<u>Unit Darcy's Law</u>

达西定律认为土中渗流的平均渗透速度与水力梯度成什么关系~

达西通过实验总结得到。1852-1855年，又称线性渗流定律。1856年由法国工程师H达西定律（Darcy's law）描述饱和土中水的渗流速度与水力坡降之间的线性关系的规律，达西进行了水通过饱和砂的实验研究，发现了渗流量Q与上下游水头差（h2- h1）和垂直于水流方向的截面积A成正比.P.G

渗透率单位是长度的平方，即与面积的单位相同。但我们称之为达西（D）,常用的单位为毫达西（md）。
渗透率是指在一定压差下，岩石允许流体通过的能力。
是表征土或岩石本身传导液体能力的参数。其大小与孔隙度、液体渗透方向上孔隙的几何形状、颗粒大小以及排列方向等因素有关，而与在介质中运动的液体性质无关。渗透率（k）用来表示渗透性的大小。
压力梯度为1时，动力黏滞系数为1的液体在介质中的渗透速度。量纲为L2。

扩展资料：
岩石渗透性的好坏，以渗透率的数值大小来表示，有绝对渗透率、有效渗透率和相对渗透率三种表示方式。

一、绝对渗透率
当单相流体通过横截面积为A、长度为L、压力差为ΔP的一段孔隙介质呈层状流动时，流体粘度为μ，则单位时间内通过这段岩石孔隙的流体量为：Q=KΔPA/μL 。
当单相流体通过孔隙介质呈层状流动时，单位时间内通过岩石截面积的液体流量与压力差和截面积的大小成正比，而与液体通过岩石的长度以及液体的粘度成反比。
式中：Q——单位时间内流体通过岩石的流量，cm3/s；A——液体通过岩石的截面积，cm2；
μ——液体的粘度，Pa·s；L——岩石的长度，cm；ΔP——液体通过岩石前后的压差，MPa；
岩石的绝对渗透率是岩石孔隙中只有一种流体(单相)存在，流体不与岩石起任何物理和化学反应，且流体的流动符合达西直线渗滤定律时，所测得的渗透率。
由于气体受压力影响十分明显，当气体沿岩石由(高压力)流向(低压力)时，气体体积要发生膨胀，其体积流量通过各处截面积时都是变数，故达西公式中的体积流量应是通过岩石的平均流量。

二、有效渗透率
英文：effective permeability
定义：在非饱和水流运动条件下的多孔介质的渗透率。
多相流体在多孔介质中渗流时，其中某一项流体的渗透率叫该项流体的有效渗透率，又叫相渗透率。
三、相对渗透率
英文： relative permeability
定义：多相流体在多孔介质中渗流时，其中某一项流体在该饱和度下的渗透系数与该介质的饱和渗透系数的比值叫相对渗透率，是无量纲量。
作为基数的渗透率可以是：
1、用空气测定的绝对渗透率；
2、用水测定的绝对渗透率；
3、在某一储层的共存水饱和度下油的渗透率。
与有效渗透率一样，相对渗透率的大小与液体饱和度有关。同一多孔介质中不同流体在某一饱和度下的相对渗透率之和永远小于1。根据测得的不同饱和度下的相对渗透率值绘制的相对渗透率与饱和度的关系曲线,称相对渗透率曲线。
参考资料来源：百度百科—渗透率

The birth of groundw ater hydrology as a quantitative science can be traced to the year 1856. It w as in that year that a French hydraulic engineer named Henry Darcy published his report on the w ater supply of the city of Dijon，France. In the report Darcy described a laboratory experiment that he had carried out to analyze the flow of w ater through sands. The results of his experiment can be generalized into the empirical law that now bears his name.

Consider an experimental apparatus like that show n in Figure 6. 1. A circular cylinder of cross section A is filled w ith sand，stoppered at each end，and outfitted w ith inflow and outflow tubes and a pair of manometers. Water is introduced into the cylinder and allow ed to flow through it until such time as all the pores are filled w ith w ater and the inflow rate Q is equal to the outflow rate. If w e set an arbitrary datum at elevation z = 0，the elevations of the manometer intakes are z₁and z₂and the elevations of the fluid levels are h₁and h₂. The distance betw een the manometer intakes is Δl.

Figure 6. 1 Experimental apparatus for the illustration of Darcy's law

We w ill define v，the specific discharge through the cylinder，as

If the dimensions of Q are ［L³T^{－ 1}］and those of A are ［L²］，v has the dimensions of a velocity ［LT^{－ 1}］.

The experiments carried out by Darcy show ed that v is directly proportional to h₁－ h₂w hen Δl is held constant，and inversely proportional to Δl when h₁－ h₂is held constant. If w e define Δh = h₂－ h₁( an arbitrary sign convention that will stand us in good stead in later developments) ，w e have v ∝ － Δh and v ∝ 1 / Δl. Darcy's law can now be w ritten as:

or，in differential form:

where h is called the hydraulic head; dh / dl is the hydraulic gradient; K is a constant of proportionality. It must be a property of the soil in the cylinder，for were we to hold the hydraulic gradient constant，the specific discharge would surely be larger for some soils than for others. In other words，if dh / dl is held constant，v ∝ K. The parameter K is known as the hydraulic conductivity. It has high values for sand and gravel and low values for clay and most rocks. Since Δh and Δl both have units of length ［L］，a quick dimensional analysis of Equation ( 6. 3) shows that K has the dimensions of a velocity ［LT－ 1］. In the following section，we will show that K is a function not only of the media，but also of the fluid flowing through it.

An alternative form of Darcy's law can be obtained by substituting Equation ( 6. 1 ) in Equation ( 6. 3) to yield:

This is sometimes compacted even further into the form:

w here I is the hydraulic gradient.

Darcy's law is valid for groundwater flow in any direction in space. With regard to Figure 6. 1 and Equation ( 6. 3) ，if the hydraulic gradient dh / dl and the hydraulic conductivity K are held constant，v is independent of the angle θ. This is true even for θ values greater than 90° when the flow is being forced up through the cylinder against gravity.

We have noted that the specific discharge v has the dimensions of a velocity，or flux. For this reason it is sometimes know n as the Darcy velocity or Darcy flux. The specific discharge is a macroscopic concept and it is easily measured. It must be clearly differentiated from the microscopic velocities associated w ith the actual paths of individual particles of w ater as they w ind their w ay through the grains of sand ( Figure 6. 2) . The microscopic velocities are real， but they are probably impossible to measure. In the remainder of the section w e w ill w ork exclusively w ith concepts of flow on a macroscopic scale. Despite its dimensions w e w ill not refer to v as a velocity; rather w e w ill utilize the more correct term，specific discharge.

This last paragraph may appear innocuous，but it announces a decision of fundamental importance. When w e decide to analyse groundw ater flow w ith the Darcian approach，itmeans，in effect，that w e are going to replace the actual ensemble of sand grains ( or clay particles or rock fragments) that make up the porous medium by a representative continuum for w hich w e can define macroscopic parameters，such as the hydraulic conductivity，and utilize macroscopic law s， such as Darcy's law ， to provide macroscopically averaged descriptions of the microscopic behavior. This is a conceptually simple and logical step to take，but it rests on some knotty theoretical foundations. Bear in 1972，in his advanced text on porous-media flow ，discussed these foundations in detail. In a later section，w e w ill further explore the interrelationships betw een the microscopic and macroscopic descriptions of groundw ater flow.

Figure 6. 2 Macroscopic and microscopic concepts of groundwater flow

Darcy's law is an empirical law. It rests only on experimental evidence. Many attempts have been made to derive Darcy's law from more fundamental physical law s，and Bear in 1972 also review ed these studies in some detail. The most successful approaches attempt to apply the Navier-Stokes equations，w hich are w idely know n in the study of fluid mechanics，to the flow of w ater through the pore channels of idealized conceptual models of porous media. Hubbert in 1956 and Irmay in 1958 w ere apparently the earliest to attempt this exercise.

This text w ill provide ample evidence of the fundamental importance of Darcy's law in the analysis of groundw ater flow ，but it is w orth nothing here that it is equally important in many other applications of porous-media flow. It describes the flow of soil moisture and is used by soil physicists，agricultural engineers，and soil mechanics specialists. It describes the flow of oil and gas in deep geological formations and is used by petroleum reservoir analysts. It is used in the design of filters by chemical engineers and in the design of porous ceramics by materials scientists. It has even been used by bioscientists to describe the flow of bodily fluids across porous membranes in the body.

( Source: Freeze et al. ，1979)

水文地质专业英语

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