94 research outputs found
Dual virtual element method for discrete fractures networks
Discrete fracture networks is a key ingredient in the simulation of physical
processes which involve fluid flow in the underground, when the surrounding
rock matrix is considered impervious. In this paper we present two different
models to compute the pressure field and Darcy velocity in the system. The
first allows a normal flow out of a fracture at the intersections, while the
second grants also a tangential flow along the intersections. For the numerical
discretization, we use the mixed virtual finite element method as it is known
to handle grid elements of, almost, any arbitrary shape. The flexibility of the
discretization allows us to loosen the requirements on grid construction, and
thus significantly simplify the flow discretization compared to traditional
discrete fracture network models. A coarsening algorithm, from the algebraic
multigrid literature, is also considered to further speed up the computation.
The performance of the method is validated by numerical experiments
Numerical Treatment of State-Dependent Permeability in Multiphysics Problems
Constitutive laws relating fluid potentials and fluxes in a nonlinear manner are common in several porous media applications, including biological and reactive flows, poromechanics, and fracture deformation. Compared to the standard, linear Darcy's law, such enhanced flux relations increase both the degree of nonlinearity, and, in the case of multiphysics simulations, coupling strength between processes. While incorporating the nonlinearities into simulation models is thus paramount for computational efficiency, correct linearization, as is needed for incorporation in Newton's method, is challenging from a practical perspective. The standard approach is therefore to ignore nonlinearities in the permeability during linearization. For finite volume methods, which are popular in porous media applications, complete linearization is feasible only for the simplest flux discretization, namely the two-point flux approximation. We introduce an approximated linearization scheme for finite volume methods that is exact for the two-point scheme and can be applied to more advanced and accurate discretizations, exemplified herein by a multi-point flux stencil. We test the new method for both nonlinear porous media flow and several multiphysics simulations. Our results show that the new linearization consistently outperforms the standard approach. Moreover our scheme achieves asymptotic second order convergence of the Newton iterations, in contrast to the linear convergence obtained with the standard approach.publishedVersio
A fully coupled numerical model of thermo-hydro-mechanical processes and fracture contact mechanics in porous media
A range of phenomena in the subsurface is characterised by the interplay
between coupled thermal, hydraulic and mechanical processes and deforming
structures such as fractures. Modelling subsurface dynamics can provide
valuable phenomenological understanding, but requires models which faithfully
represent the dynamics involved; these models, therefore are themselves highly
complex.
This paper presents a mixed-dimensional thermo-hydro-mechanical model
designed to capture the process-structure interplay using a
discrete-fracture-matrix framework. It incorporates tightly coupled
thermo-hydro-mechanical processes based on laws for momentum, mass and entropy
in subdomains representing the matrix and the lower-dimensional fractures and
fracture intersections. The deformation of explicitly represented fractures is
modelled by contact mechanics relations and a Coulomb friction law, with
particular attention on coupling of fracture dilation to the governing
equations in both fractures and matrix.
The model is discretised using multi-point finite volumes for the balance
equations and a semismooth Newton scheme for the contact conditions and is
implemented in the open source fracture simulation toolbox PorePy. Finally,
simulation studies demonstrate the model's convergence, investigate
process-structure coupling effects, explore different fracture dilation models
and show an application of the model to a 3d geothermal pressure stimulation
and long-term cooling scenario
A fully coupled numerical model of thermo-hydro-mechanical processes and fracture contact mechanics in porous media
Various phenomena in the subsurface are characterised by the interplay between deforming structures such as fractures and coupled thermal, hydraulic and mechanical processes. Simulation of subsurface dynamics can provide valuable phenomenological understanding, but requires models which faithfully represent the dynamics involved; these models therefore are themselves highly complex.
This paper presents a mixed-dimensional thermo-hydro-mechanical model designed to capture the process–structure interplay using a discrete–fracture–matrix framework. It incorporates tightly coupled thermo-hydro-mechanical processes based on balance laws for momentum, mass and energy in subdomains representing the matrix and the lower-dimensional fractures and fracture intersections. The deformation of explicitly represented fractures is modelled by contact mechanics relations and a Coulomb friction law, with a novel formulation consistently integrating fracture dilation in the governing equations.
The model is discretised using multi-point finite volume methods for the balance equations and a semismooth Newton scheme for the contact conditions and is implemented in the open-source fracture simulation toolbox PorePy. Finally, simulation studies demonstrate the model’s convergence, investigate process–structure coupling effects, explore different fracture dilation models and show an application of the model to stimulation and long-term cooling of a three-dimensional geothermal reservoir.publishedVersio
Modelling of the Shear Dilation Based Hydraulic Stimulation in Enhanced Geothermal Systems Considering Fractures in Different Scales
A numerical approach for modelling of shear dilation of existing fractures in hydraulic stimulation of geothermal reservoirs at low elevated pressures is presented. The fractured rock in the reservoir is modelled as a combination of explicitly represented fractures and the rock matrix surrounding these fractures. The efficient modelling of slip-induced permeability enhancement requires coupling of the fluid flow in fractured rock with the mechanical deformation of the rock matrix and the shear dilation of the fractures. For flow simulations, conductive fractures are represented in the domain as high-permeable discontinuities; therefore they dominate the overall flow behaviour. The rock matrix is represented by a low permeability, capturing the effect of small-scale fractures. For the mechanical deformation problem, the rock matrix is assumed to be a linear elastic material, while the fractures in the rock matrix are introduced as internal boundaries. The shear dilation of the fractures is calculated by a joint deformation model (JDM), which connects the shear slip in the fracture surfaces and additional permeability caused by shear displacement. The flow simulations and the mechanical deformation of the rock matrix are both obtained by finite volume discretizations. Several numerical experiments designed by resembling realistic reservoir parameters are conducted to provide better understanding of the shear dilation mechanism. Moreover, fractures present in different scales in a geothermal reservoir. Ignoring the effect of small-scale fractures to the fluid flow in the matrix may result in an overestimate of the permeability enhancement. Hence, the influence of rock matrix permeability on fracture aperture and the overall flow behaviour of the reservoir are examined.publishedVersio
High-accuracy phase-field models for brittle fracture based on a new family of degradation functions
Phase-field approaches to fracture based on energy minimization principles
have been rapidly gaining popularity in recent years, and are particularly
well-suited for simulating crack initiation and growth in complex fracture
networks. In the phase-field framework, the surface energy associated with
crack formation is calculated by evaluating a functional defined in terms of a
scalar order parameter and its gradients, which in turn describe the fractures
in a diffuse sense following a prescribed regularization length scale. Imposing
stationarity of the total energy leads to a coupled system of partial
differential equations, one enforcing stress equilibrium and another governing
phase-field evolution. The two equations are coupled through an energy
degradation function that models the loss of stiffness in the bulk material as
it undergoes damage. In the present work, we introduce a new parametric family
of degradation functions aimed at increasing the accuracy of phase-field models
in predicting critical loads associated with crack nucleation as well as the
propagation of existing fractures. An additional goal is the preservation of
linear elastic response in the bulk material prior to fracture. Through the
analysis of several numerical examples, we demonstrate the superiority of the
proposed family of functions to the classical quadratic degradation function
that is used most often in the literature.Comment: 33 pages, 30 figure
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