This paper presents fracture simulations of multiple, interacting, non-planar fractures in three dimensions. The paper provides a short description of the mathematical formulation of the model but the primary focus is on fracture propagation examples and illustrations of how multiple hydraulic fractures interact in three dimensions. The examples which are presented are intended to provide insight into how the number of growing fractures affects fracture shapes, how changes in fluid viscosity can cause fractures to grow together or grow apart, and how limited-entry at the perforations affects the propagation of interacting fractures. The fracture simulator discussed in this paper models the simultaneous growth of non-planar hydraulic fractures in a three-dimensional linear elastic media, and it can also incorporate stress shadows from hydraulic fractures created during earlier fracture stages. The program uses a symmetric Galerkin boundary element method to model fracture shapes and fracture growth, while flow in the fractures is modeled as power-law fluid flow in arbitrary curved channels. The program uses an effective mode-I stress intensity factor to determine which portions of each fracture will propagate and employs mixed-mode stress intensity factors, K I and K II , to determine propagation directions.

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Bare aluminum metal surfaces are highly reactive, which leads to the spontaneous formation of a protective oxide surface layer. Because many subsequent corrosive processes are mediated by water, the structure and dynamics of water at the oxide interface are anticipated to influence corrosion kinetics. Using molecular dynamics simulations with a reactive force field, we model the behavior of aqueous aluminum metal ions in water adsorbed onto aluminum oxide surfaces across a range of ion concentrations and water film thicknesses corresponding to increasing relative humidity. We find that the structure and diffusivity of both the water and the metal ions depend strongly on the humidity of the environment and the relative height within the adsorbed water film. Aqueous aluminum ion diffusion rates in water films corresponding to a typical indoor relative humidity of 30% are found to be more than 2 orders of magnitude slower than self-diffusion of water in the bulk limit. Connections between metal ion diffusivity and corrosion reaction kinetics are assessed parametrically with a reductionist model based on a 1D continuum reaction−diffusion equation. Our results highlight the importance of incorporating the properties specific to interfacial water in predictive models of aluminum corrosion.

Bare aluminum metal surfaces are highly reactive, which leads to the spontaneous formation of a protective oxide surface layer. Because many subsequent corrosive processes are mediated by water, the structure and dynamics of water at the oxide interface are anticipated to influence corrosion kinetics. Using molecular dynamics simulations with a reactive force field, we model the behavior of aqueous aluminum metal ions in water adsorbed onto aluminum oxide surfaces across a range of ion concentrations and water film thicknesses corresponding to increasing relative humidity. We find that the structure and diffusivity of both the water and the metal ions depends strongly on the humidity of the environment and the relative height within the adsorbed water film.Aqueous aluminum ion diffusion rates in water films corresponding to a typical indoor relative humidity of 30% are found to be more than two orders of magnitude slower than self-diffusion of water in the bulk limit. Connections between metal ion diffusivity and corrosion reaction kinetics are assessed parametrically with a reductionist model based on a 1D continuum reaction-diffusion equation. Our results highlight the importance of incorporating the properties specific to interfacial water in predictive models of aluminum corrosion.

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