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A 3D Gas and Water Simulator Considering Nonlinear Flow Behaviors for Abnormal High-Pressure Tight Gas Reservoirs

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Chemistry and Technology of Fuels and Oils Aims and scope

Fluid flow in tight gas reservoirs with abnormal high pressure presents nonlinear behaviors. A mathematical description of these behaviors is essential for establishing the flow model. In this study, a mathematical model is presented that describes the effect of threshold pressure gradient and rock deformation on gas flow parameters in a tight gas reservoir. A fully implicit 3D gas and water phase numerical model was derived using the finite difference method. Based on software engineering principles, a 3D gas and water simulator was developed, which can be used in research on nonlinear flow mechanisms and flow simulation in abnormal high-pressure gas reservoir. The simulator proved to be reliable through a comparison with a commercial simulator, and it was used successfully for prediction of gas production in the M reservoir.

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References

  1. Q. Yen, Q. He, L. Wei, et al., “A laboratory study on percolation characteristics of single phase flow in low-permeability reservoirs,” J.Xi’an Pet. Inst., 5, No. 2, 1-6(1990).

    Google Scholar 

  2. A. Li, S. Zhang, M. Liu, et al., “A new method of measuring starting pressure for low permeability reservoir,” J. China Univ. Pet., 32, No.1, 68-72 (2008).

    Google Scholar 

  3. Z. Yang, X. Li, S. Liu, et al., “Threshold pressure effect of low permeability tight gas reservoirs in Sulige gas field,” Acta Pet Sin., 36, No.3, 347-55 (2015).

    Google Scholar 

  4. A. Prada and F. Civan, “Modification of Darcy’s law for the threshold pressure gradient.” J. Pet Sci. Eng., 22,No.4, 237-240 (1999).

    Article  CAS  Google Scholar 

  5. Jingjing Guo, Su Zhang, Liehui Zhang, et al., “Well testing analysis for horizontal well with consideration of threshold pressure gradient in tight gas reservoirs,” J. Hydrodynam., 24, No.4, 561-568 (2012).

    Article  Google Scholar 

  6. Jingchen Ding, Shenglai Yang, Xiangrong Nie, et. al, “Dynamic threshold pressure gradient in tight gas reservoir,” J. Nat. Gas Sci. Eng., 20,155-160 (2014).

  7. Hongqing Song, Qipeng Liu Dawei Yang, et al., “Productivity equation of fractured horizontal well in a water-bearing tight gas reservoir with low-velocity non-Darcy flow,” J. Nat. Gas Sci. Eng., 18, 467473 (2014).

    Google Scholar 

  8. Daolun Lia, Wenshu Zha, Shufeng Liu, et al., “Pressure transient analysis of low permeability resent with pseudo threshold pressure gradient,” J. Pet. Sci. Eng., 147, 308-316 (2016).

    Article  Google Scholar 

  9. Weibing Tian, Aifen Li, Xiaoxia Ren, et al., “The threshold pressure gradient effect in the tight sandstone gas reservoirs with high water saturation,” Fuel, 226, 221-229 (2018).

    Article  CAS  Google Scholar 

  10. John P. Davies and Stephn A. Holditch, “Stress Dependent Permeability in Low Permeability Gas Reservoir,” Travis Peak Formation, East Texas, SPE 39917.

  11. Hong-XingWang, Guan Wang. Zhang-Xing (John) Chen, et. al, “Deformational characteristics of rock in low permeable reservoir and their effect on permeability,” .J. Pet. Sci. Eng., 75, 240-243 (2010).

  12. Juntai Shi, Xiangfang Li, Qian Li et. al, . “Gas permeability model considering rock deformation and slippage in low permeability water-bearing gas reservoirs,”J.Pet. Sci. Eng., 120, 61-72 (2014).

    Article  CAS  Google Scholar 

  13. Tapan Kidambi, Awez Hanegaonkar, Ankit Dutt, et. al, “A fully coupled flow and geomechanics model for a tight gas reservoir: Implications for compaction, subsidence and faulting,” J. Nat. Gas Sci. Eng., 38,No.2, 257-271(2017).

    Article  Google Scholar 

  14. Chunyuan Xu, Peichao Li, Zhiwei Lu, et. al, “Discrete fracture modeling of shale gas flow considering rock deformation,” J. Nat. Gas Sci. Eng., 52, No.4, 507-514 (2018).

    Article  Google Scholar 

  15. J. Lu, “Pressure behavior of a hydraulically fractured well in tight gas formation with threshold pressure gradient,” SPE Middle East Unconventional Gas Conference and Exhibition, 2012.

  16. X. Wang and J.J. Sheng, “Effect of low-velocity non-Darcy flow on well production performance in shale and tight oil reservoirs,” Fuel, 190, 41-46 (2017).

    Article  CAS  Google Scholar 

  17. J. Liu, G. Li, and Y. Zhang, “Numerical simulation of CO2, flooding of coalbed methane considering the fluid-solid coupling effect,”PloS One, 11, No.3, (2016).

    Article  Google Scholar 

  18. Ren Long, SuYuliang, Zhan Shiyuan, et al., “Fully coupled fluid-solid numerical simulation of stimulated reservoir volume (SRV)-fractured horizontal well with multi-porosity media in tight oil reservoirs,” .J. Pet. Sci. Eng., 174, 757-775 (2019).

    Article  CAS  Google Scholar 

  19. R.F. Sigal, “The pressure dependence of permeability,” Petrophysics, 43, No.2, 92-102 (2002).

    Google Scholar 

  20. J.B. Walsh, “Effect of pore pressure and confining pressure on fracture permeability,” Int. J. Rock Mech. Min. Sci Geomech. Abstr., 18, No.5, 429435 (1981).

    Article  Google Scholar 

  21. N.R Warpinski and L.W. Teufel, “Determination of the effective-stress law for permeability and deformation in low-permeability rocks,” SPE Form. Eval., 7, No.2, 123-131(1992).

    Article  CAS  Google Scholar 

  22. Xiaoqi Wang, Yanming Zhu, and Changqing Fu, “Experimental investigation of the stress-dependent permeability in the Longmaxi Formation shale,” J. Pet. Sci. Eng., 175, 932-947 (2019).

    Article  CAS  Google Scholar 

  23. Cesare Frepoli, John H. Mahaffy, and Katsuhiro Ohkawa“Notes on the implementation of a fully-implicit numerical scheme for a two-phase three-field flow model,” Nucl. Eng. Das., 225,191-217 (2003).

    Article  CAS  Google Scholar 

  24. Ling Zou, Haihua Zhao, and Hongbin Zhang, “Numerical implementation, verification and validation of two-phase flow four-equation drift flux model with Jacobian-free Newton-Kr ylov method,” Ann. Nucl. Energ., 97, 707-719 (2016).

    Article  Google Scholar 

  25. P.K.W. Vinsome, “Orthomin, an iterative method for solving sparse banded sets of simultaneous linear equation,” SPE Symposium on Numerical Simulation of Reservoir Performance, Los Angeles, California, February 19-201976SPE-5729-MS.

  26. Abe Kuniyoshi and Fujino Seiji, “On MrR (Mister R) Method for Solving Linear Equations with Symmetric Matrices,” 17thAsia Simulation Conference (AsiaSim), Melaka, Malaysia, 2017.

  27. Houzeaux G., Aubry, R., Vazquez M., “Extension of fractional step techniques for incompressible flows: The preconditioned Orthomin (1) for the pressure Schur complement,” Comput. Fluids, 44, N7-313 (2011).

    Article  Google Scholar 

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Acknowledgement

This work was financially supported by the National Science and Technology Major Project (2017ZX05013-005). The authors would also like to thank the reviewers and editors whose critical comment: were very helpful in preparing this article.

NOMENCLATURE

\( \overrightarrow{V} \) flow velocity in porous media, cm/s

P pressure, MPa

PD dimensionless pressure

Pi initial pressure, MPa

K permeability, mD

KD dimensionless permeability

Ki initial permeability, mD

Kr relative permeability, mD

μ viscosity of the fluid, mPa∙s

Φ velocity potential

λ threshold pressure gradient, MPa/m

ξ correction factor of non-Darcy flow with high velocity of gas flow, dimensionless

ϕ porosity

B volume factor, dimensionless

Q surface fluid rate per unit volume of rock, m3/d

S saturation

t time, s

\( {P}_g^0 \) reference pressure, MPa

ϕ0 porosity under conditions of reference pressure

Cr rock compressibility. MPa-1

Pcgw capillary pressure of gas and water, MPa

SUBSCRIPTS

l denotes a phase (gas or water)

g gas phase

w water phase

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Correspondence to Guoqing Feng.

Additional information

Translated from Khimiya i Tekhnologiya Topliv i Masel, No. 1, pp. 40 — 46, January — February, 2020.

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Feng, G., Huang, Z. & Yang, H. A 3D Gas and Water Simulator Considering Nonlinear Flow Behaviors for Abnormal High-Pressure Tight Gas Reservoirs. Chem Technol Fuels Oils 56, 60–72 (2020). https://doi.org/10.1007/s10553-020-01111-z

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