FM-DBEM Simulation of 3D Microvoid and Microcrack Graphite Models

The graphite is porous medium, and the geometry and size distribution of its structural deficiencies such as microcracks and microvoids at different oxidation degrees have a great influence on the overall performance. In this paper, we adopt the FM-DBEM to study 3D models which contain spheroidal microvoids and circular microcracks. The accuracy of this method is tested by a comparison to the theoretical solution to the problem of 2D microcrack and microvoid interaction problem. Two simulations are conducted: the simulation of graphite model containing a large number of randomly distributed microcracks and microvoids and the simulation of graphite model containing microcracks and growing microvoids. The simulations investigate the effective moduli versus the two microstructures’ density and the effect of microvoid’s growth on the SIF of microcrack

Efficient Geomechanical Simulations of Large-Scale Naturally Fractured Reservoirs Using the Fast Multipole-Displacement Discontinuity Method (FM-DDM)

Geothermal and unconventional reservoirs play an important role in supplying fuel for a growing energy demand in the United States. The development of such reservoirs relies on creating a fracture network to provide flow and transport conduits during injection and production operations. The Displacement Discontinuity Method (DDM) is frequently used for modeling the behavior of fractures embedded in elastic and poroelastic rocks. However, DDM requires the calculation of the influence among all fractures being computationally inefficient for large systems of cracks. It demands quadratic and cubic complexity of memory and solution time by direct methods, respectively, limiting its application to only small-scale situations. Recent fast summation techniques such as the Fast Multipole Method (FMM) have been used to speed up the solution of several boundary element problems using modest computational resources. FMM relies in accelerating matrix-vector products in iterative methods by splitting the computation of the influences among elements into near and far-field interactions. While the former are calculated similarly to the conventional DDM, the latter, where most of the interactions are found, are efficiently approximated by the FMM using analytical multipole and local expansions. However, in spite of its immediately apparent application in the geomechanic context, FMM has been limited to only certain fracture problems because those analytical expansions are only available for selected fundamental solutions and the development for new ones requires complex mathematical derivations even for those kernels of simple form. This work presents a new method called Fast Multipole–Displacement Discontinuity Method (FM-DDM) for an efficient flow-geomechanical simulation of large-scale naturally fractured reservoirs undergoing fluid injection and extraction. The approach combines both DDM and FMM using for the latter a kernel-independent version where multipole and local expansions are not required opening a range of potential applications within the geothermal and oil industries. Several case studies involving fracture networks with up to one hundred thousands of boundary elements were presented to evaluate accuracy, computational efficiency and applications of the FMM approach. From the results, FM-DDM showed an excellent agreement with well-known benchmark solutions outperforming DDM with linear complexity in both memory and execution time. In addition, a variety of large-scale geomechanical applications were efficiently evaluated with FM-DDM involving interactions between transverse hydraulic fractures and a fracture network, fast visualization of high-resolution stress distribution, and the design of exploitation strategies in elastic and poroelastic fractured reservoirs

The Third Air Force/NASA Symposium on Recent Advances in Multidisciplinary Analysis and Optimization

The third Air Force/NASA Symposium on Recent Advances in Multidisciplinary Analysis and Optimization was held on 24-26 Sept. 1990. Sessions were on the following topics: dynamics and controls; multilevel optimization; sensitivity analysis; aerodynamic design software systems; optimization theory; analysis and design; shape optimization; vehicle components; structural optimization; aeroelasticity; artificial intelligence; multidisciplinary optimization; and composites