Fundamentals of Fluid Mechanics Through Porous Media
Fluid flow through porous media widely exists in nature and artificial materials, and its theory has been used in all sorts of scientific and technological fields, such as soil mechanics, petroleum engineering, mineral engineering, environmental engineeri
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Fundamentals of Fluid Mechanics Through Porous Media
Abstract
Fluid flow through porous media widely exists in nature and artificial materials, and its theory has been used in all sorts of scientific and technological fields, such as soil mechanics, petroleum engineering, mineral engineering, environmental engineering, geothermal engineering, water supply engineering, chemical industry, micro machine, and so on. In this chapter, we will first give some basic concepts of fluid flow through porous media, such as porosity and compressibility of porous media. Then we will introduce Darcy’s law and mathematical model of fluid flow through porous media. Finally, we will utilize some principles of seepage mechanics to discuss solutions for planar one-directional flow and planar radial flow. Keywords
Porous media conductivity
6.1
Porosity
Compressibility
Darcy’s law
Hydraulic
Several Concepts
Fluid flow through porous media is an important branch of fluid mechanics, which is based on the combination of porous media theory, surface physics, physical chemistry, and biology. The characteristics of fluid flow through porous media are as follows. First, due to the large specific surface area and strong surface effect in porous media, viscous effect should be taken into consideration at all times. Second, the fluid compressibility should also be considered due to the high pressure in the formation. In addition, molecular force cannot be neglected sometimes due to the complex © Metallurgical Industry Press, Beijing and Springer Nature Singapore Pte Ltd. 2018 H. Song, Engineering Fluid Mechanics, https://doi.org/10.1007/978-981-13-0173-5_6
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Fundamentals of Fluid Mechanics Through Porous Media
pore shape, big resistance and capillary force. Finally, there often exist complex physical and chemical processes while fluid flowing through porous media.
6.1.1 Porous Media Porous media refer to solids which contain various types of capillary systems such as void, fracture, and so on [1, 2]. To sum up, the following points are often used to describe porous media: (1) Porous medium is the space occupied by multiphase medium, where the solid phase is called solid skeleton, the unoccupied space is called pore which can be filled with gas, liquid or multiphase fluid. (2) The solid phase and pores should extend throughout the whole medium. This means that taking a proper size volume from the medium, then this volume must contain a certain proportion of solid particles and pores. (3) The pore space should be interconnected so that the fluid can flows in them, and this kind of pore space is called effective pore space, while disconnected pore space or dead pore is called void pore space. For flow in porous media, void pore space is actually regarded as solid skeleton. The common pore structure is intergranular pore structure, which consists of solid particles with different sizes and shapes. The spaces between particles are usually occupied by cement; the unoccupied parts are the pores, which are the reservoirs and
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