气体性质及达西定律

V,
between
the
two
• Or
• Thus for a given quantity of gas, pV/T = a constant. The constant is designated with the symbol R when the quantity of gas is equal to one molecular weight. That is, • where VM is the volume of one molecular weight of the gas at p and T. • Therefore,
• In the first step the pressure is changed from a value of p1 to a value of p2 while temperature is held constant. This causes the volume to change from V1 to V. In Step 2, the pressure is maintained constant at a value of p2, and the temperature is changed from a value of T1 to a value of T2. • The change in volume of the gas during the first step may be described through the use of Boyle's Law since the quantity of gas and the temperature are held constant. Thus
• (ຫໍສະໝຸດ Baidu) there are no attractive or repulsive forces among the molecules.
The basis for describing ideal gas behavior comes from the combination of some of the so called gas laws proposed by early experimenters.
the equation of state molecular weight of any ideal gas is
for
one
• For n moles of ideal gas this equation becomes
• where V is the total volume of n moles of gas at temperature, T, and pressure, p. Since n is the mass of gas divided by the molecular weight, the equation can be written as
Characteristics of
•
ideal gas
(1) the volume occupied by the molecules is small compared to the total gas volume;
• (2) all molecular collisions are elastic; and
• Avogadro's Law. Avogadro's Law states that under the same conditions of temperature and pressure, equal volumes of all ideal gases contain the same number of molecules. • This is equivalent to the statement that at a given temperature and pressure one molecular weight of any ideal gas occupies the same volume as one molec­ular weight of another ideal gas. • It has been shown that there are 2.73 x 1026 molecules/lb-mole of ideal gas and that one molecular weight in pounds of any ideal gas at 60°F and 14.7 psia occupies a volume of 379.4 cu ft.
• Chapter two
Gas Properties
• The ability to calculate the performance of a gas producing system, including the reservoir and the piping system, requires knowledge of many gas properties at various, pressures and temperatures. If the natural gas is in contact with liquids, such as condensate or water, the effect of the liquids on gas properties must be evaluated. • This presentation presents the best and most widely used methods to perform the necessary calculations. Some of the information presented will be used only in reservoir calculations and some will be used only in the piping system design.
IDEAL GASES
• The understanding of the behavior of gases with respect to pressure and temperature changes is made clearer by first considering the behavior of gases at conditions near standard conditions of pressure and temperature; that is:
The Ideal Gas Law
The three gas laws described previously can be com­bined to express a relationship among pressure, volume, and temperature, called the ideal gas law. In order to combine Charles' Law and Boyle's Law to describe the behavior of an ideal gas when both temperature and pressure are changed, assume a given mass of gas whose volume is V1 at pressure pl and temperature Ti, and imagine the following process through which the gas reaches volume V2 at pressure p2 and temperature T2:
= 10.73 psia cu ft/lbmole °R
Table 2-1 gives numerical values of R for various systems of units.
• or, since m/V is the gas density,
• This expression is known by various names such as the ideal gas law, the general gas law, or the perfect gas law. This equation has limited practical value since no known gas behaves as an ideal gas; however, the equation does describe the behavior of most real gases at low pressure and gives a basis for developing equations of state which more adequately describe the behavior of real gases at elevated pressures. • The numerical value of the constant R depends on the units used to express temperature, pressure, and volume. As an example, suppose that pressure is expressed in psia, volume in cubic feet, temperature in degrees Ran-kin, and moles in pound moles. Avogadro's Law states that 1 lb-mole of any
• Charles' Law. While working with gases at low pressures, Charles observed that the volume occupied by a fixed mass of gas is directly proportional to its absolute temperature, or
• p = 14.7 psia = 101.325 kPa • T = 60°F = 520°R = 288.72°K • At these conditions the gas is said to behave ideally, and most of the early work with gases was conducted at conditions approaching these conditions.
• where V represents the volume at pressure p2 and temperature T1. Charles' Law applies to the change in the volume of gas during the second step since the pressure and the quantity of gas are maintained constant; therefore • Elimination equations : of volume,
Early Gas Laws
• Boyle's Law. Boyle observed experimentally that the volume of an ideal gas is inversely proportional to the pressure for a given weight or mass of gas when temperature is constant. This may be expressed as: