We base thiswork on the method by Castillo and Grone, which constructs mimeticgradient and divergence operators using a discrete extension of Gauss’ di-vergence theorem. We focus on the construction of two- and three-dimensionalmimetic gradient, divergence, curl, and Laplacian operators. Our applications focus on the simulation of long-term geologic sequestration of carbon dioxide. The resulting method can be used to compute the concentrations of multiple solutes in distributed-memory computers. We also introduce a matrix storage scheme and provide preliminary tests of its performance. Its parallel programming aspects, and the related utility APIs. We discuss the API's design, structure, and usage philosophy, as well as This work is then used as the theoretical foundation for the Mimetic Methods Toolkit (MTK) a C++ API implementing mimetic discretization and quadrature schemes on logically-rectangular grids. We study the mathematical foundations and the underlying algorithms to construct higher-order one-dimensional mimetic operators, and we extend this knowledge to enable systematic derivations of their higher-dimensional counterparts. This process is experimental and the keywords may be updated as the learning algorithm improves.We explore the use of mimetic finite differences as an alternative numerical method to solve the partial differential equations that model the mass transport and concentration profiles of geologically sequestered carbon dioxide. These keywords were added by machine and not by the authors. Only with this assumption, the azimuth of relief-crack populations can be related to in-situ stress azimuth, and the closing pressure of relief cracks to in-situ stress magnitudes. 7.1, the crucial assumption in core-based stress estimates is that the dominating portion of the stress-relief cracks observed in deep drill cores is caused by the relief of present-day stresses. The focus of this chapter is shifted from borehole methods to core-based methods for in-situ stress estimates. For fracturing, in particular, the stress difference between lithologies in a geological sequence is the major control on fracture-height growth. Stress magnitudes are important for wellbore stability and hydraulic fracturing. If wells are not sited properly, drainage patterns will overlap and production may be uneconomic. 7.2), is important for field development as optimum drainage in a tight reservoir will depend on the drainage from a hydraulic fracture.

The orientation of the stress field, which controls the azimuth of the hydraulic fracture (Sect. In-situ stresses are important for many processes in tight gas reservoirs, ranging from siting the well, to drilling, completion and long-term production.

Flowcode 8.1.1 crack