Chunfang Meng

Evaluation of the Eshelby solution for the ellipsoidal inclusion and heterogeneity

We present a MATLAB code that evaluates the quasi-static elastic displacement strain and stress fields for the ellipsoidal inclusion and heterogeneity, the Eshelby solution. We first give an introduction to the underlaying inclusion problem. Then we describe the Eshelby solution for the elastic field inside and outside an ellipsoidal inclusion. We introduce the equivalency between the inclusion and inhomogeneity problems and elaborate the codes functionalities. Finally, we make the ellipsoidal inclusion undergo a series of geometrical transformations to emulate a spheroid inclusion, a 2D elliptical void, and a planar crack for which the surrounding elastic field is either known or accurately approximated. By comparing the Eshelby solution against those known solutions, we conclude that the code is valid. By these emulations, we show that the Eshelby solution can encompass many special problems in a unified form.

Modeling mixed-mode fracture propagation in isotropic elastic three dimensional solid

A planar fracture when subjected to sufficient tensile and shear stresses will propagate off-plane, in what is known as mixed-mode propagation. Predicting the fracture path relies on an accurate calculation of the near-tip stress and an appropriate propagation criterion. The new criterion we present scales the propagation magnitude and direction with the near-tip tensile stress in the form of vectors that originate from the fracture tip-line. Boundary element method (BEM) models enable us to calculate the near-tip stress field of an arbitrary fracture. We use analytical Eshelby’s solution that evaluates near-tip stress of an ellipsoidal fracture to validate the BEM results. We feed the near-tip stress to the propagation criterion to determine the propagation vectors, and grow the BEM mesh by adding new tip-elements whose size and orientation are given by the propagation vectors. Then, we feed the new mesh back to the BEM to calculate the new near-tip stress. By running the BEM and the propagation criterion in a loop, we are able to model 3D fracture propagation.

Hydraulic Fracture Propagation in Pre-Fractured Natural Rocks

Abstract We conducted a series of hydraulic fracture initiation tests with fractured natural rock samples. The objective is to characterize the interaction between hydraulic fracture initiation and natural fracture infiltration and opening. The natural fracture was simulated by cleaving a rock cube into two or three layers and putting the parts back together. The hydraulic fracture is initiated by pressurizing the borehole drilled perpendicular to the layers. The test parameters include rock type (sandstones and a tight limestone), confining stress and fluid type (silicon oil and cross-linked gel). A detailed model was built to simulate the hydraulic fracture interaction with a natural fracture. Qualitative agreement was found with the test results. Introduction Natural fractures come in many different forms. As one extreme they may be just a weakness governed by the rock fabric, another extreme is a very conductive and wide open shear zone. Since shear dilatancy is not only occurring on a microscopic scale but also on macro-scale by fault block rotation, shear can generate very high conductivity along fault zones. If a hydraulic fracture grows into such a fault with a large aperture, it is likely that the fluid will flow into the fault. This is often the objective in geothermal reservoirs where hydraulic fractures are needed to connect the well to shear zones that produce large amounts of water

Benchmarking Defmod, an open source FEM code for modeling episodic fault rupture

We present Defmod, an open source (linear) finite element code that enables us to efficiently model the crustal deformation due to (quasi-)static and dynamic loadings, poroelastic flow, viscoelastic flow and frictional fault slip. Ali (2015) provides the original code introducing an implicit solver for (quasi-)static problem, and an explicit solver for dynamic problem. The fault constraint is implemented via Lagrange Multiplier. Meng (2015) combines these two solvers into a hybrid solver that uses failure criteria and friction laws to adaptively switch between the (quasi-)static state and dynamic state. The code is capable of modeling episodic fault rupture driven by quasi-static loadings, e.g. due to reservoir fluid withdraw or injection. Here, we focus on benchmarking the Defmod results against some establish results. The Defmod code is validated to model the static and/or dynamic crustal deformations.The code adaptively switches between the (quasi-)static and dynamic modes.The code enables one to model earthquakes induced by fluid withdraw and/or injection.

Acoustic Monitoring of Hydraulic Fracture Propagation in Pre-Fractured Natural Rocks

Active acoustic monitoring can capture two types of fracture behavior in rock samples, opening and closure of an existing fracture and tip movement of a propagating fracture. The first type is related to wave transmission across the fracture interface. The second one is related to the travel times of waves that diffract at the fracture tip. A series of experiment has been conducted with an acoustic system that has transducers mounted on the loading frames of a tri-axial cell situated in the Rock Mechanics Laboratory, TUDelft, the Netherlands. The existing fractures are formed by cleaving the rock samples into layers and putting them back together. The propagating fractures were created by hydraulic fracturing via bore-hole injection. The tests in this study featured both cleaved and hydraulic fractures, and aimed to characterize the interaction between them. This paper focus on the data processing that is adapted to these special tests and comparison between the monitored and recovered fractures.

A finite element and finite difference mixed approach for modeling fault rupture and ground motion

Abstract We combine a finite element (FE) code, Defmod, and a finite difference (FD) code, OpenSWPC, in modeling fault rupture and resulting ground motion. The rupturing process is modeled by the FE code, while the ground motion is modeled by the FD code. The FE-FD binding follows two steps: First, evaluate the FD grid points motion when executing the FE code; and then, impose those moving grid points to the FD domain to drive wave propagation. In order to avoid performance bottleneck, we implement this FE-FD binding in parallel. To verify this mixed approach, we evaluate two SCEC benchmark problems. The resulting synthetic waveforms agree well with the other benchmark participants. The waveform comparisons suggest that the FE-FD mixed model has less attenuation than the pure FE model.

X-Link Gel as Hydraulic Fracturing Material

Hydraulic fracturing is a fracturing processes initiated from a pressurized open borehole section into solid formations. The process is characterized by solid-fluid interaction. On the solid side, the formation is deforming with the propagation of the fracture front and pressurization of the fracture face. At the same time the fluid is driven by the borehole pressure to flow into the narrow fracture cavity. At same time, the fluid may also infiltrate into the porous rock media. The fracture cavity is supported by the fluid pressure. In turn, the fluid distribution depends on the fracture conductivity related to the cavity width (aperture). The mass balance is maintained amongst the injection rate, fracture volume increment and leak-off A series of experiments have been performed to initiate fracture in a number of natural rock samples confined by a tri-axial cell. As the tight and shale gas and oil reservoirs are found global-wise, stimulation techniques such as polymer flooding and fracturing start to draw attention. We have employed X-link gel as the fracturing material in contrast with the Newtonian viscous fluid. From the results, we found that the ability to sustain certain yielding stress made the gel unlikely to infiltrate into the porous media as leak-off and likely to create a unanimous fracture. This paper is about the tests results and analysis that describe the gel behavior.Copyright