Investigation of the influence of gravitational forces on the process of displacement of viscoplastic fluids

Authors

DOI:

https://doi.org/10.15587/2312-8372.2017.119326

Keywords:

gravitational forces, variable direction method, locally one-dimensional schemes, adaptive grid, viscoplastic fluid

Abstract

The object of research is a numerical simulation of the process of two-dimensional two-phase filtration of viscoplastic oil and water, taking into account the gravitational forces, some properties of liquids, as well as relative phase permeabilities and capillary forces.

As is known, the problems of multiphase filtration have specific features. Therefore, there is a need to develop difference schemes in adaptive grids that reduce the artificial viscosity and oscillation of the numerical solution. They also make it possible to obtain acceptable results with a small number of nodes in the computational grid.

To take into account the singularities of the solution, a difference-iteration method is used in moving grids. Based on the computational experiment, the influence of the initial pressure gradient and gravity on the displacement process is investigated.

Economical difference schemes that combine the advantages of explicit and implicit schemes are constructed and make it possible to reduce the two-dimensional problem to a chain of one-dimensional problems. A difference-iterative method is also proposed in moving grids for solving two-dimensional (axisymmetric) non-stationary filtration problems of anomalous liquids, by means of which an iterative process is constructed to find the distribution of water saturation.

The carried out calculations to determine the influence of gravity on the displacement process have shown that at z=0, even at low productive-bed thicknesses, gravitational forces influence the displacement process. And over time this influence increases: if at the time t=0.08 on the circuit the difference of water saturation was 0.0077; at t=0.24–0.0122, then at t=1.04 it becomes equal to 0.0292.

It is shown that when modeling the process without taking gravity into account it is expedient to simplify the geometry of the filtration region, i. e., to consider a plane-radial flow in view of the considerable simplicity of the calculations.

The developed algorithms can be used for hydro-gas dynamic calculations related to the development and operation of oil fields containing anomalous oil.

Author Biographies

Sardar Yusub Gasimov, Azerbaijan State University of Oil and Industry, 20, Azadlig ave., Baku, Azerbaijan, AZ1010

PhD, Associate Professor

Department of General and Applied Mathematics

Rashad Sirac Mammadov, Azerbaijan State University of Oil and Industry, 20, Azadlig ave., Baku, Azerbaijan, AZ1010

PhD, Associate Professor

Department of General and Applied Mathematics

References

  1. Pirmamedov, V. G. (1975). Ob odnom raznostno – iteratsionnom metode v podvizhnyh setkah resheniia nekotoryh nelineinyh zadach teorii fil'tratsii i teploprovodnosti. Dep. v VINITI, No. 2027-75.
  2. Musaev, G. M., Pirmamedov, V. G., Shirinov, K. F. (1983). Chislennoe modelirovanie protsessov dvuhfaznoi i trehfaznoi fil'tratsii na osnove raznostno-iteratsionnogo metoda v podvizhnyh setkah. Dinamika mnogofaznyh sred. Novosibirsk: ITPM SO AN SSSR, 223–227.
  3. Bernadiner, M. G., Entov, V. M. (1975). Gidrodinamicheskaia teoriia fil'tratsii anomal'nyh zhidkostei. Moscow, 200.
  4. Kaiumov, Yu. (1987). Chislennoe modelirovanie zadachi fil'tratsii viazkoplasticheskih fliuidov pri razlichnyh zakonah dvizheniia. Chislennye metody resheniia zadach fil'tratsii mnogofaznoi neszhimaemoi zhidkosti. Novosibirsk, 139–145.
  5. Klevchenia, A. A., Taranchuk, V. B. (1981). Chislennoe modelirovanie protsessa neustoichivogo vytesneniia nen'iutonovskoi nefti. Dinamika mnogofaznyh sred. Novosibirsk, 193–198.
  6. Pascal, H. (1984). Dynamics of moving interface in porous media for power law fluids with yield stress. International Journal of Engineering Science, 22 (5), 577–590. doi:10.1016/0020-7225(84)90059-4
  7. Elnaggar, H., Karadi, G., Krizek, R. J. (1971). Effect of non-darcian behavior on the characteristics of transient flow. Journal of Hydrology, 13, 127–138. doi:10.1016/0022-1694(71)90210-1
  8. Turetskaia, F. O., Turetskaia, F. O. (1987). Gidrodinamicheskie proiavleniia i identifikatsiia anomalii plastovyh zhidkostei. Neftianoe hoziaistvo, 5, 26–29.
  9. Samarskii, A. A. (1983). Teoriia raznostnyh shem. Moscow: Nauka, 653.
  10. Baker, G. A., Oliphant, T. A. (1960). An implicit, numerical method for solving the two-dimensional heat equation. Quarterly of Applied Mathematics, 17 (4), 361–373. doi:10.1090/qam/110207
  11. Bramble, J. H., Hubbard, B. E. (1962). On the formulation of finite difference analogues of the Dirichlet problem for Poisson’s equation. Numerische Mathematik, 4 (1), 313–327. doi:10.1007/bf01386325
  12. Buchanan, M. L. (1963). A Necessary and Sufficient Condition for Stability of Difference Schemes for Initial Value Problems. Journal of the Society for Industrial and Applied Mathematics, 11 (4), 919–935. doi:10.1137/0111067
  13. Wachspress, E. L. (1963). Extended Application of Alternating Direction Implicit Iteration Model Problem Theory. Journal of the Society for Industrial and Applied Mathematics, 11 (4), 994–1016. doi:10.1137/0111073
  14. Douglas, J., Gunn, J. E. (1964). A general formulation of alternating direction methods. Numerische Mathematik, 6 (1), 428–453. doi:10.1007/bf01386093
  15. Keller, H. B., Thomee, V. (1962). Unconditionally stable difference methods for mixed problems for quasi-linear hyperbolic systems in two dimensions. Communications on Pure and Applied Mathematics, 15 (1), 63–73. doi:10.1002/cpa.3160150105
  16. Gasimov, S. Yu., Mammadov, R. S. (2017). Numerical simulation of the process of gas and water filtration on the basis of the difference – iterative method in moving grids. Bulletin of the National Technical University «Kharkiv Polytechnic Institute»: Mechanical-Technological Systems And Complexes, 20 (1242), 89–93. Available at: http://mtsc.khpi.edu.ua/article/view/109614
  17. Aziz, K., Settari, A. (1979). Petroleum Reservoir Simulation. Applied Science Publishers, 497.

Published

2017-11-30

How to Cite

Gasimov, S. Y., & Mammadov, R. S. (2017). Investigation of the influence of gravitational forces on the process of displacement of viscoplastic fluids. Technology Audit and Production Reserves, 6(1(38), 15–21. https://doi.org/10.15587/2312-8372.2017.119326

Issue

Section

Mechanics: Original Research