Propagation regimes of buoyancy-driven hydraulic fractures with solidification

2016 ◽  
Vol 797 ◽  
pp. 1-28 ◽  
Author(s):  
E. V. Dontsov
Keyword(s):  
Hydraulic Fracture ◽  
Transfer Problem ◽  
Solidification Rate ◽  
Hydraulic Fractures ◽  
Porous Rock ◽  
Linear Elastic ◽  
Volume Balance ◽  
Elastic Fracture ◽  
Steady Propagation ◽  
Fluid Leak

This study investigates the propagation of a semi-infinite buoyancy-driven hydraulic fracture in situations when the fluid is able to solidify along the crack walls. Such problems occur when hot magma ascends from a chamber due to buoyancy forces and solidifies by interacting with colder rock. In the model, the solidification rate is calculated assuming a one-dimensional heat transfer problem, in which case it becomes mathematically equivalent to Carter’s leak-off model, which is commonly used to describe the fluid leak-off from a hydraulic fracture into a porous rock formation. In order to construct a mathematical model for a buoyancy-driven hydraulic fracture with solidification, the aforementioned thermal problem is combined with (i) linear plane-strain elasticity to ensure equilibrium of the rock surrounding the fracture, (ii) linear elastic fracture mechanics to determine the fracture propagation, (iii) lubrication theory to capture the viscous fluid flow inside the crack and to account for the effect of buoyancy, and (iv) volume balance of the magma. To address the problem, the governing equations are first rewritten in terms of one integral equation with a non-singular kernel, which significantly simplifies the analysis and the procedure for obtaining a numerical solution. The latter solution is shown to obey a multiscale behaviour near the fracture tip that is fully resolved by the numerical scheme. In order to understand the structure of the solution and to quantify the regimes of propagation (and the associated transitions), a thorough analysis of the problem has been performed. Finally, the developments are applied to investigate the non-steady propagation of a buoyancy-driven fracture that is fed by a constant flux.

scholarly journals An approximate solution for a penny-shaped hydraulic fracture that accounts for fracture toughness, fluid viscosity and leak-off

2016 ◽  
Vol 3 (12) ◽  
pp. 160737 ◽  
Author(s):  
E. V. Dontsov
Keyword(s):  
Fracture Toughness ◽  
Approximate Solution ◽  
Hydraulic Fracture ◽  
Fluid Viscosity ◽  
Solution Map ◽  
Fracture Width ◽  
Volume Balance ◽  
Wide Range ◽  
Design Calculations ◽  
Fluid Leak

This paper develops a closed-form approximate solution for a penny-shaped hydraulic fracture whose behaviour is determined by an interplay of three competing physical processes that are associated with fluid viscosity, fracture toughness and fluid leak-off. The primary assumption that permits one to construct the solution is that the fracture behaviour is mainly determined by the three-process multiscale tip asymptotics and the global fluid volume balance. First, the developed approximation is compared with the existing solutions for all limiting regimes of propagation. Then, a solution map, which indicates applicability regions of the limiting solutions, is constructed. It is also shown that the constructed approximation accurately captures the scaling that is associated with the transition from any one limiting solution to another. The developed approximation is tested against a reference numerical solution, showing that accuracy of the fracture width and radius predictions lie within a fraction of a per cent for a wide range of parameters. As a result, the constructed approximation provides a rapid solution for a penny-shaped hydraulic fracture, which can be used for quick fracture design calculations or as a reference solution to evaluate accuracy of various hydraulic fracture simulators.

Fatigue Failure Analysis Using the Theory of Critical Distance

2011 ◽  
Vol 462-463 ◽  
pp. 663-667 ◽  
Author(s):  
Ruslizam Daud ◽  
Ahmad Kamal Ariffin ◽  
Shahrum Abdullah ◽  
Al Emran Ismail
Keyword(s):  
Stress Concentration ◽  
Fatigue Failure ◽  
Notch Root ◽  
High Stress ◽  
Critical Distance ◽  
Future Research ◽  
Element Analysis ◽  
Linear Elastic ◽  
The Finite Element Analysis ◽  
Elastic Fracture

This paper explores the initial potential of theory of critical distance (TCD) which offers essential fatigue failure prediction in engineering components. The intention is to find the most appropriate TCD approach for a case of multiple stress concentration features in future research. The TCD is based on critical distance from notch root and represents the extension of linear elastic fracture mechanics (LEFM) principles. The approach is allowing possibilities for fatigue limit prediction based on localized stress concentration, which are characterized by high stress gradients. Using the finite element analysis (FEA) results and some data from literature, TCD applications is illustrated by a case study on engineering components in different geometrical notch radius. Further applications of TCD to various kinds of engineering problems are discussed.

scholarly journals Numerical simulation of the laws of fracture propagation of multi-hole linear co-directional hydraulic fracturing

2021 ◽  
pp. 014459872198899
Author(s):  
Weiyong Lu ◽  
Changchun He
Keyword(s):  
Hydraulic Fracturing ◽  
Hydraulic Fracture ◽  
Minimum Principle ◽  
Fracture Propagation ◽  
Axial Direction ◽  
Rock Breaking ◽  
Hydraulic Fractures ◽  
Directional Hydraulic Fracturing ◽  
Fracture Intersection ◽  
Expansion Stage

Directional rupture is one of the most important and most common problems related to rock breaking. The goal of directional rock breaking can be effectively achieved via multi-hole linear co-directional hydraulic fracturing. In this paper, the XSite software was utilized to verify the experimental results of multi-hole linear co-directional hydraulic fracturing., and its basic law is studied. The results indicate that the process of multi-hole linear co-directional hydraulic fracturing can be divided into four stages: water injection boost, hydraulic fracture initiation, and the unstable and stable propagation of hydraulic fracture. The stable expansion stage lasts longer and produces more microcracks than the unstable expansion stage. Due to the existence of the borehole-sealing device, the three-dimensional hydraulic fracture first initiates and expands along the axial direction in the bare borehole section, then extends along the axial direction in the non-bare hole section and finally expands along the axial direction in the rock mass without the borehole. The network formed by hydraulic fracture in rock is not a pure plane, but rather a curved spatial surface. The curved spatial surface passes through both the centre of the borehole and the axial direction relative to the borehole. Due to the boundary effect, the curved spatial surface goes toward the plane in which the maximum principal stress occurs. The local ground stress field is changed due to the initiation and propagation of hydraulic fractures. The propagation direction of the fractures between the fracturing boreholes will be deflected. A fracture propagation pressure that is greater than the minimum principle stress and a tension field that is induced in the leading edge of the fracture end, will aid to fracture intersection; as a result, the possibility of connecting the boreholes will increase.

scholarly journals Quantitative evaluation indexes of the spatial steering effect of directional perforation hydraulic fractures

2021 ◽  
pp. 014459872110102
Author(s):  
Lu Weiyong ◽  
He Changchun
Keyword(s):  
Quantitative Evaluation ◽  
Hydraulic Fracture ◽  
Deflection Angle ◽  
Hydraulic Fractures ◽  
Principal Stress Direction ◽  
Perforation Hole ◽  
Evaluation Indexes ◽  
Initiation Pressure ◽  
The Deflection Angle ◽  
Bending Fracture

To better evaluate the spatial steering effect of directional perforation hydraulic fractures, evaluation indexes for the spatial steering effect are first proposed in this paper. Then, these indexes are used to quantitatively evaluate existing physical experimental results. Finally, with the help of RFPA2D-Flow software, the influence of perforation length and azimuth on the spatial steering process of hydraulic fracture are quantitatively analysed using four evaluation indexes. It is shown by the results that the spatial deflection trajectory, deflection distance, deflection angle and initiation pressure of hydraulic fractures can be used as quantitative evaluation indexes for the spatial steering effect of hydraulic fractures. The deflection paths of directional perforation hydraulic fractures are basically the same. They all gradually deflect to the maximum horizontal principal stress direction from the perforation hole and finally represent a double-wing bending fracture. The deflection distance, deflection angle and initiation pressure of hydraulic fractures increase gradually with increasing perforation azimuth, and the sensitivity of the deflection angle to the perforation azimuth of hydraulic fractures also increases. With increasing perforation length, the deflection distance of hydraulic fractures increases gradually. However, the deflection angle and initiation pressure decrease gradually, as does the sensitivity.

scholarly journals Numerical simulation on the simultaneous stress interference of parallel multiple hydraulic fractures

2021 ◽  
pp. 014459872110019
Author(s):  
Weiyong Lu ◽  
Changchun He
Keyword(s):  
Principal Stress ◽  
Hydraulic Fracture ◽  
Stress Ratio ◽  
Fracture Network ◽  
Hydraulic Fractures ◽  
Fracture Spacing ◽  
Induced Stress ◽  
Minimum Principal Stress ◽  
Fracturing Process ◽  
Stress Ratios

During horizontal well staged fracturing, there is stress interference between multiple transverse fractures in the same perforation cluster. Theoretical analysis and numerical calculation methods are applied in this study. We analysed the mechanism of induced stress interference in a single fracture under different fracture spacings and principal stress ratios. We also investigated the hydraulic fracture morphology and synchronous expansion process under different fracture spacings and principal stress ratios. The results show that the essence of induced stress is the stress increment in the area around the hydraulic fracture. Induced stress had a dual role in the fracturing process. It created favourable ground stress conditions for the diversion of hydraulic fractures and the formation of complex fracture network systems, inhibited fracture expansion in local areas, stopped hydraulic fractures, and prevented the formation of effective fractures. The curves of the maximum principal stress, minimum principal stress, and induced principal stress difference with distance under different fracture lengths, different fracture spacings, and different principal stress ratios were consistent overall. With a small fracture spacing and a small principal stress ratio, intermediate hydraulic fractures were difficult to initiate or arrest soon after initiation, fractures did not expand easily, and the expansion speed of lateral hydraulic fractures was fast. Moreover, with a smaller fracture spacing and a smaller principal stress ratio, hydraulic fractures were more prone to steering, and even new fractures were produced in the minimum principal stress direction, which was beneficial to the fracture network communication in the reservoir. When the local stress and fracture spacing were appropriate, the intermediate fracture could expand normally, which could effectively increase the reservoir permeability.

scholarly journals Numerical Study of Elasto-Plastic Hydraulic Fracture Propagation in Deep Reservoirs Using a Hybrid EDFM–XFEM Method

Energies ◽  
2021 ◽  
Vol 14 (9) ◽  
pp. 2610
Author(s):  
Wenzheng Liu ◽  
Qingdong Zeng ◽  
Jun Yao ◽  
Ziyou Liu ◽  
Tianliang Li ◽  
...  
Keyword(s):  
Plastic Deformation ◽  
Iterative Method ◽  
Hydraulic Fracture ◽  
Iterative Procedure ◽  
Fracture Propagation ◽  
Hydraulic Fractures ◽  
Zone Model ◽  
Dilatancy Angle ◽  
Proposed Model ◽  
Hydraulic Fracture Propagation

Rock yielding may well take place during hydraulic fracturing in deep reservoirs. The prevailing models based on the linear elastic fracture mechanics (LEFM) are incapable of describing the evolution process of hydraulic fractures accurately. In this paper, a hydro-elasto-plastic model is proposed to investigate the hydraulic fracture propagation in deep reservoirs. The Drucker–Prager plasticity model, Darcy’s law, cubic law and cohesive zone model are employed to describe the plastic deformation, matrix flow, fracture flow and evolution of hydraulic fractures, respectively. Combining the embedded discrete fracture model (EDFM), extended finite element method (XFEM) and finite volume method, a hybrid numerical scheme is presented to carry out simulations. A dual-layer iterative procedure is developed based on the fixed-stress split method, Picard iterative method and Newton–Raphson iterative method. The iterative procedure is used to deal with the coupling between nonlinear deformation with fracture extension and fluid flow. The proposed model is verified against analytical solutions and other numerical simulation results. A series of numerical cases are performed to investigate the influences of rock plasticity, internal friction angle, dilatancy angle and permeability on hydraulic fracture propagation. Finally, the proposed model is extended to simulate multiple hydraulic fracture propagation. The result shows that plastic deformation can enhance the stress-shadowing effect.

Investigation on Stress and Strain Singularity in LEFM

2006 ◽  
Vol 306-308 ◽  
pp. 31-36
Author(s):  
Zheng Yang ◽  
Wanlin Guo ◽  
Quan Liang Liu
Keyword(s):  
High Stress ◽  
Crack Tip ◽  
Plane Stress State ◽  
Stress And Strain ◽  
Linear Elastic ◽  
Geometrical Nonlinear ◽  
Maximum Crack ◽  
Elastic Fracture ◽  
Plain Strain ◽  
Strain Singularity

Stress and strain singularity at crack-tip is the characteristic of Linear Elastic Fracture Mechanics (LEFM). However, the stress, strain and strain energy at crack-tip may be infinite promoting conflicts with linear elastic hypothesis. It is indicated that the geometrical nonlinear near the crack-tip should not be neglected for linear elastic materials. In fact, the crack-tip blunts under high stress and strain, and the singularity vanishes due to the deformation of crack surface when loading. The stress at crack-tip may still be very high even though the singularity vanishes. The low bound of maximum crack-tip stress is the modulus of elastic in plane stress state, while in plain strain state, it is greater than the modulus of elastic, and will increase with the Poisson’s ratio.

A New Specimen for Measuring the Interfacial Toughness of Al-0.5%Cu Thin Film on Si Substrate

2005 ◽  
Vol 297-300 ◽  
pp. 521-526
Author(s):  
Insu Jeon ◽  
Masaki Omiya ◽  
Hirotsugu Inoue ◽  
Kikuo Kishimoto ◽  
Tadashi Asahina
Keyword(s):  
Thin Film ◽  
The Finite Element Method ◽  
Si Substrate ◽  
Detailed Structure ◽  
Micro Fabrication ◽  
Interfacial Toughness ◽  
Linear Elastic ◽  
Elastic Fracture ◽  
Cu Thin Film ◽  
Research Show

A new specimen is proposed to measure the interfacial toughness between the Al-0.5%Cu thin film and the Si substrate. The plain and general micro-fabrication processes are sufficient to fabricate the specimen. With the help of the finite element method and the concepts of the linear elastic fracture mechanics, the detailed structure for this specimen is modeled and evaluated. The results obtained from this research show that the proposed specimen provides efficient and convenient method to measure the interfacial toughness between the Al-Cu thin film and the Si substrate.

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