1,721,007 research outputs found
A multi-layer reduced model for flow in porous media with a fault and surrounding damage zones
Get PDFIn this work, we present a new conceptual model to describe fluid flow in a porous media system in presence of a large fault. Geological faults are often modeled simply as interfaces in the rock matrix, but they are complex structures where the high strain core is surrounded by the so called damage zones, characterized by the presence of smaller fractures which enhance the permeability of the medium. To obtain reliable simulation outcomes, the damage zone as well as the fault, have to be accurately described. The new model proposed in this work considers both these regions as lower dimensional and embedded in the rock matrix. The model is presented, analyzed, and tested in several configurations to prove its robustness and ability to capture many important features, such as high contrast and heterogeneity of permeability
An Efficient XFEM Approximation of Darcy Flows in Arbitrarily Fractured Porous Media
Get PDFSubsurface flows are influenced by the presence of faults and large fractures which act as preferential paths or barriers for the flow. In literature models were proposed to handle fractures in a porous medium as objects of codimension 1. In this work we consider the case of a network of intersecting fractures, with the aim of deriving physically consistent and effective interface conditions to impose at the intersection between fractures. This new model accounts for the angle between fractures at the intersections and allows for jumps of pressure across the intersection. This latter property permits to describe more accurately the flow when fractures are characterised by different properties, than other models that impose pressure continuity. The main mathematical properties of the model, derived in the two-dimensional setting, are analysed. As concerns the numerical discretization we allow the grids of the fractures to be independent, thus in general non-matching at the intersection, by means of the Extended Finite Element Method (XFEM), to increase the flexibility of the method in the case of complex geometries characterized by a high number of fractures
Advances in computation of local problems for a flow-based upscaling in fractured reservoirs
Get PDFIn this article we present some numerical techniques to increase efficiency and applicability of a flow-based upscaling procedure used to solve single and multi-phase flows in naturally fractured reservoirs. These geological formations may be characterized by hundreds up to hundreds of thousands of fractures, ranging from small to medium scales, spreading all over the reservoir. In these scenarios numerical simulations using an explicit discretization of all fractures become rapidly unfeasible.
The problem may be overcome by upscaling procedures. In this work we assume that the flow in the reservoir is simulated by using a corner-point grid completely unrelated to the fracture network. The presence of the latter is accounted for by a numerical upscaled procedure that employs an embedded discrete fracture model (EDFM).
To characterize the scaled up problem, we consider a flow-based upscaling procedure where multiple sub-regions are used to derive transmissibilities, mean depths and pore volumes related to the degrees of freedom associated with fractures and rock matrix. An important aspect of the work with respect to others presented in the literature is the enhancement of the upscaling process by splitting the degrees of freedom associated with unconnected portions of the rock matrix. Numerical examples confirm the effectiveness of the proposed approach. We also compare two ways of setting up the boundary conditions of the local problems, that is a well known open issue, used to compute the upscaled transmissibility between cells. Though the experiments lead to a similar result, at the best of our knowledge, it is the first time that such a comparison is made for fractured reservoir
A multi-layer reactive transport model for fractured porous media
Get PDFAn accurate modeling of reactive flows in fractured porous media is a key ingredient to obtain reliable numerical simulations of several industrial and environmental applications. For some values of the physical parameters we can observe the formation of a narrow region or layer around the fractures where chemical reactions are focused. Here, the transported solute may precipitate and form a salt, or vice-versa. This phenomenon has been observed and reported in real outcrops. By changing its physical properties, this layer might substantially alter the global flow response of the system and thus the actual transport of solute: the problem is thus non-linear and fully coupled. The aim of this work is to propose a new mathematical model for reactive flow in fractured porous media, by approximating both the fracture and these surrounding layers via a reduced model. In particular, our main goal is to describe the layer thickness evolution with a new mathematical model, and compare it to a fully resolved equidimensional model for validation. As concerns numerical approximation we extend an operator splitting scheme in time to solve sequentially, at each time step, each physical process thus avoiding the need for a non-linear monolithic solver, which might be challenging due to the non-smoothness of the reaction rate. We consider bi- and tridimensional numerical test cases to asses the accuracy and benefit of the proposed model in realistic scenarios
A hybrid upwind scheme for two-phase flow in fractured porous media
Get PDFSimulating the flow of two fluid phases in porous media is a challenging task, especially when fractures are included in the simulation. Fractures may have highly heterogeneous properties compared to the surrounding rock matrix, significantly affecting fluid flow, and at the same time hydraulic apertures that are much smaller than any other characteristic sizes in the domain.
Generally, flow simulators face difficulties with counter-current flow, generated by gravity and pressure gradients, which hinders the convergence of non-linear solvers (Newton).
In this work, we model the fracture geometry with a mixed-dimensional discrete fracture network, thus lightening the computational burden associated to an equi-dimensional representation. We address the issue of counter-current flows with appropriate spatial discretization of the advective fluid fluxes, with the aim of improving the convergence speed of the nonlinear solver. In particular, the extension of the hybrid upwinding to the mixed-dimensional framework, with the use of a phase potential upstreaming at the interfaces of subdomains.
We test the method across several cases with different flow regimes and fracture network geometries. Results show robustness of the chosen discretization and a consistent improvements, in terms of Newton iterations, compared to using phase potential upstreaming everywhere
Application of deep learning reduced-order modeling for single-phase flow in faulted porous media
Get PDFOur research is positioned within the framework of subsurface resource utilization for sustainable economies. We concentrate on modeling the underground single-phase fluid flow affected by geological faults using numerical simulations. The study of such flows is characterized by strong uncertainites in the data defing the problem due to the difficulty of taking precise measurements in the subsoil. We aim to demonstrate the feasibility of a reduced order model that is both reliable and computationally efficient, thereby facilitating the incorporation of uncertainties. We account for the uncertainities of the properties of the rock and the geometry of the fault. The latter is achieved by using a radial basis function mesh deformation method. This approach benefits from a mixed-dimensional framework to model the rock matrix and faults as n and n-1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\end{document} dimensional domains, allowing for non-conforming meshes. Our primary focus is on a reduced-order model capable of reproducing flow variables across the entire domain. We utilize the Deep Learning Reduced Order Model (DL-ROM), a nonintrusive neural network-based technique, and we compare it against the traditional Proper Orthogonal Decomposition (POD) method across various scenarios. The most relevant contributions of this work are: the proof of concept of the use of neural network for reduced order models for subsoil flow, dealing with non-affine problems and mixed dimensional domain. Additionally, we generalize an existing mesh deformation method for discontinuous deformation maps. Our analysis highlights the capability of reduced order model, highlighting DL-ROM's capacity to expedite complex analyses with promising accuracy and efficiency, making multi-query analyses with various quantities of interest affordable
Neural network solvers for parametrized elasticity problems that conserve linear and angular momentum
Get PDFWe consider a mixed formulation of parametrized elasticity problems in terms of stress, displacement, and rotation. The latter two variables act as Lagrange multipliers to enforce the conservation of linear and angular momentum. The resulting system is computationally demanding to solve directly, especially if various instances of the model parameters need to be investigated. We therefore propose a reduced order modeling strategy that efficiently produces an approximate solution, while guaranteeing conservation of linear and angular momentum in the computed stress. First, we obtain a stress field that balances the body and the boundary forces by solving a triangular system, generated with the use of a spanning tree in the grid. Second, a trained neural network is employed to rapidly compute a correction without affecting the conservation equations. The displacement and rotation fields can be obtained by post-processing. The potential of the approach is highlighted by three numerical test cases, including a three-dimensional and a non-linear model
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