The complex analysis methods for modeling the oil displacement process by the heat transfer fluid taking into account the hydraulic fracturing effect


  • A. Ya. Bomba
  • A. M. Sinchuk
  • S. V. Yaroschak


Based on the complex analysis methods developed by the authors, an approach was developed for solving nonlinear boundary value problems of a non-isothermal multiphase filtration in the elements of flooding under conditions of the filtration flow perturbation by the hydraulic fracturing cracks. The numerical algorithm is constructed to calculate the hydrodynamic grid, the fields of temperature and saturation, the coordinates of critical points, the filtration rate of injection and production wells, the time of fracturing fluid penetration and complete flooding of wells. With this algorithm, we calculate the volume of fluid displaced during the specified amount of time and the corresponding volume remaining in the reservoir at any given time, in particular after stopping the injection, as well as determining the oil "stagnation" locations and the like. An analysis of numerical calculations of redistribution of the corresponding filtration characteristics was performed and the specific properties of the oil displacement process in cases of non-isothermal and isothermal filtrations were determined.


Bomba A.Ja., Kashtan S.S., Pryhornyts'kyj D.O., Jaroshchak S.V. Metody kompleksnoho analizu. — Rivne: NUVHP, 2013. — 415 s.

Bomba A.Ya., Yaroschak S.V. Complex approach to modeling of two-phase filtration processes under control conditions // Journal of Mathematical Sciences. — 2012. — 184, №. 1. — P. 56–69.

Bomba A.Ja., Sinchuk A.M. Kompleksnyj analiz povedinky systemy "sverdlovyny-trishchyny-plast" v elementakh ploshchadnoho zavodnennja // Visnyk NTU "KhPI". Serija "Matematychne modeljuvannja v tekhnitsi ta tekhnolohijakh". — Kharkiv: NTU "KhPI", 2013 — № 54(1027) — S. 4–15.

Bomba A.Ja., Sinchuk A.M., Jaroshchak S.V. Metod kvazikonformnykh vidobrazhen' matematychnoho modeljuvannja nelinijnykh protsesiv vytisnennja za umov isnuvannja trishchyn hidrorozryvu plasta // Rozvidka ta rozrobka naftovykh i hazovykh rodovyshch. — 2011. — № 3(40). — S. 32–36.

Bomba A.Ja., Sinchuk A.M., Jaroschak S.V. Metod kompleksnogo analiza issledovanija dvuhfaznoj fil'tratsii v gorizontal'nyh plastah s uchetom gidrorazryva // Elektronnoe modelirovanie. — 2013. — 35, № 2. — S. 25–33.

Dahi Taleghani A. Analysis of hydraulic fracture propagation in fractured reservoirs: an improved model for the interaction between induced and natural fractures, PhD Dissertation // University of of Texas at Austin. — 2009. — 216 p. —

Ber Ja., Zaslavski D., Irmej S. Fiziko-matematicheskie osnovy fil'tratsii vody. — M.: Mir, 1971. — 452 s.

Barenblatt G.I., Entov V.M., Ryzhik V.M. Teorija nestatsionarnoj fil'tratsii zhidkosti i gaza. — M.: Nedra, 1972. — 288 s.

Chekaljuk E.B. Termodinamika neftjanogo plasta. — M.: Nedra, 1965. — 238 s.





Methods of system analysis and control in conditions of risk and uncertainty