تحلیل رشد ترک هیدرولیکی در مقیاس سختی با درنظرگرفتن اثر اندرکنش فراسنج‌های ماند و گرانروی: ترم‌های مرتبۀ بالاتر

نوع مقاله : مقاله پژوهشی

نویسندگان

1 گروه مهندسی عمران، دانشکده فنی و مهندسی، دانشگاه مازندران، بابلسر، ایران

2 دانشگاه تربیت مدرس

چکیده

در فرآیند شکست هیدرولیکی معمولاً  فراسنج‌های مختلف مانند گرانروی، جرم مخصوص سیال و چقرمگی محیط اثرات مشابه و یکسانی بر چگونگی رشد ندارند و ممکن است یک یا چند تا از فراسنج‌ها اهمیت بیشتری داشته باشند؛ در نتیجه منجر به یک یا چند رژیم خاص  خواهدشد.  رژیم‌ها بر اساس روند هدر رفت انرژی نام‌گذاری می‌شوند که مهم‌ترین آن ها عبارتند از: اول( رژیم سختی که بیشترین انرژی تزریق سیال از طریق شکافتن سنگ به دلیل چقرمگی اتلاف می‌شود دوم( رژیم گرانروی که بیشترین اتلاف توان ورودی سیال ناشی از حرکت سیال لزج در ترک است. در این نوشتار به بررسی رشد ترک هیدرولیکی دو بعدی، در حالت کرنش  صفحه‌ای در یک محیط کشسان پرداخته می‌شود. سیال به صورت غیرقابل تراکم و نیوتنی فرض می‌شود و همچنین رشد ترک در قالب مکانیک شکست خطی کشسان بررسی  می‌شود. هدف از این پژوهش، دستیابی به اثرات انواع  فراسنج‌ها ازقبیل چقرمگی، گرانروی، جرم مخصوص سیال و همچنین اثربخشی اندرکنش بین برخی از فراسنج‌ها به طور خاص اثرات توام گرانروی و جرم مخصوص سیال برای یک ترک دو بعدی در رژیم سختی است. برای ارزیابی اندرکنش بین فراسنج‌های اشاره شده یک روش  اصلاح‌شده-روش اغتشاش- ارائه شده است. این روش قابلیت تحلیل مسائل مشابه با دیگر هندسه و رژیم را دارد. نتایج نشان می‌دهد که درنظرگرفتن ترم اندرکنشی باعث برآورد کمتری از طول ترک خواهد شد و طول ترک با افزایش گرانروی کاهش می‌یابد و روند کاهشی با افزایش فراسنج جرم مخصوص (ماند) شدت می‌یابد. از طرف دیگر، اثرات گرانروی سیال در فرآیند تزریق شکست هیدرولیکی بیشتر از اثرات فراسنج ماند با فرض جریان آرام می‌باشد. مسلما، در نظرنگرفتن اثرات ماند می‌تواند خطای  چشمگیری را وارد کند .این خطاها با افزایش فراسنج ماند، افزایش می‌یابد و ممکن است به 300% نیز برسد. به طور کلی نتایج با مستندات موجود مقایسه شده است که روند منطقی در آنها را تصدیق می‌کند.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Analysis of Hydraulic Fracture Propagation in Toughness Dominant with Considering Fluid Viscosity and Inertia Parameters Interaction: Higher Order Terms

نویسندگان [English]

  • Ali Asgari 1
  • ali akbar golshani 2
1 Assistant Professor of Geotechnical Engineering, Faculty of Engineering and Technology, University of Mazandaran, Babolsar, Iran.
2 استادیار دانشکده عمران و محیط زیست
چکیده [English]

In the process of hydraulic fracture, various physical parameters such as; viscosity, inertia of fluid and toughness of rock do not influence the fracture propagation identically, and it is probable that one or more of the parameters be more pronounced. Therefore, it may persuade one special regime which is named base on the dissipation of energy. In an impermeable rock, the two limiting regimes can be identified with the dominance of one or the other of the two energy dissipation mechanisms corresponding to extending the fracture in the rock and to flow of viscous fluid in the fracture, respectively. In the viscosity-dominated regime, dissipation in extending the fracture in the rock is negligible compared to the dissipation in the viscous fluid flow, and in the toughness-dominated regime, the opposite holds. It is supposed that the flow of incompressible fluid in the fracture is unidirectional and laminar. Besides, the fracture is fully fluid-filled at all times and fracture propagation is described in the framework of linear elastic fracture mechanics (LEFM). The contribution of this research is a detailed study of the evaluation parameters’ effects on the propagation of hydraulic fracture an impermeable brittle rock. Here, the modified perturbation method suggested for evaluating fluid viscosity and inertia parameters interaction (FVII). The proposed method provides a good estimate of the solution in the wide range of the viscosity/inertia parameters because of the coexistence of both small parameters in the governing equations. The results showed that considering the FVII reduce the length of the crack, and the crack length decreases with increasing viscosity parameter, and the decreasing trend will be intensified by increasing the inertia of fluid. On the other hand, the effects of fluid viscosity in the hydraulic fracture injection process are more pronounced than the effects of the inertia parameter on the assumption of a laminar flow. Neglecting the effect of the FVII result in a significant error. These errors continue to increase with the increase, and may reach about 300%. At last, the results are compared with the available references, which confirms the logical process. 

کلیدواژه‌ها [English]

  • hydraulic fracture
  • Interaction effect
  • Inertia
  • viscosity
  • Modified perturbation method
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