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Hydraulic fracturing is one of the key technologies for reservoir stimulation in low-permeability/unconventional oil and gas fields. In response to the high energy consumption and greenhouse gas emissions caused by extreme flow-limiting…
In this paper we consider various models of hydraulic hysteresis in invasive mercury porosimetry. For simulating the hydraulic hysteresis is used isotropic site percolation on three-dimensional square lattices with $(1, d)$-neighborhood.…
Shale gas recovery has seen a major boom in recent years due to the increasing global energy demands; but the extraction technologies are very expensive. It is therefore important to develop realistic transport modelling and simulation…
We analyse the cluster discovered by invasion percolation on a branching process with a power-law offspring distribution. Invasion percolation is a paradigm model of self-organised criticality, where criticality is approached without tuning…
We study the onset of the bootstrap percolation transition as a model of generalized dynamical arrest. We develop a new importance-sampling procedure in simulation, based on rare events around "holes", that enables us to access bootstrap…
We study percolation on networks, which is used as a model of the resilience of networked systems such as the Internet to attack or failure and as a simple model of the spread of disease over human contact networks. We reformulate…
We consider loop ensembles on random trees. The loops are induced by a Poisson process of links sampled on the underlying tree interpreted as a metric graph. We allow two types of links, crosses and double bars. The crosses-only case…
Integral-type nonlocal damage models describe the fracture process zones by regular strain profiles insensitive to the size of finite elements, which is achieved by incorporating weighted spatial averages of certain state variables into the…
A mechanical model is introduced for predicting the initiation and evolution of complex fracture patterns without the need for a damage variable or law. The model, a continuum variant of Newton's second law, uses integral rather than…
We introduce a model of fracture which includes the out-of-plane degrees of freedom necessary to describe buckling in a thin-sheet material. The model is a regular square lattice of elastic beams, rigidly connected at the nodes so as to…
Fractal percolation exhibits a dramatic topological phase transition, changing abruptly from a dust-like set to a system spanning cluster. The transition points are unknown and difficult to estimate. In many classical percolation models the…
We performed a set of numerical simulations to characterize the interplay of fracture network topology, upscaling, and mesh refinement on flow and transport properties in fractured porous media. We generated a set of generic…
Fractures play a critical role in governing fluid flow within subsurface energy systems, including oil and gas production, geologic carbon sequestration, and underground hydrogen storage. This study investigated the impact of pore-scale…
We present a model of the hydraulic fracturing of heterogeneous poroelastic media. The formalism is an effective continuum model that captures the coupled dynamics of the fluid pressure and the fractured rock matrix and models both the…
We detail the energy balance of a propagating hydraulic fracture. Using the linear hydraulic fracture model which combines lubrication flow and linear elastic fracture mechanics, we demonstrate how different propagation regimes are related…
In this work, we consider a mathematical model for flow in a unsaturated porous medium containing a fracture. In all subdomains (the fracture and the adjacent matrix blocks) the flow is governed by Richards' equation. The submodels are…
Film flow through networks of corners and capillary bridges can establish connections between seemingly isolated clusters during drainage in porous media. Coupled with drainage through the bulk of pores and throats, the flow through these…
Predicting the permeability of porous media in saturated and partially saturated conditions is of crucial importance in many geo-engineering areas, from water resources to vadose zone hydrology or contaminant transport predictions. Many…
In this study, we analyze the flow filtration process of slightly compressible fluids in fractured porous media. We model the coupled fractured porous media system, where the linear Darcy flow is considered in porous media and the nonlinear…
We analyze damage nucleation and localization in the random fuse model with strong disorder using numerical simulations. In the initial stages of the fracture process, damage evolves in an uncorrelated manner, resembling percolation.…