R.A. Mustafaev
ABSTRACT
Application of limited-anisotropic stratum hydrodynamic model (case kx = k, kz = ∞) for mathematicalmodeling the unsteady problem with mobile boundaries is examined. The process of oil expelling with immiscible water in the finite horizontal stratum of constant thickness at various liquid viscosities and densities in case of rectilinear parallel motion is considered. Iterative difference scheme with combination of fronts straightening method with finite difference method is composed for numerical solution. Results of numerical experiment are presented.
KEYWORDS
unsteady moving-boundaries problem, limited-anisotropic stratum model, iterative difference scheme, method of straightening of fronts, method of finite differences.
REFERENCES
1. Razvitie issledovaniy po teorii filtrachii v SSSR [Development of research in the theory of filtration in the USSR] (1969), Nauka, Moscow, Russia.
2. Charnyi, I.A. (1963), Podzemnaja gidrogazodinamika [Underground gas hydrodynamics] Gostoptekhizdat, Moscow, Russia.
3. Zigangareev, M.A. and Teplov, Yu.A. (1966), “ Calculations of shift of water-oil boundary in slope stratum and their comparison with data of modeling”, Trudy VNII neftegaz, Vol.
47, pp. 142-150.
4. Alikhashkin, Ya.I. (1961), “Numerical integration of equation of automodel motion of interface of two liquids in porous medium”, Izvestiya Akademii Nauk SSSR, OTN, Mekhanika
i mashinostroenie, no. 5, pp. 159-162.
5. Teplov, Yu.A. (1967), “On change of water-oil boundary in heterogeneous stratum” Izvestiya Akademii Nauk SSSR, MZhG, no. 5, pp. 160-164.
6. Verigin, N.N., Sarkisyan, V.S. and Shibanov, A.V. (1973), “On determining interface of two immiscible liquids in porous medium”, Izvestiya Akademii Nauk SSSR, MZhG, no. 6, pp.
155-163.
7. Verigin, N.N. and Sarkisyan, V.S. (1974), “On filtration of two liquids with different densities and viscosities under pumping in the gallery with fixed discharge” DAN SSSR, Vol.
218, no. 3, pp. 536-539.
8. Verigin, N.N. and Sarkisyan, V.S. (1975), “On filtration of two heterogeneous liquids under pressure conditions”, DAN SSSR, Vol. 221, no. 2, pp. 305-308.
9. Mustafaev, R.A. (2014), “Mathematical modeling the unsteady process of motion of two immiscible liquids in porous medium with allowance for anisotropy of stratum permeability”,
Elektronnoe modelirovanie, Vol. 36, no. 6, pp. 83-98.
10. Budak, B.M., Goldman, N.L. and Uspenskiy, A.B. (1967), “Difference schemes with straightening of fronts for solution of multifront problems of the Stefan type”, Vychislitelnye
metody i programmy. Sbornik rabot vychislit. tsentr MGU, Vol. 6, pp. 206-216.
11. Mustafaev, R.A. (2001), “Monotonous difference scheme for numerical solution of the Verigin type problem”, Izvestiya NAN of Azerbaijan, Ser. fizikotekhnicheskie i matematicheskie
nauki, Vol. 21, no. 2, pp. 165-169.