Related papers: A global sensitivity analysis and reduced order mo…
Variance based global sensitivity analysis measures the relevance of inputs to a single output using Sobol' indices. This paper extends the definition in a natural way to multiple outputs, directly measuring the relevance of inputs to the…
The rheological properties of viscoelastic materials like polymer melts are greatly affected by factors like salinity, temperature, concentration and pH of the solution. In this study, the memory of the stress affected by each of these…
We consider a two dimensional lattice model to describe the opening of a crack in hydraulic fracturing. In particular we consider that the material only breaks under tension and the fluid has no pressure drop inside the crack. For the case…
Sensitivity analysis (SA) is a procedure for studying how sensitive are the output results of large-scale mathematical models to some uncertainties of the input data. The models are described as a system of partial differential equations.…
Pore-resolved direct numerical simulations of turbulent open channel flow are performed comparing the structure and dynamics of turbulence over impermeable rough and smooth walls to a porous sediment bed at permeability Reynolds number…
In this paper, we combine concepts of the generalized multiscale finite element method and mode decomposition methods to construct a robust local-global approach for model reduction of flows in high-contrast porous media. This is achieved…
Strong interaction of closely located, nearly parallel hydraulic fractures and its influence on their propagation are studied. Both computational and physical aspects of the problem are considered. It is shown that from the computational…
An innovative computational approach to capturing the essential aspects of an Enhanced Geothermal System (EGS) is formulated. The modified finite element method is utilized to model transient heat and fluid flow within an EGS reservoir.…
We review microstructural fracture growth models suitable for the study of hydraulic fracture processes in disordered porous materials and present some basic results. It is shown that microstructural models exhibit certain similarities to…
The hierarchically orthogonal functional decomposition of any measurable function f of a random vector X=(X_1,...,X_p) consists in decomposing f(X) into a sum of increasing dimension functions depending only on a subvector of X. Even when…
Phase field model (PFM) is an efficient fracture modeling method and has high potential for hydraulic fracturing (HF). However, the current PFMs in HF do not consider well the effect of in-situ stress field and the numerical examples of…
Earthquakes induced during hydraulic fracturing operations have occurred in a number of locales. However, in-situ studies aimed to discern the triggering mechanism remains exclusively statistical in their nature. Here, we calculate the…
Models with high-dimensional parameter spaces are common in many applications. Global sensitivity analyses can provide insights on how uncertain inputs and interactions influence the outputs. Many sensitivity analysis methods face…
Given a bivariate random pair $(X,Y)$, a natural problem is to estimate, from a single sample $(X_i,Y_i)_{1\le i\le n}$, quantities such as $\mathbb{E}\left[ \mathbb{E}[ Y\mid X ]^2 \right]$. More broadly, sensitivity indices are designed…
The optimization of high dimensional functions is a key issue in engineering problems but it frequently comes at a cost that is not acceptable since it usually involves a complex and expensive computer code. Engineers often overcome this…
The objective of the current study is to utilize an innovative method called 'change probabilities' for describing fracture roughness. In order to detect and visualize anisotropy of rock joint surfaces, the roughness of one-dimensional…
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…
Recent years have seen a significant interest in using phase field approaches to model hydraulic fracture, so as to optimise a process that is key to industries such as petroleum engineering, mining and geothermal energy extraction. Here,…
The widespread use of sodium aluminosilicate glass in many engineering applications due to its mechanical and optical properties (transparency, dielectric, etc.), has become common in recent years. However, glass, a brittle material, has…
This work focuses on the simulation of $CO_2$ storage in deep underground formations under uncertainty and seeks to understand the impact of uncertainties in reservoir properties on $CO_2$ leakage. To simulate the process, a non-isothermal…