Hydraulic fracturing modeling using the discontinuous deformation analysis (DDA) method

Recent attempts to couple discontinuous deformation analysis (DDA) blocks with finite element meshes have been regarded as fruitful. The hybrid model has been proven to be reliable in modeling continuum–discontinuum problems. In this paper, a hydraulic crack initiation–propagation extension complete with a coupled hydro-mechanical analysis algorithm is introduced to the hybrid model for the simulation of fracturing problems initiated by hydraulic pressure. Several simulation cases, of which the results appear to be consistent with existing theories of hydraulic fracturing mechanisms, are presented to demonstrate the capability of the proposed algorithm in modeling hydraulic fracturing processes.     

含单个孔洞岩盐路基稳定性的无网格分析

用无网格伽辽金法计算了孔洞边缘危险点的应力。对含单个孔洞岩盐路基的稳定性进行了分析,给出了针对不同孔洞埋深的临界载荷。数值结果表明,EFGM对于解决含有单个孔洞的应力集中问题,是有效且灵活的。     

Cell to node projections: An assessment of error

Reservoir simulators typically use cell‐centered finite volume schemes and do not model directly the coupling of the flow processes with the geomechanics. Coupling of geomechanics with fluid flow can be important in many cases, but introducing fully coupled geomechanical effects in those simulators is not a trivial issue, because the geomechanics is better done by using the Galerkin vertex‐centered finite element methods by which the solid displacements are computed at the vertices of the cells. This creates difficulties in interfacing cell variables with nodal variables. Uncoupled or loosely coupled models are used by many researchers/practitioners by which a reservoir model is coupled to a geomechanical model by staggering in‐time flow and deformation via a sophisticated interface that repeatedly calls first flow and then mechanics. The method therefore requires projection of the reservoir cell variables onto the nodes of the geomechanics Galerkin finite element mesh. In this note, we attempt to quantify the errors associated with cell to node projection operations. For that purpose, we use a simple model of the pressure equation for a heterogeneous medium in one dimension. We are able to derive the exact analytical solution for this problem for both nodal and cell pressures. This allows us to compute the errors due to projection analytically, function of meshing refinement and permeability field variations. We compute upper and lower bounds for the errors, and analyze their magnitude for a variety of cases. We conclude that, in general, cell to node projection operations lead to substantial errors. Copyright © 2010 John Wiley & Sons, Ltd.     

Safety evaluation of an ancient masonry seawall structure with modified DDA method

The ancient masonry seawall along China’s Qiantang River is an important structure for defending the prosperous estuarine area, including Hangzhou, Jiaxing, and part of Shanghai, against violent floods, tides and waves. Modified discontinuous deformation analysis (DDA) is used here to analyze the failure mechanisms and stability of the blocky seawall structure. The backfilling soil is properly integrated into the DDA model, by means of the proposed soil discretization approach, and with an accurate interface shear strength model that the authors presented. According to the simulation results by the modified DDA, the existing seawall is generally in good state. Nevertheless, routine inspection and early restoration are recommended to avoid progressive failures of the seawall.     

Seismic landslide simulations in discontinuous deformation analysis

Discontinuous deformation analysis (DDA) is a numerical approach used to simulate the post-failure behavior of a blocky assembly. Three available algorithms incorporate seismic impacts into DDA simulations for earthquake-induced slope failure. The following methods are used: directly applying time-dependent accelerations to falling/sliding blocks (Method 1); adding time-dependent accelerations to base block (Method 2); and time-dependently constraining seismic displacements of the base block (Method 3). However, incorrect absolute movements of falling/sliding and base blocks were obtained using Method 1. Additionally, relative movements between falling/sliding blocks and the base block are opposite to those simulated by the other two algorithms—Methods 2 and 3. Since locating an earthquake-induced landslide before an earthquake is extremely difficult, the seismic movements of base rock are recorded. Method 1 applies recorded seismic data to sliding blocks in conflict with d’Alembert’s principle of mechanics. Additionally, in Method 2, when the computation time step must be longer than the time in seismic data, computational results reveal abnormal base block displacements due to the non-zero velocity recorded at the end time of seismic data in seismic DDA. In this study, a novel algorithm to diminish the velocity of the base rock in the seismic analysis is utilized to modify Method 2. Furthermore, this work confirms that DDA with the modified Methods 2 and 3 is a practical approach for earthquake-induced landslide simulations.     

Fully coupled methods for multiphase morphodynamics

We present numerical methods for a system of equations consisting of the two dimensional Saint–Venant shallow water equations (SWEs) fully coupled to a completely generalized Exner formulation of hydrodynamically driven sediment discharge. This formulation is implemented by way of a discontinuous Galerkin (DG) finite element method, using a Roe Flux for the advective components and the unified form for the dissipative components. We implement a number of Runge–Kutta time integrators, including a family of strong stability preserving (SSP) schemes, and Runge–Kutta Chebyshev (RKC) methods. A brief discussion is provided regarding implementational details for generalizable computer algebra tokenization using arbitrary algebraic fluxes. We then run numerical experiments to show standard convergence rates, and discuss important mathematical and numerical nuances that arise due to prominent features in the coupled system, such as the emergence of nondifferentiable and sharp zero crossing functions, radii of convergence in manufactured solutions, and nonconservative product (NCP) formalisms. Finally we present a challenging application model concerning hydrothermal venting across metalliferous muds in the presence of chemical reactions occurring in low pH environments.     

球层中高阶自由热对流格局及其变化的研究

研究了下边界为应力自由边界, 上边界为刚性边界, 纯粹从底部加热的充满了无穷大普朗特数的Boussinesq流体的同心球层中的非线性自由热对流. 借鉴将极型场和扰动温度场展成勒让德多项式（以下称零级数模型, 即此时m=0）的方法, 将它们展成6阶6级（即l=6; m=0, 1, 2, hellip;, l）的勒让德函数（以下称高级数模型）, 并用Galerkin方法求解非线性方程组, 获得了高级数模型的结果. 与零级数模型仅能获得表征物质垂直运移特征和扰动温度结构的二维南北向（rphi;）剖面相比, 高级数模型还得到了东西向（rphi;）和深度剖面（theta;phi;）, 而且对流运动的许多细特征得以体现, 有利于深化认识球层中自由热对流的特征及其导致的温度结构. 瑞利数的大小对自由热对流的格局和速率产生了重要的影响, 控制着对流层中高温热柱区和低温冷柱区的相对大小. 本文所得到的结果可能主要反映了下地幔物质运动, 其对流格局和速率在不同的位置上存在明显的差异, 可能蕴涵了重要的地球动力学含义.      

Computation of the safety factor for slope stability using discontinuous deformation analysis and the vector sum method

This study introduces the vector sum method into discontinuum-based methods by considering the sliding vector and the stress state of the discrete block system. The sliding direction computation and force projection in the new approach are detailed, and the safety factor is solved by explicit equations. The vector sum method is implemented in the discontinuous deformation analysis (DDA) program and is used to compute the safety factors for two numerical examples. A comparison of the solutions obtained with the theoretical analysis and limit equilibrium analysis demonstrates that the new method is suitable for calculating the safety factor of a slope.     

Potential for gas hydrate formation at the northwest New Zealand shelf margin - New insights from seismic reflection data and petroleum systems modelling

In this study we provide evidence for methane hydrates in the Taranaki Basin, occurring a considerable distance from New Zealand's convergent margins, where they are well documented. We describe and reconstruct a unique example of gas migration and leakage at the edge of the continental shelf, linking shallow gas hydrate occurrence to a deeper petroleum system. The Taranaki Basin is a well investigated petroleum province with numerous fields producing oil and gas. Industry standard seismic reflection data show amplitude anomalies that are here interpreted as discontinuous BSRs, locally mimicking the channelized sea-floor and pinching out up-slope. Strong reverse polarity anomalies indicate the presence of gas pockets and gas-charged sediments. PetroMod™ petroleum systems modelling predicts that the gas is sourced from elevated microbial gas generation in the thick slope sediment succession with additional migration of thermogenic gas from buried Cretaceous petroleum source rocks. Cretaceous–Paleogene extensional faults underneath the present-day slope are interpreted to provide pathways for focussed gas migration and leakage, which may explain two dry petroleum wells drilled at the Taranaki shelf margin. PetroMod™ modelling predicts concentrated gas hydrate formation on the Taranaki continental slope consistent with the anomalies observed in the seismic data. We propose that a semi-continuous hydrate layer is present in the down-dip wall of incised canyons. Canyon incision is interpreted to cause the base of gas hydrate stability to bulge downward and thereby trap gas migrating up-slope in permeable beds due to the permeability decrease caused by hydrate formation in the pore space. Elsewhere, hydrate occurrence is likely patchy and may be controlled by focussed leakage of thermogenic gas. The proposed presence of hydrates in slope sediments in Taranaki Basin likely affects the stability of the Taranaki shelf margin. While hydrate presence can be a drilling hazard for oil and gas exploration, the proposed presence of gas hydrates opens up a new frontier for exploration of hydrates as an energy source.     

Analysis and performance of a predictor‐multicorrector Time Discontinuous Galerkin method in non‐linear elastodynamics

A predictor‐multicorrector implementation of a Time Discontinuous Galerkin method for non‐linear dynamic analysis is described. This implementation is intended to limit the high computational expense typically required by implicit Time Discontinuous Galerkin methods, without degrading their accuracy and stability properties. The algorithm is analysed with reference to conservative Duffing oscillators for which closed‐form solutions are available. Therefore, insight into the accuracy and stability properties of the predictor‐multicorrector algorithm for different approximations of non‐linear internal forces is gained, showing that the properties of the underlying scheme can be substantially retained. Finally, the results of representative numerical simulations relevant to Duffing oscillators and to a stiff spring pendulum discretized with finite elements illustrate the performance of the numerical scheme and confirm the analytical estimates. Copyright © 2002 John Wiley & Sons, Ltd.