3,973 research outputs found
Geometric model of the fracture as a manifold immersed in porous media
In this work, we analyze the flow filtration process of slightly compressible
fluids in porous media containing man made fractures with complex geometries.
We model the coupled fracture-porous media system where the linear Darcy flow
is considered in porous media and the nonlinear Forchheimer equation is used
inside the fracture. We develop a model to examine the flow inside fractures
with complex geometries and variable thickness, on a Riemannian manifold. The
fracture is represented as the normal variation of a surface immersed in
. Using operators of Laplace Beltrami type and geometric
identities, we model an equation that describes the flow in the fracture. A
reduced model is obtained as a low dimensional BVP. We then couple the model
with the porous media. Theoretical and numerical analysis have been performed
to compare the solutions between the original geometric model and the reduced
model in reservoirs containing fractures with complex geometries. We prove that
the two solutions are close, and therefore, the reduced model can be
effectively used in large scale simulators for long and thin fractures with
complicated geometry
Fracture Model Reduction and Optimization for Forchheimer Flows in Reservoir
In this study, we analyze the flow filtration process of slightly
compressible fluids in fractured porous media. We model the coupled fractured
porous media system, where the linear Darcy flow is considered in porous media
and the nonlinear Forchheimer equation is used inside the fracture.
Flow in the fracture is modeled as a reduced low dimensional BVP which is
coupled with an equation in the reservoir. We prove that the solution of the
reduced model can serve very accurately to approximate the solution of the
actual high-dimensional flow in reservoir fracture system, because the
thickness of the fracture is small. In the analysis we consider two types of
Forchhemer flows in the fracture: isotropic and anisotropic, which are
different in their nature.
Using method of reduction, we developed a formulation for an optimal design
of the fracture, which maximizes the capacity of the fracture in the reservoir
with fixed geometry. Our method, which is based on a set point control
algorithm, explores the coupled impact of the fracture geometry and
beta-Forchheimer coefficient
A multiscale flux basis for mortar mixed discretizations of reduced Darcy-Forchheimer fracture models
In this paper, a multiscale flux basis algorithm is developed to efficiently
solve a flow problem in fractured porous media. Here, we take into account a
mixed-dimensional setting of the discrete fracture matrix model, where the
fracture network is represented as lower-dimensional object. We assume the
linear Darcy model in the rock matrix and the non-linear Forchheimer model in
the fractures. In our formulation, we are able to reformulate the
matrix-fracture problem to only the fracture network problem and, therefore,
significantly reduce the computational cost. The resulting problem is then a
non-linear interface problem that can be solved using a fixed-point or
Newton-Krylov methods, which in each iteration require several solves of Robin
problems in the surrounding rock matrices. To achieve this, the flux exchange
(a linear Robin-to-Neumann co-dimensional mapping) between the porous medium
and the fracture network is done offline by pre-computing a multiscale flux
basis that consists of the flux response from each degree of freedom on the
fracture network. This delivers a conserve for the basis that handles the
solutions in the rock matrices for each degree of freedom in the fractures
pressure space. Then, any Robin sub-domain problems are replaced by linear
combinations of the multiscale flux basis during the interface iteration. The
proposed approach is, thus, agnostic to the physical model in the fracture
network. Numerical experiments demonstrate the computational gains of
pre-computing the flux exchange between the porous medium and the fracture
network against standard non-linear domain decomposition approaches
Forchheimer Model for Non-Darcy Flow in Porous Media and Fractures
Imperial Users onl
Parallel numerical modeling of hybrid-dimensional compositional non-isothermal Darcy flows in fractured porous media
This paper introduces a new discrete fracture model accounting for
non-isothermal compositional multiphase Darcy flows and complex networks of
fractures with intersecting, immersed and non immersed fractures. The so called
hybrid-dimensional model using a 2D model in the fractures coupled with a 3D
model in the matrix is first derived rigorously starting from the
equi-dimensional matrix fracture model. Then, it is dis-cretized using a fully
implicit time integration combined with the Vertex Approximate Gradient (VAG)
finite volume scheme which is adapted to polyhedral meshes and anisotropic
heterogeneous media. The fully coupled systems are assembled and solved in
parallel using the Single Program Multiple Data (SPMD) paradigm with one layer
of ghost cells. This strategy allows for a local assembly of the discrete
systems. An efficient preconditioner is implemented to solve the linear systems
at each time step and each Newton type iteration of the simulation. The
numerical efficiency of our approach is assessed on different meshes, fracture
networks, and physical settings in terms of parallel scalability, nonlinear
convergence and linear convergence
Experimental Investigation of the Recovery of Gas and Oil by Spontaneous Water Imbibition
Imperial Users onl
A double scale methodology to investigate flow in karst fractured media via numerical analysis. The Cassino plain case study (Central Apennine, Italy)
A methodology to evaluate the hydraulic conductivity of the karstmedia at a regional scale has been proposed, combining pumping
tests and the hydrostructural approach, evaluating the hydraulic conductivity of fractured rocks at the block scale. Obtaining
hydraulic conductivity values, calibrated at a regional scale, a numerical flow model of the Cassino area has been developed, to
validate the methodology and investigate the ambiguity, related to a nonunique hydrogeological conceptual model. The Cassino
plain is an intermontane basin with outstanding groundwater resources.The plain is surrounded by karst hydrostructures that feed
the Gari Springs and Peccia Springs. Since the 1970s, the study area was the object of detailed investigations with an exceptional
density of water-wells and piezometers, representing one of the most important karst study-sites in central-southern Italy.
Application of the proposed methodology investigates the hydraulic conductivity tensor at local and regional scales, reawakening
geological and hydrogeological issues of a crucial area and tackling the limits of the continuum modelling in karst medi
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