Simulation of the interface motion between two immiscible liquids under flow diverter technologies conditions

Authors: E.O. Sazonov (Bashneft-Dobicha LLC, RF, Ufa)

Key words: diverter technologies, interphase boundary motion, conformance control, Lambert W-Function.

The present study considered the problem of the interface motion between two immiscible liquids. The solution of this problem for applications of flow diverter technology would be evaluation basis of the hydrodynamic medium properties changing over time, such as the fluid mobility, the saturation, pressure distribution, mean resistance and conductivity. The results were obtained for two types of filtration: radial and linear one. First case describes the physics for liquids flowing to well galleries, second - the process of contour contraction or a motion into the formation. Analytical solution for the radial case was derived for the first time. A method to assess the degree of injectivity profile smoothing after the flow diverter technologies.
References
1. Dake L.P., The Practice of reservoir engineering (Revised Edition), Elsevier
Science, 2001, 570 p.
2. Willhite G.P., Waterflooding, SPE Textbook Series, 1986.
3. Dubinov A.E., Dubinova I.D., Saykov S.K., W-funktsiya Lamberta i ee primenenie v matematicheskikh zadachakh fiziki (Lambert w function and its application in mathematical physics problems), Sarov: Publ. of RFYaTs-VNIIEF, 2006, 160 p.
4. Corless G.H., Gonnet R.M., Hare D.E.G. et al., On the lambert w function,
Advances in Computational Mathematics, 1996, V. 5, pp. 329–359.
5. Scott T.C., Fee G., Grotendorst J., Asymptotic series of generalized lambert
w function, IGSAM, ACM Special Interest Group in Symbolic and Algebraic
Manipulation, 2013, V. 47 (185), pp. 75–83.
6. Aziz K., Settari A., Petroleum reservoir simulation, Elsevier Applied Science
Publishers, 1986.
7. Dake L., Fundamentals of reservoir engineering, URL:
http://books.google.ru/books?id=grQAlQEACAAJ.
8. Chen Z., Reservoir simulation mathematical techniques in oil recovery,
Philadelphia: Society for industrial and applied mathematics, 2007, 250 r.
9. Craig F., Reservoir engineering aspects of waterflooding, H. L. Doherty
Memorial Fund of AIME, 1971, 164 p.
10. Muskat M., The flow of homogeneous fluids through porous media, Mc-
Graw-hill book company, Inc., 1937, 782 p.
11. Charnyy I.A., Podzemnaya gidrogazodinamika (Underground hydraulic
gas dynamics), Moscow – Leningrad: Gostoptekhizdat Publ., 1963, 396 p.
12. Leybenzon L.S., Dvizheniya prirodnykh zhidkostey i gazov v poristoy srede (Natural liquids and gases movement in a porous medium), Moscow –
Leningrad: OGIZ, Gosudarstvennoe tekhniko-teoreticheskoe izdatel'stvo
Publ., 1947, 244 p.

Key words: diverter technologies, interphase boundary motion, conformance control, Lambert W-Function.

The present study considered the problem of the interface motion between two immiscible liquids. The solution of this problem for applications of flow diverter technology would be evaluation basis of the hydrodynamic medium properties changing over time, such as the fluid mobility, the saturation, pressure distribution, mean resistance and conductivity. The results were obtained for two types of filtration: radial and linear one. First case describes the physics for liquids flowing to well galleries, second - the process of contour contraction or a motion into the formation. Analytical solution for the radial case was derived for the first time. A method to assess the degree of injectivity profile smoothing after the flow diverter technologies.
References
1. Dake L.P., The Practice of reservoir engineering (Revised Edition), Elsevier
Science, 2001, 570 p.
2. Willhite G.P., Waterflooding, SPE Textbook Series, 1986.
3. Dubinov A.E., Dubinova I.D., Saykov S.K., W-funktsiya Lamberta i ee primenenie v matematicheskikh zadachakh fiziki (Lambert w function and its application in mathematical physics problems), Sarov: Publ. of RFYaTs-VNIIEF, 2006, 160 p.
4. Corless G.H., Gonnet R.M., Hare D.E.G. et al., On the lambert w function,
Advances in Computational Mathematics, 1996, V. 5, pp. 329–359.
5. Scott T.C., Fee G., Grotendorst J., Asymptotic series of generalized lambert
w function, IGSAM, ACM Special Interest Group in Symbolic and Algebraic
Manipulation, 2013, V. 47 (185), pp. 75–83.
6. Aziz K., Settari A., Petroleum reservoir simulation, Elsevier Applied Science
Publishers, 1986.
7. Dake L., Fundamentals of reservoir engineering, URL:
http://books.google.ru/books?id=grQAlQEACAAJ.
8. Chen Z., Reservoir simulation mathematical techniques in oil recovery,
Philadelphia: Society for industrial and applied mathematics, 2007, 250 r.
9. Craig F., Reservoir engineering aspects of waterflooding, H. L. Doherty
Memorial Fund of AIME, 1971, 164 p.
10. Muskat M., The flow of homogeneous fluids through porous media, Mc-
Graw-hill book company, Inc., 1937, 782 p.
11. Charnyy I.A., Podzemnaya gidrogazodinamika (Underground hydraulic
gas dynamics), Moscow – Leningrad: Gostoptekhizdat Publ., 1963, 396 p.
12. Leybenzon L.S., Dvizheniya prirodnykh zhidkostey i gazov v poristoy srede (Natural liquids and gases movement in a porous medium), Moscow –
Leningrad: OGIZ, Gosudarstvennoe tekhniko-teoreticheskoe izdatel'stvo
Publ., 1947, 244 p.


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