КОНЕЧНО-ЭЛЕМЕНТНЫЙ АНАЛИЗ РАСПРОСТРАНЕНИЯ ГИДРАВЛИЧЕСКОГО РАЗРЫВА В МАССИВЕ ГОРНЫХ ПОРОД Hydraulic fracture propagation in rock mass with XFEM

Luyang Shi, YanKe Shi, Yuyi Song

Аннотация


Представлена модель распространения гидроразрыва в массиве горных пород с использованием расширенного метода конечных элементов. Предложенный алгоритм применяется к полностью связанной системе определяющих уравнений, описывающих поток жидкости и деформацию горных пород. Вода внутри трещины рассматривается как несжимаемая ньютоновская жидкость. В предлагаемой
формулировке используются обобщенные функции формы первого порядка для узлов вокруг трещин, а расширенный метод Лагранжа в сочетании с методом «склейки» (сегмент к сегменту) используется для описания контакта двух граней трещин.

Полный текст статьи публикуется в английской версии журнала
«Soil Mechanics and Foundation Engineering”, vol.60, No.5


Литература


RAAEN A.M., SKOMEDAL, E., KJØRHOLT, H., MARKESTAD, P., ØKLAND, D. Stress determination from hydraulic fracturing tests: the system stiffness approach. International Journal of Rock Mechanics and Mining Sciences,38,529-541(2001).

MURDOCH, L.C., & SLACK, W.W. Forms of hydraulic fractures in shallow fine-grained formations. Journal of Geotechnical and Geoenvironmental Engineering,128,479-487(2002).

HAINEY, B.W., KECK, R.G., SMITH, M.B., LYNCH, K.W., BARTH, J.W. On-site fracturing disposal of oilfield-waste solids in Wilmington field, California. SPE Production & Facilities ,14, 83-87(1999).

YANGQING, W., and DAOYUAN, Z. An introduction to rock mass hydraulics. ChengDu:Southwest jiaotong university press,(1995).

LECAMPION, B. An extended finite element method for hydraulic fracture problems. Communications in Numerical Methods in Engineering ,25,121-133(2009).

REN, Q.W., DONG Y.W., YU, T.T. Numerical modeling of concrete hydraulic fracturing with extended finite element method. Science in China, Series E: Technological Sciences ,52, 559-565(2009).

GORDELIY, E., and PEIRCE, A. Coupling schemes for modeling hydraulic fracture propagation using the XFEM. Computer Methods in Applied Mechanics and Engineering, 253,305-322(2013).

MOHAMMADNEJAD, T., and KHOEI, A.R. An extended finite element method for hydraulic fracture propagation in deformable porous media with the cohesive crack model. Finite Elements in Analysis and Design, 73,77-95 (2013).

RETHORE, J., DE BORST, R., ABELLAN, M.A. A two-scale approach for fluid flow in fractured porous media. International Journal for Numerical Methods in Engineering,71,780-800(2007).

RETHORE, J., DE BORST, R., ABELLAN, M.A. A two-scale model for fluid flow in an unsaturated porous medium with cohesive cracks. Computational Mechanics,42,227-238(2008).

BALTUSSEN, M.G.H.M., CHOI, Y.J., HULSEN, M.A., ANDERSON, P.D. Weakly-imposed Dirichlet boundary conditions for non-Newtonian fluid flow. Journal of non-newtonian fluid mechanics ,166,993-1003 (2011).

GUPTA, P., and DUARTE, A. Simulation of non-planar three-dimensional hydraulic fracture propagation. International Journal for Numerical and Analytical Methods in Geomechanics,38,1397-1430(2014).

REMIJ, E.W., REMMERS, J.J.C., HUYGHE, J.M., SMEULDERS, D.M.J. The enhanced local pressure model for the accurate analysis of fluid pressure driven fracture in porous materials.Computer methods in applied mechanics and engineering ,286,293-312(2015).

MESCHKE, G., and LEONHART, D. A Generalized Finite Element Method for hydro-mechanically coupled analysis of hydraulic fracturing problems using space-time variant enrichment functions. Computer methods in applied mechanics and engineering,290,438-465 (2015).

YU,W.,XIAO,L.,RUNQING,Z.,CHUNAN,T.Numerical evaluation of the shear stimulation effect in naturally fractured formations.Science China(Earth Sciences),2,371-383(2016).

YOUSEF,H.,and BERND,M. Modelling of hydraulic fracturing and fluid flow change in saturated porous domains,Proceedings in Applied Mathematics and Mechanics,17,95-98,(2017).

WENHAO,S.,FUQIAN,Y.,YA-PU,Z. Unstable crack growth in hydraulic fracturing: The combined effects of pressure and shear stress for a power-law fluid,Engineering Fracture Mechanics,23,(2018).

AFSHIN,A.,ERIK,E.Influence of tectonic stress regime on the magnitude distribution of induced seismicity events related to hydraulic.Journal of Petroleum Science and Engineering,182,(2019).

SAYANTAN,G.,SETH,B.,ROGER,M.S.Analysis and prediction of stimulated reservoir volumes through hydraulic fracturing:Examples from western Arkoma Basin.Joural of Petroleum Science and Engineering,182,(2019).

BATCHELOR, G.K. An introduction to fluid dynamics. Cambridge University Press, Cambridge, UK(1967).

LUYANG, S., TIANTANG, Y., TINH, Q. B. Numerical modeling of hydraulic fracturing in rock mass by the XFEM. Soil Mechanics and Foundation Engineering ,52(2),74-83(2015).

FRIES, T.P. A corrected XFEM approximation without problems in blending elements. International Journal for Numerical Methods in Engineering, 75,503-532(2008).

YU, T.T.,and REN Q.W. Modeling crack in viscoelastic media using the extended finite element. Science China Technological Sciences,54,1599-1606 (2011).

BUDYN, É., MOES, N., BELYTSCHKO, T. A method for multiple crack growth in brittle materials without remeshing. International Journal for Numerical Methods in Engineering , 6,1741-1770(2004).

ADACHI, J., SIEBRITS, E., PEIRCE, A. Desroches J. Computer simulation of hydraulic fractures. International Journal of Rock Mechanics & Mining Sciences,44,739-757(2007).

LIAO,X.,WANG,L.Q., YU, P.Stability of Dynamical Systems,Volume 5(Monograph Series on Nonlinear Science and Complexity),Elsevier Science(2007).

DOLBOW, J., MOES N., BELYTSCHKO, T. An extended finite element method for modeling crack growth with frictional contact. Computer Methods in Applied Mechanics and Engineering, 190, 6825-6846(2001).

RHEE, H.C., and KANNINEN, M.F. Opportunities for application of fracture mechanics for offshore structures. Applied Mechanics Reviews ,41,23-35(1988).

GEERTSMA, J., and DE KLERK, F. A rapid method of predicting width and extent of hydraulic induced fractures. Journal of Petroleum Technology, 246, 1571-1581(1969).

TALEGHANI, A.D. Analysis of hydraulic fracture propagation in fractured reservoirs: an improved model for the interaction between induced and natural fractures. The university of Texas, USA(2009).


Ссылки

  • На текущий момент ссылки отсутствуют.