Calculation Method for Equivalent Geometric Characteristics of Hydraulic Fractures in Heterogeneous Rock Based on PHF-LSM Method

doi:10.12068/j.issn.1005-3026.2023.12.011

Abstract

Abstract: The permeability-based hydraulic fracture-level set method(PHF-LSM)is a smeared fracture model based on Biot consolidation theory. The model simulates the fracture development process by weakening the fracture and rock material properties in the damaged area， so the geometric characteristics of hydraulic fractures cannot be given in the solution process. According to the average effective stress field distribution during hydraulic fracture propagation， the equivalent path and equivalent height of hydraulic fracture by PHF-LSM method are established in this paper. According to the displacement field around the equivalent propagation path， the equivalent opening of hydraulic fractures is calculated， and the effectiveness of the proposed method is verified by comparing with KGD theoretical model. At the same time， the dynamic development characteristics of equivalent geometric characteristics for fractures in both homogeneous and heterogeneous rock are calculated. The results demonstrate that the established equivalent calculation method compensates for the deficiency of PHF-LSM by allowing for the determination of geometric characteristics of hydraulic fractures.

Key words: hydraulic fracturing; PHF-LSM; equivalent geometric characteristics; crack propagation; heterogeneous rock

CLC Number:

TU443

LI Ming， HUANG Lei-peng， LIU Shi-yi， LIANG Li. Calculation Method for Equivalent Geometric Characteristics of Hydraulic Fractures in Heterogeneous Rock Based on PHF-LSM Method[J]. Journal of Northeastern University(Natural Science), 2023, 44(12): 1751-1758.

References

[1]Adachi J，Siebrits E，Peirce A.Computer simulation of hydraulic fractures［J］.International Journal of Rock Mechanics and Mining Sciences，2006，44(5):739-757.
[2]李明耀，贺甲元，苏业旺.页岩油气水力压裂的关键力学问题和数值计算方法［J］.科技导报，2016，34(23):32-42.(Li Ming-yao，He Jia-yuan，Su Ye-wang.Key mechanical problems and numerical calculation methods of shale oil and gas hydraulic fracturing［J］.Science and Technology Herald，2016，34(23):32-42.)
[3]陈勉，庞飞，金衍.大尺寸真三轴水力压裂模拟与分析［J］.岩石力学与工程学报，2000，19(sup1):868-872.(Chen Mian，Pang Fei，Jin yan.Simulation and analysis of large-scale true triaxial hydraulic fracturing ［J］.Journal of Rock Mechanics and Engineering，2000，19(sup1):868-872.)
[4]Chen M，Guo T K，Qu Z Q，et al.Numerical investigation into hydraulic fracture initiation and breakdown pressures considering wellbore compliance based on the boundary element method［J］.Journal of Petroleum Science and Engineering，2022，211:110162.
[5]赵瑜，何鹏飞.基于PPCZ模型的KGD水力压裂数值模拟［J］.煤炭学报，2018，43(10):2866-2875.(Zhao Yu，He Peng-fei.Numerical simulation of KGD hydraulic fracture based on PPCZ model ［J］.Journal of China Coal Society，2018，43(10):2866-2875.)
[6]Tian W，Li P C，Dong Y，et al.Numerical simulation of sequential，alternate and modified zipper hydraulic fracturing in horizontal wells using XFEM［J］.Journal of Petroleum Science and Engineering，2019，183:106251.
[7]Heider Y，Markert B.A phase-field modeling approach of hydraulic fracture in saturated porous media［J］.Mechanics Research Communications，2017，80:187-196.
[8]Heider Y，Reiche S，Siebert P，et al.Modeling of hydraulic fracturing using a porous-media phase-field approach with reference to experimental data［J］.Engineering Fracture Mechanics，2018，202:116-134.
[9]Carter B J，Desroches J，Ingraffea A R，et al.Simulating fully 3D hydraulic fracturing［M］.New York:John Wiley and Sons，2000:525-557.
[10]Belytschko T.Elastic crack growth in finite elements with minimal remeshing［J］.International Journal for Numerical Methods in Engineering，1999，45(5):131-156.
[11]Mohammadnejad T，Khoei A R.An extended finite element method for hydraulic fracture propagation in deformable porous media with the cohesive crack model［J］.Finite Elements in Analysis & Design，2013，73:273-289.
[12]Renato G E，Eleazar C M.Xfem modeling of stress shadowing in multiple hydraulic fractures in multi-layered formations［J］.Journal of Natural Gas Science and Engineering，2019，70(12):208-214.
[13]Hu M S，Yuan W.Development of a discontinuous approach for modeling fluid flow in heterogeneous media using the numerical manifold method［J］.International Journal for Numerical and Analytical Methods in Geomechanics，2015，39(17):619-624.
[14]Branko D，Cundall P.Application of distinct element methods to simulation of hydraulic fracturing in naturally fractured reservoirs［J］.Computers and Geotechnics，2016，71:259-306.
[15]Huang L K，Liu J J，Zhang F S.Exploring the influence of rock inherent heterogeneity and grain size on hydraulic fracturing using discrete element modeling［J］.International Journal of Solids and Structures，2019，23:176-177.
[16]Hu Y J，Chen G L，Cheng W P，et al.Simulation of hydraulic fracturing in rock mass using a smeared crack model［J］.Computers and Structures，2014，137:151-187.
[17]Pak A.Numerical modeiing of hydmuiic fracturing［D］.Edmonton: University of Alberta，1997.
[18]Dugdale D S.Yielding of steel sheets containing slits［J］.Pergamon，1960，8(2):1169-1179.
[19]Barenblatt G L.The mathematical theory of equilibrium cracks in brittle fracture［J］.Advances in Applied Mechanics，1962，7(1):55-129
[20]Sarris P P.The influence of the cohesive process zone in hydraulic fracturing modelling［J］.International Journal of Fracture，2011，167(1):807-819.
[21]Li M，Guo P J，Stolle D，et al.Modeling method and hydraulic fracture propagation for jointed rock mass using PHF-LSM method［J］.Journal of Natural Gas Science and Engineering，2019，68:138-147.
[22]Stanley O，Sethian J A.Fronts propagating with curvature-dependent speed:algorithms based on Hamilton-Jacobi formulations［J］.Journal of Computational Physics，1988，79(1):12-19.
[23]Yi L P，Li X G，Yang Z Z，et al.A fully coupled fluid flow and rock damage model for hydraulic fracture of porous media［J］.Journal of Petroleum Science and Engineering，2019，178:42-50.
[24]Li M，Guo P J，Stolle D，et al.Modeling hydraulic fracture propagation in a saturated porous rock media based on EPHF method［J］.Journal of Natural Gas Science and Engineering，2021，89:103887.
[25]李明，郭培军，李鑫，等.基于水平集法的非均质岩石建模及水力压裂传播特性研究［J］.岩土力学，2016，37(12):3591-3597，3607.(Li Ming，Guo Pei-jun，Li Xin，et al.Research on heterogeneous rock modeling and hydraulic fracturing propagation characteristics based on level set method ［J］.Geotechnical Mechanics，2016，37(12):3591-3597，3607.)
[26]赵鹏，谢凌志，杨春和，等.基于弥散式裂缝模型的水力压裂研究［J］.岩石力学与工程学报，2015，34(sup1):2593-2600.(Zhao Peng，Xie Ling-zhi，Yang Chun-he，et al.Research on hydraulic fracturing based on dispersion fracture model ［J］.Journal of Rock Mechanics and Engineering，2015，34(sup1):2593-2600.)
[27]Corey A T.The interrelation between gas and oil relative permeabilities［J］.Producers Monthly，1954，19:38-41.
[28]Li M，Guo P J，Stolle D，et al.Heterogeneous rock modelling method and characteristics of multistage hydraulic fracturing based on the PHF-LSM method［J］.Journal of Natural Gas Science and Engineering，2020，83:103518.
[29]Perlin K.An image synthesizer［J］.Computer & Graphics，1985，19(3):287-296.
[30]Wasantha P L P，Konietzky H，Xu C.Effect of in-situ stress contrast on fracture containment during single-and multi-stage hydraulic fracturing［J］.Engineering Fracture Mechanics，2019，205:175-189.