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Lattice Numerical Simulations of Lab-Scale Hydraulic Fracture and Natural Interface Interaction

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Abstract

Hydraulic fracturing is the prime technology for enhancing production from unconventional reservoirs. Design and operation of hydraulic fracturing requires adequate knowledge of formation properties, in situ stresses and fluid properties, due to its complex nature. One of the challenges, that have been the subject of many past studies, is the interaction mechanism when hydraulic fracture intersects a natural interface (e.g., natural fracture or interbed). Crossing, arresting and opening are the known interaction mechanisms. The formation properties, state of in situ stresses, stress contrast, strength properties of the interface, angle of intersection and injecting fluid characteristics affect the interaction mechanism to different extents. The use of numerical models is widespread in simulation of hydraulic fracturing. The use of methods based on the continuum (e.g., FEM) and discontinum (e.g., DEM) representation of media is subjected to some limitations in predicting the correct geometry of the propagating fracture. Lattice method, which is based on the bonded particle approach, has shown promise in simulating hydraulic fracturing. In this paper, lattice modeling is used to simulate the interaction mechanism of lab experiments carried out on mortar samples but at larger scales. The cubical mortar samples of 10 cm size had two synthetically built natural fractures with different angles of approach and filled with different types of glue. The effect of intersection angle and the mechanical properties of the interface were simulated numerically under conditions of viscosity-dominated fracture propagation regime as occurred in the lab. The results demonstrate the advantages of lattice simulation to study the impact of each parameter on the fracture interaction. A larger angle of approach and stronger glues are shown to promote the crossing mode. The shear strength and stress anisotropy are the main parameters influencing the interaction mechanism.

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Abbreviations

\(Q_{0}^{\prime }\) :

Flow rate

t :

Time

µ :

Fracturing fluid viscosity

E :

Young’s modulus

v :

Poisson’s ratio

K IC :

Toughness

\(u_{i}^{t}\) :

Position of component i

\(\dot {u}_{i}^{t}\) :

Velocity of component i

m :

Mass

Δt :

Time step

F i :

Force component

\(\omega _{i}^{{(t)}}\) :

Angular velocity of component i

\(\mathop \sum \nolimits^{} M_{i}^{{(t)}}\) :

Sum of all moment components

I :

Inertia

\(F_{i}^{{\text{N}}}\) :

Normal force

\(F_{i}^{{\text{S}}}\) :

Shear forces

k N :

Normal stiffness

k S :

Shear stiffness

\(\dot {u}_{i}^{{\text{N}}}\) :

Velocity of component i in the normal direction

\(\dot {u}_{i}^{{\text{S}}}\) :

Velocity of component i in the shear direction

β :

Dimensionless number

k r :

Relative permeability

a :

Fracture aperture

p :

Fluid pressure

ρ w :

Fluid density

ΔP :

Pressure increment

Q :

Flow rate

V :

Volume of fluid element

K f :

Apparent fluid element bulk modulus

Δt f :

Flow time step

L :

Crack half length

W :

Sample half length

σ :

Stress

References

  • Abdollahipour A, Fatehi Marji M, Yarahmadi Bafghi AR, Gholamnejad J (2015) Simulating the propagation of hydraulic fractures from a circular wellbore using the displacement discontinuity method. Int J Rock Mech Min Sci 80:281–291

    Article  Google Scholar 

  • Abdollahipour A, Fatehi Marji M, Yarahmadi Bafghi AR, Gholamnejad J (2016a) Numerical investigation of effect of crack geometrical parameters on hydraulic fracturing process of hydrocarbon reservoirs. J Min Environ 7(2):205–214

    Google Scholar 

  • Abdollahipour A, Fatehi Marji M, Yarahmadi Bafghi AR, Gholamnejad J (2016b) Time-dependent crack propagation in a poroelastic medium using a fully coupled hydromechanical displacement discontinuity method. Int J Fract 199(1):71–87

    Article  Google Scholar 

  • Abdollahipour A, Fatehi Marji M, Yarahmadi Bafghi AR, Gholamnejad J (2016c) A complete formulation of an indirect boundary element method for poroelastic rocks. Comput Geotech 74:15–25

    Article  Google Scholar 

  • Adachi J, Detournay E (2002) Self-similar solution of a plane-strain fracture driven by a power-law fluid. Int J Numer Anal Methods Geomech 26(6):579–604

    Article  Google Scholar 

  • Behnia M, Goshtasbi K, Fatehi Marji M, Golshani A (2012) The effect of layers elastic parameters on hydraulic fracturing propagation utilizing displacement discontinuity method. Anal Numer Methods Min Eng 3:1–14

    Google Scholar 

  • Blair SC, RK Thorpe F Heuze, Shaffer R (1989) Laboratory observations of the effect of geologic discontinuities on hydrofracture propagation. In: The 30th US Symposium on Rock Mechanics (USRMS), American Rock Mechanics Association

  • Blair SC, RK Thorpe, Heuze F (1990) Propagation of fluid-driven fractures in jointed rock. Part 2—physical tests on blocks with an interface or lens. Int J Rock Mech Min Sci Geomech Abstr 27(4):255–268

    Article  Google Scholar 

  • Blanton TL (1982) An experimental study of interaction between hydraulically induced and pre-existing fractures. In: SPE unconventional gas recovery symposium, Society of Petroleum Engineers

  • Bunger AP (2005) Near-surface hydraulic fracture. Ph.D, University of Minnesota

  • Damjanac B, Gil I, Pierce M, Sanchez M, Van As A, McLennan J (2010) A new approach to hydraulic fracturing modeling in naturally fractured reservoirs. In: 44th US Rock Mechanics Symposium and 5th US-Canada Rock Mechanics Symposium, American Rock Mechanics Association

  • Damjanac B, Detournay C, Cundall P, Purvance M, Hazzard J (2011) XSite—description of formulation. ITASCA Consulting Group., Inc

  • Daneshy AA (1974) Hydraulic fracture propagation in the presence of planes of weakness. SPE European Spring Meeting, Society of Petroleum Engineers

  • de Pater C, Cleary M, Quinn T, Barr D, Johnson D, Weijers L (1994) Experimental verification of dimensional analysis for hydraulic fracturing. SPE Prod Facil 9(04):230–238

    Article  Google Scholar 

  • Dehghan AN, Goshtasbi K, Ahangari K, Jin Y, Bahmani A (2017) 3D numerical modeling of the propagation of hydraulic fracture at its intersection with natural (pre-existing) fracture. Rock Mech Rock Eng 50(2):367–386

    Article  Google Scholar 

  • Fast R, Murer A, Timmer R (1994) Description and analysis of cored hydraulic fractures, Lost Hills field, Kern County, California. SPE Prod Facil 9(02):107–114

    Article  Google Scholar 

  • Fatehi Marji M, Hosseini-Nasab H, Kohsary AH (2007) A new cubic element formulation of the displacement discontinuity method using three special crack tip elements for crack analysis. JP J Solids Struct 1(1):61–91

    Google Scholar 

  • Garagash DI, Detournay E (2005) Plane-strain propagation of a fluid-driven fracture: small toughness solution. J Appl Mech 72(6):916–928

    Article  Google Scholar 

  • Haeri H, Shahriar K, Fatehi Marji M, Moarefvand P (2014) Investigation of fracturing process of rock-like Brazilian disks containing three parallel cracks under compressive line loading. Strength Mater 46(3):404–416, 2014

    Article  Google Scholar 

  • Hopkins C, Frantz J Jr, Hill D, Zamora F (1995) Estimating fracture geometry in the naturally fractured Antrim Shale. In: SPE annual technical conference and exhibition, Society of Petroleum Engineers

  • Hosseini Nasab H, Fatehi Marji M (2007) A semi-infinite higher-order displacement discontinuity method and its application to the quasistatic analysis of radial cracks produced by blasting. J Mech Mater Struct 2(3):439–458, 2007

    Article  Google Scholar 

  • Huang J, Safari R, Mutlu U, Burns K, Geldmacher I, McClure M, Jackson S (2014) Natural-Hydraulic Fracture Interaction: Microseismic Observations and Geomechanical Predictions. URTEC-1921503-MS. Unconventional Resources Technology Conference, 25–27 August, Denver, Colorado, USA

  • Itasca Consulting Group Inc., (2013). HF simulator, version 1.9, user’s guide

  • Lamont N, Jessen F (1963) The effects of existing fractures in rocks on the extension of hydraulic fractures. J Petrol Technol 15(02):203–209

    Article  Google Scholar 

  • Lhomme TPY (2005) Initiation of hydraulic fractures in natural sandstones, TU Delft, Delft University of Technology

  • Mitchell SL, Kuske R, Peirce A (2007) An asymptotic framework for finite hydraulic fractures including leak-off. SIAM J Appl Math 67(2):364–386

    Article  Google Scholar 

  • Moradi A, Tokhmechi B, Rasouli V, Fatehi Marji M (2017) A comprehensive numerical study of hydraulic fracturing process and its affecting parameters. Geotech Geol Eng 35(3):1035–1050

    Article  Google Scholar 

  • Moradi A, Tokhmechi B, Rasouli V, Fatehi Marji M (2018) Displacement discontinuity analysis of the effects of various hydraulic fracturing parameters on the crack opening displacement (COD). J Pet Sci Technol 8(3):3–13

    Google Scholar 

  • Nagel NB, Sanchez-Nagel MA, Zhang F, Garcia X, Lee B (2013) Coupled numerical evaluations of the geomechanical interactions between a hydraulic fracture stimulation and a natural fracture system in shale formations. Rock Mech Rock Eng 46(3):581–609

    Article  Google Scholar 

  • Rasouli V, Sarmadivaleh M, Nabipour A (2011) Some challenges in hydraulic fracturing of tight gas reservoirs: an experimental study. APPEA J 51(1):499–506

    Article  Google Scholar 

  • Renshaw C, Pollard D (1995) An experimentally verified criterion for propagation across unbounded frictional interfaces in brittle, linear elastic materials. Int J Rock Mech Min Sci Geomech Abstr 32:237

    Article  Google Scholar 

  • Sarmadivaleh M (2012) Experimental and numerical study of interaction of a pre-existing natural interface and an induced hydraulic fracture. Doctor of Philosophy, Curtin University

  • Sarmadivaleh M, Rasouli V (2015) Test design and sample preparation procedure for experimental investigation of hydraulic fracturing interaction modes. Rock Mech Rock Eng 48:93–105. https://doi.org/10.1007/s00603-013-0543-z

    Article  Google Scholar 

  • Sarmadivaleh M, Rasouli V, Shihab NK (2011) Hydraulic fracturing in an unconventional naturally fractured reservoir: a numerical and experimental study. APPEA J 51(1):507–518

    Article  Google Scholar 

  • Sarmadivaleh M, Rasouli V, Ramses W (2012) Numerical simulations of hydraulic fracture intersecting an interbed of sandstone. In: Qian Q, Zhou Y (eds) Harmonising rock engineering and the environment. Proceedings of the 12th ISRM international congress on rock mechanics. International Society for Rock Mechanics, Beijing, pp 1111–1115

    Google Scholar 

  • Savitski A, Detournay E (2002) Propagation of a penny-shaped fluid-driven fracture in an impermeable rock: asymptotic solutions. Int J Solids Struct 39(26):6311–6337

    Article  Google Scholar 

  • Warpinski N, Lorenz J, Branagan P, Myal F, Gall B (1993) Examination of a cored hydraulic fracture in a deep gas well (includes associated papers 26302 and 26946). SPE Prod Facil 8(03):150–158

    Article  Google Scholar 

  • Warpinski N, Branagan P, Peterson R, Wolhart S (1998) An interpretation of M-site hydraulic fracture diagnostic results. In: SPE Rocky Mountain Regional/Low-permeability Reservoirs Symposium, Society of Petroleum Engineers

  • Yushi Z, Xinfang M, Shicheng Z, Tong Z, Han L (2016) Numerical investigation into the influence of bedding plane on hydraulic fracture network propagation in shale formations. Rock Mech Rock Eng 49(9):3597–3614

    Article  Google Scholar 

  • Zeng Q, Yao J (2016) Numerical simulation of fracture network generation in naturally fractured reservoirs. J Nat Gas Sci Eng 30:430–443

    Article  Google Scholar 

  • Zhao X, Young R (2009) Numerical simulation of seismicity induced by hydraulic fracturing in naturally fractured reservoirs. In: SPE Annual Technical Conference and Exhibition, Society of Petroleum Engineers

  • Zhou J, Zhang L, Braun A, Han Z (2017a) Investigation of processes of interaction between hydraulic and natural fractures by PFC modeling comparing against laboratory experiments and analytical models. Energies 10(7):1001

    Article  Google Scholar 

  • Zhou J, Zhang L, Han Z (2017b) Hydraulic fracturing process by using a modified two-dimensional particle flow code-method and validation. Prog Comput Fluid Dyn Int J 17(1):52–62

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Mining and Metallurgical Engineering, Yazd University, Yazd, Iran

    E. Bakhshi, A. Ghorbani & M. Fatehi Marji

  2. Department of Petroleum Engineering, University of North Dakota, Grand Forks, USA

    V. Rasouli & X. Wan

  3. Itasca Consulting Group, Minneapolis, USA

    B. Damjanac

Authors
  1. E. Bakhshi
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  2. V. Rasouli
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  3. A. Ghorbani
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  4. M. Fatehi Marji
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  5. B. Damjanac
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  6. X. Wan
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Correspondence to V. Rasouli.

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Bakhshi, E., Rasouli, V., Ghorbani, A. et al. Lattice Numerical Simulations of Lab-Scale Hydraulic Fracture and Natural Interface Interaction. Rock Mech Rock Eng 52, 1315–1337 (2019). https://doi.org/10.1007/s00603-018-1671-2

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