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SUMMARY:Novel finite-volume methods for anisotropic linear elasticity and
poromechanics problems with full tensors
DTSTART;VALUE=DATE-TIME:20180515T143200Z
DTEND;VALUE=DATE-TIME:20180515T144700Z
DTSTAMP;VALUE=DATE-TIME:20210928T204101Z
UID:indico-contribution-138-621@events.interpore.org
DESCRIPTION:Speakers: Hamdi Tchelepi (Stanford University)\nWe propose a n
ovel finite volume method for anisotropic linear elasticity problem. The d
erivation of the flux approximation method for elasticity problem closely
follows our previous work [1] on the nonlinear finite volume methods for d
iffusion equation featuring positivity and discrete maximum principles. It
is based on the extensions of the harmonic point idea of [2] from the sca
lar to vector equations. We further extend the idea to coupled anisotropic
flow and mechanics\, featuring full tensors for permeability\, Biot coeff
icient and stiffness tensor. Both methods handle star-shaped polyhedral gr
ids\, admit the construction of nonlinear finite volume methods and yield
several new research directions. \n\n[1] "Cell-centered nonlinear finite-v
olume methods for the heterogeneous anisotropic diffusion problem”\, KM
Terekhov\, BT Mallison\, HA Tchelepi // Journal of Computational Physics 3
30\, 245-267\n[2] "A nine-point finite volume scheme for the simulation of
diffusion in heterogeneous media.”\, L Agelas\, Rt Eymard\, and R Herb
in // Comptes Rendus Mathematique\, 347. 11-12 (2009): 673-676.\n\nhttps:/
/events.interpore.org/event/2/contributions/621/
LOCATION:New Orleans
URL:https://events.interpore.org/event/2/contributions/621/
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SUMMARY:Multiresolution Coupled Compositional Vertical Equilibrium Model f
or Fast Flexible Simulation of CO2 Storage
DTSTART;VALUE=DATE-TIME:20180515T152600Z
DTEND;VALUE=DATE-TIME:20180515T154100Z
DTSTAMP;VALUE=DATE-TIME:20210928T204101Z
UID:indico-contribution-138-620@events.interpore.org
DESCRIPTION:Speakers: Olav Møyner (SINTEF\, NTNU)\nCO$_2$ capture and sto
rage is an important technology for mitigating climate change. Design of e
fficient strategies for safe\, long-term storage requires the capability t
o efficiently simulate processes taking place on very different temporal a
nd spatial scales. The physical laws describing CO$_2$ storage are the sa
me as for hydrocarbon recovery\, but the characteristic spatial and tempor
al scales are quite different. Petroleum reservoirs seldom extend more tha
n tens of kilometers and have operational horizons spanning decades. Injec
ted CO$_2$ needs to be safely contained for hundreds or thousands of years
\, during which it can migrate hundreds or thousands of kilometers. Becaus
e of the vast scales involved\, conventional 3D reservoir simulation quick
ly becomes computationally unfeasible. Large density difference between in
jected CO$_2$ and resident brine means that vertical segregation will take
place relatively quickly\, and depth-integrated models assuming vertical
equilibrium (VE) often represents a better strategy to simulate long-term
migration of CO$_2$ in large-scale aquifer systems. VE models have primari
ly been formulated for relatively simple rock formations and have not been
coupled to 3D simulation in a uniform way. In particular\, known VE simul
ations have not been applied to models of realistic geology in which many
flow compartments may exist in-between impermeable layers. In this work\,
we generalize the concept of VE models\, formulated in terms of well-prove
n finite-volume reservoir simulation technology\, to complex aquifer syste
ms with multiple layers and regions. The result is a hybrid discretization
strategy which couples different governing equations in different regions
based on the correct local discretization of gravity and flow terms.\n\nW
e also introduce novel formulations for multi-layered VE models by use of
both direct spill and diffuse leakage between individual layers. This new
layered 3D model is then coupled to a state-of-the-art\, 3D equation-of-st
ate compositional model. The formulation of the full model is simple and e
xploits the fact that both models can be written in terms of generalized m
ultiphase flow equations with particular choices of the relative permeabil
ities and capillary pressure functions. The resulting simulation framework
is very versatile and can be used to simulate CO$_2$ storage for (almost)
any combination of 3D and VE-descriptions\, thereby enabling the governin
g equations to be tailored to the local structure. We demonstrate the simp
licity of the model formulation by extending the standard flow-solvers fro
m the open-source Matlab Reservoir Simulation Toolbox (MRST)\, allowing im
mediate access to upscaling tools\, complex well modeling\, and visualizat
ion features. We demonstrate this capability on both conceptual and indust
ry-grade models from a proposed storage formation in the North Sea. While
the examples are taken specifically from CO$_2$ storage applications\, the
framework itself is general and can be applied to many problems in which
parts of the domain is dominated by gravity segregation. Such applications
include gas storage and hydrocarbon recovery from gas reservoirs with loc
al layering structure.\n\nhttps://events.interpore.org/event/2/contributio
ns/620/
LOCATION:New Orleans
URL:https://events.interpore.org/event/2/contributions/620/
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SUMMARY:Higher order multipoint flux mixed finite element methods on quad
rilaterals and hexahedra
DTSTART;VALUE=DATE-TIME:20180515T145000Z
DTEND;VALUE=DATE-TIME:20180515T150500Z
DTSTAMP;VALUE=DATE-TIME:20210928T204101Z
UID:indico-contribution-138-622@events.interpore.org
DESCRIPTION:Speakers: Ivan Yotov (University of Pittsburgh)\nWe develop hi
gher order multipoint flux mixed finite element (MFMFE) methods for solvin
g elliptic problems on quadrilateral and hexahedral grids that reduce to c
ell-based pressure systems. The methods are based on a new family of mixed
finite elements\, which are enhanced Raviart-Thomas spaces with bubbles t
hat are curls of specially chosen polynomials. The velocity degrees of fre
edom of the new spaces can be associated with the points of tensor-product
Gauss-Lobatto quadrature rules\, which allows for local velocity eliminat
ion and leads to a symmetric and positive definite cell-based system for t
he pressures. We prove optimal k-th order convergence for the velocity and
pressure in their natural norms\, as well as (k+1)-st order superconverge
nce for the pressure at the Gauss points. Moreover\, local postprocessing
gives a pressure that is superconvergent of order k+1 in the full L2-norm
. Numerical results illustrating the validity of our theoretical results a
re included.\n\nhttps://events.interpore.org/event/2/contributions/622/
LOCATION:New Orleans
URL:https://events.interpore.org/event/2/contributions/622/
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SUMMARY:Modeling of Additional Oil Recovery Processes by Low Salinity Wate
r Injection using the Open Source Software Platform DUNE-DUMUX
DTSTART;VALUE=DATE-TIME:20180515T150800Z
DTEND;VALUE=DATE-TIME:20180515T152300Z
DTSTAMP;VALUE=DATE-TIME:20210928T204101Z
UID:indico-contribution-138-619@events.interpore.org
DESCRIPTION:Speakers: Martin A. Diaz-Viera (INSTITUTO MEXICANO DEL PETROLE
O)\nIn this work a general model of multiphase flow and multicomponent tra
nsport in porous media to simulate\, analyze and interpret hydrocarbon rec
overy processes by injecting low salinity water using open source software
is presented. The flow model is multiphase considering capillary pressure
and relative permeabilities depending on salinity\, while the transport m
odel is multicomponent and includes several relevant physico-chemical phen
omena such as advection\, diffusion and reactions. To obtain the numerical
solution\, the finite volume method is applied in space and backward Eule
r finite difference method in time\, resulting in a fully implicit scheme.
Its computational implementation was carried out in C++ using the open so
urce software platform DUNE-DUMUX. From the methodological point of view\,
each stage of the development of the model is described (conceptual\, mat
hematical\, numerical and computational). The resulting model is applied t
o a case of study of low salinity water injection in a core at laboratory
conditions.\n\nhttps://events.interpore.org/event/2/contributions/619/
LOCATION:New Orleans
URL:https://events.interpore.org/event/2/contributions/619/
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