Numerical aspects of hydro-mechanical coupling of fluid-filled fractures using hybrid-dimensional element formulations and non-conformal meshes

Schmidt, Patrick; Steeb, Holger

doi:10.1007/s13137-019-0127-5

Cited by 16 publications

(17 citation statements)

References 31 publications

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“…In the context of hydraulic characterization of fractures, their contact mechanics may thus be reduced to an account of their normal stiffness (Pyrak-Nolte and Morris 2000). Hence, we apply a hydro-mechanical model considering the constitutive relation of normal contact following a monolithic numerical implementation (Schmidt and Steeb 2019) for the numerical determination of characteristic fracture parameters, initial width or aperture hyd 0 , and normal stiffness parameter E Fr . The third characteristic parameter, the fracture length l Fr , is an element of the modeled fracturedomain discretization.…”

Section: Methodsmentioning

confidence: 99%

“…However, hydro-mechanical phenomena, such as reverse water-level fluctuations in distant monitoring wells (Rodrigues 1983;Kim and Parizek 1997) or insensitivity of pressure responses to increases in flow rates, so-called jacking (Quirion and Tournier 2010), cannot be reproduced by pressure-diffusion models and result in inaccurate approximations of the effective fracture characteristics (Vinci et al 2014a;Murdoch and Germanovich 2006;Cappa et al 2018). Despite the growing number of treatments of hydro-mechanical coupling (Murdoch and Germanovich 2006;Girault et al 2015Girault et al , 2016Castelletto et al 2015;Schmidt and Steeb 2019), the understanding of the influence of basic geometrical and mechanical properties of fractures on their hydraulic response to flow rate or pressure perturbations remains limited; a critical obstacle to, e.g., the development of geothermal energy provision from petrothermal reservoirs.…”

Section: Introductionmentioning

confidence: 99%

“…Yet, logging and impression-packer results do not support this simple association of fracture geometry and hydraulic response. We employ a hydro-mechanical model considering radial-symmetric conditions, as applying for a radial fracture following a monolithic numerical implementation (Schmidt and Steeb 2019) to study the origin of the distinct pressure transients. Specifically, we studied the sensitivity of the hydro-mechanical model to the variation of characteristic fracture properties to identify best fits to the field data and the interdependence between the characteristic fracture properties.…”

Section: Introductionmentioning

confidence: 99%

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Investigations into the opening of fractures during hydraulic testing using a hybrid-dimensional flow formulation

2021

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We applied a hybrid-dimensional flow model to pressure transients recorded during pumping experiments conducted at the Reiche Zeche underground research laboratory to study the opening behavior of fractures due to fluid injection. Two distinct types of pressure responses to flow-rate steps were identified that represent radial-symmetric and plane-axisymmetric flow regimes from a conventional pressure-diffusion perspective. We numerically modeled both using a radial-symmetric flow formulation for a fracture that comprises a non-linear constitutive relation for the contact mechanics governing reversible fracture surface interaction. The two types of pressure response can be modeled equally well. A sensitivity study revealed a positive correlation between fracture length and normal fracture stiffness that yield a match between field observations and numerical results. Decomposition of the acting normal stresses into stresses associated with the deformation state of the global fracture geometry and with the local contacts indicates that geometrically induced stresses contribute the more the lower the total effective normal stress and the shorter the fracture. Separating the contributions of the local contact mechanics and the overall fracture geometry to fracture normal stiffness indicates that the geometrical stiffness constitutes a lower bound for total stiffness; its relevance increases with decreasing fracture length. Our study demonstrates that non-linear hydro-mechanical coupling can lead to vastly different hydraulic responses and thus provides an alternative to conventional pressure-diffusion analysis that requires changes in flow regime to cover the full range of observations.

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Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Investigations into the opening of fractures during hydraulic testing using a hybrid-dimensional flow formulation

2021

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“…Due to minor contribution to the overall solution in the investigated applications, the terms II) and III) will be neglected in the course of this work [1]. The resulting governing equations are solved by using a finite element implementation [4] and a monolithic solution strategy using zero-thickness interface elements for the fracture domain [5,6].…”

Section: Hybrid-dimensional Formulationmentioning

confidence: 99%

Investigation of heterogeneous fracture aperture distributions in a hydro mechanical setting using hybrid‐dimensional interface elements

Schmidt

Steeb

2021

Proc Appl Math and Mech

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In the community of porous and fractured geomaterials properties regarding underground fluid storage and matter are of high interest. Investigations on fluid-filled fractures require strong hydro mechanical coupling of fracture and porous domain to reproduce deformation triggered, non-local phenomena such as the Noordbergum effect. Special numerical treatment is necessary to solve the tightly coupled system consisting of high aspect ratio fractures and a surrounding porous matrix, since other approaches such as Direct Numerical Simulations fail due to technical issues (number of Degrees of Freedom (DoF)). Once heterogeneous initial aperture distributions are of interest coarse grained continuum approaches (Biot's poroelasticity theory) facing technical limitations since explicit meshing of the fracture geometry is required. This work uses hybriddimensional interface elements in a fully coupled implicit formulation to investigate its capacities regarding heterogeneous fracture surfaces in three dimensions.

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“…The numerical approaches to solve the strongly coupled hydro-mechanical fracture-flow problem addressed in literature can be divided in two groups: (i) monolithic and (ii) partitioned schemes. Monolithic approaches introduce the fracture-flow domain by zero-thickness interface elements [22,[45][46][47] and mostly require direct solution strategies to guarantee high numerical stability since distinct characteristic properties of both domains lead to poor conditioning of the global system [43]. In general, tailored meshing and integration strategies are required to discretize the fracture domain by interface elements.…”

Section: Introductionmentioning

confidence: 99%

Simulation of flow in deformable fractures using a quasi-Newton based partitioned coupling approach

et al. 2022

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We introduce a partitioned coupling approach for iterative coupling of flow processes in deformable fractures embedded in a poro-elastic medium that is enhanced by interface quasi-Newton (IQN) methods. In this scope, a unique computational decomposition into a fracture flow and a poro-elastic domain is developed, where communication and numerical coupling of the individual solvers are realized by consulting the open-source library preCICE. The underlying physical problem is introduced by a brief derivation of the governing equations and interface conditions of fracture flow and poro-elastic domain followed by a detailed discussion of the partitioned coupling scheme. We evaluate the proposed implementation and undertake a convergence study to compare a classical interface quasi-Newton inverse least-squares (IQN-ILS) with the more advanced interface quasi-Newton inverse multi-vector Jacobian (IQN-IMVJ) method. These coupling approaches are verified for an academic test case before the generality of the proposed strategy is demonstrated by simulations of two complex fracture networks. In contrast to the development of specific solvers, we promote the simplicity and computational efficiency of the proposed partitioned coupling approach using preCICE and FEniCS for parallel computations of hydro-mechanical processes in complex, three-dimensional fracture networks.

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Numerical aspects of hydro-mechanical coupling of fluid-filled fractures using hybrid-dimensional element formulations and non-conformal meshes

Cited by 16 publications

References 31 publications

Investigations into the opening of fractures during hydraulic testing using a hybrid-dimensional flow formulation

Investigations into the opening of fractures during hydraulic testing using a hybrid-dimensional flow formulation

Investigation of heterogeneous fracture aperture distributions in a hydro mechanical setting using hybrid‐dimensional interface elements

Simulation of flow in deformable fractures using a quasi-Newton based partitioned coupling approach

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