مقایسه‌ی انتشار ترک‌های هیدرولیکی دوبعدی کرنش صفحه‌ای و شعاعی در مقیاس گرانروی با رویکرد تحلیلی

نوع مقاله : مقاله پژوهشی

نویسندگان

1 استادیار، گروه مهندسی عمران، دانشکده مهندسی و فناوری، دانشگاه مازندران، بابلسر، ایران.

2 دانشیار، گروه مکانیک خاک و پی، دانشکده مهندسی عمران و محیط زیست، دانشگاه تربیت مدرس، تهران، ایران.

10.22034/hydro.2024.59590.1313

چکیده

فراسنج‌های مختلفی نظیر گرانروی، جرم مخصوص سیال و سختی محیط در فرآیند رشد شکست هیدرولیکی تاثیر دارند. این فراسنج­ها اثرات یکسانی بر چگونگی رشد ندارند و ممکن است یک یا چند تا از فراسنج‌ها تاثیر بیشتری داشته باشند؛ در نتیجه منجر به یک یا چند رژیم خاص خواهد شد. رژیم‌ها بر اساس روند هدر رفت انرژی نامگذاری می­شوند که مهمترین آن‌ها عبارتند از: اول: رژیم سختی که بیشترین انرژی تزریق سیال از طریق شکافتن سنگ به­دلیل سختی اتلاف می‌شود دوم: رژیم گرانروی که بیشترین اتلاف توان ورودی سیال ناشی از حرکت سیال لزج و در داخل ترک است. در این پژوهش به بررسی رشد ترک هیدرولیکی با شکل هندسی مختلف از قبیل ترک دوبعدی کرنش صفحه‌ای و شعاعی در یک محیط سنگی شکننده (کشسان) پرداخته می‌شود. سیال به‌صورت غیرقابل تراکم و نیوتنی فرض می‌شود و همچنین رشد ترک در قالب مکانیک شکست خطی کشسان بررسی می‌شود. هدف از این بخش، دستیابی به اثرات هندسه ترک است. نتایج نشان می‌دهد که روش‌های شبه تحلیلی ارائه شده برای حل معادلات همبسته، از دقت کافی و سرعت همگرایی بالا برخوردار است. در زمان‌های زودهنگام از فرآیند شکست هیدرولیکی، ترک‌های صفحه‌ای رشد سریعتری نسبت به ترک‌ها با هندسه‌ی سکه‌ای شکل دارند، اما در زمان‌های بعدی سرعت رشد ترک‌های سکه‌ای به‌شدت از ترک صفحه‌ای پیشی می‌گیرند. میزان بازشدگی عرض ترک صفحه‌ای از ترک سکه‌ای شکل بیشتر است و همین امر باعث شد که در رژیم گرانروی میزان رشد آن کاهش چشمگیری داشته باشد.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Comparison of 2D plane strain and radial hydraulic fracturing propagation in the viscosity dominated regime with an analytical approach

نویسندگان [English]

  • Ali Asgari 1
  • Aliakbar Golshani 2
1 Department of Civil Engineering, Faculty of Engineering and Technology, University of Mazandaran, Babolsar, Iran.
2 Associated Professor, Department of Soil and Foundation Engineering, Faculty of Civil and Environmental Engineering, Tarbiat Modares University, Tehran, Iran.
چکیده [English]

Several factors, such as fluid viscosity, density, and medium toughness, can influence the hydraulic fracture growth process. It is important to note that these parameters do not affect the growth process equally, and one or more of the parameters may have a more significant impact than the others. As a result, it can lead to one or more regimes. The regimes are named based on the process of energy dissipation, the most important of which are: first: toughness regime, where the most energy of fluid injection is dissipated due to rock failure, second: viscous regime, where the greatest input power loss is caused by the movement of viscous fluid in the crack. The research investigates crack growth in a brittle (elastic) rock medium employing linear elastic fracture mechanics (LEFM). The fluid is assumed to be incompressible and Newtonian. The study examines the growth of hydraulic cracks with various geometric shapes such as KGD and radial cracks. The results show that the semi-analytical method for solving the coupled governing equations of hydraulic fracturing has sufficient accuracy and high convergence speed. During the early stages of the hydraulic fracturing process, the KGD crack grows at a faster rate than the penny-shaped crack. However, at later stages, the growth of the penny-shaped crack greatly exceeds that of the KGD crack. Furthermore, the rate of KGD crack opening is higher than that of the penny-shaped crack. As a result, there is a significant decrease in the growth rate of the penny-shaped crack in the viscosity regime relative to KGD.

کلیدواژه‌ها [English]

  • 2D plane strain crack
  • analytical method
  • hydraulic fracture
  • penny-shape crack
  • viscous regime
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