ایجاد مدل رفتاری الاستیک- کاملاً پلاستیک عددی بر اساس معیار تسلیم موگی- کولمب

نوع مقاله: مقاله پژوهشی

نویسندگان

1 گروه مکانیک سنگ، دانشکده فنی و مهندسی، دانشگاه تربیت مدرس

2 پژوهشگر و مدرس، دانشگاه علوم و فناوری نروژ

10.29252/anm.7.14.51

چکیده

مشکلات ریزش در چاه­های نفت هزینه­های زیادی را در تولید نفت تحمیل می­نماید که یکی از علل این مشکلات می­تواند تخمین نادرست وزن گل حفاری باشد. انتخاب معیار تسلیم مناسب در تخمین وزن گل نقش اساسی دارد. در بررسی­های تحلیلی انجام شده در زمینه پایداری چاه نفت، کارایی معیار تسلیم موگیکولمب نسبت به دیگر معیارها تأیید شده است که دلیل آن در نظر گرفتن تأثیر مناسب تنش اصلی میانی است. تاکنون به بررسی عددی این معیار پرداخته نشده است. در این پژوهش مدل رفتاری الاستیککاملاً پلاستیک بر اساس معیار موگی-کولمب ایجاد و در نرم‌افزارFLAC2D اضافه شده است. برای صحت سنجی این مدل از داده­های آزمایش سه محوره بر روی سنگ بازالت استفاده شد که نتایج نشان دهنده­ی دقت قابل قبول مدل است. سپس مقایسه­ای بین سه معیار تسلیم موهر-کولمب، موگی-کولمب و دراگر-پراگر براساس مطالعه موردی از داده­های مکانیک سنگی میدان نفتی در کانادا استفاده شده است. دلیل انتخاب این سه معیار، تأثیر متفاوت نتش اصلی میانی در این معیارها است. با توجه به نتایج به دست آمده محدوده­ی پلاستیک تعیین شده توسط مدل موگی-کولمب در محدوده­ی فی‌مابین دو مدل دیگر است.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

An Elastic-Perfect Plastic Constitutive Model Based on Mogi-Coulomb Yield Criterion

نویسندگان [English]

  • Seyyed Reza Hassani Zaveh 1
  • Morteza Ahmadi 1
  • Seyyed Ali Ghoreishian Amiri 2
1 Dept. of Rock Mechanics, Tarbiat Modares University
2 Researcher & Lecturer, Norwegian University of Science and Technology (NTNU)
چکیده [English]

Summary
Wellbore instability can increase drilling time and sometimes leads to wells being side-tracked.  Appropriate estimation of the weight of drilling mud can be mentioned as the key designing factor to ensure the mechanical stability of wellbores. Considering the elastoplastic behavior of the medium, yield criterion plays a key role in this analysis and estimation. Applying the Mohr-Coulomb criterion leads to underestimation of rock strength due to ignoring the effect of the intermediate principal stress. On the other hand, the Mogi-Coulomb yield criterion is able to consider the effect of the intermediate principal stress, while preserves the simplicity of the Mohr-Coulomb model. In this study, the elastic - perfectly plastic constitutive model is developed based on the Mogi-Coulomb criterion. Model predictions for some triaxial tests are compared with experimental data, and reasonable agreement is achieved. The proposed model is also applied for analyzing a wellbore stability problem and results are compared with two popular models, Mohr-Coulomb and Drucker-Prager, to investigate the effect of the intermediate principal stress.
 
Introduction
The simplicity of the Mohr-Coulomb criterion makes it as one the most popular models in geomechanical analysis. However, ignoring the effect of the intermediate principal stress can be mentioned as the main shortcoming of this model. On the other hand, the effect of the intermediate principal stress has been widely studied in experimental and analytical investigations. The Mogi-Coulomb yield criterion, not only overcomes this shortcoming, but also conserves the simplicity of the Mohr-Coulomb model. Alajmi and Zimmerman (2005) analytically showed the ability of Mogi-Coulomb criterion in considering the effect of the intermediate principal stress. This investigation showed that this criterion can introduce a more realistic estimation of rocks strength.
 
Methodology and Approaches
An elastic-perfectly plastic constitutive model is developed based on the Mogi-Coulomb yield criterion. The proposed model is implemented to “FLAC”. Verification is done by simulating some triaxial test data. Numerical example is also conducted to investigate the efficiency of the model.
 
Results and Conclusions
Results of the numerical study shows that the Mohr-Coulomb criterion results in underestimation of rocks strength by ignoring the effect of the intermediate principal stress. On the other hand, the Drucker-Prager criterion leads to overestimation of the strength by considering identical effects for both intermediate and minimum principal stress. While the Mogi-Coulomb criterion introduces a more realistic estimation of the strength by moderating the effect of the intermediate principal stress.

کلیدواژه‌ها [English]

  • Wellbore stability
  • Weight of drilling mud
  • Constitutive model
  • Elastic - perfectly plastic
  • Mogi - Coulomb criterion
  • FLAC
[1] Fjar, E., Holt, R. M, Raaen, A. M, Risnes, R, & Horsrud, P. (2008). Petroleum related rock mechanics (Vol. 53). Elsevier.

[2] Mogi, K. (2007). Experimental rock mechanics. CRC Press.

[3] Cai, M. (2008). Influence of intermediate principal stress on rock fracturing and strength near excavation boundaries—insight from numerical modeling. International Journal of Rock Mechanics and Mining Sciences, 45(5), 763-772.

 

[4] Addis, M. A., & Wu, B. (1993, December). The role of the intermediate principal stress in wellbore stability studies: evidence from hollow cylinder tests. In International journal of rock mechanics and mining sciences & geomechanics abstracts (Vol. 30, No. 7, pp. 1027-1030). Pergamon.

[5] Xu, S. Q., & Yu, M. H. (2006). The effect of the intermediate principal stress on the ground response of circular openings in rock mass. Rock mechanics and rock engineering, 39(2), 169-181.

[6] Al-Ajmi, A. M, & Zimmerman, R. W. (2005). Relation between the Mogi and the Coulomb failure criteria. International Journal of Rock Mechanics and Mining Sciences, 42(3), 431-439.

[7] Al-Ajmi, A. M. & Zimmerman, R. W. (2006). Stability analysis of vertical boreholes using the Mogi–Coulomb failure criterion. International Journal of Rock Mechanics and Mining Sciences, 43(8), 1200-1211.

[8] Manshad, A. K., Jalalifar, H., & Aslannejad, M. (2014). Analysis of vertical, horizontal and deviated wellbores stability by analytical and numerical methods. Journal of Petroleum Exploration and Production Technology, 4(4), 359-369.

[9] S. Maleki, R. Gholami, V. Rasouli, A. Moradzadeh, R. G. Riabi, and F. Sadaghzadeh, “Comparison of different failure criteria in prediction of safe mud weigh window in drilling practice,” Earth-Science Rev., vol. 136, pp. 36–58, Sep. 2014.

[10] R. Gholami, a. Moradzadeh, V. Rasouli, and J. Hanachi, “Practical application of failure criteria in determining safe mud weight windows in drilling operations,” J. Rock Mech. Geotech. Eng., vol. 6, no. 1, pp. 13–25, Feb. 2014.

[11] Elyasi, A., & Goshtasbi, K. (2015). Using different rock failure criteria in wellbore stability analysis. Geomechanics for Energy and the Environment.

[12] Chen, W. F. & Han, D. J. (2012). Plasticity for structural engineers. Springer Science & Business Media.

[13] Manual, FLAC Users. (1998). Itasca Consulting Group Inc. Minneapolis, USA.

[14] Elyasi, A. (2011). 3-D Stability Modelling of Multilateral Oil Wells. Master's thesis. Rock Mechanics group. Tarbiat Modares University (TMU). In Persian.

[15] Alejano, L. R., & Bobet, A. (2012). Drucker–Prager Criterion. Rock mechanics and rock engineering, 45(6), 995-999.