213 research outputs found
Fluid Flows of Mixed Regimes in Porous Media
In porous media, there are three known regimes of fluid flows, namely,
pre-Darcy, Darcy and post-Darcy. Because of their different natures, these are
usually treated separately in literature. To study complex flows when all three
regimes may be present in different portions of a same domain, we use a single
equation of motion to unify them. Several scenarios and models are then
considered for slightly compressible fluids. A nonlinear parabolic equation for
the pressure is derived, which is degenerate when the pressure gradient is
either small or large. We estimate the pressure and its gradient for all time
in terms of initial and boundary data. We also obtain their particular bounds
for large time which depend on the asymptotic behavior of the boundary data but
not on the initial one. Moreover, the continuous dependence of the solutions on
initial and boundary data, and the structural stability for the equation are
established.Comment: 33 page
Analysis of the Brinkman-Forchheimer equations with slip boundary conditions
In this work, we study the Brinkman-Forchheimer equations driven under slip
boundary conditions of friction type. We prove the existence and uniqueness of
weak solutions by means of regularization combined with the Faedo-Galerkin
approach. Next we discuss the continuity of the solution with respect to
Brinkman's and Forchheimer's coefficients. Finally, we show that the weak
solution of the corresponding stationary problem is stable
Pore-scale numerical investigation of pressure drop behaviour across open-cell metal foams
The development and validation of a grid-based pore-scale numerical modelling methodology applied to five different commercial metal foam samples is described. The 3-D digital representation of the foam geometry was obtained by the use of X-ray microcomputer tomography scans, and macroscopic properties such as porosity, specific surface and pore size distribution are directly calculated from tomographic data. Pressure drop measurements were performed on all the samples under a wide range of flow velocities, with focus on the turbulent flow regime. Airflow pore-scale simulations were carried out solving the continuity and Navier–Stokes equations using a commercial finite volume code. The feasibility of using Reynolds-averaged Navier–Stokes models to account for the turbulence within the pore space was evaluated. Macroscopic transport quantities are calculated from the pore-scale simulations by averaging. Permeability and Forchheimer coefficient values are obtained from the pressure gradient data for both experiments and simulations and used for validation. Results have shown that viscous losses are practically negligible under the conditions investigated and pressure losses are dominated by inertial effects. Simulations performed on samples with varying thickness in the flow direction showed the pressure gradient to be affected by the sample thickness. However, as the thickness increased, the pressure gradient tended towards an asymptotic value
Unconfined Aquifer Flow Theory - from Dupuit to present
Analytic and semi-analytic solution are often used by researchers and
practicioners to estimate aquifer parameters from unconfined aquifer pumping
tests. The non-linearities associated with unconfined (i.e., water table)
aquifer tests makes their analysis more complex than confined tests. Although
analytical solutions for unconfined flow began in the mid-1800s with Dupuit,
Thiem was possibly the first to use them to estimate aquifer parameters from
pumping tests in the early 1900s. In the 1950s, Boulton developed the first
transient well test solution specialized to unconfined flow. By the 1970s
Neuman had developed solutions considering both primary transient storage
mechanisms (confined storage and delayed yield) without non-physical fitting
parameters. In the last decade, research into developing unconfined aquifer
test solutions has mostly focused on explicitly coupling the aquifer with the
linearized vadose zone. Despite the many advanced solution methods available,
there still exists a need for realism to accurately simulate real-world aquifer
tests
Jean-Baptiste BĂ©langer, hydraulic engineer, researcher and academic
Jean-Baptiste BÉLANGER (1790-1874) worked as a hydraulic engineer at the beginning of his career. He developed the backwater equation to calculate gradually-varied open channel flow properties for steady flow conditions. Later, as an academic at the leading French engineering schools (Ecole Centrale des Arts et Manufactures, Ecole des Ponts et Chaussées, and Ecole Polytechnique), he developed a new university curriculum in mechanics and several textbooks including a seminal text in hydraulic engineering. His influence on his contemporaries was considerable, and his name is written on the border of one of the four facades of the Eiffel Tower. BÉLANGER's leading role demonstrated the dynamism of practicing engineers at the time, and his contributions paved the way to many significant works in hydraulics
The impact of porous media heterogeneity on non-Darcy flow behaviour from pore-scale simulation
The effect of pore-scale heterogeneity on non-Darcy flow behaviour is investigated by means of direct flow simulations on 3-D images of a beadpack, Bentheimer sandstone and Estaillades carbonate. The critical Reynolds number indicating the cessation of the creeping Darcy flow regime in Estaillades carbonate is two orders of magnitude smaller than in Bentheimer sandstone, and is three orders of magnitude smaller than in the beadpack. It is inferred from the examination of flow field features that the emergence of steady eddies in pore space of Estaillades at elevated fluid velocities accounts for the early transition away from the Darcy flow regime. The non-Darcy coefficient β, the onset of non-Darcy flow, and the Darcy permeability for all samples are obtained and compared to available experimental data demonstrating the predictive capability of our approach. X-ray imaging along with direct pore-scale simulation of flow provides a viable alternative to experiments and empirical correlations for predicting non-Darcy flow parameters such as the β factor, and the onset of non-Darcy flow
On the stability and uniqueness of the flow of a fluid through a porous medium
© 2016, The Author(s). In this short note, we study the stability of flows of a fluid through porous media that satisfies a generalization of Brinkman’s equation to include inertial effects. Such flows could have relevance to enhanced oil recovery and also to the flow of dense liquids through porous media. In any event, one cannot ignore the fact that flows through porous media are inherently unsteady, and thus, at least a part of the inertial term needs to be retained in many situations. We study the stability of the rest state and find it to be asymptotically stable. Next, we study the stability of a base flow and find that the flow is asymptotically stable, provided the base flow is sufficiently slow. Finally, we establish results concerning the uniqueness of the flow under appropriate conditions, and present some corresponding numerical results
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