32 research outputs found
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
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鈥搒tructure interplay using a discrete鈥揻racture鈥搈atrix 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鈥檚 convergence, investigate process鈥搒tructure 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
Finite volume discretisation of fracture deformation in thermo-poroelastic media
This paper presents a model where thermo-hydro-mechanical processes are
coupled to a deformation model for preexisting fractures. The model is
formulated within a discrete-fracture-matrix framework where the rock matrix
and the fractures are considered as individual subdomains, and interaction
between them takes place on the matrix-fracture interfaces. A finite volume
discretisation implemented in the simulation toolbox PorePy is presented and
applied in a simulation showcasing the effects of the different mechanisms on
fracture deformation governed by contact mechanics, as well as their different
timescales.Comment: 8 pages, 4 figure
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
Flexible and rigorous numerical modelling of multiphysics processes in fractured porous media using PorePy
Multiphysics processes in fractured porous media is a research field of
importance for several subsurface applications and has received considerable
attention over the last decade. The dynamics are characterised by strong
couplings between processes as well as interaction between the processes and
the structure of the fractured medium itself. The rich range of behavior calls
for explorative mathematical modelling, such as experimentation with
constitutive laws and novel coupling concepts between physical processes.
Moreover, efficient simulations of the strong couplings between multiphysics
processes and geological structures require the development of tailored
numerical methods.
We present a modelling framework and its implementation in the open-source
simulation toolbox PorePy, which is designed for rapid prototyping of
multiphysics processes in fractured porous media. PorePy uses a
mixed-dimensional representation of the fracture geometry and generally applies
fully implicit couplings between processes. The code design follows the
paradigms of modularity and differentiable programming, which together allow
for extreme flexibility in experimentation with governing equations with
minimal changes to the code base. The code integrity is supported by a
multilevel testing framework ensuring the reliability of the code.
We present our modelling framework within a context of thermo-poroelasticity
in deformable fractured porous media, illustrating the close relation between
the governing equations and the source code. We furthermore discuss the design
of the testing framework and present simulations showcasing the extendibility
of PorePy, as well as the type of results that can be produced by
mixed-dimensional simulation tools.Comment: Run scripts at DOI:10.5281/zenodo.821147
Numerical modelling of convection-driven cooling, deformation and fracturing of thermo-poroelastic media
Convection-driven cooling in porous media influences thermo-poro-mechanical
stresses, thereby causing deformation. These processes are strongly influenced
by the presence of fractures, which dominate flow and heat transfer. At the
same time, the fractures deform and propagate in response to changes in the
stress state. Mathematically, the model governing the physics is tightly
coupled and must account for the strong discontinuities introduced by the
fractures. Over the last decade, and motivated by a number of porous media
applications, research into such coupled models has advanced modelling of
processes in porous media substantially.
Building on this effort, this work presents a novel model that couples flow,
heat transfer, deformation, and propagation of fractures with flow, heat
transfer, and thermo-poroelasticity in the matrix. The model is based on
explicit representation of fractures in the porous medium, and discretised
using multi-point finite volume methods. Frictional contact and non-penetration
conditions for the fractures are handled through active set methods, while a
propagation criterion based on stress intensity factors governs fracture
extension. Considering both forced and natural convection processes, the
numerical results show the intricate nature of thermo-poromechanical fracture
deformation and propagation
Numerical Modelling of Convection鈥慏riven Cooling, Deformation and Fracturing of Thermo鈥慞oroelastic Media
Convection-driven cooling in porous media influences thermo-poro-mechanical stresses, thereby causing deformation. These processes are strongly influenced by the presence of fractures, which dominate flow and heat transfer. At the same time, the fractures deform and propagate in response to changes in the stress state. Mathematically, the model governing the physics is tightly coupled and must account for the strong discontinuities introduced by the fractures. Over the last decade, and motivated by a number of porous media applications, research into such coupled models has advanced modelling of processes in porous media substantially. Building on this effort, this work presents a novel model that couples fracture flow and heat transfer and deformation and propagation of fractures with flow, heat transfer and thermo-poroelasticity in the matrix. The model is based on explicit representation of fractures in the porous medium and discretised using multi-point finite volume methods. Frictional contact and non-penetration conditions for the fractures are handled through active set methods, while a propagation criterion based on stress intensity factors governs fracture extension. Considering both forced and natural convection processes, numerical results show the intricate nature of thermo-poromechanical fracture deformation and propagation.publishedVersio