28 research outputs found
Post-injection normal closure of fractures as a mechanism for induced seismicity
Understanding the controlling mechanisms underlying injection-induced
seismicity is important for optimizing reservoir productivity and addressing
seismicity-related concerns related to hydraulic stimulation in Enhanced
Geothermal Systems. Hydraulic stimulation enhances permeability through
elevated pressures, which cause normal deformations, and the shear slip of
pre-existing fractures. Previous experiments indicate that fracture deformation
in the normal direction reverses as the pressure decreases, e.g., at the end of
stimulation. We hypothesize that this normal closure of fractures enhances
pressure propagation away from the injection region and significantly increases
the potential for post-injection seismicity. To test this hypothesis, hydraulic
stimulation is modeled by numerically coupling fracture deformation, pressure
diffusion and stress alterations for a synthetic geothermal reservoir in which
the flow and mechanics are strongly affected by a complex three-dimensional
fracture network. The role of the normal closure of fractures is verified by
comparing simulations conducted with and without the normal closure effect
A Comparison of Consistent Discretizations for Elliptic Problems on Polyhedral Grids
In this work, we review a set of consistent discretizations for second-order elliptic equations, and compare and contrast them with respect to accuracy, monotonicity, and factors affecting their computational cost (degrees of freedom, sparsity, and condition numbers). Our comparisons include the linear and nonlinear TPFA method, multipoint flux-approximation (MPFA-O), mimetic methods, and virtual element methods. We focus on incompressible flow and study the effects of deformed cell geometries and anisotropic permeability.acceptedVersio
Modeling and discretization of flow in porous media with thin, full-tensor permeability inclusions
When modeling fluid flow in fractured reservoirs, it is common to represent the fractures as lower-dimensional inclusions embedded in the host medium. Existing discretizations of flow in porous media with thin inclusions assume that the principal directions of the inclusion permeability tensor are aligned with the inclusion orientation. While this modeling assumption works well with tensile fractures, it may fail in the context of faults, where the damage zone surrounding the main slip surface may introduce anisotropy that is not aligned with the main fault orientation. In this article, we introduce a generalized dimensional reduced model which preserves full-tensor permeability effects also in the out-of-plane direction of the inclusion. The governing equations of flow for the lower-dimensional objects are obtained through vertical averaging. We present a framework for discretization of the resulting mixed-dimensional problem, aimed at easy adaptation of existing simulation tools. We give numerical examples that show the failure of existing formulations when applied to anisotropic faulted porous media, and go on to show the convergence of our method in both two-dimensional and three-dimensional.publishedVersio
Input and benchmarking data for flow simulations in discrete fracture networks
This article reports and describes the data related to the paper “Conforming, non-conforming and non-matching discretization couplings in discrete fracture network simulations” (Fumagalli et al., 2019). The data provided include a set of geometrical input data of Discrete Fracture Networks (DFNs) and a set of simulation results. The geometrical data describe the geometry of fracture networks of increasing complexity. These data also include the geometry of a DFN extruded from a real fracture outcrop in Western Norway. Simulation results are obtained using several different numerical schemes and provide convergence history, plots over line and upscaled output quantities related to the various considered geometries
Unified approach to discretization of flow in fractured porous media
In this paper, we introduce a mortar-based approach to discretizing flow in fractured porous media, which we term the mixed-dimensional flux coupling scheme. Our formulation is agnostic to the discretizations used to discretize the fluid flow equations in the porous medium and in the fractures, and as such it represents a unified approach to integrated fractured geometries into any existing discretization framework. In particular, several existing discretization approaches for fractured porous media can be seen as special instances of the approach proposed herein. We provide an abstract stability theory for our approach, which provides explicit guidance into the grids used to discretize the fractures and the porous medium, as dependent on discretization methods chosen for the respective domains. The theoretical results are sustained by numerical examples, wherein we utilize our framework to simulate flow in 2D and 3D fractured media using control volume methods (both two- and multi-point flux), Lagrangian finite element methods, mixed finite element methods, and virtual element methods. As expected, regardless of the ambient methods chosen, our approach leads to stable and convergent discretizations for the fractured problems considered, within the limits of the discretization schemes
PorePy: an open-source software for simulation of multiphysics processes in fractured porous media
Development of models and dedicated numerical methods for dynamics in fractured rocks is an active research field, with research moving towards increasingly advanced process couplings and complex fracture networks. The inclusion of coupled processes in simulation models is challenged by the high aspect ratio of the fractures, the complex geometry of fracture networks, and the crucial impact of processes that completely change characteristics on the fracture-rock interface. This paper provides a general discussion of design principles for introducing fractures in simulators, and defines a framework for integrated modeling, discretization, and computer implementation. The framework is implemented in the open-source simulation software PorePy, which can serve as a flexible prototyping tool for multiphysics problems in fractured rocks. Based on a representation of the fractures and their intersections as lower-dimensional objects, we discuss data structures for mixed-dimensional grids, formulation of multiphysics problems, and discretizations that utilize existing software. We further present a Python implementation of these concepts in the PorePy open-source software tool, which is aimed at coupled simulation of flow and transport in three-dimensional fractured reservoirs as well as deformation of fractures and the reservoir in general. We present validation by benchmarks for flow, poroelasticity, and fracture deformation in porous media. The flexibility of the framework is then illustrated by simulations of non-linearly coupled flow and transport and of injection-driven deformation of fractures. All results can be reproduced by openly available simulation scripts
Implementation of mixed-dimensional models for flow in fractured porous media
Models that involve coupled dynamics in a mixed-dimensional geometry are of increasing interest in several applications. Here, we describe the development of a simulation model for flow in fractured porous media, where the fractures and their intersections form a hierarchy of interacting subdomains. We discuss the implementation of a simulation framework, with an emphasis on reuse of existing discretization tools for mono-dimensional problems. The key ingredients are the representation of the mixed-dimensional geometry as a graph, which allows for convenient discretization and data storage, and a non-intrusive coupling of dimensions via boundary conditions and source terms. This approach is applicable for a wide class of mixed-dimensional problems. We show simulation results for a flow problem in a three-dimensional fracture geometry, applying both finite volume and virtual finite element discretizations
Impact of deformation bands on fault-related fluid flow in field-scale simulations
Subsurface storage of CO2 is predicted to rise exponentially in response to
the increasing levels of CO2 in the atmosphere. Large-scale CO2 injections into
the subsurface require understanding of the potential for fluid flow through
faults to mitigate risk of leakage. Here, we study how to obtain effective
permeability of deformation bands in the damage zone of faults. Deformation
bands are relatively small, low permeability features that can have a
significant effect on flow dynamics, however, the discrepancy of scales is a
challenge for field-scale simulation. A new analytical upscaling model is
proposed in order to overcome some of the shortcomings of conventional
upscaling approaches for heterogeneous porous media. The new model captures the
fine-scale impact of deformation bands on fluid flow in the near-fault region,
and can be derived from knowledge of large-scale fault properties. To test the
accuracy of the model it is compared to fine-scale numerical simulations that
explicitly include individual deformation bands. For a wide range of different
stochastically generated deformation bands networks, the upscaling model shows
improved estimate of effective permeability compared to conventional upscaling
approaches. By applying the upscaling model to a full-field simulation of the
Smeaheia storage site in the North Sea, we show that deformation bands with a
permeability contrast higher than three orders of magnitude may act as an extra
layer of protection from fluid flow through faults