Robert G. Jeffrey

Cohesive zone finite element-based modeling of hydraulic fractures

Hydraulic fracturing is a powerful technology used to stimulate fluid production from reservoirs. The fully 3-D numerical simulation of the hydraulic fracturing process is of great importance to the efficient application of this technology, but is also a great challenge because of the strong nonlinear coupling between the viscous flow of fluid and fracture propagation. By taking advantage of a cohesive zone method to simulate the fracture process, a finite element model based on the existing pore pressure cohesive finite elements has been established to investigate the propagation of a penny-shaped hydraulic fracture in an infinite elastic medium. The effect of cohesive material parameters and fluid viscosity on the hydraulic fracture behaviour has been investigated. Excellent agreement between the finite element results and analytical solutions for the limiting case where the fracture process is dominated by rock fracture toughness demonstrates the ability of the cohesive zone finite element model in simulating the hydraulic fracture growth for this case.

Measuring Hydraulic Fracture Growth in Naturally Fractured Rock

Note: SPE 124919 Reference EPFL-CONF-212832 Record created on 2015-10-08, modified on 2016-08-09

Propagation of a penny-shaped hydraulic fracture parallel to the free-surface of an elastic half-space

In this paper we analyze the problem of a penny-shaped hydraulic fracture propagating parallel to the free-surface of an elastic half-space. The fracture is driven by an incompressible Newtonian fluid injected at a constant rate at the center of the fracture. The flow of viscous fluid in the fracture is governed by the lubrication equation, while the crack opening and the fluid pressure are related by singular integral equations. We construct two asymptotic solutions based on the assumption that either the solid has no toughness or that the fluid has no viscosity. These asymptotic solutions must be understood as corresponding to limiting cases when the energy expended in the creation of new fracture surfaces is either small or large compared to the energy dissipated in viscous flow. It is shown that the asymptotic solutions, when properly scaled, depend only on the dimensionless parameter calRcal, the ratio of the fracture radius over the distance from the fracture to the free-surface. The scaled solutions can thus be tabulated once and for all and the dependence of the solution on time can be retrieved for specific parameters, through simple scaling and by solving an implicit equation.

A cohesive plastic and damage zone model for dynamic crack growth in rate-dependent materials

Mode I steady-state dynamic crack growth in rate-dependent viscoplastic solids containing damage, under small scale yielding conditions, is analyzed based on a modified cohesive zone model. A multi-scale approach is used to describe the entire non-linear zone consisting of a plastic region and a damage region, each of which has its own constitutive law. Traction in the damage region is characterized by a softening power-law, in terms of the ultimate strength, a softening index and a rate sensitivity factor. In the plastic region, the cohesive law is assumed to be both strain hardening and rate dependent. The critical crack opening displacement at the physical crack-tip controls crack growth. The governing integral equations are derived and solved by a collocation method combined with associated boundary conditions. Numerical results are presented for the traction and opening profiles along the cohesive zone, the fracture energy and lengths of the damage and non-linear zones at different crack speeds and for different material parameters. The importance of factors, such as material softening, plastic deformation, crack speed and viscosity, is identified by parametric studies. In addition, the competition of plastic flow and material damage, and its effect on crack growth, are discussed.

Evaluating Hydraulic Fracture Effectiveness in a Coal Seam Gas Reservoir from Surface Tiltmeter and Microseismic Monitoring

In developing new coalbed methane (CBM) or coal seam gas (CSG) fields or reservoirs, the effect of many parameters are important in understanding the success or potential areas for improvement of hydraulic fracturing treatments. Estimating fracture geometry relative to the reservoir architecture is critical to understanding production variability. The Walloon Coal Measures, in the Surat Basin of Eastern Queensland, Australia, are a complex reservoir containing interbedded sandstone, siltstone, carbonaceous shale and coal seams where initial attempts at hydraulic fracturing in early pilot areas of the Surat Basin yielded poor results. Thus, when a hydraulic fracturing program was planned for this reservoir, it was decided to integrate a group of diagnostics that would be useful in understanding past results as well as deriving future improvements. Data is presented from two wells in the Walloon Sub Group (WSG) where tiltmeters and microseismic monitoring were used to evaluate fracture effectiveness relative to the reservoir architecture and to assist further design work. The treatments carried out in the studied wells were typical of CSG frac treatments used in other producing areas, incorporating stages of treated, gelled and crosslinked-gelled water with increasing concentrations of sand, up to six (6) lbm/gal. During the treatments, complex fractures were inferred based on analyses of data from both tiltmeter and microseismic monitoring methods. The collaborative data set for these wells also included a large amount of other analyses and diagnostic data. It was only possible to fully explain the treatment results through the combination of multiple diagnostics and an in-depth understanding of how the created fracture interacted with the complex reservoir and stress environment. In this paper, we outline the steps used to plan the monitoring program and describe how geological data was integrated to better understand the results observed during the treatments. We describe each of six (6) stages performed across the two wells, and how the diagnostics did or did not support the overall conclusions as to the effectiveness of each stage. Finally, this paper presents a logical framework to evaluate and integrate these technologies for use in future CSG well stimulation. Copyright 2010, Society of Petroleum Engineers.

Three Dimensional Forms of Closely-Spaced Hydraulic Fractures

When creating arrays of hydraulic fractures in close proximity, stress field changes induced by previously placed hydraulic fractures can lead to deflection in subsequent fracture paths and coalescence between fractures. Any fracture coalescence can compromise the effective‐ ness of the treatment array and the fracture geometry will not be appropriately account‐ ed for in reservoir or caving models. Here we present the results of an experimental study consisting of arrays of 4 closely spaced hydraulic fractures grown sequentially in 350x350x350 mm blocks of a South Australian Gabbro under different initial stress states and for notched and un-notched wellbores. In particular we focus on insights gained from 3-dimesional serial sectioning and digital reconstruction of the hydraulic fracture pat‐ terns that were formed. The results show that the curving hydraulic fractures typically do not exhibit a high degree of radial symmetry in their paths even though the fractures grew by radiating outward from a centrally located wellbore. The results also confirm model predictions that a subsequent fracture will curve towards a previous fracture when the minimum stress is zero and that this curving is suppressed when the minimum stress is sufficiently large. Finally, fracture initiation is shown to be critical to the symmetry of the fracture pattern and preponderance of branching and therefore effective notches that lead to initiation in the eventual plane of favored propagation have a profound impact on the hydraulic fracture geometry.

Monitoring and Measuring Hydraulic Fracturing Growth During Preconditioning of a Roof Rock over a Coal Longwall Panel

Narrabri Coal Operations is longwall mining coal directly below a 15 to 20 m thick conglom‐ erate sequence expected to be capable of producing a windblast upon first caving at longwall startup and producing periodic weighting during regular mining. Site characterisation and field trials were undertaken to evaluate hydraulic fracturing as a method to precondition the conglomerate strata sufficiently to promote normal caving behaviour at longwall startup and reduce the severity of periodic weighting. This paper presents the results of the trials and illustrates the effectiveness of hydraulic fracturing as a preconditioning technique. Initial work was directed at determining if hydraulic fractures were able to be grown with a horizontal orientation, which would allow efficient preconditioning of the rock mass by placing a number of fractures at different depths through the conglomerate from vertical boreholes drilled from the surface. The measurements and trials were designed to determine the in situ principal stresses, the hydraulic fracture orientation and growth rate, and whether the fractures could be extended as essentially parallel fractures to a radius of at least 30 m. Overcore stress measurements were used to determine the orientation and magnitude of the in situ principal stresses, a surface tiltmeter array was used to determine the hydraulic fracture orientation, and stress change monitoring, pressure monitoring and temperature logging in offset boreholes were used to establish the fracture growth rate, lateral extent, and that the fractures maintained their initial spacing to a radial distance of greater than 30 metres. The measurements and trials demonstrated that horizontal fractures could be extended parallel to one another to a distance of 30 to 50 m by injection of 5,000 to 15,000 litres of water at a rate of 400 to 500 L/min. Results from the trial allowed a preconditioning plan to be developed and successfully implemented.

Development of Fracture Networks Through Hydraulic Fracture Growth in Naturally Fractured Reservoirs

A 2-D numerical study was carried out, using a fully coupled rock deformation and fluid flow hydraulic fracturing model, on fracture network formation by advancing, widening and interconnecting discrete natural fractures in a low-permeability rock, some of which are small enough to be considered as a flaw that acts as a fracture seed. The model also includes fractures connecting into one another to form a single hydraulic fracture. In contrast to previous fracture network models, fracture extension and fluid flow behavior, frictional slip, and fracture interaction are all explicitly addressed in this model. Incompressible Newtonian fluid is injected at a constant total rate into fractures to study viscous fluid effects on the network formation. The algorithm for flow division and coalescence is validated through some examples. Numerical results show that the incremental crack propagation that connects isolated natural fracture sets depends on the current stress state and the fracture arrangement. The newly created connecting fracture segments increase local conductivity since they are oriented along a path that is easier to open when pressurized by fluid and provide a new path for fluid flow. However the hydraulic fracture growth process is retarded by some of the resulting geometric changes such as intersections and offsets, and the growth-induced sliding that can impose a barrier to further fracture growth and fluid flow into parts of the network. Such barriers may eventually result in a fracture branch initiating and growing that results in a relatively shorter and more conductive path through a fracture network zone. We consider a specific fracture arrangement consisting of around 20 conductive pre-existing fractures to study the effective behavior of the hydraulic fracture growth through a natural fracture network. Mechanical responses have been studied for two different fracture and flow scenarios depending on the fluid entry details: one fracture system assumes each of four entry

Fluid‐driven nucleation and propagation of splay fractures from a permeable fault

Progressive development of opening-mode splay or branch fractures along a permeable fault in an elastic medium, subject to elevated fluid pressure from a constant influx fluid source, is studied numerically using a plane-strain hydraulic fracturing model that couples fracture deformation and fluid flow. In situ stresses are imposed so that their resultant shear stress on the fault is lower than the frictional strength. New splay fractures are initiated based on satisfying a dual criterion for both tensile strength and fracture toughness and meeting a minimum fracture spacing requirement. Numerical results demonstrate that spatial variations in permeability along faults can cause arrest of local slip and the created slip gradient can result in splay fracture initiation at a significant distance inward from the fault tips. One splay fracture generally grows first, and the kinematic coherence in displacements at the junction between it and the fault can reduce the downstream flow rate to prevent the nucleation of other splay fractures. However, the number of splay fractures can be increased when the branch growth extent is limited to a certain size; when the fault is divided into many segments, each with a linear distributed initial aperture; and if the main fault is curved. The generation of a number of splay fractures can act to increase the permeability of the rock mass. When the splay fractures are constrained by two faults, a rhomb-shaped fault zone involving multiple high-angle branches forms. The development of the second-generation splay fractures on a first-generation one is promoted by fluid penetration. Multiple fluid-driven splay fractures can be created under the condition that fluid pressure is below or slightly above the fault confining stress. This implies that generation of complex splay fracture patterns requires less energy than generating a single opening-mode fracture. Multiple fluid-driven splay fracture nucleation and growth into a horsetail pattern occur when the fault-parallel in situ normal stress becomes more tensile. In addition, the effects of fluid viscosity and tensile fracture toughness are investigated to determine their role in splay fracture initiation and growth.

Hydraulic Fracture Propagation Through an Orthogonal Discontinuity: A Laboratory, Analytical and Numerical Study

Rocks are naturally fractured, and lack of knowledge of hydraulic fracture growth through the pre-existing discontinuities in rocks has impeded enhancing hydrocarbon extraction. This paper presents experimental results from uniaxial and biaxial tests, combined with numerical and analytical modelling results to develop a criterion for predicting whether a hydraulic fracture will cross a discontinuity, represented at the laboratory by unbonded machined frictional interfaces. The experimental results provide the first evidence for the impact of viscous fluid flow on the orthogonal fracture crossing. The fracture elliptical footprint also reflects the importance of both the applied loading stress and the viscosity in fracture propagation. The hydraulic fractures extend both in the direction of maximum compressive stress and in the direction with discontinuities that are arranged to be normal to the maximum compressive stress. The modelling results of fracture growth across discontinuities are obtained for the locations of slip starting points in initiating fracture crossing. Our analysis, in contrast to previous work on the prediction of frictional crossing, includes the non-singular stresses generated by the finite pressurised hydraulic fracture. Experimental and theoretical outcomes herein suggest that hydraulic fracture growth through an orthogonal discontinuity does not depend primarily on the interface friction coefficient.