GAS PROPERTIES

Ideal Gas

·  Equal volumes of different ideal gases at same P-T conditions contain same number of molecules

·  A cylinder containing atmospheric oxygen weighs 2 times as much as a cylinder containing nascent oxygen (O) at the same P-T conditions.

Mol. wt. of O2 = 32 is 2 times the mol. wt. of O (=16)

·  Moles: Number of weight units of the compound equal to its molecular weight 1 lb-mole of O2 is equal to 32 lbs of atmospheric oxygen

·  One mole of all ideal gases contain the same number of molecules and occupy the same volume at identical conditions of P-T.

·  Note: 1 lb. equal to 453.6 gm. 1 lb-mole of ideal gas contains 453.6 times the number of molecules in 1 gm-mole of the same gas

·  State of the gas defined by P,V and T. Boyle, Charles and Avogadro’s experimentation yielded:

or more interestingly :

where V1 and V2 in same units. Pressures P1 and P2 and temperatures T1 and T2 in absolute units :

Absolute pressure = Gauge press. + atm. Pressure

Absolute temperature (oR) = oF + 460.0

(oK) = oC + 273.0

Ideal Gas Law

·  It is evident from previous slides that P, T and V of a ideal gas defines the state of the gas and also the number of molecules present. Alternate formulation:

where:

R = Universal gas constant

n = number of moles of the gas

R = psia-cu.ft./lb-mole/oR

·  Standard conditions are generally defined as 14.7 psia and 60oF.

·  1 mole of any ideal gas at standard conditions occupies a volume of 379 Cu. ft. or 22.4 litres

Application

Consider a 500 cu-ft. tank maintained at gauge pressure of 20 psig and 90oF (atm. Press = 14.4 psia). Calculate moles of gas in tank.

Applying ideal gas law:

1mole of ideal gas occupies 379.4cu.ft at std. condns.

.

If gas in container is ethane (mol.wt. = 30) then mass of gas in container equals 2.915 x 30 = 87.45 lbs.

Density/specific Gravity of an ideal gas

·  Density:

Since:

specific to the P-T condns.

·  Specific gravity of gas:

Mol. wt. of air is generally assumed to be 28.97

, independent of P-T.

Application

If specific gravity of gas is 0.75,

then molecular weight of gas is 0.75 x 28.97 = 21.7.

I lb-mole of gas weighs 21.7 lbs.

Non-ideal or real gas

·  At extreme conditions of P-T, gases deviate from ideal behaviour. State of gas at such conditions described using Equation of State (EOS).

- Van der Waal’s EOS

·  accounts for inter-molecular forces reducing the momentum of particles impinging on the walls of the vessel. Larger the V, smaller the intermolecular forces and smaller the correction.

·  b accounts for the molecular gas volumes, ignored by the ideal gas equation

·  Other EOS, Radlich-Kwong EOS, Benedict-Webb-Rubin EOS - all are empirical

·  An alternate method for treating non-ideal behaviour is based on the following observation:

If we define:

Non-ideal gas equation

Ideal gas equation:

or non-ideal gas equation

·  Z is a function of both P and T. Commonly Z = Z(p) i.e assume conditions of isothermal depletion.

Measurement of Z

·  Single phase reservoir gas sample collected using special sampling nozzles (if condensate present), or by recombining stock tank gas, seperator gas and the produced liquid or in the case of solution gas reservoirs, sampling the liberated gas.

, varying p and measuring V Z(p) at constant T can be obtained

Analytical calculation of Z

·  Hydrocarbons are complex mixture of paraffins and other non-hydrocarbon impurities. Each component has own critical point (temp. and pressure).

·  Mixture exhibits characteristics of the components. If ni is the mole-fraction of a component i, the pseudo-critical properties of the mixture can be calculated:

: = critical pressure of i

:= critical temperature of I

·  Compute pseudo-reduced pressure and temperature:

and , at desired conditions P & T

·  Generally Tpr is constant (isothermal depletion). Use Standing-Katz chart to retrieve Z as a function of Ppr at various Tpr.

Table 1.1 and Figure 1-5 of your text book.

Z from specific gravity

·  We have already seen the dependence of Z on the specific gravity of the gas. Sutton’s correlation:

Correlation good for

·  Compute pseudo-reduced parameters and the same computation as before.

·  Frequently, fluid analysis of reservoir gas is performed to identify mole fraction of components up to hexane. Heavier components are lumped together as C7+. Knowing the specific gravity of this lumped heavier fractions, the pseudo-critical properties can be calculated. Then Z can be computed using the mole-fraction approach.

·  All the above computations are valid for non-hydrocarbon impurities upto 5% in volume, experimental determination of Z-factor may have to be performed.

Formation volume factor and density

·  Reservoir pressure continually declines during the production phase. Estimates of recoverable reserves in terms of reservoir volume continually change. Volumes are therefore converted to standard surface conditions.

·  Gas formation volume factor relates the reservoir volumes of gas to the volume on the surface (i.e at std. Psc and Tsc). Assuming Z = 1 at std. conditions, 1 cu.ft. of gas at std. conditions (1 SCF) occupies:

, where P, T are reservoir condns.

Assuming and

cu. ft.

Formation volume factor:

cu. ft/SCF= bbl/SCF

Density

For a real gas or

Since and

Density:

Isothermal compressibility

·  Note compressibility of gas cg is different from the gas deviation factor Z

·  Real gas law:

Differentiating:

Or

for ideal gas: z = 1.0 (const.) i.e.