Combined Finite-Discrete Element Method for Simulation of Hydraulic Fracturing

Summary In this work, we propose a novel hydraulic solver in order to simulate key mechanisms that control fluid‐driven cracks in the framework of the combined finite‐discrete element method (FDEM). The main innovative aspect of the present work is the independence of the fluid's critical time step size with the fracture opening. This advantage is extremely important because it means that very fine meshes can be used around areas of interest, such as boreholes, without penalizing the computational cost as fractures propagate (ie, open) and the fluid flows through them. This is a great advantage over other recently introduced approaches that exhibit a dependency of the time step in the form of Δtcrit ∝ (l/a)2 where l is the element size and a is the fracture aperture. This paper presents a series of benchmark cases for the proposed solver. The rationale adopted by the authors was to benchmark and validate the implementation of the hydraulic solver in an incremental fashion, starting from the simplest cases and building in complexity. The results shown in this work clearly demonstrate that the proposed approach is able to reproduce analytical results for fluid flow through a single crack. The results presented in this paper also demonstrate that the new approach is robust enough to deal with complex fracture patterns and complex geometries; the obtained fluid‐driven fracture patterns in the vicinity of a borehole certainly stand to the scrutiny of human visual perception.

q = \frac{1}{12 μ} \frac{a^{3}}{l} normalΔ p,

where μ is the dynamic viscosity of fluid and Δ p = p 1 − p 2 is the pressure difference between the two ends of the fracture.…”

Section: Critical Time Step Calculation For Existing Approachesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Simulation of discrete cracks driven by nearly incompressible fluid via 2D combined finite‐discrete element method

Lei

Rougier

Munjiza

et al. 2019

“…However, the FDEM could only be used to perform pure mechanical fracture calculations initially. Therefore, some hydro‐mechanical coupled models based on the FDEM were developed for simulating hydraulic fracturing, which can be used to solve the fluid‐driven fracturing of media with arbitrary complex fracture networks . Later, a two‐dimensional thermo‐mechanical coupling model based on the FDEM was also developed to simulate thermal cracking .…”

Section: Introductionmentioning

confidence: 99%

A three‐dimensional heat transfer and thermal cracking model considering the effect of cracks on heat transfer

Yan

Jiao

Zheng

2019

Self Cite

Summary A simple three‐dimensional heat transfer model is developed to consider the hindering effect of cracks on heat transfer. The 3D heat transfer model can also be applied to numerical methods such as the combined finite‐discrete element method (FDEM), discrete element method (DEM), discontinuous deformation analysis (DDA), the numerical manifold method (NMM), and the finite element method (FEM) to construct thermo‐mechanical coupling models that allow these methods to solve thermal cracking problems and dynamically consider the hindering effect of cracks on heat transfer. In the 3D heat transfer model, the continuous‐discontinuous medium is discretized into independent tetrahedral elements, and joint elements are inserted between adjacent tetrahedral elements. Heat transfer calculations for continuous‐discontinuous media are converted to heat conduction in tetrahedral elements and the heat exchange between the adjacent tetrahedral elements through the joint element. If the joint element between adjacent tetrahedral elements breaks (ie, a crack generates), the heat exchange coefficient of the joint element is reduced to account for the hindering effect of cracks on heat conduction. Then the model and the FDEM are combined to build a thermo‐mechanical coupling model to simulate thermal cracking. The thermally induced deformation, stress, and cracking are investigated by the thermo‐mechanical coupling model, and the numerical results are compared with analytical solutions or experimental results. The 3D heat transfer model and thermo‐mechanical model can provide a powerful tool for simulating heat transfer and thermal cracking in a continuous‐discontinuous medium.

“…For example, Yan et al use a graph network structure to develop algorithms for updating hydraulic fracture network, within the combined finite‐discrete element method framework proposed by Munjiza . This model can capture damage and failure processes in rock, driven by hydraulic pressure.…”

Section: Introductionmentioning

confidence: 99%

Modeling the connectivity and intersection of hydraulically loaded cracks with in situ fractures in rock

Clarke

Abedi

2018

Summary The interaction of an advancing hydraulically loaded crack and in situ fracture network can yield highly complex patterns. We model the connectivity of cells in a finite element domain and in a fracture network by a simplicial complex data structure. The complete adjacency information between cells is determined by one level down facet and one level up cofacet neighborhood information. Combined with a disjoint set data structure, explicit algorithms are derived to efficiently track network connectivity and load transfer between independent fracture sets. We also propose an approach to regularize the application of hydraulic load to newly intersected in situ cracks to smoothen the transition of pressure on intersected cracks from ambient to hydraulic pressure and to avoid the sudden loading of the entire length of these cracks. Numerical results demonstrate the performance of crack connectivity and load transfer models and the effect of regularization model. The results show that as the angle between an incoming hydraulically loaded crack and an in situ crack increases, the effect of in situ crack shifts from slight realignment to diversion/offsetting of the loaded crack. As the angle difference approaches the normal angle, the loaded crack tends to penetrate through the in situ crack. The proposed schemes are also used for transient simulation of 2D reservoirs with multiple perforations surrounded by in situ cracks with and without a bias in the distribution of their orientation. It was shown that from 2 perforations with angles closer to in situ cracks at low loading rates to all perforations at higher loading rates can result in active hydraulic crack propagation. The h‐adaptive method of asynchronous space‐time discontinuous Galerkin method is used to exactly track complex fracture patterns in these dynamic fracture simulations.