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# Gas formation volume factor and density

Formation volume factor (FVF) is a useful relationship for relating gas volumes in the reservoir to the produced volume at standard conditions. Formation volume factor also enables the calculation of density. This page discusses calculation of FVF and density.

## Formation volume factor

The formation volume factor of gas is defined as the ratio of the volume of gas at the reservoir temperature and pressure to the volume at the standard or surface temperature and pressure (ps and Ts). It is given the symbol Bg and is often expressed in either cubic feet of reservoir volume per standard cubic foot of gas or barrels of reservoir volume per standard cubic foot of gas. The gas deviation factor is unity at standard conditions; hence, the equation for the gas formation volume factor can be calculated using the real gas equation:

....................(1)

The n divides out here because both volumes refer to the same quantity of mass.

When ps is 1 atm (14.696 psia or 101.325 kPa) and Ts is 60°F (519.67°R or 288.71°K), this equation can be written in three well-known standard forms:

....................(2)

where rcf/scf = reservoir cubic feet per standard cubic feet, RB = reservoir barrels, and Rm3/Sm3 = reservoir cubic meters per standard cubic meters. The formation volume factor is always in units of reservoir volumes per standard volumes.

The three forms in Eq. 2 are for specific units. In the first two equation forms, the pressure is in psia and the temperature is in °R. In the third form, the pressure is in kPa and the temperature is in K.

## Density

The density of a reservoir gas is defined as the mass of the gas divided by its reservoir volume, so it can also be derived and calculated from the real gas law:

....................(3)

## Nomenclature

 Bg = gas formation volume factor (RB/scf or Rm3/Sm3) mg = mass of gas, kg Ma = molecular weight of air Mg = average molecular weight of gas mixture n = number of moles p = absolute pressure, Pa psc = pressure at standard conditions, Pa R = gas-law constant, J/(g mol-K) T = absolute temperature, K Tsc = temperature at standard conditions, K V = volume, m3 VR = volume of gas at reservoir temperature and pressure, m3 Vsc = volume at standard conditions, m3 z = compressibility factor (gas-deviation factor) zsc = compressibility factor at standard conditions γg = specific gravity for gas ρg = density of gas, kg/m3

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