75. Write the gas state equation and call its members.

Where P – pressure

R - gas constant (for air R=287 )

– density

T – temperature

76. Give the definition of the gas compressibility; which index is used in order to characterize compressibility.

Gas Compressibility (c_g)

The compressibility of a substance is the change in volume per unit volume per unit change in pressure.  The gas compressibility should not be confused with the compressibility factor (z), which is the deviation factor from ideal gas behavior.  The gas compressibility is calculated from the BWR equation of state as published in the ERCB manual "Gas Well Testing - Theory and Practice".

 The gas compressibility is a very strong function of pressure and increases as the pressure decreases.  Mathematically, it can be expressed as: 

 Where p is the specified pressure and z is the gas compressibility factor (z) at that pressure.  Thus, the magnitude of gas compressibility (c_g) is of the order of 1 / p.  Moreover, when the pressure drawdown at the wellbore is large, the difference in compressibility values at the initial pressure (p_i) and at the flowing pressure is significant and must be accounted for by using the pseudo-time (t_a) variable, instead of regular time.

Gas Compressibility Factor (z)

The compressibility factor of a natural gas is a measure of its deviation from ideal gas behavior.  Its value is usually between 0.8 and 1.2, but it can be as low as 0.3 and as high as 2.0.  It is used in the calculation of gas pseudo-pressures (y), and in converting gas volumes and rates from standard conditions to reservoir conditions (and vice-versa).  It is sometimes called the super-compressibility factor, and is often confused with the term "compressibility" (which is the change in volume per unit volume per unit change in pressure).  The gas compressibility factor directly affects the gas compressibility (c_g). 

77. Give the definition of the gas viscosity; which index is used in order to characterize viscosity.

The viscosity of a fluid is a measure of its resistance to gradual deformation by shear stress or tensile stress. Viscosity is due to friction between neighboring parcels of the fluid that are moving at different velocities. When fluid is forced through a tube, the fluid generally moves faster near the axis and very little near the walls, therefore some stress (such as a pressure difference between the two ends of the tube) is needed to overcome the friction between layers and keep the fluid moving. For the same velocity pattern, the stress is proportional to the fluid's viscosity.

A fluid that has no resistance to shear stress is known as an ideal fluid or inviscid fluid. In the real world, zero viscosity is observed only atvery low temperatures, in superfluids. Otherwise all fluids have positive viscosity. If the viscosity is very high, such as in pitch, the fluid will seem to be a solid in the short term. In common usage, a liquid whose viscosity is less than that of water is known as a mobile liquid, while a substance with a viscosity substantially greater than water is simply called a viscous liquid.

Viscosity is a measure of the degree momentum transport in a fluid perpendicular to flow velocity due to flow shear. The momentum is ultimately carried by the individual molecules.  A gas is defined as a fluid in which the molecules are more or less free, except for discrete scattering events with other molecules. Unless the gas is ionized, the collision cross section varies little with impact velocity. Therefore, as the temperature (free velocity) increases, the molecules carry more momentum and collide more often. That means more viscous momentum transport.

Viscosity in gases arises principally from the molecular diffusion that transports momentum between layers of flow. The kinetic theory of gases allows accurate prediction of the behavior of gaseous viscosity.