Behaviour of GasesAdrian C ToddHeriot-Watt UniversityDEPARTMENT OF PETROLEUM ENGINEERING

IntroductionA gas is a homogeneous fluidNo definite volumeCompletely fills the vessel in which it is containedBehaviour vital to petroleum engineersSimple gas laws straightforwardHydrocarbon gases at reservoir conditions are more complicated.

Ideal GasesAssumptions

Volume of molecules are insignificant with respect to the total volume of the gas.There are no attractive or repulsive forces between molecules or molecules and container walls.No internal energy loss when molecules collide

Ideal GasesBoyles LaworT is constantP = pressure, V = volume, T = temperature

Ideal GasesCharles LaworP is constantPressure and temperature in both laws are in absolute units

Absolute UnitsTemperatureKelvin K = oC + 273Kelvin K = oC + 273Kelvin K = oC + 273Rankin oR = oF + 460

Avogadros LawUnder the same conditions of temperature and pressure equal volumes of all ideal gases contain the same number of molecules.That is; one molecular weight of any ideal gas occupies the same volume as the molecular weight of another ideal gas.2.73 x 1026 molecules/lb.mole of ideal gas1 lb.mole of any ideal gas at 60oF and 14.7 psia. occupies 379.4 cu.ft.1 gm.mole at 0oC and atmos. pressure occupies 22.4 litres

lb.moleOne lb.mol of methane CH4 = 16 lb.One kg.mole of methane CH4 = 16 kg.

Ideal Gas LawThe Ideal Equation of StateCombining Boyles Law and Charles Law gives an equation relating P,T & V

Universal Gas Constantpsfta

The Ideal Equation of StateFor n moles equation becomesA useful equation to compare conditions at two conditions 1 & 2therefore

Density of an Ideal Gasrg is the gas densityFor 1 mole m = MWMW= molecular weight

Standard ConditionsOil and gas occur under a whole range of temperatures and pressuresConvenient to express volumes at a reference condition.Common practise to relate volumes to surface conditions. 14.7 psia and 60oF

res - reservoir conditionsSC - standard conditionsThis equation assumes ideal behaviour. This is NOT the case for real reservoir gases

Mixtures of Ideal GasesPetroleum gases are mixtures of gases - Daltons Law and Amagats Law

Daltons Law of Partial PressuresTotal pressure is the sum of the partial pressuresThereforei.e.Thereforeyj =mole fraction of jth component

Amagats LawStates that the volume occupied by an ideal gas mixture is equal to the sum of the volumes that the pure components would occupy at the same temperature and pressure.Law of additive volumes.i.e.For ideal gas, volume fraction is equal to mole fraction

Apparent Molecular WeightA mixture does not have a molecular weight.It behaves as though it has a molecular weight.Called Apparent Molecular Weight. AMW

MWj is the molecular weight of component j.AMW for air = 28.97

Specific Gravity of a GasThe specific gravity of a gas is the ratio of the density of the gas relative to that of dry air at the same conditions. Assuming that the gas and air are idealMg = AMW of mixture, Mair = AMW of air

Behaviour of Real GasesEquations so far for ideal gasesAt high pressures and temperatures the volume of molecules are no longer negligibleand attractive forces are significant.Ideal gas law is therefore NOT applicable to light hydrocarbons.Necessary to use more refined equation.Two general methods.

Using a correction factor in equation PV=nRT By using another equation of state

Correction Factor for Natural GasesA correction factor z , a function of gas composition, pressure and temperature is used to modify ideal equation.z is the compressibility factor

Equation known as the compressibility equation of state.Z is not the compressibility

Compressibility factorTo compare states the equation now takes the formZ is an expression of the actual volume to what the ideal volume would be. i.e.ToZ = V actual / V ideal

Compressibility factor

Law of Corresponding StatesLaw of corresponding states shows that the properties of pure liquids and gases have the same value at the same reduced temperature, Tr and reduced pressure, Pr.and

Tc and Pc are the critical temperature and critical pressure.The compressibility factor follows this law.Presented as a function of Tr, and Pr.

Law of Corresponding States as Applied to MixturesThe law of corresponding states does not apply to hydrocarbon reservoir fluids.The law has been modified to be used for mixtures by defining parameters Pseudo critical temperature, Tpc and Pseudo critical pressure, Ppc .andTcj and Pcj are the critical temperatures and pressures of component j.

Pseudo critical temperature, Tpc and Pseudo critical pressure, Ppc .These pseudo critical temperatures and pressures are not the same as the real critical temperature and pressure.By definition they must lie between the extreme values of the pure components making up the mixture.

Pseudo critical pressure = 668.4 psiaPseudo critical temperature = 362.6 oR

Sheet1

GasABCDPpcTpc

ComponentMol. WghtMol. Frac.Pc-psiTc-oR

Methane16.040.921667344614.3316.8

Ethane30.070.05970855041.832.5

Propane44.090.0261666612.313.3

Total1668.4362.6

Real Critical Pressures and TemperaturesThese are not average values based on mole fractions.Averaged on weight fraction basis would give a more real value.

Critical pressure much greater than critical points of pure components.Particularly when methane is involved.

Compressibility Factors for Natural GasesThese are presented as a function of pseudoreduced pressure, Ppr and pseudoreduced temperature, Tpr.

and

Compressibility Factors for Natural Gases (Standing & Katz)From previous exercise Ppc=668psia and Tpc =362 oRZ value for this mixture at 3500psia and 150oFPpr = 5.24 and Tpr = 1.68Z=0.88

Pseudocritical Properties for Natural GasesCan be calculated from basic composition.If data not available can use correlations.Do not use composition to calculate gravity and hence Ppc & Tpc.

Standard Conditions for Real Reservoir GasesStandard volumes are used to describe quanitities of gas in the industry.Standard cubic feetStandard cubic metre.Determined at standard temperature and pressure.60oF(15.6oC) & 14.7psia (1 atmos)It is useful to consider a mass of gas in terms of standard volumes.

Gas Formation Volume FactorWe need a conversion factor to convert volumes in the reservoir to those at surface ( standard) conditions.Termed Formation Volume Factors.Gases, Gas Formation Volume Factor, Bg.Is the ratio of the volume occupied at reservoir conditions to the volume of the same mass occupied at standard conditions.

Gas Formation Volume FactorDefinitionGas Formation Volume Factor is the volume in barrels (cubic metres) that one standard cubic foot (standard cubic metre) of gas willoccupy as free gas in the reservoir at the prevailing reservoir pressure and temperature.

Gas Formation Volume FactorUnits:Bg - rb free gas / SCF gasBg - rm3 free gas / SCM gas

Gas Formation Volume Factor

Gas Formation Volume Factor

Viscosity of GasesViscosity is a measure of resistance to flow.Units: centipoise - gm./100 sec.cm.Termed: dynamic viscoisty.Divide by density.Termed kinematic viscosityUnits: centistoke -cm2/100sec

Viscosity of GasesGas viscosity reduces as pressure decreasesAt low pressures, increase in temperature increases viscosity.At high pressures, increase in temperature decreases viscosity.

Viscosity of GasesAt low pressures viscosity can be obtained from correlations.

Viscosity of pure components at 1 atmos.

Viscosity of GasesAt low pressures viscosity can be obtained from correlations.

Viscosity of gases (MW) at atmospheric pressure.

Viscosity of GasesCarr presented a method to determine viscosity at higher pressure and temperature. Uses pseudo reduced temperature and pseudo reduced pressure.

Viscosity Ratio atmos

Viscosity of MixturesA formulae which can be used for mixtures

Other equations of state, EOSThe z factor is used to modify the ideal EOS for real gas application.PV=znRTRather than use this correction factor other equations have been developed.An irony is that many of these advanced equations are used to generate z for use in the PV=znRT equation.

Van de Waal EOS, 1873Two corrective terms used to overcome limiting assumptions of ideal gas equation.Internal pressure or cohesion term a/V2.Co-volume term b. Represents volume occupied by one mole at infinite pressure.Can also be written asTermed cubic equations of state

Van de Waal EOSWhen written to solve for z becomeswhereandValues for a and b are positive constants for particular fluids.

Benedict-Webb-Rubin EOS,BWR- 1940Van de Waals equation not able to represent gas properties over wide range of T&P.BWR equation developed for light HCs and found application for thermodynamic properties of natural gases

Redlich-Kwong EOS, 1949Numerous equations with increasing number of constants for specific pure components.More recently a move to cubic EOS.

The term a and b are functions of temperatureAt the critical point

Soave,Redlich-Kwong EOS , SRK, 1972Soave modified RK equation and replaced a/T0.5 term with a temperature dependant term aT.aT =aca

a is a non dimensionless temperature dependent term. Value of 1 at critical temperaturea is fromwherew is the Pitzer accentric factor from tables

Peng Robinson EOS , PR, 1975Peng and Robinson modified the attractive term.Predictions of liquid density are improved.

anda is the same as for the SRK equation, except w function is different.

Widely Used EOSSRK and PR equations are widely used in the industry. Used in simulation software to predict behaviour in reservoirs, wells and processing.There are other EOS.Reluctance to change because of investment in associated parameters.

Application to MixturesWith mixtures mixing rules required to combine data from pure components.For both SRK and PR equation

andkij are termed binary interaction coefficients.They have NO physical property significance.Each equation has its own binary interaction coefficients.