Skip to main content
SpringerLink
Log in

Influence of the Pressure Sensitive Effect on the Accuracy of History Matching for Hydraulic Fracturing Wells

  • Research Article-Petroleum Engineering
  • Published:
Arabian Journal for Science and Engineering Aims and scope Submit manuscript

Abstract

Evaluation of the hydraulic fracturing effect of shale gas wells is helpful for the design optimization and the adjustment of hydraulic fracturing schemes. Three history matching examples were performed for shale gas wells in the Weiyuan Shale Gas Field, Sichuan Basin, China. Based on the parameters obtained through history matching, the hydraulic fracturing effect of shale gas wells was evaluated roughly. In order to obtain the history matching results with high accuracy, both the pressure-sensitive effect of the absolute permeability and that of the relative permeability need to be considered fully. If the two pressure-sensitive effects are fully considered, the total relative errors between the fitting and real data of the gas production and of the fracturing fluid recovery were both less than about 5% according to our history matching results. It was also found that the pressure-sensitive effect of the relative permeability had a greater influence on the fitting of the fracturing fluid phase flow than on the fitting of the gas phase flow. If ignoring the pressure-sensitive effect of the relative permeability, the total relative error for the gas production fitting was as low as about 5%, but for the fracturing fluid recovery fitting, the total relative error still remained at about 40%. Theoretical analysis was performed to explain this phenomenon. As a conclusion, it is emphasized that both the pressure-sensitive effect of the absolute permeability and of the relative permeability need to be considered during the history matching, especially for the fitting of the fracturing fluid phase flow.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig.15
Fig. 16

Similar content being viewed by others

Availability of Data and Material

All data generated or analyzed during this study are included in this published article.

Code Availability

The code during the current study is available from the corresponding author on reasonable request.

Abbreviations

a :

Pressure-sensitive effect coefficient for the absolute permeability, MPa−1

b :

Pressure-sensitive effect coefficient for the gas relative permeability, MPa−1

c:

Pressure-sensitive effect coefficient for the irreducible fracturing fluid saturation, MPa−1

D :

Gas diffusion coefficient, m2/s

E :

Weighted error function

g 0 :

Real gas production data, m3/day

i :

Number of grid where the discrete fracture is embedded

K :

Absolute permeability, mD

K 0 :

Initial absolute permeability, mD

\(K_{r\alpha }^{{}}\) :

Relative permeability for a phase fluid

\(K_{rg\max }^{{}}\) :

Maximum relative gas permeability

\(K_{rg\max }^{0}\) :

Initial maximum relative gas permeability

\(K_{rw\max }^{{}}\) :

Maximum relative fracturing fluid permeability

l 0 :

Real fracturing fluid recovery rate, m3/day

M :

Molecular weight of shale gas, kg/mol

N g :

Corey exponent for the gas phase

N t :

Total exploitation days

N w :

Corey exponent for the fracturing fluid phase

P 0 :

Initial reservoir pressure, MPa

P L :

Langmuir pressure, MPa

P α :

Pressure of \(\alpha\) phase fluid, MPa

P well :

Bottom hole pressure, MPa

\(q_{ads}^{{}}\) :

Mass of adsorbed gas per unit volume in a shale matrix, kg/m3

\(q_{\alpha }^{Ff}\) :

Transfer flow rate of α phase between the conductive fracture and the micro-fractures, kg/s

\(q_{\alpha }^{mf}\) :

Transfer flow rate of α phase between matrix and micro-fractures, kg/s

r :

Position vector, m

S 0 :

Initial saturation of the fracturing fluid phase

\(S_{\alpha }\) :

Saturation of the α phase fluid

S gc :

Residual gas saturation

S wc :

Irreducible fracturing fluid saturation

\(S_{wc}^{0}\) :

Initial irreducible saturation of the fracturing fluid phase

\(S_{w}^{*}\) :

Normalized fracturing fluid saturation

t :

Time, day

T :

Reservoir temperature, K

Ti :

Transmissibility coefficient of the EFDM in grid i, m3/s

V vol :

Volume of the gridblock, m3

V L :

Langmuir volume, m3/kg

V std :

Molar volume of the shale gas under standard conditions, m3/mol

\({\mathbf{V}}_{\alpha }^{{}}\) :

Velocity of α phase fluid, m/s

x :

Unknown to be fitted

\({\mathbf{y}}_{0}\) :

Target vector

\(\mu_{\alpha }\) :

Viscosity of α phase fluid, Pa·s

\(\rho_{s}\) :

Density of shale, kg/m3

\(\rho_{\alpha }\) :

Density of the α phase fluid, kg/m3

σ :

Shape factor of the dual porosity model, m−2

ϕ :

Porosity

δ :

Dirac function

λ :

Mobility, m2 /(Pa·s

References

  1. Fisher, M.K.; Warpinski, N.R.: Hydraulic fracture-height growth: real data. SPE Prod. Oper. 27, 8–19 (2012)

    Google Scholar 

  2. Vermylen, J., Zoback, M.D.: Hydraulic fracturing, microseismic magnitudes, and stress evolution in the Barnett Shale. Presented at SPE Hydraulic Fracturing Technology Conference, The Woodlands, Texas, USA, 24–26 January. SPE (2011)

  3. Wilson, K.: Analysis of drawdown sensitivity in shale reservoirs using coupled geomechanics models. Presented at the SPE Annual Technical Conference and Exhibition. Houston, Texas, USA. SPE (2015)

  4. Pedrosa, Jr. O.A.: Pressure transient response in stress-sensitive formations. Presented at SPE California Regional Meeting, Oakland, California, 2:4 April, SPE (1986)

  5. Ostensen, R.W.: The effect of stress-dependent permeability on gas production and well testing. SPE Form. Eval. 7, 227–235 (1986)

    Article  Google Scholar 

  6. Cho, Y., Apaydin, O.G., Ozkan, E.: Pressure-dependent natural-fracture permeability in shale and its effect on shale-gas well production. Presented at the SPE Annual Technical Conference and Exhibition. San Antonio, Texas. SPE 2012

  7. Clarkson, C.R.; Jensen, J.L.; Chipperfield, S.: Unconventional gas reservoir evaluation: what do we have to consider? J. Nat. Gas Sci. Eng. 6, 9–33 (2012)

    Article  Google Scholar 

  8. Clarkson, C.R.; Qanbari, F.; Nobakht, M., et al.: Incorporating geomechanical and dynamic hydraulic fracture property changes into rate-transient analysis: example from the Haynesville shale. Presented at the SPE Canadian Unconventional Resources Conference. Calgary, Canada. SPE 2012

  9. Clarkson, C.R.: Production data analysis of unconventional gas wells: review of theory and best practices. Int. J. Coal Geol. 109–110, 101–146 (2013)

    Article  Google Scholar 

  10. Kwon, O., Kronenberg, A.K., Gangi, A.F., et al.: Permeability of illite-bearing shale: 1. Anisotropy and effects of clay content and loading. J. Geophys. Res. 109(10): B10205 (2004)

  11. Soeder, D.J.: Porosity and permeability of eastern Devonian gas shale. SPE Form. Eval. 3, 116–124 (1988)

    Article  Google Scholar 

  12. Kanfar, M.S.; Clarkson, C.R.: Reconciling flowback and production data: a novel history matching approach for liquid rich shale wells. J. Nat. Gas Sci. Eng. 33, 1134–1148 (2016)

    Article  Google Scholar 

  13. Ali, H.S., Al-Marhoun, M.A., Abu-Khamsin, S.A., et al.: The Effect of Overburden Pressure on Relative Permeability. Presented at the Fifth SPE middle east oil show, Mananma Bahrain, 7–10 March. SPE (1987)

  14. Jones, C., Al-Quraishi, A.A., Somerville, J.M., et al.: Stress sensitivity of saturation and end-point relative permeabilities. In: International Symposium of the Society of Core Analysts 1–12 (2001)

  15. Lei, G.; Dong, P.; Wu, Z., et al.: A fractal model for the stress-dependent permeability and relative permeability in tight sandstones. J. Can. Petro. Technol. 54, 36–48 (2015)

    Article  Google Scholar 

  16. Xiong, Y.; Xua, H.; Wang, Y., et al.: The variation mechanism of petrophysical properties and the effect of compaction on the relative permeability of an unconsolidated sandstone Reservoir. Mar. Petrol. Geol. 92, 754–763 (2018)

    Article  Google Scholar 

  17. Fisher, M.K., Heinze, M.K., Harris, C.D., et al.: Optimizing horizontal completion techniques in the Barnett Shale using microseismic fracture mapping. In: Presented at SPE Annual Technical Conference and Exhibition, Houston, Texas 26–29. SPE (2004)

  18. Mayerhofer, M.J.; Lolon, E.; Cipolla, C.J., et al.: What is stimulated reservoir volume? SPE Prod. Oper. 25, 8–98 (2010)

    Google Scholar 

  19. Freeman, C.M.; Moridis, G.J.; Ilk, D.; Blasingame, T.A.: A numerical study of performance for tight gas and shale gas reservoir systems. In: Presented at SPE Annual Technical Conference and Exhibition, New Orleans, Louisiana, 4–7 October. SPE (2009)

  20. Kazemi, H.; Merrill, L.S.; Porterfield, K.L., et al.: Numerical simulation of water-oil low in naturally fractured reservoirs. SPE J. 16, 201–210 (1976)

    Google Scholar 

  21. Rossen, R.H.; Shen, E.I.: Simulation of gas-oil drainage and water-oil imbibition in naturally fractured reservoirs. SPE Reserv. Eval. Eng. 4, 464–470 (1989)

    Article  Google Scholar 

  22. Rossen, R.H.: Simulation of naturally fractured reservoir with semi-implicit source terms. SPE J. 17, 201–210 (1997)

    Google Scholar 

  23. Thomas, L.K., Dixon, T., Pierson, R.G.: Fractured reservoir simulation. In: Presented at SPE annual technical conference and exhibition, Dallas, Texas, 21–24 September. SPE (1983)

  24. Mengal, S.A., Wattenbarger, R.A.: Accounting for adsorbed gas in shale gas reservoirs. SPE (2011)

  25. Baca, R.G.; Arnett, R.C.; Langford, D.W.: Modelling fluid flow in fractured-porous rock masses by finite-element techniques. Int. J. Num. Meth. Fl. 4, 337–348 (1984)

    Article  Google Scholar 

  26. Noorishad, J.; Mehran, M.: An upstream finite element method for solution of transient transport equation in fractured porous media. Water Resour. Res. 18, 588–596 (1982)

    Article  Google Scholar 

  27. Karimi-Fard, M., Firoozabadi, A,.: Numerical simulation of water injection in 2D fractured media using discrete-fracture model. In: SPE annual technical conference and exhibition, 30 September-3 October, New Orleans, Louisiana, https://doi.org/https://doi.org/10.2118/71615-MS, (2001)

  28. Lough, M.F.; Lee, S.H.; Kamath, J.: An efficient boundary integral formulation for flow through fractured porous media. J. Comput. Phys. 143, 462–483 (1998)

    Article  MathSciNet  Google Scholar 

  29. Lee, S.H., Jensen, C.L., Lough, M.F.: An efficient finite difference model for flow in a reservoir with multiple length-scale fractures. In: Presented at SPE annual technical conference and exhibition, Houston, Texas 3–6 October. SPE (1999)

  30. Li, L.; Lee, S.H.: Efficient field-scale simulation of black oil in a naturally fractured reservoir through discrete fracture networks and homogenized media. SPE Reserv. Eval. Eng. 11, 750–758 (2008)

    Article  Google Scholar 

  31. Zhou, F.; Shi, A.; Wang, X.: An efficient finite difference model for multiphase flow in fractured reservoirs. Petrol. Exploration and Development 41, 262–266 (2014)

    Article  Google Scholar 

  32. Mayerhofer, M.J.; Lolon, E.P.; Youngblood, J.E.; et al.: Integration of microseismic fracture mapping results with numerical fracture network production modeling in the Barnett Shale. In: Presented at SPE annual technical conference and exhibition, San Antonio, Texas, USA, 24–27 September. SPE (2006)

  33. Warpinski, N.R.; Branagan, P.T.; Peterson, R.E., et al.: Mapping hydraulic fracture growth and geometry using microseismic events detected by a wireline retrievable accelerometer array. Presented at SPE Gas Technology Symposium, Calgary, Alberta, Canada, 15–18 March. SPE (1998)

  34. Warpinski, N.R.: Integrating microseismic monitoring with well completions, reservoir behavior, and rock mechanics. In: Presented at SPE Tight Gas Completions Conference, San Antonio, Texas, USA. SPE (2009)

  35. Warpinski, N.R.; Mayerhofer, M.; Agarwal, K., et al.: Hydraulic-fracture geomechanics and microseismic-source mechanisms. SPE J. 18, 766–780 (2013)

    Article  Google Scholar 

  36. Mohammed, A.; Wei, Y.; Kamy, S.; Erich K.; Reid, S.; Andrew, J.: Estimating the size and orientation of hydraulic fractures using microseismic Events. In: Presented at the unconventional resources technology conference held in Austin, Texas, USA, 20–22 July (2020)

  37. Ehsan, S.; Ebrahim, N.L.; Mohammad, P.: An accurate empirical correlation for predicting natural gas viscosity. J. Nat. Gas Chem. 20, 654–658 (2011)

    Article  Google Scholar 

  38. Lee, A. L., Gonzalez, M. H., Eakin, B. E.: J. Petr. Techn. August:997 (1966)

  39. Wu, K.; Li, X.; Wang, C., et al.: Model for surface diffusion of adsorbed gas in nanopores of shale gas reservoirs. Ind. Eng. Chem. Res. 54, 3225–3236 (2015)

    Article  Google Scholar 

  40. Dranchuk, P.M., Purvis, R.A., Robinson, D.B.: Computer calculation of natural gas compressibility factors using the standing and Katz Correlation. Petroleum Soc Canada. 73–112 (1973)

  41. Langmuir, I.: The adsorption of gases on plane surfaces of glass, mica and platinum. J. Am. Chem. Soc. 40, 1361–1370 (1918)

    Article  Google Scholar 

  42. Moinfar, A.; Varavei, A.; Sepehrnoori, K.: Development of an efficient embedded discrete fracture model for 3d compositional reservoir simulation in fractured reservoirs. SPE 19, 289–303 (2014)

    Article  Google Scholar 

  43. Kikani, J.; Pedrosa, O.A., Jr.: Perturbation analysis of stress-sensitive reservoirs. SPE Form. Eval. 6, 379–386 (1991)

    Article  Google Scholar 

  44. Brooks, R.H.: Properties of porous media affecting fluid flow. J. Irrig. Drain. Eng. 92, 61–88 (1966)

    Article  Google Scholar 

  45. Polak, E.: Optimization: Algorithms and Consistent Approximations. 56–70 (1997)

Download references

Funding

The authors disclose receipt of the following financial support for the research, authorship, and publication of this article: This work was supported by National Science and Technology Major Project of China (No.2017ZX05072-005) and the CNPC-CAS Science and Technology Cooperation Project (Grant Number No.2015A-4812).

Author information

Author notes

  1. Both Zhanke Li and Anfeng Shi are joint first authors, contributing equally to this work.

Authors and Affiliations

  1. Department of Thermal Science and Energy Engineering, University of Science and Technology of China, Hefei, 230027, China

    Zhanke Li, Anfeng Shi, Xiaohong Wang, Zhifeng Liu, Ming Wang & Zhifan Liu

Authors
  1. Zhanke Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Anfeng Shi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Xiaohong Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Zhifeng Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Ming Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Zhifan Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zhifeng Liu.

Ethics declarations

Conflict of Interest

The authors declare no potential conflicts of interest with respect to the research, authorship or publication of this article.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, Z., Shi, A., Wang, X. et al. Influence of the Pressure Sensitive Effect on the Accuracy of History Matching for Hydraulic Fracturing Wells. Arab J Sci Eng 46, 6949–6965 (2021). https://doi.org/10.1007/s13369-021-05370-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13369-021-05370-8

Keywords

Search

Navigation