Modeling of impact of hydraulic fractures on the process of fluid displacement from low-permeability sedimentary rocks

Authors

DOI:

https://doi.org/10.15587/1729-4061.2016.73368

Keywords:

numerical methods for quasiconformal mappings, hydraulic fractures, pattern waterflooding, nonlinear problems

Abstract

Mathematical modeling of fluid displacement from low­permeability (shale) sedimentary rocks in the pattern waterflooding elements considering the impact of hydraulic fractures is performed. Based on numerical methods of comprehensive analysis (quasiconformal mappings), numerical algorithms for the calculation of filtration characteristics: saturation field, velocity quasipotential, time of the displacing fluid breakthrough to the production well and its complete waterflooding are developed. The algorithm also allows determining the coordinates of the critical “suspension” points and their quasipotential values, fluid interface position at different time points, the overall filtration rate of the production well, the dependence of oil fraction in it. For an effective analysis of the research, calculations of the volume of the displaced fluid in the reservoir within a certain time and the volume of the remaining fluid in the reservoir at an arbitrary time are performed. This allowed predicting the rate of waterflooding of production wells and identifying the features of operation under the projected arrangement of wells and hydraulic fractures on them. It was found that the “transverse direction” (with respect to injection wells) of hydraulic fractures accelerates the time of the displacing reagent breakthrough to the production well (although provides some growth of oil withdrawal values at the initial stages), and their “longitudinal” direction reduces the number of oil stagnation zones.

Author Biographies

Andriy Bomba, Rivne State Humanitarian University S. Bandery str., 12, Rivne, Ukraine, 33028

Doctor of technical sciences, Professor, head of the department

Department of Computer Science and Applied Mathematics

Alesya Sinchuk, Rivne State Humanitarian University S. Bandery str., 12, Rivne, Ukraine, 33028

PhD, Teacher

Department of Computer Science and Applied Mathematics

References

  1. Kanevskaya, R. D. (1999). Mathematical modeling of development of oil and gas fields with the use of hydraulic fracturing. Moscow: OOO "Core-business centers", 212.
  2. Fazlyev, R. T. (2008). Pattern flooding oil fields. Мoscow: Izhevsk, IKI, SIC RHD, 256.
  3. Taleghani, А. D. (2009). Analysis of hydraulic fracture propagation in fractured reservoirs: an improved model for the interaction between induced and natural fractures. University of Texas at Austin, 216.
  4. Bomba, А. Ya., Sinchuk, A. M., Yaroschak, S. V. (2016). Modeling of filtration processes in the oil and gas seams numerical methods quasiconformal mappings. Rivne: LLC «Assol», 238.
  5. Bomba, A. Ya., Myslyuk, M. A., Yaroschak, S. V. (2015). Mathematic modelling of thermodynamic effects in well bore zone of gas formation under hydraulic fracturing conditions. Journal of Hydrocarbon Power Engineering, 2 (1), 1–5.
  6. Bomba, А. Ya., Sinchuk, A. M., Yaroschak, S. V. (2015). Method of complex analysis of modeling of the displacement of oil based coolant effect of hydraulic fracturing. International scientific journal "System Research and Information Technologies", 1, 130–140.
  7. Astafjev, V. I. (2007). Modeling of fluid filtration in the presence of hydraulic fracture formation. Bulletin of the Samara State tehnical University. Ser. Sci. Science, 2 (15), 128–132.
  8. Wang, H. (2015). Numerical modeling of non-planar hydraulic fracture propagation in brittle and ductile rocks using XFEM with cohesive zone method. Journal of Petroleum Science and Engineering, 135, 127–140. doi: 10.1016/j.petrol.2015.08.010
  9. Wang, X., Shi, F., Liu, H., Wu, H. (2016). Numerical simulation of hydraulic fracturing in orthotropic formation based on the extended finite element method. Journal of Natural Gas Science and Engineering, 33, 56–69. doi: 10.1016/j.jngse.2016.05.001
  10. Abdollahipour, A., Fatehi Marji, M., Yarahmadi Bafghi, A., Gholamnejad, J. (2015). Simulating the propagation of hydraulic fractures from a circular wellbore using the Displacement Discontinuity Method. International Journal of Rock Mechanics and Mining Sciences, 80, 281–291. doi: 10.1016/j.ijrmms.2015.10.004
  11. Miehe, Ch., Mauthe, S. (2016) Crack driving forces in hydro-poro-elasticity and hydraulic fracturing of fluid-saturated porous media. Computer methods in applied mechanics and engineering, 304, 619–655.
  12. Salimzadeh, S., Khalili, N. (2015). A three-phase XFEM model for hydraulic fracturing with cohesive crack propagation. Computers and Geotechnics, 69, 82–92. doi: 10.1016/j.compgeo.2015.05.001
  13. Jahandideh, A., Jafarpour, B. (2016). Optimization of hydraulic fracturing design under spatially variable shale fracability. Journal of Petroleum Science and Engineering, 138, 174–188. doi: 10.1016/j.petrol.2015.11.032
  14. Zhang, S., Yin, S. (2014). Determination of in situ stresses and elastic parameters from hydraulic fracturing tests by geomechanics modeling and soft computing. Journal of Petroleum Science and Engineering, 124, 484–492. doi: 10.1016/j.petrol.2014.09.002
  15. Samarskiy, А. А. (1983). The theory of difference schemes. Moscow: Nauka, 616.

Downloads

Published

2016-08-24

How to Cite

Bomba, A., & Sinchuk, A. (2016). Modeling of impact of hydraulic fractures on the process of fluid displacement from low-permeability sedimentary rocks. Eastern-European Journal of Enterprise Technologies, 4(8(82), 49–55. https://doi.org/10.15587/1729-4061.2016.73368

Issue

Vol. 4 No. 8(82) (2016): Energy-saving technologies and equipment

Section

Energy-saving technologies and equipment

License

Copyright (c) 2016 Andriy Bomba, Alesya Sinchuk

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

The consolidation and conditions for the transfer of copyright (identification of authorship) is carried out in the License Agreement. In particular, the authors reserve the right to the authorship of their manuscript and transfer the first publication of this work to the journal under the terms of the Creative Commons CC BY license. At the same time, they have the right to conclude on their own additional agreements concerning the non-exclusive distribution of the work in the form in which it was published by this journal, but provided that the link to the first publication of the article in this journal is preserved.

A license agreement is a document in which the author warrants that he/she owns all copyright for the work (manuscript, article, etc.).
The authors, signing the License Agreement with TECHNOLOGY CENTER PC, have all rights to the further use of their work, provided that they link to our edition in which the work was published.
According to the terms of the License Agreement, the Publisher TECHNOLOGY CENTER PC does not take away your copyrights and receives permission from the authors to use and dissemination of the publication through the world's scientific resources (own electronic resources, scientometric databases, repositories, libraries, etc.).
In the absence of a signed License Agreement or in the absence of this agreement of identifiers allowing to identify the identity of the author, the editors have no right to work with the manuscript.
It is important to remember that there is another type of agreement between authors and publishers – when copyright is transferred from the authors to the publisher. In this case, the authors lose ownership of their work and may not use it in any way.