Member-only story

Buoyancy Driven Flow in Fluid Saturated Porous Media Near Bounding Surface

Ivan Turgenev

·5k Followers· Follow

Published in Buoyancy Driven Flow In Fluid Saturated Porous Media Near A Bounding Surface (SpringerBriefs In Applied Sciences And Technology)

4 min read · 1 month before

297 View Claps

16 Respond

Save

Listen

Buoyancy-Driven Flow in Fluid-Saturated Porous Media near a Bounding Surface (SpringerBriefs in Applied Sciences and Technology)

4 out of 5

Language	:	English
File size	:	10830 KB
Text-to-Speech	:	Enabled
Enhanced typesetting	:	Enabled
Word Wise	:	Enabled
Print length	:	167 pages
Screen Reader	:	Supported

Buoyancy driven flow in fluid saturated porous media near bounding surface is a fundamental problem in many areas of science and engineering, including groundwater hydrology, petroleum engineering, and environmental engineering. In this phenomenon, a fluid-saturated porous medium is subjected to a gravitational force, which causes the fluid to flow from regions of high density to regions of low density. The presence of a bounding surface can significantly affect the flow pattern and the distribution of pressure and velocity within the porous medium.

Governing Equations

The governing equations for buoyancy driven flow in fluid saturated porous media near bounding surface are the Darcy-Brinkman equations, which are given by:

∇·(μ∇p) + ρg = 0 μ∇²u - ∇p = 0

where μ is the fluid viscosity, p is the pressure, ρ is the fluid density, g is the gravitational acceleration, and u is the velocity vector.

Analytical Solutions

In some cases, it is possible to obtain analytical solutions to the Darcy-Brinkman equations. For example, in the case of a one-dimensional flow in a vertical column, the following analytical solution can be obtained:

p(z) = ρgz - μQ/k u(z) = -Q/k

where Q is the flow rate and k is the permeability of the porous medium.

Numerical Methods

In most cases, it is necessary to use numerical methods to solve the Darcy-Brinkman equations. There are a variety of numerical methods that can be used, including the finite difference method, the finite element method, and the boundary element method.

Applications

Buoyancy driven flow in fluid saturated porous media near bounding surface has a wide range of applications, including:

* Groundwater hydrology: Buoyancy driven flow is responsible for the movement of groundwater through aquifers. * Petroleum engineering: Buoyancy driven flow is responsible for the migration of oil and gas through reservoirs. * Environmental engineering: Buoyancy driven flow is responsible for the transport of contaminants in groundwater and soil.

Buoyancy driven flow in fluid saturated porous media near bounding surface is a complex phenomenon that can have a significant impact on the flow pattern and the distribution of pressure and velocity within the porous medium. The governing equations for this phenomenon are the Darcy-Brinkman equations, which can be solved analytically in some cases and numerically in most cases. This phenomenon has a wide range of applications in groundwater hydrology, petroleum engineering, and environmental engineering.

Buoyancy-Driven Flow in Fluid-Saturated Porous Media near a Bounding Surface (SpringerBriefs in Applied Sciences and Technology)

4 out of 5