Effect of non-Darcy flow on induced stresses around a wellbore in an anisotropic in-situ stress field

Document Type : Research Article

Authors

1 Department of Civil and Environmental Engineering, Amirkabir University of Technology, Tehran, Iran.

2 Department of Petroleum Engineering, University of North Dakota, Grand Forks, ND, USA.

Abstract

After drilling a well, the  stresses will be altered and the induced stresses present the new state of stress. These induced stresses which result in geomechanical problems. The studies indicate that the flow of hydrocarbon into the wellbore influences the induced stresses. Darcy equation has been used in the past; however, the laminar flow assumption embedded in this equation cannot correctly model the flow of fluid when a non-Darcy flow dominates near a wellbore. Example of such situation includes the gas wells. In this study, analytical equations are developed to incorporate the effect of non-Darcy flow on the induced stresses around a wellbore. These equations developed based on Forchheimer flow equation. Then the simplified solutions were presented by considering the second term of Forchheimer flow equation. It was found that the difference between the results from Darcy and non-Darcy flow models is proportional to the drawdown pressure. Further studies included numerical simulation of non-Darcy fluid flow in a typical reservoir. Comparison of the results with the analytical models indicated that the magnitude of stresses in non-Darcy flow is larger than of Darcy flow. Finally, sensitivity of the reservoir properties on the induced stresses in the non-Darcy flow regime was investigated.

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Main Subjects

References

References:
1. Kang, Y., Yu, M., Miska, S.S.Z., Takach, N., et al. "Wellbore stability: A critical review and introduction to DEM", SPE Annu. Tech. Conf. Exhib., no. October, pp. 4-7 (2009).
2. Acock, A., ORuarke, T., Shirmboh, D., et al. "Practical approaches to sand management", Oil F. Rev., 16(1), pp. 10-27 (2004).
3. Fjaer, E., Holt, R.M., Raaen, A.M., Risnes, R., and Horsrud, P., Petroleum Related Rock Mechanics, 53, Elsevier (2008).
4. Risnes, R., Bratli, R.K., Horsrud, P., et al. "Sand stresses around a wellbore", Soc. Pet. Eng. J., 22(6), pp. 883-898 (1982).
5. Agheshlui, H. and Matthai, S.K. "The impact of layering and heterogeneity on stresses around boreholes", in ECMOR XIV-15th European Conference on the Mathematics of Oil Recovery (2016).
6. Ong, S., Atlas, B., Ramos, R., Exploration, A., Technology, P., and Zheng, Z. "Sand production prediction in high rate, perforated and open-hole gas wells", Production (2000).
7. Han, G. and Dusseault, M.B. "Description of fluid flow around a wellbore with stress-dependent porosity and permeability", J. Pet. Sci. Eng., 40(1-2), pp. 1-16 (2003).
8. Chen, G., Jin, Y., Li, L., and Zhou, B. "Analysis of vertical well collapse volume in radial porous media  flows of a high pressure gas", In 50th US Rock Mechanics/ Geomechanics Symposium (2016).
9. Hassani, A.H., Veyskarami, M., Al-ajmi, A.M., and Masihi, M. "Rock mechanics & mining sciences. A modified method for predicting the stresses around producing boreholes in an isotropic in-situ stress field", Int. J. Rock Mech. Min. Sci., 96, October 2016, pp. 85-93 (2017).
10. Li, D. and Engler, T.W. "Literature review on correlations of the non-Darcy coefficient", SPE Permian Basin Oil Gas Recover. Conf., no. 2, pp. 1-8 (2013).http://www.onepetro.org/doi/10.2118/70015-MS.
11. Al-Hussainy, R., Ramey Jr, H.J., Crawford, P.B., et al. "The  flow of real gases through porous media", J. Pet. Technol., 18(5), pp. 624-636 (1966).
12. Wang, J.G., Kabir, A., Liu, J., and Chen, Z. "Effects of non-Darcy  flow on the performance of coal seam gas wells", Int. J. Coal Geol., 93, pp. 62-74 (2012).
13. Miskimins, J.L., Lopez, H.D.J., Barree, R.D., et al. "Non-Darcy  flow in hydraulic fractures: does it really matter?", in SPE Annual Technical Conference and Exhibition (2005).
14. Detournay, E. and Cheng, A.D. "Poroelastic response of a borehole in a non-hydrostatic stress field", Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 25(3), pp. 171-182 (1988).
15. Amao, A.M. "Mathematical model for Darcy Forchheimer flow with applications to well performance analysis", PhD Thesis, Texas Tech University (2007).
16. Kundu, P., Kumar, V., and Mishra, I.M. "Experimental and numerical investigation of fluid flow hydrodynamics in porous media: Characterization of Darcy and non-Darcy flow regimes", Powder Technol, 303, pp. 278-291 (2016).
17. Cheng, A.H.-D., Detournay, E., and Abousleiman, Y., Poroelasticity, 27, Springer (2016).
18. Timoshenko, S.P. and Gere, J.M. "Theory of elastic stability", Courier Corporation (2009).
19. Bradley, W.B. "Failure of inclined boreholes", J. Energy Resour. Technol., 101(4), p. 232 (1979).
20. Fairhurst, C. "Methods of determining in-situ rock stresses at great depths: Tech", Rep. TRI-68, Mo. River Div. Corps Eng., Omaha, Nebr (1968).
21. Santarelli, F.J., Brown, E.T., and Maury, V. "Analysis of borehole stresses using pressure-dependent, linear elasticity", in International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 23(6), pp. 445-449 (1986).
22. Li, P., Wang, K., and Lu, D. "Analytical solution of plane-strain poroelasticity due to surface loading within a finite rectangular domain", Int. J. Geomech., 17(4), p. 4016089 (2016).
23. Olson, J.E. and Srinivasan, S. "The impact of shale properties on wellbore stability", PhD Thesis (2005).
24. Wang, Z., Peden, J.M., and Damasena, E.S.H., et al. "The prediction of operating conditions to constrain sand production from a gas well", in SPE Production Operations Symposium (1991).
25. Ong, S.H., Ramos, G.G., and Zheng, Z. "Method of predicting the on-set of formation solid production in high-rate perforated and open hole gas wells", Google Patents (2007).
26. Irmay, S. "On the theoretical derivation of Darcy and Forchheimer formulas", Eos, Trans. Am. Geophys. Union, 39(4), pp. 702-707 (1958).
27. Al-Attar, H. and Al-Zuhair, S. "A general approach for deliverability calculations of gas wells", J. Pet. Sci. Eng., 67(3-4), pp. 97-104 (2009).
28. Systemes, D. "Abaqus analysis users manual", Simulia Corp. Provid. RI, USA (2007).
29. Zamanipour, Z., Miska, S.Z., Hariharan, P.R., et al. "Effect of transient surge pressure on stress distribution around directional wellbores", in IADC/SPE Drilling Conference and Exhibition (2016).
30. Heidarian, M., Jalalifar, H., Schaffie, M., Jafari, S., et al. "New analytical model for predicting the unstable zone around the borehole", SPE J., 19(6), pp. 1-177 (2014).
31. Al-Shaaibi, S.K., Al-Ajmi, A.M., and Al-Wahaibi, Y. "Three dimensional modeling for predicting sand production", J. Pet. Sci. Eng., 109, pp. 348-363 (2013).
Scientia Iranica
Volume 26, Issue 3
Transactions on Civil Engineering (A)
May and June 2019
Pages 1182-1193

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History

  • Receive Date: 28 January 2017
  • Revise Date: 29 July 2017
  • Accept Date: 02 December 2017

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