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

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

Andriy Bomba, Alesya Sinchuk

#### 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.

#### Keywords

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

#### Full Text:

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#### References

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.

Fazlyev, R. T. (2008). Pattern flooding oil fields. Мoscow: Izhevsk, IKI, SIC RHD, 256.

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.

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.

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.

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.

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.

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

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

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

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.

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

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

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

Samarskiy, А. А. (1983). The theory of difference schemes. Moscow: Nauka, 616.

#### GOST Style Citations

Kanevskaya, R. D. Mathematical modeling of development of oil and gas fields with the use of hydraulic fracturing [Text] / R. D. Kanevskaya. – Moscow: OOO "Core-business centers", 1999. – 212 p.

Fazlyev, R. T. Pattern flooding oil fields [Text] / R. T. Fazlyev. – Мoscow: Izhevsk, IKI, SIC RHD, 2008. – 256 p.

Taleghani, А. D. Analysis of hydraulic fracture propagation in fractured reservoirs: an improved model for the interaction between induced and natural fractures [Text]: PhD Dissertation / А. D. Taleghani. – University of Texas at Austin, 2009. – 216 p.

Bomba, А. Ya. Modeling of filtration processes in the oil and gas seams numerical methods quasiconformal mappings [Text]: monograph / А. Ya. Bomba, A. M. Sinchuk, S. V. Yaroschak. – Rivne: LLC «Assol», 2016. – 238 p.

Bomba, A. Ya. Mathematic modelling of thermodynamic effects in well bore zone of gas formation under hydraulic fracturing conditions [Text] / A. Ya. Bomba, M. A. Myslyuk, S. V. Yaroschak // Journal of Hydrocarbon Power Engineering. – 2015. – Vol. 2, Issue 1. – P. 1–5.

Bomba, А. Ya. Method of complex analysis of modeling of the displacement of oil based coolant effect of hydraulic fracturing [Text] / А. Ya. Bomba, A. M. Sinchuk, S. V. Yaroschak // International scientific journal "System Research and Information Technologies". – 2015. – Vol. 1. – P. 130–140.

Astafjev, V. I. Modeling of fluid filtration in the presence of hydraulic fracture formation [Text] / V. I. Astafjev // Bulletin of the Samara State tehnical University. Ser. Sci. Science. – 2007. – Vol. 2, Issue 15. – P. 128–132.

Wang, H. Numerical modeling of non-planar hydraulic fracture propagation in brittle and ductile rocks using XFEM with cohesive zone method [Text] / H. Wang // Journal of Petroleum Science and Engineering. – 2015. – Vol. 135. – P. 127–140. doi: 10.1016/j.petrol.2015.08.010

Wang, X. Numerical simulation of hydraulic fracturing in orthotropic formation based on the extended finite element method [Text] / X. Wang, F. Shia, H. Liu, H. Wu // Journal of Petroleum Science and Engineering. – 2016. – Vol. 33. – P. 56–69. doi: 10.1016/j.jngse.2016.05.001

Abdollahipour, A. Simulating the propagation of hydraulic fractures from a circular wellbore using the displacement discontinuity method [Text] / A. Abdollahipour, M. F. Marji, A. Ya. Bafghi, J. Gholamnejad // International Journal of Rock Mechanics and Mining Sciences. – 2015. – Vol. 80. – P. 281–291. doi: 10.1016/j.ijrmms.2015.10.004

Miehe, Ch. Crack driving forces in hydro-poro-elasticity and hydraulic fracturing of fluid-saturated porous media [Text] / Ch. Miehe, S. Mauthe // Computer methods in applied mechanics and engineering. – 2016. – Vol. 304. – P. 619–655.

Salimzadeh, S. A three-phase XFEM model for hydraulic fracturing with cohesive crack propagation [Text] / S. Salimzadeh, N. Khalili // Computers and Geotechnics. – 2015. – Vol. 69. – P. 82–92. doi: 10.1016/j.compgeo.2015.05.001

13. Jahandideh, A. Optimization of hydraulic fracturing design under spatially variable shale fracability [Text] / A. Jahandideh, B. Jafarpour // Journal of Petroleum Science and Engineering. – 2016. – Vol. 138. – P. 174–188. doi: 10.1016/j.petrol.2015.11.032

Zhang, Sh. Determination of in situ stresses and elastic parameters from hydraulic fracturing tests by geomechanics modeling and soft computing [Text] / Sh. Zhang, Sh. Yin // Journal of Petroleum Science and Engineering. – 2014. – Vol. 124. – P. 484–492. doi: 10.1016/j.petrol.2014.09.002

Samarskiy, А. А. The theory of difference schemes [Text] / А. А. Samarskiy. – Moscow: Nauka, 1983. – 616 p.

### Cited-by:

1. Modeling the process of oil displacement by a heat carrier considering the capillary effect
Olga Michuta, Alesia Sinchuk, Serhii Yaroshchak
Eastern-European Journal of Enterprise Technologies  Vol: 4  Issue: 5 (100)  First page: 49  Year: 2019
doi: 10.15587/1729-4061.2019.174439

Copyright (c) 2016 Andriy Bomba, Alesya Sinchuk