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SUMMARY:Fully-coupled Geomechanics and Flow with Embedded Meshes
DTSTART;VALUE=DATE-TIME:20180517T195600Z
DTEND;VALUE=DATE-TIME:20180517T201100Z
DTSTAMP;VALUE=DATE-TIME:20210928T184826Z
UID:indico-contribution-184-257@events.interpore.org
DESCRIPTION:Speakers: Guotong Ren (University of Tulsa)\nGeomechanical eff
ects can have a first-order effect on production from naturally and hydrau
lically fractured reservoirs. Unstructured discrete fracture-matrix method
s utilize conforming meshes with fractures represented by N-1 dimensional
elements with local mesh refinement about them. Numerous coupled mechanics
and flow models are employed on such mesh topologies. While these methods
can offer attractive properties in terms of accuracy\, they do rely on th
e availability powerful mesh generators. Moreover\, their application to f
racture propagation modeling requires mesh adaptivity. Embedded mesh meth
ods on the other hand aim to couple independently constructed meshes for t
he matrix and fractures without the need for the meshes to conform. One ti
mely challenge is the design of accurate and efficient numerical schemes f
or coupled mechanics and multiphase flow.\nIn this work\, a hybrid discret
ization is proposed\; pEDFM (projection-based embedded discrete fracture)
is adopted for multiphase flow and is fully-coupled (monolithic) to an ex
tended finite element method (XFEM) for geomechanics. Three aspects of th
e scheme are analyzed: accuracy\, nonlinear solvability\, and the efficacy
of linear preconditioners for the resulting linearized residual systems.
The grid refinement is performed to test the convergence rates for differe
nt physical variables (pressure\, saturation and displacement). We use th
e block LDU factorization so that two different AMG (algebraic multigrid m
ethod) for XFEM and EDFM can be applied separately. AMG will be called whe
never it is required by the outer loop solver\, FGMRES.\n\nhttps://events.
interpore.org/event/2/contributions/257/
LOCATION:New Orleans
URL:https://events.interpore.org/event/2/contributions/257/
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SUMMARY:A C++ parallel solver for flow in networks of fractures
DTSTART;VALUE=DATE-TIME:20180517T192000Z
DTEND;VALUE=DATE-TIME:20180517T193500Z
DTSTAMP;VALUE=DATE-TIME:20210928T184826Z
UID:indico-contribution-184-252@events.interpore.org
DESCRIPTION:Speakers: Fabio Vicini (Politecnico di Torino)\nThe present wo
rk deals with the highly efficient parallel implementation of an optimizat
ion-based solver for the flow in Discrete Fracture Networks (DFNs).\nA DFN
is a sets of mutually intersecting planar polygons in the three dimension
al space\, resembling a system of fractures in the subsoil. Fracture netw
orks are stochastically generated to tackle uncertainty and lack of observ
ations on geometrical properties of the fractures (density\, orientation\,
size) and on hydraulic properties (transmissivity). These random networks
can be extremely complex\, with a large number of fractures and intricate
intersections\, such that conventional simulation approaches have limited
applicability in this context\, mainly for the necessity of generating a
conforming mesh of the whole network. \nRecently a novel approach was pres
ented to overcome the issue of mesh conformity in DFN flow simulations [1
2 3 4 5]. The method is based on the PDE-constrained minimization of a cos
t functional\, which is introduced to handle matching conditions at fractu
re intersections with non conforming meshes. The minimization of the funct
ional can be performed via a conjugate gradient approach\, and the computa
tion of the descent direction at each iteration of the method only asks fo
r the resolution of small linear system on each fracture of the network. T
his structure naturally leads to a parallel approach. Here details on the
implementation of this approach in the C++ language on distributed memory
devices is discussed. The code aims at minimizing the number of communicat
ions among different processes\, and the communication phases are organize
d in order to maximize the time occurring between the delivery of the data
to their reception\, thus shadowing the communication overhead.\n\nhttps:
//events.interpore.org/event/2/contributions/252/
LOCATION:New Orleans
URL:https://events.interpore.org/event/2/contributions/252/
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SUMMARY:BLOCK PRECONDITIONING IN THE NUMERICAL SIMULATION OF FRACTURED MED
IA
DTSTART;VALUE=DATE-TIME:20180517T193800Z
DTEND;VALUE=DATE-TIME:20180517T195300Z
DTSTAMP;VALUE=DATE-TIME:20210928T184826Z
UID:indico-contribution-184-255@events.interpore.org
DESCRIPTION:Speakers: Massimiliano Ferronato (University of Padova)\nAccur
ate simulation of fault and fracture mechanics is a key component in a wid
e number of subsurface engineering applications. Faults and fractures are
typically treated by modelers as discontinuity surfaces embedded in three
dimensional (3D) continuous media. From a mathematical standpoint\, they a
re described as internal boundaries whose behavior is governed by the disp
lacement and stress fields acting on the surrounding continuum. Displaceme
nts and stresses are in turn influenced by geometrical features of the dom
ain\, thus yielding a strongly coupled non-linear problem where the domain
boundary definition is itself part of the solution. Here\, we focus on ef
ficient preconditioning techniques for the linear systems arising from the
discretization and linearization of the governing equations that describe
the mechanics of faulted and fractured geological media based on a Lagran
ge-multiplier formulation.\n\nThe application of the fracture model to lar
ge-scale problems gives rise to a set of sparse discrete systems of linear
ized equations with a generalized non-symmetric saddle point structure. Th
e quality and performance of the preconditioner relies on two factors: (i)
the preconditioning of the leading (1\,1) block and (ii) the Schur comple
ment computation. In this work\, we propose and compare various approximat
ions for both elements.\n\nThe preconditioner of the leading block has to
be selected among the wide set of choices available for elastic problems\,
i.e.\, incomplete factorizations\, approximate inverses and multigrid app
roaches\, especially on a parallel environment. On the other hand\, the co
mputation of the Schur complement can be addressed by using a sparse appro
ximate inverse of the leading block or a physically-based block diagonal a
lgorithm. The Schur complement must be inverted\, thus other possibilities
come in. The approximate Schur complement can be solved exactly\, or its
inverse can be directly approximated by a least-square commutator projecti
ng the displacement variables on the space of the Lagrange multipliers. So
me test cases are presented to investigate the computational performance a
nd highlight pros and cons of the proposed approaches. Finally\, real-worl
d examples are presented and solved in an HPC environment.\n\nhttps://even
ts.interpore.org/event/2/contributions/255/
LOCATION:New Orleans
URL:https://events.interpore.org/event/2/contributions/255/
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SUMMARY:A stress-driven DFN model to account for fracture network geometri
cal complexity
DTSTART;VALUE=DATE-TIME:20180517T201400Z
DTEND;VALUE=DATE-TIME:20180517T202900Z
DTSTAMP;VALUE=DATE-TIME:20210928T184826Z
UID:indico-contribution-184-259@events.interpore.org
DESCRIPTION:Speakers: Etienne Lavoine (Itasca Consultants SAS)\nDiscrete F
racture Network (DFN) models are the geometrical basis for flow simulation
of poro-fractured media in many industrial projects such as deep waste di
sposal\, hydrogeology or petroleum resources. Because the spatial organiza
tion of fractures may control the hydrological and mechanical behavior of
the fractured rock mass\, the geometrical complexity of the network is a k
ey point of the modeling workflow. This complexity is beyond the reach of
purely stochastic DFN models\, referred as “Poisson models”\, which ne
glect the potential importance of fracture-to-fracture interactions\, and
the consequent modifications of the spatial organization and connectivity
of the network. Fracture network development is a complex feedback-loop pr
ocess between the propagation of fractures and the emergence of new ones.
Using genetic models of fracture networks to replace the lack of field inf
ormation may be a solution for realism. Recent papers (Davy et al.\, 2010\
; Davy et al.\, 2013) have proposed a genetic model of DFN\, called “UFM
model”\, using simplified fracturing-relevant rules for nucleation\, gr
owth and arrest of fractures. With simple kinematic rules that mimic the m
ain mechanical processes\, the model produces fracture size distributions
and fracture intersections that are consistent with observations. Our obje
ctive is to improve the model by explicitly considering the control of loc
al stresses in both nucleation and fracture growth. This has the advantage
of linking the geometry and topology of fracture networks with the assume
d conditions of their formation. We introduce a stress-driven nucleation i
n the timewise process of this kinematic model to study the correlations b
etween nucleation\, growth and existing fracture patterns. The method calc
ulates the stress field generated by existing fractures and the allegedly
known remote stress as an input for a Monte-Carlo sampling of nuclei cente
rs at each time step. The orientation and growth rate of each newly genera
ted fracture is then a function of the local stress field at the selected
center. Networks generated by this so-called “stress-driven UFM model”
are found to have fractal correlations. We also perform a lacunarity anal
ysis of fracture densities to quantify the textural heterogeneity of fract
ure patterns with observation scale. We show that our model brings closer
to natural data in terms of spatial variability in comparison with “Pois
son models”. This heterogeneity in the fractures spatial organization ha
s important consequences on the connectivity and flow properties of the ro
ck mass.\n\nhttps://events.interpore.org/event/2/contributions/259/
LOCATION:New Orleans
URL:https://events.interpore.org/event/2/contributions/259/
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SUMMARY:Simulation of injectivity decline in fractured near-well regions
DTSTART;VALUE=DATE-TIME:20180517T203200Z
DTEND;VALUE=DATE-TIME:20180517T204700Z
DTSTAMP;VALUE=DATE-TIME:20210928T184826Z
UID:indico-contribution-184-253@events.interpore.org
DESCRIPTION:Speakers: Xavier Raynaud (SINTEF)\nAccumulation of large parti
cles on well faces decreases the injectivity. This issue is particularly a
ccute in the case of produced water reinjection (PWRI) and polymer floodin
g. To maintain operational rates\, the injection pressure is increased\, w
hich causes fracturing or reopening of existing fractures. Then\, the inje
ctivity may be recovered or even increased\, but only temporarily\, as fil
ter cakes start building up on the freshly opened fracture walls. In this
talk\, we will show simulation results of injectivity decline. We will pre
sent the models and the simulation methods we have chosen for the main rel
evant processes: Transport in discrete fracture networks for the large par
ticles\, external filter cake build-up on the fracture faces\, poroelastic
y to determine the fracture apertures.\n\nhttps://events.interpore.org/eve
nt/2/contributions/253/
LOCATION:New Orleans
URL:https://events.interpore.org/event/2/contributions/253/
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