Andrew P. Bunger

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

Interference Fracturing: Nonuniform Distributions of Perforation Clusters That Promote Simultaneous Growth of Multiple Hydraulic Fractures

© 2015 Society of Petroleum Engineers. One of the important hurdles in horizontal-well stimulation is the generation of hydraulic fractures (HFs) from all perforation clusters within a given stage, despite the challenges posed by stress shadowing and reservoir variability. In this paper, we use a newly developed, fully coupled, parallel-planar 3D HF model to investigate the potential to minimize the negative impact of stress shadowing and thereby to promote more-uniform fracture growth across an array of HFs by adjusting the location of the perforation clusters. In this model, the HFs are assumed to evolve in an array of parallel planes with full 3D stress coupling while the constant fluid influx into the wellbore is dynamically partitioned to each fracture so that the wellbore pressure is the same throughout the array. The model confirms the phenomenon of inner-fracture suppression because of stress shadowing when the perforation clusters are uniformly distributed. Indeed, the localization of the fracture growth to the outer fractures is so dominant that the total fractured area generated by uniform arrays is largely independent of the number of perforation clusters. However, numerical experiments indicate that certain nonuniform cluster spacings promote a profound improvement in the even development of fracture growth. Identifying this effect relies on this new models ability to capture the full hydrodynamical coupling between the simultaneously evolving HFs in their transition from radial to Perkins-Kern-Nordgren (PKN)-like geometries (Perkins and Kern 1961; Nordgren 1972).

Sustained acoustic emissions following tensile crack propagation in a crystalline rock

We show that simple breakage of a crystalline rock (gabbro) in tension begets further breakage of rock in the area around the first crack that is self-sustaining and spontaneous and that is detected via sustained acoustic emissions (AE). The result is a sequence of AE events that is statistically similar to aftershocks from earthquakes, that scales with the size of the main crack, and that we were able to observe for days following the initial breakage in laboratory-scale experiments. A new model for aftershock generation that is based on residual strain relaxation is shown to be consistent with the observed hyperbolic decay of the event rate with time and with the manner in which the decay law scales with the size of the main rupture.

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.

Numerical Simulation of Hydraulic Fracturing in the Viscosity-Dominated Regime

Most hydraulic fracturing treatments are in the viscositydominated regime. Hence, fracture growth does not depend on the rock toughness and it can be shown that the fracture aperture w near the fracture front, when viewed at the scale of the whole fracture, is not characterized by the classical square root behavior predicted by linear elastic fracture mechanics 12 ~ ws / , where s is the distance from the tip. Instead, the asymptotic tip aperture that reflects the predominance of viscous dissipation is of the form 23 ~ ws / , under conditions of large efficiency and small fluid lag. After demonstrating the intimate connection between the tip aperture and the fracture propagation regime, we report the results of hydraulic fracturing laboratory experiments in PMMA and glass blocks that employ a novel optical technique to measure the fracture opening. These experiments provide incontrovertible evidence that the power law index, characterizing the fracture aperture near the tip, depends on the propagation regime in accordance with theoretical findings. Finally, we demonstrate that a coarsely-meshed planar hydraulic fracture simulator can produce accurate results relative to benchmark solutions provided that the appropriate tip behavior is embedded in the algorithm. Through theoretical, experimental, and computational considerations, these results make it clear that advances in the accuracy and efficiency of fracture simulators critically depend on a sophisticated treatment of the near-tip aperture that goes beyond basic linear elastic fracture considerations.

Experiments versus theory for the initiation and propagation of radial hydraulic fractures in low‐permeability materials

We compare numerical predictions of the initiation and propagation of radial fluid-driven fractures with laboratory experiments performed in different low permeability materials (PMMA, cement). In particular, we choose experiments where the time evolution of several quantities (fracture width, radius, wellbore pressure) were accurately measured and for which the material and injection parameters were known precisely. Via a dimensional analysis, we discuss in detail the different physical phenomena governing the initiation and early stage of growth of radial hydraulic fractures from a notched wellbore. The scaling analysis notably clarifies the occurence of different regimes of propagation depending on the injection rate, system compliance, material parameters, wellbore and initial notch sizes. In particular, the comparisons presented here provide a clear evidence of the difference between the wellbore pressure at which a fracture initiates and the maximum pressure recorded during a test (also known as the breakdown pressure). The scaling analysis identifies the dimensionless numbers governing the strong fluid-solid effects at the early stage of growth, which are responsible for the continuous increase of the wellbore pressure after the initiation of the fracture. Our analysis provides a simple way to quantify these early time effects for any given laboratory or field configuration. The good agreement between theoretical predictions and experiments also validates the current state of the art hydraulic fracture mechanics models, at least for the simple fracture geometry investigated here.

Blade-Shaped Hydraulic Fracture Driven by a Turbulent Fluid in an Impermeable Rock

High flow rate, water-driven hydraulic fractures are more common now than ever in the oil and gas industry. Although the fractures are small, the high injection rate and low viscosity of the water, lead to high Reynolds numbers and potentially turbulence in the fracture. Here we present a semi-analytical solution for a blade-shaped (PKN) geometry hydraulic fracture driven by a turbulent fluid in the limit of zero fluid leak-off to the formation. We model the turbulence in the PKN fracture using the Gaukler-Manning-Strickler parametrization, which relates the the flow rate of the water to the pressure gradient along the fracture. The key parameter in this relation is the Darcy-Weisbach friction factor for the roughness of the crack wall. Coupling this turbulence parametrization with conservation of mass allows us to write a nonlinear pde for the crack width as a function of space and time. By way of a similarity ansatz, we obtain a semi-analytical solution using an orthogonal polynomial series. Embedding the asymptotic behavior near the fracture tip into the polynomial series, we find very rapid convergence: a suitably accurate solution is obtained with two terms of the series. This closed-form solution facilitates clear comparisons between the results and parameters for laminar and turbulent hydraulic fractures. In particular, it resolves one of the well known problems whereby calibration of models to data has difficulty simultaneously matching the hydraulic fracture length and wellbore pressure.

Deep geothermal: The ‘Moon Landing’ mission in the unconventional energy and minerals space

Deep geothermal from the hot crystalline basement has remained an unsolved frontier for the geothermal industry for the past 30 years. This poses the challenge for developing a new unconventional geomechanics approach to stimulate such reservoirs. While a number of new unconventional brittle techniques are still available to improve stimulation on short time scales, the astonishing richness of failure modes of longer time scales in hot rocks has so far been overlooked. These failure modes represent a series of microscopic processes: brittle microfracturing prevails at low temperatures and fairly high deviatoric stresses, while upon increasing temperature and decreasing applied stress or longer time scales, the failure modes switch to transgranular and intergranular creep fractures. Accordingly, fluids play an active role and create their own pathways through facilitating shear localization by a process of time-dependent dissolution and precipitation creep, rather than being a passive constituent by simply following brittle fractures that are generated inside a shear zone caused by other localization mechanisms. We lay out a new theoretical approach for the design of new strategies to utilize, enhance and maintain the natural permeability in the deeper and hotter domain of geothermal reservoirs. The advantage of the approach is that, rather than engineering an entirely new EGS reservoir, we acknowledge a suite of creep-assisted geological processes that are driven by the current tectonic stress field. Such processes are particularly supported by higher temperatures potentially allowing in the future to target commercially viable combinations of temperatures and flow rates.

Mechanics of two interacting magma‐driven fractures: A numerical study

To understand magma focusing from broad melting zones in the crust, propagation in brittle rocks of two interacting dikes ascending from a single deep source has been modeled using a time-dependent plane strain hydraulic fracturing model. The source is assumed to generate a constant influx rate to feed the dike growth, which is also aided by buoyancy effects. In contrast to uncoupled model results, the simultaneous parallel growth of two dikes to a certain distance is found to occur provided that the two dikes are initially of different heights, which might be produced either by previous magma intrusion or during nucleation. The shorter dike will chase the longer one and they can either progressively merge or continue subparallel growth at a reduced spacing, depending on the deviator stress between the vertical and horizontal stresses and the initial lateral separation, with parameters given in dimensionless forms. Numerical results reveal the mechanics for simultaneous ascents of two subparallel dikes, in that dike interaction can produce a low-stress field, which is just above the tip of the shorter dike, favorable to growth of the shorter dike. The energy analysis indicates that the energy required for two subparallel dikes is less than that for a single dike during the late-time buoyancy-viscosity propagation stage where considerable ascent occurs. This growth behavior might provide the mechanism for simultaneous, instead of sequential, growth of various dikes in a single set.