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

Document Type : Article


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.


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.


Main Subjects

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 uid ow 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 ows 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 modi_ed method for predicting the stresses around producing boreholes in an isotropic in-situ stress _eld", 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 coe_cient", 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 ow 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. E_ects of non-Darcy ow 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 ow 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 _eld", Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 25(3), pp. 171-182 (1988). 15. Amao, A.M. Mathematical model for Darcy Forchheimer ow with applications to well performance analysis", PhD Thesis, Texas Tech University (2007). A. Tohidi et al./Scientia Iranica, Transactions A: Civil Engineering 26 (2019) 1182{1193 1191 16. Kundu, P., Kumar, V., and Mishra, I.M. Experimental and numerical investigation of uid ow hydrodynamics in porous media: Characterization of Darcy and non-Darcy ow 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 _nite 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. Syst_emes, D. Abaqus analysis users manual", Simulia Corp. Provid. RI, USA (2007). 29. Zamanipour, Z., Miska, S.Z., Hariharan, P.R., et al. E_ect of transient surge pressure on stress distribution around directional wellbores", in IADC/SPE Drilling Conference and Exhibition (2016). 30. Heidarian, M., Jalalifar, H., Scha_e, 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).