.V., Nikiforov G.A., Chislennoe modelirovanie dvukhfaznoy fil'tratsii v peremennykh skorost' – nasyshchennost' (Numerical modeling of two-phase filtration in variables velocity – saturation), Collected papers “Aktual'nye problemy mekhaniki sploshnoy sredy. K 20-letiyu IMM KazNTs RAN” (Actual problems of continuum mechanics. To the 20th anniversary of Institute of Mechanics and Engineering), Kazan': Publ. of Institute of Mechanics and Engineering, 2011, pp. 161–180.The paper considers the problem of isothermal filtration of a binary hydrocarbon mixture in a porous medium, taking into account capillary pressure and the presence of retrograde regions of the phase diagram. The thermodynamic properties of the model mixture were calculated using the Peng – Robinson equations of state. The Lorentz – Bray – Clark relations were used to determine the viscosity of the phases, and the Gillespie – Lerberg equation was used to determine the chemical potentials. The functions of the relative phase permeability were specified in the form of empirical formulas of Chen Chzhun Xiang. The system of differential equations describing the modeled process was solved by the finite element method in the FlexPDE environment. It is shown that for given thermobaric conditions for filtering a binary mixture through a porous medium, time-varying changes in saturation, mixture composition, and mass flow rate of the liquid and vapor phases at the exit of the experimental model are possible. For the case of filtration of a model gas-condensate mixture of methane - butane, the problem was solved in an equilibrium and non-equilibrium formulation, and in both cases, the calculation results confirm the assumption about the cyclic formation of a liquid plug and its movement inside the simulated section. It is shown that taking into account nonequilibrium leads to a change in the pressure field along the filtration path, the amplitude and shape of the resulting self-oscillations in the flow rate of the vapor and liquid phases. These features must be taken into account when interpreting unsteady regimes of real (nonequilibrium) flows of reservoir fluids in the bottomhole formation zone. The proposed model can be used to assess the effectiveness of technologies for increasing the flow rate of gas condensate wells by affecting the bottomhole formation zone, as well as when calculating the flow rate of a well, taking into account the possibility of unsteady filtration modes.

References

1. Mitlin V.S., Self-oscillatory flow regimes of two-phase multicomponent mixtures through porous media (In Russ.), Doklady AN SSSR, 1987, V. 296, pp. 1323–1327.

2. Makeev B.V., Mitlin V.S., Self-oscillation in distributed systems: phase change filtering (In Russ.), Doklady AN SSSR, 1990, V. 310, no. 6, pp. 1315–1319.

3. Zaychenko V.M., Torchinskiy V.M., Sokotushchenko V.N., Kolebaniya i volny v gazokondensatnykh sistemakh (Oscillations and waves in gas condensate systems), Moscow: Publ. of Joint Institute for High Temperatures of the Russian Academy of Sciences, 2017, 146 p., ISBN 978-5-9500112-1-4.

4. Grigor'ev B.A., Zaychenko V.M., Molchanov D.A. et al., Math simulation of gas condensate mixture isothermal filtering for different flow patterns (In Russ.), Vesti gazovoy nauki. Aktual'nye voprosy issledovaniy plastovykh sistem mestorozhdeniy uglevodorodov, 2016, V. 28, no. 4, pp. 37–40.

5. Kachalov V.V., Molchanov D.A., Zaichenko V.M., Sokotushchenko V.N., Mathematical modeling of gas-condensate mixture filtration in porous media taking into account non-equilibrium of phase transitions, J. Phys.: Conf. Ser., 2016, V. 774, DOI:10.1088/1742-6596/774/1/012043.

6. Zemlyanaya E.V., Kachalov V.V., Volokhova A.V. et al., Numerical investigation of the gas-condensate mixture flow in a porous medium (In Russ.), Zhurnal komp'yuternye issledovaniya i modelirovanie, 2018, V. 10, no. 2, pp. 209–219.

7. Sokotushchenko V.N., Mathematical and experimental modeling filtration processes of hydrocarbons in a gas condensate reservoir (In Russ.), Vestnik Mezhdunarodnogo universiteta prirody, obshchestva i cheloveka “Dubna”. Ser. Estestvennye i inzhenernye nauki, 2018, no. 1 (38), pp. 32–38.

8. Basniev K.S., Kochina I.N., Maksimov V.M., Podzemnaya gidromekhanika (Underground hydromechanics), Moscow: Nedra Publ., 1993, 416 p.

9. PVTi referens manual, Schlumberger, 2009.1.

10. Peng D.Y., Robinson D.B., A new two-constant equation of state, Industrial and Engineering Chemistry Fundamentals, 1976, V. 15, pp. 59–64.

11. Krichevskiy I.R., Ponyatiya i osnovy termodinamiki (Thermodynamics concepts and basics), Moscow: Khimiya Publ., 1970, 440 p.

12. Gubaydullin D.A., Sadovnikov R.V., Nikiforov G.A., Chislennoe modelirovanie dvukhfaznoy fil'tratsii v peremennykh skorost' – nasyshchennost' (Numerical modeling of two-phase filtration in variables velocity – saturation), Collected papers “Aktual'nye problemy mekhaniki sploshnoy sredy. K 20-letiyu IMM KazNTs RAN” (Actual problems of continuum mechanics. To the 20th anniversary of Institute of Mechanics and Engineering), Kazan': Publ. of Institute of Mechanics and Engineering, 2011, pp. 161–180.